The Best Textbooks on Every Subject

16th Jan 2011

39Yoav Ravid

4Jan Christian Refsgaard

2Pablo

1Yoav Ravid

31komponisto

5Spurlock

10komponisto

2arundelo

0komponisto

0Spurlock

3[anonymous]

3soundchaser

5komponisto

2TessPope

6komponisto

1phenylphenol

1Bill_McGrath

3komponisto

2Bill_McGrath

2komponisto

0Bill_McGrath

25[anonymous]

7Douglas_Knight

3realitygrill

2komponisto

3[anonymous]

6komponisto

3SilasBarta

3steven0461

2[anonymous]

1HeuristicWorld

1lukeprog

0jsumr

23jsalvatier

10jsalvatier

3lukeprog

2Adam Zerner

0XFrequentist

2jsalvatier

0beoShaffer

22joshkaufman

8lukeprog

7Dr_Manhattan

6lukeprog

3FrF

1joshkaufman

4Duke

13joshkaufman

8Duke

9joshkaufman

5Duke

3[anonymous]

3MichaelGR

3Cyan

1bgf419

20Epictetus

1lukeprog

1SanguineEmpiricist

2Epictetus

1SanguineEmpiricist

2hairyfigment

2Richard_Kennaway

-2SanguineEmpiricist

1Oxide

0JoshuaZ

1SanguineEmpiricist

0pinyaka

0Boogie

16gwern

27lukeprog

9nazgulnarsil

4Will_Sawin

11XiXiDu

4Ben Pace

15orthonormal

5Princess_Stargirl

2orthonormal

2lukeprog

1TimS

0[anonymous]

0komponisto

0[anonymous]

14lukeprog

14kjmiller

13Zetetic

3lukeprog

6[anonymous]

0lukeprog

1Zetetic

0lukeprog

1Zetetic

13[anonymous]

13rwallace

11barrkel

0Mimi

7[anonymous]

1rwallace

5lukeprog

1rwallace

1Mimi

12[anonymous]

8[anonymous]

-2[anonymous]

1komponisto

0rich

0JoshuaZ

5Will_Sawin

0[anonymous]

0JoshuaZ

0jsalvatier

11Dr_Manhattan

11badger

5lukeprog

3joshuabecker

2roobee

1gilch

11SK2

3lukeprog

11jwhendy

8lukeprog

1michaba03m

1jwhendy

10madhadron

6pragmatist

2Max D Porter

1lukeprog

10sriku

1sriku

0lukeprog

10Cyan

4Maxwell Peterson

3lukeprog

9Cyan

2tel

1Cyan

0Zetetic

2tel

0lukeprog

9pscheyer

9Arepo

1Karmakaiser

9wbcurry

4cursed

4Lu93

1Max D Porter

0Lu93

0Mimi

0orthonormal

9Hurt

1jsalvatier

7Hurt

0[anonymous]

9Jonathan_Graehl

2Mimi

2Mimi

2Mimi

0Jonathan_Graehl

1lukeprog

7gjm

3Jonathan_Graehl

0gjm

1Shubhorup Biswas

1Shubhorup Biswas

1Shubhorup Biswas

0Mimi

2gjm

0Davidmanheim

0Jonathan_Graehl

8magfrump

8BrandonReinhart

6fiddlemath

1john-lawrence-aspden

1alphaSquared

7Peacewise

7jsteinhardt

7InquilineKea

6John_Maxwell

6SatvikBeri

2lukeprog

3richard_reitz

1lukeprog

6Bundle_Gerbe

0magfrump

6DBreneman

6Alex_Altair

7golwengaud

4Anatoly_Vorobey

6realitygrill

0Pablo

0lukeprog

6jsalvatier

1anonym

6James_Miller

6orthonormal

5Lukey

5Crab

5SatvikBeri

2lukeprog

1[anonymous]

2SatvikBeri

5lukeprog

5bgaesop

3Lukas Finnveden

1Niklas Lehmann

5Alex Flint

11PhilGoetz

5michaba03m

11randallsquared

-2gimpf

6wedrifid

0waveman

4Yoav Ravid

4adamShimi

5Yoav Ravid

4adamShimi

2Garrett Baker

4adamShimi

3Waifod

4George3d6

1Matthew Barnett

1George3d6

4transh

4John_Maxwell

4iDante

4Chris_Cooper

4etymologik

9Rafael T dos Santos

2etymologik

1etymologik

4lukeprog

4Tiiba

11lukeprog

0Tiiba

1lukeprog

3NihilCredo

2prase

0Tiiba

4PhilGoetz

0tel

4David_Gerard

3Mimi

2Curiouskid

0DSimon

4nazgulnarsil

3Ben

3Abraham Al-Janabi

4Yoav Ravid

3Jurij Fedorov

1Yoav Ravid

3krnsll

3Dahlen

2Risto_Saarelma

2Vaniver

0gjm

0Risto_Saarelma

0gjm

1Vaniver

2Gram_Stone

1Vaniver

1Dahlen

0Lumifer

4Vaniver

0Lumifer

0Dahlen

0Lumifer

3ChrisHallquist

3Gram_Stone

0lukeprog

3Natha

0lukeprog

3JohnWittle

3rhodium

1ghodith

0Manfred

3strange

3Craig_Heldreth

3Fhyve

1Mimi

2Natha

3lukeprog

2somervta

3fr00t

1Barry_Cotter

0diegocaleiro

0kjmiller

3BrandonReinhart

3lukeprog

2Ruby

1Pretentious Penguin

2Doug Hess

2Kieran Marray

2Niklas Lehmann

2Rudi C

1Yoav Ravid

2Elo

2DrEinstein10

2Elo

2DrEinstein10

0Elo

2Crab

2PeterDonis

2justwanttorecommend

1zedzed

2Smaug123

2sixes_and_sevens

2JohnWittle

1whowhowho

2JohnWittle

-2whowhowho

2JohnWittle

-1whowhowho

2JoshuaZ

2whowhowho

0JoshuaZ

2Pablo

2lukeprog

2sweeticetea

2lukeprog

3PPaul

1PPaul

2Mimi

1ArthurRainbow

2gjm

2caustic

0Mimi

2Alex Flint

2lukeprog

2lukeprog

7[anonymous]

1Dr_Manhattan

0lukeprog

1Vlad

1Matt_Simpson

2Davidmanheim

0PeterisP

0Davidmanheim

0PeterisP

2bgaesop

6lukeprog

0michaba03m

1YoungFolks

0bgaesop

2sark

2lukeprog

5Vaniver

8nykos

6Kaj_Sotala

2PeterisP

1CstineSublime

1stableunicorn

1Going Durden

1Arden

1Danila Medvedev

1Axioms

2Ruby

1Axioms

1Axioms

1Дмитрий Зеленский

1Yoav Ravid

2Jurij Fedorov

1Pablo

1Will_BC

0zedzed

1lukeprog

3Davidmanheim

0marai2

1AuroraDragon

1[anonymous]

1Vaniver

1[anonymous]

1reydv

0lukeprog

1jsalvatier

3Barry_Cotter

0jsalvatier

2badger

0jsalvatier

3badger

0jsalvatier

3badger

0jsalvatier

1Swimmer963 (Miranda Dixon-Luinenburg)

1[anonymous]

5dlthomas

0ata

1squigglier

3lukeprog

1Jonathan_Graehl

0Niklas Lehmann

0SatvikBeri

0Jotto999

0Plubbingworth

0Karmakaiser

0thomblake

0fbs42

0Dr_Manhattan

0lukeprog

0Dr_Manhattan

1lukeprog

1realitygrill

0lukeprog

0lukeprog

0magfrump

-2[anonymous]

-2realitygrill

-6PP

12Raemon

0again72al

-6Clippy

1Doug Hess

1Arden

1Danila Medvedev

1Danila Medvedev

New Comment

413 comments, sorted by Click to highlight new comments since: Today at 1:49 PM

Some comments are truncated due to high volume. (⌘F to expand all)

books added since the list was last updated -

On **applied Bayesian statistics**, Dr_Manhattan recommends *Lambert's **A student's guide to Bayesian Statistics* over McEarlath's *Statistical Rethinking, *Kruschke's *Doing Bayesian Data Analysis*, and Gelman's *Bayesian Data Analysis.*

On **Functional Analysis, **krnsll recommends Brezis's *Functional Analysis, Sobolev Spaces and Partial Differential Equations* over Kreyszig's and Lax's.

On **Probability Theory**, crab recommends Feller's *An Introduction to Probability Theory *over Jaynes' *Probability Theory: The Logic of Science *and MIT OpenCoursewar's *Introduction to Probability and Statistics.*

On **History of Economics**, Pablo_Stafforini recommends Sandmo's *Economics Evolving** *over Robbins' *A History of Economic Thought* and Schumpeter's *History of Economic Analysis*.

On **Relativity**,** **PeterDonis recommends Carroll's *Spacetime and Geometry* over Taylor & Wheeler's *Spacetime Physics, *Misner, Thorne, & Wheeler's *Gravitation, *Wald's *General Relativity*, and Hawking & Ellis's *The Large Scale Structure of Spacetime.*

On **Category Theory**, adamShimi recommends Awodey's Category Theory over Maclane's *category theory for the working mathematician.*

On **General Psycology**, J...

43y

I have written a review of the 5 most popular Applied Bayesian Statistics books
Where I recommended:
* Statistical Rethinking
* Up to speed fast, no integrals, very intuitive approach.
* Doing Bayesian Data Analysis
* This is the easiest book. If your goal is only to create simple models and you aren't interested in understanding the details, then this is the book for you.
* A Student’s Guide to Bayesian Statistics
* This book has the opposite focus of the Dog book. Here the author slowly goes through the philosophy of Bayes with an intuitive mathematical approach.
* Regression and Other Stories
* Good if you want a slower and thorough approach where you also learn the Frequentest perspective.
* Bayesian Data Analysis
* The most advanced text, very math heavy, best as a second book after reading one or two of the others, unless you are already a statistician.

23y

Thanks for the update!
The word 'chaotic' was an adjective I chose to describe the book's content, rather than part of the book's title. :)

13y

whoops, fixed it :)

**Music theory**: *An Introduction to Tonal Theory* by Peter Westergaard.

Comparing this book to others is almost unfair, because in a sense, this is the only book on its subject matter that has ever been written. Other books purporting to be on the same topic are really on another, wrong(er) topic that is properly regarded as superseded by this one.

However, it's definitely worth a few words about what the difference is. The approach of "traditional" texts such as Piston's *Harmony* is to come up with a historically-based taxonomy (and a rather awkward one, it must be said) of common musical tropes for the student to memorize. There is hardly so much as an attempt at non-fake explanation, and certainly no understanding of concepts like reductionism or explanatory parsimony. The best analogy I know would be trying to learn a language from a phrasebook instead of a grammar; it's a GLUT approach to musical structure.

(Why is this approach so popular? Because it doesn't require much abstract thought, and is easy to give students tests on.)

Not all books that follow this traditional line are quite as bad as Piston, but some are even worse. An example of not-quite-so-bad would be Aldwel...

513y

I've always found traditional music theory to be useless if not actively damaging (seems to train people in bad thought habits for writing/appreciating music). Can you summarize Westergaard's approach? I know why the typical methods are bad, but I'm interested in what exactly his alternative is.

Can you summarize Westergaard's approach? I know why the typical methods are bad, but I'm interested in what exactly his alternative is.

In ITT itself, Westergaard offers the following summary (p.375):

we can generate all the notes of any tonal piece from the pitches of its tonic triad by successive application of a small set of operations, and moreover

the successive stages in the generation process show how we understand the notes of that piece in terms of one another

(This, of course, is very similar to the methodology of theoretical linguistics.)

Westergaard basically considers tonal music to be a complex version of species counterpoint --- layers upon layers of it. He inherits from Schenker the idea of systematically reversing the process of "elaboration" to reveal the basic structures underlying a piece (or passage) of music, but goes even further than Schenker in completely explaining away "harmony" as a component of musical structure.

Notes are considered to be elements of *lines*, not "chords". They operations by which they are generated within lines are highly intuitive. They essentially reduce to two: step motion, and borrowing from othe...

213y

Thanks for the summary. I may get this book.
You can defeat automatic list formatting if your source code looks like this:
4\. Species counterpoint##
5\. Simple species##
6\. Combined species
except with spaces instead of "#" (to prevent the list items from being wrapped into one paragraph). Edit: If the list items have blank lines between them, the trailing spaces are not necessary.
(The creator of the Markdown format says "At some point in the future, Markdown may support starting ordered lists at an arbitrary number.")

013y

Thanks, fixed.

013y

Interesting, thanks. I don't know if that sounds right or even useful, but it definitely sounds interesting, I'll be putting it on my "books to check out" list. I get the impression that it's very reductionist approach, which is a promising sign.

3[anonymous]2y

I've found traditional music theory to be useless in the practical sense mainly because of their GLUT nature. You essentially have to look at written music to learn the practical part of it, with reference to the GLUT, which you can do without and is essentially useless because all it does is giving names to different stuff in music theory. They aren't functional names either, like names that helps with the functionality of the implementations of the theories. Some stuff like rules of the octave are rather practical. The scale degrees have so many different names, totally unnecessary. These things, GLUT, basically have made the subject, music theory, more complex than it really needs to be. Do you really need to know that the 5th degree, is called the 5th degree, dominant, sol, etc.
I can't really think of any other subject that's as of a joke as music theory.

313y

I have been using Harmony and Voice Leading for a little while. Is An Introduction to Tonal Theory really that much better?
I've always felt that the way they explain concepts is very hand wavy and doesn't really explain anything and I tend to prefer things to be more mathematical or abstract.
I'll probably pick this book up on your suggestion.

513y

Yes.
Don't get me wrong, Aldwell and Schachter are about the best you can do while still remaining in the traditional "vocabulary of chords" paradigm. (You can even see how they tried to keep the number of "chords" down to a minimum.) Unfortunately, that paradigm is simply wrong.
Also, Aldwell and Schachter, brilliant musicians though they may be (especially Schachter), lack the deeper intellectual preoccupations that Westergaard possesses in abundance. One should perhaps think of their book as being written for students at Mannes or Julliard, and of Westergaard's as being written for students at Columbia or Princeton. (There is a certain literal truth to these statements.)
You'll love ITT.

213y

"One should perhaps think of their book as being written for students at Mannes or Julliard and of Westergaard's as being written for students at Columbia or Princeton. (There is a certain literal truth to these statements.)"
As a graduate of Juilliard I am curious about this assertion. Care to elaborate? Not that I personally have ever had much use as a performer for abstract notions about music theory. My experience has been that it gets in the way of actually performing music. Which leads to the question 'why should this be so' ? Those of my colleagues who were great adepts at theory were uninspired performers of the music they seemed to understand so well. All head and no heart. But why? I can understand that they are different skill sets, but why should they not be complementary skill sets?
I imagine that on this site, alarm bells may go off as I make an observation from experience, but I do not think that it would be possible to use any sort of methodology or system analysis to determine who is and who is not an inspired performer. Just try figuring out how orchestral auditions are run! Now that is a sloppy business!
Regarding textbooks: have any of you read W.A. Mathieu's
W.A. Mathieu Harmonic Experience: Tonal Harmony from Its Natural Origins to Its Modern Expression (1997) Inner Traditions Intl Ltd. ISBN 0-89281-560-4.

613y

It's a complicated question, but the short answer is that what usually passes for "music theory" is the wrong theory. At least, it's certainly the wrong theory for the purposes of turning people into inspired performers, because as you point out, it doesn't.
But then, if you'll forgive my cynicism, that isn't the purpose of music theory class, any more than the purpose of high-school Spanish class is to teach people Spanish. The purpose of such classes is to provide a test for students that's easy to grade them on and makes the school look good to outside observers.
(Nor, by the way, do students typically show up at Juilliard for the purpose of turning themselves from uninspired into inspired performers; rather, in order to get there in the first place they already have to be "inspired enough" by the standards of current musical culture, and are there simply for the purposes of networking and career-building.)
But music theory isn't inherently counterproductive to or useless for becoming a good performer or composer; it's just that you need a different theory for that. Ultimately, inspired performers are that way because they know certain information that their less-inspired counterparts don't; to see what this sort of information looks like when written down, see Chapter 9 of Westergaard. (And after reading that chapter, tell me if you still think that knowledge of music theory "gets in the way of actually performing music".)

15y

For those interested in a scientific perspective, David Huron's Voice Leading: The Science Behind a Musical Art is really unparalleled.

112y

Is this text useful for actually learning to write harmony, or does it teach about music theory in a more abstract kind of way?
I'm preparing for an exam for a teaching diploma in a few months' time, and I need to relearn harmony and counterpoint. (I was okay enough at them a few years ago to get by, but never really mastered them.) Also, I want to learn them for their own sake, it's just a useful skill to have.
I was planning on getting Lovelock's textbooks on harmony - they come recommended with the warning that it's very much harmony-by-the-numbers, but that they teach it systematically. I reckon a healthy skepticism towards his advice would minimize the damage done.

312y

It depends on what you mean by "write harmony". I will say that if "abstract" is a bad word for you, you probably won't like it. However, that isn't typically an issue for LW readers.
Here is what Westergaard says in the preface (in the "To the teacher" section):
The best way to know if you'll like the book would be to take a look at it and see. Failing that, my advice would be as follows: if you want to actually learn how music works, this is the book to read. If you merely want to pass some kind of exam without actually learning how music works in the process, you probably don't need it.
(Added: I see that you're interested in reading about music cognition. In that case, you will definitely be interested in Westergaard.)

212y

By abstract, I meant like Schenker (I then saw that you compare Schenker and Westergaard's approaches elsewhere in the thread). Schenker was pretty adamant that his method was for analysis only, and not a compositional tool. So I was wondering if the book gave an overview of how Westergaard thinks music works, or if it does this and also teaches how to do harmony exercises, perform species counterpoint, and the like.
To break it down into my goals: I have a general goal of learning how music actually works (I've got a reasonably good grasp as it is; kinda important to me professionally), hence the interest in music cognition. However, as a specific goal I need to pass this exam!
It certainly looks interesting; it seems a little too expensive for me to get right now, but if I can get a cheap copy or a loan, I'll look into it.
Cheers for the advice!

212y

Oh, the book certainly contains exercises, and is definitely intended as a practical textbook as opposed to a theoretical treatise (in fact, I actually wish a more comprehensive treatise on Westergaardian theory existed; the book is pretty much the only source). It's true that Westergaard's theory itself is descended from Schenker's, but his expository style is quite different! Part II of the book is basically a species counterpoint course on its own.
What the book doesn't contain is "harmony" exercises in the traditional sense. (In fact, I think the passage I quoted above might be the only time the word "harmony" occurs in the book!) However, this is not an omission, any more than the failure of chemistry texts to discuss phlogiston is. "Harmony" does not exist in Westergaard's theory; instead, its explanatory role is filled by other, better concepts (mainly the "borrowing" operation introduced in Section 7.7 -- of which the species rule B3 of Chapter 4 is a "toy" version).
So in place of harmony exercises, it has Westergaardian exercises, which are strictly superior.
If you have access to a university library, there's a good chance you can find a copy there; at the very least, you should be able to get one through interlibrary loan.

012y

Right. Well to pass this exam, seeing as I'll be required to perform harmony exercises, I will possibly keep the other approach in mind.
My college library doesn't have a copy according to the online database; besides I'm actually finished my degree so I can't borrow stuff from there from next month on anyway. I'll try convince someone to get it out for me from another college.

Subject: Representation Theory

Recommendation: Group Theory and Physics by Shlomo Sternberg.

This is a remarkable book pedagogically. It is the most extremely, ridiculously concrete introduction to representation theory I've ever seen. To understand representations of finite groups you literally start with crystal structures. To understand vector bundles you think about vibrating molecules. When it's time to work out the details, you literally work out the details, concretely, by making character tables and so on. It's unique, so far as I've read, among math textbooks on any subject whatsoever, in its shameless willingness to draw pictures, offer physical motivation, and give examples with (gasp) *literal numbers.*

Math for dummies? Well, actually, it *is* rigorous, just not as general as it could potentially be. Also, many people's optimal learning style is quite concrete; I believe your first experience with a subject should be example-based, to fix ideas. After all, when you were a kid you played around with numbers long before you defined the integers. There's something to the old Dewey idea of "learning by doing." And I have only seen it tried *once* in advanced m...

713y

Won't do what? Almost everything you say about Sternberg seems to me to apply to Fulton & Harris. I have not looked at Sternberg, and it may well be better in all these ways, but your binary dismissal of F&H seems odd to me.

313y

Have you ever read Group Theory and Its Applications in Physics by Inui, Tanabe, Onodera? I have never been able to find this book and it's been recommended to me several times as the pedagogically best math/physics book they've ever read.

213y

I hasten to point out (well, actually I didn't hasten, I waited a day or two, but...) that while this is true for many people, it isn't true for all, and, in particular, it isn't true for me. (See here.)
I don't think the way I learned mathematics as a young child (or indeed in school at any time, up to and including graduate school) was anywhere near optimal for the way my mind works.
The best way for me would have been to work through Bourbaki, chapter by chapter, book by book, in order. I'm dead serious. (If I were making an edition for my young self I would include plenty of colorful but abstract pictures/diagrams.)

3[anonymous]13y

I assumed there were some folks like you but I'd never met one. Shame on me for making too many assumptions.

613y

It's not as stark as that. For example, Alicorn, whom I believe you've met, shares with me a psychological need for concepts to be presented in logical order.
In my case, if you're curious, I think the reason I'm the way I am comes down to efficient memory. To remember something reliably I have to be able to mentally connect it to something I already know, and ultimately to something inherently simple. The reason I can't stand ad-hoc presentations of mathematics is that remembering their contents (let alone being able to apply those contents to solve problems) is extremely cognitively burdensome. It requires me to create a new mental directory when I would prefer to file new material as a subdirectory under an existing directory. (I don't mind having lots of nested layers, but strongly prefer to minimize the number of directories at any given level; I like to expand my tree vertically rather than horizontally.)
This explains why it took me forever to learn the meaning of "k-algebra". The reason was that (for a long time) every time I encountered the term, the definition was always being presented in passing, on the way to explaining something else (usually some problem in algebraic geometry, no doubt), instead of being included among The Pantheon Of Algebraic Structures: Groups, Rings, Fields etc. -- so my brain didn't know where to store it.

313y

Interesting. That sounds like my habit of making sure everything I learn plugs into my model for everything else, and how I'm bothered if it doesn't (literature and history class, I'm looking in your general direction here). Likewise, how I don't regard myself as understanding a subject until my model is working and plugged in (level 2 in my article).
This is why I've usually found it easy to explain "difficult" topics to people, at least in person: per my comment here, I just find the inferentially-nearest thing we both understand, and build out stepwise from there. And, in turn, why I'm bothered by those who can't likewise explain -- after all, what insights are they missing by having such a comparmentalized (level 1) understanding of the topic?

313y

I find it takes much more effort to learn things when different sources don't coordinate well on definitions, notation, and the material's hierarchical structure. For example, if everyone agreed on how to present the Nine Great Laws of Information Theory, that would make them much easier for me to remember them. It's as if, instead of learning the overlap between different presentations, my brain shuts down and doesn't trust any of them. But it's hard to settle on such cognitive coordination equilibria.

2[anonymous]13y

Well, I can see the need to have the concepts fit together. What I need on a first pass through a subject is something that can attach to the pre-abstract part of my brain. A picture, even a "real-world example." Something to keep in mind while I later fill in the structure.
The way I see it (which I realize is more of a metaphor than an explanation) human brains evolved to help us operate in large social groups of other primates. We're very good at understanding stories, socialization, human faces, sex and politics. I think for a lot of people (myself included) the farther we get from that core, the more help we need understanding concepts. I need to make concessions to human frailty by adding pictures and applications, if I want to learn as well as possible. (This is something that people in abstract fields rarely admit but I think LessWrong is a good place to be frank.)

16y

Subject: Psychology as a Science
Recommendation: Understanding Psychology as a Science: An Introduction to Scientific and Statistical Inference
Excellent intro book to Psychology as a science and the methodologies." An accessible and illuminating exploration of the conceptual basis of scientific and statistical inference and the practical impact this has on conducting psychological research. The book encourages a critical discussion of the different approaches and looks at some of the most important thinkers and their influence."

113y

Thanks for all the detail! I've added it to the list above.

09y

Has anyone been to OpenStax College?
http://openstaxcollege.org/books
If so, are their textbooks good?

**Update** see my comment for new thoughts

Topic: Introductory Bayesian Statistics (as distinct from more advanced Bayesian statistics)

Recommendation: *Data Analysis: A Bayesian Tutorial* by Skilling and Sivia

Why: Sivia's book is well suited for smart people who have not had little or no statistical training. It starts from the basics and covers a lot of important ground. I think it takes the right approach, first doing some simple examples where analytical solutions are available or it is feasible to integrate naively and numerically. Then it teaches into maximum likelihood estimation (MLE), how to do it and why it makes sense from a Bayesian perspective. I think MLE is a very very useful technique, especially so for engineers. I would overall recommend just Part I: The Essentials, I don't think the second half is so useful, except perhaps the MLE extensions chapter. There are better places to learn about MCMC approximation.

Why not other books?

*Bayesian Data Analysis* by Gelman - Geared more for people who have done statistics before.

*Bayesian Statistics* by Bolstad - Doesn't cover as much as Sivia's book, most notably doesn't cover MLE. Goes kinda slowly and spends a lot of time on comparin...

Brandon Reinhart used both Sivia's book and Bolstad's book and found (3rd message) Bolstad's book better for those with no stats experience:

For statistics, I recommend An Introduction to Bayesian Statistics by William Bolstad. This is superior to the "Data Analysis" book if you're learning stats from scratch. Both "Data Analysis" and "Bayesian Data Analysis" assume a certain base level of familiarity with the material. The Bolstad book will bootstrap you from almost no familiarity with stats through fairly clear explanations and good supporting exercises.

Nonetheless, it's something you should do with other people. You may not notice what you aren't completely comprehending otherwise. Do the exercises!

Based on these comments, I think I was underestimating inferential distance, and I now change my recommendation. You should read Bolstad's book first (skipping the parts comparing bayesian and frequentist methods unless that's important to you) and then read Sivia's book. If you have experience with statistics you may start with Sivia's book.

313y

Nice!

22y

See also https://stats.stackexchange.com/questions/125/what-is-the-best-introductory-bayesian-statistics-textbook.

011y

Any in particular? I came to this thread seeking exactly this.

211y

I don't have an especially awesome place, but Bayesian Data Analysis by Gelman introduces the basics of Metropolis Hastings and Gibbs Sampling (those are probably the first ones to learn). There are probably quite a few other places to learn about these two algorithms too (including wikipedia). MCMC using Hamiltonian Dynamics by Neal, is the standard reference for Hamiltonian Monte Carlo (what I would suggest learning after those two).

012y

Is Gleman's book a good recommendation for people who have done frequentist statistics and/or combinatorics? I have free access to it and basic familiarity with both.

**Business**: *The Personal MBA: Master the Art of Business* by Josh Kaufman.

I'm the author, so feel free to discount appropriately. However, the entire reason I wrote this book is because I spent *years* searching for a comprehensive introductory primer on business practice, and I couldn't find one - so I created it.

Business is a critically important subject for rationalists to learn, but most business books are either overly-narrow, shallow in useful content, or overly self-promotional. I've read thousands of them over the past six years, including textbooks.

Business schools typically fragment the topic into several disciplines, with little attempt to integrate them, so textbooks are usually worse than mainstream business books. It's possible to read business books for years (or graduate from business school) without ever forming a clear understanding of what businesses fundamentally *are*, or how they actually work.

If you're familiar with Charlie Munger's "mental model" approach to learning, you'll recognize the approach of *The Personal MBA* - identify and master the set of business-related mental models that will actually help you operate a real business successfully.

Because mak...

812y

My summary of chapter 9, for anyone who cares:
Fear kills work. Inspire coworkers by showing them appreciation, courtesy, and respect. Show them they're important. Get them to work in their comparative advantage, and where they are intrinsically motivated. Explain the reasons why you ask for things. Someone must be responsible and accountable for each task. Avoid clanning; get staff to work together on shared projects and enjoy relaxation time together. Measure things, to see what works. Avoid unrealistic expectations. Shield workers from non-essential bureaucracy.

713y

I like the book so far, it seems to pretty much a solid implementation of Munger's approach.
Spends a bit too much energy dissuading me from business school, including some arguments I found rhetorical (e.g. biz. schools started from people measuring how many seconds a railway worker does something or other. by this logic we should outlaw chemistry), but it might be useful to someone (though there are quite a few people in line to take their places).

613y

Rather phenomenal Amazon reviews you have, sir.

313y

I remember the interview Josh did with Ben Casnocha as being very interesting. (Site contains links to streaming video and MP3 download + written interview summary.)

113y

Thanks - glad people are finding it useful.

413y

This book, or, to be accurate, the 20 or so pages I read, are terrible. For someone who prefers dense and thorough examinations of topics, The Personal MBA is cotton candy. It is viscerally pleasing, but it offers little to no sustenance. My advice: don't get an MBA or read this book.
The mistake I made was considering the author's appearance in this thread as strong evidence that his book would offer value to a rationalist. In fact, the author is a really good marketer whose book has little value to offer. Congratulations to him, however, since he got me to buy a brand-new copy of a book, something I rarely do.

Wow, Duke - that's a bit harsh.

It's true that the book is not densely written or overly technical - it was created for readers who are relatively new to business, and want to understand what's important as quickly as possible.

Not everyone wants what you want, and not everyone values what you value. For most readers, this is the first book they've ever read about how businesses actually operate. The *worst thing I could possibly do* is write in a way that sounds and feels like a textbook or academic journal.

I don't know you personally, but from the tone of your comment, it sounds like you're trying to signal that you're too sophisticated for the material. That may be true. Even so, categorical and unqualified statements like "terrible" / "cotton candy" / and "little value to offer" do a disservice to people who are in a better position to learn from this material than you are.

That said, I'll repeat my earlier comment: if you've read another solid, comprehensive primer on general business practice, I'd love to hear about it.

813y

For the sake of clarity, my criticism of Josh's book was developed within the context of Josh promoting his book in a LW thread titled "The Best Textbooks on Every Subject."

913y

Useful clarification. In that case, you should know that the book is currently being used by several undergraduate and graduate business programs as an introductory business textbook.
The book is designed to be a business primer ("an elementary textbook that serves as an introduction to a subject of study"), and business is a very important area of study that rewards rationality. At the time of my original post, no one had recommended a general business text. That's why I mentioned the book in this thread.
I appreciate your distaste for perceived self-promotion: as a long-time LW lurker, my intent was to contribute a resource LW readers might find valuable, nothing more.
If you're interested in the general topic and want a more academic treatment, you may enjoy Bevelin's Seeking Wisdom. I found it a bit disorganized and overly investment-focused, but you may find it's more to your liking.

513y

I think the title--and especially the subtitle, " Mastering the Art of Business,"--signals that the book will be a thorough examination of business principles. As well, I think that hocking your book in a thread called "The Best Textbooks on Every Subject" signals that the book will be, at least, textbook-like in range, complexity and information containment. You now call your book "not densely written or overly technical." I call it cotton candy.

3[anonymous]13y

I upvote you solely for the chutzpah of your self-promotion.
Which, in hindsight, is mostly what you're selling.

313y

I've added it to my list. I'm currently reading Poor Charlie's Almanack and liking it a lot so far.
The best business book I've read is probably The Essays of Warren Buffett (second ed.), but it's certainly not exhaustive in what it covers.
Update: I've got my copy from Amazon.ca (really fast shipping - 2 days). Will probably have a chance to read it in February.

313y

I'm reading it now. I fully endorse this recommendation, but I haven't read any other business books, so take that for what it's worth.

13y

I know this comment/thread is a decade old, but I come back to the chapter on business models multiple times a year because it's a concise overview and particularly useful in combinatoric idea generation.
Figured I'd give my thanks knowing there's a chance the author will read this comment... Thanks Josh!!

I suppose I can think up a few tomes of eldritch lore that I have found useful (college math specifically):

**Calculus**:

Recommendation: Differential and Integral Calculus

Author: Richard Courant

Contenders:

Stewart, *Calculus: Early Transcendentals*:
This is a fairly standard textbook for freshman calculus. Mediocre overall.

Morris Kline, *Calculus: An Intuitive and Physical Approach*:
Great book. As advertised, focuses on building intuition. Provides a lot of examples that aren't the usual contrived "applications". This would work well as a companion piece to the recommended text.

Courant, *Differential and Integral Calculus* (two volumes):
One of the few math textbooks that manages to properly explain and motivate things *and* be rigorous at the same time. You'll find loads of actual applications. There are plenty of side topics for the curious as well as appendices that expand on certain theoretical points. It's quite rigorous, so a companion text might be useful for some readers. There's an updated version edited by Fritz John (*Introduction to Calculus and Analysis*), but I am unfamiliar with it.

**Linear Algebra**:

Recommended Text: Linear Algebra

Author: Georgi Shilov

Contenders:

David Lay, *L*...

19y

Updated, thanks!

19y

How can baby rudin possibly be recommended in almost all use cases there is something better -_-, less wrong is supposed to give good advice not status-signaling type.
Rudin = Bourbaki and I thought we were anti-bourbaki here
Alternatives: Abbot & Bressoud combo(has mathematica code), Pugh, or Strichartz's book(the one patrick says is good)

29y

I recommend Rudin because he dives right into the topology and metric space approach. It's a lot easier to pick it up when it's used to develop the familiar theory of calculus. It also helps put a lot of point-set topology into perspective. I appreciated it once I started studying functional analysis and all those texts basically assumed the reader was familiar with the approach. The problems are great to work through and the terseness is a sign of things to come for a reader who wants to go on to advanced texts.
There is a caveat. Rudin is not a good text for a student's first foray into the rigors of real analysis. IF one has already seen a rigorous development of calculus, Rudin bridges the gap with a minimum of fluff. If not, the reader is better served elsewhere.
I'm no expert in undergraduate math texts so maybe there's something else that works better. I read Rudin on my own in undergrad and with my background at the time I got a lot out of it, so I'm recommending it.
Bourbaki has its place. There comes a time when you need a good reference for the general theory and that's where the Bourbaki style shines. It makes for bad pedagogy and is cruel to foist upon beginners, but on the other hand good pedagogical books tend to limit their scope and seldom make good references.

19y

I agree with this post much more. My concern was more ability to learn the subject & less wrong aesthetic in this direction which I think is correct.

29y

What? Did I miss an anti-Bourbaki fatwa? The one mention of their name in the post does not come close to a general stance on Bourbaki, and in any case there must be someone on the site who likes them. In fact, here's one.

24y

Here's another. I learnt point-set topology from Bourbaki, borrowing the books from the public library.

-29y

Just use patrick's recs for analysis and use yours for pretty much the other stuff(strang for lin algebra?). No serious person would recommend baby rudin give me a break.

14y

Why not? I used it and thought it was wonderful.

09y

Echoing Hairyfigment here, what is wrong with Bourbaki?

19y

not meant for learning except for stuff like lang, conversations like this deserve a thread. sleep apnea related sleep deprivation is hitting me so i will update this later with more info
if less wrong is to have any aesthetic imo we should be able to keep mathematical orientations like this, i'm interested in Eliezer's opinions on this

09y

I purchased Shilov's Linear Algebra and put it on my bookshelf. When I actually needed to use it to refresh myself on how to get eigenvalues and eigenvectors I found all the references to preceding sections and choppy lemma->proof style writing to be very difficult to parse. This might be great if you actually work your way through the book, but I didn't find it useful as a refresher text.
Instead, I found Gilbert Strang's Introduction to Linear Algebra to be more useful. It's not as thorough as Shilov's text, but seems to cover topics fairly thoroughly and each section seems to be relatively self contained so that if there's a section that covers what you want to refresh your self on, it'll be relatively self contained.

09y

How about Piskunov? I've tried James Stewart, Thomas Finn and Guidorizzi before but now I'm studying through Piskunov and I think it is a good one. But since I didn't finished already I'm more inclined ti hear what is good and bad with this book.

I can't help but question this post.

Textbook recommendations are *all over*. From the old SIAI reading shelf to books individually recommended in articles and threads to wiki pages to here (is this even the first article to try to compile a reading list? I don't think it is.)

Maybe we would be better off adding pages to the LW wiki. So for `[[Economics]]`

a brief description why economics is important to know, links to relevant LW posts, and then a section `== Recommended reading ==`

. And so on for all the other subjects here.

Work smarter, not harder!

The problem is that lots of textbook recommendations are not very good. I've been recommended lots of bad books in my life. That's what is unique about this post: it demands that recommendations be given only by people who are fairly well-read on the subject (at least 3 textbooks).

But yes, adding this data to the Wiki would be great.

913y

agreed, but the idea to add this info to the wiki once the thread has matured is a good one.

413y

However, a centralized repository-of-textbooks is also a good idea.

Textbook recommendations are all over.

Since the parent omitted a link: singinst.org/reading/

411y

Link dead; try here: http://www.librarything.com/catalog/siai

**Calculus:** Spivak's Calculus over Thomas' Calculus and Stewart's Calculus. This is a bit of an unfair fight, because Spivak is an introduction to proof, rigor, and mathematical reasoning disguised as a calculus textbook; but unlike the other two, reading it is actually exciting and meaningful.

**Analysis in R^n (not to be confused with Real Analysis and Measure Theory):** Strichartz's The Way of Analysis over Rudin's Principles of Mathematical Analysis, Kolmogorov and Fomin's Introduction to Real Analysis (yes, they used the wrong title; they wrote it decades ago). Rudin is a lot of fun if you already know analysis, but Strichartz is a much more intuitive way to learn it in the first place. And after more than a decade, I still have trouble reading Kolmogorov and Fomin.

**Real Analysis and Measure Theory (not to be confused with Analysis in R^n):** Stein and Shakarchi's Measure Theory, Integration, and Hilbert Spaces over Royden's Real Analysis and Rudin's Real and Complex Analysis. Again, I prefer the one that engages with heuristics and intuitions rather than just proofs.

**Partial Differential Equations:** Strauss' Partial Differential Equations over Evans' Partial Differential Equations and Ho...

59y

In my opinion the "good stuff" in evans is in chapters 5-12. Evans is a pretty good into book on the modern "theory" of Linear and Non-linear PDEs. Strauss by comparison is a much less demanding book that is concerned with concrete examples and applications to physics. (less demanding is a good thing if the material covered is similar, but in this case its not).
Possibly Strass is overall the better book. And I really dislike Evan's chapter 1-4 (he does not use Fourier theory when it helps, his discussion of the underlying physics of some equations is very lacking, etc). But directly comparing Strauss and Evans seems odd to me. The books have very different goals and target audiences.
If the comparison is evans 1-4 vs strauss then I too would recommend Strauss. And this restricted comparison makes a ton of sense imo.

29y

I'll agree with that. Evans would be better for a second course on PDEs than a first course.

29y

Thanks! Added.

111y

Spivak was a lot of fun - and very readable. Amusing footnotes, too. (I still remember the rant against Newtonian notation for derivatives).

0[anonymous]11y

If you like Spivak, they've reprinted his five volume epic on differential geometry. It's pretty glorious.

011y

Huh. I've always liked Kolmogorov and Fomin. (And shouldn't it be under "Real Analysis and Measure Theory"?)
Have you looked at Jost's Postmodern Analysis, by chance? (I found the title irresistibly curiosity-provoking, and the book itself rather good, at least if memory serves.)

0[anonymous]11y

I'm confused. Did you mean the entire 4-volume set of Hormander -- in which case, it's not remotely comparable to Evans or Strauss -- or the first volume that you linked -- in which case, it's not even really about PDEs?
In terms of introductory PDE books, I'd favor Folland over all three.

**Introduction to Neuroscience**

**Recommendation:** Neuroscience:Exploring the Brain by Bear, Connors, Paradiso

**Reasons:**
BC&P is simply much better written, more clear, and intelligible than it's competitors *Neuroscience* by Dale Purves and *Fundamentals of Neural Science* by Eric Kandel. Purves covers almost the same ground, but is just not written well, often just listing facts without really attempting to synthesize them and build understanding of theory. Bear is better than Purves in every regard. Kandel is the Bible of the discipline, at 1400 pages it goes into way more depth than either of the others, and way more depth than you need or will be able to understand if you're just starting out. It is quite well-written, but it should be treated more like an encyclopedia than a textbook.

I also can't help recommending *Theoretical Neuroscience* by Peter Dayan and Larry Abbot, a fantastic introduction to computational neuroscience, *Bayesian Brain*, a review of the state of the art of baysian modeling of neural systems, and *Neuroeconomics* by Paul Glimcher, a survey of the state of the art in *that* field, which is perhaps the most relevant of all of this to LW-type interests. The second tw...

**Subject**: Problem Solving

**Recommendation**: Street-Fighting Mathematics
The Art of Educated Guessing and Opportunistic Problem Solving

**Reason**: So, it has come to my attention that there is a freely available .pdf for the textbook for the MIT course Street Fighting Mathematics. It can be found here. I have only been reading it for a short while, but I would classify this text as something along the lines of 'x-rationality for mathematics'. Considerations such as minimizing the number of steps to solution minimizes the chance for error are taken into account, which makes it very awesome.

in any event, I feel that this should be added to the list, maybe under problem solving? I'm not totally clear about that, it seems to be in a class of its own.

313y

If you come up with relevant comparison volumes, let me know!

6[anonymous]13y

Seemingly relevant comparison volumes:
Numbers Rule Your World: The Hidden Influence of Probabilities and Statistics on Everything You Do
Back-of-the-Envelope Physics
How Many Licks? Or, How to Estimate Damn Near Anything
Guesstimation: Solving the World's Problems on the Back of a Cocktail Napkin
Also, the books below are listed as related resources in another class on approximation in science & engineering by the author of the Street-Fighting textbook on OCW, so they may be relevant for comparison, too, or at least interesting.
Engel, Arthur. Problem-solving Strategies. New York, NY: Springer, 1999. ISBN: 9780387982199.
Schmid-Nielsen, Knut. Scaling: Why is Animal Size So Important? New York, NY: Cambridge University Press, 1984. ISBN: 9780521319874.
Vogel, Steven. Life in Moving Fluids. 2nd rev. ed. Princeton, NJ: Princeton University Press, 1996. ISBN: 9780691026169.
Vogel, Steven. Comparative Biomechanics: Life's Physical World. Princeton, NJ: Princeton University Press, 2003. ISBN: 9780691112978.
Pólya, George. Induction and Analogy in Mathematics. Vol. 1, Mathematics and Plausible Reasoning. 1954. Reprint, Princeton, NJ: Princeton University Press, 1990. ISBN: 9780691025094.

013y

Great list, thanks!

113y

Well, they aren't necessarily comparison volumes, but the author suggested that the book should be used as a compliment to the following:
How to Solve It, Mathematics and Plausible Reasoning, Vol. II, The Art and Craft of Problem Solving
He implies that his book is more rough and ready for applications, but those books are more geared towards solving clearly stated problems in, say, a competition setting.
I would add Putnam and Beyond to the list, classifying it as advanced competition style problem solving (some of the stuff in that book is pretty tough).

013y

Have you read any of those? If so, what did you think of them in comparison to 'Street-Fighting Mathematics'?

113y

I have only read/skimmed through/worked a few problems out of Putnam and Beyond. I can attest to its advanced level (compared to other problem solving books, I have looked at a few before and found that they were geared more towards high school level subject matter; you won't find any actually advanced [read; grad level] topics in it) and systematic presentation, but that is about it. Its problems are mainly chosen from actual math competitions, and it seems to present a useful bag of tricks via well thought out examples and explanations. I am currently working through it and have a ways to go.
I've heard How to Solve It mentioned a number of times, but I've never really looked into it. I can't really say anything about the other books beyond what the author said about them.

General programming: *Structure and Interpretation of Computer Programs*. Focuses on the essence of the subject with such clarity that a novice can understand the first chapter, yet an expert will have learned something by the last chapter.

Specific programming languages: *The C Programming Language*, *The C++ Programming Language*, *CLR via C#*. Informative to a degree that rarely coexists with such clarity and readability.

AI: *Artificial Intelligence: a Modern Approach*. Perhaps the rarest virtue of this work is that not only does it give about as comprehensive a survey of the field as will fit in a single book, but casts a cool eye on the limitations as well as strengths of each technique discussed.

Compiler design: *Compilers: Principles, Techniques and Tools*. The standard textbook for good reason.

I don't agree on the dragon book (Compilers: Principles, Techniques and Tools). It focuses too much on theory of parsing for front end stuff, and doesn't really have enough space to give a good treatment on the back end. It's a book I'd recommend if you were writing another compiler-compiler like yacc.

I'd rather suggest Modern Compiler Implementation in ML; even though there are C and Java versions too, a functional language with pattern matching makes writing a compiler a much more pleasant experience.

(I work on a commercial compiler for a living.)

012y

+1 for ML (and purely functional languages) used for implementing compilers.

7[anonymous]13y

Is "The C Programming Language" Kernighan & Ritchie? (titles are often very generic so it's nice to see authors as well.)

113y

Yes.

513y

rwallace,
Thanks for your recommendations! Your comment made me realize I was not specific enough in my list of rules, so I modified the third rule to the following:
"You must briefly name the other books you've read on the subject and explain why you think your chosen textbook is superior to them."
Would you please do us the favor of naming the other books you've read on these subjects, and why your recommendations are superior to them? That would be much appreciated.

113y

A problem is that in many cases it was long enough ago (e.g. I got into C programming in the 1980s, C++ around 1990) that I don't remember the names of the other books I read. The ones that stuck in my mind were the memorably good ones. (Memorably bad things can do likewise of course, but few textbooks fall into that category -- the point of this post after all is that textbooks tend to have higher standards than most media.)

112y

Disagree with "C++ the programming language" as a C++ textbook. Anything by Lippman, Koenig or Moo would be better.

On (real) analysis: Bartle's **A Modern Theory of Integration**.

Even Bayesian statistics (presumably the killer app for analysis in this crowd) is going to stumble over measure theory at some point. So this recommendation is made with that in mind.

The traditional textbooks for modern integration in this context are (the first chapters of) Rudin's **Real and Complex Analysis** and (the first chapters of) Royden's **Real Analysis**.

I can't recommend Rudin because in the second chapter he goes on this ridiculously long tangent on Urysohn's lemma that makes absolutely no sense to anyone who hasn't seen topology before. Further, the exercises tend to have a difficulty curve that starts a bit too high for the non-mathically inclined.

Royden is slightly better in this respect. The first four chapters are excellent, but still probably too theoretical. Further, eventually one will encounter measure spaces that aren't based on the real numbers and the Lebesgue measure, and because of the way Royden is set up the sections on Lebesgue theory and abstract measure theory are separated by a refresher on metric spaces and topology. Unlike the tangent in Rudin, this digression isn't as avoidable.

My recommendat...

8[anonymous]13y

Hmm. Upvoted for contributing to a good topic but I'm not sure I agree.
I just looked up the gauge integral because I wasn't familiar with it. For those curious about the debate, here's the introduction to the gauge integral I found, which has a lot of relevant information. My beef with this is precisely that it doesn't use the general background of measure theory (sigma-algebras, measurable functions, etc.) and you're going to need that background to do useful things. The gauge integral approach doesn't give you the tools to generalize to scenarios like Brownian motion where you need to construct different measures; also, the gauge integral doesn't come with a lot of nice convergence theorems the way the Lebesgue measure does.
I don't find the standard treatment of measure theory especially hard; it takes about a month to understand everything up to the Lebesgue integral, which isn't an obscene time commitment.
Also, there's some virtue to just being familiar with the definitions and concepts that everybody else is. (It's not just mathematicians "refusing to update." I know for sure that economists, and potentially people in other fields, speak the language of standard measure theory. But maybe it's not everyone. What are you using measure theory for?)
If you're looking for an easier, more straightforward treatment than Rudin, I'd recommend Cohn's Measure Theory. I'm not sure why, but it feels friendlier and less digressive.

-2[anonymous]13y

And Bartle covers them, but later. Section 19.
I have on my desk right now Steven Shreve's Stochastic Calculus for Finance II, and the construction of the Wiener process is in slightly different language the limit of a sequences of functions defined on a sequence of tagged partitions. I'm just now learning stochastic-flavored things, so I don't know if this is canonical.
Section 8 covers the main three (Monotone, Fatou's Lemma, and Dominated Convergence).
Sunken cost fallacy.
I'm a grad student doing PDEs. I think there are two issues that need to be separated here. The first is pedagogical. People doing probability theory do need to learn measure theory eventually, yes. Royden takes this same approach -- show the Lebesgue measure on R to start and then progress to abstract measure spaces. Unfortunately he fills the middle bits between chapters five and nine (I think) with a lot of topology.
The second is practical. There are more gauge-integrable functions than Lebesgue-integrable functions. There are nice lemmas for estimating gauge integrals, and they tend to be slightly more concrete.
I also rank Halmos higher than Cohn in terms of measure theory books. Your mileage may vary.

113y

Halmos, by the way, is a top-notch mathematical author in general. Every one of his books is excellent. Finite-Dimensional Vector Spaces in particular is a classic.

013y

I think that's the only book I kept from my Maths degree. In hardback, too. I have lent it to a colleague and keep a careful eye on where it is every couple of weeks...

013y

I'm not sure why you consider the gauge integral to be easier to understand the Lebesgue integral. It may be due to learning Lebesgue first, but I find it much more intuitive.
Also:
Yes, this is a good thing. One doesn't understand a structure until one understands which parts of a structure are forcing which properties. Moreover, this supplies useful counterexamples that helps one understand what sort of things one necessarily will need to invoke if one wants certain results.

513y

It is much easier to understand what the words in the definition of the gauge integral mean. It is harder to understand why they are there.

0[anonymous]13y

I'm not sure you made it to the end of that sentence. It is a good thing, but Royden obscures the connection with this four-chapter long digression into metric spaces and Banach spaces.
Maybe I misunderstand the needs of a budding Bayesian analyst. I agree that these sorts of counterexamples are useful, but perhaps not up front. I find it hard to imagine they'd encounter measure spaces that are either 1) not discrete or 2) not a subspace of R^n on a regular basis.

013y

Yes, I did make it to the end of the sentence. But I misinterpreted the sentence to be having two distinct criticisms when there was only one.

013y

I haven't studied real analysis, could you explain what advantages the guage integral is better than the lebesgue integral? Edit: maybe just respond to SarahC.

Recommending Ben Lambert's "A student's guide to Bayesian Statistics" as the best all-in-one intro to *applied* Bayesian statistics

The book starts with very little prerequisites, explains the math well while keeping it to a minimum necessary for intuition, (+has good illustrations) and goes all the way to building models in Stan. (Other good books are McEarlath Statistical Rethinking, Kruschke's Doing Bayesian Data Analysis and Gelman's more math-heavy Bayesian Data Analysis). I recommend Lambert for being the most holistic coverage.

I have read McEarlath Statistical Rethinking and Kruschke's Doing Bayesian Data Analysis, skimmed Gelman's Bayesian Data Analysis. Recommend Lambert if you only read 1 book or as your first book in the area.

PS. He has a playlist of complementary videos to go along with the book

**Subject:** Introductory Decision Making/Heuristics and Biases

**Recommendation:** Judgment in Managerial Decision Making by Max Bazerman and Don Moore.

This book wins points by being comprehensive, including numerous exercises to demonstrate biases to the reader, and really getting to the point. Insights pop out at every page without lots of fluffy prose. The recommendations are also more practical than other books.

**Alternatives:**

- Rational Choice in an Uncertain World by Reid Hastie and Robyn Dawes. A good, well-rounded alternative. Its primary weakness is the lack of exercises.
- Making Better Decisions: Decision Theory in Practice by Itzhak Gilboa. Filled with exercises, this book would be a great supplement to a course on this subject, but it wouldn't stand alone on self-study. This book specializes in probability and quantitative models, so it's not as practical, but if you've read Bazerman and Moore, read this next if you want to see more of the economic/decision theory approach.
- How to Think Straight about Psychology by Keith Stanovich. Slanted towards what science is and how to perform and evaluate experiments, this is still a decent introduction.
- Smart Choices by John Hammond, Ralph

513y

Excellent. I also like Baron's Thinking and Deciding.

36y

If I'm interested in learning about the claims made by the science/study of decision-making, and not looking to make decisions myself (so perhaps exercises don't matter?) would that change your recommendation? You can further assume that I am moderately well trained in probability theory.

26y

Judgment is also available for free at archive.org

16y

Free to "borrow".

Luke -- I wonder if either permalinks to comments answering the task, or direct quotes of them could be added to your main post (say, after two+ weeks have passed)? I know in other posts where a question is asked it can be very difficult to sift through the "meta" comments and the actual answers, especially as comments get into the 100-200+ range!

813y

I was thinking this myself. For example for michaba03m's recommendation below, I could add a line which reads:
* on economics, michaba03m recommends Mankiw's Macroeconomics over Varian's Intermediate Microeconomics and Katz & Rosen's Macroeconomics.

113y

Sorry Luke I rushed that a little bit and didn't check before hitting 'comment'. In economics I would say you should read macroeconomics and microeconomics separately, and most college-level textbooks are on either one rather than both anyway. So Mankiw is definitely the best on Macro, whilst Varian is the best for Micro, but his is quite dry and mathsy, whereas for a Micro alternative Katz and Rosen is more readable but less mathematical.
So for Macro, go for Mankiw, and for Micro go Katz and Rosen if you can't handle Varian.
Hope that clears that up!

113y

Love it -- I also wondered if you might be planning something like this... figured it didn't hurt to suggest it anyway, though!

I'd love to give recommendations on probability, but I learned it from a person, not a book, and I have yet to find a book that really fits the subject as I know it. The one I usually recommend is Grimmett and Stirzaker. It develops the algebra of probability well without depending on too much measure theory, has decent exercises, and provides a usable introduction to most of the techniques of random processes. I found Feller's exposition of basic probability less clear, though his book's a useful reference for the huge amount of material on specific distribution in it. Feller also naturally covers much less ground (probability and stochastic processes has developed a lot since he wrote that book). Kolmogorov's little book (mentioned elsewhere in the threads) is typical Kolmogorov: deliciously elegant if you know probability theory and like symbols. I would love to be able to recommend Radically Elementary Probability Theory by Nelson, and it's certainly worth a read as a supplement to Grimmett and Stirzaker, but I would hesitate to hand it to someone trying to understand the subject for the first time.

For statistics, I favor Kiefer's 'Introduction to Statistical Inference'. It beg...

612y

A small point, but an important one I think: Reichl is a woman.

25y

I would anti-recommend Purcell, but I acknowledge that for some people it’s the best. It’s more wordy and “tell rather than show” than e.g. Griffiths.
On Reichl’s book, I want to note from what I’ve heard (not personally read) that the 2nd edition has much more explanation and intuition that the 3rd edition cut out. I haven’t read other statistical mechanics books and so can’t compare to others.

112y

Thanks for all your recommendations! Purcell's Electricity and Magnetism is not out of print.

**Subject**: Basic mathematical physics

**Recommendation**: Bamberg and Sternberg's A Course in Mathematics for Students of Physics. (two volumes)

**Reason**: It is difficult to compare this book with other text books since it is *extremely* accessible, going all the way from 2D linear algebra to exterior calculus/differential geometry, covering electrodynamics, topology and thermodynamics. There is potential for insights into electrodynamics even compared to Feynman's lectures (which I've slurped) or Griffith's. For ex: treating circuit theory and Maxwell's equations as the same mathematical thing. The treatment of exterior calculus is more accessible than the only other treatment I've read which is in Misner Thorne Wheeler's *Gravitation*.

113y

I must add that I kept both volumes with me under continuous reborrowal from the univ library for an entire year during my undergrad! Sad and glad that nobody else wanted it :)

013y

Thanks for this! I can't add it to the list because the comparison examples don't quite fit the bill. Though I understand this may be because there simply are no comparisons. If you think of more/better comparisons, please add them so I can reconsider adding it to the list above.

43y

I just made the same recommendation on a different post. My reasons for recommending Gelman over Jaynes here is the practical value of working through the problems in Gelman's book. The problems Jaynes gives are focused on the theoretical, but the problems in BDA are applied, computational, and this is true from the beginning of the book: I used R for many of the problems at the end of chapter 2. By the end of chapter 3 I could already see ways I could apply the things I learned from BDA to my work as a Data Scientist. Jaynes also gives far fewer exercises - there are maybe 20-30 in the whole book, but in BDA there are 15 or so per chapter so far.
I read Jaynes's book cover-to-cover, but should confess I'm only through chapter 3 of BDA. So maybe it goes off the deep end and I come back here in 6 months and withdraw my recommendation. But right now I'm recommending Bayesian Data Analysis.

313y

Cyan,
Could you give us some reasons?

913y

Both Jaynes's and Bernardo's texts have a lot of material on why one ought to do Bayesian statistics; Gelman text excels in showing how to do it.

213y

Gelman's text is very specifically targeted at the kinds of problems he enjoys in sociology and politics, though. If you're interested in solving problems in that field or like it (highly complex unobservable mechanisms, large number of potential causes and covariates, sensible multiple groupings of observations, etc) then his book is great. If you're looking at problems more like in physics, then it won't help you at all and you're better off reading Jaynes'.
(Also recommended over Gelman's Applied Regression and Modeling if the above condition holds.)

113y

Ah, interesting. I used the material I learned from that book in my thesis on data analysis for proteomics, so you can expand the list of topics to include biological data too; biology problems tend to fit your list of problem characteristics.

013y

Hmm, I might be totally off base here, but wouldn't that sort of thing be useful for reasoning about highly powerful optimization processes that would be driven to maximize their expected utility by figuring out what actions would decrease the entropy of a desirable portion of state space by working from massive amounts of input data? Maybe I should check it out either way.

213y

I'm sorry, as I'm reading it that sounds rather vague. Gelman's work stems largely from the fact that there is no central theory of political action. Group behavior is some kind of sum of individual behaviors, but with only aggregate measurements you cannot discern the individual causes. This leads to a tendency to never see zero effect sizes, for instance.

013y

Thanks. I added this to the list.

Subject: Warfare, History Of and Major Topics In

Recommendation: Makers of Modern Strategy from Machiavelli to the Nuclear Age, by Peter Paret, Gordon Craig, and Felix Gilbert.

I recommend this book specifically over 'The Art of War' by Sun Tzu or 'On War' by Clausewitz, which seem to come up as the 'war' books that people have read prior to (poorly) using war as a metaphor. The Art of War is unfortunately vague- most of the recommendations could be used for any course of action, which is sort of a common problem with translations from chinese due to the hea...

I don’t know how relevant improv is to Less Wrongers, but I find it helpful for everyday social interactions, so:

**Primary recommendation:**
Salinsky & Frances-White’s The Improv Handbook.

**Reason**
It’s one of the only improv books which actually suggests physical strategies for you to try out that might improve your ability rather than referring to concepts that the author has a pet phrase for that they use as a substitute for explaining what it means. Not all of the suggetions worked for me, and they’re based on primarily on anecdotal evidence (plus the s...

112y

This will be a study project to me after the semester so thanks for the recommendations.

Non-relativistic Quantum Mechanics: Sakurai's Modern Quantum Mechanics

This is a textbook for graduate-level Quantum Mechanics. It's advantages over other texts, such as Messiah's Quantum Mechanics, Cohen-Tannoudji's Quantum Mechanics, and Greiner's Quantum Mechanics: An introduction is in it's use of experimental results. Sakurai weaves in these important experiments when they can be used to motivate the theoretical development. The beginning, using the Stern-Gerlach experiment to introduce the subject, is the best I have ever encountered.

413y

What are the prerequisites for reading this? What level of mathematics and background of classical physics?

49y

You need some solid Linear Algebra: Vector Space, dual vector space, unitary and hermitian matrices, eigenvectors and eigenvalues, trace... Mind that you should learn these things with mathematical approach, for example, vectors are elements of vector space which has certain axioms, and not 3D arrows, like pupils learn in school. Since book has this approach (matrix mechanics, rather than wave mechanics), you don't need too strong analysis, you can just trust that some things are working that way, but if you want to understand it fully, i recommend taking some analysis course as well, to be able to understand decomposition in eigenfunctions. Integrals and derivatives are MUST, however.

15y

I’m surprised to see Sakurai here rather than Griffiths. The latter is the classic undergraduate introduction, which would seem better targeted to this audience. The topics Sakurai has that Griffith’s doesn’t are more technical than any non-physicist is likely to care about (e.g. the Heisenberg representation). Griffiths’ strength is that he “speaks to you”, making it feel like 1-on-1 tutoring rather than a theory paper. I learned from Griffith’s 2nd edition (blue cover), and although the 3rd edition is out now (red cover) its reviews so far seem mixed: https://www.amazon.com/Introduction-Quantum-Mechanics-David-Griffiths-ebook/dp/B07G15LW25.

09y

I found this book very good as well. I want to add a comment, though.
If you start reading it, and you get lost, just stop reading that chapter and go to the next one. Read this book lightly at first, then start clarifying everything afterwards. Reading introduction of every chapter first is very clever.

012y

Why don't you like Cohen-Tannoudji?

013y

I second the recommendation, although I haven't read other textbooks.

While the following isn't really a textbook, I highly recommend it for helping you to improve your skill as a reader. "How to Read a Book" by Mortimer Adler and Charles Van Doren. It covers a variety of different techniques from how to analytically take apart a book to inspectional techniques for getting a quick overview of a book.

I never knew how to read analytically, I had never been taught any techniques for actually learning from a book. I always just assumed you read through it passively.

http://www.amazon.com/How-Read-Book-Touchstone-book/dp/0671212095

113y

It looks interesting, but I am surprised it's 400 pages long, is there really that much in the way of reading strategies?

713y

It has a fairly large appendix (~70 pgs) of recommended reading and sample tests/examples at the end of the book. It also has several sections on reading subject specific matter i.e. How to read History, Philosophy, Science, Practical books, etc. It also covers agreeing or disagreeing with an author, fairly criticizing a book, aids to reading. I think reading strategies may have been too narrow a choice of words. It really covers the "Art of Reading". A good set of English classes would probably cover similar ground, although I didn't see anything like this in my high school or undergraduate education.

0[anonymous]13y

Second the vote for this book, though there is quite a bit of fluff (most of the chapters on strategies for readings specific topics I found less than useful) - it really does a great job of explaining how to extract information from a book.
The key insight I took away was that a book isn't just a long string of words broken up into various sections - a book is a little machine that produces an argument, and to really understand that argument you need to figure out what the machine is doing.

Subjects: algorithms/computational complexity, physics, Bayesian probability, programming

Introduction to Algorithms (Cormen, Rivest) is good enough that I read it completely in college. The exercises are nice (they're reasonably challenging and build up to useful little results I've recalled over my programming career). I think it's fine for self-study; I prefer it to the undergrad intro level or language-specific books. Obviously the interesting part about an algorithm is not the Java/Python/whatever language rendering of it. I also prefer it to Knuth's t...

212y

For an AI text, I think any (text)book on a subject of your interest by Judea Pearl would fit the bill.
"Symbolic Logic and Mechanical Theorem Proving" by Chang and Lee is still an exceptionally lucid introduction to non-probabilistic AI.

212y

I also prefer Hopcroft+Ullman (original edition) to later alternatives like their own later edition, Papadimitriou, and even Sipser who is widely regarded as having written the definitive intro text.

212y

"A Discipline of Programming" is rather hard to follow. Dromey gives an introductory treatment that's a bit too introductory, "Progamming Pearls" by Bently includes another even more informal treatment, and Gries's "Science of Programming" would be the textbook version that I might recommend covering this material. All three are somewhat dated. More modern treatment would be either Apt's "Verification of Sequential and Concurrent Programs" or Manna's "The Calculus of Computation." and depending on your focus one would be better than the other. However, the ultimate book I would recommend in this field is "Interactive Theorem Proving and Program development" by Yves Bertot. It doesn't teach Hoare's invariant method like the other books, but uses a more powerful technique in functional programming for creating provably correct software.

012y

I'll look for Bertot's book. I agree that "A Discipline" is not a pleasant read (though I found it rewarding).

113y

Jonathan_Graehl,
Thanks for your recommendations, though I've set a rule that I won't add recommendations to the list in the original post unless those recommendations conform to the rules. Would you mind adding to what you've written above so as to conform to rule #3?
For example, you could list two other books on algorithms and explain why you prefer Introduction to Algorithms to those other books. And you could do the same for the subject of physics, and the subject of programming, and so on.

713y

Well, let me do Jonathan's job for him on one of those.
Introduction to Algorithms by Cormen, Leiserson, Rivest, and (as of the second edition) Stein is a first-rate single-volume algorithms text, covering a good selection of topics and providing nice clean pseudocode for most of what they do. The explanations are clear and concise. (Readers whose tolerance for mathematics is low may want to look elsewhere, though.)
Two obvious comparisons: Knuth's TAOCP is wonderful but: very, very long; now rather outdated in the range of algorithms it covers; describes algorithms with wordy descriptions, flowcharts, and assembly language for a computer of Knuth's own invention. When you need Knuth, you really need Knuth, but mostly you don't. Sedgwick's Algorithms (warning: it's many years since I read this, and recent editions may be different) is shallower, less clearly written, and frankly never gave me the same the-author-is-really-smart feeling that CLRS does.
(If you're going to get two algorithms books rather than one, a good complement to CLRS might be Skiena's "The algorithm design manual", more comments on which you can find on my website.)

313y

Thanks. I really didn't have the ability to easily recall names of what few alternatives I've read (although in the area of programming in general, there are dozens of highly recommended books I've actually read - Design Patterns (ok), Pragmatic Programmer (ok), Code Complete (ok), Large Scale C++ Software Design (ok), Analysis Patterns (horrible), Software Engineering with Java (textbook, useless), Writing Solid Code (ok), object-oriented software construction (ok, sells the idea of design-by-contract), and I could continue listing 20 books, but what's the point. These are hardly textbooks anyway.
On algorithms, other than Knuth (after my disrecommendation of his work, I just bought his latest, "Combinatorial Algorithms, part 1"), really the only other one I read is "Data Structures in C" or some similar lower level textbook, which was unobjectionable but did not have the same quality.

013y

You're welcome! (Of the other books you mention that I've read, I agree with your assessment except that I'd want to subdivide the "ok" category a bit.)

13y

I would like to suggest Algorithm Design by Kleinberg and Tardos over CLRS.
I find it superior to CLRS although I have not read either completely.
In my undergrad CS course we used CLRS for Intro to Algorithms and Kleinberg Tardos was a recommended text for an advanced(but still mandatory, for CS) algorithms course, but I feel it does not have prerequisites much higher than CLRS does.
I feel that while KT 'builds on' knowledge and partitions algorithms by paradigm(and it develops each of these 'paradigms'—i.e. Dynamic Programming, Greedy, Divide and Conquer— from the start) CLRS is more like a cookbook or a list of algorithms.

13y

I would like to suggest \href{Algorithm Design by Kleinberg and Tardos}{http://www.cs.sjtu.edu.cn/~jiangli/teaching/CS222/files/materials/Algorithm%20Design.pdf} over CLRS.
I find it superior to CLRS although I have not read either completely.
In my undergrad CS course we used CLRS for Intro to Algorithms and Kleinberg Tardos was a recommended text for an advanced(but still mandatory, for CS) algorithms course, but I feel it does not have prerequisites much higher than CLRS does.
I feel that while KT 'builds on' knowledge and partitions algorithms by paradigm(and it develops each of these 'paradigms'—i.e. Dynamic Programming, Greedy, Divide and Conquer— from the start) CLRS is more like a cookbook or a list of algorithms.

13y

I would like to suggest \href{Algorithm Design by Kleinberg and Tardos}{http://www.cs.sjtu.edu.cn/~jiangli/teaching/CS222/files/materials/Algorithm%20Design.pdf} over CLRS.
I find it superior to CLRS although I have not read either completely.
In my undergrad CS course we used CLRS for Intro to Algorithms and Kleinberg Tardos was a recommended text for an advanced(but still mandatory, for CS) algorithms course, but I feel it does not have prerequisites much higher than CLRS does.
I feel that while KT 'builds on' knowledge and partitions algorithms by paradigm(and it develops each of these 'paradigms'—i.e. Dynamic Programming, Greedy, Divide and Conquer— from the start) CLRS is more like a cookbook or a list of algorithms.

012y

Manber's "Algorithms--a creative approach" is better than Cormen, which I agree is better than Knuth. It's also better than Aho's book on algorithms as well. It's better in that you can study it by yourself with more profit. On the other hand, Cormen's co-author has a series of video lectures at MIT's OCW site that you can follow along with.

212y

What about Manber's book makes it more fruitful for self-study than CLRS? How does it compare with CLRS in other respects? (Coverage of algorithms and data structures; useful pseudocode; mathematical rigour; ...)

013y

As a counterpoint to Hopcroft+Ullman, from another who has not read other books, Problem Solving in Automata, Languages, and Complexity by Ding-Zhu Du and Ker-I Ko was terrific. I did it as an undergraduate independent study class, completely from this book, and found it to be easy to follow if you are willing to work through problems.
Maybe we need someone who knows something more on the subject?

013y

Hopcroft+Ullman is very proof oriented. Sometimes the proof is constructive (by giving an algorithm and proving its correctness). I liked it. There may be much better available for self-study.
Specialty algorithms: I briefly referenced Numerical Optimization and it seems better than Numerical Recipes in C. I didn't read it cover to cover.
Algorithms on Strings, Trees, and Sequences (Gusfield) was definitely a good source for computational biology algorithms (I don't do computation biology, but it explains fairly well things like suffix trees and their applications, and algorithms matching a set of patterns against substrings of running text).
Foundations of Natural Language Processing is solid. I don't think there's a better textbook (for the types of dumb, statistics/machine-learning based, analysis of human speech/text that are widely practiced). It's better than "Natural Language Understanding" (Allen), which is more old-school-AI.

For Elliptic Curves:

I recommend Koblitz' "Elliptic Curves and Modular Forms"

It stays more grounded and focused than Silverman's "Arithmetic of Elliptic Curves," and provides much more detail and background, as well as more exercises, than Cassel's "Lectures on Elliptic Curves."

Is this thread still being maintained? There was a recommendation for it to be a wiki page which seems like a great idea; I'd be willing to put the initial page together in a couple weeks if it hasn't been done but I don't think I can commit to maintaining it.

613y

MacKay's Information Theory, Inference, and Learning Algorithms may not be exactly what you're looking for. But I've heard it highly recommended by people with pretty good taste, and what I've read of it is fantastic. Also, the pdf's free on the author's website.

113y

I highly recommend this book, but then it's currently my introduction to both Information Theory and Bayesian Statistics, and I haven't read any others to compare it to. I find it difficult to imagine a better one though.
Clear, logical, rigorous, readable, and lots of well chosen excellent exercises that illuminate the text.

16y

Thomas Cover did a great many interesting things. His work on universal data compression and the universal portfolio could provide very efficient and useful optimization approaches for use in AI & AGI.
Cover’s universal optimization approaches grow out of the beginnings of information theory, especially John Kelly’s work at Bell Labs in the 1950s.
In his "universal" approaches, Cover developed the theoretical optimization framework for identifying, at successive time steps, the mean rank-weighting “portfolio” of agents/algorithms/performace from an infinite number of possible combinations of the inputs.
Think of this as a multi-dimensional regular simplex with rank weightings as a hyper-cap. One can then find the mean rank-weighted “portfolio” geometrically.
Cover proved that successively following that mean rank-weighted “portfolio” (shifting the portfolio allocation at each time step) converges asymptotically to the best single “portfolio” of agents at any future time step with a probability of 1.
Optimization without Monte Carlo. No requirements for any distribution of the inputs. Incredibly versatile.
I don’t know of anyone that has incorporated Cover’s ideas into AI & AGI. Seems like a potentially fruitful path.
I’ve also wondered, if human brains might optimize their responses to the world by some Cover-like method. Brains as prediction machines. Cover's approach would seems to correspond closely with the wet-ware.

World War II.

"A World at Arms" by Gerhard L. Weinberg is my preferred single book textbook (as a reference) on World War II.

It is a suitably weighty volume on WW2, and does well in looking at the war from a global perspective, it's extensive bibliography and notes are outstanding. In comparison with Churchill's "The Second World War" - in it's single volume edition, Weinburg's writing isn't as readable but does tend to be less personal. Churchill on the other hand is quite personal, when reading his tome, it's almost as if he is sitti...

For topology, I prefer Topology by Munkres to either Topology by Amstrong or Algebraic Topology by Massey (the latter already assumes knowledge of basic topology, but the second half of Munkres covers some algebraic topology in addition to introducing point-set topology in the first half).

Both Armstrong and Massey try to make the subject more "intuitive" by leaving out formal details. I personally just found this confusing. Munkres is very careful about doing everything rigorously at the beginning, but this lets him cover much more material more ...

It really depends on your learning style, and whether you learn best through examples=>generalizations or generalizations=>examples.

Similarly, some people may learn faster from a non-rigorous approach (and fill in the gaps later), while others may learn faster from a more rigorous approach. Some people might stare at a text for hours, but might be able to motivate themselves to learn the material much faster if they had some concrete examples first (using the Internet as a supplementary resource can help in that). I actually find it easier to learn ...

Subject: Introductory Real (Mathematical) Analysis:

Recommendation: Real Mathematical Analysis by Charles Pugh

The three *introductory* Analysis books I've read cover-to-cover are Lang's, Pugh's, and Rudin's.

What makes Pugh's book stand out is simply that he focuses on building up repeatedly useful machinery and concepts-a broad set of theorems that are clearly motivated and widely applicable to a lot of problems. Pugh's book is also chock-full of examples, which make understanding the material much faster. And finally, Pugh's book has a very large number of e...

29y

Thanks! Added.

39y

"Baby Rudin" refers to "Principles of Mathematical Analysis", not "Real and Complex Analysis" (as was currently listed up top.) (Source)

19y

Fixed, thanks!

For abstract algebra I recommend Dummit and Foote's *Abstract Algebra* over Lang's *Algebra*, Hungerford's *Algebra*, and Herstein's *Topics in Algebra*. Dummit and Foote is clearly written and covers a great deal of material while being accessible to someone studying the subject for the first time. It does a good job focusing on the most important topics for modern math, giving a pretty broad overview without going too deep on any one topic. It has many good exercises at varying difficulties.

Lang is not a bad book but is not introductory. It covers a huge amoun...

011y

I'll second this; I used Herstein a lot but after the classes it was assigned for I have never referenced anything but Dummit and Foote.

It's not exactly a textbook series, but I've found the videos at khan academy http://www.khanacademy.org/#browse to be really helpful with getting the basics of a lot of things. The most advanced math it covers is calculus, which will get you a long way, and the language of the videos is always simple and straightforward.

... Guess I need to recommend it against other video series, to keep to the rules here.

I *do* recommend watching the stanford lecture videos http://www.youtube.com/user/StanfordUniversity?blend=1&ob=5 , but I recommend Khan over them fo...

Subject: Electromagnetism, Electrodynamics

Recommendation: Introduction to Electrodynamics by David J. Griffiths

I first received this textbook for a sophomore-level class in electrodynamics. It was reused for a few more classes. I admit that I don't have much to compare it with, though I have looked at Feynman's lectures, a couple giant silly freshman physics tomes, and J. D. Jackson's Electrodynamics, and I know what textbooks are like in general.

I was *repeated floored* by the quality of this book. I felt personally lead through the theory of electrodynami...

713y

I found that Griffiths is an excellent undergraduate textbook. It does, as you say, provide an astoundingly good conceptual understanding of electrodynamics.
I was very disappointed, however, at the level of detail and rigour. Jackson, (in my limited experience), while it may not provide the same amount of explanation at an intuitive level, shows exactly what happens and why, mathematically, and in many more cases.
This speaks to an important distinction between undergraduate and graduate textbooks. Graduate textbooks provide more detail, more rigour, and more material, while undergraduate textbooks provide insight.
There is something of a similar situation in quantum mechanics: Townsend's /A Modern Approach to Quantum Mechanics/ is very much an undergrad textbook, and indeed something of a dumbed-down version of (the first half of) Sakurai's /Modern Quantum Mechanics/. At this point I strongly prefer Sakurai, but I don't think I would be able to understand it without all the time I spent studying Townsend's more elementary presentation of the same approach.

413y

To give yet another example, I've been slowly trying to teach myself GR, and while I love the approach and the rigor of Wald's General Relativity, it was too hard for me to follow on its own terms. I found that Schutz's A First Course in General Relativity provides both the insight and better grounding in some of the necessary math (tensor analysis, getting used to Einstein's summation convention, using the metric to flip indices around) through gentler approach and richer examples. Having studied Schutz for some time, I feel (almost) ready to come back to Wald now.

Subject: Economics

Recommendation: Introduction to Economic Analysis (www.introecon.com)

This is a very readable (and free) microecon book, and I recommend it for clarity and concision, analyzing interesting issues, and generally taking a more sophisticated approach - you know, when someone further ahead of you treats you as an intelligent but uninformed equal. It could easily carry someone through 75% of a typical bachelor's in economics. I've also read Case & Fair and Mankiw, which were fine but stolid, uninspiring texts.

I'd also recommend Wilkinson's ...

07y

Luke's post, based on this recommendation, reads as follows:
I believe the books realitygrill is referring to are instead Mankiw's Principles of Microeconomics and Case & Fair's Principles of Microeconomics, since McAfee's is a microeconomics (not a macroeconomics) textbook.

07y

Fixed, thanks.

Since many people will be buying books here, this is a good place to recommend that people use a book-price search engine to find the best possible price on a book. I have found the best one to be BooksPrice. DealOz is also decent. I am not affiliated with either of these in any way.

113y

There are also price alert services that will email you when a book reaches a certain price. I've found this really useful, because while the latest version of a textbook might be $100 new and $60 used, you can sometimes get the same version used in great condition for much lower than the normal used price, especially after the end of a semester.
This is really useful when you don't need the book soon but know that you'd like to buy it at some point.

Subject: Microeconomics

Recommendation: My Textbook

Obviously I have some massive bias issues in evaluating my own book, but the kind of person who regularly reads and contributes to LessWrong is probably the kind of person who would write a textbook LessWrongers might want to read. Plus, a used copy costs only $3 at Amazon.

My book even briefly discusses the singularity.

Mankiw's Principles of Microeconomics and Heyne's The Economic Way of Thinking are also good.

613y

I'm glad you mentioned that you've written a textbook, but I'd discount your recommendation for obvious reasons. Has anyone else read Miller's Principles of Microeconomics?

I don't have any recommendations yet, but want to note that some Books can be read and downloaded at archive.org, for example Spivak's Calculus: https://archive.org/details/Calculus_643. For some Books you'll have to sign up to "loan" a Book Online.

It would be useful for me if some of you guys shared your methodology of choosing textbook / course / whatever for learning X, especially if X has something to do with math, computer science or programming.

My methodology (in no particular order):

- Go to this thread and look at recommendations
- Go to libgen, search for the keyword and sort by the publisher or by year
- Check rating on goodreads and/or on amazon
- Check top comments by usefulness on goodreads and/or amazon
- Download the book, look at the
*Contents*section, see how much I like what I see - Google
*best*

Subject: Commutative Algebra

Recommendation: *Introduction to Commutative Algebra* by Atiyah & MacDonald

Contenders: the introductory chapters of *Commutative Algebra With a View Towards Algebraic Geometry* by Eisenbud and the commutative algebra chapters of *Algebra* by Lang.

Atiyah & MacDonald is a short book that covers the essentials of Commutative Algebra, while most books cover significantly more material. So this review should be seen as comparing Atiyah & MacDonald to the corresponding chapters of other Commutative Algebra books. There are a few...

29y

Thanks! Added.

1[anonymous]11y

Atiyah-MacDonald isn't comparable to Eisenbud, as the latter covers a vastly wider swath of commutative algebra and algebraic geometry.

211y

Good point. I've edited the comment to explicitly compare to the introductory chapters of Eisenbud.

I would like to **request a book on Game Theory**. I went to my school's library and grabbed every book I could find, and so I have *Introduction to Game Theory* by Peter Morris, *Game Theory 2nd Edition* by Guillermo Owen, *Game Theory and Strategy* by Philip Straffin, *Game Theory and Politics* by Steven Brams, *Handbook of Game Theory with Economic Applications* edited by Aumann and Hart, *Game Theory and Economic Modeling* by David Kreps, and *Gaming the Vote* by William Poundstone because I also like voting theory.

My brief glances make *Game Theory and Strategy* look lik...

36y

Did you ever read any of those? I'd love to know if any were good.

12y

I have read several textbooks on game theory (there are quite a lot of books out there). I found all of them okay but none outstanding. What I did find very useful was the YouTube-Playlist Game Theory 101 by William Spaniel. He also has published a book with the same title on amazon.

**Machine learning**: *Pattern Recognition and Machine Learning* by Chris Bishop

Good Bayesian basis, clear exposition (though sometimes quite terse), very good coverage of the most modern techniques. Also thorough and precise, while covering a huge amount of material. Compared to *AI: A modern approach* it is much more clearly based in Bayesian statistics, and compared to *Probabilistic robotics* it's much more modern.

Bishop, vs Russell & Norvig, are not in the same category. There's only two chapters in R&N that overlap with Bishop.

Within the category of planning, symbolic AI, and agent-based AI, I recommend Russell & Norvig, "Artificial Ingelligence: A Modern Approach", or Luger & Stubblefield, "Artificial Intelligence". They are aware of non-symbolic approaches and some of the tradeoffs involved. I do not recommend Charniak & McDermott, "An intro to artificial intelligence", or Nilsson, "Principles of artificial intelligence", or Winston, "Artificial Intelligence", as they go into too much detail about symbolic techniques that you'll probably never use, like alpha-beta pruning, and say nothing about non-symbolic techniques. A more complete treatement of symbolic AI is Barr & Feigenbaum, "The Handbook of Artificial Intelligence", but that's a reference work, and I'm recommending textbooks. I do recommend a symbolic AI reference work, Shapiro, "Encyclopedia of Artificial Intelligence", because the essays are reasonably short and easy to read.

Within machine learning, data mining, and pattern recogn...

For elementary economics: "Macroeconomics" by Mankiw, is without a doubt the best on the market. It is incredibly well written, and it's so good once you've read the book it fools you into thinking you understand absolutely everything on the topic! "Intermediate Microeconomics" by Varian, is arguably the one to get. It can be a tad dry, and he uses lots of maths. If you don't like the idea of that then "Microeconomics" by Katz and Rosen is a very readable and less mathematical, though not quite as comprehensive as Varian.

-2[anonymous]13y

My dear, for no profession of the earth a single book can provide more than just an elementary course on everything or something on one element of it, please explain what is bad to a book containing merely the former? Especially, when you want to start learning on a topic.
(FWIW, I do not know the book in question.)

613y

There is something about that kind of introduction that makes me reach toward the downvote button. Especially when used in the context of a sentence that does not make grammatical sense and a comment that demonstrates an incorrect understanding of the position being refuted.
"If you must be patronising then at least make sure you're right, for crying out loud!" tends to be my attitude. But maybe that is just me being excessively picky. :)

010y

Two issues with this recommendation
1. It is a macroeconomics text and has very little on microeconomics - a large and arguably the more useful part of economics.
2. This is not an introductory text. For someone starting on economics Mankiw has another very readable text "Principles of Economics" which I recently read and recommend. This will get you up to speed on the main concepts and then you can happily proceed to more advanced texts with plenty of math. As an introductory text I would prefer this to Samuelson "Economics" which I found covered similar material but too slowly.
A lot of what people think of as "Economics" is another related discipline called "Finance" - which is about investing, and speculating, more or less. No recommendations there as all the books I have read on the subject are pretty bad.
Edit: reading the above post you seem to be actually recommending a book on macro and one on micro also, though this is not entirely clear (eg the top level poster managed to misunderstand it). That may be OK provided the reader is prepared for a very steep learning curve. I would suggest that time spend reading an introductory text first would be well spent.
BTW I have a copy of Mankiw's introduction if any LWer in Australia would like to read it.

Any recommendations for Mechanism Design textbooks?

In Introduction to Mechanism Design Badger recommended A Toolbox for Economic Design (2009) and An Introduction to the Theory of Mechanism Design (2015).

In the the preface to the latter, the author mentions a few other books too:

**Designing Economic Mechanisms**(2006) by Leonid Hurwicz and Stanley Reiter.*"The focus of this text is on informational efficiency and privacy preservation in mechanisms. Incentive aspects play a much smaller role than they do in this book."***Communication in Mechanism Design: A Diffe**

For category theory, I would recommend Category Theory by Awodey instead of Category Theory for the Working Mathematician by Maclane. Awodey gives a lot of intuition, and explain through examples many of the subtleties, while still being formal. Maclane is a great reference book, but it is to terse for first learning the field, in my opinion.

54y

I added your suggestion here

44y

Thanks!

22y

I disagree with this suggestion. I tried Awodey as an intro text, and it was very confusing & slow-going. I recommend Conceptual Mathematics by Lawvere & Schanuel for those who want a high-school level intro to category theory, or An Introduction to Category Theory by Simmons if you have some prior mathematical maturity, but are not at the incredibly high level Awodey implicitly expects of his readers (even though he thinks this level is very low, it's not!).

42y

Oh, I'm all for better recommendation than Amodey. My comment was mostly about not starting with Maclane, which is still a recommendation people give.

32y

I second Conceptual Mathematics for people who do not have mathematical maturity, but I would suggest Category Theory in Context by Emily Riehl as an intro for mathematicians (to be intended broadly). The textbook is rather gentle and provides lots of examples which are not heavy on theory (unlike Categories for the Working Mathematician), plus a tour of all of the main theorems (unlike Simmons), either proven or as doable exercises. It also introduces different approaches to achieving some results by presenting a graphical language to talk about natural transformations, which is useful when moving on to Enriched Category Theory. Riehl's book is available online for free on her website.
Riehl herself suggests Leinster's Basic Category Theory for people who want a lighter and easier introduction, but be aware that it covers way fewer topics and I can not vouch for it as I have not read it. It is available for free on arXiv.
A suggestion for more advanced readers who already have a high level understanding of the main theory and want to dive deeper would be Borceux's series Handbook of Categorical Algebra, which has both more breadth and details, covering even Topos Theory, Enriched Category Theory and so on. Many statements left by Riehl as exercises do have proofs there. You can find the first volume here.
Regarding ∞-Category Theory, people should approach it through Cisinski's Higher Categories and Homotopical Algebra, which is the most accessible complete introduction right now and also the only one developing a full theory of localizations. You can download the latest version for free on Cisinski's website. This book gives a less terse exposition than Lurie's Higher Topos Theory (the original complete reference) and many more proofs and details than all of the other introductions, like Land's Introduction to ∞-Categories.
Updated to introduce comparisons with other materials.

Is this list still being maintained and/or discussed over ?

I feel like the ML text-book being recommended *could* at least use an alternative in the form of: http://www.deeplearningbook.org/ , it takes a purely frequentist perspective (but consider that's basically the "practical" perspective at the moment, with even the bayesianNN work being... not so Bayesian), but it's much more concise, does a good job at explaining the math and skips over historical stuff that people either know of already (e.g DT) or that is essentially useless ou...

14y

Are you sure? I haven't read too much of it (though I read some from time to time), but it seems solidly agnostic about the debate. What do you think the book lacks that would be found in an equivalent Bayesian textbook?

14y

Hmh, I interpret standard nerual netwroks (which are the ones it focuses on) to be frequentist, since you are essentially maximising a likelihood without any priors and without an built-in uncertainty.
There's the whole bayesian nn world where the focus is on being able to easily embed priors and treating every cell as a probability distribution and obtaining a probability distribution for every output cell (which is the important part).
In practice this doesn't differ much, since you're essentially just adding a few more terms to every weight and bias, but it seems to be a field that's picking up speed... then again, I might just be stuck in my own reading bubble.
I guess upon further consideration I could scratch that whole thing, I'm honestly unsure if baesyan/frequentist is even a relevant distinction to be made anymore about modern ML/statistics/

This guy reviewed 5 freely available calculus textbooks and chose Elementary Calculus: An Approach Using Infinitesimals by Jerome H. Keisler as his favorite. Note that the book uses a nonstandard approach.

Here are some physics and quantum mechanics recommendations that may not meet the "read three books" requirement.

Another strategy for finding good textbooks is to surf around Amazon and see what seems to have good reviews.

Special relativity: Spacetime Physics by Taylor and Wheeler is excellent. It reminds me of the general style of the Feynman lectures, but is in depth and has good problem sets. Like the Feynman lectures it is based on developing intuition, which is important for relativity because, like QM, every single human is born with the wrong intuition. It takes time and practice to develop. Also like Feynman, the writing style isn't akin to a barren wasteland like most textbooks. It is written to teach, not as an accompaniment to a university course. Finally, the pr...

Recommended for LINGUISTICS: "Contemporary Linguistics", by William O'Grady, John Archibald, Mark Aronoff, & Janie Rees-Miller. Truly comprehensive, addressing ALL the areas of interesting work in linguistics -- phonetics, phonology, morphology, syntax, semantics, historical linguistics, comparative linguistics & language universals, sign languages, language acquisition and development, second language acquisition, psycholinguistics, neurolinguistics, sociolinguistics & discourse analysis, written vs spoken language, animal communicat...

95y

I appreciate your recommendation, it's been useful to me. However, I should point this out: I'm currently researching on second language acquisition, and the section dedicated to that does not even mention the main authors in the field. There are some very, very important hypotheses being tested and debated in the last decades, as Stephen Krashen's, which are not mentioned at all.
Oh, maybe this is not the case anymore: I only had access to the 1996 edition. I just saw a 2017 one in Amazon. It would be good if anybody could review the latest version, at least in the SLA section, where I found this problem.

2[anonymous]13y

I would also like to recommend two superb encyclopedia-style works on linguistics:
(1) "The Cambridge Encyclopedia of Language", by David Crystal (2) "The Cambridge Encyclopedia of the English Language," by David Crystal
Both are characterized by lot of short articles, sidebars, pictures, cartoons, and examples of texts to the point at hand. I read them both cover to cover, and have refered to them again and again when beginning to explore a new topic in the field.

113y

I would also like to recommend two superb encyclopedia-style works on linguistics:
(1) "The Cambridge Encyclopedia of Language", by David Crystal
(2) "The Cambridge Encyclopedia of the English Language," by David Crystal
Both are characterized by lot of short articles, sidebars, pictures, cartoons, and examples of texts to the point at hand. I read them both cover to cover, and have refered to them again and again when beginning to explore a new topic in the field.

In the wake of publishing Scientific Self-Help: The State of Our Knowledge, I realized there is another subject on which I have read at least three textbooks: self-help!

**Subject**: Self-Help

**Recommendation**: *Psychology Applied to Modern Life* by Weiten, Dunn, and Hammer

**Reason**: Tucker-Ladd's *Psychological Self-Help* is a 2,000 page behemoth of references from a passionate, life-long researcher in self-help. It was a work-in-progress for 20 years, and never mass-published. It's an excellent research resource, though it's now out-of-date. John Santrock's *Human Adjus*...

In college, I found most of the time that the professor's lecture notes contain almost everything of value that both the textbook and the lecture contains, but they contain ten times less text. This led me to believe that textbooks are a terribly inefficient way to convey facts, by comparison to the format of lecture notes. Books are words, words, words, flowery metaphors, digressions, etc. Hell, I don't know what they spend all those words on. But I know that, potentially, lecture notes are one fact after another.

013y

They get ME bored. Every book is six hundred to a thousand pages, and when you're done with it, you've got a hundred pages worth of knowledge. I think it's better to memorize some passwords, then separately look up specific ideas that didn't make sense.

113y

Fair enough. :)
I love reading a good textbook. Good nonfiction is so much more exciting for me than good fiction. And of course, I learn far more from good nonfiction.

313y

I usually find that (good) textbooks can let you learn the subject matter by yourself, whereas lecture notes are excellent reference material but, if you didn't attend the lectures, they're just not going to make for good building material on their own.

213y

I join NihilCredo and lukeprog in this. Textbooks usually have less text than what I would find ideal, not more. Lecture notes (and many textbooks which seemingly obey the even formula to text ratio) take me more time to read than a book which contains the same number of formulas and four times as much text. I can't continue reading after having stumbled upon something which looks like an inconsistency, non-sequitur or counterintuitive definition (that usually first happens on page 5 or so) and then have to spend time trying to find out what is wrong (and if I fail, then must spend some more time persuading myself that it doesn't matter and reading can continue). On the other hand, if the author spends some time and pages explaining, such events occur much less frequently.

013y

You guys do what works for you, and I'll do what works for me. Maybe I just don't have the patience. Or maybe you don't have something required to understand lossily compressed info. Or both. I just know that books take all day long and help as much as short online tutorials. And the tutorials are often free.

413y

How about you start a thread for recommending online tutorials?

013y

If lecture notes contain as much relevant information as a book, then you should be able to, given a set of notes, write a terse but comprehensible textbook. If you're genuinely able to get that much out of notes, then yes that definitely works for you.
The concern is instead if reading a textbook only conveys a sparse, unconvincing, and context-free set of notes (which is my general impression of most lecture notes I've seen).
Both depend heavily on the quality of notes, textbook, subject, and the learning style you use, but I think it's a lot of people's experience that lecture notes alone convey only a cursory understanding of a topic. Practically enough sometimes, test-taking enough surely, but never too many steps toward mastery.

Software engineering: everything by Andrew Tanenbaum. The standard texts in the field for good reason.

312y

Tannenbaum wrote some Operating System books (including one on networking). He's not so much concerned with software engineering.

29y

I've not finished reading either book, but Tanenbaum's OS book seemed very dry to me compared to "Operating System Concepts" (which has just been delightful to read!).

0[anonymous]13y

Seconded.

Sometimes two textbooks on the exact same topic serve completely different purposes. There are "I want to learn this thing I don't know" textbooks, and there are "I am an expert but I still want this book on hand as a tool to help me with my experting". Below I describe the most extreme examples I am aware of, which are unfortunately on different topics:

Nonlinear Dynamics and Chaos by Strogatz is incredibly readable. You can sit with it on a train and read non-stop without needing to look anything up and you will keep wanting to relate the next amazi...

For years, my self-education was stupid and wasteful. I learned by consuming blog posts, Wikipedia articles, classic texts, podcast episodes, popular books, video lectures, peer-reviewed papers, Teaching Company courses, and Cliff's Notes. How inefficient!

I've since discovered that

textbooksare usually the quickest and best way to learn new material. That's what they aredesignedto be, after all. Less Wrong has often recommended the "read textbooks!" method. Make progress by accumulation, not random walks.But textbooks vary widely in quality. I was forced to read some awful textbooks in college. The ones on American history and sociology were memorably bad, in my case. Other textbooks are exciting, accurate, fair, well-paced, and immediately useful.

What if we could compile a list of the best textbooks on every subject? That would be

extremelyuseful.Let's do it.

There have been other pages of recommended reading on Less Wrong before (and elsewhere), but this post is unique. Here are

the rules:Rules #2 and #3 are to protect against recommending a bad book that only seems impressive because it's the only book you've read on the subject. Once, a popular author on Less Wrong recommended Bertrand Russell's

A History of Western Philosophyto me, but when I noted that it was more polemical and inaccurate than the other major histories of philosophy, he admitted he hadn't really done much other reading in the field, and only liked the book because it was exciting.I'll start the list with three of my own recommendations...

Subject: History of Western PhilosophyRecommendation:The Great Conversation, 6th edition, by Norman MelchertReason: The most popular history of western philosophy is Bertrand Russell'sA History of Western Philosophy, which is exciting but also polemical and inaccurate. More accurate but dry and dull is Frederick Copelston's 11-volumeA History of Philosophy. Anthony Kenny's recent 4-volume history, collected into one book asA New History of Western Philosophy, is both exciting and accurate, but perhaps too long (1000 pages) and technical for a first read on the history of philosophy. Melchert's textbook,The Great Conversation, is accurate but also the easiest to read, and has the clearest explanations of the important positions and debates, though of course it has its weaknesses (it spends too many pages on ancient Greek mythology but barely mentions Gottlob Frege, the father of analytic philosophy and of the philosophy of language). Melchert's history is also the only one to seriously cover the dominant mode of Anglophone philosophy done today: naturalism (what Melchert calls "physical realism"). Be sure to get the 6th edition, which has major improvements over the 5th edition.Subject: Cognitive ScienceRecommendation:Cognitive Science, by Jose Luis BermudezReason: Jose Luis Bermudez'sCognitive Science: An Introduction to the Science of Minddoes an excellent job setting the historical and conceptual context for cognitive science, and draws fairly from all the fields involved in this heavily interdisciplinary science. Bermudez does a good job of making himself invisible, and the explanations here are some of the clearest available. In contrast, Paul Thagard'sMind: Introduction to Cognitive Scienceskips the context and jumps right into a systematic comparison (by explanatory merit) of the leading theories of mental representation: logic, rules, concepts, analogies, images, and neural networks. The book is only 270 pages long, and is also more idiosyncratic than Bermudez's; for example, Thagard refers to the dominant paradigm in cognitive science as the "computational-representational understanding of mind," which as far as I can tell is used only by him and people drawing from his book. In truth, the term refers to a set of competing theories, for example the computational theory and the representational theory. While not the best place to start, Thagard's book is a decent follow-up to Bermudez's text. Better, though, is Kolak et. al.'sCognitive Science: An Introduction to Mind and Brain. It contains more information than Bermudez's book, but I prefer Bermudez's flow, organization and content selection. Really, though, both Bermudez and Kolak offer excellent introductions to the field, and Thagard offers a more systematic and narrow investigation that is worth reading after Bermudez and Kolak.Subject: Introductory Logic for PhilosophyRecommendation:Meaning and Argumentby Ernest LeporeReason: For years, the standard textbook on logic was Copi'sIntroduction to Logic, a comprehensive textbook that has chapters on language, definitions, fallacies, deduction, induction, syllogistic logic, symbolic logic, inference, and probability. It spends too much time on methods that are rarely used today, for example Mill's methods of inductive inference. Amazingly, the chapter on probability does not mention Bayes (as of the 11th edition, anyway). Better is the current standard in classrooms: Patrick Hurley'sA Concise Introduction to Logic.It has a table at the front of the book that tells you which sections to read depending on whether you want (1) a traditional logic course, (2) a critical reasoning course, or (3) a course on modern formal logic. The single chapter on induction and probability moves too quickly, but is excellent for its length. Peter Smith's An Introduction to Formal Logic instead focuses tightly on the usual methods used by today's philosophers: propositional logic and predicate logic. My favorite in this less comprehensive mode, however, is Ernest Lepore'sMeaning and Argument, because it (a) is highly efficient, and (b) focuses not so much on the manipulation of symbols in a formal system but on the arguably trickier matter of translating English sentences into symbols in a formal system in the first place.I would love to read recommendations from experienced readers on the following subjects: physics, chemistry, biology, psychology, sociology, probability theory, economics, statistics, calculus, decision theory, cognitive biases, artificial intelligence, neuroscience, molecular biochemistry, medicine, epistemology, philosophy of science, meta-ethics, and much more.

Please, post your own recommendations! And, follow the rules.

Recommendations so far(that follow the rules; this list updated 02-25-2017):history of western philosophy, lukeprog recommends Melchert'sThe Great Conversationover Russell'sA History of Western Philosophy, Copelston'sHistory of Philosophy, and Kenney'sA New History of Western Philosophy.cognitive science, lukeprog recommends Bermudez'sCognitive Scienceover Thagard'sMind: Introduction to Cognitive Scienceand Kolak'sCognitive Science.introductory logic for philosophy, lukeprog recommends Lepore'sMeaning and Argumentover Copi'sIntroduction to Logic, Hurley'sA Concise Introduction to Logic, and Smith'sAn Introduction to Formal Logic.economics, michaba03m recommends Mankiw'sMacroeconomicsover Varian'sIntermediate Microeconomicsand Katz & Rosen'sMacroeconomics.economics, realitygrill recommends McAfee'sIntroduction to Economic Analysisover Mankiw'sPrinciples of Microeconomicsand Case & Fair'sPrinciples of Macroeconomics.representation theory, SarahC recommends Sternberg'sGroup Theory and Physicsover Lang'sAlgebra, Weyl'sThe Theory of Groups and Quantum Mechanics, and Fulton & Harris'Representation Theory: A First Course.statistics, madhadron recommends Kiefer'sIntroduction to Statistical Inferenceover Hogg & Craig'sIntroduction to Mathematical Statistics, Casella & Berger'sStatistical Inference, and others.advanced Bayesian statistics, Cyan recommends Gelman'sBayesian Data Analysisover Jaynes'Probability Theory: The Logic of Scienceand Bernardo'sBayesian Theory.basic Bayesian statistics, jsalvatier recommends Skilling & Sivia'sData Analysis: A Bayesian Tutorialover Gelman'sBayesian Data Analysis, Bolstad'sBayesian Statistics, and Robert'sThe Bayesian Choice.real analysis, paper-machine recommends Bartle's A Modern Theory of Integration over Rudin'sReal and Complex Analysisand Royden'sReal Analysis.non-relativistic quantum mechanics, wbcurry recommends Sakurai & Napolitano'sModern Quantum Mechanicsover Messiah'sQuantum Mechanics, Cohen-Tannoudji'sQuantum Mechanics, and Greiner'sQuantum Mechanics: An Introduction.music theory, komponisto recommends Westergaard'sAn Introduction to Tonal Theoryover Piston'sHarmony, Aldwell and Schachter'sHarmony and Voice Leading, and Kotska and Payne'sTonal Harmony.business, joshkaufman recommends Kaufman'sThe Personal MBA: Master the Art of Businessover Bevelin'sSeeking Wisdomand Munger'sPoor Charlie's Alamanack.machine learning, alexflint recommends Bishop'sPattern Recognition and Machine Learningover Russell & Norvig'sArtificial Intelligence: A Modern Approachand Thrun et. al.'sProbabilistic Robotics.algorithms, gjm recommends Cormen et. al.'sIntroduction to Algorithmsover Knuth'sThe Art of Computer Programmingand Sedgwick'sAlgorithms.electrodynamics, Alex_Altair recommends Griffiths'Introduction to Electrodynamicsover Jackson'sElectrodynamicsand Feynman'sLectures on Physics.electrodynamics, madhadron recommends Purcell'sElectricity and Magnetismover Griffith'sIntroduction to Electrodynamics, Feynman'sLectures on Physics, and others.systems theory, Davidmanheim recommends Meadows'Thinking in Systems: A Primerover Senge'sThe Fifth Discipline: The Art & Practice of The Learning Organizationand Kim'sIntroduction to Systems Thinking.self-help, lukeprog recommends Weiten, Dunn, and Hammer'sPsychology Applied to Modern Lifeover Santrock'sHuman Adjustmentand Tucker-Ladd'sPsychological Self-Help.probability theory, SarahC recommends Feller'sAn Introduction to Probability Theory+Vol. 2over Ross'A First Course in Probabilityand Koralov & Sinai'sTheory of Probability and Random Processes.probability theory, madhadron recommends Grimmett & Stirzaker'sProbability and Random Processesover Feller'sIntroduction to Probability Theory and Its Applicationsand Nelson'sRadically Elementary Probability Theory.topology, jsteinhardt recommends Munkres'Topologyover Armstrong'sTopologyand Massey'sAlgebraic Topology.linguistics, etymologik recommends O'Grady et al.'sContemporary Linguisticsover Hayes et al.'sLinguistics: An Introduction to Linguistic Theoryand Carnie'sSyntax: A Generative Introduction.meta-ethics, lukeprog recommends Miller'sAn Introduction to Contemporary Metaethicsover Jacobs'The Dimensions of Moral Theoryand Smith'sEthics and the A Priori.decision-making & biases, badger recommends Bazerman & Moore'sJudgment in Managerial Decision Makingover Hastie & Dawes'Rational Choice in an Uncertain World, Gilboa'sMaking Better Decisions, and others.neuroscience, kjmiller recommends Bear et al'sNeuroscience: Exploring the Brainover Purves et al'sNeuroscienceand Kandel et al'sPrinciples of Neural Science.World War II, Peacewise recommends Weinberg'sA World at Armsover Churchill'sThe Second World Warand Day'sThe Politics of War.elliptic curves, magfrump recommends Koblitz'Introduction to Elliptic Curves and Modular Formsover Silverman'sArithmetic of Elliptic Curvesand Cassel'sLectures on Elliptic Curves.improvisation, Arepo recommends Salinsky & Frances-White'sThe Improv Handbookover Johnstone'sImpro, Johnston'sThe Improvisation Game, and others.thermodynamics, madhadron recommends Hatsopoulos & Keenan'sPrinciples of General Thermodynamicsover Fermi'sThermodynamics, Sommerfeld'sThermodynamics and Statistical Mechanics, and others.statistical mechanics, madhadron recommends Landau & Lifshitz'Statistical Physics, Volume 5over Sethna'sEntropy, Order Parameters, and Complexityand Reichl'sA Modern Course in Statistical Physics.criminal justice, strange recommends Fuller'sCriminal Justice: Mainstream and Crosscurrentsover Neubauer & Fradella'sAmerica's Courts and the Criminal Justice Systemand Albanese'Criminal Justice.organic chemistry, rhodium recommends Clayden et al'sOrganic Chemistryover McMurry'sOrganic Chemistryand Smith'sOrganic Chemistry.special relativity, iDante recommends Taylor & Wheeler'sSpacetime Physicsover Harris'Modern Physics, French'sSpecial Relativity, and others.abstract algebra, Bundle_Gerbe recommends Dummit & Foote'sAbstract Algebraover Lang'sAlgebraand others.decision theory, lukeprog recommends Peterson'sAn Introduction to Decision Theoryover Resnik'sChoicesand Luce & Raiffa'sGames and Decisions.calculus, orthonormal recommends Spivak'sCalculusover Thomas'Calculusand Stewart'sCalculus.analysis in R, orthonormal recommends Strichartz's^{n}The Way of Analysisover Rudin'sPrinciples of Mathematical Analysisand Kolmogorov & Fomin'sIntroduction to Real Analysis.real analysis and measure theory, orthonormal recommends Stein & Shakarchi'sMeasure Theory, Integration, and Hilbert Spacesover Royden'sReal Analysisand Rudin'sReal and Complex Analysis.partial differential equations, orthonormal recommends Strauss'Partial Differential Equationsover Evans'Partial Differential Equationsand Hormander'sAnalysis of Partial Differential Operators.introductory real analysis, SatvikBeri recommends Pugh's Real Mathematical Analysis over Lang'sReal and Functional Analysisand Rudin'sPrinciples of Mathematical Analysis.commutative algebra, SatvikBeri recommends MacDonald'sIntroduction to Commutative Algebraover Lang'sAlgebraand Eisenbud'sCommutative Algebra With a View Towards Algebraic Geometry.animal behavior, Natha recommends Alcock'sAnimal Behavior, 6th editionover Dugatkin'sPrinciples of Animal Behaviorand newer editions of the Alcock textbook.calculus, Epictetus recommends Courant'sDifferential and Integral Calculusover Stewart'sCalculusand Kline'sCalculus.linear algebra, Epictetus recommends Shilov'sLinear Algebraover Lay'sLinear Algebra and its Appicationsand Axler'sLinear Algebra Done Right.numerical methods, Epictetus recommends Press et al.'sNumerical Recipesover Bulirsch & Stoer'sIntroduction to Numerical Analysis, Atkinson'sAn Introduction to Numerical Analysis, and Hamming'sNumerical Methods of Scientists and Engineers.ordinary differential equations, Epictetus recommends Arnold'sOrdinary Differential Equationsover Coddington'sAn Introduction to Ordinary Differential Equationsand Enenbaum & Pollard'sOrdinary Differential Equations.abstract algebra, Epictetus recommends Jacobson'sBasic Algebraover Bourbaki'sAlgebra, Lang'sAlgebra, and Hungerford'sAlgebra.elementary real analysis, Epictetus recommends Rudin'sPrinciples of Mathematical Analysisover Ross'Elementary Analysis, Lang'sUndergraduate Analysis, and Hardy'sA Course of Pure Mathematics.