The Best Textbooks on Every Subject

lukeprog

750 The Best Textbooks on Every Subject

16th Jan 2011

9 min read

750

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 textbooks are usually the quickest and best way to learn new material. That's what they are designed to 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 extremely useful.

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:

Post the title of your favorite textbook on a given subject.
You must have read at least two other textbooks on that same subject.
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.

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 Philosophy to 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 Philosophy

Recommendation: The Great Conversation, 6th edition, by Norman Melchert

Reason: The most popular history of western philosophy is Bertrand Russell's A History of Western Philosophy, which is exciting but also polemical and inaccurate. More accurate but dry and dull is Frederick Copelston's 11-volume A History of Philosophy. Anthony Kenny's recent 4-volume history, collected into one book as A 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 Science

Recommendation: Cognitive Science, by Jose Luis Bermudez

Reason: Jose Luis Bermudez's Cognitive Science: An Introduction to the Science of Mind does 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's Mind: Introduction to Cognitive Science skips 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.'s Cognitive 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 Philosophy

Recommendation: Meaning and Argument by Ernest Lepore

Reason: For years, the standard textbook on logic was Copi's Introduction 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's A 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's Meaning 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):

On history of western philosophy, lukeprog recommends Melchert's The Great Conversation over Russell's A History of Western Philosophy, Copelston's History of Philosophy, and Kenney's A New History of Western Philosophy.
On cognitive science, lukeprog recommends Bermudez's Cognitive Science over Thagard's Mind: Introduction to Cognitive Science and Kolak's Cognitive Science.
On introductory logic for philosophy, lukeprog recommends Lepore's Meaning and Argument over Copi's Introduction to Logic, Hurley's A Concise Introduction to Logic, and Smith's An Introduction to Formal Logic.
On economics, michaba03m recommends Mankiw's Macroeconomics over Varian's Intermediate Microeconomics and Katz & Rosen's Macroeconomics.
On economics, realitygrill recommends McAfee's Introduction to Economic Analysis over Mankiw's Principles of Microeconomics and Case & Fair's Principles of Macroeconomics.
On representation theory, SarahC recommends Sternberg's Group Theory and Physics over Lang's Algebra, Weyl's The Theory of Groups and Quantum Mechanics, and Fulton & Harris' Representation Theory: A First Course.
On statistics, madhadron recommends Kiefer's Introduction to Statistical Inference over Hogg & Craig's Introduction to Mathematical Statistics, Casella & Berger's Statistical Inference, and others.
On advanced Bayesian statistics, Cyan recommends Gelman's Bayesian Data Analysis over Jaynes' Probability Theory: The Logic of Science and Bernardo's Bayesian Theory.
On basic Bayesian statistics, jsalvatier recommends Skilling & Sivia's Data Analysis: A Bayesian Tutorial over Gelman's Bayesian Data Analysis, Bolstad's Bayesian Statistics, and Robert's The Bayesian Choice.
On real analysis, paper-machine recommends Bartle's A Modern Theory of Integration over Rudin's Real and Complex Analysis and Royden's Real Analysis.
On non-relativistic quantum mechanics, wbcurry recommends Sakurai & Napolitano's Modern Quantum Mechanics over Messiah's Quantum Mechanics, Cohen-Tannoudji's Quantum Mechanics, and Greiner's Quantum Mechanics: An Introduction.
On music theory, komponisto recommends Westergaard's An Introduction to Tonal Theory over Piston's Harmony, Aldwell and Schachter's Harmony and Voice Leading, and Kotska and Payne's Tonal Harmony.
On business, joshkaufman recommends Kaufman's The Personal MBA: Master the Art of Business over Bevelin's Seeking Wisdom and Munger's Poor Charlie's Alamanack.
On machine learning, alexflint recommends Bishop's Pattern Recognition and Machine Learning over Russell & Norvig's Artificial Intelligence: A Modern Approach and Thrun et. al.'s Probabilistic Robotics.
On algorithms, gjm recommends Cormen et. al.'s Introduction to Algorithms over Knuth's The Art of Computer Programming and Sedgwick's Algorithms.
On electrodynamics, Alex_Altair recommends Griffiths' Introduction to Electrodynamics over Jackson's Electrodynamics and Feynman's Lectures on Physics.
On electrodynamics, madhadron recommends Purcell's Electricity and Magnetism over Griffith's Introduction to Electrodynamics, Feynman's Lectures on Physics, and others.
On systems theory, Davidmanheim recommends Meadows' Thinking in Systems: A Primer over Senge's The Fifth Discipline: The Art & Practice of The Learning Organization and Kim's Introduction to Systems Thinking.
On self-help, lukeprog recommends Weiten, Dunn, and Hammer's Psychology Applied to Modern Life over Santrock's Human Adjustment and Tucker-Ladd's Psychological Self-Help.
On probability theory, SarahC recommends Feller's An Introduction to Probability Theory + Vol. 2 over Ross' A First Course in Probability and Koralov & Sinai's Theory of Probability and Random Processes.
On probability theory, madhadron recommends Grimmett & Stirzaker's Probability and Random Processes over Feller's Introduction to Probability Theory and Its Applications and Nelson's Radically Elementary Probability Theory.
On topology, jsteinhardt recommends Munkres' Topology over Armstrong's Topology and Massey's Algebraic Topology.
On linguistics, etymologik recommends O'Grady et al.'s Contemporary Linguistics over Hayes et al.'s Linguistics: An Introduction to Linguistic Theory and Carnie's Syntax: A Generative Introduction.
On meta-ethics, lukeprog recommends Miller's An Introduction to Contemporary Metaethics over Jacobs' The Dimensions of Moral Theory and Smith's Ethics and the A Priori.
On decision-making & biases, badger recommends Bazerman & Moore's Judgment in Managerial Decision Making over Hastie & Dawes' Rational Choice in an Uncertain World, Gilboa's Making Better Decisions, and others.
On neuroscience, kjmiller recommends Bear et al's Neuroscience: Exploring the Brain over Purves et al's Neuroscience and Kandel et al's Principles of Neural Science.
On World War II, Peacewise recommends Weinberg's A World at Arms over Churchill's The Second World War and Day's The Politics of War.
On elliptic curves, magfrump recommends Koblitz' Introduction to Elliptic Curves and Modular Forms over Silverman's Arithmetic of Elliptic Curves and Cassel's Lectures on Elliptic Curves.
On improvisation, Arepo recommends Salinsky & Frances-White's The Improv Handbook over Johnstone's Impro, Johnston's The Improvisation Game, and others.
On thermodynamics, madhadron recommends Hatsopoulos & Keenan's Principles of General Thermodynamics over Fermi's Thermodynamics, Sommerfeld's Thermodynamics and Statistical Mechanics, and others.
On statistical mechanics, madhadron recommends Landau & Lifshitz' Statistical Physics, Volume 5 over Sethna's Entropy, Order Parameters, and Complexity and Reichl's A Modern Course in Statistical Physics.
On criminal justice, strange recommends Fuller's Criminal Justice: Mainstream and Crosscurrents over Neubauer & Fradella's America's Courts and the Criminal Justice System and Albanese' Criminal Justice.
On organic chemistry, rhodium recommends Clayden et al's Organic Chemistry over McMurry's Organic Chemistry and Smith's Organic Chemistry.
On special relativity, iDante recommends Taylor & Wheeler's Spacetime Physics over Harris' Modern Physics, French's Special Relativity, and others.
On abstract algebra, Bundle_Gerbe recommends Dummit & Foote's Abstract Algebra over Lang's Algebra and others.
On decision theory, lukeprog recommends Peterson's An Introduction to Decision Theory over Resnik's Choices and Luce & Raiffa's Games and Decisions.
On calculus, orthonormal recommends Spivak's Calculus over Thomas' Calculus and Stewart's Calculus.
On analysis in Rⁿ, orthonormal recommends Strichartz's The Way of Analysis over Rudin's Principles of Mathematical Analysis and Kolmogorov & Fomin's Introduction to Real Analysis.
On real analysis and measure theory, orthonormal recommends Stein & Shakarchi's Measure Theory, Integration, and Hilbert Spaces over Royden's Real Analysis and Rudin's Real and Complex Analysis.
On partial differential equations, orthonormal recommends Strauss' Partial Differential Equations over Evans' Partial Differential Equations and Hormander's Analysis of Partial Differential Operators.
On introductory real analysis, SatvikBeri recommends Pugh's Real Mathematical Analysis over Lang's Real and Functional Analysis and Rudin's Principles of Mathematical Analysis.
On commutative algebra, SatvikBeri recommends MacDonald's Introduction to Commutative Algebra over Lang's Algebra and Eisenbud's Commutative Algebra With a View Towards Algebraic Geometry.
On animal behavior, Natha recommends Alcock's Animal Behavior, 6th edition over Dugatkin's Principles of Animal Behavior and newer editions of the Alcock textbook.
On calculus, Epictetus recommends Courant's Differential and Integral Calculus over Stewart's Calculus and Kline's Calculus.
On linear algebra, Epictetus recommends Shilov's Linear Algebra over Lay's Linear Algebra and its Appications and Axler's Linear Algebra Done Right.
On numerical methods, Epictetus recommends Press et al.'s Numerical Recipes over Bulirsch & Stoer's Introduction to Numerical Analysis, Atkinson's An Introduction to Numerical Analysis, and Hamming's Numerical Methods of Scientists and Engineers.
On ordinary differential equations, Epictetus recommends Arnold's Ordinary Differential Equations over Coddington's An Introduction to Ordinary Differential Equations and Enenbaum & Pollard's Ordinary Differential Equations.
On abstract algebra, Epictetus recommends Jacobson's Basic Algebra over Bourbaki's Algebra, Lang's Algebra, and Hungerford's Algebra.
On elementary real analysis, Epictetus recommends Rudin's Principles of Mathematical Analysis over Ross' Elementary Analysis, Lang's Undergraduate Analysis, and Hardy's A Course of Pure Mathematics.

If there are no recommendations for the subject you want to learn, you can start by checking the Alibris textbooks category for your subject, and sort by 'Top-selling.' But you'll have to do more research than that. Check which textbooks are asked for in the syllabi of classes on your subject at leading universities. Search Google for recommendations and reviews.

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The Best Textbooks on Every Subject

39Yoav Ravid

4Jan Christian Refsgaard

1john-lawrence-aspden

1Swimmer963 (Miranda Dixon-Luinenburg)

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[-]Yoav Ravid6y390

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... (read more)

4Jan Christian Refsgaard4y

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.

2Pablo4y

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. :)

1Yoav Ravid4y

whoops, fixed it :)

[-]komponisto14y320

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... (read more)

5Spurlock14y

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.

[-]komponisto14y110

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... (read more)

2arundelo14y

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.")

0komponisto14y

Thanks, fixed.

0Spurlock14y

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.

3soundchaser14y

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.

5komponisto14y

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.

3TessPope14y

"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.

8komponisto14y

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".)

1phenylphenol5y

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

1Bill_McGrath13y

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.

3komponisto13y

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.)

2Bill_McGrath13y

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!

2komponisto13y

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.

0Bill_McGrath13y

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.

[-][anonymous]14y250

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... (read more)

7Douglas_Knight14y

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.

3realitygrill14y

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.

2komponisto14y

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]14y

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

7komponisto14y

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.

4steven046114y

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.

3[anonymous]14y

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.)

3SilasBarta14y

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?

1HeuristicWorld6y

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."

1lukeprog14y

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

0jsumr10y

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

[-]jsalvatier14y230

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... (read more)

[-]jsalvatier13y100

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.

3lukeprog14y

Nice!

2Adam Zerner2y

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

0XFrequentist11y

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

2jsalvatier11y

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).

0beoShaffer13y

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.

[-]joshkaufman14y220

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... (read more)

8lukeprog13y

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.

7Dr_Manhattan14y

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).

6lukeprog14y

Rather phenomenal Amazon reviews you have, sir.

3FrF14y

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.)

1joshkaufman14y

Thanks - glad people are finding it useful.

4Duke13y

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.

[-]joshkaufman13y130

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.

8Duke13y

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."

9joshkaufman13y

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.

5Duke13y

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.

3MichaelGR14y

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.

3Cyan14y

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.

2bgf4194y

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!!

[-]Epictetus10y200

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... (read more)

1lukeprog10y

Updated, thanks!

1SanguineEmpiricist10y

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)

2Epictetus10y

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.

1SanguineEmpiricist10y

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.

2hairyfigment10y

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.

2Richard_Kennaway4y

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

-2SanguineEmpiricist10y

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.

1Oxide4y

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

0JoshuaZ10y

Echoing Hairyfigment here, what is wrong with Bourbaki?

1SanguineEmpiricist10y

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

0pinyaka9y

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.

0Boogie10y

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.

[-]gwern14y160

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!

[-]lukeprog14y261

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.

9nazgulnarsil14y

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

4Will_Sawin14y

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

[-]XiXiDu14y110

Textbook recommendations are all over.

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

4Ben Pace11y

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

[-]orthonormal12y150

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... (read more)

5Princess_Stargirl10y

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.

2orthonormal10y

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

2lukeprog10y

Thanks! Added.

1TimS12y

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

0[anonymous]12y

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

0komponisto12y

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]12y

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.

[-]lukeprog8y140

Lists of textbook award winners like this list might also be useful.