The "step-by-step what I did before each physics exam" sounds interesting and useful, would you be open to sharing it here?
If you're doing well in a class then great. Keep doing what you are doing. There is no need to change anything. If you are doing poorly then, at the end of each chapter in your textbook, read each practice problem (even if it wasn't assigned as homework). If you can do it, then skip it. Otherwise, do it.
I had a professor who made all the homework due on exam day on the theory that people would procrastinate and do everything the night before and thus automatically get a good review of the exam material. Worked well for me at least.
The University of Washington offers the following introductory math classes:
I took Accelerated [Honors] Calculus.
Accelerated [Honors] Calculus starts with the Peano axioms. The Peano axioms are a set of nine assertions like "0 is a natural number", "" and "if the ". It is possible to derive all of number theory using just the Peano axioms. Add the Cauchy Completeness Axiom and you can derive calculus too.[1]
Our assignment was to to derive calculus.
I tried out CSE 143: Computer Programming II too. CSE 143 used Java. The class was based around memorizing words like "polymorphism" and "postorderal traversal". My friend majoring in Human Centered Design and Engineering felt like CSE 143 was hard. I felt like I was watching a multi-level marketing campaign for Oracle development tools. I resolved to just teach myself how computers worked. That was the last computer science class I ever took.
Accelerated [Honors] Calculus lasts one year. By the end of the year, everyone with a shred of economic sense has quit to study Computer Science instead. The rest of us took Accelerated [Honors] Advanced Calculus in our second [sophomore] year of college.
My sophomore year of college was mostly "staying up after midnight in the library with my classmates doing calculus homework" and "working at the physics tutoring center where I helped other students with their calculus homework".
Was it worth it?
If college is about signaling to employers then "no". If college is about partying and finding a mate then "no, definitely not". If college is about learning things that make you smarter then "yes".
A physics student wrote an email to the tutors at my tutoring center. She had been getting bad scores on her exams and worried she wasn't smart enough for physics. I replied to her with an email that explained step-by-step what I did before each physics exam.
Her reply: "Oh. I guess I'm just not studying hard enough."
My memories of the class are hazy. Please correct me if I'm wrong about which axioms are necessary to prove what. ↩︎