Fundamentals
Last Update: 20220318
“You must not fool yourself, and you are the easiest person to fool.” — Richard P. Feynman
I was recently asked by a younger (science & engineering inclined) student about fundamental concepts they should learn about over the course of their education. I was unsure whether there existed an objective (and widely accepted) process by which to figure out which concepts should be classified as fundamental or not. So instead I decided to share concepts that I observed appeared more frequently in my personal “dependencies graph”.
I came up with the following list of books, articles, videos, and courses, that I thought would be useful to share more broadly^{1}.
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Mathematics
Linear Algebra
Prerequisite: 3b1b  Linear Algebra
Core: MIT 18.06 (OCW)  Linear Algebra
Differential Equations
Prerequisite: 3b1b  Differential Equations
Core: MIT 18.03 (OCW)  Differential Equations
Probability + Statistics
Prerequisite: 3b1b  Probability
Core: Harvard Stat 110  Probability
(Single Variable) Calculus
Prerequisite: 3b1b  Calculus
Core: MIT 18.01 (OCW)  Single Variable Calculus
Physics
Prerequisites
Surely You’re Joking, Mr.Feynman!
The Feynman Lectures on Physics
Classical Mechanics
Prerequisite: Linear Algebra, Differential Equations, (Single Variable) Calculus
Core: Theoretical Minimum  Classical Mechanics
Book: The Theoretical Minimum: What You Need to Know to Start Doing Physics
Quantum Mechanics
Prerequisite: Linear Algebra, Differential Equations, (Single Variable) Calculus, Probability + Statistics
Core: Theoretical Minimum  Quantum Mechanics
Book: Quantum Mechanics: The Theoretical Minimum
Computer Science
Algorithms
Core: Stanford CS161 (Coursera)  Design and Analysis of Algorithms
Book: Algorithms Illuminated
Computer Systems
Core: CMU 15213  Intro to Computer Systems
Book: Computer Systems: A Programmer’s Perspective
Theoretical CS
Core: CMU 15251  Great Ideas in Theoretical Computer Science)
Culture
The New Hacker’s Dictionary (aka Jargon File)
Hackers: Heroes of the Computer Revolution
Humanities + Social Sciences
Psychology
MIT 9.00 (OCW)  Intro to Psychology
Philosophy
MIT 24.09 (Open Learning)  Minds and Machines
Economics
MIT 14.01 (OCW)  Principles of Microeconomics
Finance
Yale Econ 252  Financial Markets
Footnotes

I do believe autodidacticism is the future (and interestingly enough was also the distant past)! My observation is that programming is easier to pick up through selflearning, likely due to having an interactive system to help out (e.g. the compiler / interpreter). MOOCs are great, but have a drop out rate close to 90% (see this)! Figuring out more structured learning mechanisms for non interactive (and rigorous) material is an important problem to solve. ↩︎