These notes, broken into 24 lessons, are a math curriculum for very motivated folks who wanna get into physics, machine learning, etc but don't have special math background beyond highschool math plus intellectual maturity. By intellectual maturity I mean that invaluable bag of attitudes and understandings that recognizes how names and named are different, that learns general patterns from specific examples, that values "what if"s, etc.
Topic-wise, it's my reworking of the actually practical parts of college math. Whereas college math in my country typically focuses a lot on Calculus, I think that concepts relating to Probability and Linear maps are more important, for a well-educated-hence-happier citizenry, than most of the calculus details in current curricula. So here we have 4 lessons each on: Probability, then Calculus, then Linear Maps; we then mix these ideas when examining Geometry in the Small and Uncertainty about the Infinite; we end with a grab bag of Special topics that illustrate how these math ideas help us analyze interesting problems.
At a finer grain, here's what's inside:
Grades of belief ; Bayes law and independence ; Expectations and abstraction ; Application: minimax game theory ; Limits, Derivatives ; Integration, DiffEQs, Exp ; Texture of the Continuum: Taming Pathology ; Taylor Series and Asymptotics ; Maps as Matrices ; Dimension and Determinant ; Vectors vs Covectors ; Inner Products and Geometry ; Taylor in Multiple Variables ; Densities and Integration ; Vector Fields ; Gaussians and Spheres ; Probability Densities ; Central limit theorem ; Theory of measurement: statistics and error propagation ; Statistical manifolds ; Fourier analysis and oscillations ; Control theory and optimization ; Regression and smooth models ; Energy-based models and statmech
The idea is that we have a bunch of statements --- each apt to be true-or-false (rather than a command, or question, or super-vague) --- and we want to put a number on each statement that says how much we believe it.
Author --- Title --- Year