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| | Ask HN: Mathematicians, what textbooks are best for learning these math topics? | |
125 points by smithmayowa on April 9, 2019 | hide | past | favorite | 33 comments |
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| So I have just decide to self-learn mathematics up to undergraduate level, and after researching I decided that learning these topics will do the trick for learning to the undergraduate level, but sadly I don't know the best resources(textbooks) to use for easily self-learning them. Pure Mathematics 1).Group Theory(rubics cube,e.t.c) 2).Order Theory 3).Combinatorics(trees,graphs,e.t.c) 4).Fractal Geometry 5).Topology(cup = donut) 6).Measure Theory 7).Differential Geometry 8).Vector Calculus 9).Dynamical Systems(Fliud flow,ecosysytems,Control Theory) 10).Chaos Theory(Butterfly effect) 11).Complex Analysis(Functions with complex numbers) Applied Mathematics 1). Numerical Analysis 2). Game Theory 3). Probability 4). Statistics 5). Optimization 6). Cryptography 7). Computer Science Foundations 1).Mathematical Logic 2).Set Theory 3).Category Theory 4).Godel Incompleteness Theorems P.s: I have a diploma in Marine Engineering and so I am not a total noob to math in general. |
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Pure math :
1)Group Theory - Milne
5)Topology - Mukres
6)Measure Theory - Terrence Tao has a course, Robert Ash has a book on probability theory, and it is recommended that you study a bit of real analysis before you do this.
7) Differential Geometry and Statistics - Murray and Rice
9, 10 ) Non linear dynamics and chaos - Strogatz
11) Complex analysis - There exists a set of 4 books covering real, complex and functional analysis by Stein and Shakarchi, which should serve your purpose
Applied Math :
3) Probability - Grinstead and Snell, Durrett both have good books.
4) All of Statistics by Larry Wasserman for a more ML bent to it
5) Optimization by Boyd and Vanderberghe
7) There's no single topic called "Computer Science", but going with the theme of the topics you are looking at, Algorithms by Cormen, Leiserson et. al, Theory of Computation by Michael Sipser should be good starting points.
Note that for a lot of these, you can find high quality material online (Both videos as well as course material). Just do a search for "Topic MIT OCW", replacing "Topic" with your choice.