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I'm not really a mathematician, my experience comes from machine learning / statistics. Note that most math books tend to be known by the name of the author, as
by govg 8y ago
I'm not really a mathematician, my experience comes from machine learning / statistics. Note that most math books tend to be known by the name of the author, as opposed to a fixed title.
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.
- philip-b 8y agoRemark: Optimization by Boyd and Vanderberghe is actually Convex optimization. It doesn't cover non-convex stuff.
- govg 8y agoOf course, you're correct. I chose to ignore that aspect since Boyd's book covers a lot of basic material, and I'm not actually aware of any such text covering non-convex methods in general ( and considering how fast research is in this space, I'm not sure of any general work, in contrast to work like [1] ). [1] - Non Convex Optimization for Machine Learning - Jain and Kar (https://arxiv.org/abs/1712.07897 https://arxiv.org/abs/1712.07897)
- smithmayowa 8y agoThanks for taking the time to write this list, I will definitely get them and MIT OCW could really come in handy in providing a kind of lecturing feel to this goal.