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Some math topics I like to read about / play with: - Measure theory / lebesque/daniell integration / stochastic calculus -- super useful but very beautiful. I
by snicker7 6y ago
Some math topics I like to read about / play with:
- Measure theory / lebesque/daniell integration / stochastic calculus -- super useful but very beautiful. I have a background in mathematical finance.
- Combinatorial topology -- Simplicial complexes, polytopes. A more finite/computational flavor of algebraic topology.
- Dynamical systems: Highly interdisciplinary. Brings together physics, fractals, calculus, and computer simulations.
- Multilinear Algebra -- tensors, grassman algebras.
- History of Mathematics -- love reading about the development of mathematics throughout the centuries.
- melling 6y ago“History of Mathematics" Anyone have good book recommendations?
- eigenvalue 6y agoThe World of Mathematics by James R. Newman is a classic, filled with great biographies and short essays about various parts of math.
- orange3xchicken 6y agoI just finished The Nothing That Is - it was alright. The illustrations were cool, but the writing and content were only okay imo. I really enjoyed Fermat's Last Theorem. I've also heard good things about - Zero: The Biography of a Dangerous Idea - Journey Through Genius
- snicker7 6y ago"Huygens and Barrow, Newton and Hooke" by Vladimir Arnold (would literally recommend any of his books).
- Koshkin 6y agoStillwell's Mathematics and Its History.
- joycian 6y agoSeconding this. His other books are great as well (Reverse Mathematics, Naive Lie Theory). Great writer.
- iamcreasy 6y agoI only took 1 semester of a grad-level Linear algebra course. Is there any newbie friendly book for Multilinear Algebra with emphasis on Application that you know of? Thank you!
- Koncopd 6y agoThere is a wonderful book "Linear Algebra via Exterior Products" by Sergei Winitzki. You can download it for free from his site - https://sites.google.com/site/winitzki/linalg https://sites.google.com/site/winitzki/linalg
- iamcreasy 6y agoThanks. But this book seems to be mostly theoretical. I was looking for one with an emphasis on practical/real life problems.
- Koncopd 6y agoHm, this book applies exterior algebra to linear algebra. I don't think there are a lot of applications of multilinear algebra outside of math, it is mostly needed to study differential geometry (forms and so on).
- spekcular 6y agoIt's "Lebesgue," not "Lebesque." See here for more on the history of this unfortunately common typo: https://math.stackexchange.com/questions/1433899/why-is-lebesgue-so-often-spelled-lebesque https://math.stackexchange.com/questions/1433899/why-is-lebe....
- aaron-santos 6y agoAny stochastic calculus resource recommendations? Tangentially, I've been interested in getting into SDEs, specifically parameter estimation, but don't know enough about the topic to know good resources from bad.
- snicker7 6y agoIn grad school, I used "Stochastic Calculus for Mathematical Finance II" by Shreve. Its pretty rigorous/technical (don't bother with volume I, imo). I don't know of any decent books on estimating parameters for SDE's. Though I suppose one way of going about it is as follows: convert the SDE to a discrete time series using Euler method and use maximum likelihood estimation.