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Comment by snicker7 | Hacker News Reader

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.

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I 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!

There 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

Thanks. But this book seems to be mostly theoretical. I was looking for one with an emphasis on practical/real life problems.

Hm, 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).

It's "Lebesgue," not "Lebesque." See here for more on the history of this unfortunately common typo: https://math.stackexchange.com/questions/1433899/why-is-lebe....

Any 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.

In 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.

“History of Mathematics"

Anyone have good book recommendations?

The World of Mathematics by James R. Newman is a classic, filled with great biographies and short essays about various parts of math.

I 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

"Huygens and Barrow, Newton and Hooke" by Vladimir Arnold (would literally recommend any of his books).

Stillwell's Mathematics and Its History.

Seconding this. His other books are great as well (Reverse Mathematics, Naive Lie Theory). Great writer.

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