Ask HN: What kind of math do you study in your free time?

Re:Ask HN: What kind of math do you study in your free time? by snicker7 on Thursday June 11, 2020 @02:02PM (#23491582)

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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Re:Ask HN: What kind of math do you study in your free time? by iamcreasy on Thursday June 11, 2020 @02:30PM (#23491849)

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!

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Re:Ask HN: What kind of math do you study in your free time? by Koncopd on Thursday June 11, 2020 @07:49PM (#23494432)

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

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Re:Ask HN: What kind of math do you study in your free time? by iamcreasy on Thursday June 11, 2020 @09:43PM (#23495142)

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

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Re:Ask HN: What kind of math do you study in your free time? by Koncopd on Friday June 12, 2020 @04:42AM (#23497294)

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).

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Re:Ask HN: What kind of math do you study in your free time? by spekcular on Thursday June 11, 2020 @02:57PM (#23492167)

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....

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Re:Ask HN: What kind of math do you study in your free time? by aaron-santos on Thursday June 11, 2020 @04:46PM (#23493125)

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.

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Re:Ask HN: What kind of math do you study in your free time? by snicker7 on Friday June 12, 2020 @03:03PM (#23502496)

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.

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Re:Ask HN: What kind of math do you study in your free time? by melling on Thursday June 11, 2020 @02:15PM (#23491693)

“History of Mathematics"

Anyone have good book recommendations?

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Re:Ask HN: What kind of math do you study in your free time? by snicker7 on Thursday June 11, 2020 @02:38PM (#23491949)

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

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Re:Ask HN: What kind of math do you study in your free time? by orange3xchicken on Thursday June 11, 2020 @02:22PM (#23491758)

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

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Re:Ask HN: What kind of math do you study in your free time? by eigenvalue on Thursday June 11, 2020 @02:16PM (#23491708)

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

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Re:Ask HN: What kind of math do you study in your free time? by Koshkin on Thursday June 11, 2020 @03:04PM (#23492246)

Stillwell's Mathematics and Its History.

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Re:Ask HN: What kind of math do you study in your free time? by joycian on Thursday June 11, 2020 @04:33PM (#23493032)

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

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