Ask HN: What kind of math do you study in your free time? • Hacker News Board

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

#91

Post by elric » Fri, Jun 12, 2020, 5:50 AM UTC

ivansavz wrote: post #88

elric wrote: post #6

I'm working my way through Ivan Savov's "No bullshit guide to math & physics" - https://www.goodreads.com/book/show/22876442-no-bullshit-gui... Would recommend it to anyone whose maths needs a bit of a brush up, or anyone who's interested in basic mechanics! Oh and I'm using Khan Academy for extra practice, which I can warmly recommend as well.

Thanks for the plug elric! Anyone interested in seeing what the book is about can check the (slightly outdated) preview here: https://minireference.com/static/excerpts/noBSguide_v5_previ... (a more descriptive title would be high-school math, mechanics, and single-variable calculus three-in-one) I also have a followup book on linear algebra, which you can preview as PDF here: https://minireference.com/static/excerpts…

Thanks for writing the book! It's a fun read, and it packs a big punch. It's making me regret not spending more time on maths before.

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

#92

Post by Koncopd » Fri, Jun 12, 2020, 8:42 AM UTC

iamcreasy wrote: post #80

Koncopd wrote: post #75

Earlier quoted context omitted.

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).

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

#93

Post by exDM69 » Fri, Jun 12, 2020, 11:46 AM UTC

ghostpepper wrote: post #33

exDM69 wrote: post #31

Orbital mechanics and related mathematics like Stumpff series and Universal variables. Got inspired from playing too much Kerbal Space Program and Orbiter.

I've wanted to do this for a while. What's your process like? I have a few books (Introduction to Space Dynamics, the BMW book, etc) but I'm not sure if I should read it cover to cover or try to design a curriculum etc. Do you use any simulation software or just pen and paper?

I started with Bate, Mueller, White: Fundamentals of Astrodynamics, which is US Air force material. It contains two courses, so you should skip some of the chapters at first.

Then I read a bunch of research papers and more in depth literature. Richard Battin's work for example.

I've been hacking on a two body orbital mechanics library in C with SIMD extensions, and an interactive sandbox with OpenGL. I wrote both from scratch.

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

#94

Post by dorchadas » Fri, Jun 12, 2020, 3:22 PM UTC

iamcreasy wrote: post #81

dorchadas wrote: post #60

I'm currently working through books on Linear Algebra (Friedman), Real Analysis (Bloch) and Abstract Algebra (Pinter) with guided help from a math PhD I found via Reddit/Discord. It's going great, and I'm getting feedback on my proofs and learning quite a lot. I studied physics in undergrad, and am now a math/science teacher, but I feel I missed my true calling in deciding on physics over math; it's just so much more…

Can you please elaborate on how you found a tutor via Reddit/Discord? I would love to study with someone who can help me if I am stuck with a problem.

I saw the person advertising on Reddit for his own Discord server in a /r/math thread about learning after graduation, etc., so got quite lucky. I think he still lurks around /r/math and /r/learnmath if you go and ask if anyone can help.

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

#95

Post by snicker7 » Fri, Jun 12, 2020, 7:03 PM UTC

aaron-santos wrote: post #71

snicker7 wrote: post #17

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 com…

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.

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

#96

Post by iamcreasy » Sat, Jun 13, 2020, 1:30 AM UTC

dorchadas wrote: post #94

iamcreasy wrote: post #81

Earlier quoted context omitted.

Can you please elaborate on how you found a tutor via Reddit/Discord? I would love to study with someone who can help me if I am stuck with a problem.

I saw the person advertising on Reddit for his own Discord server in a /r/math thread about learning after graduation, etc., so got quite lucky. I think he still lurks around /r/math and /r/learnmath if you go and ask if anyone can help.

Nice! I usually try Crossvalidate SE first. But I'll cross-post to those subreddits as well.

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

#97

Post by racl101 » Mon, Jun 15, 2020, 5:20 PM UTC

nickcw wrote: post #14

There is loads of great maths stuff on YouTube. For some reason this is my favourite channel: black pen red pen. The author solves unusual algebra or calculus problems. I find it quite relaxing! https://www.youtube.com/user/blackpenredpen

I find this girl's analysis of Fibonacci series and the Golden Ratio concepts and seeing how it applies to plants to be fascinating:

https://www.youtube.com/watch?v=ahXIMUkSXX0

I wish she would edit the video and slow it down a bit (don't like that rapid fire style of tutorial that so many people YouTubers adopt lately) but the presentation is amazing.