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

81 points by dunefox ↗ HN
Currently, I'm working through Gilber Strangs new book "Linear Algebra and Learning from Data"

96 comments

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There's lectures for that book if you're interested (I don't own the book yet) https://ocw.mit.edu/courses/mathematics/18-065-matrix-method...

In my free time I attempt to work through The Nature of Computation by Stephan Mertens & Cristopher Moore. Edit: Forgot to add, there's lectures for the TCS book too in this playlist specifically 'CS Theory Toolkit' https://www.youtube.com/channel/UCWnu2XymDtORV--qG2uG5eQ/pla...

Nice, thanks!

That sounds interesting. Sadly, I have a huge backlog already...

I'm working through Oscar Levin's "Discrete Mathematics" - http://discrete.openmathbooks.org/dmoi3.html

I studied philosophy in college and am hoping several years of programming experience since will shed some new and interesting light on one of my favorite topics.

I am reading "The Art of Statistics" by David Spiegelhalter.
I just finished that. Great book!
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.

Great book, too bad it's got such an offensive title. The book could be used more widely without it.
How is it offensive? Because of the word bullshit?
Yes. Can you imagine this used in a professional or collegiate setting?
You don’t have to show it to your professor.
Yes, I don't see why not? Maybe this is a cultural thing, but I don't know anyone who would be offended by the word bullshit, professionally or otherwise.
To be honest, I think the book is used widely because of the title. There are many (hundreds, perhaps even thousands) of good math books out there with standard titles, and from what I have seen, most learners will not bother with them, even though they are totally capable of understanding math AND the books would do a decent job at explaining.

The irreverent title gives me just one extra moment of attention with the cold-reader, and if I can capture their interest in that moment (the first section also has a swearword in it), and get them to bring their "math guard" down for fifteen minutes, then I can "convert" them to the beautiful subject.

You're right that the same "feature" of wow-this-book-seems-to-be-different is also a turn-off for most people who are already pro-math. This cannot be serious math if there is a swearword in the title. Some readers have said they get the sleazy "learn math in three-easy-steps feeling!" when they see the title. That's just life—you win some you lose some ;) I am less worried about people who already like math, since they, having already overcome the fear of math, can learn all the other good books out there.

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/noBSguide2LA_previ... or as spoken tutorial + SymPy notebooks https://github.com/minireference/noBSLAnotebooks#no-bullshit...

Other goodies and free stuff on the website: https://minireference.com/#freestuff

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.
The predicate calculus. I regularly review Predicate Calculus and Program Semantics[1] to increase my fluency in the techniques. I also recommend A Discipline of Programming[2] as a gentler introduction to the subject for those who do not consider themselves particularly mathematically inclined. For me it was a natural progression from doing TDD. I still code test first, but now the structure of those tests and programs is guided by a better understanding of program semantics, greatly increasing my code quality.

[1] https://www.amazon.com/Predicate-Calculus-Semantics-Monograp...

[2] https://www.amazon.com/Discipline-Programming-Edsger-W-Dijks...

Mostly crawling through ml papers on arxiv. Also going over "The Theory That Would Not Die", though this is in the realm of popular science books but it's an enjoyable getaway from it all.

Edit: How to by Randall Munroe for the math-comedy realm.

Less focused but enjoyed Eddie Woo's and 3blue1brown's more recent videos on Youtube

Also challenged by Tom Duff's trigonometry page - http://www.iq0.com/notes/trig.html

Enjoy learning how to derive identities and equations from first principles - quite like differential of x^2 => 2x and the quadratic eqn via completing the square

Sigmoid / logistic and bell curves to try and predict Covid-19 progress.
Bartosz Milewski's lectures on category theory are great. Also, the accompanying book is well written (and free)!

lectures -> https://www.youtube.com/user/DrBartosz

book -> https://github.com/hmemcpy/milewski-ctfp-pdf

Another good category theory read is Pierce's Category Theory for Computer Scientists
What practical applications does it present for programmers? I've looked at this a bit and it just seems like a regular category theory book.
Sometimes it is helpful to really understand what the hell you are actually doing when you write code (design patterns, data types and all). Otherwise, not much (unless you write Haskell, that is.)
You don't get scared when you read stuff about Haskell because you know what most the fancy words mean
On the other hand it would be easier to just avoid Haskell.
I've always been partial to Galois theory.
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.

Been going through Conway's (and Conway related) books since his unfortunate passing. His biography by Siobhan Roberts was a great starting point to ease into it (lots of direct quotes from Conway, which makes it a very easy read that still touches on the important concepts in his work, in his own words; also highly recommend all the Numberphile videos featuring him for that)- then:

Winning Ways for your Mathematical Plays is really fun to thumb through.

The Book of Numbers is fantastic and something I would gift to any mathematically curious, somewhat independent, child.

Knuth's Surreal Numbers is also a great read.

Got On Numbers and Games coming in the mail, and am trying to track down a reasonably priced copy of The Symmetries of Things.

I'm tempted to get the Atlas for my collection, but I don't think I'd actually get much from reading it (:

In non-Conway recommendations, The Princeton Companion to Mathematics is a huge brick of a volume, but is a very complete math encyclopedia that I love to keep on my desk and thumb through when I feel distracted. You always end up learning something new.

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.

“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.
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).
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.

For combinatorics, I highly recommend Miklos Bona's A Walk Through Combinatorics[0]. Combinatorics is intuitive and approachable to begin with, and this book is particularly accessible as far as math texts go.

[0] - https://people.clas.ufl.edu/bona/books/

I always come back to playing with the Exterior (Multilinear) Algebra because it seems like there's some deep structure hiding inside of it that connects a bunch of different fields of math.
Not sure if it counts as "free time" as I study math for a living :) but optimization theory is always on my list.

If you like Strang's new book, I think you'll be quite partial to Boyd's VMLS [0] which is (in my admittedly horrible opinion) even more clear and practical and serves as an incredibly good and basic introduction to both linear algebra and basic optimization (via least squares). It assumes nothing more than pre-calculus level math and some slight familiarity with derivatives.

Honestly, I really, truly highly recommend reading it, even if you're already familiar with linear algebra. It's a joy to flip through the pages and do some of the problems (both theoretical and practical!).

-----

[0] http://vmls-book.stanford.edu

> I study math for a living

You get paid for studying math?

It is what Maths researcher do. Relatively common thing, usually found in universities.
Yes! Well, at least, for the most part.

I am also coincidentally paid whenever I discover math and explain it to an audience, but this case is much rarer than the former.

> If you like Strang's new book, I think you'll be quite partial to Boyd's VMLS [0]

I actually had that on my list until I forgot about it! Thanks for reminding me. I'm learning Julia as well and there's a companion.

Thanks! I just took Linear Algebra and Regression Analysis class, and this book seems to be a perfect bridge between these two courses.
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.

Related: do people have good recommendations of "casual" math books for more advanced topics? I.e. ones that an educated reader with a background in math can read through in one pass (unlike most textbooks) but nonetheless have real math in them? (And has fun exercises!)

I can start with some. Feynman's Lectures on Computing. Scott Aaronson's Quantum Computing Since Democritus (though it assumes some background knowledge of quantum computing). I think Colin Adam's "The Knot Book" (on knot theory in topology) as well.

Understanding Digital Signal Processing, by Richard G Lyons. It's one of the most accessible books on the topic since it's aimed at undergraduate juniors.
Visual Complex Analysis. I’d hesitate to call it casual, but it’s extremely accessible to someone with some basic mathematical knowledge.
Also, Visual Group Theory.
I used Visual Group theory as the basis for some workshops. It's a really good read.
Roger Penrose' book _The Road to Reality_ is pretty good in this respect. It's a little skewed towards geometry (instead of, e.g., Hilbert spaces and operator algebra), but hey, what do you expect from Penrose.
Heh, this one is only for casual reading if you are already well-versed in the material. (This is a weird book - the author tends to dwell on simple things and then to rush through complex topics. Not recommended for an uninitiated. His later book, Fashion, Faith, and Fantasy, is more accessible but is primarily focused on discussing physics.)
John Baez's blogs (Azimuth, This Weeks Finds) are pretty accessible.
Susskind's Theoretical Minimum series might be to your liking?
Not a bad choice really, even though this one is more about physics than math - but hey, what is theoretical physics if not math mostly, right?