
Ask HN: What kind of math do you study in your free time? - dunefox
Currently, I&#x27;m working through Gilber Strangs new book &quot;Linear Algebra and Learning from Data&quot;
======
xyzal
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](https://www.youtube.com/user/DrBartosz)

book -> [https://github.com/hmemcpy/milewski-ctfp-
pdf](https://github.com/hmemcpy/milewski-ctfp-pdf)

~~~
spekcular
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.

~~~
wfdctrl
You don't get scared when you read stuff about Haskell because you know what
most the fancy words mean

~~~
Koshkin
On the other hand it would be easier to just avoid Haskell.

------
snicker7
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
“History of Mathematics"

Anyone have good book recommendations?

~~~
Koshkin
Stillwell's _Mathematics and Its History_.

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

------
LolWolf
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](http://vmls-book.stanford.edu)

~~~
Koshkin
> _I study math for a living_

You get paid for _studying_ math?

~~~
LolWolf
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.

------
bear8642
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](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

------
elric
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...](https://www.goodreads.com/book/show/22876442-no-bullshit-guide-to-
math-and-physics)

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.

~~~
ARandomerDude
Great book, too bad it's got such an offensive title. The book could be used
more widely without it.

~~~
elric
How is it offensive? Because of the word bullshit?

~~~
ARandomerDude
Yes. Can you imagine this used in a professional or collegiate setting?

~~~
elric
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.

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

------
User23
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...](https://www.amazon.com/Predicate-Calculus-Semantics-Monographs-
Computer/dp/1461279240)

[2] [https://www.amazon.com/Discipline-Programming-Edsger-W-
Dijks...](https://www.amazon.com/Discipline-Programming-Edsger-W-
Dijkstra/dp/013215871X)

------
hackermailman
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...](https://ocw.mit.edu/courses/mathematics/18-065-matrix-methods-in-
data-analysis-signal-processing-and-machine-learning-spring-2018/)

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...](https://www.youtube.com/channel/UCWnu2XymDtORV--
qG2uG5eQ/playlists)

~~~
dunefox
Nice, thanks!

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

------
7kay
I'm interested in fractional calculus.

It all started with an argument I had with my high school math teacher about
whether something like a half derivative is a thing. Turns out fractional
calculus is a real thing and shows up in many applied areas of math. The
Fractional Calculus by Oldham and Spanier I have lying around treats its
applications to diffusion problems, for example. As an EE student fractional
PID controller design and fractional signal processing are interesting as
well.

For a quick peek into that subject I would recommend watching Dr Peyam's
videos on half derivatives[0].

[0]:
[https://www.youtube.com/watch?v=eB3OUl5TVSY](https://www.youtube.com/watch?v=eB3OUl5TVSY)

------
kyawzazaw
I am reading "The Art of Statistics" by David Spiegelhalter.

~~~
nickcw
I just finished that. Great book!

------
dorchadas
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 fun, in my opinion. I'd love to maybe eventually do an online math
bachelors and then get a masters in it later (or skip the bachelors and get a
masters), but all that will depend on if I decide to shift out of teaching or
not.

~~~
iamcreasy
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.

~~~
dorchadas
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.

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

------
tgb
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.

~~~
User23
Visual Complex Analysis. I’d hesitate to call it casual, but it’s extremely
accessible to someone with some basic mathematical knowledge.

~~~
joycian
Also, Visual Group Theory.

~~~
ylem
I used Visual Group theory as the basis for some workshops. It's a really good
read.

------
jll29
The topics that resonate with me the most are graph theory and probability.
Incidentally, they are also the most useful for my day job. Graphs are such a
beautiful and intuitive concept, it is amazing; basic probability is
unbelievably useful for general problem solving, making decisions, modeling
the world; both have been written about a lot, yet there is so much more to
discover and apply.

Things I'd love to read about if I had more time are: topology (knots are
weird interesting things), meta-mathematics (Gödelization and all that, read
Gödel, Escher, Bach if you'd like to wet your appetite), paraconsistent logic
(how to contain inconsitencies in systems of logic so that they don't become
arbitrary - as from contradiction, anything follows). Digesting maths requires
a _lot_ of time, wish I could be a student again to sit in whatever lecture
that sounds interesting.

As a kid, I loved reading about history of maths; many discovery stories made
me become a scientist (applied computer science researcher), and I still enjoy
reading about it (also biographies or even mathematically related fiction e.g.
The Solitude of Prime Numbers).

------
GuiA
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.

------
lukifer
I'm a big fan of Schelling's ideas on game theory, and focal points in
particular:
[https://en.wikipedia.org/wiki/Thomas_Schelling#The_Strategy_...](https://en.wikipedia.org/wiki/Thomas_Schelling#The_Strategy_of_Conflict_\(1960\))

I'd love any further suggestions on complex/multipolar/iterated game theory.

------
kdamica
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/](https://people.clas.ufl.edu/bona/books/)

------
dhosek
My capsule reviews of what I've read in mathematics over the last 22 years.
[http://don.dream-in-
color.net/books/archive.php4?iSubject=79](http://don.dream-in-
color.net/books/archive.php4?iSubject=79)

------
ajkjk
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.

------
verdverm
I'm currently looking at propagator networks
[https://github.com/ekmett/propagators](https://github.com/ekmett/propagators)

------
excitednumber
I'd love to raise awareness of
[https://www.stat.berkeley.edu/~aldous/Real_World/RW.html](https://www.stat.berkeley.edu/~aldous/Real_World/RW.html)
(Probability and the Real World)
[https://www.stat.berkeley.edu/~aldous/](https://www.stat.berkeley.edu/~aldous/)
Professor David Aldous. This is a wonderful resource. I hope you all enjoy.

------
S4M
I tried to learn Galois theory on Coursera a few years ago (the course was in
French, which is my mother tongue, but probably few HNers can understand it),
and failed the class partly due to lack of time. Since then I've been trying
from time to time to read about it, which refreshed knowledge of Group theory,
but so far I haven't gotten to the point where I understand Galois's idea to
prove that some polynomial equations are not solvable by radicals.

~~~
Koshkin
You can try this little essay by Stillwell:
[http://www.math.jhu.edu/~smahanta/Teaching/Spring10/Stillwel...](http://www.math.jhu.edu/~smahanta/Teaching/Spring10/Stillwell.pdf).

------
dentldir
I filled a Kindle with just about every paper related to the proof of Fermat's
Last Theorem and chip away at it when I can. When I get stuck there, I switch
over to trying to understand Ono's closed form solution of the partition
function. Both subjects provide hours and hours of diversions into areas of
math I never got to learn studying physics.

------
nickcw
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](https://www.youtube.com/user/blackpenredpen)

~~~
racl101
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](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.

------
notduncansmith
I’m obsessed with the Mandelbrot Set, so a lot of the mathematics I read
recreationally branches from that: fractals, complex numbers, Riemannian and
Hermitian manifolds, and related topics.

As a software developer, I explore lots of computer/data-science related
topics as well, e.g. cellular automata, dynamics, and some statistics.

------
pc86
I failed Linear Algebra in college because I was more interested in partying,
it wasn't essential to my degree (Poli Sci), and I incorrectly assumed I could
drift through it and get a C like my other hard science requirements. I am
currently working through Friedberg's textbook on it.

------
davidivadavid
I've enjoyed this series of lectures on Youtube:

"Lectures on Geometrical Anatomy of Theoretical Physics" [0]

[0]
[https://www.youtube.com/playlist?list=PLPH7f_7ZlzxTi6kS4vCmv...](https://www.youtube.com/playlist?list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic)

------
kk58
Can someone recommend an accessible book to learn multilinear algebra,tensors
with focus on applications

------
axegon_
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.

------
Koshkin
Highly recommended: [https://jeremykun.com/2013/04/03/homology-theory-a-
primer/](https://jeremykun.com/2013/04/03/homology-theory-a-primer/)

------
tootie
Common Core because my kids are in school. I've heard a lot of parents
complain, but I actually love it. I've always had a knack for doing arithmetic
in my head and common core is teaching all the stuff I do intuitively.

------
Koshkin
This:
[https://arxiv.org/abs/math/0608040v4](https://arxiv.org/abs/math/0608040v4).

------
exDM69
Orbital mechanics and related mathematics like Stumpff series and Universal
variables. Got inspired from playing too much Kerbal Space Program and
Orbiter.

~~~
ghostpepper
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?

~~~
exDM69
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.

------
agentultra
Presently working through Harvard's online Abstract Algebra course and adjunct
to that Bartoz's notes on category theory and some type theory.

------
aaron695
In high school I read Vašek Chvátal - Linear Programming after buying it
second hand for a few dollars thinking it was a computer text book.

I liked it at the time.

------
mistrial9
certainly some statistics thoery, when following any MachineLearning core..
(not big on DeepLearning here, all the other ones) Small bits of
'Understanding Machine Learning: From Theory to Algorithms'

Some clustering theory.. some computer vision components, including
segmentation methods

Some "data mining" approaches, which are sets and stats, basically..

------
dboreham
I've always been partial to Galois theory.

------
acd
Sigmoid / logistic and bell curves to try and predict Covid-19 progress.

------
jdkee
Discrete most recently but I am looking into category theory.

------
alphachloride
I study no kind of math in my free time.

~~~
rocketcity
Ditto

------
king_magic
Topology

------
Sohcahtoa82
_(Points at username)_

Trigonometry.

------
m_j_g
homotopy type theory!

~~~
marius_k
What are you reading/watching? Are there any self-contained material on this
topic?

~~~
joycian
Not sure what you mean by self-contained, but there is the Homotopy Type
Theory book:

[https://homotopytypetheory.org/book/](https://homotopytypetheory.org/book/)

------
pps43
Applied statistics.

