13 ms·

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

81 points by dunefox 6y ago

Currently, I'm working through Gilber Strangs new book "Linear Algebra and Learning from Data"

hackermailman 6y ago
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-methods-in-data-analysis-signal-processing-and-machine-learning-spring-2018/ 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/playlists https://www.youtube.com/channel/UCWnu2XymDtORV--qG2uG5eQ/pla...
- dunefox 6y ago
  Nice, thanks! That sounds interesting. Sadly, I have a huge backlog already...
jshawl 6y ago
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.
kyawzazaw 6y ago
I am reading "The Art of Statistics" by David Spiegelhalter.
- nickcw 6y ago
  I just finished that. Great book!
nickcw 6y ago
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 6y ago
  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.
elric 6y ago
I'm working my way through Ivan Savov's "No bullshit guide to math & physics" - https://www.goodreads.com/book/show/22876442-no-bullshit-guide-to-math-and-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.
- ARandomerDude 6y ago
  Great book, too bad it's got such an offensive title. The book could be used more widely without it.
  - elric 6y ago
    How is it offensive? Because of the word bullshit?
    - ARandomerDude 6y ago
      Yes. Can you imagine this used in a professional or collegiate setting?
      - Koshkin 6y ago
        You don’t have to show it to your professor.
      - elric 6y ago
        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.
  - ivan_ah 6y ago
    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.
User23 6y ago
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-Monographs-Computer/dp/1461279240 https://www.amazon.com/Predicate-Calculus-Semantics-Monograp... [2] https://www.amazon.com/Discipline-Programming-Edsger-W-Dijkstra/dp/013215871X https://www.amazon.com/Discipline-Programming-Edsger-W-Dijks...
axegon_ 6y ago
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.
bear8642 6y ago
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
acd 6y ago
Sigmoid / logistic and bell curves to try and predict Covid-19 progress.
xyzal 6y ago
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
- iambrj 6y ago
  Another good category theory read is Pierce's Category Theory for Computer Scientists
- spekcular 6y ago
  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.
  - Koshkin 6y ago
    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.)
  - wfdctrl 6y ago
    You don't get scared when you read stuff about Haskell because you know what most the fancy words mean
    - Koshkin 6y ago
      On the other hand it would be easier to just avoid Haskell.
dboreham 6y ago
I've always been partial to Galois theory.
lukifer 6y ago
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_of_Conflict_(1960) https://en.wikipedia.org/wiki/Thomas_Schelling#The_Strategy_... I'd love any further suggestions on complex/multipolar/iterated game theory.
GuiA 6y ago
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.
snicker7 6y ago
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 6y ago
  “History of Mathematics" Anyone have good book recommendations?
  - eigenvalue 6y ago
    The World of Mathematics by James R. Newman is a classic, filled with great biographies and short essays about various parts of math.
  - orange3xchicken 6y ago
    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
  - snicker7 6y ago
    "Huygens and Barrow, Newton and Hooke" by Vladimir Arnold (would literally recommend any of his books).
  - Koshkin 6y ago
    Stillwell's Mathematics and Its History.
    - joycian 6y ago
verdverm 6y ago
I'm currently looking at propagator networks https://github.com/ekmett/propagators https://github.com/ekmett/propagators
kdamica 6y ago
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/
alphachloride 6y ago
I study no kind of math in my free time.
- rocketcity 6y ago
  Ditto
ajkjk 6y ago
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.
davidivadavid 6y ago
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_7ZlzxTi6kS4vCmv4ZKm9u8g5yic https://www.youtube.com/playlist?list=PLPH7f_7ZlzxTi6kS4vCmv...
LolWolf 6y ago
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 6y ago
  > I study math for a living You get paid for studying math?
  - giomasce 6y ago
    It is what Maths researcher do. Relatively common thing, usually found in universities.
  - LolWolf 6y ago
    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.
- dunefox 6y ago
  > 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.
- iamcreasy 6y ago
  Thanks! I just took Linear Algebra and Regression Analysis class, and this book seems to be a perfect bridge between these two courses.
king_magic 6y ago
Topology
exDM69 6y ago
Orbital mechanics and related mathematics like Stumpff series and Universal variables. Got inspired from playing too much Kerbal Space Program and Orbiter.
- ghostpepper 6y ago
  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 6y ago
    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.
tgb 6y ago
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.
- vermarish 6y ago
  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.
  - Koshkin 6y ago
    This one is amazing and not to be missed: http://www.dspguide.com/pdfbook.htm http://www.dspguide.com/pdfbook.htm.
- User23 6y ago
  Visual Complex Analysis. I’d hesitate to call it casual, but it’s extremely accessible to someone with some basic mathematical knowledge.
  - joycian 6y ago
    Also, Visual Group Theory.
    - ylem 6y ago
      I used Visual Group theory as the basis for some workshops. It's a really good read.
- auntienomen 6y ago
  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.
dhosek 6y ago
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
Sohcahtoa82 6y ago
(Points at username) Trigonometry.
agentultra 6y ago
Presently working through Harvard's online Abstract Algebra course and adjunct to that Bartoz's notes on category theory and some type theory.
pc86 6y ago
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.
tootie 6y ago
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.
excitednumber 6y ago
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.
m_j_g 6y ago
homotopy type theory!
- marius_k 6y ago
  What are you reading/watching? Are there any self-contained material on this topic?
  - joycian 6y ago
    Not sure what you mean by self-contained, but there is the Homotopy Type Theory book: https://homotopytypetheory.org/book/ https://homotopytypetheory.org/book/
jll29 6y ago
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).
kk58 6y ago
Can someone recommend an accessible book to learn multilinear algebra,tensors with focus on applications
mistrial9 6y ago
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..
Koshkin 6y ago
Highly recommended: https://jeremykun.com/2013/04/03/homology-theory-a-primer/ https://jeremykun.com/2013/04/03/homology-theory-a-primer/
aaron695 6y ago
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.
dorchadas 6y ago
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 6y ago
  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 6y ago
    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 6y ago
      Nice! I usually try Crossvalidate SE first. But I'll cross-post to those subreddits as well.
dentldir 6y ago
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.
pps43 6y ago
Applied statistics.
7kay 6y ago
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
jdkee 6y ago
Discrete most recently but I am looking into category theory.
S4M 6y ago
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 6y ago
  You can try this little essay by Stillwell: http://www.math.jhu.edu/~smahanta/Teaching/Spring10/Stillwell.pdf http://www.math.jhu.edu/~smahanta/Teaching/Spring10/Stillwel....
notduncansmith 6y ago
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.
Koshkin 6y ago
This: https://arxiv.org/abs/math/0608040v4 https://arxiv.org/abs/math/0608040v4.

81 points by dunefox 6y ago

Currently, I'm working through Gilber Strangs new book "Linear Algebra and Learning from Data"

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-methods-in-data-analysis-signal-processing-and-machine-learning-spring-2018/ 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/playlists https://www.youtube.com/channel/UCWnu2XymDtORV--qG2uG5eQ/pla...

dunefox 6y ago
Nice, thanks! That sounds interesting. Sadly, I have a huge backlog already...

jshawl 6y ago

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.

kyawzazaw 6y ago

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

nickcw 6y ago
I just finished that. Great book!

nickcw 6y ago

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 6y ago
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.

elric 6y ago

I'm working my way through Ivan Savov's "No bullshit guide to math & physics" - https://www.goodreads.com/book/show/22876442-no-bullshit-guide-to-math-and-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.

ARandomerDude 6y ago
Great book, too bad it's got such an offensive title. The book could be used more widely without it.
- elric 6y ago
  How is it offensive? Because of the word bullshit?
  - ARandomerDude 6y ago
    Yes. Can you imagine this used in a professional or collegiate setting?
    - Koshkin 6y ago
      You don’t have to show it to your professor.
    - elric 6y ago
      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.
- ivan_ah 6y ago
  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.

User23 6y ago

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-Monographs-Computer/dp/1461279240 https://www.amazon.com/Predicate-Calculus-Semantics-Monograp... [2] https://www.amazon.com/Discipline-Programming-Edsger-W-Dijkstra/dp/013215871X https://www.amazon.com/Discipline-Programming-Edsger-W-Dijks...

axegon_ 6y ago

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.

bear8642 6y ago

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

acd 6y ago

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

xyzal 6y ago

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

iambrj 6y ago
Another good category theory read is Pierce's Category Theory for Computer Scientists
spekcular 6y ago
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.
- Koshkin 6y ago
  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.)
- wfdctrl 6y ago
  You don't get scared when you read stuff about Haskell because you know what most the fancy words mean
  - Koshkin 6y ago
    On the other hand it would be easier to just avoid Haskell.

dboreham 6y ago

I've always been partial to Galois theory.

lukifer 6y ago

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_of_Conflict_(1960) https://en.wikipedia.org/wiki/Thomas_Schelling#The_Strategy_... I'd love any further suggestions on complex/multipolar/iterated game theory.

GuiA 6y ago

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.

snicker7 6y ago

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 6y ago
“History of Mathematics" Anyone have good book recommendations?
- eigenvalue 6y ago
  The World of Mathematics by James R. Newman is a classic, filled with great biographies and short essays about various parts of math.
- orange3xchicken 6y ago
  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
- snicker7 6y ago
  "Huygens and Barrow, Newton and Hooke" by Vladimir Arnold (would literally recommend any of his books).
- Koshkin 6y ago
  Stillwell's Mathematics and Its History.
  - joycian 6y ago

verdverm 6y ago

I'm currently looking at propagator networks https://github.com/ekmett/propagators https://github.com/ekmett/propagators

kdamica 6y ago

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/

alphachloride 6y ago

I study no kind of math in my free time.

rocketcity 6y ago
Ditto

ajkjk 6y ago

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.

davidivadavid 6y ago

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_7ZlzxTi6kS4vCmv4ZKm9u8g5yic https://www.youtube.com/playlist?list=PLPH7f_7ZlzxTi6kS4vCmv...

LolWolf 6y ago

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 6y ago
> I study math for a living You get paid for studying math?
- giomasce 6y ago
  It is what Maths researcher do. Relatively common thing, usually found in universities.
- LolWolf 6y ago
  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.
dunefox 6y ago
> 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.
iamcreasy 6y ago
Thanks! I just took Linear Algebra and Regression Analysis class, and this book seems to be a perfect bridge between these two courses.

king_magic 6y ago

Topology

exDM69 6y ago

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

ghostpepper 6y ago
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 6y ago
  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.

tgb 6y ago

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.

vermarish 6y ago
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.
- Koshkin 6y ago
  This one is amazing and not to be missed: http://www.dspguide.com/pdfbook.htm http://www.dspguide.com/pdfbook.htm.
User23 6y ago
Visual Complex Analysis. I’d hesitate to call it casual, but it’s extremely accessible to someone with some basic mathematical knowledge.
- joycian 6y ago
  Also, Visual Group Theory.
  - ylem 6y ago
    I used Visual Group theory as the basis for some workshops. It's a really good read.
auntienomen 6y ago
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.

dhosek 6y ago

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

Sohcahtoa82 6y ago

(Points at username) Trigonometry.

agentultra 6y ago

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

pc86 6y ago

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.

tootie 6y ago

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.

excitednumber 6y ago

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.

m_j_g 6y ago

homotopy type theory!

marius_k 6y ago
What are you reading/watching? Are there any self-contained material on this topic?
- joycian 6y ago
  Not sure what you mean by self-contained, but there is the Homotopy Type Theory book: https://homotopytypetheory.org/book/ https://homotopytypetheory.org/book/

jll29 6y ago

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).

kk58 6y ago

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

mistrial9 6y ago

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..

Koshkin 6y ago

Highly recommended: https://jeremykun.com/2013/04/03/homology-theory-a-primer/ https://jeremykun.com/2013/04/03/homology-theory-a-primer/

aaron695 6y ago

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.

dorchadas 6y ago

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 6y ago
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 6y ago
  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 6y ago
    Nice! I usually try Crossvalidate SE first. But I'll cross-post to those subreddits as well.

dentldir 6y ago

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.

pps43 6y ago

Applied statistics.

7kay 6y ago

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

jdkee 6y ago

Discrete most recently but I am looking into category theory.

S4M 6y ago

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 6y ago
You can try this little essay by Stillwell: http://www.math.jhu.edu/~smahanta/Teaching/Spring10/Stillwell.pdf http://www.math.jhu.edu/~smahanta/Teaching/Spring10/Stillwel....

notduncansmith 6y ago

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.

Koshkin 6y ago

This: https://arxiv.org/abs/math/0608040v4 https://arxiv.org/abs/math/0608040v4.