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Ask HN: How to self-learn math?

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Re: Ask HN: How to self-learn math?

#131

Post by richardjdare »

I guess I'm similar in that I left high school with very little mathematical knowledge. I've struggled with many many maths books over the years which usually assume you have a certain background, or don't explain things very well, or only explain things using notation which they don't explain.

The books that helped me the most are "Mastering Mathematics", and "Mastering Advanced Pure Mathematics" both by Geoff Buckwell. They will take you through UK GCSE and A-Level maths, from nothing to calculus. They have plenty of examples and exercises to work through. Just start at the beginning and work through them.

They are based on a UK curriculum though, so that may or may not be what you want.

Re: Ask HN: How to self-learn math?

#132

Post by psychedelic »

ivansavz wrote: post #15

I have just the book for you: the essentials of high school math for adults: http://www.lulu.com/shop/ivan-savov/no-bullshit-guide-to-mat... If you like this one, you can followup with the MATH&PHYS book which covers mechanics (PHYS101) and calculus. And if you like that one, you can follow up with the liner algebra book. All along the way, I recommend you try solving exercises and problems using pen and paper. Ideal…

Came here to recommend this one as well. I bought it several years ago as an adult trying to revisit math. I'm always surprised at how few people know of this gem.

Re: Ask HN: How to self-learn math?

#133

Post by mtreis86 »

synthmeat wrote: post #69
gradschool wrote: post #68

Earlier quoted context omitted.

The Princeton Companion to Mathematics is a good resource consisting of a huge collection of detailed articles on many mathematical subjects by knowledgeable contributors. It requires no specialized background and is curated by Fields Medalist Tim Gowers. Whoever reads it from cover to cover is my hero, but failing that there's always an interesting article to jump to. Don't just be a consumer but write something as…

> The Princeton Companion to Mathematics is a good resource... I think Princeton Companion to Physics curated by Frank Wilczek, a Nobelist, is due to be published this year. > Whoever reads it from cover to cover is my hero... Yeah, I'd die an accomplished man if I would grok just a few books I treasure, amongst which are TPCTM and MICMAM. > Don't just be a consumer but write something as soon as you're inspired. Abs…

What is MICMAM?

Whitepapers, lectures, and speech transcriptions are also good motivation, and useful resources. Sometimes overwhelming, especially if reading mathematical text is as a foreign language. And sometimes it takes you down a rabbit hole.

My biggest block for learning math has really been all the unlearning. After a while ideas like negative numbers and zeros and processes like addition and subtraction stop making as much sense as I thought.

Here is my favorite rabbit hole:

http://www.turingarchive.org/viewer/?id=465&title=01

leads to:

http://www.digizeitschriften.de/dms/img/?PID=GDZPPN002278499...

leads to:

http://www.jamesrmeyer.com/pdfs/godel-original-english.pdf

Where to go from there - philosophy or computation? Lambda calculus is only a couple clicks away. Lisp papers, perhaps?

Re: Ask HN: How to self-learn math?

#134

Post by mathing »

Khan academy. I also blundered my way through high school math, getting near-failing grades and quitting as soon as possible. I got super interested in it and while I was regularly studying khan academy was the best way of actually learning the material. The exercises are a bit slow but ideally you'd learn from the lectures and then supplement them with a book of just exercises.

Re: Ask HN: How to self-learn math?

#135

Post by candu »

There are several amazing suggestions in this thread already.

I'll toss in vote N+1 for "How to Solve It" by Pólya: once you get past the hurdle of just understanding notation / language and some of the basic concepts, mathematics becomes much more about problem-solving.

Aside from that...

Oliver Byrne's Euclid: https://www.math.ubc.ca/~cass/euclid/byrne.html - a graphical treatment of Euclid's Elements. Much, much more accessible than earlier renditions, and a great introduction to methods of proof.

Vi Hart's videos: https://www.youtube.com/user/Vihart - she does a wonderful job of conveying the wonder of mathematics in a clear, informative manner.

A Mathematical Mosaic: https://www.amazon.ca/Mathematical-Mosaic-Patterns-Problem-S... - this was one of the books that got me excited about mathematics as a kid. The material is advanced by high school standards, but presented in a way that invites you to think / learn / generalize.

Re: Ask HN: How to self-learn math?

#136

Post by 123212321 »

Work extremely slowly, possibly with a tutor through Principles of Mathematical Analysis by Rudin. The book lays down the real foundations of calculus and higher math. Learn the math as you come to it. Dont waste time going extensively through lower mathematics. You will get bored and life is too short for that.

Re: Ask HN: How to self-learn math?

#137

Post by jbduler »

I recommend the excellent (and free) book from Jean Gallier @ the Department of Computer and Information Science, University of Pennsylvania: Fundamentals of Linear Algebra and Optimization. Everything you need to know, all the way up to machine learning algs. Download here: http://www.seas.upenn.edu/~cis515/linalg.pdf Enjoy!

Re: Ask HN: How to self-learn math?

#138

Post by tensor_rank_0 »

take pre-calculus and do every assignment immediately as it is assigned. then review before the next class. pre-calculus is designed to give people like you the tools to move onto the maths you want to learn.

after that, echoing another top-level comment: take calculus and physics. take 2 semesters of each.

after those 3 classes, you'll know more math than 90% of the world's population. more importantly you'll be prepared to move on to differential equations, linear algebra, and vector calculus.

Re: Ask HN: How to self-learn math?

#140

Post by rizn »

I was in your position as well and my recommendation is to buy a good book.

I personally chose Precalculus by James Stewart and it works for me. It's a thick 1000 pages book with excercises and tests.

It quite well explains all topics, which you would have in high school (from basic arithmetics to everything you need to start calculus).

I do maths in my spare time (a few hours a week) and I completed 700 pages over past 3 years.

This year I should complete the book and be ready to do more advanced mathematics.

95% is self explanatory (if you focus and re-read) and explains well proofs. When I didn't understand something I found answer on google or asked a few questions on math stack exchange.

My point. You can absolutely do maths on your own. You don't need classes with a teacher, but it only depends what kind person you are and what works for you.

EDIT: Do all exercices and never skip to the next bit if you don't understand something from the previous part.

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