Ask HN: How to Think Like a mathematician? | Hacker News Reader

Ask HN: How to Think Like a mathematician?

9 pointsleeshire6 comments

what are some recommended good books or videos to learn this subject of beautiful math? I think Khanacademy is actually amazing which is the only thing I been using so far but any amazing book or mooc or anything else out there would be great too?

I did math a few years ago in college but I forgot most of it and now I have to relearn it to get into this program I'm starting in a few months.

I want to learn everything from the basics all the way up to the Calculus basically but nothing too advanced just very useful everyday math I can use to better my life.

I just really love learning stuff and math is so fun to me just being able to figure out algebra problems makes me happy.

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Honestly it is expensive but a life-time brilliant.org subscription is $599.99 US Dollars.

It’s a super great service I bought it myself and find it fun to go through some of the courses on my free time. The logic courses are fun. The basic math courses do some cool explanations of divisibility rules. It’s quite a bit different than Khan Academy as it’s a lot less plug and chug, but instead it focuses on teaching small lessons and letting you use intuition and problem solving skills which to me are the fun parts of math. Besides Math it also has Computer Science, Physics, Probability, and other Sciences. I would recommend maybe trying it for one month maybe if they have a free trial or something and then decide if you want to sink the $599.99 into it. The month by month subscriptions are quite a bit cheaper, but if you want to use it long term it may be worth it to buy the lifetime subscription.

Spivak's Calculus & Calculus on Manifolds are both fantastic books to start with (they're named calculus but they're really more analysis)

There's a Youtube channel 3Blue1Brown which is fantastic [1] as well. In fact, his videos are among the best if not the best for visually illustrating beautiful concepts in mathematics. The concepts covered are almost always widely applicable in problem solving and useful to know.

He's got a wide variety, but the series on Calculus and Linear Algebra are good refreshers for the two main subjects applicable to real engineering.

[1]: https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw

Amazing books that are a joy to read:

Polya's How To Solve It is great for 'how to think like a mathematician'.

I love Knuth et al's Concrete Mathematics. Discrete maths plus jokes in the margins.

Stillwell's Mathematics and its History - meet the main strands of mathematics, their origins, and the great mathematicians.

Needham's Visual Complex Analysis - complex functions, differentiation & integration, Möbius transformations, hyperbolic geometry, vector fields etc - explained with a lot of pictures.

Honestly, beautiful maths mostly starts “after Calculus”: Analysis, Abstract Algebra, and beauty is in proofs.

Although, you can check Combinatorics, Geometry, and Number Theory up to some point.

A good book I could recommend is Concrete Mathematics: https://en.m.wikipedia.org/wiki/Concrete_Mathematics

Book of Proof by Hammack is a very good free resource.

https://www.people.vcu.edu/~rhammack/BookOfProof/

Numberphile on YouTube is good

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