
Ask HN: How to Think Like a mathematician? - leeshire
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?<p>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&#x27;m starting in a few months.<p>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.<p>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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johnsonjo
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.

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johnmorrison
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](https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw)

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yesenadam
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.

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playing_colours
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](https://en.m.wikipedia.org/wiki/Concrete_Mathematics)

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

[https://www.people.vcu.edu/~rhammack/BookOfProof/](https://www.people.vcu.edu/~rhammack/BookOfProof/)

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sesuximo
Numberphile on YouTube is good

