Found 12 comments on HN
synthmeat · 2018-03-11 · Original thread
I’m going to go with a few assumptions here:

a) You don’t do this full time.

b) By “bottoms up” you just mean “with firm grasp on fundamentals”, not logic/set/category/type theory approach.

c) You are skilled with programming/software in general.

In a way, you’re ahead of math peers in that you don’t need to do a lot of problems by hand, and can develop intuition much faster through many software tools available. Even charting simple tables goes a long way.

Another thing you have going for yourself is - you can basically skip high school math and jump right in for the good stuff.

I’d recommend getting great and cheap russian recap of mathematics up to 60s [1] and a modern coverage of the field in relatively light essay form [2].

Just skimming these will broaden your mathematical horizons to the point where you’re going to start recognizing more and more real-life math problems in your daily life which will, in return, incite you to dig further into aspects and resources of what is absolutely huge and beautiful landscape of mathematics.

[1] https://www.amazon.com/Mathematics-Content-Methods-Meaning-V...

[2] https://www.amazon.com/Princeton-Companion-Mathematics-Timot...

hyporthogon · 2017-03-06 · Original thread
This is awesome, thanks.

Obligatory 'zoomout' recommendation: https://www.amazon.com/Mathematics-Content-Methods-Meaning-V..., which I learned about from HN (http://hackernewsbooks.com/book/mathematics-its-content-meth...). Wish I had read/pondered this before grad math classes.

whitepoplar · 2016-11-30 · Original thread
This book is fantastic and should get you pretty far: https://www.amazon.com/Mathematics-Content-Methods-Meaning-V...
dpflan · 2015-09-20 · Original thread
This is always a good topic with numerous HN submissions and comments:

Just from a search, there are some great results:

1. Mathematics for Computer Science - HN Submissions: https://news.ycombinator.com/item?id=9311752, https://news.ycombinator.com/item?id=3694448

2. How to Read Mathematics - HN Submissions: https://news.ycombinator.com/item?id=4030812, https://news.ycombinator.com/item?id=1576969

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Here are some other excellent mathematics books:

1. Mathematics: Its Content, Methods and Meaning

Containing the thoughts and direction of numerous mathematicians including Kolmogorov, this is a great survey of the field of mathematics. It touches upon Analysis, Analytic Geometry, Probability, Linear Algebra, Topology, and more. [1.]

2. Concrete Mathematics: A Foundation for Computer Science

Containing the thoughts and direction of mathematician and computer scientists such as Donald Knuth, this is a great reference for computer science related mathematical concepts focusing on continuous and discrete concepts. [2.]

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[1.] http://www.amazon.com/Mathematics-Content-Methods-Meaning-Do...

[2.] http://www.amazon.com/Concrete-Mathematics-Foundation-Comput...

nabla9 · 2015-02-04 · Original thread
Usually good books travel from English speaking world to other languages as translations.

One of the masterpieces that has gone the opposite direction is:

Mathematics: Its Content, Methods and Meaning (three volumes bound as one) by A. D. Aleksandrov, A. N. Kolmogorov, M. A. Lavrent'ev (18 authors total) http://www.amazon.com/Mathematics-Content-Methods-Meaning-Do...

This book is really good companion for autodidacts. It's basically overview of mathematics.

wallflower · 2014-12-28 · Original thread
This isn't a course but this book has been consistently word-of-mouth recommended as a comprehensive survey of undergraduate mathematics.

http://www.amazon.com/Mathematics-Content-Methods-Meaning-Do...

brandonmenc · 2014-12-04 · Original thread
Mathematics: Its Content, Methods and Meaning by Aleksandrov, Kolmogorov, and Lavrent'ev

http://www.amazon.com/Mathematics-Content-Methods-Meaning-Do...

Covers something like three years of an undergraduate degree in mathematics. Lots of words - but that text is used to develop an understanding of the concepts and images. Considered a masterpiece. An enjoyable read.

ivan_ah · 2014-10-03 · Original thread
I've looked at a bunch of these math compendiums while researching what to include in my book, and this one seemed the best so far: http://www.amazon.com/Mathematics-Content-Methods-Meaning-Do... The writing isn't very hand-holdy, but it covers a lot of important topics, and without too much fluff.

For a more "math for general culture" I'd recommend this one: http://www.amazon.ca/Mathematics-1001-Absolutely-Everything-... which covers a lot of fundamental topics in an intuitive manner.

I have both books on the shelf, but not finished reading through all of them so I can't give my full endorsement, but from what I've seen so far, they're good stuff.

fensterbrett · 2014-09-02 · Original thread
Mathematics: Its Content, Methods and Meaning by A. D. Aleksandrov et al.

http://www.amazon.com/Mathematics-Content-Methods-Meaning-Do...

oskarth · 2014-04-12 · Original thread
Not the same type of book, but you could do a lot worse than reading through Mathematics: Its Content, Methods and Meaning, by M. A. Lavrent’ev, A. D. Aleksandrov, A. N. Kolmogorov. It's an amazing book which gives a mathematical (but not rigorous in the sense of proofs etc.) overview of most of mathematics.

http://www.amazon.com/Mathematics-Content-Methods-Meaning-Do...

nabla9 · 2013-12-28 · Original thread
May I present one of the greatest math books for general audience: Mathematics: Its Content, Methods and Meaning by A. D. Aleksandrov, A. N. Kolmogorov, M. A. Lavrent’ev.

http://www.amazon.com/Mathematics-Its-Content-Methods-Meanin...

Math books rarely move from the Soviet Union to west, but this did and for really good reason. Just look at the list of writers included. So far I have not seen any math books that come even close to this. Reading this book together with the The Princeton Companion to Mathematics was real treat.

This book looks awesome. Mathematics is so vast that as a student its hard to know what classes you should take, or even what the map of the territory looks like. That is one of the reasons I got frustrated with my pure math BS.

The Russian school put out some pretty massive volumes, like

http://www.amazon.com/Mathematics-Its-Content-Methods-Meanin...

but I found those to be a little too caught up in the proposition/proof cycle to be useful as a guide to the uninitiated.

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