Getting back to higher math
February 21, 2014 7:03 PM   Subscribe

I'd like book/course suggestions to do a slow gentle study of higher Math by myself. I did a bachelor's degree in Math (and Economics) several years ago by myself as an external course (from the Univ of London and LSE), on the side of a whole lot of other things. I did reasonably well, enjoyed parts of it very much, but I've forgotten most of it now. I taught high school Math for a couple of years after that but now work in a totally different field (communication design). I love my work, but miss the brainwork Math required. I'd also like to slowly internalise more Math vocabulary and the structure of the subject, which didn't happen during my Bachelors.

I'd be especially happy with a sort of gentle book that doesn't plunge too deep right at the start. I loved number theory and my entire abstract math course when I studied it. After a certain point, advanced calculus threw me off a little, but I didn't have enough time to study it thoroughly at that point.
posted by miaow to Education (6 answers total) 36 users marked this as a favorite
Some broad book recommendations:

Princeton Companion to Mathematics

Mathematics: Its Content, Methods, and Meaning

Proofs from the Book

There are number of cheap Dover paperback classics that may be good for self-study (the Mathematics: Content-Methods-Meaning book above is also in this category), for example:

Number Theory

Introduction to Topology

A Book of Abstract Algebra
posted by leopard at 7:32 PM on February 21, 2014 [1 favorite]

How many years ago are we talking? I thinkthat might help with the suggestions.
posted by klausman at 7:33 PM on February 21, 2014

This is mostly random (and probably overkill):

Read the arxiv's new math section regularly.

Train yourself to look at the On-Line Encyclopedia of Integer Sequences whenever possible.

the Stacks project

Flajolet's Analytic Combinatorics is a brilliant exposition about generating functions and combinatorics

the NIST's Digital Library of Mathematical Functions is worth looking at (it's the successor to Abramowitz and Stegun)

Look at John Baez's archived This week's finds in mathematical physics column.

Elias Wegert's Visual complex functions talks about phase portraits in the complex plane.

Alan Hatcher's Algebraic Topology is a good introduction.

And and mathoverflow are good places to ask questions.
posted by oonh at 7:35 PM on February 21, 2014 [3 favorites]

I finished my degree 4 years ago, if that helps. But as I said, I was a part-time student, and quite preoccupied with other things.

(thanks for the suggestions so far!)
posted by miaow at 7:41 PM on February 21, 2014

I've always loved Understanding Analysis by Stephen Abbott. It's geared towards undergraduate students taking their first real analysis or advanced calculus class, and it's wonderfully written. There's often a nice tidbit of historical motivation for the material. It's maybe slightly less rigorous than a real real analysis textbook would be, but since this is for self-study, that's probably ok.
posted by bluefly at 9:12 AM on February 22, 2014

At least 3 generations of British engineers are indebted to K.A.Stroud. Don't be out off that the titles are engineering mathematics, look at the contents list for the topics you want. They are unbeatable for self study.
posted by Dr Ew at 3:06 PM on February 22, 2014

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