21–30 of 92 posts
The Chicago undergraduate mathematics bibliography is a fantastic list: http://www.ocf.berkeley.edu/~abhishek/chicmath.htm .
Update: yeah this list was last updated in 2000.
https://math.stackexchange.com/questions/62190/mathematical-...
(comparing to Feynman's Lectures on Physics rather than SICP.)
However, I agree with zodiac: Math is a much broader field and I think very few living people have the kind knowledge you're talking about: consistent and broad knowledge in all areas.
I have the same background as you and I started doing exactly this about 8 years ago. I'm just finishing my PhD in math. I'll give you some advice. First, studying math for its own sake by yourself is extremely hard. That's one reason I ended up back in academia. If you can't go back to school, still find some kind of community. Second, rather than studying generally, try to identify a goal to work towards. What are you trying to understand or figure out? Third, try to model your plan on a rigorous undergrad program, e.g., MIT. Then, in each main undergrad area (algebra, analysis, topology, geometry, etc.) try to find the "SICP" and study that. For general book recommendations, I like Fowler's A Mathematics Autodidact's Aid:
I share exactly the same interest. Can anybody suggest some outline for what topics (more or less) should somebody cover to be on "undergrad-math" level? Unfortunately I have to hold my own tongue this time, because books I found useful are mainly in russian and they surely aren't like SICP. And I still lack the whole understanding of the area anyway.
For first-year stuff, I would recommend No bullshit guide to math and physics[1] and the No bullshit guide to linear algebra[2] of which I am the author.
I share exactly the same interest. Can anybody suggest some outline for what topics (more or less) should somebody cover to be on "undergrad-math" level? Unfortunately I have to hold my own tongue this time, because books I found useful are mainly in russian and they surely aren't like SICP. And I still lack the whole understanding of the area anyway.
My idea was to cover 6 topics, which would be equivalent to a broad freshman and 1/2 sophomore math education: * Set theory * Linear algebra * Geometry * Real analysis * Combinatorics * Probability theory
Topology, number theory, abstract algebra (I mean, real one, not CS-course basics), statistics, tensor analysis? Isn't that "undergrad math"?
For things like Set theory/combinatorics/logic basics I'd recommend Rosen's "Discrete Math and Applications"[1]. CS oriented, simple, interesting, broad. Covers all the basic stuff.
Linear algebra — two books, "Linear algebra done Right" and "Linear algebra done Wrong". Second one more math-oriented, the first one — pretty simple, pretty clear, fun to read.
Real analysis ("calculus" you mean?) — I personally learned from different sources and probably the most concise book I read is Fichtengolz's "differential and integral calculus", but I don't know if it's available in english. I guess, almost any book on topic is fine.
Geometry & Probability theory — not sure what to recommend, because books on topic vary in depth dramatically, I would appreciate myself if somebody would outline the borders for what to cover first. Anyway, most of what I read and found useful is in russian, unfortunately. But still, what do you mean by geometry and prob. theory? Differential geometry, Riemannian geometry, erlangen program covered or only basic euclidean/analytic geometry stuff? Same goes for probability. If you care only for very basics — Khan's academy (or any random youtube videos) is fine. Any intro book on statistics covers it as well.
[1] - http://www.amazon.com/Discrete-Mathematics-Applications-Kenn...
You might be interested in this math.SE question I asked: https://math.stackexchange.com/questions/62190/mathematical-... (comparing to Feynman's Lectures on Physics rather than SICP.) However, I agree with zodiac: Math is a much broader field and I think very few living people have the kind knowledge you're talking about: consistent and broad knowledge in all areas. I have the same background as you and I started do…
That's great one! Thank you for pointing this out very much.
I share exactly the same interest. Can anybody suggest some outline for what topics (more or less) should somebody cover to be on "undergrad-math" level? Unfortunately I have to hold my own tongue this time, because books I found useful are mainly in russian and they surely aren't like SICP. And I still lack the whole understanding of the area anyway.
It's not nearly as easy to work through as SICP is but Principles of Mathematical Analysis by Walter Rudin (sometimes referred to as little Rudin) is a great place to start if you're interested in analysis. It's a hard book, but it's pretty much the standard for undergrad analysis.
Not Math, but Physics/Mechanics, by Sussman again. Title ? SICM hehe https://mitpress.mit.edu/sites/default/files/titles/content/...
Don't be fooled by the title and authors of the book!