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I was planning to structure my learning around linear algebra and real analysis, sort of like Harvard's Math 55 does.

Apart from that I wanted to expand on basic set theory, geometry, combinatorics and probability theory to have a well-rounded basic education.

My ultimate goal is to be able to digest advanced probability and statistics books.



I don't know an answer to your original question.

Re: statistics and such though, I have heard very good things about http://www.indiana.edu/~kruschke/DoingBayesianDataAnalysis/

If you are interested in a Math 55 approach (yikes! I took 25), you could consider using their syllabus. http://abel.math.harvard.edu/~elkies/M55a.02/index.html


Set theory: You should definitely look at Naive Set Theory by Halmos. Despite the name, it's totally rigorous development of ZF set theory with discussion on the meaning and equivalent statements of AC.


What about Lawvere's Conceptual Mathematics or Sets for Mathematics?




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