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The Mathematics Autodidact’s Aid (2005) [pdf]

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Re: The Mathematics Autodidact’s Aid (2005) [pdf]

#41

Post by ue_ »

narrator wrote: post #13
lunchladydoris wrote: post #9

I enjoy a mathematics textbook as much as the next person, but what annoys me is the lack of solutions to the problems in so many of the books I've skimmed outside of classes.

That's why Khan Academy is awesome. I'm working through their calculus and differential equations curriculum right now to refresh my math and the amount and quality of autograded excercises is fantastic! The other nice thing is it periodically tests knowledge of previously studied material.

Oh, differential equations.

I'm doing ECE at university now and I have an exam in about 7 weeks. I've found that it's quite hard to identify what sort of differential equation a given problem is, and then how to solve it. However I've found that by looking around for other material I can understand it better.

For example web searching "type 4 differential equation" bought up this gem: https://www.math.ucdavis.edu/~thomases/W11_16C1_lec_1_7_11.p...

I think I'll try out Khan Academy because I've found that the lecturer's problem sheets probably aren't enough on their own.

Re: The Mathematics Autodidact’s Aid (2005) [pdf]

#42

Post by sampo »

MichaelMoser123 wrote: post #5

maybe i am just stupid, but I find that many texts in mathematics like to skip over details, or I get stuck because there is an ambiguity in the text and there is no one to ask about it.. What do we do in this kind of situation?

You can try asking at http://math.stackexchange.com/

Re: The Mathematics Autodidact’s Aid (2005) [pdf]

#44

Post by wolfgke »

imakecomments wrote: post #31
fmap wrote: post #29

Earlier quoted context omitted.

What exactly are you trying to learn? Mathematical logic is a huge field in its own right, with plenty of topics that are of historical interest and a lot of active research areas. If you want to learn modern mathematical logic you're in for a rough time, since you'll basically have to learn category theory in order to understand the few really excellent textbooks which exist (e.g. Sketches of An Elephant). If you ar…

I'm mostly interested in "modern" mathematical logic then. I'm very interested in learning category theory and its connections to programming language theory. I already know a little bit of category theory, but am open to any good beginner sources. I'm also interested in classic recursion theory and a bit of proof theory with its connections to CS. I don't know many people doing any of this and it doesn't seem that p…

Category theory is not logic.

Re: The Mathematics Autodidact’s Aid (2005) [pdf]

#45

Post by nicklaf »

tribe wrote: post #33

For another list of recommendations by topic, check out this (very popular) list: https://github.com/ystael/chicago-ug-math-bib

Much better. Looking through the intermediate and advanced sections, I see that this guide suffers from none of the omissions which I had complained about in my post (specifically, the omissions of classic works by Arnold and Spivak).

(I still think it would be crazy not to buy the PCtM somewhere before reaching the advanced part of this guide, and it may as well be before the intermediate as well. Consider that without the PCtM, you may never realize that your initial (probably false) assumptions about the scope of mathematics may mean that you will never even get past the beginner section at all!)

Re: The Mathematics Autodidact’s Aid (2005) [pdf]

#46

Post by gtani »

jwdunne wrote: post #34
mrkgnao wrote: post #19

Earlier quoted context omitted.

Pugh, by any chance?

Krantz. Seems to be at a decent pace. No idea if it's any good though - problem of not having a mentor!

That book got good reviews. /r/math has lots of threads on this, recommend Abbott, Tao, Pugh, Spivak etc

https://www.reddit.com/r/math/comments/50m4ib/what_are_the_m...

https://www.reddit.com/r/math/comments/4jopme/is_it_prematur...

https://www.reddit.com/r/math/comments/512p2p/analysis_text_...

Re: The Mathematics Autodidact’s Aid (2005) [pdf]

#47

Post by gtani »

tribe wrote: post #33

For another list of recommendations by topic, check out this (very popular) list: https://github.com/ystael/chicago-ug-math-bib

I think the guy who wrote that original U of C list has stated that it's mainly of historical interest, given the many omissions noted, and that the lists by Baez and Univ. Cambridge that i pushed there are better starting points, or this one: https://www.reddit.com/r/math/wiki/faq

There's lot sof other lists of recommended texts after calc3, https://www.math.ucla.edu/ugrad/courses/math/ and

https://math.berkeley.edu/courses/archives/announcements/fal...

and http://mathoverflow.net/questions/761/undergraduate-level-ma...

Re: The Mathematics Autodidact’s Aid (2005) [pdf]

#48

Post by jwdunne »

gtani wrote: post #46
jwdunne wrote: post #34

Earlier quoted context omitted.

Krantz. Seems to be at a decent pace. No idea if it's any good though - problem of not having a mentor!

That book got good reviews. /r/math has lots of threads on this, recommend Abbott, Tao, Pugh, Spivak etc https://www.reddit.com/r/math/comments/50m4ib/what_are_the_m... https://www.reddit.com/r/math/comments/4jopme/is_it_prematur... https://www.reddit.com/r/math/comments/512p2p/analysis_text_...

Thank you :) I'm currently reading Calculus by Spivak too. Fantastic book.

I find getting a taste and moving forward breadth-first keeps things fresh.

Re: The Mathematics Autodidact’s Aid (2005) [pdf]

#49

Post by mindcrime »

mindcrime wrote: post #35
xemdetia wrote: post #30

Earlier quoted context omitted.

It is also important to look for primers from multiple decades because what sometimes can be confusing is the current state of the art, thesis papers (PhD students are struggling to learn it the first time too, but often they hold the complete supporting material with references), and the original paper for the field. A lot of those papers are struggling to explain the new concept so they draw more analogies and you…

It is also important to look for primers from multiple decades because what sometimes can be confusing is the current state of the art, thesis papers (PhD students are struggling to learn it the first time too, but often they hold the complete supporting material with references), and the original paper for the field. True, but the fly-in-the-ointment here is that sometimes notation changes over the years, and compar…

That should have read:

... comparing papers / textbooks across decades can add even ...

Re: The Mathematics Autodidact’s Aid (2005) [pdf]

#50

Post by Chris2048 »

medymed wrote: post #8
MichaelMoser123 wrote: post #5

maybe i am just stupid, but I find that many texts in mathematics like to skip over details, or I get stuck because there is an ambiguity in the text and there is no one to ask about it.. What do we do in this kind of situation?

One approach is to look at a few different but overlapping primers on the same matter and do the exercises. If one treatment doesn't click, another might. And for well-known subjects, topics are often covered in roughly the same order. Maybe not for graduate classes, not sure, but linear algebra, set theory, group theory, analysis it's generally the case. Unless you can afford a tutor to teach it several different wa…

perhaps one approach to this is a wiki linking to different approaches for describing the same concepts?

Plus, there are enough old math books (out of copyright) to just include scans directly. I actually collect math books, have a few infitesimal calculus books even.

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