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I have only recently discovered an interested in mathematics and I could only take a year off work to be back at school. Needless to say, for financial reasons (couple of mortgages) I will need to return to work soon. Luckily though, I will be setting up a nice office with whiteboard etc to do some serious thinking in!

I have found some examples as well as a lot of resources for first and second year courses, though by time I return to work basically any 2nd year math class that my university offers as well as most of the third year ones I will have taken.

I know there are a ton of math professors on here, so I'm wondering if anyone can recommend a good textbook for learning.

  • PDE (never done, save for some physics related stuff)
  • Topology (never done but I am extremely interested in this topic)
  • Complex Calculus (complex being imaginary numbers)
  • Abstract Algebra (done second year only)
  • Chaos (done intro only)
  • Advanced ODE

As well as any other texts/books you find interesting (Graph theory etc) most things involving logic I find very intriguing basically anything but statistics.

I will have also completed a third year level analysis course so hopefully I can get through the math language. That being said, as dummy-proof of a layout as possible is preferred. Anyone out there that happens to have some material lying around to a related course that wouldn't mind emailing it to me or leaving there website below so I could steal some assignments and solutions I would really appreciate that as well. Most stuff I find on the internet isn't at the 3rd/4th year undergraduate level.

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    $\begingroup$ Complex Numbers A to Z is a great book . $\endgroup$ – Inceptio Mar 25 '13 at 9:06
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    $\begingroup$ Look at the lecture notes and excercises at OCW, check out Coursera. William Chen's lecture notes for first/second year are nice. $\endgroup$ – vonbrand Mar 25 '13 at 14:29
  • $\begingroup$ ramanujan.math.trinity.edu/wtrench/texts/… Real Analysis Textbook $\endgroup$ – Faust May 4 '13 at 20:25
  • $\begingroup$ math.psu.edu/katok_a/TOPOLOGY its not the one linked below but its a free res has some hw prblms as well by author Topology txtbook $\endgroup$ – Faust May 8 '13 at 5:23
  • $\begingroup$ What book did you use for your analysis course? $\endgroup$ – Austin Stromme Jul 23 '14 at 23:22
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1, PDE : PDE by Fritz John

  1. Topology : Basic topology by Armstrong

  2. Complex Calculus : Complex analysis by T W Gmaelin

  3. Abstract Algebra : Topics in algebra by herstein , Abstract algebra by dummit and foote

  4. ODE and Chaos : Differential equations, dynamical systems, and an introduction to chaos by Hirsch , DE with historical notes by simmons

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