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My question is very elementary, but I hope that you will endure it.

I am currently in a CS Master's program and I notice that my skills in mathematics are lacking. My calculus course was 10 years ago. I know I can take remedial courses, but I was hoping to do some self study to learn mathematics because it is something that I have always wished to understand, just never had a lot of time nor knew exactly what order in which to learn topics.

What books could anyone recommend that would take me from College Algebra to Calculus and anything beyond.

Also, does anyone know a hierarchical structure of all mathematical fields?

Thanks, xeralti

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can you mention what is your end goal? –  Vikram Aug 21 '13 at 11:53
    
Sure. I am currently in a CS Master's program and I notice that my skills in mathematics are lacking. My calculus course was 10 years ago. I know I can take remedial courses, but I was hoping to do some self study to learn mathematics because it is something that I have always wished to understand, just never had a lot of time nor knew exactly what order in which to learn topics. –  xeralti Aug 21 '13 at 12:05
    
For theoretical computer science, perhaps you should look at books on discrete mathematics, logic, group theory, coding theory, finite-state machines, rings and fields, boolean algebra, combinatorics, graph theory, etc. –  Joel Reyes Noche Aug 21 '13 at 13:04
    
@xeralti, since you are in master's program, why can't you refer to the graduate program books(the one which you used while getting the degree)?, the books that I have mentioned are if you are self learning for the first time and they are the starting point(I doubt you would like to refresh from the starting point), if you already have done it properly in past then (mostly) any book can help you refresh things. –  Vikram Aug 21 '13 at 13:25
    
I have the Calculus book that I had during undergraduate studies; however, it does not cover some of the areas that the courses I am taking now need. Some of the big areas I need are linear algebra, calculus, and probabilities with calculus. I still want to stress that I have always wished to have a great handle of mathematic concepts, just not known where to start. –  xeralti Aug 21 '13 at 13:33

4 Answers 4

If you didn't save your books, the Dover book series is a great and inexpensive way to get started, as you can find many of the books used on Amazon.
If you did save them, just go back and rework the problems, but pay extra special attention to the proofs. I am currently doing that while I look for a full time job and it's really helping my overall understanding of math as a whole.

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Mathematical Classifications

Book References on MSE

Web Resources

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Excellent, Amzoti! (+1) –  amWhy Aug 21 '13 at 15:58
    
@amWhy: Thank you! Have a great day! :-) –  Amzoti Aug 21 '13 at 16:03

You should really define your goal better. Here are some suggestions, with links to amazon.

Mathematics and physics for programmers by Danny Kodicek, this if you are interested in game programming: http://www.amazon.com/Mathematics-Physics-Programmers-Charles-Development/dp/1584503300/ref=sr_1_15?s=books&ie=UTF8&qid=1377089245&sr=1-15&keywords=mathematics+for+computer+science

Comprehensive mathematics for computer scientist, volume 1 and 2, by Guerino Mazzola, Gérard Milmeister and Jody Weissmann. This includes a lot of topics from which to pick and choose! http://www.amazon.com/Comprehensive-Mathematics-Computer-Scientists-Universitext/dp/3540208615/ref=sr_1_18?s=books&ie=UTF8&qid=1377089385&sr=1-18&keywords=mathematics+for+computer+science

Concrete mathematics, A foundation for computer science, by Ronald Graham, Don Knuth and Oren Patashnik. This is useful for analysis of algorithms, and a lot of fun. Really calculus one with integrals replaced by sums. http://www.amazon.com/s/ref=sr_pg_2?rh=n%3A283155%2Ck%3Amathematics+for+computer+science&page=2&keywords=mathematics+for+computer+science&ie=UTF8&qid=1377089202

Geometric algebra for computer science: an object-oriented approach to geometry. By Leo Dorst, Daniel Fontijne and Stephen Mann. This is a new approach to geometry, giving a good basis for making geometry problem solving more algorithmical! Fun and interesting. http://www.amazon.com/Geometric-Algebra-Computer-Science-Revised/dp/0123749425/ref=sr_1_31?s=books&ie=UTF8&qid=1377089757&sr=1-31&keywords=mathematics+for+computer+science

Phase change: the computer revolution in science and mathematics, by Douglas S Robertson. This is another kind of book, and a very important one, discussing in which ways the computer revolution is changing science and mathematics! Read this one. http://www.amazon.com/Geometric-Algebra-Computer-Science-Revised/dp/0123749425/ref=sr_1_31?s=books&ie=UTF8&qid=1377089757&sr=1-31&keywords=mathematics+for+computer+science

Digital dice: computational solutions to practical probability problems, by Paul J Nahin. Fun!!!! http://www.amazon.com/Geometric-Algebra-Computer-Science-Revised/dp/0123749425/ref=sr_1_31?s=books&ie=UTF8&qid=1377089757&sr=1-31&keywords=mathematics+for+computer+science

I stop the list here, having avoided the pure drill books. There are a lot more good books out there, you should really indicate your area of interest if none of this suit you.

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  1. Calculus - Thomas and Finney
  2. Linear algebra - William Gareth or David Lay for gentle introduction and then any Set, Logic and proof strategy book (Daniel Solow or Richard Hammack) plus Friedberg or Artin
  3. Multi variate Calculus - R C Buck or C H Edwards
  4. Real Analysis - Terrence Tao (I am not sure if you need to know this subject throughly)
  5. Matrix Computations - Golub
  6. ODE - M Braun
  7. PDE - Farlow
  8. Prob and statistics - (depending on "Calculus based" or "not calculus based" books differ, not sure which one you need)
  9. Numerical Recipes (Cambridge Publication)

I am myself using the above mentioned books for self study but for a different track/goal.

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