Beginning with math

Question

I am studying computer science since 3 years now. It is really math heavy and I like it. However the problem that I have is that I never really had math in school it was too basic and I lack some important knowledge.

The first year at my university I had so many courses that I skipped the "Analysis" course. We have basically only two courses Analysis and Linear Algebra.

Now all other courses build on the math courses and it was really hard for me. But I managed to get though somehow with decent marks.

Now I am taking the Analysis course again and I am struggling. I mean I even have big problems with transformations.

I can not learn math just from listening to it is just not possible for me. I need to solve problems by myself. I can learn many programming languages without writing a single line of code and still read 1000 sites without getting into trouble. But this is not possible in math.

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I would need something that fills my lack of knowledge. Maybe I should start with the basics again. I also tried kahnacedemy but the generated math problems are just too basic and don't really help me much.

I really want to get my hands dirty, what would you recommend me to do and where should I start?

Answer 1

A short (but might be helpful) answer is to consult the MIT open-course site: I'll link you to Analysis I, which has supplementary notes and problem sets with solutions, for practice, etc. Feel free to scope out the calculus sequence at MIT, too, for background (refreshing your calculus skills). This will give you both support material (to read), and problem-sets (to DO!).

• Here is the MIT "menu" of math classes available through MIT's OCW. You'll also find linear algebra, e.g.

• See also Wikipedia's entry for Open Course Ware: there are links to universities and resources that are available (free of charge) to the public at large. You can scope them out, in terms of what's available mathematically, to see if one or more of the resources might be helpful.

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That said, do not feel you "aren't good at math" simply because you find that you have to solve problems (and can't simply "read" it) to understand it. That's true for most of us:

"Math is not a spectator sport".

So your eagerness to get your "hands dirty" is exactly what you (and I venture to guess, all of us,) need to do to master math (along with patience, persistence, and practice).

Answer 2

Go to the library with a sheet of paper and a pen. Pick up a copy of Tom.M Apostol and bury yourself in the book. It comes with exercises: do most of them. Understand every proof you come upon. If you want to learn anything about mathematics you need to do it for yourself. Just reading is useless. Another great book is introduction to calculus and analysis by Courant. Remember If you have read through a page and haven’t stopped to think or written anything down you are most likely doing something wrong. Hope this helps.

I am reading a book called basic linear algebra and linear algebra done right.

Links to the books:

http://books.google.com.mx/books?id=vTpbq0UPDaQC&dq=apostol+calculus+volume+1&hl=en&sa=X&ei=Z4HcULCcOLL02wW784DgBQ&ved=0CDEQ6AEwAA

http://books.google.com.mx/books?id=-Oh3MQEACAAJ&dq=courant+calculus&hl=en&sa=X&ei=jIHcUL74BYKi2QX00oC4Bg&ved=0CDgQ6AEwAg

http://books.google.com.mx/books/about/Basic_Linear_Algebra.html?id=40HnLsET7OEC&redir_esc=y

http://books.google.com.mx/books?id=ovIYVIlithQC&printsec=frontcover&dq=linear+algebra+done+right&hl=en&sa=X&ei=P4HcUPy-LIrm2QWop4GIDw&ved=0CDYQ6AEwAA

Answer 3

This set of free lecture notes, transcribed virtually verbatim, by Fields Medal winner (in case you are not familiar, it's the equivalent of a Nobel prize) Vaughan Jones on real analysis is excellent for what you are looking for.

It is self-contained, building on what has been clearly presented along the way. Needless to say, his treatment of the material is full of insights, giving you an intuitive grasp of the material.

You can download here:

https://sites.google.com/site/math104sp2011/lecture-notes