# Beginning with math

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.

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?

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Sit down and read, read, write, write, read again and so on. –  Sigur Dec 27 '12 at 16:17
There is a lot of good opencourseware on the internet. khanacademy should only be used if you have absolutely no idea what you're doing, or maybe if you want to form a decent intuition, but they certainly aren't enough to master a subject. MIT opencourseware is very renowned too, but the same applies here. My tip: Don't use opencourseware unless you don't understand it at all, just use a good book and make exercises. Opencourseware will waste a lot of time (for example, in explaining things you already understand). –  JohnPhteven Dec 27 '12 at 16:30

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.

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).

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Yes, Spivak is good: in terms of being a resource for self-study, there is also a solution book to accompany the text you link to. –  amWhy Dec 27 '12 at 16:35
As in 'functions'? That is certainly in Spivak, and Spivak is a good start (although that should be calculus, not analysis). Everyone struggles learning math - classmates saying they don't are full of it, and just show unfortunately typical behavior. When I started way back, a strong classmate told me: "if you see a classmate's prettier solution, just assume he copied it from a prettier book." –  gnometorule Dec 27 '12 at 16:40
Math is a thinker's game, so you don't get your hands dirty. You rather get your mind dirty. It follows that all the mathematicians have dirty minds! :-) –  Asaf Karagila Dec 27 '12 at 17:00
What would we do without you, @Asaf !? –  amWhy Dec 27 '12 at 17:02
Am I leaving? I was not informed! :-) –  Asaf Karagila Dec 27 '12 at 17:07

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.

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This looks really good, but it's very similar to my university. You'll find defentions, theroms and proofs. But how would I practice those topics? –  Maik Klein Dec 27 '12 at 18:48
@MaikKlein Here is the course webpage math.berkeley.edu/~vfr/MATH10411/index.html You can find problem sets and solutions. Also you can ask here about problems. If they are hw from your courses, be sure to indicate that and show your work or effort, which will be well received. If you are working on one of the problems, e.g., from this link you can say you are self-studying it. Good luck. –  Andrew Dec 27 '12 at 18:55

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.