How do I become better in math, after being a programmer for several years [duplicate]_问答_开发者

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How to improve my math skills to become a better programmer
Basic Math Book for a Programmer

I've had quite a weird career till now. First I graduated from a medical school. Then I went into marketing (pharmaceuticals). And then umm, after some time, I decided to go for my (till then) hobby and became a "professional" programmer. I've been quite successful at this ever since. I have quite some languages "under my belt". I earn not bad and I have been involved in the opensource community quite heavily.

The thing is that I suck at math :). Well, not totally of course, as I get my work done. But I don't know how much I suck. And I don't know how to find out.

Math has never really been of any priority during my middle/high school years. I only picked as little as I could afford, because I was always getting ready to go for Medicine. Of course I know the basics of algebra. Things like "normal" and square equations. Also the basics of geometry. But well, there are things that I have missed. And lately I am being fascinated by things like probability theory, infinity, chaos/order etc. But every time I try to learn something about these topics, I hit a wall of terminolog开发者_运维知识库y, special symbols, and some special kind of thinking, that is quite like mine (a programmer), but also a lot different (and appears weird to me).

So, what kinds of books would you recommend me? It's very hard to find something suitable. All that I find are either too easy (and boring) or totally impenetrable.

Assuming you have your basic algebra down, I'd start with single variable calculus. I've used several calc books, and found Larson's to be the best. Hope you can find it at a library.

Move on to linear algebra shortly after. This book is free and very good.

Don't worry about mastering everything, you'll probably want to come back to linear algebra.

Then find a book that emphasizes proofs, sets, relations, functions, and axioms. I liked Analysis with an introduction to proof by Lay. Learn proof by induction especially well.

From here, you should be able to break that impenetrable wall you've found yourself against. You will be armed with the terminology to read just about any undergraduate mathematics textbook.

I recommend graph theory, combinatorics, and linear algebra, for their applications in computer science.

Good luck!

Of course I know the basics of algebra. Things like "normal" and square equations. Also the basics of geometry. But well, there are things that I have missed. And lately I am being fascinated by things like probability theory, infinity, chaos/order etc.

I find that mathematics is a one-way door: if you don't get through early, it's hard to go back. It's not impossible to pick up, but it is more difficult without discipline.

The key is doing problems. You don't just read math books - you do problems to work the mechanics into your brain. If you're just reading, I'd say it's impossible to learn it.

Best to go back to what you know and work up. If you feel okay about basic algebra and geometry, start thinking about intro calculus or statistics. Start with the basic stuff: one variable differential and/or integral calculus or statistics. Do a lot of problems and get comfortable.

If you're a computer scientist, you'll find discrete math, graphs, numerical methods, and linear algebra helpful.

Don't expect to do it quickly, especially if you're casual about it.

I'd recommend two wonderful resources:

Verzani - Using R for Introductory Statistics
Gil Strang MIT Linear Algebra

Both are free; both are excellent.

You might check out some of the free course material available online from MIT.

The basics:

Basic understanding of real and complex numbers, functions, sets etc.
(Real) analysis in one variable
(Real) linear algebra
(Real) analysis in several variables
Discrete mathematics
Vector calculus
Complex analysis
Complex linear algebra
Statistics and probability theory

More advanced stuff:

Abstract algebra
Fourier analysis (much more important than one may think) (Basic video course from Stanford)
Transform theory (other than Fourier analysis)
Differential geometry
Functional analysis
Partial differential equations
Non-linear phenomena and chaos

Investigate available math classes at a local junior college. Typically, they offer them during the day for enrolled students but they sometimes have night classes as well. Talk to the professor to see if your math skills are sufficient for the class before enrolling, however, or you'll be struggling right out of the gate.