What are the steps to learn and become fluent in Mathematics?

well, regarding math in computer science, you want to learn discrete math. Trig and geometry, while interesting, will not be of any serious help. Counting, logic, sets, arithmetic, algebra (linear algebra, matrices), statistics, and calculus (diff eq's) are the most important, probably in that order. The first four of those subjects can be understood (not mastered, but have a functional grip on) within a month. They're also a great foundation for understand what math is and how to approach further applications. They're a little more abstract and difficult to learn, but that's not due to math pre-requisites-- you can just about learn them from scratch.

Learning the history of Mathematics often gives you a deep insight into how it really works. It will at least help you appreciate what you learn even more.

Check out the sidebar over there ->. You'll find lots of free resources and more appropriate links

http://code.reddit.com/wiki/help/faqs/math#HowdoIlearnmathWheredoIstart

You say you've done a bit of programming in different languages, but how much time have you spent learning just about algorithms? That's where the crux of a good programmer really comes in, how efficiently they can solve problems, particularly when this is relevant to whether the problem can be solved in a realistic time frame. When you sit down to solve a problem, you don't want to get bogged down in the syntax of a particular language, you should be solving the problem intuitively on paper, a good programmer will then select the best language (tool) for the job.

Once you've picked up a language or two, it shouldn't be too hard for you to pick up the syntax for similar languages. Eg. C, C++, Java, C#, etc. really aren't all that different, but I still refuse to ever use Java, and if you know a couple of those, Python is fairly easy to pick up on the go, and worth learning before if you don't. If you want a challenge there, go learn something like Lisp, Haskell or Prolog, they will give you new ways of approaching problems.

Some people seem to try and learn programming from books and/or online tutorials. I have never found that particularly fun/efficient, except for learn you a haskell (haskell still confuses the hell out of me, but I'm slowly getting there). If you ever get stuck, google is your friend with finding out how to do something. Eg. I mostly use c++, there are a couple of good reference sites that just list the functions available for anything in the standard library, if I forget the syntax for something or simply don't know it, it's very easy to look it up.

There are plenty of resources on the internet for doing simple programming projects where you will both learn a lot and have a heap of fun. For example:

1. Project Euler has a bunch of maths problems (with increasing difficulty) for people to solve, most of the time you write a program to solve the problem, although occasionally you will get the whole problem out on paper, other times you will at least come up with really neat simplifications for the problems.

2. There are plenty of websites with general programming problems designed to be solved by various known algorithms. ACM contests specialise in problems like this, you can find a bunch of such problems on sites like this.

3. AI contests are a lot of fun, although sometimes quite repetitive with how awesome game trees are. My favourite of the bunch that are available are the Google AI Challenges. There should be a new contest up in a month or so, and it's usually fairly easy for people to get started in their favourite language, you communicate with the engine using standard input/output and basically get to go to town with your strategy implementation, constrained by the time limits of course.

You don't need to know a huge amount of mathematics to be a good programmer, however there are some things you really ought to know. Having said that, the more maths you do learn, the larger your toolbox for tackling problems to which you can't see a simple solution.

Learn some combinatorics, it's all about counting things (and efficiently), which is something programmers do quite often.

Learn what matrices are (they're just table's of elements with given dimensions, indexed by [row][column]), and at least the common operations (addition and multiplication), you should really try to get the idea of what the inverse of a matrix is and how that is used to solve a system of linear equations. If you want more of this, go and learn some linear algebra, a simple rule of thumb is that anybody interested in something vaguely relevant to mathematics can never know too much linear algebra.

If you ever want to do some computer graphics, with a bit of linear algebra and trigonometry, you've pretty much covered your maths pre reqs for understanding the concepts.

Well, first, there's a subreddit for this: /r/learnmath

I also strongly suggest Khan Academy for online learning. Click "do exercises" there and log in with your google or facebook credentials, and you'll be presented a set of challenges starting with basic arithmetic and moving up through calculus, in exactly the sort of progression you're looking for.

A good really basic book to start with is Arithmetic and Algebra Again. You could also try watching videos on Khan Academy. Or start with Introduction to Algebra from artofproblemsolving.com.

http://hbpms.blogspot.com/

All you need to know.

I'm an engineer, so I had to take 4 semesters of calculus. I'm a tutor for a circuits class, and I've found the biggest problem with students is their algebra skills.

I don't personally think algebra is hard, but I think that it is where people screw up the most. I would spend most of your time learning algebra. Supplement that with some trigonometry. Once you master all of that, study rates of changes and limits (essentially pre-calc).

IMO, you don't need a LOT of math for programming. I program just fine, and I don't think I've ever used calculus to program, although I'm sure the practice in calculus made me a better problem solver. It's all really arithmetic and algebra.

Programming follows a slightly different order of operations than mathematics when it comes to mult, division, powers, addition, etc. I'm not sure off the top of my head what the differences in the two are, but I remember there being something. I'm sure there are specifics to each given language too.

But, keep in mind, I've heard that pure theoretical computer scientists are essentially mathematicians. It's all about algorithms!

EDIT: Actually, now that I think about it, I had to write some programs in MATLAB to do numerical integrals and derivatives. So there's a little bit of calc, I suppose.

Could you talk more about why you think mathematics is what's holding you back in programming? If you don't mind me asking, I'm studying mathematics education and mathematical thinking and practices interest me.

Is it because of specific tasks you're trying to accomplish for projects, or is it because of some difficulty you're having in understanding in programming in a more general sense?

What situations do you find yourself in when this plateau occurs to you?

What do you usually do to try to get around the plateau?

I was in a similar boat. I'm fairly proficient in programming (I'm already a freelance programmer) and I am an undergrad in math.

The mindset in programming is breaking problems up into steps, etc. In math, the mindset is that of logical reasoning. Obviously you are familiar with that, and I'd say in some way the mindset of programming is contained in the mindset of doing math. Reasoning in math is usually more general and abstract, and I think the first step of learning math is to familiarize yourself with that, learning some mathematical theories in the process.

Start with logic: propositional logic and predicate logic. Being a programmer this should be especially good to follow. You don't even have to get that deep into it. Just learn how to use logical operators, implication, if and only if, predicates, and the universal and existential quantifiers. This should also get you used to seeing symbols.

After that you need to learn to do mathematical proofs. This is using logic to prove mathematical statements. The thing is that you'll need a topic to prove things about. I have a few recommendations: number theory, graph theory and linear algebra. You will learn to do direct proofs, proof by induction, proof by contradiction. Every theory will be based on some assumptions, and by using definitions and logic to prove theorems (logical statements about the subject) and using more theorems that are based on other theorems, the entire theory is built up.

There should be elementary books and internet resources on all the subjects I mentioned.

So learn what logic is, learn what proofs are, then learn some theory to get practice using logic and writing proofs.

This, I think is the way to learning real mathematics. Good luck.

Edit: Note that if you go the way of logic, proofs, graph theory you hardly even have to know multiplication. Math is not just about numbers, and I think my post conveys that pretty well. The way of thinking that goes with mathematics is a very healthy one I think, and it should benefit you as a programmer and a human.

Edit 2: Also learn basic set theory.

Do not think that just because schools attempt to teach mathematics linearly that it is best learned linearly. Also, do not think that this will be an easy or forgiving task. I would recommend, given your background, to start reading a discrete mathematics textbook, for example M. Rosen's is a standard (and far from the only or best one). When you get to something you do not understand (even just a line in an argument) think about it for a good bit but don't get too derailed. After this, move on to whatever topic seems interesting.

I highly doubt your programming obstruction is due to a lack of knowledge of High school algebra or trig. Its much more likely that you need exposure to abstraction. "Quest" after this.

Set theory... everything is set theory these days... nevermind... it's all algebra. Begin with the order of operations, get into the groove of substituting letters for numbers; after that... should be good to go.

Here's a simple link: <a href="http://www.math.com/school/subject2/lessons/S2U1L2GL.html">math.com</a>

There's a mindset for doing mathematics; if that is unavailable, all one can do is work the problems until the conceptual framework builds in the mind.