Learning math effectively

Many students face with problems and serious difficulties when they start learning mathematics. Of course, we can name hundreds of reasons but let’s try to be laconic and underline the main aspects of this phenomenon.

Firstly, math is not a subject that can be simply memorized by repeating formulas again and again. The same math concepts, theorems and techniques can be used to solve completely different problems and there is no ready-to-use template for every specific task. It is not enough for you just to know the theorem – you need to understand every detail, every step of a proof. Every time when you hear something new, you should ask yourself "why so?".

Reasoning is very important for understanding and it brings interest to your studying. You may even try to predict theorems and statements which will be revealed in your next lecture notes. This will bring you deep understanding of mathematical principles. One more important thing is to feel connection between theoretical and practical knowledge you obtain. Sometimes while applying algorithms you have studied for solving different problems you don’t see their connection with theoretical materials you have learnt before. It is very important to be capable to apply theory in practice.

However, pure mathematics is not enough for solving real-life problems. Mathematical apparatus is only a tool for modeling real processes. If you want to solve practical problems you should additionally know some programming languages, computational engines, quantitative techniques. A lot of mathematical forums and websites require using LaTeX language for typing formulas. It can be quite useful for students searching for help in the Internet.  

And the last but one of the most important things is self-education. Lectures give poor knowledge with limited number of notions. But when you need to understand others mathematical notions and expressions you should read additional literature. It is important to learn standard notations of mathematical objects. When you follow all the steps mentioned above and you have finally become a good expert in some branch of math, it is a very nice experience to write new or edit existing articles about math in web. In some universities teachers make their students to publish new articles on Wikipedia. This is a good idea because when you share your knowledge and try to explain something you get deeper understanding of the material. You may also sign in in different math forums and help other people with their studying.

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