The Math Tutor material is arranged according to topics and points of view that correspond to different needs of students.


Points of view.

Math Tutor can be used for instance like this: If you have troubles with understanding the notions, Theory with its explanatory remarks could help. You can also find there explanation of methods that are basic in the area and that form building blocks for further understanding and applications. Basically you find there everything you need to know before you start solving problems.

If you have a feeling that you have some idea what is going on, but have trouble with practical application of your knowledge, try Methods Survey. Here we attempt to systematize knowledge, from mastered basic methods we develop algorithms for solving specific types of problems. For instance, if you are studying integrals, it is assumed that when reading Methods Survey, you already know how to perform (mechanically) substitution, integration by parts and partial fractions decomposition (they are covered in Theory); this knowledge is then applied to various types of integral.

Solved problems are really useful if you already know something about the methods (best if you have already learend the material in Methods Survey), so when you are reading a solution, you can compare the chosen procedure with what you learned theoretically.

Exercises are chosen to cover typical problems of varying difficulty. It is strongly recommended that you first attempt to solve them on your own. You learn best if you first try to solve a problem, and only after finishing the calculation (or getting stuck) ask what to do (the frustration and other strong emotions will then etch the solution in your memory). If you do not have enough time, it may still help if you just loook at a problem, think of the method you would apply and then check whether you were correct; in this way you will strengthen the association between types of problems and corresponding methods.