# Introduction

Mathwiki is a self-study environment, which consist, at the moment, of six topics:
asymptotics,
divisibility and modular arithmetics,
finite fields,
linear algebra,
number theory,
probability theory.

These topics are the ones which most often are needed by students of informatics in their studies. For example, asymtotics for comparing performances of algorithms or programs (time efficiency, memory efficiency). Or modular arithmetics and finite field theory which teach us how to operate with bits - the basic building blocks of all programs. The understanding of bit-wise operations and their properties gives additional ways of creating better programs and computer systems. Probability theory gives us tools for analyzing risks of information systems and computers related security.

Actually, the list of math knowledge needed in order to be a very good computer scientist, can not be limited to any list. And also the selected topics here are just a start.

How to use Mathwiki?

The topics are ordered alphabetically, and can be studied in any order. However, the topics are not completely independent of each other. Sometimes within a topic you can find the suggestion to read another topic before continuing. These suggestions are there for a reason: you may not understand the topic fully if you skip the suggested topic.

• Each topic consist of lessons. These lessons are meant for reading in the order they have been listed there.
• For moving on to the next lesson, you can use the link at the bottom the lesson.
• For moving back to any lesson you have always visited on the present day, you can use TRACE bar at the top.
• Each lesson contain several exercises which help you to understand the theory and lesson properly - do as many exercises as possible by yourself.
• Most of the exercises are equipped with an example solution (opened by clicking on the word “solution”). Check the solution only after you yourself have solved the exercise.
• As you know, there are mostly several ways of solving one and the same exercise. So, if your solution is different from the one give here, it does not mean its wrong.
 …… denotes definitions, import results and conclusions …… denotes a usual exercises or tasks meant for solving by the reader …… denotes a theory quiz, i.e. a important result in the corresponding theory meant to investigate by the reader

Authors:

Jaan Vajakas
Aleksei Lissitsin
Marje Johanson
Sven Laur
Dominique Unruh
Peeter Laud 