Название: Mathematics for Computer Scientists: A Practice-Oriented Approach
Автор: Peter Hartmann
Издательство: Springer
Год: 2023
Страниц: 583
Язык: английский
Формат: pdf (true)
Размер: 40.9 MB

This textbook contains the mathematics needed to study computer science in application-oriented computer science courses. The content is based on the author's many years of teaching experience.

The three parts of the book cover discrete mathematics and linear algebra, analysis including numerical methods, and finally the basics of probability theory and statistics. Within each chapter, the definitions and theorems are consecutively numbered, a second consecutive numbering in round brackets is given to formulas to which reference is later made. At the beginning of each chapter I summarize the learning objectives. At the end of each chapter you will find comprehension questions and exercises. The comprehension questions serve to quickly check understanding. After working through a chapter you should be able to answer them without much calculation. The exercises are intended to deepen and practice the presented material. Most of them can be solved on paper, some are intended for programming or need a computer algebra system. For this I use the open source tool SageMath. The exercises are mostly not too difficult; if you have completed the corresponding chapter, you should be able to solve most of the associated problems. In each chapter, you will find a weblink to the answers for the comprehension questions and to suggested solutions to the end of chapter exercises.

Textbook Features:

You will always find applications to Computer Science in this book.
Not only will you learn mathematical methods, you will gain insights into the ways of mathematical thinking to form a foundation for understanding computer science.
Proofs are given when they help you learn something, not for the sake of proving.

Mathematics is initially a necessary evil for many students. The author explains in each lesson how students can apply what they have learned by giving many real world examples, and by constantly cross-referencing math and computer science. Students will see how math is not only useful, but can be interesting and sometimes fun.

The Content:

Sets, logic, number theory, algebraic structures, cryptography, vector spaces, matrices, linear equations and mappings, eigenvalues, graph theory.
Sequences and series, continuous functions, differential and integral calculus, differential equations, numerics.
Probability theory and statistics.

The Target Audiences:
Students in all computer science-coursework, and independent learners.