Mathematics for Computer Scientists

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 translation of the original German 7^th edition Mathematik für Informatiker by Peter Hartmann was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content.

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-related coursework, and independent learners.

DISCRETE MATHEMATICS AND LINEAR ALGEBRA. - Sets and mappings. - Logic. - Natural numbers, complete induction, recursion. - Some number theory. - Algebraic structures. - Vector spaces. - Matrices. - Gaussian algorithm and systems of linear equations. - Eigenvalues, eigenvectors and basis transformations. - Scalar product and orthogonal maps. - Graph theory. - ANALYSIS. - The real numbers. - Sequences and series. - Continuous functions. - Differential calculus. - Integral calculus. - Differential equations. - Numerical methods. - PROBABILITY AND STATISTICS. - Probability spaces. - Random variables. - Important distributions and stochastic processes. - Statistical methods. - Appendix.