The somewhat different math textbook: Mathematics that computer scientists (and not just them!) truly need, implemented directly on the computer in the form of small algorithms, numerical experiments, and interactive visualizations. You learn how to let the computer handle calculations while maintaining an overview of the mathematics, avoiding typical mistakes, and correctly interpreting the results. Along the way, you also learn the popular programming language Python and how to use a computer algebra system. At the same time, mathematics is not downgraded to a mere auxiliary science. The author motivates and justifies in a conversational tone with concrete examples and puzzles, encouraging the reader to participate and think along. Ideally, by the end, you not only learn something but also feel a desire for more and perhaps see mathematics in a new light. With computer science-specific applications, including those from cryptography, coding and complexity theory, as well as computer graphics. Supported by many colorful graphics, about 1000 exercises with solutions, and not least hundreds of videos where you can have the author explain what you've read once more personally. New in the second edition is particularly a chapter on continuous Fourier transformation. The chapter on information theory has been expanded to include sections on Huffman codes and arithmetic coding. Additionally, new exercises, videos, illustrations, and smaller additions have been incorporated in various places.