Gareth A. Jones Knihy

This text is an elementary introduction to information and coding theory. The first part focuses on information theory, covering uniquely decodable and instantaneous codes, Huffman coding, entropy, information channels, and Shannon’s Fundamental Theorem. In the second part, linear algebra is used to construct examples of such codes, such as the Hamming, Hadamard, Golay and Reed-Muller codes. Contains proofs, worked examples, and exercises.

This book aims to provide an elementary introduction to number theory that requires minimal mathematical background, allowing readers to engage with the material independently. The initial chapters are grounded in A-level mathematics, while subsequent ones introduce basic group theory. Advanced topics, including recent developments, are covered in the final chapters, necessitating some familiarity with first-year undergraduate mathematics concepts. The authors prioritize clarity and thorough explanations, featuring numerous worked examples and outline solutions for exercises. Number theory is chosen for its rich history and significant contributions from renowned mathematicians, making it an excellent lens through which to explore the evolution of mathematics, including its successes and failures. The explicit nature of number theory's problems, which focus on fundamental properties of integers, renders it particularly accessible for presenting modern mathematical concepts in an elementary fashion.