The Elements of Advanced Mathematics

The book emphasizes the art of proof, presents unsolved problems in number theory, revises the discussion of equivalence relations, and expands the coverage of the RSA cryptosystem. It also introduces groups earlier as an example of an axiomatic theory.

Format: Hardback
Length: 296 pages
Publication date: 03 June 2022
Publisher: Taylor & Francis Ltd

Rewritten text:

The book emphasizes the art of proof, presenting a comprehensive and engaging exploration of mathematical concepts. The enhanced number theory chapter offers a selection of easily accessible yet challenging problems, including the renowned Goldbach conjecture, the twin-prime conjecture, and numerous other intriguing puzzles.

In the revised discussion of equivalence relations, the author introduces reflexivity, symmetry, and transitivity before defining equivalence relations. This approach ensures a solid foundation for understanding the concept of equivalence relations.

Chapter 10, on the RSA cryptosystem, has been expanded to provide a more detailed and comprehensive explanation of this important cryptographic technique. The author also introduces groups earlier in the book, utilizing them as an insightful example of an axiomatic theory. The coverage of group theory, previously located in Chapter 11, has been moved up to align with this revised structure.

By emphasizing the art of proof, presenting challenging problems, and introducing fundamental concepts such as equivalence relations and groups, this book offers a comprehensive and rigorous introduction to mathematics. Whether you are a student, professional, or enthusiast, this book will provide you with valuable insights and skills for further mathematical exploration.

Weight: 740g
Dimension: 234 x 156 (mm)
ISBN-13: 9781032102757
Edition number: 5 ed