Algebraic Topology

Algebraic Topology is a textbook that covers the basics of surface theory, group theory, the fundamental group, and homology. It is designed for advanced high-school students and assumes no background in abstract algebra or real analysis. It contains many examples and exercises and can be used for self-study or as an introductory undergraduate topology course.

Format: Paperback / softback
Length: 209 pages
Publication date: 20 June 2021
Publisher: Springer Nature Switzerland AG

Algebraic Topology is a comprehensive textbook designed for advanced high-school students attending the Stanford University Mathematics Camp (SUMaC). Authored by experienced instructors, this textbook serves as an introductory guide to the field. Each chapter, or lecture, corresponds to a day of instruction at SUMaC, ensuring a thorough and systematic coverage of the subject matter.

The book begins with the necessary preliminaries for formally defining a surface, laying the foundation for subsequent discussions. The text then delves into various topics, including surface classification, group theory, the fundamental group, and homology.

One of the key strengths of this book is its accessibility. It assumes no prior knowledge in abstract algebra or real analysis, presenting these subjects as needed within the text. This makes the book suitable for undergraduates or high-school students who may not have the typical background in algebraic topology. The book is filled with numerous examples and exercises, enabling self-study and serving as a valuable resource for an introductory undergraduate topology course.

By offering a comprehensive and approachable introduction to algebraic topology, this textbook serves as an invaluable tool for students eager to explore this fascinating branch of mathematics.

Weight: 388g
Dimension: 156 x 234 x 28 (mm)
ISBN-13: 9783030706074
Edition number: 1st ed. 2021