Study Guide
GEOMETRY AND TOPOLOGY Textbook
PROBLEMS IN LINEAR ALGEBRA AND MATRIX THEORY
BOOKS
by Fuzhen Zhang (Nova Southeastern University, USA)
LECTURES ON ALGEBRAIC TOPOLOGY
by Haynes Miller (Massachusetts Institute of Technology, USA)
This is the revised and expanded edition of the problem book Linear Algebra: Challenging Problems for Students, now entitled Problems in Linear Algebra and Matrix Theory. This new edition contains about fifty-five examples and many new problems, based on the author’s lecture notes of Advanced Linear Algebra classes at Nova Southeastern University (NSU-Florida) and short lectures Matrix Gems at Shanghai University and Beijing Normal University.
Algebraic Topology and basic homotopy theory form a fundamental building block for much of modern mathematics. These lecture notes represent a culmination of many years of leading a two-semester course in this subject at MIT. The style is engaging and student-friendly, but precise. Every lecture is accompanied by exercises. It begins slowly in order to gather up students with a variety of backgrounds, but gains pace as the course progresses, and by the end the student has a command of all the basic techniques of classical homotopy theory.
The book is intended for upper division undergraduate and beginning graduate students, and it can be used as text or supplement for a second course in linear algebra. Each chapter starts with Definitions, Facts, and Examples, followed by problems. Hints and solutions to all problems are also provided.
Contents: Singular Homology; Computational Methods; Cohomology and Duality; Basic Homotopy Theory; The Homotopy Theory of CW Complexes; Vector Bundles and Principal Bundles; Spectral Sequences and Serre Classes; Characteristic Classes, Steenrod Operations, and Cobordism.
Contents: Vector Spaces; Determinants, Inverses, Rank, and Systems of Linear Equations; Similarity, Eigenvalues, Matrix Decompositions, and Linear Transformations; Special Matrices; Inner Product Spaces; Miscellaneous Problems; Solutions to all Problems. Readership: College/university students and instructors in mathematics, physics, statistics, computer science, etc. Upper division/ beginning graduate level.
Readership: Ideal for a beginning graduate course, aimed at students familiar with general topology and basic modern algebra; also good for researchers who need to use the methods of algebraic topology, in mathematics at large and in theoretical physics.
460pp Nov 2021 978-981-123-979-3 US$118 £105 978-981-123-908-3(pbk) US$58 £50
300pp Oct 2021 978-981-123-124-7 US$98 £85 978-981-123-285-5(pbk) US$48 £40 16
Advance Book Information • September – October 2021
