Linear Algebra A Problem–Centered Approach

Determinants, matrices, and systems of linear equations begin the book. This unique ordering offers insights from determinants early on, while also admitting re-ordering if desired. Chapters on vector spaces, linear maps, and eigenvalues and eigenvectors follow. Bilinear functions and Euclidean spaces build on the foundations laid in the first half of the book to round out the core material. Applications in combinatorics include Hilbert's third problem, Oddtown and Eventown problems, and Sidon sets, a favorite of Paul Erdős. Coding theory applications include error-correction, linear, Hamming, and BCH codes. An appendix covers the algebraic basics used in the text.
Ideal for students majoring in mathematics and computer science, this textbook promotes a deep and versatile understanding of linear algebra. Familiarity with mathematical proof is assumed, though no prior knowledge of linear algebra is needed. Supplementary electronic materials support teaching and learning, with selected answers, hints, and solutions, and an additional problem bank for instructors.
Readership
Undergraduate students interested in linear algebra; instructors seeking linear algebra problems for active learning.