Exercises in Algebra: A Collection of Exercises in Algebra, Linear Algebra and Geometry

Algebra becomes clearer through practice: following a proof is one thing; deciding how to begin a problem is another. Exercises in Algebra gathers problems across higher algebra, linear algebra and geometry, moving from foundational tools to more abstract structures.

Edited by Alexei I. Kostrikin, the collection is arranged in three parts that reflect a broad university-level course. Its range makes it useful for working through a topic systematically or returning to a specific area for focused practice.

From equations to algebraic structures

The opening part develops foundations through sets and maps, linear equations, determinants, matrices, complex numbers and polynomials. The next part turns to vector spaces, bilinear and quadratic functions, linear operators, metric spaces, tensors, and affine, Euclidean and projective geometry. The final part takes up groups, rings, fields and elements of representation theory.

Practice with room to stretch

The preface describes a collection shaped by university seminar teaching, with standard exercises alongside more demanding problems. That mix gives students a way to consolidate familiar methods while also meeting questions that call for deeper work. Hints and answers are provided, and selected theoretical material, definitions, notation and an index round out the volume.

For serious mathematics study

This is a substantial exercise collection for students studying higher algebra, linear algebra or geometry, as well as instructors seeking problems for seminars. Its breadth also makes it a useful reference point when moving between related subjects—from matrix calculations and polynomial questions to groups, rings and representations.

For readers who want mathematics not only explained but actively worked through, this volume offers plenty of problems to think with.