Matroids: A Geometric Introduction

Matroid theory is a vibrant area of research that provides a unified way to understand graph theory, linear algebra and combinatorics via finite geometry. This book provides the first comprehensive introduction to the field which will appeal to undergraduate students and to any mathematician interested in the geometric approach to matroids. Written in a friendly, fun-to-read style and developed from the authors' own undergraduate courses, the book is ideal for students. Beginning with a basic introduction to matroids, the book quickly familiarizes the reader with the breadth of the subject, and specific examples are used to illustrate the theory and to help students see matroids as more than just generalizations of graphs. Over 300 exercises are included, with many hints and solutions so students can test their understanding of the materials covered. The authors have also included several projects and open-ended research problems for independent study.

1. A tour of matroids; 2. Cryptomorphisms; 3. New matroids from old; 4. Graphic matroids; 5. Finite geometry; 6. Representable matroids; 7. Other matroids; 8. Matroid minors; 9. The Tutte polynomial; Projects; Appendix: matroid axiom systems; Bibliography; Index.

Gary Gordon is a Professor in the Mathematics Department at Lafayette College, Pennsylvania.
Jenny McNulty is a Professor in the Department of Mathematical Sciences at the University of Montana, Missoula.