Finite And Discrete Mathematics

Discrete mathematics has now established its place in most undergraduate mathematics courses. This textbook provides a concise, readable and accessible introduction to a number of topics in this area, such as enumeration, graph theory, Latin squares and designs. It is aimed at second-year undergraduate mathematics students, and provides them with many of the basic techniques, ideas and results. It contains many worked examples, and each chapter ends with a large number of exercises, with hints or solutions provided for most of them. As well as including standard topics such as binomial coefficients, recurrence, the inclusion-exclusion principle, trees, Hamiltonian and Eulerian graphs, Latin squares and finite projective planes, the text also includes material on the ménage problem, magic squares, Catalan and Stirling numbers, and tournament schedules.

SYMMETRY AND GEOMETRY. One of the core concepts essential to understanding natural phenomena and the dynamics of social systems is the concept of “relation”. Furthermore, scientists rely on relational structures with high levels of symmetry because of their optimal behavior and highperformance. Humanfriendships, socialandinterconnectionnetworks, trafficsystems, chemical structures, etc., can beexpressed asrelational structures. A mathematical model capturing the essence of this situation is a combinatorial object exhibiting a high level of symmetry, and the underlying mathematical discipline is algebraic combinatorics—the most vivid expression of the concept of symmetry in discrete mathematics.