Embark on an illuminating journey through the landscape of college mathematics with Putnam and Beyond. Authored by Răzvan Gelca, this 2nd edition, published by Springer on October 3, 2017, delves into pivotal concepts across polynomials, linear algebra, real analysis, differential equations, coordinate geometry, trigonometry, elementary number theory, combinatorics, and probability. The preliminary sections offer a foundational understanding of proof techniques such as contradiction, induction, the pigeonhole principle, ordered sets, and invariants. Each chapter meticulously explores a distinct subject, with problems grouped by topic within each section. The exposition is enriched by nearly 1300 problems and examples sourced globally, many of which are original contributions, with citations for sources, authors, and historical context provided where applicable. Comprehensive solutions are included at the end of the book. This revised edition features new sections on quadratic polynomials, curves in the plane, quadratic fields, combinatorics of numbers, and graph theory, alongside expanded problems and theoretical content on polynomials, matrices, abstract algebra, limits of sequences and functions, derivatives and their applications, Stokes’ theorem, analytical geometry, combinatorial geometry, and counting strategies.

ISBN-10: 3319589865
ISBN-13: 978-3319589862