This book takes the reader on a journey through the world of college mathematics, focusing on some of the most important concepts and results in the theories of polynomials, linear algebra, real analysis, differential equations, coordinate geometry, trigonometry, elementary number theory, combinatorics, and probability. Preliminary material provides an overview of common methods of proof: argument by contradiction, mathematical induction, pigeonhole principle, ordered sets, and invariants. Each chapter systematically presents a single subject within which problems are clustered in each section according to the specific topic. The exposition is driven by nearly 1300 problems and examples chosen from numerous sources from around the world; many original contributions come from the authors. The source, author, and historical background are cited whenever possible. Complete solutions to all problems are given at the end of the book. This second edition includes new sections on quadratic polynomials, curves in the plane, quadratic fields, combinatorics of numbers, and graph theory, and added problems or theoretical expansion of sections on polynomials, matrices, abstract algebra, limits of sequences and functions, derivatives and their applications, Stokes' theorem, analytical geometry, combinatorial geometry, and counting strategies.Using the W.L. Putnam Mathematical Competition for undergraduates as an inspiring symbol to build an appropriate math background for graduate studies in pure or applied mathematics, the reader is eased into transitioning from problem-solving at the high school level to the university and beyond, that is, to mathematical research. This work may be used as a study guide for the Putnam exam, as a text for many different problem-solving courses, and as a source of problems for standard courses in undergraduate mathematics. Putnam and Beyond is organized for independent study by undergraduate and graduate students, as well as teachers and researchers in the physical sciences who wish to expand their mathematical horizons.
✔ Author(s): Răzvan Gelca,Titu Andreescu
✔ Title: Putnam and Beyond
✔ Rating : 4.5 out of 5 base on (45 reviews)
✔ ISBN-10: 3319589865
✔ ISBN-13: 9783319589862
✔ Language: English
✔ Format ebook: PDF, EPUB, Kindle, Audio, HTML and MOBI
✔ Device compatibles: Android, iOS, PC and Amazon Kindle
Readers' opinions about Putnam and Beyond by Răzvan Gelca
Daphne Garner
The author's writing style is so captivating; I couldn't put the book down. Every sentence was beautifully crafted, and the descriptions painted vivid images in my mind. A true literary gem.
Tasha Cobbett
I loved the powerful messages hidden within the story. The book tackled important social issues and made me ponder the world we live in. It's a must-read for everyone.
Laura Hill
The rich historical context of the book added a layer of depth that I found fascinating. It was like stepping back in time and experiencing history firsthand.
