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89543391
Volume 2: Counting (Rigorous Elementary Mathematics, Second Edition)
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Barang #:
89543391
IDR 456680
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- Counting is one of the four pillars of mathematical contests and olympiads. Volume 2: Counting, Second Edition builds the subject from the ground up. It contains various counting principles, including bijections, casework, complementary counting, combinatorial multiplication and division, and inclusion-exclusion. For proving identities, double counting and algebraic methods are presented. Special topics include variations of the pigeonhole principle, ways of distributing balls across boxes, and graph theory with Ramsey theory. Later chapters are about probability, including the probabilistic method, recursive sequences like Fibonacci and Catalan, and linear recurrences. The final chapter forays into applications of basic group theory to combinatorics using Burnside’s lemma. The key insight of this volume is the understanding that combinatorics is about finding the cardinality of finite sets. The three recurring themes are: writing the same object in multiple ways, breaking up equality using antisymmetry, and using equivalence relations. There are dozens of substantive problems included for the reader’s practice, with complete solutions provided. This second edition includes additional theorems and problems, refreshed diagrams, and corrections. It is suggested that the book be read by students and teachers who have prior experience with mathematical proofs and problem-solving.
| Publisher | Existsforall Academy Inc. |
| Publication date | June 8, 2026 |
| Language | English |
| Print length | 185 pages |
| ISBN-10 | 1738950190 |
| ISBN-13 | 978-1738950195 |
| Item Weight | 1.26 pounds (570 grams) |
| Dimensions | 8.27 x 0.42 x 11.69 inches (21 x 1.1 x 29.7 cm) |
| Book 2 of 5 | Rigorous Elementary Mathematics, Second Edition |
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Volume 2: Counting (Rigorous Elementary Mathematics, Second Edition)
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IDR 456680
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