Combinatorics Modeling Elementary Number Theory
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Combinatorics, Modeling, Elementary Number Theory
"A unique textbook devoted to introductory combinatorics, modeling and elementary number theory It is relatively simple to use in the classroom: 1 Chapter is designed for 2 weeks, and the notes can be provided designed for remote teaching or to display in the classroom Some of the advanced topics are good for research projects; the most popular ones in the author's classes were dimers, modeling tree growth, Magic squares and Pisano periods via finite fields Elementary number theory is exposed systematically (with complete proofs and good ones) An impressive collection of about 135 problems and 270 exercises (mostly with hints and answers) It contains a lot of history of mathematics and the games of chance, and many topics traditional in recreational mathematics The book also serves motivated high-school students, teachers of mathematics, and specialists in neighboring fields interested in combinatorics and its applications"--
Combinatorics, Modeling, Elementary Number Theory
Author: Ivan Cherednik
language: en
Publisher: World Scientific Publishing Company
Release Date: 2023
"A unique textbook devoted to introductory combinatorics, modeling and elementary number theory It is relatively simple to use in the classroom: 1 Chapter is designed for 2 weeks, and the notes can be provided designed for remote teaching or to display in the classroom Some of the advanced topics are good for research projects; the most popular ones in the author's classes were dimers, modeling tree growth, Magic squares and Pisano periods via finite fields Elementary number theory is exposed systematically (with complete proofs and good ones) An impressive collection of about 135 problems and 270 exercises (mostly with hints and answers) It contains a lot of history of mathematics and the games of chance, and many topics traditional in recreational mathematics The book also serves motivated high-school students, teachers of mathematics, and specialists in neighboring fields interested in combinatorics and its applications"--
Combinatorics, Modeling, Elementary Number Theory: From Basic To Advanced
This book is mostly based on the author's 25 years of teaching combinatorics to two distinct sets of students: first-year students and seniors from all backgrounds. The prerequisites are kept to a minimum; essentially, only high school algebra is required. The design is to go quickly from zero knowledge to advanced themes and various applications with a lot of topics intended for additional reading and research projects. It contains an all-inclusive collection of 135 problems and 275 exercises with four difficulty levels: solutions, hints and answers are provided.Some themes of the book:Enumerative combinatorics and basic graph theory: Introduction to dimers, tilings, magic and Latin squares, permutations, combinations, generating functions, games of chance, random walks, binomial and Poisson distributions. Catalan numbers, their generalizations and applications, including roulette and pricing derivatives. Euler and Hamiltonian paths, linear and planar graphs, labeled trees and other topics on graphs; many of them are presented as exercises.Modeling: Linear recurrence relations, Fibonacci rabbits, population growth, tree growth, epidemic spread and reinfections, resonances and nuclear reactors, predator-prey relationships and stopping times.Elementary number theory: Residues, finite fields, Pisano periods, quadratic reciprocity, Pell's equation, continued fractions, and Frobenius coin problem. Applications to cryptography, designs and magic squares, error-correcting codes and nonattacking queens.