Combinatorics, Modeling, Elementary Number Theory: From Basic To Advanced
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A01=Ivan V Cherednik
Author_Ivan V Cherednik
Bell Numbers
Bessel Functions
Binomial Distribution
Bridge
Catalan Numbers
Category=PBH
Category=PBV
Combinations
Combinatorics
Computer Science
Continued Fractions
Derangements
Dice
Dimers
Epidemic Spread
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Euclid Algorithm
Eulerian Circuits
Fibonacci Numbers
Finite Fields
Fission Reactors
Frobenius Coin Problem
Gauss Reciprocity
Generating Functions
Golden Ratio
Graphs
Hamiltonian Cycles
Inclusion-Exclusion Principle
Invasion Ecology
Labeled Trees
Lah Numbers
Latin Squares
Line Graphs
Lottery
Lucas Numbers
Magic Squares
Mathematical Biology
Mathematical Economics
Mathematical Finance
Modeling
Neural Networks
Newton's Binomial
Normal Distribution
Number Theory
Pascal's Triangle
Pell Numbers
Pell's Equation
Permutations
Pisano Periods
Plaquettes
Poisson Distribution
Poker
Population Growth
Pricing Options
Primitive Roots
Probabilities
Quadratic Residues
Recurrence Relations
Reinfections
Residues
Resonances
Statistical Physics
Statistics
Stirling Numbers
Tilling
Tree Growth
Product details
- ISBN 9789811265396
- Publication Date: 05 Jun 2023
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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.
