Combinatorial and Algorithmic Mathematics

Detailed review of optimisation from first principles, supported by rigorous maths and computer science explanations and various learning aids.

Supported by rigorous maths and computer science foundations, Combinatorial and Algorithmic Mathematics: From Foundation to Optimization provides a from-scratch understanding of the field of optimisation. It discusses 70 algorithms with roughly 220 illustrative examples and 160 non-trivial end-of-chapter exercises, with complete solutions to ensure readers can apply appropriate theories, principles, and concepts when required. The book also includes Matlab codes that solve specific problems, helping readers to develop mathematical maturity, including skills such as handling increasingly abstract ideas, recognising mathematical patterns, and generalising from specific examples to broad concepts.

Starting from first principles of mathematical logic, set-theoretic structures, and analytic and algebraic structures, this book covers both combinatorics and algorithms in separate sections, then brings the material together in a final section on optimisation. This book focuses on topics essential for anyone wanting to develop and apply their understanding of optimisation to areas such as data structures, algorithms, artificial intelligence, machine learning, data science, computer systems, networks, and computer security.

Combinatorial and Algorithmic Mathematics includes discussion on:

• Propositional logic and predicate logic, set-theoretic structures such as sets, relations, and functions, and basic analytic and algebraic structures such as sequences, series, subspaces, convex structures, and polyhedra.
• Recurrence-solving techniques, counting methods, permutations, combinations, arrangements of objects and sets, and graph basics and properties.
• Asymptotic notations, techniques for analysing algorithms, and computational complexity of various algorithms.
• Linear optimisation and its geometry and duality, simplex and non-simplex algorithms for linear optimisation, second-order cone programming, and semidefinite programming.

Combinatorial and Algorithmic Mathematics is an ideal textbook resource for students studying discrete structures, combinatorics, algorithms, and optimisation. It also caters to scientists across diverse disciplines that incorporate algorithms and academics and researchers who wish to better understand some modern optimisation methodologies.