The mathematical combinatorics is a subject that applying combinatorial notion to all mathematics and all sciences for understanding the reality of things in the universe. The International J. Mathematical Combinatorics is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly, which publishes original research papers and survey articles in all aspects of mathematical combinatorics, Smarandache multi-spaces, Smarandache geometries, non-Euclidean geometry, topology and their applications to other sciences.

The Mathematical Combinatorics (International Book Series) is a fully refereed international book series with ISBN number on each issue, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly comprising 110-160 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences.

International J. Mathematical Combinatorics is a fully refereed international journal. Topics in detail to be covered are: Smarandache multi-spaces with applications to other sciences, such as those of algebraic multi-systems, multi-metric spaces; Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics; Mathematical theory on gravitational fields; Mathematical theory on parallel universes; Other applications of Smarandache multi-space and combinatorics.

Detailed review of optimization from first principles, supported by rigorous math and computer science explanations and various learning aids Supported by rigorous math and computer science foundations, Combinatorial and Algorithmic Mathematics: From Foundation to Optimization provides a from-scratch understanding to the field of optimization, discussing 70 algorithms with roughly 220 illustrative examples, 160 nontrivial end-of-chapter exercises with complete solutions to ensure readers can apply appropriate theories, principles, and concepts when required, and Matlab codes that solve some specific problems. This book helps readers to develop mathematical maturity, including skills such as handling increasingly abstract ideas, recognizing mathematical patterns, and generalizing 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 optimization. This book focuses on topics essential for anyone wanting to develop and apply their understanding of optimization 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 analyzing algorithms, and computational complexity of various algorithms Linear optimization and its geometry and duality, simplex and non-simplex algorithms for linear optimization, second-order cone programming, and semidefinite programming Combinatorial and Algorithmic Mathematics is an ideal textbook resource on the subject for students studying discrete structures, combinatorics, algorithms, and optimization. It also caters to scientists across diverse disciplines that incorporate algorithms and academics and researchers who wish to better understand some modern optimization methodologies.