Discrete mathematics

From its origins in algebraic number theory, the theory of non-unique factorizations has emerged as an independent branch of algebra and number theory.

In recent years, applied mathematics has been used in all novel disciplines of scientific development.

This Element explores the relations between dynamics and modularity on networks, emphasising the importance of time scale separation and network symmetry.

Designed for the intellectually curious, this book provides a solid foundation in basic probability in an informal style, without jargon.

A Tour Through Graph Theory introduces graph theory to students who are not mathematics majors.

"e;Among the many expositions of Godel's incompleteness theorems written for non-specialists, this book stands apart.

Monomial Algebras, Second Edition presents algebraic, combinatorial, and computational methods for studying monomial algebras and their ideals, including Stanley-Reisner rings, monomial subrings, Ehrhart rings, and blowup algebras.

Designed for advanced undergraduate and beginning graduate students in linear or abstract algebra, Advanced Linear Algebra covers theoretical aspects of the subject, along with examples, computations, and proofs.

Graph Theory: An Introduction to Proofs, Algorithms, and ApplicationsGraph theory is the study of interactions, conflicts, and connections.

Combinatorial theory is one of the fastest growing areas of modern mathematics.

Logic Colloquium '02 includes articles from some of the world's preeminent logicians.

In one sense, the problem of finding the densest packing of congruent circles in a square is easy to understand.

Graph Theory is a branch of discrete mathematics.

Fundamentals of Data Science: Theory and Practice presents basic and advanced concepts in data science along with real-life applications.

An update of the most accessible introductory number theory text available, Fundamental Number Theory with Applications, Second Edition presents a mathematically rigorous yet easy-to-follow treatment of the fundamentals and applications of the subject.

This monograph focuses on the application of the solution strategy known as branch-and-bound to problems of combinatorial data analysis.

More than 250 exercises and solutions on properties and applications of Catalan numbers, at levels ranging from recreational to research.

Algebra & Geometry: An Introduction to University Mathematics, Second Edition provides a bridge between high school and undergraduate mathematics courses on algebra and geometry.

Combinatorics and Matrix Theory have a symbiotic, or mutually beneficial, relationship.

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This textbook introduces enumerative combinatorics through the framework of formal languages and bijections.

A captivating introduction to key results of discrete mathematics through the work of Paul Erdős, blended with first-hand reminiscences.

Finite Fields are fundamental structures of Discrete Mathematics.

This unique and contemporary text not only offers an introduction to proofs with a view towards algebra and analysis, a standard fare for a transition course, but also presents practical skills for upper-level mathematics coursework and exposes undergraduate students to the context and culture of contemporary mathematics.

Combinatorial and Geometric Structures and Their Applications

A broad survey written by acknowledged international experts in the field.

This combinatorics text provides in-depth coverage of recurrences, generating functions, partitions, and permutations, along with some of the most interesting graph and network topics, design constructions, and finite geometries.

From the Rosetta Stone to public-key cryptography, the art and science of cryptology has been used to unlock the vivid history of ancient cultures, to turn the tide of warfare, and to thwart potential hackers from attacking computer systems.

Geometry and Martingales in Banach Spaces provides a compact exposition of the results explaining the interrelations existing between the metric geometry of Banach spaces and the theory of martingales, and general random vectors with values in those Banach spaces.

The Tutte Polynomial touches on nearly every area of combinatorics as well as many other fields, including statistical mechanics, coding theory, and DNA sequencing.

Student Handbook for Discrete Mathematics with Ducks is a Student Reference, Review, Supplemental Learning, and Example Handbook (SRRSLEH) that mirrors the content of the author's popular textbook Discrete Mathematics with Ducks (DMwD).

Continuing in the bestselling, informative tradition of the first edition, the Handbook of Combinatorial Designs, Second Edition remains the only resource to contain all of the most important results and tables in the field of combinatorial design.

A concise introduction, aimed at young researchers, to recent developments of a geometric and topological nature in random graphs.

A Beginner's Guide to Mathematical Proof prepares mathematics majors for the transition to abstract mathematics, as well as introducing a wider readership of quantitative science students, such as engineers, to the mathematical structures underlying more applied topics.

A graduate-level introduction to finite geometry and its applications to other areas of combinatorics.

Exploring one of the most dynamic areas of mathematics, Advanced Number Theory with Applications covers a wide range of algebraic, analytic, combinatorial, cryptographic, and geometric aspects of number theory.

Detailed algorithms for string processes and pattern matching have examples from natural language processing, molecular sequencing, and databases.

This book constitutes refereed proceedings of the 20th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2021, held in Irkutsk, Russia, in July 2021.

This book constitutes the thoroughly refereed workshop post-proceedings of the 17th International Workshop on Approximation and Online Algorithms, WAOA 2019, held in Munich, Germany, in September 2019 as part of ALGO 2019.

This book discusses two questions in Complexity Theory: the Monotonicity Testing problem and the 2-to-2 Games Conjecture.

The most recent methods in various branches of lattice path and enumerative combinatorics along with relevant applications are nicely grouped together and represented in this research contributed volume.

This book presents a study on the foundations of a large class of paraconsistent logics from the point of view of the logics of formal inconsistency.

The author, who died in 1984, is well-known both as a person and through his research in mathematical logic and theoretical computer science.

Covering a wide range of Random Graphs subjects, this volume examines series-parallel networks, properties of random subgraphs of the n-cube, random binary and recursive trees, random digraphs, induced subgraphs and spanning trees in random graphs as well as matchings, hamiltonian cycles and closure in such structures.

One of the most effective ways to stimulate students to enjoy intellectual efforts is the scientific competition.

This proceedings volume presents selected, peer-reviewed contributions from the 26th National School on Algebra, which was held in Constanta, Romania, on August 26-September 1, 2018.

Foreword by James L.