Algebraic Combinatorics

Walks, Trees, Tableaux, and More

Nonfiction, Science & Nature, Mathematics, Combinatorics, Graphic Methods
Cover of the book Algebraic Combinatorics by Richard P. Stanley, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Richard P. Stanley ISBN: 9783319771731
Publisher: Springer International Publishing Publication: June 6, 2018
Imprint: Springer Language: English
Author: Richard P. Stanley
ISBN: 9783319771731
Publisher: Springer International Publishing
Publication: June 6, 2018
Imprint: Springer
Language: English

Written by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the author’s extensive knowledge of combinatorics and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfound understanding to mathematical, engineering, and business models. Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and rudiments of group theory. The topics in each chapter build on one another and include extensive problem sets as well as hints to selected exercises. Key topics include walks on graphs, cubes and the Radon transform, the Matrix-Tree Theorem, de Bruijn sequences, the Erdős–Moser conjecture, electrical networks, the Sperner property, shellability of simplicial complexes and face rings. There are also three appendices on purely enumerative aspects of combinatorics related to the chapter material: the RSK algorithm, plane partitions, and the enumeration of labeled trees.

The new edition contains a bit more content than intended for a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory. Instructors may pick and choose chapters/sections for course inclusion and students can immerse themselves in exploring additional gems once the course has ended. A chapter on combinatorial commutative algebra (Chapter 12) is the heart of added material in this new edition. The author gives substantial application without requisites needed for algebraic topology and homological algebra. A sprinkling of additional exercises and a new section (13.8) involving commutative algebra, have been added.

From reviews of the first edition:

“This gentle book provides the perfect stepping-stone up. The various chapters treat diverse topics … . Stanley’s emphasis on ‘gems’ unites all this —he chooses his material to excite students and draw them into further study. … Summing Up:  Highly recommended. Upper-division undergraduates and above.”

—D. V. Feldman, Choice, Vol. 51(8), April, 2014

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

Written by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the author’s extensive knowledge of combinatorics and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfound understanding to mathematical, engineering, and business models. Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and rudiments of group theory. The topics in each chapter build on one another and include extensive problem sets as well as hints to selected exercises. Key topics include walks on graphs, cubes and the Radon transform, the Matrix-Tree Theorem, de Bruijn sequences, the Erdős–Moser conjecture, electrical networks, the Sperner property, shellability of simplicial complexes and face rings. There are also three appendices on purely enumerative aspects of combinatorics related to the chapter material: the RSK algorithm, plane partitions, and the enumeration of labeled trees.

The new edition contains a bit more content than intended for a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory. Instructors may pick and choose chapters/sections for course inclusion and students can immerse themselves in exploring additional gems once the course has ended. A chapter on combinatorial commutative algebra (Chapter 12) is the heart of added material in this new edition. The author gives substantial application without requisites needed for algebraic topology and homological algebra. A sprinkling of additional exercises and a new section (13.8) involving commutative algebra, have been added.

From reviews of the first edition:

“This gentle book provides the perfect stepping-stone up. The various chapters treat diverse topics … . Stanley’s emphasis on ‘gems’ unites all this —he chooses his material to excite students and draw them into further study. … Summing Up:  Highly recommended. Upper-division undergraduates and above.”

—D. V. Feldman, Choice, Vol. 51(8), April, 2014

More books from Springer International Publishing

Cover of the book Food Hygiene and Applied Food Microbiology in an Anthropological Cross Cultural Perspective by Richard P. Stanley
Cover of the book Driving and Engine Cycles by Richard P. Stanley
Cover of the book Big Data Analytics and Knowledge Discovery by Richard P. Stanley
Cover of the book Coherent Vortex Structures in Fluids and Plasmas by Richard P. Stanley
Cover of the book Internal Erosion in Earthdams, Dikes and Levees by Richard P. Stanley
Cover of the book Antibody Therapy by Richard P. Stanley
Cover of the book Acute Elbow Trauma by Richard P. Stanley
Cover of the book Trends in Applications of Mathematics to Mechanics by Richard P. Stanley
Cover of the book E-Learning and Games by Richard P. Stanley
Cover of the book Sub-Riemannian Geometry and Optimal Transport by Richard P. Stanley
Cover of the book African Female Entrepreneurship by Richard P. Stanley
Cover of the book Proceedings of the Future Technologies Conference (FTC) 2018 by Richard P. Stanley
Cover of the book Women Phenomenologists on Social Ontology by Richard P. Stanley
Cover of the book Collaborative Computing: Networking, Applications, and Worksharing by Richard P. Stanley
Cover of the book How Systems Form and How Systems Break by Richard P. Stanley
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy