Discrete And Combinatorial Mathematics is a comprehensive text for students who wish to learn the fundamentals and principles of the Combinatorics and Discrete branches of Mathematics.
Summary Of The Book
Combinatorial and Discrete Mathematics are important branches of Mathematics. Combinatorics is the branch that studies finite discrete structures. It includes combinatorial designs, extremal combinatorics, matroid theory and combinatorial optimization. Discrete Mathematics, on the other hand, studies the mathematical structures which are discontinuous and discrete. In this book, Ralph P. Grimaldi and B. V. Ramana focus on the basics of both Discrete and Combinatorial Mathematics.
Discrete And Combinatorial Mathematics has 16 chapters. The book begins with the Fundamental Principles of Counting like the Rules of Sum and Product, Combinations, and Permutations and Combinations with Repetition. The authors then tackle topics such as the Fundamentals of Logic, Properties of the Integers, Set Theory, Relations and Functions.
Part II of the book focuses on Further Topics in Enumeration like the Principle of Inclusion, Principle of Exclusion, Generating Functions and Recurrence Relations. It offers coverage on topics such as The Summation Operator, The Method of Generating Functions, Partition of Integers, Rook Polynomials, and The Exponential Generating Function.
The next section discusses Graph Theory and Applications. It gives the readers an Introduction to Graph Theory and Trees. It discusses Vertex Degree, Planar Graphs, Hamilton Paths and Cycles. Rooted Trees, Weighted Trees, Prefix Codes, Graph Coloring and Chromatic Polynomials are also discussed.
The last section is on Modern Applied Algebra. It covers Rings and Modular Arithmetic, Algebraic Structures, Monoids, Semigroups, Coding theory, and Polya's Method of Enumeration. It also includes coverage on topics like Finite Fields and Combinatorial Designs. The book is inclusive of appendices on the Exponential and Logarithmic Functions, Countable and Uncountable Sets, Matrices, Matrix Operations, and Determinants.
With clear examples, the book offers comprehensive coverage on all the important topics of Discrete and Combinatorial Mathematics. The book includes a Summary and a Historical Review at the end of each chapter. The book gives importance to the applications and algorithms. It is inclusive of exercise sets and computer science applications that can help students gain a better understanding of the subject.
About The Authors
Ralph Peter Grimaldi is a mathematician and professor from America.
Other books by him include Student Solutions Manual for Discrete and Combinatorial Mathematics, Fibonacci and Catalan Numbers: An Introduction, and Graph Theory and Combinatorics (for VTU).
Born in New York City, he received his degree from the State University of New York at Albany. He received his Ph. D. in Mathematical
Sciences from New Mexico State University. He has been a professor at the State University of New York at Oswego.
B. V. Ramana is a distinguished professor from India.
He has also written Higher Engineering Mathematics.
Ramana has over 30 years of teaching experience at various universities like IIT Mumbai, NIT Warangal, and Federal University of Technology, Nigeria.
Kuldeep Singh Maurya
14 May, 2017
26 Oct, 2016