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Combinatorial Reasoning: An Introduction To The Art Of Counting
Duane Detemple, William Webb
Synopsis "Combinatorial Reasoning: An Introduction To The Art Of Counting"
With A Focus On Beginning Combinatorics, This Book Features Complete Exposition Of The Discussed Topics And Over 700 Exercises That Illustrate The Presented Concepts And Methodology. The Book Covers Fundamental Topics In Enumeration, All Of Which Are Explored In Great Depth. The Authors` Approach Is Very Reader - Friendly And Avoids The Scholarly Tone Found In Many Other Related Books. Abstract Ideas Are Grounded In Familiar Concrete Settings, And There Are Far More Diagrams Within The Book Than Are Found In Most Other Related Texts. In Addition, Simple Cases Are Treated First Before General And Advanced Cases, And The Notations Are Kept Simple And Helpful. To Help Readers Learn How Combinatorics Interacts With Other Subjects As A Tool Or As An Application, The Book Provides Brief Summaries Of Basic Concepts From Probability, Power Series, And Group Theory. Each Chapter Begins With An Introduction To The Topics Covered Within The Chapter, Followed By Sections That Are Each Accompanied By A Large Number Of Exercises That Range From Basic Calculations To More Challenging Problems. The Exercises Are Carefully Structured To Range From The Routine To The More Advanced. The Beginning Level Problems Are Designed To Confirm And Develop Students` Understanding Of The Fundamental Concepts And Calculations, Where A Calculation Is Most Often Based On Combinatorial Reasoning Rather Than Algebraic Manipulation. More Advanced Exercises Allow Students To Explore And More Deeply Understand The Topics In The Chapter And Apply The Techniques To More Complex Combinatorial Situations. Each Chapter Also Contains A Brief Summary Of The Most Important Concepts Covered. Finally, Each Chapter Ends With A Few Additional Problems That Further Synthesize The Ideas That Were Presented In The Chapter. Chapter Coverage Includes: Initial Encounters With Combinatorial Reasoning; Arrangements, Selections, And Distributions; Binomial Series And Generating Functions; Alternating Sums, Inclusion - Exclusion, And Rook Polynomials; Recurrence Relations; Special Numbers; Linear Spaces And Recurrences Sequences; And Counting Symmetric Arrangements
