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Introduction to Combinatorics
Praise for the First Edition “This excellent text should prove a useful accoutrement for any developing mathematics program . . . it’s short, it’s sweet, it’s beautifully written.” —The Mathematical Intelligencer “Erickson has prepared an exemplary work . . . strongly recommended for inclusion in undergraduate-level library collections.” —Choice Featuring a modern approach, Introduction to Combinatorics, Second Edition illustrates the applicability of combinatorial methods and discusses topics that are not typically addressed in literature, such as Alcuin’s sequence, Rook paths, and Leech’s lattice. The book also presents fundamental results, discusses interconnection a...
Introduction to Combinatorics
This gradual, systematic introduction to the main concepts of combinatorics is the ideal text for advanced undergraduate and early graduate courses in this subject. Each of the book's three sections--Existence, Enumeration, and Construction--begins with a simply stated first principle, which is then developed step by step until it leads to one of the three major achievements of combinatorics: Van der Waerden's theorem on arithmetic progressions, Polya's graph enumeration formula, and Leech's 24-dimensional lattice. Along the way, Professor Martin J. Erickson introduces fundamental results, discusses interconnection and problem-solving techniques, and collects and disseminates open problems t...
Beautiful Mathematics
Mathematical ideas with aesthetic appeal for any mathematically minded person.
Introduction to Number Theory
One of the oldest branches of mathematics, number theory is a vast field devoted to studying the properties of whole numbers. Offering a flexible format for a one- or two-semester course, Introduction to Number Theory uses worked examples, numerous exercises, and two popular software packages to describe a diverse array of number theory topi
A Student's Guide to the Study, Practice, and Tools of Modern Mathematics
A Student's Guide to the Study, Practice, and Tools of Modern Mathematics provides an accessible introduction to the world of mathematics. It offers tips on how to study and write mathematics as well as how to use various mathematical tools, from LaTeX and Beamer to Mathematica and Maple to MATLAB and R. Along with a color insert, the text include
Pearls of Discrete Mathematics
Methods Used to Solve Discrete Math ProblemsInteresting examples highlight the interdisciplinary nature of this area Pearls of Discrete Mathematics presents methods for solving counting problems and other types of problems that involve discrete structures. Through intriguing examples, problems, theorems, and proofs, the book illustrates the relationship of these structures to algebra, geometry, number theory, and combinatorics. Each chapter begins with a mathematical teaser to engage readers and includes a particularly surprising, stunning, elegant, or unusual result. The author covers the upward extension of Pascal�s triangle, a recurrence relation for powers of Fibonacci numbers, ways to...
Pearls of Discrete Mathematics
Methods Used to Solve Discrete Math ProblemsInteresting examples highlight the interdisciplinary nature of this areaPearls of Discrete Mathematics presents methods for solving counting problems and other types of problems that involve discrete structures. Through intriguing examples, problems, theorems, and proofs, the book illustrates the relation
Mathematics for the Liberal Arts
Presents a clear bridge between mathematics and the liberal arts Mathematics for the Liberal Arts provides a comprehensible and precise introduction to modern mathematics intertwined with the history of mathematical discoveries. The book discusses mathematical ideas in the context of the unfolding story of human thought and highlights the application of mathematics in everyday life. Divided into two parts, Mathematics for the Liberal Arts first traces the history of mathematics from the ancient world to the Middle Ages, then moves on to the Renaissance and finishes with the development of modern mathematics. In the second part, the book explores major topics of calculus and number theory, in...
Aha! Solutions
Every mathematician (beginner, amateur, and professional alike) thrills to find simple, elegant solutions to seemingly difficult problems. Such happy resolutions are called 'aha! solutions,' a phrase popularized by mathematics and science writer Martin Gardner. Aha! solutions are surprising, stunning, and scintillating: they reveal the beauty of mathematics. This collection includes one hundred problems in the areas of arithmetic, geometry, algebra, calculus, probability, number theory, and combinatorics. The problems start out easy and generally get more difficult as you progress through the book. A few solutions require the use of a computer. An important feature of the book is the discussion of related mathematics that follows the solution of each problem. This material is there to entertain and inform you or point you to new questions.
