ISBN: 978-1-1182-3002-2
Hardcover
544 pages
February 2012
After a brief review of first-order differential equations, this book focuses on second-order equations with constant coefficients that derive their general solution using only results described previously. Higher-order equations are provided since the patterns are more readily grasped by students. Stability and fourth order equations are also discussed since these topics typically appear in further study for engineering and science majors. In addition to applications to engineering systems, applications from the biological and life sciences are emphasized. Ecology and population dynamics are featured since they involve both linear and nonlinear equations, and these topics form one application thread that weaves through the chapters. Diffusion of material, heat, and mechanical and electrical oscillators are also important in biological and engineering systems and are discussed throughout. A complete Instructor Solution Manual is available upon request and contains solutions to all exercises as well as Maple? code. While the book is not dependent on the use of one specific software, some of the exercises do call on the use of such systems to solve certain differential equations or to plot the results. A Student Solutions Manual is available to supplement the book, and while the first manual will feature Maple?, the author is also preparing versions using Mathematica and MATLAB to accommodate instructor preferences. Chapter coverage includes First-Order Differential Equations; Higher-Order Linear Equations; Applications of Higher-Order Linear Equations; Systems of Linear Differential Equations; Laplace Transform; Series Solution; Systems of Nonlinear Differential Equations; and Appendices on Partial Fraction Expansions, Determinants, Gauss Elimination, and Complex Numbers and the Complex Plane.
ISBN: 978-0-470-63157-7
Hardcover
384 pages
January 2012
In this one-of-a-kind book, Ralph Grimaldi uses his extensive experience from the classroom and as a leader of mini-courses to present an accessible, single resource on the topics of Fibonacci Numbers and Catalan Numbers . The book first embarks on a complete treatment of Fibonacci numbers. Starting with a historical background on the topic, the author goes on to present the properties of Fibonacci numbers, a slew of introductory-level examples, and in-depth discussion of related topics including compositions and palindromes; tiling and Fibonacci numbers; solving linear recurrence relations; graph theory; Lucas numbers; and alternate Fibonacci numbers. The second half of the book explores Catalan numbers, and the author builds a complete foundation to the topic using a historical background and introductory examples, along with coverage of partial orders, total orders, topological sorting, graph theory, rooted ordered binary trees, pattern avoidance, and the Narayana numbers. Coverage of both topics are accompanied by interesting, real-world examples from areas such as sports, botany, and computer science. Each section concludes with detailed exercise sets that can also serve as extended examples of the presented material along with selected solutions. An Instructor's Manual featuring complete solutions is available upon written request, and extensive reference sections outline resources for further study of the discussed topics.
ISBN: 978-1-1181-3535-8
Hardcover
560 pages
January 2012
This Fourth Edition of Introduction to Abstract Algebra is a self-contained introduction to the basic structures of abstract algebra: groups, rings, and fields. This book is intended for a one or two semester abstract algebra course. The writing style is appealing to students, and great effort has been made to motivate and be very clear about how the topics and applications relate to one another. Over 500 solved examples are included to aid reader comprehension as well as to demonstrate how results in the theory are obtained. Many applications (particularly to coding theory, cryptography, and to combinatorics) are provided to illustrate how the abstract structures relate to real-world problems. In addition, historical notes and biographies of mathematicians put the subject into perspective. Abstract thinking is difficult when first encountered and this is addressed in this book by presenting concrete examples (induction, number theory, integers modulo n, permutations) before the abstract structures are defined. With this approach, readers can complete computations immediately using concepts that will be seen again later in the abstract setting. Special topics such as symmetric polynomials, nilpotent groups, and finite dimensional algebras are also discussed.
January 2012, c2011
The new 6th edition of Applied Combinatorics builds on the previous editions with more in depth analysis of computer systems in order to help develop proficiency in basic discrete math problem solving. As one of the most widely used book in combinatorial problems, this edition explains how to reason and model combinatorically while stressing the systematic analysis of different possibilities, exploration of the logical structure of a problem, and ingenuity. Although important uses of combinatorics in computer science, operations research, and finite probability are mentioned, these applications are often used solely for motivation. Numerical examples involving the same concepts use more interesting settings such as poker probabilities or logical games.
This book is designed for use by students with a wide range of ability and maturity (sophomores through beginning graduate students). The stronger the students, the harder the exercises that can be assigned. The book can be used for one-quarter, two-quarter, or one-semester course depending on how much material is used.
Prelude.
Part One: Graph Theory.
Chapter 1: Elements of Graph Theory.
Chapter 2: Covering Circuits and Graph coloring.
Chapter 3: Trees and Searching.
Chapter 4: Network Algorithms.
Part Two: Enumeration.
Chapter 5: General Counting Methods for Arrangements and Selections.
Chapter 6: Generating Functions.
Chapter 7: Recurrence Relations.
Chapter 8: Inclusion-Exclusion.
Part Three: Additional Topics.
Chapter 9: Polya's Enumeration Formula.
Chapter 10: Games with Grapes.
Postlude.
Appendix.
Hardback
Series: Classroom Resource Materials
ISBN:9780883857762
Dimensions: 247 x 174 mm
available from April 2012
The author of this book believes that there is too much rote learning and not enough creative exploration in mathematical education. To remedy this he has produced a book that promotes intellectual play and adaptability of thought by engaging the reader in mathematical activities. Twenty-six chapters examine a wide variety of mathematical teasers and problems and the mathematics behind them is explained and proved via natural and accessible means. This is an excellent recreational maths book that also serves as a source of inspiration for teachers of mathematics. Pick and read essays in no particular order and enjoy the mathematical stories that unfold. Be inspired for your courses, your math clubs and your math circles, and enjoy for yourself the bounty of additional research questions and intriguing puzzles that lie within.
Introduction
Newsletters and commentaries
1. Arctangents
2. Benford's Law
3. Braids
4. CLIP Theory
5. Dots and dashes
6. Factor trees
7. Folding fractions and conics
8. Folding patterns and dragons
9. Folding and pouring
10. Fractions
11. Integer triangles
12. Lattice polygons
13. Layered tilings
14. The middle of a triangle
15. Partitions
16. Personalized polynomials
17. Playing with Pi
18. Pythagoras's Theorem
19. On reflection
20. Repunits and primes
21. The Stern?Brocot Tree
22. Tessellations
23. Theon's ladder and squangular numbers
24. Tilings and theorems
25. The Tower of Hanoi
26. Weird multiplication
Appendices: 1. Numbers that are the sum of two squares
2. Pick's theorem
3. The Mobius function
4. The Borsuk-Ulam theorem
5. Galilean ratios
6. A candy-sharing game
7. Bending Buffon's needle
8. On separating dots
Indexes: 1. Index of terms
2. Index of topics
3. Classic theorems proved.