Thoroughly revised for a one-semester course, this well-known and highly regarded book is an outstanding text for undergraduate discrete mathematics. It has been updated with new or extended discussions of order notation, generating functions, chaos, aspects of statistics, and computational biology. Written in a lively, clear style, the book is unique in its emphasis on algorithmics and the inductive and recursive paradigms as central mathematical themes. It includes a broad variety of applications, not just to mathematics and computer science, but to natural and social science as well.

What is discrete algorithmic mathematics. Mathematical preliminaries. Algorithms. Mathematical induction. Graphs and trees. Fundamental counting methods. Difference equations. Probability. An introduction to mathematical logic. Algorithmic linear algebra. Infinite processes in discrete mathematics. Sorting things out with sorting.

The Concise Encyclopedia of Computer Science has been adapted from the full Fourth Edition to meet the needs of students, teachers and professional computer users in science and industry. As an ideal desktop reference, it contains shorter versions of 60% of the articles found in the Fourth Edition, putting computer knowledge at your fingertips. Organised to work for you, it has several features that make it an invaluable and accessible reference. These include: Cross references to closely related articles to ensure that you don’t miss relevant information Appendices covering abbreviations and acronyms, notation and units, and a timeline of significant milestones in computing have been included to ensure that you get the most from the book. A comprehensive index containing article titles, names of persons cited, references to sub-categories and important words in general usage, guarantees that you can easily find the information you need. Classification of articles around the following nine main themes allows you to follow a self study regime in a particular area: Hardware Computer Systems Information and Data Software Mathematics of Computing Theory of Computation Methodologies Applications Computing Milieux. Presenting a wide ranging perspective on the key concepts and developments that define the discipline, the Concise Encyclopedia of Computer Science is a valuable reference for all computer users.

Written for the one-term course, the Third Edition of Essentials of Discrete Mathematics is designed to serve computer science majors as well as students from a wide range of disciplines. The material is organized around five types of thinking: logical, relational, recursive, quantitative, and analytical. This presentation results in a coherent outline that steadily builds upon mathematical sophistication. Graphs are introduced early and referred to throughout the text, providing a richer context for examples and applications. tudents will encounter algorithms near the end of the text, after they have acquired the skills and experience needed to analyze them. The final chapter contains in-depth case studies from a variety of fields, including biology, sociology, linguistics, economics, and music.

The teaching and learning of mathematics in Saskatchewan—one of three Canadian provinces sharing a border with Montana—has a long and storied history. An integral part of the past 50 years (1961-2011) of history has been vinculum: Journal of the Saskatchewan Mathematics Teachers' Society (in its many different renditions). This monograph, which presents ten memorable articles from each of the past five decades (i.e., 50 articles from the past 50 years of the journal), provides an opportunity to share this rich history with a wide range of individuals interested in the teaching and learning of mathematics and mathematics education. Each decade begins with an introduction, providing a historical context, and concludes with a decade-specific commentary by a prominent member of the Saskatchewan mathematics education community. As a result, this monograph provides a historical account as well as a contemporary view of many of the trends and issues (e.g., curriculum, technology) in the teaching and learning of mathematics. This book is meant to serve as a resource for a variety of individuals, including teachers of mathematics, mathematics teacher educators, mathematics education researchers, historians, and undergraduate and graduate students and, further, as a celebratory retrospective on the work of the Saskatchewan Mathematics Teachers' Society.

Discrete mathematics is the branch of mathematics that deals with arrangements of distinct objects. It includes a wide variety of topics and techniques that arise in everyday life, such as how to find the best route from one city to another, where the objects are cities arranged on a map. It also includes how to count the number of different combinations of toppings for pizzas, how best to schedule a list of tasks to be done, and how computers store and retrieve arrangements of information on a screen.

The strong algorithmic emphasis of "Discrete Mathematics" is independent of a specific programming language, allowing students to concentrate on foundational problem-solving and analytical skills. Instructors get the topical breadth and organizational flexibility to tailor the course to the level and interests of their students. Algorithms are presented in English, eliminating the need for knowledge of a particular programming language. Computational and algorithmic exercise sets follow each chapter section and supplementary exercises and computer projects are included in the end-of-chapter material. This Fifth Edition features a new Chapter 3 covering matrix codes, error correcting codes, congruence, Euclidean algorithm and Diophantine equations, and the RSA algorithm. MARKET: Intended for use in a one-semester introductory course in discrete mathematics.

This 1998 yearbook aims to stimulate and answer questions that all educators of mathematics need to consider to adapt school mathematics for the 21st century. The papers included in this book cover a wide variety of topics, including student-invented algorithms, the assessment of such algorithms, algorithms from history and other cultures, ways that algorithms grow and change, and the importance of algorithms in a technological world. Chapters include: (1) "Whither Algorithms? Mathematics Educators Express Their Views" (Lorna J. Morrow); (2) "Paper-and-Pencil Algorithms in a Calculator-and-Computer Age" (Zalman Usiskin); (3) "What Is an Algorithm? What Is an Answer?" (Stephen B. Maurer); (4) "Algorithmic and Recursive Thinking: Current Beliefs and Their Implications for the Future" (Tabitha T.Y. Mingus and Richard M. Grassl); (5) "Teaching Mental Algorithms Constructively" (Alistair McIntosh); (6) "What Criteria for Student-Invented Algorithms?" (Patricia F. Campbell, Thomas E. Rowan, and Anna R. Suarez); (7) "The Importance of Algorithms in Performance-Based Assessments" (Dominic Peressini and Eric Knuth); (8) "A Brief History of Algorithms in Mathematics" (Janet Heine Barnett); (9) "Understanding Algorithms from Their History" (Barnabas Hughes); (10) "An Exploration of the Russian Peasant Method of Multiplication" (Laura Sgroi); (11) "Hammurabi's Calculator" (Clifford Wagner); (12) "Capsule Lessons in Alternative Algorithms for the Classroom" (Diane E. Mason); (13) "Historical Algorithms: Sources for Student Projects" (Rheta N. Rubenstein); (14)"Alternative Algorithms for Whole-Number Operations" (William M. Carroll and Denise Porter); (15) "My Family Taught Me This Way" (Pilar Ron); (16) "Calculators in Primary Mathematics: Exploring Number Before Teaching Algorithms" (Susie Groves and Kaye Stacey); (17) "The Harmful Effects of Algorithms in Grades 1-4" (Constance Kamii and Ann Dominick); (18) "A Contextual Investigation of Three-Digit Addition and Subtraction" (Kay McClain, Paul Cobb, and Janet Bowers); (19) "Children's Invented Algorithms for Multidigit Multiplication Problems" (Jae-Meen Baek); (20) "The 'Write' Way To Mathematical Understanding" (David J. Whitin and Phyllis E. Whitin); (21) "Letting Fraction Algorithms Emerge through Problem Solving" (DeAnn Huinker); (22) "Developing Algorithms for Adding and Subtracting Fractions" (Glenda Lappan and Mary K. Bouck); (23) "A Constructed Algorithm for the Division of Fractions" (Janet Sharp); (24) "Dividing Fractions by Using the Ratio Table" (Jonathan L. Brendefur and Ruth C. Pitingoro); (25) "Teaching Statistics: What's Average?" (Susan N. Friel); (26) "Algorithms for Solving Nonroutine Mathematical Problems" (Jinfa Cai and Connie Laughlin); (27) "Algebra and Technology" (Ann Bruner, Kathy Coskey, and Sharon K. Sheehan); (28) "A New Look at an Old Algorithm: The Semiaverage Line" (Michael McNamara); (29) "Random-Number Generators: A Mysterious Use of Algorithms" (Stephanie O. Robinson and Donald J. Dessart); (30) "Algorithmic Problem Solving in Discrete Mathematics" (Eric W. Hart); (31) "The Traveling Salesperson: Some Algorithms Are Different" (Lowell Leake); and (32) "Using Algorithms To Generate Objects of Mathematical Interest" (Elaine Simmt). (ASK)