Discrete Mathematics and Its Applications, Seventh Edition, is intended for one or two term introductory Discrete Mathematics courses taken by students from a wide variety of majors, including Computer Science, Mathematics, and Engineering. This renowned best-selling text, which has been used at over 500 institutions around the world, gives a focused introduction to the primary themes in a Discrete Mathematics course and demonstrates the relevance and practicality of Discrete Mathematics to a wide variety of real-world applications—from Computer Science to Data Networking, to Psychology, to Chemistry, to Engineering, to Linguistics, to Biology, to Business, and many other important fields.
Chapter 1: The Foundations: Logic and Proofs
Chapter 2: Basic Structures: Sets, Functions, Sequences, Sums, Matrices
Chapter 3: Algorithms
Chapter 4: Number Theory and Cryptography
Chapter 5: Induction and Recursion
Chapter 6: Counting
Chapter 7: Discrete Probability
Chapter 8: Advanced Counting Techniques
Chapter 9: Relations
Chapter 10: Graphs
Chapter 11: Trees
Chapter 12: Boolean Algebra
Chapter 13: Modeling Computation
New to this Edition
Rosen's Discrete Mathematics and Its Applications—seventh edition, includes the power of McGraw-Hill’s LearnSmart. LearnSmart is a proven adaptive learning program that helps students learn faster, study more efficiently, and retain more knowledge for greater success.
More Flexible Organization—the dependence of chapters on previous material has been minimized to allow instructors flexibility to pick and choose topics. Each chapter is divided into sections of approximately the same length, and each section is divided into subsections that form natural blocks of material for teaching. Instructors can easily pace their lectures using these blocks. Separate chapters on Algorithms, Number Theory, and Cryptography.
Expanded Coverage of Logic & Sets—helps students better understand these fundamental concepts using well known examples like Sudoku and Hilbert's Grand Hotel.
New & Enhanced Features in the Text—the seventh edition offers improvements that make the text easier and more rewarding to use. Added to this edition were Margin notes, expanded explanations/details, and revised examples/problems. The Bourbaki's "dangerous bend" symbol has also been added to alert students to topics that require extra attention.
Improved Introduction & Organization—for the seventh edition, the first part of the book has been restructured to present core topics in a more efficient, more effective, and more flexible way.
Exercises & Worked Examples—the text included over 3800 exercises and 750 examples, from straight forward problems that develop basic skills to a large number of intermediate and challenging exercises. Exercise sets also contain special discussions that develop new concepts not covered in the text, enabling students to discover new ideas through their own work. Answers to odd numbered problems are in the back of the book. Worked out solutions for these odd numbered problems are in the printed Student's Solutions Guide (0077353501). Complete solutions for the even numbered problems are available for the instructor only in the Instructor's Resource Guide.
Historical Information, Biographies, & Updates on Latest Discoveries—the background of many topics are succinctly described in the text using historical footnotes and brief biographies of more than 65 mathematicians and computer scientists who were (and are) important contributors to Discrete Mathematics.
Clarity & Precision—Rosen’s writing style is direct and pragmatic. Precise mathematical language is used without excessive formalism and abstraction. Care has been taken to balance the mix of notation and words in mathematical statements.
Accessibility—this text has proven to be easy to read and understand by beginning students. There's no mathematical prerequisites beyond College Algebra for almost all of this text, and the few places in the book where Calculus is referred to are explicitly noted.
•An updated Web Resources Guide containing new links to hundreds of external websites relevant to the text material.
•An updated Applications of Discrete Mathematics supplement containing in-depth explorations of applications, with exercises and projects.
•Additional instructor resources for in-class use such as: printable tests, image banks, lecture notes, and materials donated by our community of users.