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**About this book :- **
**Discrete Mathematics with Applications (5E) ** written by
** Susanna Samuels Epp **

Susanna Epp's Discrete Mathematics with Applications (5th Edition) provides a clear introduction to discrete mathematics. This text explains complex, abstract concepts with clarity and precision and provides a strong foundation for computer science and upper-level mathematics courses of the computer age. Author Susanna Epp presents not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical thought. Students develop the ability to think abstractly as they study the ideas of logic and proof. While learning about such concepts as logic circuits and computer addition, algorithm analysis, recursive thinking, computability, automata, cryptography and combinatorics, students discover that the ideas of discrete mathematics underlie and are essential to today's science and technology.

The author write this book was to provide a clear, accessible treatment of discrete mathematics for students majoring or minoring in computer science, mathematics, mathematics education, and engineering. The goal of the book is to lay the mathematical foundation for computer science courses such as data structures, algorithms, relational database theory, automata theory and formal languages, compiler design, and cryptography, and for mathematics courses such as linear and abstract algebra, combinatorics, probability, logic and set theory, and number theory. By combining discussion of theory and practice, He has tried to show that mathematics has engaging and important applications as well as being interesting and beautiful in its own right.

A good background in algebra is the only prerequisite; the course may be taken by students either before or after a course in calculus. Previous editions of the book have been used successfully by students at hundreds of institutions in North and South America, Europe, the Middle East, Asia, and Australia.

Recent curricular recommendations from the Institute for Electrical and Electronic Engineers Computer Society (IEEE-CS) and the Association for Computing Machinery (ACM) include discrete mathematics as the largest portion of "core knowledge" for computer science students and state that students should take at least a one-semester course in the subject as part of their first-year studies, with a two-semester course preferred when possible. This book includes all the topics recommended by those organizations and can be used effectively for either a one-semester or a two-semester course.

At one time, most of the topics in discrete mathematics were taught only to upper-level undergraduates. Discovering how to present these topics in ways that can be understood by first- and second-year students was the major and most interesting challenge of writing this book. The presentation was developed over a long period of experimentation during which my students were in many ways my teachers. Their questions, comments, and written work showed me what concepts and techniques caused them difficulty, and their reaction to my exposition showed me what worked to build their understanding and to encourage their interest. Many of the changes in this edition have resulted from continuing interaction with students.

**Book Detail :- **
** Title: ** Discrete Mathematics with Applications
** Edition: ** 5th
** Author(s): ** Susanna Samuels Epp
** Publisher: ** Cengage Learning
** Series: **
** Year: ** 2019
** Pages: ** 1057
** Type: ** PDF
** Language: ** English
** ISBN: ** 1337694193, 978-1337694193
** Country: ** US

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**About Author :- **

Author ** Susanna Samuels Epp ** was born in 1943, Susanna Epp is an author, mathematician, and professor. Her interests include discrete mathematics, mathematical logic, cognitive psychology, and mathematics education, and she has written numerous articles, publications, and textbooks. She is currently professor emerita at
** DePaul University ** , where she chaired the Department of Mathematical Sciences and was Vincent de Paul Professor in Mathematics.

Epp holds degrees in mathematics from Northwestern University and the University of Chicago, where she completed her doctorate in 1968 under the supervision of Irving Kaplansky. She also taught at Boston University and at the University of Illinois at Chicago before becoming a professor at DePaul University.

Initially researching commutative algebra, Epp became interested by cognitive psychology, especially in education of Mathematics, Logic, Proof, and the Language of mathematics. She wrote several articles about teaching logic and proof in American Mathematical Monthly, and the Mathematics Teacher, a Journal by the National Council of Teachers of Mathematics. She is the author of several books including Discrete Mathematics with Applications.

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**Book Contents :- **
**Discrete Mathematics with Applications (5E) ** written by
** Susanna Samuels Epp **
cover the following topics.

1. Speaking Mathematically

2. The Logic of Compound Statements

3. The Logic of Quantified statements

4. Elementary Number theory and methods of Proof

5. Sequences, mathematical induction, and recursion

6. set theory

7. Properties of Functions

8. Properties of relations

9. counting and Probability

10. Theory of Graphs and trees

11. Analysis of algorithm efficiency

12. Regular expressions and Finite-state automata 828

Appendix A Properties of the Real Numbers

Appendix B Solutions and Hints to Selected Exercises

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- Boolean Algebra
- Graph Theory
- Linear Algebra
- Number Theory
- Set Theory
- Mathematical Induction
- Discrete Geometry
- Discrete Probability

- Abstract Algebra
- Calculus
- Differential Equations
- Engineering Mathematics
- Linear Algebra
- Math Magic
- Real Analysis