Discrete Structures

Discrete Structures Introduces Readers To The Mathematical Structures And Methods That Form The Foundation Of Computer Science And Features Multiple Techniques That Readers Will Turn To Regularly Throughout Their Careers In Computer And Information Sciences. Over The Course Of Five Modules, Students Learn Specific Skills Including Binary And Modular Arithmetic, Set Notation, Methods Of Counting, Evaluating Sums, And Solving Recurrences. They Study The Basics Of Probability, Proof By Induction, Growth Of Functions, And Analysis Techniques. The Book Also Discusses General Problem-solving Techniques That Are Widely Applicable To Real Problems. Each Module Includes Motivation Applications, Technique, Theory, And Further Opportunities For Application. Informed By Extensive Experience Teaching In Computer Science Programs, Discrete Structures Has Been Developed Specifically For First-year Students In Those Programs. The Material Is Also Suitable For Courses In Computer Engineering, As Well As Those For Students Who Are Transferring From Other Disciplines And Just Beginning Their Computer Science Or Engineering Education. Harriet Fell Holds A Ph.d. In Mathematics From The Massachusetts Institute Of Technology, And Is A Professor Emerita Of Computer Science At Northeastern University. Dr. Fell Is A Double Patent Holder Who Has Received Grants From The National Institute Of Health, The National Science Foundation, And The U.s. Department Of Education. Javed A. Aslam Holds A Ph.d. In Computer Science From The Massachusetts Institute Of Technology And Is A Professor Of Computer Science At Northeastern University And The Associate Dean Of Faculty In The College Of Computer And Information Science. Dr. Aslam's Research Interests Include Information Retrieval, Machine Learning, And The Design And Analysis Of Algorithms. Table of Contents Preface Part I: Computers and Computing: Numbers, Circuits, and Logic Chapter 1 Chapter 2 Chapter 3 Chapter 4 Part II: Cryptography: Integers and Modular Arithmetic Chapter 5 Chapter 6 Chapter 7 Part III: Combinatorics: Sets, Counting, and Probability Chapter 8 Chapter 9 Chapter 10 Part IV: Algorithmic Analysis: Searching and Sorting Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Part V: Networks: Graphs and Trees Chapter 17 Part VI: Relations: Properties and Applications Chapter 18 Part VII: Appendices Appendix A Appendix B Appendix C Appendix D Solutions to Selected Exercises Bibliography Index Introduces readers to the mathematical structures and methods that form the foundation of computer science and features multiple techniques that readers will turn to regularly throughout their careers in computer and information sciences. Informed by extensive experience teaching in computer science programs, this book has been developed specifically for first-year students in those programs.