Discrete Mathematics with Coding

ISBN-13: 9781032398525 / Angielski

Hugo D. Junghenn

Opis

This book, for a first undergraduate course in Discrete Mathematics, systematically exploits the relationship between discrete mathematics and computer programming. Unlike most discrete mathematics texts focusing on one of the other, the book explores the rich and important connection between these two disciplines and shows how each discipline reinforces and enhances the other.

The mathematics in the book is self-contained, requiring only a good background in precalculus and some mathematical maturity. New mathematical topics are introduced as needed.

The coding language used is VBA Excel. The language is easy to learn, has intuitive commands, and the reader can develop interesting programs from the outset. Additionally, the spreadsheet platform in Excel makes for convenient and transparent data input and output and provides a powerful venue for complex data manipulation. Manipulating data is greatly simplified using spreadsheet features and visualizing the data can make programming and debugging easier.

The VBA language is seamlessly integrated into the spreadsheet environment with no other resources required. Furthermore, as some of the modules in the book show, intricate patterns, graphs, and animation in the form of moving cells is possible.

Features

• Introduces coding in VBA Excel assuming no previous coding experience.
• Develops programs in Linear Analysis, Logic, Combinatorics, Probability, and Number Theory.
• Contains over 90 fully tested and debugged programs. The code for these is as well as the exercises is available on the author's website.
• Contains numerous examples that gradually introduce the reader to coding techniques.
• Includes programs that solve systems of linear equations, linear programming problems, combinatorial problems, Venn diagram problems and programs that produce truth tables from logic statements and logic statements from switching and gate circuits, encrypt and decrypt messages and simulate probability experiments.

Spis treści

1. Introduction. 2. VBA Operators. 3. Conditional Statements. 4. Loops, 5. Arrays. 6. String Functions. 7. Grids. 8. Recursion. 9. Charts and Graphs, 10. Random Numbers. 11. Linear Equations. 12. Linear Programming. 13. Matrix Algebra. 14. Determinants. 15. Propositional Logic. 16. Switching Circuits. 17. Gates and Logic Circuits. 18. Sets. 19. Counting. 20. Probability. 21. Random Variables. 22. Markov Chains. 23. Divisibility and Prime Numbers. 24. Congruence. 25. The Enigma Machine. 26. Large Numbers.

O autorze

Hugo D. Junghenn is Professor of Mathematics at The George Washington University. He has published numerous journal articles and is the author of several books, including A Course in Real Analysis and Principles of Analysis: Measure, Integration, Functional Analysis, and Applications. His research interests include functional analysis, semigroups, and probability.