Journey Into Discrete Mathematics
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Journey into Discrete Mathematics
Author: Owen D. Byer
language: en
Publisher: American Mathematical Soc.
Release Date: 2018-11-13
Journey into Discrete Mathematics is designed for use in a first course in mathematical abstraction for early-career undergraduate mathematics majors. The important ideas of discrete mathematics are included—logic, sets, proof writing, relations, counting, number theory, and graph theory—in a manner that promotes development of a mathematical mindset and prepares students for further study. While the treatment is designed to prepare the student reader for the mathematics major, the book remains attractive and appealing to students of computer science and other problem-solving disciplines. The exposition is exquisite and engaging and features detailed descriptions of the thought processes that one might follow to attack the problems of mathematics. The problems are appealing and vary widely in depth and difficulty. Careful design of the book helps the student reader learn to think like a mathematician through the exposition and the problems provided. Several of the core topics, including counting, number theory, and graph theory, are visited twice: once in an introductory manner and then again in a later chapter with more advanced concepts and with a deeper perspective. Owen D. Byer and Deirdre L. Smeltzer are both Professors of Mathematics at Eastern Mennonite University. Kenneth L. Wantz is Professor of Mathematics at Regent University. Collectively the authors have specialized expertise and research publications ranging widely over discrete mathematics and have over fifty semesters of combined experience in teaching this subject.
A Brief Journey in Discrete Mathematics
The goal of this book is to showcase the beauty of mathematics as revealed in nine topics of discrete mathematics. In each chapter, properties are explored through a series of straightforward questions that terminate with results that lie at the doorstep of a field of study. Each step along the way is elementary and requires only algebraic manipulation. This frames the wonder of mathematics and highlights the complex world that lies behind a series of simple, mathematical, deductions. Topics addressed include combinatorics, unifying properties of symmetric functions, the Golden ratio as it leads to k-bonacci numbers, non-intuitive and surprising results found in a simple coin tossing game, the playful, trick question aspect of modular systems, exploration of basic properties of prime numbers and derivations of bewildering results that arise from approximating irrational numbers as continued fraction expansions. The Appendix contains the basic tools of mathematics that are used in the text along with a numerous list of identities that are derived in the body of the book. The mathematics in the book is derived from first principles. On only one occasion does it rely on a result not derived within the text. Since the book does not require calculus or advanced techniques, it should be accessible to advanced high school students and undergraduates in math or computer science. Senior mathematicians might be unfamiliar with some of the topics addressed in its pages or find interest in the book's unified approach to discrete math.
Gateway to Discrete Mathematics
Author: Pasquale De Marco
language: en
Publisher: Pasquale De Marco
Release Date: 2025-08-15
In a world increasingly shaped by data and algorithms, "Gateway to Discrete Mathematics" emerges as an indispensable guide to understanding the fundamental principles that underpin our digital age. This comprehensive book, meticulously crafted for an American audience, unravels the intricacies of discrete mathematics, revealing its profound impact on computer science, engineering, biology, social sciences, and beyond. With a conversational tone that invites readers to engage with the subject matter, "Gateway to Discrete Mathematics" embarks on a captivating journey through the fascinating world of sets, relations, functions, logic, and graph theory. Readers will discover the elegance and versatility of mathematical structures, unlocking their potential to solve real-world problems and make informed decisions. Delving into the realm of number theory, the book unveils the secrets of prime numbers, modular arithmetic, and Diophantine equations, showcasing their applications in cryptography, coding theory, and beyond. It then explores the realm of combinatorics, delving into permutations, combinations, generating functions, and recurrence relations, highlighting their significance in probability, computer science, and optimization. Moving on to graph theory, the book unravels the complexities of trees, connectivity, Eulerian and Hamiltonian paths, and planar graphs, revealing their applications in network analysis, scheduling, and routing problems. It then delves into algebraic structures, introducing groups, rings, fields, and vector spaces, and explores their profound implications in coding theory, error correction, and cryptography. With its comprehensive coverage, engaging writing style, and abundance of illustrative examples, "Gateway to Discrete Mathematics" is an invaluable resource for students, educators, professionals, and anyone seeking to expand their knowledge of discrete mathematics. It promises an enlightening journey through the realm of numbers, sets, structures, algorithms, and codes—a journey that will leave readers with a newfound appreciation for the elegance and power of mathematical thinking. If you like this book, write a review!