Focusing on discrete mathematics, this book serves as a comprehensive resource for introductory courses essential to mathematics and computer science. It covers key topics while also fostering critical thinking skills unique to each discipline. Suitable for lower-division undergraduates and graduate students, it aims to equip learners with foundational knowledge and modes of thought necessary for further study in these fields.
Exploring the intersection of mathematics and electoral systems, this book delves into topics such as simple ballots, complex elections, and the concepts of fairness and manipulation in voting. It begins with a foundational overview of the mathematical principles underlying election methods, guiding readers through a thorough analysis of significant theories like Condorcet's Principle and Arrow's Theorem. This comprehensive examination offers insights into both fair and unfair voting practices, making it a valuable resource for understanding electoral mathematics.
Exploring the practical applications of mathematics, this book delves into how mathematical concepts shape our everyday lives and influence various fields such as science, engineering, and economics. Through engaging examples and real-world scenarios, it highlights the importance of mathematical reasoning and problem-solving skills. Readers will discover how mathematics is not just an abstract discipline but a vital tool for understanding and navigating the complexities of the modern world.
Focusing on the intersection of combinatorial designs and graph theory, this book serves as both a graduate-level textbook and a professional reference. It begins with a concise overview of basic graph theory, making it accessible to readers with some foundational knowledge. Subsequent chapters delve into one-factors and one-factorizations, exploring their applications in combinatorial arrays and tournaments. This structured approach not only aids in understanding essential concepts but also highlights the practical implications of one-factorizations in various mathematical contexts.