Mathematics: A Discrete Introduction

Mathematics: A Discrete Introduction serves as a foundational text for undergraduate mathematics students transitioning from computational to abstract mathematics. The book covers core topics in discrete mathematics including logic, set theory, functions, relations, graphs, and combinatorics. Each chapter contains detailed explanations, worked examples, and practice problems that progress from basic to advanced applications. The text emphasizes proof-writing techniques and formal mathematical reasoning while maintaining connections to practical computer science concepts. Students work through the material in a structured sequence, beginning with fundamental logical principles and building toward more complex mathematical structures. The book includes chapter summaries, review questions, and supplementary exercises to reinforce learning. This text bridges the gap between concrete arithmetic and abstract mathematical thinking, preparing students for upper-level coursework in pure mathematics and theoretical computer science. The emphasis on rigorous proof methods makes it relevant for mathematics majors developing their analytical skills.

Readers describe this textbook as clear and accessible for undergraduate students new to proof writing and discrete math. Many note it provides a gentle introduction to mathematical reasoning with helpful examples and exercises. Likes: - Step-by-step explanations of proof techniques - Informal, conversational writing style - Good balance of theory and practice problems - Effective coverage of sets, logic, counting, and graphs Dislikes: - Some find the pace too slow for advanced students - A few readers wanted more challenging exercises - Limited coverage of some discrete math topics - Solutions manual not readily available Ratings: Goodreads: 4.0/5 (21 ratings) Amazon: 4.4/5 (31 ratings) One student reviewer noted: "The author takes time to explain concepts thoroughly - perfect for self-study." Another mentioned: "The informal tone helped make abstract concepts more approachable." Several math instructors praised its use as a first proofs course text, though some preferred more rigorous alternatives like Velleman's "How to Prove It."

Discrete Mathematics and Its Applications by Kenneth Rosen Provides comprehensive coverage of discrete mathematics with emphasis on algorithms and applications in computer science.

A Walk Through Combinatorics by Miklos Bona Presents combinatorial concepts through concrete examples and builds from elementary to advanced topics in discrete mathematics.

Concrete Mathematics by Ronald Graham, Donald Knuth, Oren Patashnik Bridges the gap between continuous and discrete mathematics while focusing on mathematical techniques used in computer science.

Discrete Mathematics with Applications by Susanna S. Epp Develops mathematical maturity through rigorous proofs and discrete mathematics concepts used in computer programming.

Mathematical Structures for Computer Science by Judith L. Gersting Connects discrete mathematics to computer science through data structures, algorithms, and computational problems.

📚 Edward Scheinerman served as the Vice Dean for Engineering Education at Johns Hopkins University's Whiting School of Engineering. 🎓 The book bridges the gap between high school algebra and university-level discrete mathematics, making it particularly valuable for computer science students. 📐 While most discrete mathematics textbooks focus heavily on proofs, this book places equal emphasis on problem-solving techniques and practical applications. 🔢 The text includes extensive coverage of graph theory, which is essential for understanding computer networks and social media algorithms. 🌟 Professor Scheinerman has received multiple teaching awards, including the Mathematical Association of America's Deborah and Franklin Tepper Haimo Award for Distinguished College or University Teaching of Mathematics.