This textbook bridges the gap between lower-division mathematics courses and advanced mathematical thinking. Featuring clear writing and appealing topics, the book introduces techniques for writing proofs in the context of discrete mathematics. By illuminating the concepts behind techniques, the authors create opportunities for readers to sharpen critical thinking skills and develop mathematical maturity.

Beginning with an introduction to sets and logic, the book goes on to establish the basics of proof techniques. From here, chapters explore proofs in the context of number theory, combinatorics, functions and cardinality, and graph theory. A selection of extension topics concludes the book, including continued fractions, infinite arithmetic, and the interplay among Fibonacci numbers, Pascal's triangle, and the golden ratio.

A Discrete Transition to Advanced Mathematics is suitable for an introduction to proof course or a course in discrete mathematics. Abundant examples and exercises invite readers to get involved, and the wealth of topics allows for course customization and further reading. This new edition has been expanded and modernized throughout, featuring:

• A new chapter on combinatorial geometry;
• An expanded treatment of the combinatorics of indistinguishable objects;
• New sections on the inclusion-exclusion principle and circular permutations;
• Over 365 new exercises.

Ancillaries:

• Student Solutions Manual (Selected Problems)
• Instructor's Manual

Undergraduate students who need a strong conceptual foundation for higher mathematical thinking.