John D'Angelo-Vice President of Facilities Management at Northwestern University.Douglas West is a professor of graph theory at University of Illinois at Urbana-Champaign.

PART I. ELEMENTARY CONCEPTS.

Chapter 1. Numbers, Sets and Functions.

Chapter 2. Language and Proofs.

Chapter 3. Induction.

Chapter 4. Bijections and Cardinality.

PART II. PROPERTIES OF NUMBERS.

Chapter 5. Combinatorial Reasoning.

Chapter 6. Divisibility.

Chapter 7. Modular Arithmetic.

Chapter 8. The Rational Numbers.

PART III. DISCRETE MATHEMATICS.

Chapter 9. Probability.

Chapter 10. Two Principles of Counting.

Chapter 11. Graph Theory.

Chapter 12. Recurrence Relations.

PART IV. CONTINUOUS MATHEMATICS.

Chapter 13. The Real Numbers.

Chapter 14. Sequences and Series.

Chapter 15. Continuous Functions.

Chapter 16. Differentiation.

Chapter 17. Integration.

Chapter 18. The Complex Numbers."

Emphasis on understanding rather than manipulation—Stresses full comprehension rather than rote symbolic manipulation for mastery of proof techniques and mathematical ideas.

Engaging examples—Interesting applications introduce and motivate the underlying mathematics.

Hints for selected exercises—Provides immediate hints for some exercises and hints for others in an appendix.

Superior exercise sets—Offers over 850 exercises ranging from relatively straightforward applications of ideas in the text to subtle problems requiring some ingenuity.

Gradation of exercises—Distinguishes easier exercises by (—), harder by (+), and particularly valuable or instructive exercises by (!)."