Foundations of Higher Mathematics

This textbook introduces students to the basic techniques of writing clear and correct proofs, and features extensive coverage of induction as well as plenty of exercises. Chapter 1 distinguishes between proof by contrapositive and proof by contradiction and introduces enough logic to justify these and other methods of proof. Chapter 3 provides a thorough discussion of mathematical induction, allowing the student to master its uses. The study of equivalence relations and partitions in Chapter 4 is motivated both by geometric examples and algebraic examples. The final four chapters offer students the chance to apply what they have learned to the study of numbers, infinite sets, basic modern algebra, and real analysis.