Mathematical Method A Transition to Advanced Mathematics

1. Induction. Ordinary Induction. Recursion. Summation. Well-ordering and Strong Induction. Binomial Coefficients. 2. Number Theory. The Division Theorem. Divisibility. Prime Numbers. Congruence. Congruence Classes. 3. The Real Numbers. Fields. Ordered Fields. Nested Intervals and Completeness. Isomorphism of Fields. Null Sequences and Limits. The Complex Number Field. 4. Cardinality. Finite and Infinite Sets. Countable and Uncountable Sets. Uncountable Sets. Appendix A. Sets. Elements and Sets. Pairs and Products. Relations. Appendix B. Functions. Functions and Maps. Composition of Functions. Injections and Surjections. Sequences and Families. Appendix C. Equivalence Relations. Equivalence Relations. Partitions. Appendix D. The Integers. Natural Numbers: Working Assumptions. Natural Numbers: Peano Postulates. Integers: Working Assumptions. Integers: Construction. Rational and Real Numbers. Index.Eisenberg, Murray is the author of 'Mathematical Method A Transition to Advanced Mathematics' with ISBN 9780131270022 and ISBN 0131270028.