An Elementary Transition to Abstract Mathematics (Hardcover)

A Look Back: Precalculus Math A Look Back: Calculus About Proofs and Proof Strategies Mathematical Induction The Well-Ordering Principle Sets Equivalence Relations Functions Cardinality of Sets Permutations Complex Numbers Matrices and Sets with Algebraic Structure Divisibility in Z and Number Theory Primes and Unique Factorization Congruences and the Finite Sets Zn Solving Congruences Fermat’s Theorem Diffie-Hellman Key Exchange Euler’s Formula and Euler’s Theorem RSA Cryptographic System Groups-Definition and Examples Groups-Basic Properties Groups-Subgroups Groups-Cosets Groups-Lagrange’s Theorem Rings Subrings and Ideals Integral Domains Fields Vector Spaces Vector Space Properties Subspaces of Vector Spaces Polynomials Polynomials-Unique Factorization Polynomials over the Rational, Real and Complex Numbers Suggested Solutions to Selected Examples and Exercises