Reading, Writing, and Proving A Closer Look at Mathematics /

• Main Authors: Daepp, Ulrich. (Author), Gorkin, Pamela. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: New York, NY : Springer New York, 2003.
• Series: Undergraduate Texts in Mathematics,
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Mathematical logic.; Number theory.; Mathematical Logic and Foundations.; Analysis.; Number Theory.
• Online Access: View fulltext via EzAccess

This book, which is based on P©đlya's method of problem solving, aids students in their transition from calculus (or precalculus) to higher-level mathematics. The book begins by providing a great deal of guidance on how to approach definitions, examples, and theorems in mathematics. It ends by...

Table of Contents:

• The How, When, and Why of Mathematics
• Logically Speaking
• Introducing the Contrapositive and Converse
• Set Notation and Quantifiers
• Proof Techniques
• Sets
• Operations on Sets
• More on Operations on Sets
• The Power Set and the Cartesian Product
• Relations
• Partitions
• Order in the Reals
• Functions, Domain, and Range
• Functions, One-to-One, and Onto
• Inverses
• Images and Inverse Images
• Mathematical Induction
• Sequences
• Convergence of Sequences of Real Numbers
• Equivalent Sets
• Finite Sets and an Infinite Set
• Countable and Uncountable Sets
• Metric Spaces
• Getting to Know Open and Closed Sets
• Modular Arithmetic
• FermatỚ"s Little Theorem
• Projects.