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

• Κύριοι συγγραφείς: Daepp, Ulrich (Συγγραφέας), Gorkin, Pamela (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: New York, NY : Springer New York, 2003.
• Σειρά: Undergraduate Texts in Mathematics,
• Θέματα: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Mathematical logic.; Number theory.; Mathematical Logic and Foundations.; Analysis.; Number Theory.

This book, which is based on Pólya'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...

Πίνακας περιεχομένων:

• 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
• Fermat’s Little Theorem
• Projects.