Reading, writing, and proving

A closer look at mathematics

Ulrich Daepp, Pamela Gorkin

412 pages

Ajouter à une liste

Indisponible

Résumé

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 providing projects for independent study.

Students will follow Pólya's four step process: learn to understand the problem; devise a plan to solve the problem; carry out that plan; and look back and check what the results told them. Special emphasis is placed on reading carefully and writing well. The authors have included a wide variety of examples, exercises with solutions, problems, and over 40 illustrations, chosen to emphasize these goals. Historical connections are made throughout the text, and students are encouraged to use the rather extensive bibliography to begin making connections of their own. While standard texts in this area prepare students for future courses in algebra, this book also includes chapters on sequences, convergence, and metric spaces for those wanting to bridge the gap between the standard course in calculus and one in analysis.

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
Back to Functions
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

Appendix
References
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Ulrich Daepp, Pamela Gorkin
Nb. de pages	412
Format	16 x 24
Couverture	Relié
Poids	690g
Intérieur	Noir et Blanc
EAN13	9780387008349
ISBN13	978-0-387-00834-9