This book, based on Pólya's method of problem solving, aids students in their transition to higher-level mathematics. It begins by providing a great deal of guidance on how to approach definitions, examples, and theorems in mathematics and 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.
Rezensionen / Stimmen
From the reviews: U. Daepp and P. Gorkin Reading, Writing, and Proving A Closer Look at Mathematics "Aids students in their transition from calculus (or precalculus) to higher-level mathematics ... The authors have included a wide variety of examples, exercises with solutions, problems, and over 40 illustrations." -L'ENSEIGNEMENT MATHEMATIQUE "Daepp and Gorkin (both, Bucknell Univ.) offer another in the growing genre of books designed to teach mathematics students the rigor required to write valid proofs ... . The book is well written and should be easy for a first- or second- year college mathematics student to read. There are many 'tips' offered throughout, along with many examples and exercises ... . A book worthy of serious consideration for courses whose goal is to prepare students for upper-division mathematics courses. Summing Up: Highly recommended." (J.R. Burke, CHOICE, 2003) "The book Reading, Writing, and Proving ... provides a fresh, interesting, and readable approach to the often-dreaded 'Introduction to Proof' class. ... RWP contains more than enough material for a one-semester course ... . I was charmed by this book and found it quite enticing. ... My students found the overall style, the abundance of solved exercises, and the wealth of additional historical information and advice in the book exceptionally useful. ... well-conceived, solidly executed, and very useful textbook." (Maria G. Fung, MAA online, December, 2004) "The book is intended for undergraduate students beginning their mathematical career or attending their first course in calculus. ... Throughout the book ... students are encouraged to 1) learn to understand the problem, 2) devise a plan to solve the problem, 3) carry out that plan, and 4) look back and check what the results told them. This concept is very valuable. ... The book is written in an informal way, which will please the beginner and not offend the more experienced reader." (EMS Newsletter, December, 2005)
Reihe
Auflage
Softcover reprint of hardcover 1st ed. 2003
Sprache
Verlagsort
Zielgruppe
Für Beruf und Forschung
Lower undergraduate
Produkt-Hinweis
Illustrationen
49 s/w Abbildungen
1, black & white illustrations
Maße
Höhe: 23.5 cm
Breite: 15.5 cm
Dicke: 21 mm
Gewicht
ISBN-13
978-1-4419-1840-6 (9781441918406)
DOI
Schweitzer Klassifikation
Preface
1 The How, When, and Why of Mathematics
Spotlight: George Polya
Tips on Doing Homework
2 Logically Speaking
3 Introducing the Contrapositive and Converse
4 Set Notation and Quantifiers
Tips on Quantification
5 Proof Techniques
Tips on Definitions
6 Sets
Spotlight: Paradoxes
7 Operations on Sets
8 More on Operations on Sets
9 The Power Set and the Cartesian Product
Tips on Writing Mathematics
10 Relations
Tips on Reading Mathematics
11 Partitions
Tips on Putting It All Together
12 Order in the Reals
Tips: You Solved it. Now What?
13 Functions, Domain, and Range
Spotlight: The Definition of Function
14 Functions, One-to-one, and Onto
15 Inverses
16 Images and Inverse Images
Spotlight: Minimum or Infimum
17 Mathematical Induction
18 Sequences
19 Convergence of Sequences of Real Numbers
20 Equivalent Sets
21 Finite Sets and an Infinite Set
22 Countable and Uncountable Sets
23 Metric Spaces
24 Getting to Know Open and Closed Sets
25 Modular Arithmetic
26 Fermat's Little Theorem
Spotlight: Public and Secret Research
27 Projects
Tips on Talking about Mathematics
27.1 Picture Proofs
27.2 The Best Number of All
27.3 Set Constructions
27.4 Rational and Irrational Numbers
27.5 Irrationality of $e$ and $\pi $
27.6 When does $f^{-1} = 1/f$?
27.7 Pascal's Triangle
27.8 The Cantor Set
27.9 The Cauchy-Bunyakovsky-Schwarz Inequality
27.10 Algebraic Numbers
27.11 The RSA Code
Spotlight: Hilbert's Seventh Problem
28 Appendix
28.1 Algebraic Properties of $\@mathbb {R}$
28.2 Order Properties of $\@mathbb {R}$
28.3 Polya's List
References
Index