Muutke küpsiste eelistusi

Reading, Writing, and Proving: A Closer Look at Mathematics 1st ed. Softcover of orig. ed. 2003 [Pehme köide]

  • Formaat: Paperback / softback, 416 pages, kõrgus x laius x paksus: 234x156x21 mm, kaal: 581 g, 1, black & white illustrations
  • Sari: Undergraduate Texts in Mathematics
  • Ilmumisaeg: 29-Nov-2010
  • Kirjastus: Springer-Verlag New York Inc.
  • ISBN-10: 144191840X
  • ISBN-13: 9781441918406
Teised raamatud teemal:
  • Pehme köide
  • Hind: 107,20 €*
  • * saadame teile pakkumise kasutatud raamatule, mille hind võib erineda kodulehel olevast hinnast
  • See raamat on trükist otsas, kuid me saadame teile pakkumise kasutatud raamatule.
  • Kogus:
  • Lisa ostukorvi
  • Tasuta tarne
  • Lisa soovinimekirja
Reading, Writing, and Proving: A Closer Look at Mathematics 1st ed. Softcover of orig. ed. 2003
  • Formaat: Paperback / softback, 416 pages, kõrgus x laius x paksus: 234x156x21 mm, kaal: 581 g, 1, black & white illustrations
  • Sari: Undergraduate Texts in Mathematics
  • Ilmumisaeg: 29-Nov-2010
  • Kirjastus: Springer-Verlag New York Inc.
  • ISBN-10: 144191840X
  • ISBN-13: 9781441918406
Teised raamatud teemal:
This book, based on Polya'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 Polya'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.

Arvustused

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)

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