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MATHEMATICAL THINKING PROBLEM-SOLVING AND PROOFS
D`ANGELO J. WEST D. wydawnictwo: PRENTICE HALL , rok wydania 2000, wydanie II cena netto: 237.00 Twoja cena 225,15 zł + 5% vat - dodaj do koszyka Mathematical Thinking:
Problem-Solving and Proofs, 2/e
John P. D'Angelo , University
of Illinois, Urbana
Douglas B. West , University of Illinois, Urbana
Published December 1999 by
Engineering/Science/Mathematics
Copyright 2000, 412 pp.
Cloth ISBN 0-13-014412-6
Summary
For one/two-term courses in
Transition to Advanced Mathematics or Introduction to Proofs. Also suitable for courses in
Analysis or Discrete Math.
This text is designed to
prepare students thoroughly in the logical thinking skills necessary to understand and
communicate fundamental ideas and proofs in mathematics-skills vital for success
throughout the upperclass mathematics curriculum. The text offers both discrete and
continuous mathematics, allowing instructors to emphasize one or to present the
fundamentals of both. It begins by discussing mathematical language and proof techniques
(including induction), applies them to easily-understood questions in elementary number
theory and counting, and then develops additional techniques of proof via important topics
in discrete and continuous mathematics. The stimulating exercises are acclaimed for their
exceptional quality.
Features
- NEW-A
clearly outlined transition course-Rearranges material to facilitate a clearly defined
and more accessible transition course using Chs. 1-5, initial parts of Chs. 6,8 and Chs.
13-14.
- By
narrowing the focus, makes it easy to present a course with rich content to beginning
students in a transition course without overwhelming them.
- NEW-"Approaches
to Problems"-In selected chapters. Summarizes key points and presents problem-solving
strategies relevant to exercises.
- In
the transition course, helps students organize their understanding of the chapter, avoid
typical pitfalls, and learn ways to approach problems of moderate difficulty.
- NEW-A
clearly outlined analysis course-Now contains an excellent course in analysis using Part
I as background, touching briefly on Ch. 8, and covering Part IV in depth.
- Provides
review reading on proof methods in Part I while being as thorough and accessible as
introductory texts in Part IV.
- NEW-Expanded
and improved selection of exercises-New, easier exercises check mastery of concepts;
some difficult exercises are clarified.
- Enlarged
selection of easier exercises provides greater encouragement for beginning students;
clarifications make other exercises more accessible.
- NEW-Reorganization
of material-Provides smoother development and clearer focus on essential material.
- Makes
it easier for students to follow the mathematical development and how to know what
assumption can be used when working problems.
- NEW-Definitions
in bold-Terms being defined are in bold type with almost all definitions in numbered
terms.
- Makes
definitions easier for students to find.
- NEW-More
accessible presentation-Some terse discussions expanded, examples added, and more
computations placed in displays.
- Makes
material easier for students to comprehend and conveys a greater sense of progress by
making pages less dense.
- Engaging
examples-Interesting applications introduce and motivate the underlying mathematics.
- Engage
student interest and commitment from the beginning and keep the material lively.
- Logical
Organization-Introduces concepts as needed with each item carefully selected.
Distinguishes between Lemmas/Theorems (the mathematical development) and
Examples/Solutions (the illustration or application of mathematical results).
- Enables
students to find fundamental results easily and learn more efficiently. Helps students
understand the difference between mathematical tools and their application in
problem-solving.
- Flexibility
in course design-Mathematical background in Part I can be treated quickly with strong
students or in detail for beginners. Rich variety of subsequent topics permits a broad
introduction to mathematics or a focus on discrete mathematics (Part III) or Analysis
(Part IV).
- Enables
instructors to design courses appropriate to students' abilities; a two-semester treatment
offers a thorough introduction to mathematics.
- Emphasis
on understanding rather than manipulation-Stresses full comprehension rather than rote
symbolic manipulation for mastery of proof techniques and mathematical ideas.
- Helps
students develop critical thinking skills and appreciation of coherent arguments,
preparing them both for later courses in mathematics and for problem-solving situations
outside school.
- Emphasis
on clear communication-Discusses the use of language and requires written arguments in
many exercises.
- Helps
students develop or remediate their written communication skills, both in forming English
sentences and in presenting coherent arguments. Supports the efforts of instructors to
apply such skills in a mathematical context.
- Richness
of Topics-After the elementary material, provides a wealth of "intellectual highs"
from diophantine equations to Fermat's Little Theorem to Pythagorean triples, Bertrand's
Ballot Problem, the pigeonhole principle, the Euler totient, Hall's Marriage Condition,
the theory of calculus, interchange of limiting operations, series of functions, the
existence of continuous nowhere differentiable functions, complex numbers, and the
Fundamental Theorem of Algebra.
- Permits
the inclusion of topics to enrich the mathematical experience. Depending on the talents of
students, these can be presented in class or left for outside reading.
- Hints
for selected exercises-Provides immediate hints for some exercises and hints for others
in an appendix.
- Gives
students the flexibility to learn at their own pace; weaker students have more opportunity
to be successful, and stronger students have more opportunity to be stimulated.
- Superior
exercise sets-Offers over 850 exercises ranging from relatively straightforward
applications of ideas in the text to subtle problems requiring some ingenuity.
- Helps
students at all levels to understand the ideas of the course and to broaden their
mathematical interests.
- Gradation
of exercises-Distinguishes easier exercises by (-), harder by (+), and particularly
valuable or instructive exercises by (!).
- Aids
instructor in selecting appropriate exercises and students in practicing for tests.
- Instructor's
Manual-Contains solutions to exercises and pedagogical suggestions. Only available
directly through editor.
Table of Contents
I. ELEMENTARY CONCEPTS.
1. Numbers, Sets and
Functions.
2. Language and Proofs.
3. Induction.
4. Bijections and Cardinality.
II. PROPERTIES OF NUMBERS.
5. Combinatorial Reasoning.
6. Divisibility.
7. Modular Arithmetic.
8. The Rational Numbers.
III. DISCRETE MATHEMATICS.
9. Probability.
10. Two Principles of Counting.
11. Graph Theory.
12. Recurrence Relations.
IV. CONTINUOUS MATHEMATICS.
13. The Real Numbers.
14. Sequences and Series.
15. Continuous Functions.
16. Differentiation.
17. Integration.
18. The Complex Numbers.
Po otrzymaniu zamówienia poinformujemy, czy wybrany tytuł polskojęzyczny lub
anglojęzyczny jest aktualnie na półce księgarni.
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