ISBN13: 978-0534421489

ISBN10: 0534421482

Cover type:

Edition/Copyright: 04

Publisher: Wadsworth, Inc

Published: 2004

International: No

ISBN10: 0534421482

Cover type:

Edition/Copyright: 04

Publisher: Wadsworth, Inc

Published: 2004

International: No

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Liberal Arts mathematics books often cover much more material than can be addressed in a one-semester course. Karl Smith has created a solution to this problem with his new book: THE NATURE OF PROBLEM SOLVING IN GEOMETRY AND PROBABILITY. Loyal customers of Karl Smith's books laud his clear writing, coverage of historical topics, selection of topics, and emphasis on problem solving. Based on the successful NATURE OF MATHEMATICS text, this new book is designed to give you only the chapters and information you need, when you need it. Smith takes great care to provide insight into precisely what mathematics is--the nature of mathematics--what it can accomplish, and how it is pursued as a human enterprise. At the same time, Smith emphasizes Polya's problem-solving method throughout the text so students can take from the course an ability to estimate, calculate, and solve problems outside the classroom. Moreover, Smith's writing style gives students the confidence and ability to function mathematically in their everyday lives. This new text emphasizes problem solving and estimation, which, along with numerous in-text study aids, encourage students to understand the concepts as well as mastering techniques.

**Benefits: **

- The Book Companion Web site at www.mathnature.com includes section-by-section homework hints, projects, links to the World Wide Web, as well as a summary of essential ideas for that section.
- "Group Research Projects" require collaborative research work and are suitable for larger-scale class projects.
- Chapters are independent of one another and allow maximum teaching flexibility.
- Chapter Summaries include important terms, types of problems, and a sample examination.
- Historical Notes show mathematics as the result of both history and current research.
- News Clips demonstrate mathematics in the media, and optional technology sections are included.
- A glossary is included at the back of the book.
- Problems range from easy to challenging and vary by type. "A" problems are mechanical or drill. "B" problems require the understanding of concepts; "Problem-Solving Problems" require critical thinking.
- BCA Tutorial---Interactive tutorial software that's so sophisticated, it's simple! BCA Tutorial is browser-based, making it an intuitive mathematical guide even for students with little technological proficiency. BCA Tutorial allows students to work with real math notation in real time, providing instant analysis and feedback. The tracking program (built into the instructor's version) enables instructors to carefully monitor student progress.
- In addition to robust tutorial services, your students also receive anytime, anywhere access to InfoTrac College Edition. This online library offers the full text of articles from almost 4000 scholarly and popular publications, updated daily and going back as much as 22 years. Both adopters and their students receive unlimited access for four months.
- For your online and distance learning needs, WebTutor? Toolbox on WebCT and Blackboard can be packaged with this text! With WebTutor's text-specific, pre-formatted content and total flexibility, you can easily create and manage your own personal Web site!
- Polya's method of problem solving is used throughout the text.
- A chapter on set theory enables instructors the flexibility to cover this topic in more detail.
- A chapter on networks and graph theory helps students see the applications of mathematics to logistical problems.
- Sections on finite and infinite percents, binomial theorem, and binomial probabilities are included.
- An innovative Prologue provides an overview of the history of mathematics. It asks the question, "Why study math?". An Epilogue shows how the material in the text relates to the natural sciences, social sciences, and the humanities. It also asks the question, "Why not study math?".
- "In Your Own Words" problems provide students with practice in communicating the concepts they've learned.
- Each chapter opener poses an "In the Real World" problem, and concludes with "Revisiting the Real World", which reviews a method for solving the problem. This structure motivates the chapter topic and provides a forum for review.
- "Individual Research Projects" help students apply what they are learning to familiar situations. These projects require research or library work, further reinforcing the student's understanding of mathematical concepts in a variety of fields.

Prologue Why Math? An Historical Overview.

1. THE NATURE OF PROBLEM SOLVING.

Problem Solving. Inductive and Deductive Reasoning. Scientific Notation and Estimation. Finite and Infinite.

2. THE NATURE OF LOGIC.

Deductive Reasoning. Truth Tables and the Conditional. Operators and Laws of Logic. The Nature of Proof. Problem Solving Using Logic. Logic Circuits.

3. THE NATURE OF SET THEORY AND COUNTING.

Sets, Subsets, and Venn Diagrams. Combined Operations with Sets. Counting Formulas. Permutations. Combinations. Binomial Theorem. Counting without Counting. Rubik''s Cube and Instant Insanity.

4. THE NATURE OF PROBABILITY.

Introduction to Probability. Mathematical Expectation. Probability Models. Calculated Probabilities. Binomial Probabilities. Guest Essay: Extrasensory Perception.

5. THE NATURE OF STATISTICS.

Frequency Distributions and Graphs. Measures of Central Tendency. Measures of Dispersion. The Normal Curve. Correlation and Regression. Polls and Margin of Error.

6. THE NATURE OF GEOMETRY.

Geometry. Polygons and Angles. Triangles. Similar Triangles. Right Triangle Trigonometry. Golden Rectangles. Projective and Non-Euclidian Geometries.

7. THE NATURE OF MEASUREMENT.

Perimeter. Area. Surface Area, Volume and Capacity. Miscellaneous Measurements.

8. THE NATURE OF GROWTH.

Logarithms and Exponents. Exponential Equations. Logarithmic Equations. Applications of Growth and Decay.

9. THE NATURE OF NETWORKS AND GRAPH THEORY.

Euler Circuits and Hamiltonian Cycles. Trees and Minimum Spanning Trees. Topology and Fractals. Guest Essay: Chaos.

Epilogue Why Not Math? Mathematics In The Natural Sciences, Social

Sciences, And In The Humanities.

Appendices:

A. Glossary.

B. Selected Answers.

C. Credits.

D. Index.

ISBN10: 0534421482

Cover type:

Edition/Copyright: 04

Publisher: Wadsworth, Inc

Published: 2004

International: No

Liberal Arts mathematics books often cover much more material than can be addressed in a one-semester course. Karl Smith has created a solution to this problem with his new book: THE NATURE OF PROBLEM SOLVING IN GEOMETRY AND PROBABILITY. Loyal customers of Karl Smith's books laud his clear writing, coverage of historical topics, selection of topics, and emphasis on problem solving. Based on the successful NATURE OF MATHEMATICS text, this new book is designed to give you only the chapters and information you need, when you need it. Smith takes great care to provide insight into precisely what mathematics is--the nature of mathematics--what it can accomplish, and how it is pursued as a human enterprise. At the same time, Smith emphasizes Polya's problem-solving method throughout the text so students can take from the course an ability to estimate, calculate, and solve problems outside the classroom. Moreover, Smith's writing style gives students the confidence and ability to function mathematically in their everyday lives. This new text emphasizes problem solving and estimation, which, along with numerous in-text study aids, encourage students to understand the concepts as well as mastering techniques.

**Benefits: **

- The Book Companion Web site at www.mathnature.com includes section-by-section homework hints, projects, links to the World Wide Web, as well as a summary of essential ideas for that section.
- "Group Research Projects" require collaborative research work and are suitable for larger-scale class projects.
- Chapters are independent of one another and allow maximum teaching flexibility.
- Chapter Summaries include important terms, types of problems, and a sample examination.
- Historical Notes show mathematics as the result of both history and current research.
- News Clips demonstrate mathematics in the media, and optional technology sections are included.
- A glossary is included at the back of the book.
- Problems range from easy to challenging and vary by type. "A" problems are mechanical or drill. "B" problems require the understanding of concepts; "Problem-Solving Problems" require critical thinking.
- BCA Tutorial---Interactive tutorial software that's so sophisticated, it's simple! BCA Tutorial is browser-based, making it an intuitive mathematical guide even for students with little technological proficiency. BCA Tutorial allows students to work with real math notation in real time, providing instant analysis and feedback. The tracking program (built into the instructor's version) enables instructors to carefully monitor student progress.
- In addition to robust tutorial services, your students also receive anytime, anywhere access to InfoTrac College Edition. This online library offers the full text of articles from almost 4000 scholarly and popular publications, updated daily and going back as much as 22 years. Both adopters and their students receive unlimited access for four months.
- For your online and distance learning needs, WebTutor? Toolbox on WebCT and Blackboard can be packaged with this text! With WebTutor's text-specific, pre-formatted content and total flexibility, you can easily create and manage your own personal Web site!
- Polya's method of problem solving is used throughout the text.
- A chapter on set theory enables instructors the flexibility to cover this topic in more detail.
- A chapter on networks and graph theory helps students see the applications of mathematics to logistical problems.
- Sections on finite and infinite percents, binomial theorem, and binomial probabilities are included.
- An innovative Prologue provides an overview of the history of mathematics. It asks the question, "Why study math?". An Epilogue shows how the material in the text relates to the natural sciences, social sciences, and the humanities. It also asks the question, "Why not study math?".
- "In Your Own Words" problems provide students with practice in communicating the concepts they've learned.
- Each chapter opener poses an "In the Real World" problem, and concludes with "Revisiting the Real World", which reviews a method for solving the problem. This structure motivates the chapter topic and provides a forum for review.
- "Individual Research Projects" help students apply what they are learning to familiar situations. These projects require research or library work, further reinforcing the student's understanding of mathematical concepts in a variety of fields.

Table of Contents

Prologue Why Math? An Historical Overview.

1. THE NATURE OF PROBLEM SOLVING.

Problem Solving. Inductive and Deductive Reasoning. Scientific Notation and Estimation. Finite and Infinite.

2. THE NATURE OF LOGIC.

Deductive Reasoning. Truth Tables and the Conditional. Operators and Laws of Logic. The Nature of Proof. Problem Solving Using Logic. Logic Circuits.

3. THE NATURE OF SET THEORY AND COUNTING.

Sets, Subsets, and Venn Diagrams. Combined Operations with Sets. Counting Formulas. Permutations. Combinations. Binomial Theorem. Counting without Counting. Rubik''s Cube and Instant Insanity.

4. THE NATURE OF PROBABILITY.

Introduction to Probability. Mathematical Expectation. Probability Models. Calculated Probabilities. Binomial Probabilities. Guest Essay: Extrasensory Perception.

5. THE NATURE OF STATISTICS.

Frequency Distributions and Graphs. Measures of Central Tendency. Measures of Dispersion. The Normal Curve. Correlation and Regression. Polls and Margin of Error.

6. THE NATURE OF GEOMETRY.

Geometry. Polygons and Angles. Triangles. Similar Triangles. Right Triangle Trigonometry. Golden Rectangles. Projective and Non-Euclidian Geometries.

7. THE NATURE OF MEASUREMENT.

Perimeter. Area. Surface Area, Volume and Capacity. Miscellaneous Measurements.

8. THE NATURE OF GROWTH.

Logarithms and Exponents. Exponential Equations. Logarithmic Equations. Applications of Growth and Decay.

9. THE NATURE OF NETWORKS AND GRAPH THEORY.

Euler Circuits and Hamiltonian Cycles. Trees and Minimum Spanning Trees. Topology and Fractals. Guest Essay: Chaos.

Epilogue Why Not Math? Mathematics In The Natural Sciences, Social

Sciences, And In The Humanities.

Appendices:

A. Glossary.

B. Selected Answers.

C. Credits.

D. Index.

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