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by Usiskin, Peressini, Marchisotto and Stanley

ISBN13: 978-0130449412

ISBN10: 0130449415

Edition: 03

Copyright: 2003

Publisher: Prentice Hall, Inc.

Published: 2003

International: No

ISBN10: 0130449415

Edition: 03

Copyright: 2003

Publisher: Prentice Hall, Inc.

Published: 2003

International: No

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For algebra or geometry courses for teachers; courses in topics of mathematics; capstone courses for teachers or other students of mathematics; graduate courses for practicing teachers; or students who want a better understanding of mathematics.

Filling a wide gap in the market, this text provides current and prospective high school teachers with an advanced treatment of mathematics that will help them understand the connections between the mathematics they will be teaching and the mathematics learned in college. It presents in-depth coverage of the most important concepts in high school mathematics: real numbers, functions, congruence, similarity, and more.

Features

- Two semesters worth of material.
- Gives instructors a wide variety of material from which to choose. Serves as a reference book to students throughout their career.

- Independent chapters.
- Allows instructors to tailor the course to students' specific needs and backgrounds. Allows students to start the book at any point they choose.

- In-depth coverage of core concepts.
- Gives students an in-depth understanding of the important concepts that are taught in high school mathematics.

- In-depth analyses of problems--Including alternate methods of solution, extension, and generalization of standard problems.
- Provides the instructor with a generalized approach to treat problems. Gives students a much deeper understanding of problems they will be teaching, and gives them an approach to teach their students.

- Detailed concept analyses--Including historical and conceptual development of mathematical concepts, and alternate language, notation, and characterizations of ideas.
- Gives the instructor choices in the selection of notation and provides historical and conceptual perspective. Gives students a flexibility that is critical to making choices about what they teach; provides multiple approaches to teaching; and includes information helpful in responding to high school student questions.

- Connections between concepts, between different areas of mathematics, among various uses of ideas.
- Helps students understand that mathematics is a unified whole and provides multiple perspectives for looking at mathematical ideas. Allows the instructor to relate the material in the course to almost any other course.

- Approximately 1400 problems.
- Gives students ample opportunity to practice the concepts learned.

- Questions within the reading.
- Encourages the student to be an active reader.

INTRODUCTION.

1. What is Meant by "An Advanced Perspective"?

I. ALGEBRA AND ANALYSIS WITH CONNECTIONS TO GEOMETRY.

2. Real Numbers and Complex Numbers.

3. Functions.

4. Equations.

5. Integers and Polynomials.

6. Number System Structures.

II. GEOMETRY WITH CONNECTIONS TO ALGEBRA AND ANALYSIS.

7. Congruence.

8. Distance and Similarity.

9. Trigonometry.

10. Area and Volume.

11. Axiomatics and Euclidean Geometry.

Usiskin, Peressini, Marchisotto and Stanley

ISBN13: 978-0130449412ISBN10: 0130449415

Edition: 03

Copyright: 2003

Publisher: Prentice Hall, Inc.

Published: 2003

International: No

For algebra or geometry courses for teachers; courses in topics of mathematics; capstone courses for teachers or other students of mathematics; graduate courses for practicing teachers; or students who want a better understanding of mathematics.

Filling a wide gap in the market, this text provides current and prospective high school teachers with an advanced treatment of mathematics that will help them understand the connections between the mathematics they will be teaching and the mathematics learned in college. It presents in-depth coverage of the most important concepts in high school mathematics: real numbers, functions, congruence, similarity, and more.

Features

- Two semesters worth of material.
- Gives instructors a wide variety of material from which to choose. Serves as a reference book to students throughout their career.

- Independent chapters.
- Allows instructors to tailor the course to students' specific needs and backgrounds. Allows students to start the book at any point they choose.

- In-depth coverage of core concepts.
- Gives students an in-depth understanding of the important concepts that are taught in high school mathematics.

- In-depth analyses of problems--Including alternate methods of solution, extension, and generalization of standard problems.
- Provides the instructor with a generalized approach to treat problems. Gives students a much deeper understanding of problems they will be teaching, and gives them an approach to teach their students.

- Detailed concept analyses--Including historical and conceptual development of mathematical concepts, and alternate language, notation, and characterizations of ideas.
- Gives the instructor choices in the selection of notation and provides historical and conceptual perspective. Gives students a flexibility that is critical to making choices about what they teach; provides multiple approaches to teaching; and includes information helpful in responding to high school student questions.

- Connections between concepts, between different areas of mathematics, among various uses of ideas.
- Helps students understand that mathematics is a unified whole and provides multiple perspectives for looking at mathematical ideas. Allows the instructor to relate the material in the course to almost any other course.

- Approximately 1400 problems.
- Gives students ample opportunity to practice the concepts learned.

- Questions within the reading.
- Encourages the student to be an active reader.

Table of Contents

INTRODUCTION.

1. What is Meant by "An Advanced Perspective"?

I. ALGEBRA AND ANALYSIS WITH CONNECTIONS TO GEOMETRY.

2. Real Numbers and Complex Numbers.

3. Functions.

4. Equations.

5. Integers and Polynomials.

6. Number System Structures.

II. GEOMETRY WITH CONNECTIONS TO ALGEBRA AND ANALYSIS.

7. Congruence.

8. Distance and Similarity.

9. Trigonometry.

10. Area and Volume.

11. Axiomatics and Euclidean Geometry.

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