2020;
375 pp;
Softcover

MSC: Primary 97; 00;

**Print ISBN: 978-1-4704-5676-4
Product Code: MBK/132**

List Price: $50.00

AMS Member Price: $40.00

MAA Member Price: $45.00

**Electronic ISBN: 978-1-4704-6005-1
Product Code: MBK/132.E**

List Price: $50.00

AMS Member Price: $40.00

MAA Member Price: $45.00

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#### Supplemental Materials

# Algebra and Geometry

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*Hung-Hsi Wu*

This is the second of three volumes that,
together, give an exposition of the mathematics of grades 9–12
that is simultaneously mathematically correct and grade-level
appropriate. The volumes are consistent with CCSSM (Common Core State
Standards for Mathematics) and aim at presenting the mathematics of
K–12 as a totally transparent subject.

The first part of this volume is devoted to the study of standard
algebra topics: quadratic functions, graphs of equations of degree 2
in two variables, polynomials, exponentials and logarithms, complex
numbers and the fundamental theorem of algebra, and the binomial
theorem. Having translations and the concept of similarity at our
disposal enables us to clarify the study of quadratic functions by
concentrating on their graphs, the same way the study of linear
functions is greatly clarified by knowing that their graphs are
lines. We also introduce the concept of formal algebra in the study of
polynomials with complex coefficients. The last three chapters in
this volume complete the systematic exposition of high school geometry
that is consistent with CCSSM. These chapters treat the geometry of
the triangle and the circle, ruler and compass constructions, and a
general discussion of axiomatic systems, including non-Euclidean
geometry and the celebrated work of Hilbert on the foundations.

This book should be useful for current and future teachers of
K–12 mathematics, as well as for some high school students and
for education professionals.

#### Readership

Teachers of middle school mathematics; students and professionals interested in mathematical education.

#### Table of Contents

# Table of Contents

## Algebra and Geometry

- Cover Cover11
- Title page iii4
- Contents vii8
- Contents of the Companion Volumes and Structure of the Chapters ix10
- Preface xi12
- To the Instructor xix20
- To the Pre-Service Teacher xxxiii34
- Prerequisites xxxvii38
- Some Conventions xxxix40
- Chapter 1. Linear Functions 142
- Chapter 2. Quadratic Functions and Equations 63104
- Chapter 3. Polynomial and Rational Functions 121162
- Chapter 4. Exponential and Logarithmic Functions 135176
- Chapter 5. Polynomial Forms and Complex Numbers 175216
- Chapter 6. Basic Theorems of Plane Geometry 213254
- 6.1. Review 214255
- 6.2. SSS and first consequences 220261
- 6.3. Pedagogical comments 229270
- 6.4. Proof of FTS 230271
- 6.5. The angle sum of a triangle 238279
- 6.6. Characterization of isometries 244285
- 6.7. Some basic properties of a triangle 254295
- 6.8. Basic properties of the circle 269310
- 6.9. Power of a point with respect to a circle 297338
- 6.10. Two interesting theorems about the circle 300341

- Chapter 7. Ruler and Compass Constructions 305346
- Chapter 8. Axiomatic Systems 331372
- Appendix: Facts from [Wu2020a] 351392
- Glossary of Symbols 361402
- Bibliography 363404
- Index 367408
- Back Cover Back Cover1417