Algebra and Geometry
About this Title
Hung-Hsi Wu, University of California, Berkeley, CA
Publication: AMS Non-Series Monographs
Publication Year: 2020; Volume 132
ISBNs: 978-1-4704-5676-4 (print); 978-1-4704-6005-1 (online)
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.
Teachers of middle school mathematics; students and professionals interested in mathematical education.
Table of Contents
- Linear functions
- Quadratic functions and equations
- Polynomial and rational functions
- Exponential and logarithmic functions
- Polynomial forms and complex numbers
- Basic theorems of plane geometry
- Ruler and compass constructions
- Axiomatic systems
- Facts from [Wu2020a]