## Thinking Mathematics! (10 volumes)

**Prices**: Most are $27.50 (but Volume 6: SOME CALCULUS, a hefty piece, is $36.00 and Volume 7: SOME MORE CALCULUS is $30.00.)

**Availability**: Purchase online at Lulu.com

**Description**: A refreshingly clear, multi-volume series for teachers and students looking for high-school mathematics explained

**VOLUME 1: Arithmetic = Gateway to All** (368 pages)

Chapter 1: The Counting Numbers

Chapter 2: Figurate Numbers

Chapter 3: Factors and Primes

Chapter 4: Negative Numbers

Chapter 5: Parity

Chapter 6: Base Machines

Chapter 7: The Galley Method

Chapter 8: Divisibility Rules

Chapter 9: Euclidean Algorithm

Chapter 10: Fundamental Theorem of Arithmetic

Chapter 11: Fractions

Chapter 12: Rationals and Irrationals

Chapter 13: Exponents and Logarithms

Chapter 14: Induction

Chapter 15: Graph Theory

APPENDIX I: Solving Quadratics (and Cubics)

APPENDIX II: The Algebra of Polynomials

**VOLUME 2: Advanced Counting and Advanced Number Systems** (312 pages)

Chapter 16: Counting Principles

Chapter 17: A Grid of Numbers

Chapter 18 Difference Methods

Chapter 19: Generating Functions

Chapter 20: Pigeonhole Principle

Chapter 21: Vector Spaces

Chapter 22: Complex Numbers

Chapter 23: Modular Arithmetics

Chapter 24: Symmetry Groups

Chapter 25: Burnside’s Lemma

Chapter 26: Algebra Systems

Chapter 27: Matrices and their Algebra

Chapter 28: Polynomial Algebras

Chapter 29: Infinity

**VOLUME 3: Lines, Circles, Trigonometry and Conics** (196 pages)

Chapter 1: What Makes a Line Straight?

Chapter 2: Equations of Lines

Chapter 3: Pythagoras’s Theorem and Two Modern Applications

Chapter 4: Parallel Lines, Perpendicular Lines, Distance from a Line

Chapter 5: Circle-ometry

Chapter 6: Trigonometry as the Typical First Experience

Chapter 7: Conics

Appendix I: The Algebra of an Ellipse

Appendix II: Proofs: Folding Properties, Reflection Properties

**VOLUME 4: Functions and Their Graphs **(194 pages)

Chapter 1: Absolute Value as Distance

Overview of Pythagoras’s theorem, the distance formula, the equations of circles and spheres and their connections to absolute value.

Chapter 2: Function Theory – Definition of a function, the notation of functions, composition, iteration, inverse functions and graphs of basic functions.

Chapter 3: Transformations of Graph…and all that! Clever ways to sketch quadratics.

Chapter 4: Polynomials and their Graphs – Definitions and graphs of polynomials in factored form. Limits to infinity.

Chapter 5: Rational Functions and their Graphs – Definitions, limits to infinity, asymptotes, graphs of rational functions.

Chapter 6: Graphs of Special Functions – Graphs of exponential functions, logarithmic functions, and basic trigonometric functions.

Chapter 7: Fitting Functions to Data – Lines between two points, exponential functions between two points, polynomials that fit data EXACTLY(!), trigonometric functions fitting data.

Appendix I: INFINITY – The modern use of function theory to define infinity.

Appendix II: Brief Review of Exponents and Logarithms

**VOLUME 5: Slope, e, i, pi and all that!** (196 pages)

Chapter 1: Slope

Chapter 2: The Number e

Chapter 3: Complex Numbers

Chapter 4: Trigonometry

Chapter 5: Radian Measure and

Chapter 6: Polar Coordinates and Complex Roots

Chapter 7: Parametric Equations

APPENDIX: Alternative Definitions of e

**VOLUME 6: SOME CALCULUS (AB high school/Basic First Semester College) **(604 pages)

Chapter 1: Leaps of Faith

Chapter 2: Function Theory

Chapter 3: Limits and Continuity

Chapter 4: Historical Problem Number 1

Chapter 5: Historical Problem Number 2

Chapter 6: Differential Calculus

Chapter 7: Differentiation Continued

Chapter 8: Applications of the Derivative

Chapter 9: Graphing and Maxima and Minima

Chapter 10: Return of the Integral

Chapter 11: Applications of the Integral

Chapter 12: Loose Ends

Chapter 13: Numerical Methods

Appendix I: Graphing Rational Functions

Appendix II: Exponents and Logarithms

Appendix III: Trigonometry

**VOLUME 7: SOME MORE CALCULUS (BC High School/ Basic Second Semester College) ** (202 pages)

Chapter 14: Some more Integration Techniques

Chapter 15: Parametric Equations

Chapter 16: Polar Coordinates

Chapter 17: Series – A Motivation

Chapter 18: Series

Chapter 19: Convergent Series

Chapter 20: Taylor Series

**VOLUME 8: Probability and Statistics **(232 pages)

Part 1: Probability

Part 2: Counting and Counting Principles

Part 3: Statistics

Part 4: Brief Introduction to Advanced Topics

**VOLUME 9: What is Wrong With Calculus and How to Fix it **(IN PREPARATION)

**VOLUME 10: Index of Topics and Solutions **(IN PREPARATION)