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)
