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.)
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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)


    QUADRATICS, Permutations and Combinations, EXPLODING DOTS, and more!

    Written for educators - and their students too! - this website, slowly growing, takes all the content Tanton has developed in his books, videos, and workshops, and organizes it into short, self-contained, and complete, curriculum units proving that mathematics, at all points of the school curriculum, can be joyous, fresh, innovative, rich, deep-thinking, and devoid of any rote doing! Let's teach generations of students to be self-reliant thinkers, willing to flail and to use their common sense to "nut their way" through challenges, to assess and judge results, and to adjust actions to find success. (Great life skills!)


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