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Chapter 1 Fundamentals
Sets and Counting
Set Basics
Descartes and Analytic Geometry
dense number set
Complex Numbers
Complex Number
Transcendental Number
Algebraic Number
Imaginary Number
Imaginary Number
Real Numbers
Real Number
Irrational Numbers
Irrational Number
Rational Numbers
Rational Numbers
Integers
Integers
Whole Numbers
Natural Numbers
Counting Numbers
Number Sets
Sets of Numbers and Their Properties
Sets
Topics in Precalculus
SOS Math - Algebra
Diophantus of Alexandria (200-284)
Euclid of Alexandria (265 BC - 325 BC)
Fran?ois Vi?te (1540-1603)
Alan Mathison Turing (1912-1954)
George P?lya (1887-1985)
Sets and Counting
John Venn
Augustus De Morgan
Georg Cantor's Theory of Infinite Sets
A Crash Course in the Mathematics Of Infinite Sets
Chapter 2 Functions
Functions and Linear Models
History of Least Squares
Chronology of Least Squares
Carl Frederich Gauss (1777-1855)
Linear Least Squares Method PDF
Donald Ervin Knuth (1938- )
Sofia Vasilyevna Kovalevskaya (1850-1891)
Pythagoras of Samos (569 BC - 475 BC)
Archimedes and the Computation of Pi
Fibonacci Numbers and Nature
Solving Equations Through the Ages
Even and Odd Functions
Geometric Transformation of Functions
Compositions
Inverse Functions
Chapter 3 Polynomial and Rational Functions
A Short History of Algebra
History of Algebra I
History of Algebra II
THE ART OF ALGEBRA FROM AL-KHWARIZMI TO VI?TE: A STUDY IN THE NATURAL SELECTION OF IDEAS
The Quadratic Formula - Mathematics and the Liberal Arts
The Conic Sections
Geometric Definition of Conic Sections
1=2: A Proof using Beginning Algebra
Johann Carl Friedrich Gauss (1777-1855)
Gauss
Gauss, Carl Friedrich.
Gauss, Karl Friedrich (1777-1855) -- from Mathworld
Johann Karl Friedrich Gauss
http--www-history.mcs.st-andrews.ac.uk-history-Bookpages-Newt
Orbits
Evariste Galois (1811-1832)
Leonhard Euler (1707-1783)
Girolamo Cardano (1501-1576)
Srinivasa Aiyangar Ramanujan (1887-1920)
The History of Polynomial Equations
Solving the Quintic with Mathematica
A Short History of Solving the Quintic
Chapter 4 Exponential and Logaritmic Functions
John Napier (1550-1617)
Logarithmic and Exponential Functions
Exploring Exponential Functions
Does the number e have any real physical meaning?
Definition of e
How does "e" relate to continued fractions?
What is e?
Transcendental Number
The Number e
e The Story of a Number
About e
Logarithm Tutorial
Exponential Tutorial
Logarithm
Logs
Logarithms: History and Use
Napierian Logarithm
HISTORY OF THE LOGARITHMS
Exponential Regression on the TI-83/84
Using the TI-83/84 for Regression
Regression on the TI-83/84 PDF
Chapter 5 Trignometric Functions of Real Numbers
Archimedes and the Computation of Pi
Even and Odd Functions
A history of Pi
The Unit Circle pdf
Trigonometry Links - Good Stuff
Trigonometric Delights by Eli Maor
Frontmatter
Preface
Prologue: Ahmes the Scribe, 1650 B.C.
Sidebar Recreational Mathematics in Ancient Egypt
Chapter 1. Angles
Chapter 2. Chords
Sidebar Plimpton 322: The Earliest Trigonometric Table
Chapter 3. Six Functions Come of Age
Chapter 6 Trignometric Functions of Angles
Aristarchus of Samos (310 BC - 230 BC)
Eratosthenes of Cyrene (276 BC - 194 BC)
Eratosthenes and the Mystery of the Stades
The Greeks Measure the Universe
Aristarchus of Samos (310 BC - 230 BC)
Bhaskara I (600?-680)
Bhaskara II (1114-1185)
Pierre de Fermat (1601-1665)
Hipparchus of Rhodes (190 BC - 120 BC)
Thales of Miletus (624 BC - 527 BC)
Fermat's last theorem
The four colour theorem
The trigonometric functions
The Unit Circle pdf
Trigonometry Links - Good Stuff
Trigonometric Delights by Eli Maor
Frontmatter
Preface
Prologue: Ahmes the Scribe, 1650 B.C.
Sidebar Recreational Mathematics in Ancient Egypt
Chapter 1. Angles
Chapter 2. Chords
Sidebar Plimpton 322: The Earliest Trigonometric Table
Chapter 3. Six Functions Come of Age
Chapter 7 Analytic Trigonometry
Trigonometric Delights by Eli Maor
Sidebar Johann Muller alias Regiomonianus
Chapter 4. Trigonometry Becomes Analytic
Sidebar Francois Viete
Chapter 5. Measuring Heaven and Earth
Sidebar Abraham De Moivre
Chapter 6. Two Theorems from Geometry
Chapter 8 Polar Coordinates and Vectors
Jean Baptiste Joseph Fourier (1768-1830)
Abraham de Moivre (1667-1754)
a pdf on Abraham de Moivre
Complex Number Arithmetic
Good pdf on complex numbers
An Introduction to Complex numbers and Polar Coordinates
Polar Coordinates Tutorial
Polar Coordinates 101 pdf
Vectors 101
Even and Odd Functions
Polar Form of a Complex Number
Polar Coordinates and Vectors
Vectors
Vector Algebra pdf
Vector Addition Tutorial
A good Vectors 101 pdf
A different version of a Vectors 101 pdf
HMC Elementary Vector Algebra
Forces in Two Directions: Inclined Plane
The Unit Circle pdf
Trigonometry Links - Good Stuff
Trigonometric Delights by Eli Maor
Chapter 7. Epicycloids and Hypocycloids
Sidebar Maria Agnesi and Her "Witch"
Chapter 8. Variations on a Theme by Gauss
Chapter 9. Had Zeno Only Known This!
Chapter 10. (sin x) / x
Chapter 11. A Remarkable Formula
Sidebar Jules Lissajous and His Figures
Chapter 12. tan x
Chapter 9 Systems of Equations and Inequalities
Arthur Cayley (1821-1895)
David Hilbert (1862-1943)
Emmy Amalie Noether (1882-1935)
Julia Hall Bowman Robinson (1919-1985)
Olga Taussky-Todd (1906-1995)
Orbits and gravitation
Mathematics in Egyptian Papyri
Systems of Linear Rquations and Matrices
Matrix Algebra
SOS Math: Matrix Math
HMC Matrix Algebra
Elements of Matrix Algebra
Linear System of Equations
Elementary Row Operations
The Gaussian Elimination Method
The Gauss-Jordan Method
Inverse Matrix
Matrix Equation
Determinant
Determinant Expansion by Minors
Cramer's Rule Method
Carl Friedrich Gauss
Guillaume De l'H?pital
Arthur Cayley
Matrices and Determinants
A Short History of Linear and Matrix Algebra
Wassily Leontief
History of Matrices and Determinants
Systems of Linear Equations
Gauss-Jordan Elimination
Continued Fractions
Introduction to Continued Fractions
Continued Fraction
Chapter 10 Analytic Geometry
PDF for Conic Section App for TI-83
Conic Sections I
An Introduction To Conic Sections
Conic Sections II
Conic Sections III
Conic Section Gallery
The Conic Sections in Polar Coordinates
Conic Sections IV
Conic Sections in Ancient Greece
Apollonius of Perga
Parametric Equations I
Parametric Equations Tutorial
Parametric Equations
Parametric Equations II
Trigonometric Delights by Eli Maor
Chapter 13. A Mapmaker's Paradise
Chapter 14. sin x = 2: Imaginary Trigonometry
Sidebar Edmund Landau: The Master Rigorist
Chapter 15. Fourier's Theorem
Appendixes
App 1. Let's Revive an Old Idea
App 2. Barrow's Integration of sec [phi]
App 3. Some Trigonometric Gems
App 4. Some Special Values of sin [alpha]
Bibliography
Credits for Illustrations
Index
Chapter 11 Sequences and Series
TI-83, Sequences and series, and PDF
Using TI-83 with Sequences and Series
Chapter 12 Limits: A Preview of Calculus
Eratosthenes of Cyrene (276 BC - 194 BC)
Sir Isaac Newton (1643-1727)
Isaac Newton (1642 - 1727)
Newton
Newton, Isaac (1642-1727) -- from Eric Weisstein's World of S
Sir Isaac Newton - Home
Sir Isaac Newton - newton.org.uk
Sir Isaac Newton Scientist and Mathematician
Isaac Newton (1642 - 1727)
Leonardo Pisano Fibonacci (1170-1250)
The life and numbers of Fibonacci
Science News Online (6-12-99) Fibonacci at Random
The Fibonacci Numbers
The Fibonacci Numbers and Golden section in Nature - 1
Blaise Pascal (1623-1662)
All You Ever Want to Know About Pascal's Triangle
The Golden ratio
Prime numbers
Visual Calculus - Sequences and Series
Precalculus Material on Sequences and Series
ThinkQuest - Sequences and Series
Wikipedia - Math Induction
ThePrinciple of Math Induction
Understanding Math Induction
Last update: May 18, 2005