Foundations of Algebra

Mathematics
By OgbonLab

The pre-calculus toolkit, rebuilt for the way you'll actually use it.

Pre-calculus foundations: numbers, algebra, geometry, coordinates, trigonometry, and functions.

18 parts 68 sections Free, browser-native
Start reading → First up: The Integers

Table of contents

Every section is a working session: text, math, code, interactive widgets. Click any title to jump in.

Part 1: Chapter 1: Number Systems and Their Properties

  1. The Integers
  2. Rules for Addition
  3. Rules for Multiplication
  4. Rational Numbers
  5. Multiplicative Inverses
  6. Even and Odd Integers; Divisibility

Part 2: Chapter 2: Reading, Writing, and Notating Mathematics

  1. On Reading Mathematics
  2. Mathematical Notation
  3. Sets and Elements
  4. Logic

Part 3: Chapter 3: Systems of Linear Equations

  1. Equations in Two Unknowns
  2. Equations in Three Unknowns

Part 4: Chapter 4: The Real Number Line

  1. Addition and Multiplication of Real Numbers
  2. Real Numbers: Positivity
  3. Inequalities
  4. Powers and Roots

Part 5: Chapter 5: Quadratic Equations and the Discriminant

  1. Solving Quadratic Equations

Part 6: Chapter 6: Distance, Angles, and the Pythagorean Theorem

  1. Measuring Distance
  2. Measuring Angles
  3. The Pythagorean Theorem

Part 7: Chapter 7: Areas and Circumferences of Circles

  1. Circumference of a Circle
  2. Area of a Disc

Part 8: Chapter 8: Plane Isometries, Rigid Motions

  1. Standard Plane Mappings: Translations, Rotations, Reflections
  2. What Is an Isometry?
  3. Composing Isometries
  4. Inverse Isometries
  5. Classifying Isometries
  6. Congruent Figures

Part 9: Chapter 9: The Coordinate Plane

  1. Cartesian Coordinates and the Plane
  2. The Distance Formula
  3. Circles in the Coordinate Plane
  4. Rational Points and Diophantine Circles

Part 10: Chapter 10: Vectors and Operations on Points

  1. Vector Addition and the Parallelogram Law
  2. Dilations, Reflections, and Other Transformations

Part 11: Chapter 11: Lines, Rays, and Segments

  1. Lines in the Plane
  2. The Equation of a Line
  3. Line Segments
  4. Rays and Half-Lines

Part 12: Chapter 12: Trigonometry of the Unit Circle

  1. Radians and Arc Length
  2. Sine and Cosine on the Unit Circle
  3. The Tangent Function
  4. Graphs of the Trigonometric Functions
  5. Sum and Difference Identities
  6. Rotation as a Trigonometric Operation

Part 13: Chapter 13: Conic Sections in the Coordinate Plane

  1. Lines Revisited: Slope and General Form
  2. The Parabola
  3. The Ellipse
  4. The Hyperbola
  5. Rotated Conics and Their Equations

Part 14: Chapter 14: Functions and Their Graphs

  1. What Is a Function?
  2. Plotting and Reading Graphs
  3. Polynomial Functions
  4. Exponential Functions
  5. Logarithmic Functions

Part 15: Chapter 15: Mappings and Permutations

  1. Mappings as Generalized Functions
  2. Composition and Inverse Mappings
  3. Permutations of Finite Sets

Part 16: Chapter 16: Complex Numbers

  1. Complex Arithmetic in the Plane
  2. Polar and Exponential Form

Part 17: Chapter 17: Mathematical Induction and Summation

  1. The Principle of Mathematical Induction
  2. Sigma Notation and Finite Sums
  3. Geometric Series

Part 18: Chapter 18: Matrices and Determinants

  1. Matrix Operations and Algebra
  2. The 2x2 Determinant
  3. Properties of 2x2 Determinants
  4. The 3x3 Determinant
  5. Properties of 3x3 Determinants
  6. Cramer's Rule for Linear Systems

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