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The book comes in three volumes. Volumes 2 and 3 both build on Volume 1 but not on each other. Chapter numbers are shared across all three, so they match the companion code (ch17_derivatives/ is Chapter 17).

Volume 1: Foundations to Precalculus

Numbers, algebra, geometry, functions, trigonometry, sequences and complex numbers: the shared foundation for Volumes 2 and 3.

Part I: Foundations
  1. Numbers, the Number Line, and Arithmetic
  2. Fractions, Decimals, Percentages, and Ratios
  3. Exponents, Roots, and Scientific Notation
Part II: Algebra
  1. The Language of Algebra: Variables, Expressions, and Equations
  2. Linear Equations and Inequalities
  3. Systems of Equations
  4. Polynomials and Factoring
  5. Quadratics
Part III: Geometry
  1. Euclidean Geometry: Shapes, Angles, Similarity, and Proof
  2. Coordinate Geometry
Part IV: Functions, Trigonometry, and Precalculus
  1. Functions and Their Graphs
  2. Exponentials and Logarithms
  3. Trigonometry
  4. Sequences, Series, and Summation Notation
  5. Complex Numbers
Download Volume 1 (PDF)

Volume 2: Continuous Mathematics

Calculus, linear algebra and numerical mathematics: change, space, and how computers actually compute with them.

Part V: Calculus
  1. Limits and Continuity
  2. The Derivative
  3. Using Derivatives: Optimisation, Approximation, and Newton’s Method
  4. The Integral
  5. Multivariable Calculus and the Gradient
Part VII: Linear Algebra
  1. Vectors
  2. Matrices as Transformations
  3. Eigenvectors, Bases, and Applications
Part IX: Numerical Mathematics
  1. Numerical Mathematics: How Computers Actually Compute
Download Volume 2 (PDF)

Volume 3: Discrete and Probabilistic Mathematics

Logic, proof, number theory, combinatorics, graphs, probability and statistics, ending with the Horizons capstone on optimisation, machine learning and information.

Part VI: Discrete Mathematics
  1. Logic and Sets
  2. Proof and Induction
  3. Integers, Divisibility, and Modular Arithmetic
  4. Counting and Combinatorics
  5. Graph Theory
Part VIII: Probability and Statistics
  1. Probability
  2. Random Variables and Distributions
  3. Statistics and Inference
Part X: Horizons
  1. Horizons: Optimisation, Machine Learning, and Information
Download Volume 3 (PDF)

Appendices