A Mathematics Refresher

A Mathematics Refresher

From counting to the mathematics behind machine learning. This is the complete book, online — version 1.27, July 2026. Every chapter is also in the PDF and EPUB.

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  1. Preface
  2. Part I — The Foundations
  3. 1Numbers: The Raw Material
  4. 2Algebra: The Grammar of Mathematics
  5. Part II — High School Mathematics (10+2)
  6. 3Functions and Their Graphs
  7. 4Quadratics and Polynomials
  8. 5Exponentials and Logarithms
  9. 6Trigonometry
  10. 7Coordinate Geometry and the Conic Sections
  11. 8Sequences, Series, and the Binomial Theorem
  12. 9Counting and Probability
  13. 10Vectors
  14. 11Complex Numbers
  15. 12Matrices and Determinants
  16. 13Calculus I: Limits and Derivatives
  17. 14Calculus II: Integration
  18. Part III — BSc Mathematics
  19. 15Real Analysis: Calculus Grows Up
  20. 16Linear Algebra: The Study of Flat Things
  21. 17Multivariable Calculus
  22. 18Differential Equations
  23. 19Abstract Algebra: The Mathematics of Symmetry
  24. 20Probability Theory and Statistics
  25. Part IV — The Mathematics of Artificial Intelligence
  26. Part IV — The Mathematics of Artificial Intelligence
  27. 21Vectors, Matrices, and Data
  28. 22The Calculus of Learning
  29. 23Probability, Information, and Learning
  30. Epilogue: The View from Here
  31. Appendix A: Worked Solutions
  32. Appendix B: The Drill Bank — Graded Practice
  33. Appendix C: A Pocket Glossary of Symbols
  34. Appendix D: Corrections and Changes