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Real-Life Mathematics — A Practical Guide for Software / AI / Network / Security Engineers

From "why does 0.1 + 0.2 != 0.3 " to deriving backpropagation, breaking down why RSA-2048 is safe, and computing how many /24s fit in a /16. You do not need a math degree to start. You need arithmetic, curiosity, and a terminal with Python.

40 chapters · 4 h 13 min of reading

Contents

40 chapters, one page each. Prefer one long page? Read the whole book on one page.

  1. What you will be able to do at the end1 min
  2. How to use this guide1 min
  3. Contents1 min
  4. Role-based learning paths1 min
  5. Notation cheat sheet15 min
  6. How to read a formula (the skill nobody teaches)2 min
  7. Part 1 — Beginner: The Foundations Everyone Needs
  8. 1. Number Systems & Bit-Level Math7 min
  9. 2. Modular Arithmetic3 min
  10. 3. Boolean Algebra & Logic4 min
  11. 4. Sets, Relations, and Functions3 min
  12. 5. Exponents & Logarithms3 min
  13. 6. Sequences, Series & Growth Rates3 min
  14. 7. Geometry & Trigonometry Essentials3 min
  15. 8. Basic Probability8 min
  16. 9. Basic Statistics8 min
  17. Part 2 — Intermediate: Core Engineering Mathematics
  18. 10. Linear Algebra I — Vectors & Matrices10 min
  19. 11. Linear Algebra II — Eigenvalues, Eigenvectors, Determinants9 min
  20. 12. Calculus I — Limits, Derivatives, Rates of Change12 min
  21. 13. Calculus II — Gradients, Partial Derivatives, the Chain Rule10 min
  22. 14. Probability Distributions11 min
  23. 15. Combinatorics & Counting3 min
  24. 16. Bayes' Theorem6 min
  25. 17. Graph Theory8 min
  26. 18. Complexity & Asymptotic Analysis4 min
  27. 19. Number Theory Basics10 min
  28. Part 3 — Expert: Domain-Specific Deep Dives (Senior Level)
  29. 20. Linear Algebra for AI/ML (SVD, PCA, Tensors)9 min
  30. 21. Optimization & Backpropagation9 min
  31. 22. Statistics for ML & Experimentation8 min
  32. 23. Information Theory7 min
  33. 24. Cryptographic Mathematics15 min
  34. 25. Network & Systems Mathematics10 min
  35. 26. Quantitative Security10 min
  36. 27. Signal Processing Basics9 min
  37. 28. Game Theory & Adversarial Thinking7 min
  38. 29. Control Theory Basics (Feedback Loops, PID)8 min
  39. Part 4 — Putting It Together
  40. Formula cheat sheet4 min
  41. Theorem index6 min
  42. Practice labs (hands-on, in order of difficulty)1 min
  43. Further Reading4 min
  44. Topics Not Covered (and where they'd fit)2 min

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