Foundations

Read these first

1. 01Classic Inequalities: Cauchy-Schwarz and AM-GM

   Two inequalities that show up in half of all quant interview maths. Cauchy-Schwarz caps how large a product-sum can be; AM-GM says an average never falls below a geometric average. Together they bound correlations, explain volatility drag, and solve optimisation problems without calculus.

Then the rest

1. 02Probability Spaces
2. 03Random Variables & Distributions
3. 04Expectation, Variance & Moments
4. 05Common Distributions
5. 06Moment Generating Functions
6. 07The Law of Large Numbers
7. 08The Central Limit Theorem
8. 09Bayes' Theorem
9. 10Markov Chains
10. 11Martingales
11. 12Linear Algebra for Quants
12. 13Eigenvalues & Eigenvectors
13. 14Singular Value Decomposition
14. 15Positive Semidefinite Matrices
15. 16Convex Optimization
16. 17Lagrange Multipliers & KKT Conditions
17. 18Conditional Probability
18. 19Correlation
19. 20Counting: Permutations and Combinations
20. 21Expected Value
21. 22Indicator Random Variables
22. 23Joint and Marginal Distributions
23. 24Logarithms and Exponentials
24. 25Mathematical Induction
25. 26Set Theory Basics
26. 27Standard Deviation
27. 28The Binomial Distribution
28. 29The Exponential Distribution
29. 30The Geometric Distribution
30. 31The Law of Total Probability
31. 32The Normal Distribution
32. 33The Poisson Distribution
33. 34The Random Walk
34. 35The Time Value of Money
35. 36The Uniform Distribution
36. 37Variance, Intuitively
37. 38Conditional Expectation
38. 39Entropy and Information
39. 40First-Step Analysis
40. 41Gambler's Ruin
41. 42Geometric Brownian Motion
42. 43Jensen's Inequality
43. 44KL Divergence
44. 45Markov and Chebyshev Inequalities
45. 46Monte Carlo Integration
46. 47Order Statistics
47. 48The Hypergeometric Distribution
48. 49The Multivariate Normal Distribution
49. 50The Negative Binomial Distribution
50. 51The Poisson Process
51. 52Copulas
52. 53Importance Sampling
53. 54Optional Stopping Theorem