JOSE SUÁREZ ARES - W0LFPY
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Mathematical Foundations

A structured record of the mathematical foundations I have studied and continue to develop for quantitative finance, machine learning, and computing.

Linear Algebra

MATH-101
  • Vector Spaces & Subspaces
  • Eigenvalues & Eigenvectors
  • Singular Value Decomposition (SVD)
  • Principal Component Analysis (PCA)
fx A = U Σ V^T

Calculus & Real Analysis

MATH-201
  • Limits and Continuity
  • Multivariate Calculus
  • Taylor Series Expansion
  • Measure Theory Basics
  • Sequences and Series
  • Metric Spaces
fx f(x) = Σ f⁽ⁿ⁾(a)(x-a)ⁿ / n!

Probability Theory

STAT-301
  • Axiomatic Probability
  • Random Variables & Distributions
  • Law of Large Numbers
  • Central Limit Theorem
fx P(A|B) = P(A ∩ B) / P(B)

Statistics

STAT-302
  • Hypothesis Testing
  • Maximum Likelihood Estimation
  • Linear Regression Models
  • Time Series Analysis (ARIMA, GARCH)
  • Bayesian Inference
fx E[Rᵢ] - Rf = βᵢ(E[Rm] - Rf)

Books

  • [1]
    Differential Calculus (Ron Larson, Bruce Edwards). Calculus & Real Analysis. [Study Notes]
  • [2]
    Integral Calculus (Ron Larson, Bruce Edwards). Calculus & Real Analysis. [Study Notes]
  • [3]
    A First Course in Probability (Sheldon Ross). Base Probability Theory. [Study Notes]
  • [4]
    Probability Theory: The Logic of Science (E. T. Jaynes). Base Probability Theory. [Study Notes]
  • [5]
    Probability and Measure (Patrick Billingsley). Rigorous Probability Theory. [Study Notes]
  • [6]
    Foundations of Modern Probability (Olav Kallenberg). Rigorous Probability Theory. [Study Notes]
  • [7]
    Probabilities and Potential (Dellacherie, Meyer). Rigorous Probability Theory. [Study Notes]
  • [8]
    Statistical Inference (George Casella, Roger L. Berger). Statistics & Inference. [Study Notes]
  • [9]
    Bayesian Data Analysis (Andrew Gelman, John B. Carlin, Hal S. Stern, David B. Dunson, Aki Vehtari, Donald B. Rubin). Statistics & Inference. [Study Notes]
  • [10]
    The Elements of Statistical Learning (Trevor Hastie, Robert Tibshirani, Jerome Friedman). Statistics & Inference. [Study Notes]
  • [11]
    Convex Optimization (Stephen Boyd, Lieven Vandenberghe). Optimization. [Study Notes]
  • [12]
    Convex Optimization Theory — Dimitri Bertsekas (Dimitri Bertsekas). Optimization. [Study Notes]
  • [13]
    Numerical Optimization (Jorge Nocedal, Stephen J. Wright). Optimization & Numerical Methods. [Study Notes]
  • [14]
    Operations Research and Management: Quantitative Methods for Planning and Decision-Making in Business and Economics (Franz W. Peren, Thomas Neifer). Optimization & Numerical Methods. [Study Notes]
  • [15]
    Stochastic Differential Equations: An Introduction with Applications (Bernt Øksendal). Stochastic Processes & Stochastic Calculus. [Study Notes]
  • [16]
    Continuous Martingales and Brownian Motion (Daniel Revuz, Marc Yor). Stochastic Processes & Stochastic Calculus. [Study Notes]
  • [17]
    Stochastic Calculus for Finance I: The Binomial Asset Pricing Model (Steven Shreve). Financial Mathematics. [Study Notes]
  • [18]
    Stochastic Calculus for Finance II: Continuous-Time Models (Steven Shreve). Financial Mathematics. [Study Notes]
  • [19]
    Finding Alphas: A Quantitative Approach to Building Trading Strategies (Igor Tulchinsky). Quantitative Finance and Financial Applications. [Study Notes]
  • [20]
    Theory of Games and Economic Behavior (John von Neumann, Oskar Morgenstern). Game Theory & Economics. [Study Notes]