abhi[dot]wadhwa[at] columbia [dot] edu

undergraduate and graduate coursework in math, in descending order. * marks graduate courses.

mathematics @ columbia

• * APMA E4306 — stochastic analysis
  Brownian motion and diffusion processes. Ito calculus, stochastic differential equations, martingale theory, and connections to partial differential equations. Applications to mathematical finance and filtering.

  Oksendal, Stochastic Differential Equations
• * COMS W4252 — computational learning
  Theoretical foundations of machine learning. PAC learning, VC dimension, Rademacher complexity, boosting, online learning, and kernel methods. Computational and statistical tradeoffs.

  Shalev-Shwartz & Ben-David, Understanding Machine Learning
• * ECBM E4040 — deep learning
  Neural network architectures and training. Convolutional and recurrent networks, optimization methods, regularization, attention mechanisms, and generative models. Emphasis on implementation.

  Goodfellow, Bengio & Courville, Deep Learning
• * APMA E4150 — functional analysis
  Banach and Hilbert spaces, bounded linear operators, spectral theory, compact operators, and the Hahn-Banach, open mapping, and closed graph theorems. Applications to differential equations.

  Kreyszig, Introductory Functional Analysis with Applications
• * APMA E4200 — partial differential equations
  Classification of PDEs. Heat, wave, and Laplace equations. Fourier methods, Green's functions, method of characteristics, energy methods, and maximum principles.

  Evans, Partial Differential Equations
• * IEOR E6613 — convex optimization
  Convex sets and functions, duality theory, optimality conditions. Interior-point methods, conic and semidefinite programming. Modeling applications in engineering, finance, and machine learning.

  Boyd & Vandenberghe, Convex Optimization
• * STAT GR5241 — machine learning theory
  Statistical learning theory and methods. Regularization, kernel machines, ensemble methods, EM algorithm, graphical models, and high-dimensional inference.

  Hastie, Tibshirani & Friedman, The Elements of Statistical Learning

mathematics @ usc

• * MATH 501 — numerical analysis and computation
  Floating-point arithmetic, polynomial interpolation, numerical quadrature, iterative methods for linear systems, eigenvalue algorithms, and numerical solutions of ODEs.

  Burden & Faires, Numerical Analysis
• * MATH 541a — introduction to mathematical statistics
  Theory of estimation and hypothesis testing. Sufficiency, completeness, maximum likelihood, uniformly most powerful tests, confidence intervals, and asymptotic methods.

  Casella & Berger, Statistical Inference
• MATH 520 — complex analysis
  Analytic and meromorphic functions, Cauchy's theorem and integral formula, Taylor and Laurent series, residue calculus, conformal mappings, and analytic continuation.

  Ahlfors, Complex Analysis
• * MATH 505a — applied probability
  Markov chains, Poisson processes, renewal theory, continuous-time Markov chains, queuing models, and martingale convergence. Applications in operations research and engineering.

  Ross, Introduction to Probability Models
• MATH 425a — fundamental concepts of analysis
  Rigorous treatment of the real number system, metric spaces, sequences and series, continuity, differentiation, and the Riemann-Stieltjes integral.

  Rudin, Principles of Mathematical Analysis
• MATH 467 — theory and computational methods for optimization
  Linear and nonlinear programming. Simplex method, duality, KKT conditions, gradient and Newton methods, interior-point algorithms, and constrained optimization.

  Nocedal & Wright, Numerical Optimization
• MATH 471 — topics in linear algebra
  Canonical forms, inner product spaces, spectral theorem, singular value decomposition, matrix factorizations, and applications to data analysis.

  Axler, Linear Algebra Done Right
• MATH 448 — complex variables · uiuc
  Functions of a complex variable, contour integration, residue theorem, argument principle, conformal mapping, and applications to potential theory and fluid flow.

  Churchill & Brown, Complex Variables and Applications
• MATH 408 — mathematical statistics
  Point and interval estimation, hypothesis testing, likelihood methods, regression analysis, and analysis of variance. Emphasis on both theory and applications.

  Wackerly, Mendenhall & Scheaffer, Mathematical Statistics
• MATH 407 — probability theory
  Combinatorial probability, random variables and distributions, expectation, moment-generating functions, joint distributions, limit theorems, and the central limit theorem.

  Ross, A First Course in Probability
• MATH 395 — seminar in problem solving
  Putnam-style competition mathematics. Problem-solving strategies across algebra, analysis, combinatorics, and number theory. Weekly problem sets and presentations.

  Larson, Problem-Solving Through Problems
• MATH 245 — mathematics of physics and engineering I
  Ordinary differential equations, Laplace transforms, Fourier series, boundary-value problems, and Sturm-Liouville theory. Emphasis on physical and engineering applications.

  Boyce & DiPrima, Elementary Differential Equations
• MATH 226 — calculus III
  Multivariable calculus. Partial derivatives, multiple integrals, vector fields, line and surface integrals, Green's, Stokes', and the divergence theorem.

  Stewart, Calculus: Early Transcendentals
• MATH 126 — calculus II
  Techniques of integration, improper integrals, sequences and series, Taylor and Maclaurin series, parametric equations, and polar coordinates.

  Stewart, Calculus: Early Transcendentals

economics, finance & business

• FBE 435 — applied finance in fixed income securities · usc
  Bond pricing, yield curve construction, duration and convexity, interest rate derivatives, mortgage-backed securities, and credit risk modeling.

  Tuckman & Serrat, Fixed Income Securities
• FBE 423 — introduction to venture capital and private equity · usc
  Fund structure and governance, deal sourcing, term sheets, valuation methods for early-stage companies, portfolio management, and exit strategies.

  Metrick & Yasuda, Venture Capital and the Finance of Innovation
• BUAD 308 — advanced business finance · usc
  Capital structure theory, mergers and acquisitions, real options, risk management, and corporate governance. Quantitative models for financial decision-making.

  Berk & DeMarzo, Corporate Finance
• ACCT 410 — foundations of accounting · usc
  Financial statement preparation and analysis, accrual accounting, revenue recognition, ratio analysis, and reporting standards under GAAP.

  Libby, Libby & Hodge, Financial Accounting
• ECON 305 — intermediate macroeconomic theory · usc
  National income accounting, IS-LM and AD-AS models, economic growth, monetary and fiscal policy, inflation, unemployment, and open-economy macroeconomics.

  Mankiw, Macroeconomics
• ECON 303 — intermediate microeconomic theory · usc
  Consumer and producer theory, general equilibrium, welfare economics, market failures, externalities, game theory, and information economics.

  Varian, Intermediate Microeconomics

policy, philosophy & law

• PHIL 246 — cognitive science · usc
  Foundations of mind and cognition. Perception, language, reasoning, consciousness, and the computational theory of mind. Intersections of philosophy, psychology, neuroscience, and artificial intelligence.

  Thagard, Mind: Introduction to Cognitive Science
• PPD 225 — solving public problems · usc
  Frameworks for diagnosing and addressing collective-action problems. Stakeholder analysis, institutional design, evidence-based policy, and the politics of implementation.

  Bardach & Patashnik, A Practical Guide for Policy Analysis
• PPD 240 — citizenship and public ethics · usc
  Ethical obligations of citizens and public officials. Democratic participation, distributive justice, rights and liberties, civic virtue, and the moral foundations of policy.

  Sandel, Justice: What's the Right Thing to Do?
• LAW 225 — constitutional law · usc
  Structure and interpretation of the U.S. Constitution. Separation of powers, federalism, judicial review, due process, equal protection, and individual rights under the Bill of Rights.

  Chemerinsky, Constitutional Law: Principles and Policies