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18.S096

Special Subject in Mathematics

Units arranged · Undergraduate

Opportunity for group study of subjects in mathematics not otherwise included in the curriculum. Offerings are initiated by members of the Mathematics faculty on an ad hoc basis, subject to departmental approval.

January IAP 2023 · Matrix Calculus for Machine Learning and Beyond

We all know that calculus courses such as {{% resource_link "54fb3d8f-10d8-493c-94d7-17d7859a8c87" "*18.01 Single Variable Calculus*" %}} and {{% resource_link "6fcb92d1-f2a8-467a-b462-14945ef4fca6" "*18.02 Multivariable Calculus*" %}} cover univariate and vector calculus, respectively. Modern applications such as machine learning and large-scale optimization require the next big step, "matrix calculus" and calculus on arbitrary vector spaces. This class covers a coherent approach to matrix calculus showing techniques that allow you to think of a matrix holistically (not just as an array of scalars), generalize and compute derivatives of important matrix factorizations and many other complicated-looking operations, and understand how differentiation formulas must be reimagined in large-scale computing.

Fall 2015 · Topics in Mathematics of Data Science

Topics

  • Overview and Two Open Problems
  • Principal Component Analysis in High Dimensions and the Spike Model
  • Graphs, Diffusion Maps, and Semi-supervised Learning
  • Spectral Clustering and Cheeger’s Inequality
  • Concentration Inequalities, Scalar and Matrix Versions
  • Johnson-Lindenstrauss Lemma and Gordon’s Theorem
  • Local Convergence of Graphs and Enumeration of Spanning Trees
  • Compressed Sensing and Sparse Recovery
  • Group Testing and Error-Correcting Codes
  • Approximation Algorithms and Max-Cut
  • Community Detection and the Stochastic Block Model
  • Synchronization Problems and Alignment
  • Project Presentations
  • Project Report
Fall 2013 · Topics in Mathematics with Applications in Finance

Topics

  • Linear Algebra
  • Probability Theory
  • Matrix Primer
  • Stochastic Processes I
  • Regression Analysis
  • Value At Risk (VAR) Models
  • Time Series Analysis I
  • Volatility Modeling
  • Regularized Pricing and Risk Models
  • Time Series Analysis II
  • Time Series Analysis III
  • Commodity Models
  • Portfolio Theory
  • Factor Modeling
  • Portfolio Management
  • Stochastic Processes II
  • Itō Calculus
  • Option Price and Probability Duality
  • Stochastic Differential Equations
  • Calculus of Variations and its Application in FX Execution
  • Quanto Credit Hedging
  • HJM Model for Interest Rates and Credit
  • Ross Recovery Theorem

Prerequisites & course information

Prereq: Permission of instructor U (IAP) Units arranged Can be repeated for credit.

Sources