CH5019 - Mathematical Foundations of Data Analysis
Syllabus, Jan-May 2023
Objectives: The course will introduce students to the fundamental mathematical concepts
required for a program in data science
Course contents:
1.
Basics of Data Science (DS): Introduction; Typology of problems; Basics of
DS, ML and AI. Importance of linear algebra, statistics and optimization from a data
science perspective; Structured thinking for solving data science problems.
2.
Linear Algebra for DS: Matrices and their properties (determinants, traces,
rank, nullity, etc.); Eigenvalues and eigenvectors; Matrix factorizations; Inner
products; Distance measures; Projections; Notion of hyperplanes; half-planes.
3.
Probability, Statistics and Random Processes for DS: Probability theory and
axioms; Random variables; Probability distributions and density functions (univariate
and multivariate); Expectations and moments; Covariance and correlation; Statistics
and sampling distributions; Hypothesis testing of means, proportions, variances and
correlations; Confidence (statistical) intervals; Correlation functions; White-noise
process.
4.
Optimization for DS: Unconstrained optimization; Necessary and
sufficient conditions for optima; Gradient descent methods; Constrained
optimization, KKT conditions; Introduction to non-gradient techniques;
Introduction to least squares optimization; Optimization view of machine learning.
5.
Introduction to DS Methods: Linear regression as an exemplar
function approximation problem; Linear classification problems.
Text Book:
1.
G. Strang (2016). Introduction to Linear Algebra,
Wellesley-Cambridge Press, Fifth edition, USA.
2.
Bendat, J. S. and A. G. Piersol (2010). Random Data: Analysis
and Measurement Procedures. 4th Edition. John Wiley & Sons, Inc., NY,
USA:
3.
Montgomery, D. C. and G. C. Runger (2011). Applied Statistics
and Probability for Engineers. 5th Edition. John Wiley & Sons, Inc., NY,
USA:
4.
David G. Luenberger (1969). Optimization by Vector Space
Methods, John Wiley & Sons (NY)
5. Cathy O’Neil and Rachel Schutt (2013). Doing Data Science, O’Reilly Media