Modern Mathematics: Discrete Methods

Catalog description

This is the first part of a theoretical (i.e., proof-based) freshman sequence in mathematics. Math 61DM covers linear algebra, differential calculus in multiple variables, and applications in combinatorics, data science and machine learning. The linear algebra topics include general vector spaces, linear maps, matrices, the inner product, projections, eigenvalues, the spectral theorem, and singular value decomposition. The multivariable calculus topics include limits, continuity and differentiability in R^n, open/closed sets, optimization and classification of critical points. Examples of applications: linear recurrences, least squares regression, error correcting codes, spectral clustering, and low-rank approximation. The linear algebra content is covered jointly with Math 61CM. The 60DM sequence provides the necessary mathematical background for majors in Mathematics, Computer Science, Data Science, Economics, and most Natural Sciences and Engineering majors. Those who plan to major in Physics are recommended to take Math 61CM.