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Foundations of Data Science combines an introductory look into the fundamental skills and concepts of computer programming and inferential statistics with hands-on experience in analyzing datasets by using common tools within the industry. Additionally, the course investigates ethical issues surrounding Data Science, such as data privacy.

Topics include real vector spaces, subspaces, linear dependence, span, matrix algebra, determinants, basis, dimension, inner product spaces, linear transformations, eigenvalues, eigenvectors, and proofs. Ordinary differential equations and first-order linear systems of differential equations; explicit solutions; qualitative analysis of solution behavior; linear structure, existence, and uniqueness of solutions. Partial differential equations.

Ordinary differential equations and first order linear systems of differential equations; methods of explicit solution; qualitative methods for the behavior of solutions; theoretical results for the linear structure, existence, and uniqueness of solutions.

Real vector spaces, subspaces, linear dependence and span, matrix algebra and determinants, basis and dimension, inner product spaces, linear transformations, eigenvalues and eigenvectors, proofs of basic results.

Set theory, logic, proof techniques, mathematical induction, relations and functions, recursion, combinatorics, elementary number theory, trees and graphs, analysis of algorithms. Emphasis on topics of relevance to mathematics and computer science majors.