Bridges the gap between computational, algorithmic mathematics courses and more abstract, theoretical courses. Emphasizes the structure of modern mathematics: axioms, postulates, definitions, examples conjectures, counterexamples, theorems, and proofs. Builds skill in reading and writing proofs. Includes careful treatment of sets, functions, relations, cardinality, and construction of the integers, and the rational, real, and complex number systems.
Vector spaces, linear independence, basis and dimension, linear mappings, matrices, linear equations, determinants, Eigen values, and quadratic forms.
This course introduces descriptive and inferential statistics coupled with basic probability theory. Both traditional (normal and t-distribution) and simulation approaches including confidence intervals and hypothesis testing on means (one-sample, two-sample, paired), proportions (one-sample, two-sample), regression, and correlation are covered. Students will be introduced to numerous examples of real-world applications of statistics that are designed to help you develop a conceptual understanding of statistics. R and R Studio (free statistical software) will be used for lab exercises and final projects. The concepts and techniques in this course serve as building blocks for the inference and modeling used in later courses.