MATH 317 - Honors Calculus IV

3 units (fi 6)(SECOND, 4-0-0)

Implicit function theorem. Proof of the Change of Variables Theorem. Line integrals. Theorems of Green, Gauss and Stokes in their classical form. Differential forms and Stokes' Theorem in their context. Sequences and series of functions. Uniform convergence. Prerequisite: MATH 217.

MATH 467 - Theory of Probability

3 units (fi 6)(EITHER, 3-0-0)

Probability Measures, Lebesgue Measure on R, Random Variables, Probability Densities and Distributions, Lebesgue-Stieltjes integration, Independence, Convergence (almost surely, in probability, and in distribution), Product Probabilities, Key Inequalities (Markov, Chebyshev, Hölder, Jensen, and Paley-Zygmund), Characteristic functions, Law of Large Numbers, Central Limit Theorem, Concentration Inequalities, Applications to problems in analysis, geometry, and combinatorics Prerequisites: MATH 214 and MATH 216, or MATH 217.

STAT 571 - Probability and Measure

3 units (fi 6)(EITHER, 3-0-0)

Probability Measures, Lebesgue Measure on R, Random Variables, Probability Densities and Distributions, Lebesgue-Stieltjes integration, Independence, Convergence (almost surely, in probability, and in distribution), Product Probabilities, Key Inequalities (Markov, Chebyshev, Hölder, Jensen, and Paley-Zygmund), Characteristic functions, Law of Large Numbers, Central Limit Theorem, Concentration Inequalities, Applications to problems in analysis, geometry, and combinatorics. Prerequisite: STAT 512.