Course note and presentations, textbook references, syllabus and exercises of some of the courses I taught.
Foundations Seminar – MATH 1150
The seminars offer challenging and interesting mathematical topics that require only high school mathematics.
Calculus II – MATH 1952
Differentiation and integration of functions of one variable especially focusing on the theory, techniques and applications of integration. Prerequisite: MATH 1951
Calculus I – MATH 1951
Limits, continuity, differentiation of functions of one variable, applications of the derivative. This course counts toward the Analytical Inquiry: The Natural and Physical World requirement. Prerequisite: MATH 1070 or equivalent.
Intro. Probability Theory – MATH 4510/5510 – SUMMER
Studies axioms, combinatorial analysis, independence and conditional probability, discrete and absolutely continuous distributions, expectation and distribution of functions of random variables, laws of large numbers, central limit theorems, and simple Markov chains if time permits
Intro. Probability and Statistics – MATH 3510 – SUMMER
Introduces the basic notions of Probability: random variables, expectation, conditioning, and the standard distributions (Binomial, Poisson, Exponential, Normal). This course also covers the Law of Large Numbers and Central Limit Theorem as they apply to statistical questions: sampling from a random distribution, estimation, and hypothesis testing.
Intro. to Discrete Mathematics – MATH 2001
Introduces the ideas of rigor and proof through an examination of basic set theory, existential and universal quantifiers, elementary counting, discrete probability, and additional topics.
Topics in Mathematical Probability – MATH 6534
Offers selected topics in probability such as sums of independent random variables, notions of convergence, characteristic functions, Central Limit Theorem, random walk, conditioning and martingales, Markov chains and Brownian motion.
Intro. to Mathematical Statistics – STAT 4520/5520
Examines point and confidence interval estimation. Principles of maximum likelihood, sufficiency, and completeness: tests of simple and composite hypotheses, linear models, and multiple regression analysis if time permits. Analyzes various distribution-free methods. Same as MATH 5520 and STAT 4520 and STAT 5520.
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