Course note and presentations, textbook references, syllabus and exercises of some of the courses I taught.
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.
Intro. Probability and Statistics – MATH 3510
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. Probability Theory – MATH 4510/5510
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
Linear Algebra – MATH 2130
This course is an introduction to linear algebra. Topics we will cover include basic properties of systems of linear equations, matrices and matrix algebra, determinants, vector spaces, subspaces, linear independence of vectors, basis and dimension of subspaces, linear transformations, eigenvalues and eigenvectors of a matrix, orthogonality of vectors, inner product and length of vectors.
Rodrigo Ribeiro 