Official course description. Links to the textbook by Louis-Pierre Arguin, A First Course in Stochastic Calculus: AMS Bookstore, Colgate library access.
40 lectures---each corresponding to a 50-minute class---covering the completeness of the reals; sequences and series; topology on the real line; limits and continuity; differentiation; and Riemann integration. Culminated with Lebesgue's theorem on Riemann integrability.
41 lectures---each corresponding to a 50-minute class---based loosely on Gilbert Strang's Introduction to Linear Algebra (5th ed.) This version had a stronger emphasis on numerical linear algebra; preparation for future study in data analysis; and a cohesive account of the fundamental theorem of linear algebra. Quick MATLAB commands for matrix operations & decompositions were indicated as much as possible. The course culminated with the 5 characterizations of a positive definite matrix, and the singular value decomposition (SVD) of a matrix.
P.S.: The Colgate version of Undergraduate Probability was harder than the UConn version. I covered more thoroughly transformations of univariate distributions, and assigned the proof of Hoeffding's inequality on the final assignment.
An independent study course. We covered roughly the first 12 of Dan Spielman's course notes, some functional analysis (Laplacian ↔ Dirichlet form ↔ semigroup, connection to Markov chains), and Doyle and Snell's "Random walks and electric networks".
Some of the materials I've used in teaching this course have been adapted in the current iteration of MATH 3160. See the UConn Undergraduate Probability OER.
I taught the Honors version of MATH 3160 (to be renamed MATH 3165 in 2017) in Spring 2015 and Fall 2015.
For a history of Honors probability at UConn, see my report [pdf].
Tom Roby and I recorded Lightboard video lectures for MATH 3160 in Fall 2015, with the assistance of the Center for Excellence in Teaching & Learning. UConn affiliates can access the video catalog using their NetIDs and passwords. If you are not a UConn affiliate and wish to access the videos, please contact me or Tom.