Alexei Kolesnikov

I decided to group the courses by instruction techniques I used. The links will send you to the syllabus of the latest incarnation of each course.

Student teams

Here are the courses that I taught using the student teams approach. My experience has been that teamwork is an unfamiliar way for the students to study, but I take it as an argument for, rather than against, employing teams. Keys to success: keep teams as non-homogeneous as possible (this means in particular that the instructor picks the teams, not the students); change the teams twice during the semester (this helps students who are struggling with their team get a "fresh start" and prevents students from being "boxed into" specific roles in the teams); do make sure that the team member roles change from one week to the next.

Introduction to Abstract Mathematics. Elements of peer-instruction are perfect for students mastering problem-solving techniques and dealing, perhaps for the first time, with things like equivalence relations, partitions, and connections between them.
Mathematical Structures II. This is the second in the series of three mathematics courses for the students who are on their way to become elementary school teachers. I found that these students study much better in teams than individually: even the weaker students who actively participated in teams have done very well on (individual) assessments.
Introduction to Abstract Algebra. High level of abstraction calls for a combination of individual study time and group discussions.


Here is a list of courses that were taught with additional technology (WeBWorK, Mathematica, or both):
I used WeBWorK in Precalculus, Calculus for Applications, and Linear Algebra. For more information on the online homework, please visit the WeBWorK page on my website.
I used both WeBWorK and Mathematica in Calculus I, Calculus II, and Calculus III. Mathematica laboratories are a required component in all Calculus courses taught at Towson. For more about my experience with Mathematica, please visit the Mathematica page on my website.

Research component

These are the courses in which I included a research component. Additional information about the undergraduate student research projects that were completed as the result of the courses is on the Student research page on my website.
Applied Mathematics Laboratory. I did write a syllabus for the first of the four semesters I was involved with the course. The syllabus helped set expectations in the beginning; ultimately, the team meetings were a combination of project updates, brainstorming, and working on the chosen tasks.
Senior Seminar. After some initial hesitation, the majority of students welcomed the student-taught style of lectures. The evaluation criteria for oral presentations worked out quite well. It was important to give (private) nearly immediate feedback on the presentations at the start of the semester.
Applied Combinatorics. Despite its name, the course is a part of curriculum only for the pure mathematics concentration students (it is an elective for that concentration). The remaining three concentrations (including the applied mathematics) do not list the course even as an elective. As the result, the course ran only once in the last 12 years. The syllabus above is from that rare instance. However, I have directed several independent study courses using essentially this syllabus. One of those courses has resulted in a very nice research project by the student.