Linear Algebra Matrices and systems of linear equations, the Euclidean space of three dimensions and other real vector spaces, independence and dimensions, scalar products and orthogonality, linear transformations and matrix representations, eigenvalues and similarity, determinants, the inverse of a matrix and Cramer's rule.

Graph Theory       A graph (or network) is a useful mathematical model when studying a set of discrete objects and the relationships among them.  We often represent an object with a vertex (node) and a relation between a pair with an edge (line).  With the graph in hand, we then ask questions, such as: Is it connected? Can one traverse each edge precisely once and return to a starting vertex? For a fixed k/, is it possible to “color” the vertices using /k colors so that no two vertices that share an edge receive the same color?  More formally, we study the following topics: trees, distance, degree sequences, matchings, connectivity, coloring, and planarity.  Proof writing is emphasized.

Multivariable Calculus The calculus of functions of more than one variable. Introductory vector analysis, analytic geometry of three dimensions, partial differentiation, multiple integration, line integrals, elementary vector field theory, and applications.

Combinatorics       Combinatorics is the “art of counting.”  Given a finite set of objects and a set of rules placed upon these objects, we will ask two questions.  Does there exist an arrangement of the objects satisfying the rules?  If so, how many are there?  These are the questions of existence and enumeration.  As such, we will study the following combinatorial objects and counting techniques: permutations, combinations, the generalized pigeonhole principle, binomial coefficients, the principle of inclusion-exclusion, recurrence relations, and some basic combinatorial designs.

Linear Algebra Methods Seminar A tutorial in linear algebra methods for students who have completed work in Linear Algebra (and possibly Abstract Algebra) and at least one of Combinatorics, Graph Theory and Number Theory. We will study the linear algebra method through applications to combinatorics, graph theory, number theory, and incidence geometry. Working independently and in small groups, students will gain experience reading advanced sources and communicating their insights in expository writing and oral presentations. Fulfills the capstone senior work requirement for the mathematics major.

Calculus II A continuation of MATH 0121, may be elected by first-year students who have had an introduction to analytic geometry and calculus in secondary school. Topics include a brief review of natural logarithm and exponential functions, calculus of the elementary transcendental functions, techniques of integration, improper integrals, applications of integrals including problems of finding volumes, infinite series and Taylor's theorem, polar coordinates, ordinary differential equations.

The Polynomial Method A tutorial in the Polynomial Method for students who have completed work in Abstract Algebra and at least one of Combinatorics, Graph Theory, and Number Theory.  We will study Noga Alon’s Combinatorial Nullstellensatz and related theorems, along with their applications to combinatorics, graph theory, number theory, and incidence geometry.  Working independently and in small groups, students will gain experience reading advanced sources and communicating their insights in expository writing and oral presentations.  Fulfills the capstone senior work requirement for the mathematics major.  (Approval required; MATH 0302 and one of the following: MATH 0241, MATH 0247, or MATH 0345).

John Schmitt

Reviews and ratings for John Schmitt at Middlebury College.John Schmitt teaches Linear Algebra, Graph Theory, Multivariable Calculus and more.  Explore top rated instructors and find the best for you.Is John Schmitt good ? Find out on MiddCourses.

Schmitt is a wonderful professor who cares about his students. It’s impressive how well he understands/remembers what learning linear for the first time is like even though what he’s teaching must be like second nature to him. 

Honestly, I really did not enjoy this course. It was probably the most boring math class I've been in. I believe this is more a function of Linear Algebra than it is of Middlebury or the instructor. ww

Prof. Schmitt is very passionate about the material that he teaches, and his passion got me even more interested in the concepts we were learning. I really liked his teaching style, and how he encouraged questions during lectures.