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.

Combinatorial Games and Puzzles Games and puzzles with a combinatorial flair (based on counting and arrangement) have entertained and frustrated people for millennia.  Mathematicians have developed new areas of research and discovered non-trivial mathematics upon examining these amusements.  Students will play games (including nim, hex, dots-and-boxes, clobber, and Mastermind®) and be presented with puzzles (including instant insanity and mazes) in an attempt to develop strategy and mathematics during play.  Basic notions in graph theory, design theory, combinatorics, and combinatorial game theory will be introduced.   Despite the jargon, this course will be accessible to all regardless of background.

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. MATH 0121 or equivalent, or by placement)

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, Combinatorial Games & Puzzles and more.  Explore top rated instructors and find the best for you.Is John Schmitt good ? Find out on MiddCourses.

Professor Schmitt is very passionate about linear algebra and makes the lectures as fun as possible. His analogies of some concepts make topics easier to grasp. Homework is assigned after each class and the problems are reflected on exams.

For context, I've always been a pretty good math student, but I've had to work for it. Problem sets are assigned every class. Some are very difficult a took me hours. Exams required a lot of preparation and were still hard. The material is repetitive, but there is a lot of memorization and it doesn't feel like a math class.

Schmitt is eccentric but grows on you as the course progresses, he's very passionate about linear & math in general. Uses lots of great analogies and puns to help explain difficult and conceptual topics. 2 midterms + 1 final make up 90% of the grade (30% each). Homework is due each day of class and is 10%. Exams are difficult but don't test anything that hasn't been covered in class; grading for them is harsh but fair. Definitely a difficult class but Schmitt makes it enjoyable, I don't know anyone in the class who dislikes/dreads it.