John Schmitt
MATH
Linear Algebra
MATH 0200Linear 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.
12 reviewsF24Graph Theory
MATH 0247Graph 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.
3 reviewsF24Multivariable Calculus
MATH 0223Multivariable 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.
9 reviewsS24Combinatorics
MATH 0345Combinatorics 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.
5 reviewsS24Linear Algebra
MATH 0200Linear 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.
11 reviewsF23Linear Algebra Methods
MATH 0746Linear 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.
0 reviewsF23Linear Algebra
MATH 0200Linear 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.
11 reviewsS23Graph Theory
MATH 0247Graph 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.
6 reviewsS23Calculus II
MATH 0122Calculus 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.
0 reviewsF22Polynomial Method Seminar
MATH 0745The 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).
0 reviewsF22Linear Algebra
MATH 0200Linear 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.
1 reviewF21Combinatorics
MATH 0345Combinatorics 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.
2 reviewsF21Multivariable Calculus
MATH 0223Multivariable 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.
0 reviewsS21Graph Theory
MATH 0247Graph 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.
1 reviewS2190% of the grade were the 3 exams, with the other 10% being homework, which was stressful. Class is pretty well structured, with homework being due every time the class met. Professor Schmitt seemed to really enjoy teaching linear algebra
Professor Schmitt was enthusiastic and clear in his lectures. Class time was very well spent and entertaining and he made an effort to make everyone feel involved (and never skimped on the dad jokes). Exams were very attainable especially since we were given previous years' exams to study from.
Professor Schmitt did an outstanding job in explaining the concepts covered in the course. He is also humorous occasionally with his jokes and anecdotes. The exams encompass a large percentage of the course grade, thus it is crucial to be prudent in each.