Course Offerings

Winter 2015

See complete information about these courses in the course offerings database. For more information about a specific course, including course type, schedule and location, click on its title.

Calculus I

MATH 101 - Dymacek (Multiple Sections)

An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem.  

Fall 2014 descriptions:  

MATH 101: Calculus I (3). This section assumes that students have already seen some calculus, yet want to start over at the beginning of the calculus sequence. Students who have never seen calculus should instead take 101B (note that 101, 101B, and 101E all lead into Math 102). An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem. The class meets four days a week. (FM) Dymàcek, Keller, Staff.  

MATH 101B: Calculus I for Beginners: A First Course (3). This class is restricted to and specially tailored for those who are beginning their study of calculus. Students who have already taken calculus cannot take this section. Students who have already seen calculus, yet wish to retake it, must register for 101 or 101E instead of 101B. An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem. This section meets four days per week. (FM) Staff.  

MATH 101E: Calculus I with Biology Applications (3). Prerequisite: Instructor consent. Corequisite: BIOL 111 or CHEM 110. This section has a strong emphasis on biological applications, and is intended to benefit students interested in biological majors and health-related careers. It is designed and specially tailored for First-Years who took high school biology and who are taking a college lab science course concurrently. It is intended both for those students who have never had calculus before and also for those who have seen some calculus yet want to start over at the beginning of the calculus sequence. Mathematical concepts include the study of limits, derivatives, extrema, integrals, and the fundamental theorem of calculus. This section meets four days per week. Toporikova.

Calculus II

MATH 102 - Denne, Luery (Multiple Sections)

A continuation of MATH 101, including techniques and applications of integration, transcendental functions, and infinite series.

Introduction to Statistics

MATH 118 - Luery

Elementary probability and counting. Mean and variance of discrete and continuous random variables. Central Limit Theorem. Confidence intervals and hypothesis tests concerning parameters of one or two normal populations.

Discrete Mathematics I

MATH 121 - Keller

A study of concepts fundamental to the analysis of finite mathematical structures and processes. These include logic and sets, algorithms, induction, the binomial theorem, and combinatorics.

Discrete Mathematics II

MATH 122 - Richards

Applications of 121 include probability theory in finite sample spaces and properties of the binomial distribution. This course also includes relations on finite sets, equivalence classes, partial orderings, and an introduction to graph theory and enumeration.

Multivariable Calculus

MATH 221 - Feldman (Multiple Sections)

Motion in three dimensions, parametric curves, differential calculus of multivariable functions, multiple integrals, line integrals, and Green's Theorem.

Linear Algebra

MATH 222 - Richards (Multiple Sections)

Introductory linear algebra: systems of linear equations, matrices and determinants, vector spaces over the reals, linear transformations, eigenvectors, and vector geometry.

Complex Analysis

MATH 303 - McRae

Algebra of complex numbers, polar form, powers, and roots. Derivatives and geometry of elementary functions. Line integrals, the Cauchy Integral Theorem, the Cauchy Integral formula, Taylor and Laurent Series, residues, and poles. Applications.

Real Analysis II

MATH 312 - Beanland (Multiple Sections)

Riemann integration, nature and consequences of various types of convergence of sequences and series of functions, some special series, and related topics.

Abstract Algebra II

MATH 322 - Dresden (Multiple Sections)

Rings, including ideals, quotient rings, Euclidean rings, polynomial rings. Fields of quotients of an integral domain. Further field theory as time permits.

Partial Differential Equations

MATH 333 - Feldman

An introduction to the study of boundary value problems and partial differential equations. Topics include modeling heat and wave phenomena, Fourier series, separation of variables, and Bessel functions. Techniques employed are analytic, qualitative, and numerical.

Modern Geometry

MATH 342 - McRae

A survey of recent developments in geometry. Topics vary and may include such subjects as the geometry of curves and surfaces, singularity and catastrophe theory, geometric probability, integral geometry, convex geometry, and the geometry of space-time.

Calculus on Manifolds

MATH 345 - Denne

This course builds on material from both multivariable calculus and linear algebra. Topics covered include: manifolds, derivatives as linear transformations, tangent spaces, inverse and implicit function theorems, integration on manifolds, differential forms, and the generalized Stokes's Theorem.

Combinatorics

MATH 363 - Keller

Topics include counting methods, permutations and combinations, binomial identities, recurrence relations. generating functions, special sequences, partitions, and other topics as time and student interest permit.

Directed Individual Study

MATH 403 - McRae

Individual conferences. May be repeated for degree credit if the topics are different.

Fall 2014 topic:

MATH 403-01: Derivatives Markets (3): Prerequisite: Instructor consent required. This course is designed to prepare students for Exam MFE (Models for Financial Economics) from the Society of Actuaries. McRae. Fall 2014

Directed Individual Research

MATH 422 - Toporikova

Directed independent work in mathematics, especially for honors candidates. May be repeated for degree credit if the topics are different.

Honors Thesis

MATH 493 - Bush, Dymacek (Multiple Sections)

Honors Thesis.


Fall 2014

See complete information about these courses in the course offerings database. For more information about a specific course, including course type, schedule and location, click on its title.

Calculus I

MATH 101 - Dymacek, Keller, Luery, McRae (Multiple Sections)

An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem.  

Fall 2014 descriptions:  

MATH 101: Calculus I (3). This section assumes that students have already seen some calculus, yet want to start over at the beginning of the calculus sequence. Students who have never seen calculus should instead take 101B (note that 101, 101B, and 101E all lead into Math 102). An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem. The class meets four days a week. (FM) Dymàcek, Keller, Staff.  

MATH 101B: Calculus I for Beginners: A First Course (3). This class is restricted to and specially tailored for those who are beginning their study of calculus. Students who have already taken calculus cannot take this section. Students who have already seen calculus, yet wish to retake it, must register for 101 or 101E instead of 101B. An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem. This section meets four days per week. (FM) Staff.  

MATH 101E: Calculus I with Biology Applications (3). Prerequisite: Instructor consent. Corequisite: BIOL 111 or CHEM 110. This section has a strong emphasis on biological applications, and is intended to benefit students interested in biological majors and health-related careers. It is designed and specially tailored for First-Years who took high school biology and who are taking a college lab science course concurrently. It is intended both for those students who have never had calculus before and also for those who have seen some calculus yet want to start over at the beginning of the calculus sequence. Mathematical concepts include the study of limits, derivatives, extrema, integrals, and the fundamental theorem of calculus. This section meets four days per week. Toporikova.

Calculus I

MATH 101B - Richards (Multiple Sections)

An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem.  

Fall 2014 descriptions:  

MATH 101: Calculus I (3). This section assumes that students have already seen some calculus, yet want to start over at the beginning of the calculus sequence. Students who have never seen calculus should instead take 101B (note that 101, 101B, and 101E all lead into Math 102). An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem. The class meets four days a week. (FM) Dymàcek, Keller, Staff.  

MATH 101B: Calculus I for Beginners: A First Course (3). This class is restricted to and specially tailored for those who are beginning their study of calculus. Students who have already taken calculus cannot take this section. Students who have already seen calculus, yet wish to retake it, must register for 101 or 101E instead of 101B. An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem. This section meets four days per week. (FM) Staff.  

MATH 101E: Calculus I with Biology Applications (3). Prerequisite: Instructor consent. Corequisite: BIOL 111 or CHEM 110. This section has a strong emphasis on biological applications, and is intended to benefit students interested in biological majors and health-related careers. It is designed and specially tailored for First-Years who took high school biology and who are taking a college lab science course concurrently. It is intended both for those students who have never had calculus before and also for those who have seen some calculus yet want to start over at the beginning of the calculus sequence. Mathematical concepts include the study of limits, derivatives, extrema, integrals, and the fundamental theorem of calculus. This section meets four days per week. Toporikova.

Calculus I

MATH 101E - Toporikova

An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem.  

Fall 2014 descriptions:  

MATH 101: Calculus I (3). This section assumes that students have already seen some calculus, yet want to start over at the beginning of the calculus sequence. Students who have never seen calculus should instead take 101B (note that 101, 101B, and 101E all lead into Math 102). An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem. The class meets four days a week. (FM) Dymàcek, Keller, Staff.  

MATH 101B: Calculus I for Beginners: A First Course (3). This class is restricted to and specially tailored for those who are beginning their study of calculus. Students who have already taken calculus cannot take this section. Students who have already seen calculus, yet wish to retake it, must register for 101 or 101E instead of 101B. An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem. This section meets four days per week. (FM) Staff.  

MATH 101E: Calculus I with Biology Applications (3). Prerequisite: Instructor consent. Corequisite: BIOL 111 or CHEM 110. This section has a strong emphasis on biological applications, and is intended to benefit students interested in biological majors and health-related careers. It is designed and specially tailored for First-Years who took high school biology and who are taking a college lab science course concurrently. It is intended both for those students who have never had calculus before and also for those who have seen some calculus yet want to start over at the beginning of the calculus sequence. Mathematical concepts include the study of limits, derivatives, extrema, integrals, and the fundamental theorem of calculus. This section meets four days per week. Toporikova.

Calculus II

MATH 102 - Beanland, Denne, McRae (Multiple Sections)

A continuation of MATH 101, including techniques and applications of integration, transcendental functions, and infinite series.

Discrete Mathematics I

MATH 121 - Dymacek

A study of concepts fundamental to the analysis of finite mathematical structures and processes. These include logic and sets, algorithms, induction, the binomial theorem, and combinatorics.

Multivariable Calculus

MATH 221 - Richards

Motion in three dimensions, parametric curves, differential calculus of multivariable functions, multiple integrals, line integrals, and Green's Theorem.

Multivariable Calculus

MATH 221A - Finch (Multiple Sections)

Motion in three dimensions, parametric curves, differential calculus of multivariable functions, multiple integrals, line integrals, and Green's Theorem.

Linear Algebra

MATH 222 - Finch

Introductory linear algebra: systems of linear equations, matrices and determinants, vector spaces over the reals, linear transformations, eigenvectors, and vector geometry.

Real Analysis I

MATH 311 - Beanland (Multiple Sections)

Basic properties of real numbers, elementary topology of the real line and Euclidean spaces, and continuity and differentiability of real-valued functions on Euclidean spaces.

Abstract Algebra I

MATH 321 - Dresden (Multiple Sections)

Groups, including normal subgroups, quotient groups, permutation groups. Cauchy's theorem and Sylow's theorems.

Ordinary Differential Equations

MATH 332 - Luery (Multiple Sections)

First and second order differential equations, systems of differential equations, and applications. Techniques employed are analytic, qualitative, and numerical.

Geometric Topology

MATH 341 - Denne

A study of the shape of space focusing on characteristics not detected by geometry alone. Topics are approached pragmatically and include point set topology of Euclidean space, map-coloring problems, knots, the shape of the universe, surfaces, graphs and trees, the fundamental group, the Jordan Curve Theorem, and homology.

Graph Theory

MATH 361 - Keller

Graphs and digraphs, trees, connectivity, cycles and traversability, and planar graphs. Additional topics selected from colorings, matrices and eigenvalues, and enumeration.

Directed Individual Study

MATH 401 - Dresden

Individual conferences. May be repeated for degree credit if the topics are different.  

Fall 2014 topics:  

MATH 401-01: Actuarial Problem Solving (1). Prerequisite: Instructor consent. An investigation of various problem-solving techniques in preparation for Exam P, the probability and statistics actuary exam. Beanland.  

MATH 401-02: GRE Problem Solving (1). Prerequisite: Instructor consent. An investigation of various problem-solving techniques in preparation for the GRE math subject exam. Students are required to register for and take the GRE math subject exam (in the middle of November) as part of this course. Denne and Keller.  

MATH 401-03: Counting Permutations with Restricted Positions (1). Prerequisite: Instructor consent. An examination of the number of permutations on n letters with various restrictions. Dymàcek.

MATH 401-04: Putnam Problem Solving (1). Prerequisite: Instructor consent. An investigation of various problem-solving techniques in preparation for the Putnam math exam. Students are required to register for and take the Putnam exam (the first Saturday of December) as part of this course. Luery and Richards.

Directed Individual Study

MATH 401 - Denne / Keller

Individual conferences. May be repeated for degree credit if the topics are different.  

Fall 2014 topics:  

MATH 401-01: Actuarial Problem Solving (1). Prerequisite: Instructor consent. An investigation of various problem-solving techniques in preparation for Exam P, the probability and statistics actuary exam. Beanland.  

MATH 401-02: GRE Problem Solving (1). Prerequisite: Instructor consent. An investigation of various problem-solving techniques in preparation for the GRE math subject exam. Students are required to register for and take the GRE math subject exam (in the middle of November) as part of this course. Denne and Keller.  

MATH 401-03: Counting Permutations with Restricted Positions (1). Prerequisite: Instructor consent. An examination of the number of permutations on n letters with various restrictions. Dymàcek.

MATH 401-04: Putnam Problem Solving (1). Prerequisite: Instructor consent. An investigation of various problem-solving techniques in preparation for the Putnam math exam. Students are required to register for and take the Putnam exam (the first Saturday of December) as part of this course. Luery and Richards.

Directed Individual Study

MATH 401 - Dymacek

Individual conferences. May be repeated for degree credit if the topics are different.  

Fall 2014 topics:  

MATH 401-01: Actuarial Problem Solving (1). Prerequisite: Instructor consent. An investigation of various problem-solving techniques in preparation for Exam P, the probability and statistics actuary exam. Beanland.  

MATH 401-02: GRE Problem Solving (1). Prerequisite: Instructor consent. An investigation of various problem-solving techniques in preparation for the GRE math subject exam. Students are required to register for and take the GRE math subject exam (in the middle of November) as part of this course. Denne and Keller.  

MATH 401-03: Counting Permutations with Restricted Positions (1). Prerequisite: Instructor consent. An examination of the number of permutations on n letters with various restrictions. Dymàcek.

MATH 401-04: Putnam Problem Solving (1). Prerequisite: Instructor consent. An investigation of various problem-solving techniques in preparation for the Putnam math exam. Students are required to register for and take the Putnam exam (the first Saturday of December) as part of this course. Luery and Richards.

Directed Individual Study

MATH 401 - Luery / Richards

Individual conferences. May be repeated for degree credit if the topics are different.  

Fall 2014 topics:  

MATH 401-01: Actuarial Problem Solving (1). Prerequisite: Instructor consent. An investigation of various problem-solving techniques in preparation for Exam P, the probability and statistics actuary exam. Beanland.  

MATH 401-02: GRE Problem Solving (1). Prerequisite: Instructor consent. An investigation of various problem-solving techniques in preparation for the GRE math subject exam. Students are required to register for and take the GRE math subject exam (in the middle of November) as part of this course. Denne and Keller.  

MATH 401-03: Counting Permutations with Restricted Positions (1). Prerequisite: Instructor consent. An examination of the number of permutations on n letters with various restrictions. Dymàcek.

MATH 401-04: Putnam Problem Solving (1). Prerequisite: Instructor consent. An investigation of various problem-solving techniques in preparation for the Putnam math exam. Students are required to register for and take the Putnam exam (the first Saturday of December) as part of this course. Luery and Richards.

Directed Individual Study

MATH 403 - McRae

Individual conferences. May be repeated for degree credit if the topics are different.

Fall 2014 topic:

MATH 403-01: Derivatives Markets (3): Prerequisite: Instructor consent required. This course is designed to prepare students for Exam MFE (Models for Financial Economics) from the Society of Actuaries. McRae. Fall 2014

Honors Thesis

MATH 493 - Bush, Dymacek (Multiple Sections)

Honors Thesis.


Spring 2014

See complete information about these courses in the course offerings database. For more information about a specific course, including course type, schedule and location, click on its title.

Fundamental Concepts of Mathematics

MATH 301 - Bush, Humke (Multiple Sections)

Basic analytical tools and principles useful in mathematical investigations, from their beginning stages, in which experimentation and pattern analysis are likely to play a role, to their final stages, in which mathematical discoveries are formally proved to be correct. Strongly recommended for all prospective mathematics majors.

The Mathematics of Puzzles and Games

MATH 369 - Dymacek

The application of mathematics to puzzles and games. A brief survey on the designs of tournaments. The puzzles and games include but are not limited to the Rubik's Cube, poker, blackjack, and peg solitaire.

Seminar

MATH 383 - Beanland

Readings and conferences for a student or students on topics agreed upon with the directing staff. May be repeated for degree credit if the topics are different.

Spring 2014 topic:

MATH 383: Set Theory and Logic (4). The goal of this course is to acquaint students with the basics of naïve set theory including cardinal and ordinal numbers, well ordering, the Axiom of Choice, and Zorn's Lemma, as well as applications of these principles to other areas of mathematics. Beanland. Spring 2014

Winter 2014 topic:

Math 383:  Geometry of Groups (3). Prerequisite: Math 321. This course introduces the subject of geometric group theory. We study groups as geometric objects and see groups acting on geometric objects. Topics include Cayley graphs and Cayley complexes, group actions, the word problem in group theory, growth of groups, graphs of groups, groups acting on trees, etc.  Examples we encounter include free groups, Coxeter groups, braid groups, right-angled Artin groups, lamplighter groups, Baumslag-Solitar groups, and more. Abrams.