# Course Offerings

**Jump to:**- Spring 2015
- Winter 2015
- Fall 2014

## Spring 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.

### Fundamental Concepts of Mathematics

**MATH 301 - Denne, Dresden, Keller (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.

### Numerical Analysis

**MATH 353 - Finch**

Analysis, implementation, and applications of algorithms for solving equations, fitting curves, and numerical differentiation and integration. Theorems and proofs are complemented by hands-on programming exercises fostering a concrete understanding of accuracy, efficiency and stability, as well as an awareness of potential pitfalls in machine arithmetic. No previous programming experience is required.

## 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, Dresden, McRae (Multiple Sections)**

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

### Introduction to Statistics

**MATH 118 - Beanland**

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 401 - Finch**

Individual conferences. May be repeated for degree credit if the topics are different. Winter 2015 topics:

MATH 401-01: Actuarial Prep (1). Prepares students for the FM (Financial Mathematics) actuary exam. Finch.

MATH 401-02: Combinatorics of Partially Ordered Sets (1) Prerequiisite: Instructor consent. Introduction to partially ordered sets: Dilworth's theorem, linear extensions, linear discrepancy, interval orders, and online algorithms for posets. 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.

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 - Keller**

Individual conferences. May be repeated for degree credit if the topics are different. Winter 2015 topics:

MATH 401-01: Actuarial Prep (1). Prepares students for the FM (Financial Mathematics) actuary exam. Finch.

MATH 401-02: Combinatorics of Partially Ordered Sets (1) Prerequiisite: Instructor consent. Introduction to partially ordered sets: Dilworth's theorem, linear extensions, linear discrepancy, interval orders, and online algorithms for posets. 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.

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 401-04: 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. Winter 2015 topics:

MATH 401-01: Actuarial Prep (1). Prepares students for the FM (Financial Mathematics) actuary exam. Finch.

MATH 401-02: Combinatorics of Partially Ordered Sets (1) Prerequiisite: Instructor consent. Introduction to partially ordered sets: Dilworth's theorem, linear extensions, linear discrepancy, interval orders, and online algorithms for posets. Keller.

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 401-04: 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

### 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**

Fall 2014 descriptions:

### 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**

### Directed Individual Study

**MATH 401 - Denne / Keller**

### Directed Individual Study

**MATH 401 - Dymacek**

### Directed Individual Study

**MATH 401 - Luery / 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.