# Course Offerings

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

## 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. Dymacek.

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. Dymacek.

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. Dymacek.

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:

### 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.

## Winter 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 (Multiple Sections)**

Winter 2014 description:

Math 101E: Calculus I for Beginners with Biology Applications (3). Prerequisite: Instructor consent. Students who have already taken calculus cannot take this section. This section has a strong emphasis in biology. An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem. This class is restricted to and specially tailored for those who are beginning their study of calculus. (Students who have already seen calculus, yet wish to retake it, must register for 101 instead of 101B.) This section meets four days per week. (FM) Toporikova.

Fall 2013 descriptions:

MATH 101: Calculus I (3). An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem. 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 both 101 and 101B lead into Math 102). The class meets three days a week. (FM) Abrams, Beanland, Keller.

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

### Calculus I

**MATH 101E - Toporikova**

Winter 2014 description:

Math 101E: Calculus I for Beginners with Biology Applications (3). Prerequisite: Instructor consent. Students who have already taken calculus cannot take this section. This section has a strong emphasis in biology. An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem. This class is restricted to and specially tailored for those who are beginning their study of calculus. (Students who have already seen calculus, yet wish to retake it, must register for 101 instead of 101B.) This section meets four days per week. (FM) Toporikova.

Fall 2013 descriptions:

MATH 101: Calculus I (3). An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem. 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 both 101 and 101B lead into Math 102). The class meets three days a week. (FM) Abrams, Beanland, Keller.

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

### Calculus II

**MATH 102 - Abrams, Feldman (Multiple Sections)**

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

### 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.

### Multivariable Calculus

**MATH 221 - Dresden, Keller (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 - Abrams, McRae (Multiple Sections)**

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

### Financial and Actuarial Mathematics

**MATH 270 - Dresden**

Topics include the time value of money, the force of interest, annuities, yield rates, amortization schedules, bonds, contracts, options, swaps, and arbitrage. Equal emphasis is given to both the theoretical background and to the computational aspects of interest theory. This course helps prepare students for the Financial Mathematics actuary exam.

### Mathematical Statistics II

**MATH 310 - McRae (Multiple Sections)**

Sampling distributions, point and interval estimation, testing hypotheses, regression and correlation, and analysis of variance.

### 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 - Bush, Dymacek (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.

### Number Theory

**MATH 365 - Bush**

Topics include prime numbers, Euclidean algorithm, congruences, Chinese Remainder Theorem, Fermat's Little Theorem, Euler's Theorem, arithmetic functions, Euler's phi function, perfect numbers, the quadratic reciprocity law, continued fractions, and other topics as time and student interest permit.

### Directed Individual Study

**MATH 401 - Dresden**

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

Winter 2014 Topic:

MATH 401-01: Dir Study:Actuarial Prep (1). This course covers material necessary to prepare students for the Financial Mathematics exam of the Society of Actuaries. Topics include annuities, time value of money, present values of cash flows, derivatives, options, forwards, and strategies for hedging. Dresden.

Fall 2013 Topics:

MATH 401-01: 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 401-02: 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. Bush.

MATH 401-03: Problems in Algebraic Number Theory (1). Prerequisite: Instructor consent. An introduction to algebraic number theory through an investigation of the classical problems in the field. Finch.

MATH 401-04: Algebraic Topology (1). Pass/Fail only. Prequisite: Instructor consent. An introduction to algebraic topology. Abrams

MATH 401-05: Functional Analysis (1). Pass/Fail only. Prequisite: Instructor consent. An introduction to the basic tools of functional analysis including Banach spaces, Hilbert spaces, linear operators, and spectral theory. Feldman

### Directed Individual Study

**MATH 401 - Beanland**

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

Winter 2014 Topic:

MATH 401-01: Dir Study:Actuarial Prep (1). This course covers material necessary to prepare students for the Financial Mathematics exam of the Society of Actuaries. Topics include annuities, time value of money, present values of cash flows, derivatives, options, forwards, and strategies for hedging. Dresden.

Fall 2013 Topics:

MATH 401-01: 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 401-02: 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. Bush.

MATH 401-03: Problems in Algebraic Number Theory (1). Prerequisite: Instructor consent. An introduction to algebraic number theory through an investigation of the classical problems in the field. Finch.

MATH 401-04: Algebraic Topology (1). Pass/Fail only. Prequisite: Instructor consent. An introduction to algebraic topology. Abrams

MATH 401-05: Functional Analysis (1). Pass/Fail only. Prequisite: Instructor consent. An introduction to the basic tools of functional analysis including Banach spaces, Hilbert spaces, linear operators, and spectral theory. Feldman

### Directed Individual Study

**MATH 403 - Bush**

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

### Honors Thesis

**MATH 493 - Dresden, Dymacek (Multiple Sections)**

Honors Thesis.