# Course Offerings

**Jump to:**- Fall 2020
- Spring 2020
- Winter 2020

## Fall 2020▲

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.

### The Art of Mathematical Thinking: An Introduction to the Beauty and Power of Mathematical Ideas

**MATH 100 - McRae, Alan**

Topics vary from term to term. Mathematics is a creative process whose artistic outcome is often a powerful tool for the sciences. This course gives you a new perspective into the world of mathematics while also developing your analytical reasoning skills.

Fall 2020, MATH 100-01: The Art of Mathematical Thinking: Viewpoints: Mathematical Perspective and Fractal Geometry in Art (3). A fusion of mathematical ideas with practical aspects of fine art, designed for liberal arts students and highly activity-based. Each subject begins with a hands-on art activity to introduce the mathematics being taught. Beginning with the use of perspective, not only in drawing but also in viewing perspective paintings, the exercises serve as motivation for our study of geometry and projective geometry, completing this section with anamorphic art. We then move into fractal geometry in nature and art. (FM) McRae .

Fall 2020, MATH 100-02: The Art of Mathematical Thinking: Viewpoints: Mathematical Perspective and Fractal Geometry in Art (3). A fusion of mathematical ideas with practical aspects of fine art, designed for liberal arts students and highly activity-based. Each subject begins with a hands-on art activity to introduce the mathematics being taught. Beginning with the use of perspective, not only in drawing but also in viewing perspective paintings, the exercises serve as motivation for our study of geometry and projective geometry, completing this section with anamorphic art. We then move into fractal geometry in nature and art. (FM) McRae .

Spring 2020, MATH 100-01: The Art of Mathematical Thinking: Solving Puzzles and Games Using Mathematics (3). Any high school mathematics class is sufficient preparation for this material. Students gain a new perspective into the world of mathematics while also developing their analytical and creative reasoning skills. In so doing, they gain an understanding of how theoretical results and concepts can be developed, used for problem-solving or for further investigation, and then how to clearly and coherently communicate their ideas and discoveries to others. In this course, we focus on mathematical reasoning to analyze various puzzles and games, which then leads to figuring out how to increase our chances of winning. The springboard for our discussion comes from the answers to the following questions: 1) Is there a good way to predict the winner of a game before the game ends? 2) Is there a strategy that will improve a player's chance of winning a game? 3) Is the game fair? The answers depend on what we mean by good and fair. We start by carefully and precisely formulating environments in which we can discuss approaches to solving puzzles and playing games. Then, we contemplate criteria that capture the notions of goodness and fairness within these environments. Along the way, students learn the importance of precise definitions and consistent rules of logic in mathematical reasoning. (FM) Finch-Smith.

### Calculus I

**MATH 101 - Dresden, Gregory P.**

An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem. Sections meet either 3 or 4 days a week, with material in the latter presented at a more casual pace.

### Calculus I

**MATH 101 - Hardy, Stephen R.**

An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem. Sections meet either 3 or 4 days a week, with material in the latter presented at a more casual pace.

### Calculus I

**MATH 101 - Beanland, Kevin J.**

An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem. Sections meet either 3 or 4 days a week, with material in the latter presented at a more casual pace.

### Calculus I

**MATH 101 - Bush, Michael R.**

### Calculus II

**MATH 102 - Dresden, Gregory P.**

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

### Calculus II

**MATH 102 - Swindle, Erica K.**

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

### Calculus II

**MATH 102 - Bush, Michael R.**

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

### Discrete Mathematics I

**MATH 121 - Dymacek, Wayne M.**

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.

### Bridges to Advanced Mathematics

**MATH 201 - Finch-Smith, Carrie E.**

The course explores various important mathematical constructions and ideas, with a particular emphasis on mathematical inquiry and reasoning. Topics include: sets, functions, equivalence relations, modular arithmetic, and basic properties of the integers, real numbers, and complex numbers.

### Multivariable Calculus

**MATH 221 - Feldman, Nathan S.**

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

### Multivariable Calculus

**MATH 221 - Swindle, Erica K.**

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

### Linear Algebra

**MATH 222 - Abrams, Aaron D.**

Linear algebra is the backbone of much of mathematics. Students in this course learn to identify and explain the basic principles, terminology, and theories used in linear algebra, and apply quantitative and/or qualitative reasoning skills to solve problems posed in linear algebra, primarily through applications of to both mathematics and the sciences, and also by writing proofs In mathematics.

### Probability

**MATH 309 - Prince Nelson, Sybil**

Probability, probability density and distribution functions, mathematical expectation, discrete and continuous random variables, and moment generating functions.

### Abstract Algebra

**MATH 321 - Beanland, Kevin J.**

An introduction to basic algebraic structures common throughout mathematics. These include rings, fields, groups, homomorphisms and quotient structures. Additional topics vary by instructor.

### Ordinary Differential Equations

**MATH 332 - Feldman, Nathan S.**

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

### Geometry

**MATH 343 - Abrams, Aaron D.**

This course is an introduction to geometric techniques through study of Euclidean and non-Euclidean geometries and their transformations. Additional topics vary by instructor.

### Graph Theory

**MATH 361 - Dymacek, Wayne M.**

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

### Topics in Abstract Algebra

**MATH 392A - Finch-Smith, Carrie E.**

Topics vary but can include field and Galois theory, geometric and combinatorial group theory, representation theory, number theory, algebraic number theory, commutative algebra, algebraic geometry, arithmetic geometry, advanced linear algebra, algebraic coding theory and cryptography, algebraic topology, homological algebra, and graph theory, May be repeated for degree credit if the topic is different.

### Honors Thesis

**MATH 493 - Dymacek, Wayne M.**

Honors Thesis.

## Spring 2020▲

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.

### The Art of Mathematical Thinking: An Introduction to the Beauty and Power of Mathematical Ideas

**MATH 100 - Finch-Smith, Carrie E.**

Topics vary from term to term. Mathematics is a creative process whose artistic outcome is often a powerful tool for the sciences. This course gives you a new perspective into the world of mathematics while also developing your analytical reasoning skills.

Spring 2020, MATH 100-01: The Art of Mathematical Thinking: Solving Puzzles and Games Using Mathematics (3). Any high school mathematics class is sufficient preparation for this material. Students gain a new perspective into the world of mathematics while also developing their analytical and creative reasoning skills. In so doing, they gain an understanding of how theoretical results and concepts can be developed, used for problem-solving or for further investigation, and then how to clearly and coherently communicate their ideas and discoveries to others. In this course, we focus on mathematical reasoning to analyze various puzzles and games, which then leads to figuring out how to increase our chances of winning. The springboard for our discussion comes from the answers to the following questions: 1) Is there a good way to predict the winner of a game before the game ends? 2) Is there a strategy that will improve a player's chance of winning a game? 3) Is the game fair? The answers depend on what we mean by good and fair. We start by carefully and precisely formulating environments in which we can discuss approaches to solving puzzles and playing games. Then, we contemplate criteria that capture the notions of goodness and fairness within these environments. Along the way, students learn the importance of precise definitions and consistent rules of logic in mathematical reasoning. (FM) Finch-Smith.

Winter 2020, MATH 100-01: The Art of Mathematical Thinking: Introduction to Codes (3) . Students gain a new perspective into the world of mathematics while also developing their analytical and creative reasoning skills. In so doing, they gain an understanding of how theoretical results and concepts can be developed, used for problem-solving or for further investigation, and then how to clearly and coherently communicate their ideas and discoveries to others. In this section, students explore the use of and questions about the numbers and codes which are everywhere. You might have a driver's license number, a Social Security Number, a student identification number, a telephone number, credit-card numbers--the list goes on and on. If you're filing out a form and you're asked for an identification number, will anyone be able to tell right away if you've made up a number? If someone is typing your information into a computer, is there a way to make sure they haven't made any errors? How are credit-card numbers kept safe when we make online purchases? We discuss types of errors, algorithms for checking for errors, and some methods for encrypting information to keep it secure. The only skills needed to enter this course are arithmetic and intellectual curiosity. Students learn how to analyze algorithms and develop problem-solving skills throughout the course. (FM) Finch-Smith.

Fall 2019, MATH 100-01: The Art of Mathematical Thinking: The Mathematics of Politics (3). Students gain a new perspective into the world of mathematics while also developing their analytical and creative reasoning skills. In so doing, they gain an understanding of how theoretical results and concepts can be developed, used for problem-solving or for further investigation, and then how to clearly and coherently communicate their ideas and discoveries to others. In this course, we focus on mathematical reasoning about politics. What makes this course mathematical is not numbers or formulas but rather reasoning. Students must think about what is possible and what is impossible. Is there a good way to determine winners of elections? Is there a good way to apportion congressional seats? Is there a good way to make decisions in situations of conflict and uncertainty? We begin by carefully and precisely formulating environments in which we can discuss approaches to elections, apportionment, and rational decision-making. We contemplate criteria that capture the notions of goodness within these environments, and see importance of precise definitions and consistent rules of logic in mathematical reasoning. Throughout the course, we pay attention to the way that technical words are defined so that the precise technical meaning is not confused with the ordinary meaning that the word carries in natural language. (FM) Finch-Smith.

Fall 2019, MATH 100-02: The Art of Mathematical Thinking: The Mathematics of Politics (3). Students gain a new perspective into the world of mathematics while also developing their analytical and creative reasoning skills. In so doing, they gain an understanding of how theoretical results and concepts can be developed, used for problem-solving or for further investigation, and then how to clearly and coherently communicate their ideas and discoveries to others. In this course, we focus on mathematical reasoning about politics. What makes this course mathematical is not numbers or formulas but rather reasoning. Students must think about what is possible and what is impossible. Is there a good way to determine winners of elections? Is there a good way to apportion congressional seats? Is there a good way to make decisions in situations of conflict and uncertainty? We begin by carefully and precisely formulating environments in which we can discuss approaches to elections, apportionment, and rational decision-making. We contemplate criteria that capture the notions of goodness within these environments, and see importance of precise definitions and consistent rules of logic in mathematical reasoning. Throughout the course, we pay attention to the way that technical words are defined so that the precise technical meaning is not confused with the ordinary meaning that the word carries in natural language. (FM) Finch-Smith.

### Topics in Mathematics

**MATH 383 - Bush, Michael R.**

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 2020, MATH 383-01:Topic: The Mathematics of Information (4). Prerequisites: MATH 201 and 222 or instructor consent. The modern world runs on information. Huge numbers of bits (0s and 1s) are passing invisibly through the wires and air around you right now. These bits encode various types of data including text, pictures, audio/video signals etc. In 1948, a pioneering paper by Claude Shannon founded a new research area-- information theory--which, among other things, investigates the process of converting streams of symbols from one form to another and various associated questions that are still the focus of much modern research. For example, what is the most efficient way to go about encoding a stream of data so that it can be transmitted as quickly as possible over some channel or stored using a minimal amount of space? How can one build in redundancy so that errors due to noise (scratches on a CD/DVD, electromagnetic interference, etc.) can be detected and corrected? What should you do if privacy/secrecy is important? In this course, you will see how these sorts of questions can be formalized and addressed mathematically. Bush.

### Topics in Mathematics

**MATH 383 - Dymacek, Wayne M.**

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 2020, MATH 383-03: Topic: Mathematics of Puzzles and Games (4). Prerequisite: MATH 321. An examination of some of the mathematics of the following ten games and puzzles: Rubik's cube, Sam Lloyd's 15 puzzle, Sudoku and similar puzzles, poker, blackjack, craps, twister, cribbage, darts, and peg solitaire. Six other games or puzzles chosen by the students are also examined. Dymàcek .

## Winter 2020▲

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.

### The Art of Mathematical Thinking: An Introduction to the Beauty and Power of Mathematical Ideas

**MATH 100 - Finch-Smith, Carrie E.**

Topics vary from term to term. Mathematics is a creative process whose artistic outcome is often a powerful tool for the sciences. This course gives you a new perspective into the world of mathematics while also developing your analytical reasoning skills.

Spring 2020, MATH 100-01: The Art of Mathematical Thinking: Solving Puzzles and Games Using Mathematics (3). Any high school mathematics class is sufficient preparation for this material. Students gain a new perspective into the world of mathematics while also developing their analytical and creative reasoning skills. In so doing, they gain an understanding of how theoretical results and concepts can be developed, used for problem-solving or for further investigation, and then how to clearly and coherently communicate their ideas and discoveries to others. In this course, we focus on mathematical reasoning to analyze various puzzles and games, which then leads to figuring out how to increase our chances of winning. The springboard for our discussion comes from the answers to the following questions: 1) Is there a good way to predict the winner of a game before the game ends? 2) Is there a strategy that will improve a player's chance of winning a game? 3) Is the game fair? The answers depend on what we mean by good and fair. We start by carefully and precisely formulating environments in which we can discuss approaches to solving puzzles and playing games. Then, we contemplate criteria that capture the notions of goodness and fairness within these environments. Along the way, students learn the importance of precise definitions and consistent rules of logic in mathematical reasoning. (FM) Finch-Smith.

Winter 2020, MATH 100-01: The Art of Mathematical Thinking: Introduction to Codes (3) . Students gain a new perspective into the world of mathematics while also developing their analytical and creative reasoning skills. In so doing, they gain an understanding of how theoretical results and concepts can be developed, used for problem-solving or for further investigation, and then how to clearly and coherently communicate their ideas and discoveries to others. In this section, students explore the use of and questions about the numbers and codes which are everywhere. You might have a driver's license number, a Social Security Number, a student identification number, a telephone number, credit-card numbers--the list goes on and on. If you're filing out a form and you're asked for an identification number, will anyone be able to tell right away if you've made up a number? If someone is typing your information into a computer, is there a way to make sure they haven't made any errors? How are credit-card numbers kept safe when we make online purchases? We discuss types of errors, algorithms for checking for errors, and some methods for encrypting information to keep it secure. The only skills needed to enter this course are arithmetic and intellectual curiosity. Students learn how to analyze algorithms and develop problem-solving skills throughout the course. (FM) Finch-Smith.

Fall 2019, MATH 100-01: The Art of Mathematical Thinking: The Mathematics of Politics (3). Students gain a new perspective into the world of mathematics while also developing their analytical and creative reasoning skills. In so doing, they gain an understanding of how theoretical results and concepts can be developed, used for problem-solving or for further investigation, and then how to clearly and coherently communicate their ideas and discoveries to others. In this course, we focus on mathematical reasoning about politics. What makes this course mathematical is not numbers or formulas but rather reasoning. Students must think about what is possible and what is impossible. Is there a good way to determine winners of elections? Is there a good way to apportion congressional seats? Is there a good way to make decisions in situations of conflict and uncertainty? We begin by carefully and precisely formulating environments in which we can discuss approaches to elections, apportionment, and rational decision-making. We contemplate criteria that capture the notions of goodness within these environments, and see importance of precise definitions and consistent rules of logic in mathematical reasoning. Throughout the course, we pay attention to the way that technical words are defined so that the precise technical meaning is not confused with the ordinary meaning that the word carries in natural language. (FM) Finch-Smith.

Fall 2019, MATH 100-02: The Art of Mathematical Thinking: The Mathematics of Politics (3). Students gain a new perspective into the world of mathematics while also developing their analytical and creative reasoning skills. In so doing, they gain an understanding of how theoretical results and concepts can be developed, used for problem-solving or for further investigation, and then how to clearly and coherently communicate their ideas and discoveries to others. In this course, we focus on mathematical reasoning about politics. What makes this course mathematical is not numbers or formulas but rather reasoning. Students must think about what is possible and what is impossible. Is there a good way to determine winners of elections? Is there a good way to apportion congressional seats? Is there a good way to make decisions in situations of conflict and uncertainty? We begin by carefully and precisely formulating environments in which we can discuss approaches to elections, apportionment, and rational decision-making. We contemplate criteria that capture the notions of goodness within these environments, and see importance of precise definitions and consistent rules of logic in mathematical reasoning. Throughout the course, we pay attention to the way that technical words are defined so that the precise technical meaning is not confused with the ordinary meaning that the word carries in natural language. (FM) Finch-Smith.

### Calculus I

**MATH 101 - Feldman, Nathan S.**

### Calculus I

**MATH 101 - Dymacek, Wayne M.**

### Calculus I

**MATH 101 - Bush, Michael R.**

### Calculus II

**MATH 102 - Denne, Elizabeth J.**

### Calculus II

**MATH 102 - Beanland, Kevin J.**

### Bridges to Advanced Mathematics

**MATH 201 - Colbert, Cory H.**

The course explores various important mathematical constructions and ideas, with a particular emphasis on mathematical inquiry and reasoning. Topics include: sets, functions, equivalence relations, modular arithmetic, and basic properties of the integers, real numbers, and complex numbers.

### Multivariable Calculus

**MATH 221 - Swindle, Erica K.**

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

### Linear Algebra

**MATH 222 - Hardy, Stephen R.**

Linear algebra is the backbone of much of mathematics. Students in this course learn to identify and explain the basic principles, terminology, and theories used in linear algebra, and apply quantitative and/or qualitative reasoning skills to solve problems posed in linear algebra, primarily through applications of to both mathematics and the sciences, and also by writing proofs In mathematics.

### Financial and Actuarial Mathematics

**MATH 270 - Dresden, Gregory P.**

An introduction to some of the fundamental topics in financial and actuarial mathematics. Possible topics include calculating present and accumulated values for various streams of cash and the theoretical basis of corporate finance and financial models and the application of those models to insurance and other financial risks.

### Mathematical Statistics

**MATH 310 - Hardy, Stephen R.**

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

### Real Analysis

**MATH 311 - Swindle, Erica K.**

A systematic study of concepts basic to calculus, such as topology of the real numbers, limits, differentiation, integration, sequences and series. Additional topics vary by instructor.

### Abstract Algebra

**MATH 321 - Dresden, Gregory P.**

An introduction to basic algebraic structures common throughout mathematics. These include rings, fields, groups, homomorphisms and quotient structures. Additional topics vary by instructor.

### Ordinary Differential Equations

**MATH 332 - Finch-Smith, Carrie E.**

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

### Geometry

**MATH 343 - Denne, Elizabeth J.**

This course is an introduction to geometric techniques through study of Euclidean and non-Euclidean geometries and their transformations. Additional topics vary by instructor.

### Topics in Analysis

**MATH 391 - Beanland, Kevin J.**

Topics vary but can include complex analysis, topology, differential equations, differential topology, numerical analysis, functional analysis, measure theory, fractal geometry, Lebesgue integration and Fourier analysis, harmonic analysis, and analytic number theory. May be repeated for degree credit if the topic is different.

### Topics in Abstract Algebra

**MATH 392 - Dymacek, Wayne M.**

Topics vary but can include field and Galois theory, geometric and combinatorial group theory, representation theory, number theory, algebraic number theory, commutative algebra, algebraic geometry, arithmetic geometry, advanced linear algebra, algebraic coding theory and cryptography, algebraic topology, homological algebra, and graph theory, May be repeated for degree credit if the topic is different.

### Topics in Geometry and Topology

**MATH 393 - McRae, Alan**

Topics vary but can include knot theory, topology and geometry of surfaces, differential geometry, Riemann surfaces, 3-manifolds, tilings, geometric probability, geometry of spacetime, finite geometry, computational geometry, differential topology, and projective geometry. May be repeated for degree credit if the topic is different.

### Directed Individual Study

**MATH 401 - Dresden, Gregory P.**

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

Winter 2020, Math 401-01: Directed Individual Study: FM Prep (1). Prerequisite: Instructor consent . A study of problem-solving techniques in preparation for the Society of Actuaries Exam FM, which covers financial mathematics. Dresden.

### Directed Individual Study

**MATH 401 - McRae, Alan**

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

### Directed Individual Study

**MATH 401 - Bush, Michael R.**

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

### Directed Individual Study

**MATH 402 - McRae, Alan**

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

Winter 2020, Math 402-01: Directed Individual Study: Discrete Models of Financial Markets (2) . Prerequisite: MATH 221 and 222. This course explains in simple settings the fundamental ideas of financial market modeling and derivative pricing, using the No Arbitrage Principle. Relatively elementary mathematics leads to powerful notions and techniques--viability, completeness, self-financing and replicating strategies, arbitrage and equivalent martingale measures--which are directly applicable in practice. McRae.