# Course Offerings

## Spring 2022▲

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

Spring 2022, MATH 100-01: The Art of Mathematical Thinking: The Mathematics of Puzzles and Games (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.

Spring 2022, MATH 100A-01: The Art of Mathematical Thinking: Mathematical Foundations of Data Science (3).  This course is intended to introduce mathematical foundations of data science. We will focus on linear algebra, numerical computation, data science and the programming language. After successfully completing this course, students will develop the necessary mathematical background for data science and will be able to solve a variety of real-world data-based problems. Furthermore, via numerous examples in real life, we learn how to access information logically, understand connection analytically, and model questions mathematically. (FM) Wang.

Winter 2022, MATH 100-02: The Art of Mathematical Thinking: Mathematics of Tilings and Patterns (3).  In this course we study tiling and counting proofs for many famous formulas involving the Fibonacci numbers, the Lucas numbers, continued fractions, and binomial coefficients. No prior knowledge is needed. (FM) Dresden.

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

MATH 100A - Wang, Chong

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

Spring 2022, MATH 100-01: The Art of Mathematical Thinking: The Mathematics of Puzzles and Games (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.

Spring 2022, MATH 100A-01: The Art of Mathematical Thinking: Mathematical Foundations of Data Science (3).  This course is intended to introduce mathematical foundations of data science. We will focus on linear algebra, numerical computation, data science and the programming language. After successfully completing this course, students will develop the necessary mathematical background for data science and will be able to solve a variety of real-world data-based problems. Furthermore, via numerous examples in real life, we learn how to access information logically, understand connection analytically, and model questions mathematically. (FM) Wang.

Winter 2022, MATH 100-02: The Art of Mathematical Thinking: Mathematics of Tilings and Patterns (3).  In this course we study tiling and counting proofs for many famous formulas involving the Fibonacci numbers, the Lucas numbers, continued fractions, and binomial coefficients. No prior knowledge is needed. (FM) Dresden.

### Art + Math

MATH 175 - McRae, Alan

A course in mathematics and art suitable for liberal arts students. Our approach is highly activity and experience based. Our goal is to explore how some of the greatest mathematical ideas had parallel developments in the world of art, all told through a narrative of culture and the history of ideas.

### Topics in Mathematics

MATH 383A - 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 2022, MATH 383A-01: The Mathematics of Information (3).  Prerequisite: MATH 201 and MATH 222.  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. Among other things, this 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, we will see how some of these questions can be formalized and addressed mathematically. Bush.

### Topics in Mathematics

MATH 383B - Abrams, Aaron D.

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 2022, MATH 383B-01: Configuration Spaces (3).  Prerequisite: MATH 201 or MATH 221 or MATH 222.   A configuration space is a mathematical object that encodes all the possible states of a system that has multiple moving parts. Examples of such systems include mechanical linkages as well as physical brain-teasers like the Rubik's cube. The mathematical study of configuration spaces is applied widely in a number of practical fields, such as robotics. In this course we will study the configuration spaces associated to various types of mechanisms, puzzles, and gadgets. We will learn how to analyze the complexity of mechanical linkages and the difficulty of logic-based puzzles such as Sudoku. Students will have the opportunity to design and build their own examples. Abrams.

## Winter 2022▲

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

Spring 2022, MATH 100-01: The Art of Mathematical Thinking: The Mathematics of Puzzles and Games (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.

Spring 2022, MATH 100A-01: The Art of Mathematical Thinking: Mathematical Foundations of Data Science (3).  This course is intended to introduce mathematical foundations of data science. We will focus on linear algebra, numerical computation, data science and the programming language. After successfully completing this course, students will develop the necessary mathematical background for data science and will be able to solve a variety of real-world data-based problems. Furthermore, via numerous examples in real life, we learn how to access information logically, understand connection analytically, and model questions mathematically. (FM) Wang.

Winter 2022, MATH 100-02: The Art of Mathematical Thinking: Mathematics of Tilings and Patterns (3).  In this course we study tiling and counting proofs for many famous formulas involving the Fibonacci numbers, the Lucas numbers, continued fractions, and binomial coefficients. No prior knowledge is needed. (FM) Dresden.

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

MATH 100 - Dresden, Gregory P.

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

Spring 2022, MATH 100-01: The Art of Mathematical Thinking: The Mathematics of Puzzles and Games (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.

Spring 2022, MATH 100A-01: The Art of Mathematical Thinking: Mathematical Foundations of Data Science (3).  This course is intended to introduce mathematical foundations of data science. We will focus on linear algebra, numerical computation, data science and the programming language. After successfully completing this course, students will develop the necessary mathematical background for data science and will be able to solve a variety of real-world data-based problems. Furthermore, via numerous examples in real life, we learn how to access information logically, understand connection analytically, and model questions mathematically. (FM) Wang.

Winter 2022, MATH 100-02: The Art of Mathematical Thinking: Mathematics of Tilings and Patterns (3).  In this course we study tiling and counting proofs for many famous formulas involving the Fibonacci numbers, the Lucas numbers, continued fractions, and binomial coefficients. No prior knowledge is needed. (FM) Dresden.

### Calculus I

MATH 101 - Wang, Chong

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 - Abrams, Aaron D.

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 - McRae, Alan

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 II

MATH 102 - Feldman, Nathan S.

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

### Calculus II

MATH 102 - Denne, Elizabeth J.

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

### Discrete Mathematics I

MATH 121 - Broda, James

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.

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 - Dresden, Gregory P.

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

### Linear Algebra

MATH 222 - Bush, Michael 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.

### Mathematical Statistics

MATH 310 - Prince Nelson, Sybil

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

### Real Analysis

MATH 311 - Broda, James

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 - Bush, Michael R.

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

### Partial Differential Equations

MATH 333 - Feldman, Nathan S.

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.

### 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.

### Topics in Abstract Algebra

MATH 392A - Colbert, Cory H.

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.

Winter 2022, Math 392A-01: Topics in Abstract Algebra: Rings, Fields, and Galois Theory (3).
Prerequisite: MATH 321. Rings, ring homomorphisms, modules, module homomorphisms, Euclidean domains, PIDs, UFDs, field extensions, degree, algebraic numbers, automorphisms, irreducible polynomials, Galois groups, Galois correspondence. Colbert.

### Topics in Geometry and Topology

MATH 393A - Denne, Elizabeth J.

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.

Winter 2021, MATH 393A-01: Topics in Geometry and Topology: Experimenting with Geometry (3). Prerequisite: MATH 342 or 343. This course will be run in an experimental format modeled on the notion of a "Geometry Lab."  Students will study unsolved problems in geometry, learning whatever background material is relevant for understanding and approaching the selected problems.  Topics are likely to include algebraic geometry, hyperbolic geometry, and projective geometry. Abrams.

### Directed Individual Study

MATH 401 - Prince Nelson, Sybil

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

### Directed Individual Study

MATH 403A - Toporikova, Natalia

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

### Honors Thesis

MATH 493 - Abrams, Aaron D.

Honors Thesis.

### Honors Thesis

MATH 493 - Bush, Michael R.

Honors Thesis.

### Honors Thesis

MATH 493 - Finch-Smith, Carrie E.

Honors Thesis.

## Fall 2021▲

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

Spring 2022, MATH 100-01: The Art of Mathematical Thinking: The Mathematics of Puzzles and Games (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.

Spring 2022, MATH 100A-01: The Art of Mathematical Thinking: Mathematical Foundations of Data Science (3).  This course is intended to introduce mathematical foundations of data science. We will focus on linear algebra, numerical computation, data science and the programming language. After successfully completing this course, students will develop the necessary mathematical background for data science and will be able to solve a variety of real-world data-based problems. Furthermore, via numerous examples in real life, we learn how to access information logically, understand connection analytically, and model questions mathematically. (FM) Wang.

Winter 2022, MATH 100-02: The Art of Mathematical Thinking: Mathematics of Tilings and Patterns (3).  In this course we study tiling and counting proofs for many famous formulas involving the Fibonacci numbers, the Lucas numbers, continued fractions, and binomial coefficients. No prior knowledge is needed. (FM) Dresden.

### Calculus I

MATH 101 - Prince Nelson, Sybil

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.

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 - Feldman, Nathan S.

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 - Wang, Chong

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 II

MATH 102 - Feldman, Nathan S.

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

### Calculus II

MATH 102 - Abrams, Aaron D.

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

MATH 201 - Abrams, Aaron D.

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.

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 - Denne, Elizabeth J.

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

### Multivariable Calculus

MATH 221 - Dresden, Gregory P.

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

### Linear Algebra

MATH 222 - Colbert, Cory H.

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.

### Real Analysis

MATH 311 - Finch-Smith, Carrie E.

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.

### Real Analysis

MATH 311 - Dresden, Gregory P.

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 - Bush, Michael R.

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 - Broda, James

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 391A - Wang, Chong

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.

Fall 2021, MATH 391A-01: Topics in Analysis: Numerical Mathematics for Data Science (3). Prerequisite: MATH 311.  This course is designed to introduce knowledge of numerical computation and analysis, in order to equip students with necessary numerical techniques to address practical questions arising from data science and other fields. We will discuss useful methods to construct mathematical models from given data and powerful algorithms to solve large scale systems of linear equations which are formulated during the creation of mathematical models. Students will also learn computational complexity, accuracy, stability, conditioning, and other mathematical concepts of numerical analysis which are fundamental in developing an efficient numerical algorithm. MATLAB will be the programming language used for this course. Wang.

### Directed Individual Study

MATH 401 - Denne, Elizabeth J.

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.

### Honors Thesis

MATH 493 - Bush, Michael R.

Honors Thesis.

### Honors Thesis

MATH 493 - Abrams, Aaron D.

Honors Thesis.

### Honors Thesis

MATH 493 - Finch-Smith, Carrie E.

Honors Thesis.