# Courses

Courses offered in the past four years. Courses offered currently are as noted.

###
MATH 0100

A World of Mathematics

Course Description

**A World of Mathematics**

How long will oil last? What is the fairest voting system? How can we harvest food and other resources sustainably? To explore such real-world questions we will study a variety of mathematical ideas and methods, including modeling, logical analysis, discrete dynamical systems, and elementary statistics. This is an alternative first mathematics course for students not pursuing the calculus sequence in their first semester. The only prerequisite is an interest in exploring contemporary issues using the mathematics that lies within those issues. (Approval required; This course is not open to students who have had a prior course in calculus or statistics.) 3 hrs lect./disc.

Terms Taught

Requirements

**DED**

###
MATH 0101

Mathematical Problem-Solving

Course Description

**Mathematical Problem-Solving**

This course is designed primarily for students concurrently enrolled in MATH 121 or MATH 122 who would benefit from structured support to reinforce their mathematical backgrounds, and these students will be given priority at registration. We will emphasize problem-solving rather than a collection of procedures, using problems selected to strengthen students’ conceptual understanding of the material and their strategic competence. In an inquiry-based setting, students will practice and improve their algebra and trigonometry skills, with an emphasis on effective exposition of mathematical arguments.(This is a half credit course.)(Approval required.) 1.5 hrs. disc.

Terms Taught

###
MATH 0102
Current

Exps/Logs and Applications

Course Description

**Exponents, Logarithms, and Their Applications** (Half Credit)

Students will explore the fundamental concepts of exponents and logarithms and gain proficiency in algebraic manipulation of these functions. We will explore their wide-ranging applications across various fields of mathematics and real-world scenarios, including compound interest, population growth, radioactive decay and carbon dating, and the pH scale. We will discuss strategies for how to be successful as a student in a college-level math class, how to work together to solve problems, and how to harness students’ strengths for maximum efficiency in learning. Emphasis is placed on developing problem-solving skills and mathematical reasoning in preparation for calculus and related fields. (Students are encouraged, but not required, to enroll in MATH 0103 in the same semester) (by waiver)

Terms Taught

###
MATH 0103
Current

Functions

Course Description

**Functions**

Students will explore various topics essential for success in calculus. These include solving equations and inequalities, functions and their transformations, polynomial and rational functions, exponential and logarithmic functions, and trigonometric functions and their applications. Students will develop proficiency in algebraic manipulation and graphing skills to visualize functions and analyze their characteristics. We will discuss strategies for how to be successful as a student in a college-level math class, how to work together to solve problems, and how to harness students’ personal strengths for maximum efficiency in learning. Emphasis is placed on developing problem-solving skills and mathematical reasoning in preparation for calculus and related fields. (Students are encouraged, but not required, to enroll in MATH 102 in the same semester) (by waiver)

Terms Taught

###
MATH 0105
Current

Exponents Logarithms Functions

Course Description

**Exponents, Logarithms, Functions**

Students will explore various topics essential for success in calculus. Students will explore the fundamental concepts of exponents and logarithms and explore their wide-ranging applications across various fields of mathematics and real-world scenarios, including compound interest, population growth, radioactive decay and carbon dating, and the pH scale. Solving equations and inequalities, functions and their transformations, polynomial and rational functions, and trigonometric functions and their applications will also be discussed. Students will develop proficiency in algebraic manipulation and graphing skills to visualize functions and analyze their characteristics. We will discuss strategies for how to be successful as a student in a college-level math class, how to work together to solve problems, and how to harness students’ personal strengths for maximum efficiency in learning. Emphasis is placed on developing problem-solving skills and mathematical reasoning in preparation for calculus and related fields. (Equivalent to MATH 102 + MATH 103) (by waiver)

Terms Taught

###
MATH 0106

Math and Board Games

Course Description

**Math and Board Games**

Have you ever spent minutes agonizing over which move to make in a board game? Out of all the possible options, how could you possibly determine which move is best? Was there even an objectively best decision? In this course, we will explore the mathematics and underlying gameplay structures of several modern board games. In addition to playing these games during class, we’ll use math and logic to assess and quantify the value of a range of possible in-game decisions. Using formal mathematical proofs, papers, and in-class discussions, we’ll analyze the fairness and equity of strategies across a wide variety of games. We’ll finish the course by designing our own board game based on what we’ve learned! (Students who have completed FYSE1216 are not eligible to enroll in MATH 0106.)

Terms Taught

Requirements

**CW**,

**DED**

###
MATH 0109

Mathematics for Teachers

Course Description

**Mathematics for Teachers**

What mathematical knowledge should elementary and secondary teachers have in the 21st century? Participants in this course will strengthen and deepen their own mathematical understanding in a student-centered workshop setting. We will investigate the number system, operations, algebraic thinking, measurement, data, and functions, and consider the attributes of quantitative literacy. We will also study recent research that describes specialized mathematical content knowledge for teaching. (Students looking for a course in elementary school teaching methods should consider EDST 0315 instead.) 3 hrs. lect.

Terms Taught

Requirements

**DED**

###
MATH 0110

Making Data Visual

Course Description

**Making Data Visual**

Information can be used to inform, persuade, excite, and build community identity. Being able to move between data in a spreadsheet to a story that uses data that highlights information responsibly is a critical skill. In this course we will learn about communication standards for sharing data with experts and non-experts alike. Gaining skills in programs such as Canva, Photoshop and R, we will work to build data visualizations that are accurate, interesting, and responsibly represented. In the final project we will turn to our own community using data to tell a story about experiences at Middlebury.

Terms Taught

Requirements

**DED**

###
MATH 0116

Intro to Statistical Science

Course Description

**Introduction to Statistical Science**

A practical introduction to statistical methods and the examination of data sets. Computer software will play a central role in analyzing a variety of real data sets from the natural and social sciences. Topics include descriptive statistics, elementary distributions for data, hypothesis tests, confidence intervals, correlation, regression, contingency tables, and analysis of variance. The course has no formal mathematics prerequisite, and is especially suited to students in the physical, social, environmental, and life sciences who seek an applied orientation to data analysis. (Credit is not given for MATH 0116 if the student has taken ECON 0111 (formerly ECON 0210) or PSYC 0201 previously or concurrently.) 3 hrs. lect./1 hr. computer lab.

Terms Taught

Requirements

**DED**

###
MATH 0118

Introduction to Data Science

Course Description

**Introduction to Data Science**

In this course students will gain exposure to the entire data science pipeline: forming a statistical question, collecting and cleaning data sets, performing exploratory data analyses, identifying appropriate statistical techniques, and communicating the results, all the while leaning heavily on open source computational tools, in particular the R statistical software language. We will focus on analyzing real, messy, and large data sets, requiring the use of advanced data manipulation/wrangling and data visualization packages. Students will be required to bring alaptop (owned or college-loaned) to class as many lectures will involve in-class computational activities. (formerly MATH216) 3 hrs lect./disc. (Not open to students who have taken BIOL 1230, ECON 1230, ENVS 1230, FMMC 1230, HARC 1230, JAPN 1230, LNGT 1230, NSCI 1230, MATH 1230, SOCI 1230, LNGT 1230, PSCI 1230, WRPR 1230, or GEOG 1230.)

Terms Taught

Requirements

**DED**

###
MATH 0121
Current
Upcoming

Calculus I

Course Description

**Calculus I**

Introductory analytic geometry and calculus. Topics include limits, continuity, differential calculus of algebraic and trigonometric functions with applications to curve sketching, optimization problems and related rates, the indefinite and definite integral, area under a curve, and the fundamental theorem of calculus. Inverse functions and the logarithmic and exponential functions are also introduced along with applications to exponential growth and decay. (by waiver) 4 hrs. lect./disc.

Terms Taught

Requirements

**DED**

###
MATH 0122
Current
Upcoming

Calculus II

Course Description

**Calculus II**

A continuation of MATH 0121, may be elected by first-year students who have had an introduction to analytic geometry and calculus in secondary school. Topics include a brief review of natural logarithm and exponential functions, calculus of the elementary transcendental functions, techniques of integration, improper integrals, applications of integrals including problems of finding volumes, infinite series and Taylor's theorem, polar coordinates, ordinary differential equations. 4 hrs. lect/disc.

Terms Taught

Requirements

**DED**

###
MATH 0200
Current
Upcoming

Linear Algebra

Course Description

**Linear Algebra**

Matrices and systems of linear equations, the Euclidean space of three dimensions and other real vector spaces, independence and dimensions, scalar products and orthogonality, linear transformations and matrix representations, eigenvalues and similarity, determinants, the inverse of a matrix and Cramer's rule. (MATH 0121 or equivalent) 3 hrs. lect./disc.

Terms Taught

Requirements

**DED**

###
MATH 0201

Adv Intro to Stat and Data Sci

Course Description

**Advanced Introduction to Statistical and Data Sciences**

An introduction to statistical methods and the examination of data sets for students with a background in calculus. Topics include descriptive statistics, elementary distributions for data, hypothesis tests, confidence intervals, and regression. Students develop skills in data cleaning, wrangling, visualization, and model fitting using the Statistical Software R. Emphasis will be placed on reproducibility. (MATH 0121 or APAB 4 or APBC 3, or by waiver) (Not open to students who have taken MATH 0116, ECON 0111 (formerly ECON 0210), PSYC 0201, BIOL 1230, ECON 1230, ENVS 1230, FMMC 1230, HARC 1230, JAPN 1230, LNGT 1230, NSCI 1230, MATH 1230, SOCI 1230, LNGT 1230, PSCI 1230, WRPR 1230, or GEOG 1230.)

Terms Taught

Requirements

**DED**

###
MATH 0211

Regression

Course Description

**Regression Theory and Applications**

Regression is a popular statistical technique for making predictions and for modeling relationships between variables. In this course we will discuss the theory and practical applications of linear, log-linear, and logistic regression models. Topics include least squares estimation, coding for categorical predictors, analysis of variance, and model diagnostics. We will apply these concepts to real datasets using R, a statistical programming language. (MATH 0200; and MATH 0116 or MATH 0311) 3 hrs lect./disc.

Terms Taught

Requirements

**DED**

###
MATH 0216

Introduction to Data Science

Course Description

**Introduction to Data Science**

In this course students will gain exposure to the entire data science pipeline: forming a statistical question, collecting and cleaning data sets, performing exploratory data analyses, identifying appropriate statistical techniques, and communicating the results, all the while leaning heavily on open source computational tools, in particular the R statistical software language. We will focus on analyzing real, messy, and large data sets, requiring the use of advanced data manipulation/wrangling and data visualization packages. Students will be required to bring their own laptops as many lectures will involve in-class computational activities. 3 hrs lect./disc.

Terms Taught

Requirements

**DED**

###
MATH 0218

Statistical Learning

Course Description

**Statistical Learning**

This course is an introduction to modern statistical, machine learning, and computational methods to analyze large and complex data sets that arise in a variety of fields, from biology to economics to astrophysics. The theoretical underpinnings of the most important modeling and predictive methods will be covered, including regression, classification, clustering, resampling, and tree-based methods. Student work will involve implementation of these concepts using open-source computational tools. (MATH 0118, or MATH 0216, or BIOL 1230, or ECON 1230, or ENVS 1230, or FMMC 1230, or HARC 1230, or JAPN 1230, or LNGT 1230, or NSCI 1230, or MATH 1230 or SOCI 1230) 3 hrs. lect./disc.

Terms Taught

Requirements

**DED**

###
MATH 0223
Current
Upcoming

Multivariable Calculus

Course Description

**Multivariable Calculus**

The calculus of functions of more than one variable. Introductory vector analysis, analytic geometry of three dimensions, partial differentiation, multiple integration, line integrals, elementary vector field theory, and applications. (MATH 0122 and MATH 0200 or by waiver) 3 hrs. lect./disc.

Terms Taught

Requirements

**DED**

###
MATH 0225

Topics in Linear Alg & Diff Eq

Course Description

**Topics in Linear Algebra and Differential Equations**

Topics may include diagonalization of matrices, quadratic forms, inner product spaces, canonical forms, the spectral theorem, positive matrices, the Cayley-Hamilton theorem, ordinary differential equations of arbitrary order, systems of first-order differential equations, power series, and eigenvalue methods of solution, applications. (MATH 0200 or by waiver) 3 hrs. lect./disc.

Terms Taught

Requirements

**DED**

###
MATH 0226
Current
Upcoming

Differential Equations

Course Description

MATH 0226, Differential Equations

This course provides an introduction into ordinary differential equations (ODEs) with an emphasis on linear and nonlinear systems using analytical, qualitative, and numerical techniques. Topics will include separation of variables, integrating factors, eigenvalue method, linearization, bifurcation theory, and numerous applications. In this course, we will introduce MATLAB programming skills and develop them through the semester. (MATH 0122 and MATH 0200 or by waiver) (formerly MATH 0225) 3 hrs. lect./disc.

Terms Taught

Requirements

**DED**

###
MATH 0228

Intro to Numerical Analysis

Course Description

**Introduction to Numerical Analysis**

We will study the development, analysis, and implementation of numerical methods for approximating solutions to mathematical problems. We will begin with applications of Taylor polynomials, computer representation of numbers, and types of errors. Other topics will include polynomial and spline interpolation, numerical integration and differentiation, rootfinding, and numerical solutions of differential equations. Accuracy will be quantified by the concept of numerical error. Additionally, we will study the stability, efficiency, and implementation of algorithms. We will utilize the software MATLAB throughout to demonstrate concepts, as well as to complete assignments and projects. (MATH 0122)

Terms Taught

Requirements

**DED**

###
MATH 0230
Upcoming

Euc and Non-Euc Geometries

Course Description

**Euclidean and Non-Euclidean Geometries**

In roughly 300 BCE, Euclid set down his axioms of geometry which subsequently became the standard by which people understood the mathematics of the world around them. In the first half of the 19th century, mathematicians realized, however, that they could remove one of Euclid’s axioms, the one known as the “parallel postulate,” and still produce logically consistent examples of geometries. These new geometries displayed behaviors that were wildly different from Euclidean geometry. In this course we will study examples of these revolutionary non-Euclidean geometries, with a focus on Klein's Erlangen Program, which is a modern way of understanding them. (MATH 0200 or by waiver) 3 hrs. lect.

Terms Taught

Requirements

**DED**

###
MATH 0241

Elementary Number Theory

Course Description

**Elementary Number Theory**

Divisibility and prime factorization. Congruences; the theorems of Lagrange, Fermat, Wilson, and Euler; residue theory; quadratic reciprocity. Diophantine equations. Arithmetic functions and Mobius inversion. Representation as a sum of squares. (MATH 0122 or by waiver)

Terms Taught

Requirements

**DED**

###
MATH 0247
Current

Graph Theory

Course Description

**Graph Theory**

A graph (or network) is a useful mathematical model when studying a set of discrete objects and the relationships among them. We often represent an object with a vertex (node) and a relation between a pair with an edge (line). With the graph in hand, we then ask questions, such as: Is it connected? Can one traverse each edge precisely once and return to a starting vertex? For a fixed *k/, is it possible to “color” the vertices using /k* colors so that no two vertices that share an edge receive the same color? More formally, we study the following topics: trees, distance, degree sequences, matchings, connectivity, coloring, and planarity. Proof writing is emphasized. (MATH 0200 or by waiver) 3 hrs. lect./disc.

Terms Taught

Requirements

**DED**

###
MATH 0261

History of Mathematics

Course Description

**History of Mathematics**

This course studies the history of mathematics chronologically beginning with its ancient origins in Babylonian arithmetic and Egyptian geometry. The works of Euclid, Apollonius, and Archimedes and the development of ancient Greek deductive mathematics is covered. The mathematics from China, India, and the Arab world is analyzed and compared. Special emphasis is given to the role of mathematics in the growth and development of science, especially astronomy. European mathematics from the Renaissance through the 19th Century is studied in detail including the development of analytic geometry, calculus, probability, number theory, and modern algebra and analysis. (MATH 0122 or waiver)

Terms Taught

Requirements

**CMP**,

**DED**

###
MATH 0302
Current
Upcoming

Abstract Algebra I

Course Description

**Abstract Algebra**

Groups, subgroups, Lagrange's theorem, homomorphisms, normal subgroups and quotient groups, rings and ideals, integral domains and fields, the field of quotients of a domain, the ring of polynomials over a domain, Euclidean domains, principal ideal domains, unique factorization, factorization in a polynomial ring. (MATH 0200 or by waiver) 3 hrs. lect./disc.

Terms Taught

Requirements

**DED**

###
MATH 0310
Current
Upcoming

Probability

Course Description

**Probability**

An introduction to the concepts of probability and their applications, covering both discrete and continuous random variables. Probability spaces, elementary combinatorial analysis, densities and distributions, conditional probabilities, independence, expectation, variance, weak law of large numbers, central limit theorem, and numerous applications. (concurrent or prior MATH 0223 or by waiver) 3 hrs. lect./disc.

Terms Taught

Requirements

**DED**

###
MATH 0311

Statistical Inference

Course Description

**Statistical Inference**

An introduction to the mathematical methods and applications of statistical inference using both classical methods and modern resampling techniques. Topics will include: permutation tests, parametric and nonparametric problems, estimation, efficiency and the Neyman-Pearsons lemma. Classical tests within the normal theory such as F-test, t-test, and chi-square test will also be considered. Methods of linear least squares are used for the study of analysis of variance and regression. There will be some emphasis on applications to other disciplines. This course is taught using R. (MATH 0310) 3 hrs. lect./disc.

Terms Taught

Requirements

**DED**

###
MATH 0315
Current

Mathematical Modeling

Course Description

**Mathematical modeling**

An introduction into the process of developing and interpreting mathematical models within the framework of numerous applications. In this course, we will utilize discrete, continuous, and probabilistic approaches to explore applications such as population dynamics, epidemiology, and neuron activity. Time permitting, we may also introduce the derivation of spatiotemporal models. MATLAB will be used to implement and analyze several of these models. (MATH 0200 and MATH 0225 or MATH 0226, or by instructor approval) 3 hrs. lect./disc

Terms Taught

Requirements

**CW**,

**DED**

###
MATH 0318

Operations Research

Course Description

**Operations Research**

Operations research is the utilization of quantitative methods as an aid to managerial decisions. In the course, several of these methods will be introduced and studied in both a mathematical context and a physical context. Topics included will be selected from the following: classification of problems and the formulation of models, linear programming, network optimization, transportation problems, assignment problems, integer programming, nonlinear programming, inventory theory, and game theory. (MATH 0200 or waiver)

Terms Taught

Requirements

**DED**

###
MATH 0323
Current

Real Analysis

Course Description

**Real Analysis**

An axiomatic treatment of the topology of the real line, real analysis, and calculus. Topics include neighborhoods, compactness, limits, continuity, differentiation, Riemann integration, and uniform convergence. (MATH 0223) 3 hrs. lect./disc.

Terms Taught

Requirements

**DED**

###
MATH 0325

Complex Analysis

Course Description

**Complex Analysis**

An introduction to functions of a complex variable. Mappings of the complex plane, analytic functions, Cauchy Integral Theorem and related topics. (MATH 0223 or by waiver) 3 hrs. lect./disc.

Terms Taught

Requirements

**DED**

###
MATH 0326

Partial Differential Equations

Course Description

**Partial Differential Equations**

An introduction to partial differential equations (PDEs) with an emphasis on first and second-order linear equations. Using analytical, qualitative, and numerical techniques, we will study the Laplace, heat, and wave equations, as well as their applications. MATLAB will be used where applicable. (MATH 0223 and either of MATH 0225 or MATH 0226) 3 hr lect.

Terms Taught

Requirements

**DED**

###
MATH 0328
Upcoming

Numerical Linear Algebra

Course Description

**Numerical Linear Algebra**

Numerical linear algebra is the study of algorithms for solving problems such as finding solutions of linear systems and eigenvalues of matrices. Many real-life applications simplify to these scenarios and often involve millions of variables. We will analyze shortcomings of direct methods such as Gaussian Elimination, which theoretically produces the true solution but fails in practical applications. In contrast, iterative methods are often more practical and precise, and continually evolve with changing technology and our understanding of mathematics. Our study will include the First Order Richardson, Steepest Descent, and Conjugate Gradient algorithms for linear systems, and the power method for eigenvalue problems. (MATH 0200) 3 hrs. lect.

Terms Taught

Requirements

**CW**,

**DED**

###
MATH 0332

Elementary Topology

Course Description

**Elementary Topology**

An introduction to the concepts of topology. Theory of sets, general topological spaces, topology of the real line, continuous functions and homomorphisms, compactness, connectedness, metric spaces, selected topics from the topology of Euclidean spaces including the Jordan curve theorem. (MATH 0122 or MATH 0200 or by waiver) (formally MATH 0432) 3 hrs. lect./disc.

Terms Taught

Requirements

**CW**,

**DED**

###
MATH 0335

Differential Geometry

Course Description

**Differential Geometry**

This course will be an introduction to the concepts of differential geometry. For curves in space, we will discuss arclength parameterizations, Frenet formulas, curvature, and torsion. On surfaces, we will explore the Gauss map, the shape operator, and various types of curvature. We will apply our knowledge to understand geodesics, metrics, and isometries of general geometric spaces. If time permits, we will consider topics such as minimal surfaces, constant curvature spaces, and the Gauss-Bonnet theorem. (MATH 0200 and MATH 0223) 3 hr. lect./disc.

Terms Taught

Requirements

**DED**

###
MATH 0345

Combinatorics

Course Description

**Combinatorics**

Combinatorics is the “art of counting.” Given a finite set of objects and a set of rules placed upon these objects, we will ask two questions. Does there exist an arrangement of the objects satisfying the rules? If so, how many are there? These are the questions of existence and enumeration. As such, we will study the following combinatorial objects and counting techniques: permutations, combinations, the generalized pigeonhole principle, binomial coefficients, the principle of inclusion-exclusion, recurrence relations, and some basic combinatorial designs. (MATH 0200 or by waiver) 3 hrs. lect./disc.

Terms Taught

Requirements

**DED**

###
MATH 0410
Upcoming

Stochastic Processes

Course Description

**Stochastic Processes**

Stochastic processes are mathematical models for random phenomena evolving in time or space. This course will introduce important examples of such models, including random walk, branching processes, the Poisson process and Brownian motion. The theory of Markov chains in discrete and continuous time will be developed as a unifying theme. Depending on time available and interests of the class, applications will be selected from the following areas: queuing systems, mathematical finance (Black-Scholes options pricing), probabilistic algorithms, and Monte Carlo simulation. (MATH 0310) 3 hrs. lect./disc.

Terms Taught

Requirements

**DED**

###
MATH 0500
Current
Upcoming

Advanced Study

Course Description

**Advanced Study**

Individual study for qualified students in more advanced topics in algebra, number theory, real or complex analysis, topology. Particularly suited for those who enter with advanced standing. (Approval required) 3 hrs. lect./disc.

Terms Taught

###
MATH 0701

Galois Theory

Course Description

**Galois Theory**

This course is a tutorial in Galois theory for students who have completed Abstract Algebra. Starting from the concept of a ring, we will develop the theory of polynomial rings over fields, and use this to carry out an in-depth investigation of field extensions. Our work together will culminate in proving the fundamental theorem of Galois theory. Working independently and in small groups, students will explore related areas of algebra and communicate their insights in expository writing and oral presentations. This course fulfills the capstone senior work requirement for the mathematics major. (MATH 0302) 3 hrs. sem.

Terms Taught

Requirements

**DED**

###
MATH 0702

Adv Topics Algebra/Ellip Curve

Course Description

**Advanced Topics in Algebra: The Arithmetic of Elliptic Curves**

The study of elliptic curves has fascinated mathematicians for the last 120 years.

It is the meeting place of algebra, number theory, and analysis. There's something for everyone. It combines hands-on computational with deep theoretical implications. Elliptic curves played a central role in Wiles' proof of Fermat's Last Theorem. They are used in factoring algorithms and elliptic curve cryptosystems have become the backbone of credit card and internet transactions. If you want to become rich and famous The Clay Institute has put a $1 million bounty on the Birch and Swinnerton-Dyer Conjecture which connects the algebraic and analytic theory of elliptic curves. (MATH 0302; Approval required) 3 hrs. sem.

Terms Taught

###
MATH 0703

Finite Fields Seminar

Course Description

**Finite Fields Seminar**

This course is a tutorial in the theory and applications of finite fields, which lie in the intersection of algebra and number theory. Working in small groups, students will study the fundamental structure and properties of finite fields (also known as Galois fields). They will then work independently, exploring applications in cryptography, coding theory, or other areas. Students will gain experience reading advanced sources and communicating their insights in expository writing and oral presentations. This course fulfills the capstone senior work requirement for the mathematics major. (MATH 0241 or MATH 0302; Approval required) 3 hrs. Sem

Terms Taught

###
MATH 0705
Upcoming

Quadratic Number Fields

Course Description

**Quadratic Number Fields**

In this senior seminar we will explore the algebra and arithmetic of quadratic extensions of the rational numbers. We will study the rings of integers in these extensions, the structure of the unit group in these rings and unique factorization of ideals in Dedekind domains. We will investigate fractional ideals, splitting of primes, the class group and the finiteness of the class number. Some of the ideas and topics introduced are methods, p-adic methods, cyclotomic theory, *Dirichlet’s Units Theorem*, *Quadratic and Biquadratic Reciprocity* and quadratic forms. Using these ideas as a springboard students will investigate a topic of their choosing and write their thesis.

Terms Taught

Requirements

**DED**

###
MATH 0710
Current

Advanced Probability Seminar

Course Description

**Advanced Probability Seminar**

An introduction to the mathematical foundations of Probability for students who have completed work in Probability and Real Analysis. The central ideas correspond to the Lebesgue theory of measure and integration. Probability provides additional perspective and motivates intriguing applications of the theory, which students will explore in their final projects. Working independently and in small groups, students will gain experience reading advanced sources and communicating their insights through expository writing and oral presentations. This course fulfills the capstone senior work requirement for the mathematics major. (MATH 310 and MATH 323)

Terms Taught

###
MATH 0711

Statistics Capstone Seminar

Course Description

**Statistics Capstone Seminar**

In this course we will work with community partners to solve real-world problems using modern statistical and data science techniques. Students will work in small groups to translate research questions into actionable analysis and visualizations. Students will select a project of interest from a subset of community partners, maintain contact and collaboration with the community partner, and present their findings in a final symposium. (MATH 0218, MATH 0311, or by approval) 3 hrs. sem.

Terms Taught

Requirements

**DED**

###
MATH 0715

Advanced Math Modeling Seminar

Course Description

**Advanced Mathematical Modeling Seminar**

A tutorial on advanced mathematical model building and analysis for students who have completed work in Differential Equations and Probability. We will study deterministic and stochastic models of interacting populations with a focus on mathematical ecology and epidemiology. Working independently and in small groups, students will gain experience reading advanced sources and communicating their insights in expository writing and oral presentations. Fulfills the capstone senior work requirement for the mathematics major. (Approval Only) 3 hrs. Sem.

Terms Taught

Requirements

**DED**

###
MATH 0728

Math Fluid Dynamics Seminar

Course Description

**Mathematical Methods in Fluid Dynamics**

This course is an introduction to the mathematical models and methods used in modern fluid dynamics. Students will derive and analyze fundamental equations of fluid flow, explore their applications, as well as examine theoretical and practical solution techniques. Equations of study will include the Poisson, diffusion, and Navier-Stokes equations. We will also introduce basic methods of computational fluid dynamics. Working independently and in small groups, students will gain experience reading advanced sources and communicating their insights in expository writing and oral presentations. Fulfills the capstone senior work requirement for the mathematics major. 3 hrs. Lect./Lab (Approval Only)

Terms Taught

Requirements

**DED**

###
MATH 0732

Topology Seminar

Course Description

**Topology Seminar**

Topology is the rigorous mathematical study of shape at the most fundamental level—for example, the shapes of the letters I and U are topologically equivalent, but neither is equivalent to that of the letter O. In this senior seminar students will encounter topological objects such as manifolds, braids, and knots, studying them using tools ranging from combinatorial to geometric to algebraic. Working independently and in small groups, students will gain experience reading advanced sources and communicating their insights in expository writing and oral presentations. This course fulfills the capstone senior work requirement for the mathematics major. (MATH 0302) 3 hrs sem.

Terms Taught

###
MATH 0741

Advanced Number Theory

Course Description

**Advanced Number Theory**

A senior tutorial on some topics in advanced elementary number theory and an introduction to analytic number theory. In this course we will review key areas of elementary number theory and abstract algebra followed by the study of integer partitions, continued fractions, rational approximations of irrationals, primes and primality testing, the average order of magnitude of several number theoretic functions, the Basel problem, Bernoulli numbers, and the Riemann zeta function. (MATH 0241 or MATH 0302) 3 hrs. sem.

Terms Taught

Requirements

**DED**

###
MATH 0745

Polynomial Method Seminar

Course Description

**The Polynomial Method**

A tutorial in the Polynomial Method for students who have completed work in Abstract Algebra and at least one of Combinatorics, Graph Theory, and Number Theory. We will study Noga Alon’s Combinatorial Nullstellensatz and related theorems, along with their applications to combinatorics, graph theory, number theory, and incidence geometry. Working independently and in small groups, students will gain experience reading advanced sources and communicating their insights in expository writing and oral presentations. Fulfills the capstone senior work requirement for the mathematics major. (Approval required; MATH 0302 and one of the following: MATH 0241, MATH 0247, or MATH 0345).

Terms Taught

###
MATH 0746

Linear Algebra Methods

Course Description

**Linear Algebra Methods Seminar**

A tutorial in linear algebra methods for students who have completed work in Linear Algebra (and possibly Abstract Algebra) and at least one of Combinatorics, Graph Theory and Number Theory. We will study the linear algebra method through applications to combinatorics, graph theory, number theory, and incidence geometry. Working independently and in small groups, students will gain experience reading advanced sources and communicating their insights in expository writing and oral presentations. Fulfills the capstone senior work requirement for the mathematics major. (MATH 0200; helpful to have MATH 0241 or MATH 0247 or MATH 0345)

Terms Taught

###
MATH 1001
Upcoming

The Game of Go

Course Description

**The Game of Go**

Go is the most ancient of all East Asian board games and the most challenging in play. It combines the logic of mathematics with the aesthetic appeal of music and art. Despite this, it is a simple game to learn and is enjoyed by approximately 40 million enthusiasts the world over including over 1000 dedicated professionals. The course will involve playing, recording, analyzing, and critiquing our games and learning about its history and the cultures in which it flourishes. We will also read and write about various related Japanese arts and traditions including the latest AI developments.

Terms Taught

Requirements

**DED**,

**WTR**

###
MATH 1010

Introduction to Networks

Course Description

**Introduction to Networks**

In this course we will explore the ubiquity of networks and the beautiful mathematics that helps us understand them. Together we will cover the basics of graph theory, introduce real world social, informational, and biological networks, explore how information (or a virus) can diffuse or cascade through a network, and learn about popular social and graph phenomena like the six degrees of separation and the friendship paradox. We will utilize jupyter notebooks and python libraries to build a toolset for studying networks and you will have the opportunity to analyze an empirical network using the ideas and tools you develop over the course of this class. No previous coding or mathematical experience is necessary: we will cover all concepts together.

*Izabel Aguiar is a PhD candidate in Computational and Mathematical Engineering at Stanford University where she is lucky to be advised by Johan Ugander./*

Terms Taught

Requirements

**WTR**

###
MATH 1011
Upcoming

Math Circus

Course Description

**Math Circus**

Each class will entail small group work solving various logic and puzzle problems, mathematical conundrums, and devising winning strategies for various games and challenges. Students will present their solutions to the class and work on their own puzzles and games pamphlet to be completed by the end of the term. Elementary mathematical, logical, game theoretic, and probability concepts will be introduced as needed with the goal of increasing everyone's problem solving and analytical thinking skills. The class will meet four days a week (2 hours per class).

Terms Taught

Requirements

**DED**,

**WTR**

###
MATH 1230
Upcoming

DataScience Across Disciplines

Course Description

**Data Science Across Disciplines**

In this course, we will gain exposure to the entire data science pipeline—obtaining and cleaning large and messy data sets, exploring these data and creating engaging visualizations, and communicating insights from the data in a meaningful manner. During morning sessions, we will learn the tools and techniques required to explore new and exciting data sets. During afternoon sessions, students will work in small groups with one of several faculty members on domain-specific research projects in Geography, Political Science, Restorative Justice, or Healthcare. This course will use the R programming language. No prior experience with R is necessary.

**MATH/STAT 1230:** Students will explore pediatric healthcare data to better understand the risks correlated with various childhood illnesses through an emphasis on the intuition behind statistical and machine learning techniques. We will practice making informed decisions from noisy data and the steps to go from messy data to a final report. Students will become proficient in R and gain an understanding of various statistical techniques.

**GEOG 1230:** In this section, students will use data science tools to explore the ways migration systems in the United States changed during the COVID-19 pandemic. We will draw on data collected from mobile phones recording each phone’s monthly place of residence at the census tract level. The dataset includes monthly observations from January 2019 through December 2021 allowing the analysis to compare migration systems pre-pandemic with those during the pandemic.

**INTD 1230A:** Data is a powerful tool for improving health outcomes by making programmatic choices to support justice. In this afternoon section of Data Across the Disciplines, students will be working with Addison County Restorative Justice (ACRJ) on understanding patterns in the occurrence of driving under the influence. ACRJ has over 1,000 cases and would like to better understand their data and come up with ways to access information. We will explore how identity, geography, and support impact outcomes from DUI cases. Using statistical analysis and data visualizations, along with learning about ethical data practices, we will report our findings.

**INTD 1230B:** Let’s dive into the minutes and reports of local towns to develop an accessible news and history resource. Could this be a tool for small newspapers to track local news more easily? Can we map this fresh data for a new look across geographies? Do you want to help volunteer town officials make decisions and better wrangle with their town’s history and data?

In this course we will develop a focused database of documents produced by several municipal boards and commissions. We will engage in conversation with local officials, researchers, and journalists. This course aims to introduce students to making data from real world documents and the people that make them to generate useful information that is often open but frequently difficult to sift through.

**PSCI 1230:** How do candidates for U.S. national office raise money? From whom do they raise it? In this section we will explore these questions using Federal Election Commission data on individual campaign contributions to federal candidates. Our analysis using R will help us identify geographic patterns in the data, as well as variations in funds raised across types of candidates. We will discuss what implications these patterns may have for the health and functioning of democracy in the U.S.

Terms Taught

Requirements

**DED**,

**SCI**,

**WTR**

###
STAT 0116
Current
Upcoming

Intro to Statistical Science

Course Description

**Introduction to Statistical Science** (formerly MATH 0116)

A practical introduction to statistical methods and the examination of data sets. Computer software will play a central role in analyzing a variety of real data sets from the natural and social sciences. Topics include descriptive statistics, elementary distributions for data, hypothesis tests, confidence intervals, correlation, regression, contingency tables, and analysis of variance. The course has no formal mathematics prerequisite, and is especially suited to students in the physical, social, environmental, and life sciences who seek an applied orientation to data analysis. (Credit is not given for MATH 0116 if the student has taken ECON 0111 (formerly ECON 0210) or PSYC 0201 previously or concurrently.) 3 hrs. lect./1 hr. computer lab.

Terms Taught

Requirements

**DED**

###
STAT 0118
Current
Upcoming

Introduction to Data Science

Course Description

**Introduction to Data Science** (formerly MATH 0118)

In this course students will gain exposure to the entire data science pipeline: forming a statistical question, collecting and cleaning data sets, performing exploratory data analyses, identifying appropriate statistical techniques, and communicating the results, all the while leaning heavily on open source computational tools, in particular the R statistical software language. We will focus on analyzing real, messy, and large data sets, requiring the use of advanced data manipulation/wrangling and data visualization packages. Students will be required to bring alaptop (owned or college-loaned) to class as many lectures will involve in-class computational activities. (formerly MATH 0216) 3 hrs lect./disc. (Not open to students who have taken BIOL 1230, ECON 1230, ENVS 1230, FMMC 1230, HARC 1230, JAPN 1230, LNGT 1230, NSCI 1230, MATH 1230, SOCI 1230, LNGT 1230, PSCI 1230, WRPR 1230, or GEOG 1230.)

Terms Taught

Requirements

**DED**

###
STAT 0201
Current
Upcoming

Adv Intro to Stat and Data Sci

Course Description

**Advanced Introduction to Statistical and Data Sciences**

An introduction to statistical methods and the examination of data sets for students with a background in calculus. Topics include descriptive statistics, elementary distributions for data, hypothesis tests, confidence intervals, and regression. Students develop skills in data cleaning, wrangling, visualization, and model fitting using the Statistical Software R. Emphasis will be placed on reproducibility. (MATH 0121 or APAB 4 or APBC 3, or by waiver) (Not open to students who have taken MATH 0116, MATH 0118, ECON 0111 (formerly ECON 0210), PSYC 0201, STAT 0116, STAT 0118, BIOL 1230, ECON 1230, ENVS 1230, FMMC 1230, HARC 1230, JAPN 1230, LNGT 1230, NSCI 1230, MATH 1230, SOCI 1230, LNGT 1230, PSCI 1230, WRPR 1230, or GEOG 1230.)

Terms Taught

Requirements

**DED**

###
STAT 0211
Current

Regression

Course Description

**Regression Theory and Applications** (formerly MATH 0211)

Regression is a popular statistical technique for making predictions and for modeling relationships between variables. In this course we will discuss the theory and practical applications of linear, log-linear, and logistic regression models. Topics include least squares estimation, coding for categorical predictors, analysis of variance, and model diagnostics. We will apply these concepts to real datasets using R, a statistical programming language. (MATH 0200; and MATH 0116 or STAT 0116, or STAT 0201 or MATH 0311 or STAT 0311) (Not open to students who have taken ECON 0211) 3 hrs lect./disc.

Terms Taught

Requirements

**DED**

###
STAT 0218
Current
Upcoming

Statistical Learning

Course Description

**Statistical Learning** (formerly MATH 0218)

This course is an introduction to modern statistical, machine learning, and computational methods to analyze large and complex data sets that arise in a variety of fields, from biology to economics to astrophysics. The theoretical underpinnings of the most important modeling and predictive methods will be covered, including regression, classification, clustering, resampling, and tree-based methods. Student work will involve implementation of these concepts using open-source computational tools. (MATH 0118, or MATH 0216, or BIOL 1230, or ECON 1230, or ENVS 1230, or FMMC 1230, or HARC 1230, or JAPN 1230, or LNGT 1230, or NSCI 1230, or MATH 1230 or SOCI 1230) 3 hrs. lect./disc.

Terms Taught

Requirements

**DED**

###
STAT 0219
Current

Time Series Analysis

Course Description

**Time Series Analysis**

An introduction to statistical methods for time series analysis for students with a background in statistics. Topics include time series regression, auto-regressive models, moving average models, and ARIMA models, with an emphasis on estimation and forecasting with real data applications. Students will develop skills visualizing and summarizing serially correlated data structures and fitting time series models in various statistical software packages, including R and Julia. (STAT 116 or STAT 201 and MATH 0200 concurrently, or by waiver.)

Terms Taught

Requirements

**DED**

###
STAT 0310
Current
Upcoming

Probability

Course Description

**Probability**

An introduction to the concepts of probability and their applications, covering both discrete and continuous random variables. Probability spaces, elementary combinatorial analysis, densities and distributions, conditional probabilities, independence, expectation, variance, weak law of large numbers, central limit theorem, and numerous applications. (concurrent or prior MATH 0223 or by waiver) 3 hrs. lect./disc.

Terms Taught

Requirements

**DED**

###
STAT 0311
Upcoming

Statistical Inference

Course Description

**Statistical Inference**

An introduction to the mathematical methods and applications of statistical inference using both classical methods and modern resampling techniques. Topics will include: permutation tests, parametric and nonparametric problems, estimation, efficiency and the Neyman-Pearsons lemma. Classical tests within the normal theory such as F-test, t-test, and chi-square test will also be considered. Methods of linear least squares are used for the study of analysis of variance and regression. There will be some emphasis on applications to other disciplines. This course is taught using R. (MATH 0310) 3 hrs. lect./disc.

Terms Taught

Requirements

**DED**

###
STAT 0410
Upcoming

Stochastic Processes

Course Description

**Stochastic Processes**

Stochastic processes are mathematical models for random phenomena evolving in time or space. This course will introduce important examples of such models, including random walk, branching processes, the Poisson process and Brownian motion. The theory of Markov chains in discrete and continuous time will be developed as a unifying theme. Depending on time available and interests of the class, applications will be selected from the following areas: queuing systems, mathematical finance (Black-Scholes options pricing), probabilistic algorithms, and Monte Carlo simulation. (MATH 0310) 3 hrs. lect./disc.

Terms Taught

Requirements

**DED**

###
STAT 0412

Bayesian Statistics

Course Description

**Bayesian Statistics** (formerly MATH 0412)

In this course, we will learn about the Bayesian paradigm of statistics, in which one’s inferences about parameters or hypotheses are updated as evidence accumulates. The goals of the course include understanding basic concepts of Bayesian inference; deriving posterior distributions; assessing the adequacy of Bayesian models; and effectively communicating results. Topics covered include one-parameter models, conjugacy, and Gibbs samplers. Real-world data and applications will feature heavily in this course. (MATH 0311 or STAT 0311) 2.5 hr. lect.

Terms Taught

Requirements

**DED**

###
STAT 0500
Current
Upcoming

Advanced Study

Course Description

**Independent Study**

Individual study for qualified students in more advanced topics in statistics. Particularly suited for those who enter with advanced standing. (Approval required) 3 hrs. lect./disc.

Terms Taught

###
STAT 0710
Current

Advanced Probability Seminar

Course Description

**Advanced Probability Seminar**

An introduction to the mathematical foundations of Probability for students who have completed work in Probability and Real Analysis. The central ideas correspond to the Lebesgue theory of measure and integration. Probability provides additional perspective and motivates intriguing applications of the theory, which students will explore in their final projects. Working independently and in small groups, students will gain experience reading advanced sources and communicating their insights through expository writing and oral presentations. This course fulfills the capstone senior work requirement for the mathematics major. (MATH 310 and MATH 323)

Terms Taught

###
STAT 0711
Upcoming

Statistical Consulting

Course Description

**Statistical Consulting**

In this course we will work with community partners to solve real-world problems using modern statistical and data science techniques. Students will work in small groups to translate research questions into actionable analysis and visualizations. Students will select a project of interest from a subset of community partners, maintain contact and collaboration with the community partner, and present their findings in a final symposium. (MATH 0218, MATH 0311, or by approval) 3 hrs. sem.

Terms Taught

Requirements

**DED**

###
STAT 0712

Advanced Hierarchical Modeling

Course Description

**Advanced Hierarchical Modeling** (formerly MATH 0712)

Hierarchical or multilevel models provide a principled way to model data that are naturally grouped in order to take advantage of the relationship between observations in the same group, but also allow for borrowing of information across groups. In this senior seminar, we will introduce a variety of multilevel models, with a balance between the theoretical and conceptual foundations, as well as implementation and interpretation of the results. This seminar will focus on multilevel linear and logistic models. Every student will write a senior capstone paper. (MATH 311 or STAT 0311; MATH 412 or STAT 0412 suggested)

Terms Taught

###
STAT 1230
Upcoming

DataScience Across Disciplines

Course Description

**Data Science Across Disciplines**

In this course, we will gain exposure to the entire data science pipeline—obtaining and cleaning large and messy data sets, exploring these data and creating engaging visualizations, and communicating insights from the data in a meaningful manner. During morning sessions, we will learn the tools and techniques required to explore new and exciting data sets. During afternoon sessions, students will work in small groups with one of several faculty members on domain-specific research projects in Geography, Political Science, Restorative Justice, Healthcare, or. This course will use the R programming language. No prior experience with R is necessary.

**MATH/STAT 1230:** Students will explore pediatric healthcare data to better understand the risks correlated with various childhood illnesses through an emphasis on the intuition behind statistical and machine learning techniques. We will practice making informed decisions from noisy data and the steps to go from messy data to a final report. Students will become proficient in R and gain an understanding of various statistical techniques.

**GEOG 1230:** In this section, students will use data science tools to explore the ways migration systems in the United States changed during the COVID-19 pandemic. We will draw on data collected from mobile phones recording each phone’s monthly place of residence at the census tract level. The dataset includes monthly observations from January 2019 through December 2021 allowing the analysis to compare migration systems pre-pandemic with those during the pandemic.

**INTD 1230A:** Data is a powerful tool for improving health outcomes by making programmatic choices to support justice. In this afternoon section of Data Across the Disciplines, students will be working with Addison County Restorative Justice (ACRJ) on understanding patterns in the occurrence of driving under the influence. ACRJ has over 1,000 cases and would like to better understand their data and come up with ways to access information. We will explore how identity, geography, and support impact outcomes from DUI cases. Using statistical analysis and data visualizations, along with learning about ethical data practices, we will report our findings.

**INTD 1230B:** Let’s dive into the minutes and reports of local towns to develop an accessible news and history resource. Could this be a tool for small newspapers to track local news more easily? Can we map this fresh data for a new look across geographies? Do you want to help volunteer town officials make decisions and better wrangle with their town’s history and data?

In this course we will develop a focused database of documents produced by several municipal boards and commissions. We will engage in conversation with local officials, researchers, and journalists. This course aims to introduce students to making data from real world documents and the people that make them to generate useful information that is often open but frequently difficult to sift through.

**PSCI 1230:** How do candidates for U.S. national office raise money? From whom do they raise it? In this section we will explore these questions using Federal Election Commission data on individual campaign contributions to federal candidates. Our analysis using R will help us identify geographic patterns in the data, as well as variations in funds raised across types of candidates. We will discuss what implications these patterns may have for the health and functioning of democracy in the U.S.

Terms Taught

Requirements

**DED**,

**SCI**,

**WTR**