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

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

Fall 2020, Spring 2022

Requirements

DED

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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

Fall 2022

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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)

Terms Taught

Fall 2024

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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)

Terms Taught

Fall 2024

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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

Fall 2022

Requirements

CW, DED

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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

Fall 2021

Requirements

DED

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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

Fall 2022

Requirements

DED

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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

Fall 2020, Spring 2021, Fall 2021, Spring 2022, Fall 2022, Spring 2023

Requirements

DED

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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

Fall 2021, Spring 2022, Fall 2022, Spring 2023

Requirements

DED

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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

Fall 2020, Spring 2021, Fall 2021, Spring 2022, Fall 2022, Spring 2023, Fall 2023, Spring 2024, Fall 2024, Spring 2025

Requirements

DED

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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

Fall 2020, Spring 2021, Fall 2021, Spring 2022, Fall 2022, Spring 2023, Fall 2023, Spring 2024, Fall 2024, Spring 2025

Requirements

DED

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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

Fall 2020, Spring 2021, Fall 2021, Spring 2022, Fall 2022, Spring 2023, Fall 2023, Spring 2024, Fall 2024, Spring 2025

Requirements

DED

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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

Fall 2023, Spring 2024

Requirements

DED

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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

Spring 2022

Requirements

DED

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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

Fall 2020, Spring 2021

Requirements

DED

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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

Spring 2021, Fall 2021, Spring 2022, Fall 2022, Spring 2023

Requirements

DED

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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

Fall 2020, Spring 2021, Fall 2021, Spring 2022, Fall 2022, Spring 2023, Fall 2023, Spring 2024, Fall 2024, Spring 2025

Requirements

DED

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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

Fall 2020, Spring 2021

Requirements

DED

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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

Fall 2021, Spring 2022, Fall 2022, Spring 2023, Fall 2023, Spring 2024, Fall 2024, Spring 2025

Requirements

DED

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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

Fall 2021, Spring 2024

Requirements

DED

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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

Spring 2023, Spring 2025

Requirements

DED

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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

Spring 2022, Spring 2024

Requirements

DED

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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

Spring 2021, Spring 2023, Fall 2024

Requirements

DED

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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

Fall 2020

Requirements

CMP, DED

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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

Fall 2020, Spring 2021, Fall 2021, Fall 2022, Spring 2023, Fall 2023, Fall 2024, Spring 2025

Requirements

DED

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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

Fall 2020, Fall 2021, Fall 2022, Fall 2023, Spring 2024, Fall 2024, Spring 2025

Requirements

DED

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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

Spring 2021, Spring 2022, Spring 2023, Spring 2024

Requirements

DED

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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

Spring 2021, Fall 2022, Fall 2024

Requirements

CW, DED

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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

Spring 2023

Requirements

DED

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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

Fall 2020, Fall 2021, Spring 2022, Fall 2022, Fall 2023, Spring 2024, Fall 2024

Requirements

DED

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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

Spring 2021, Spring 2023

Requirements

DED

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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

Spring 2022, Fall 2023

Requirements

DED

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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

Fall 2020, Fall 2022, Spring 2025

Requirements

CW, DED

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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

Spring 2022, Fall 2023

Requirements

CW, DED

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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

Fall 2020, Fall 2023

Requirements

DED

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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

Fall 2021, Spring 2024

Requirements

DED

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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

Spring 2021, Spring 2023, Spring 2025

Requirements

DED

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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

Fall 2020, Winter 2021, Spring 2021, Fall 2021, Winter 2022, Spring 2022, Fall 2022, Winter 2023, Spring 2023, Fall 2023, Winter 2024, Spring 2024, Fall 2024, Winter 2025, Spring 2025

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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

Spring 2023

Requirements

DED

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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

Spring 2021

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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

Fall 2022

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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

Spring 2025

Requirements

DED

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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

Spring 2022, Fall 2024

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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

Spring 2022

Requirements

DED

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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

Fall 2021, Spring 2023

Requirements

DED

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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

Spring 2021, Spring 2024

Requirements

DED

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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

Fall 2020

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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

Fall 2021, Fall 2023

Requirements

DED

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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

Fall 2020, Fall 2022

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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

Fall 2023

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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

Winter 2025

Requirements

DED, WTR

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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

Winter 2023

Requirements

WTR

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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

Winter 2024, Winter 2025

Requirements

DED, WTR

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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

Winter 2022, Winter 2024, Winter 2025

Requirements

DED, SCI, WTR

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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

Fall 2023, Spring 2024, Fall 2024, Spring 2025

Requirements

DED

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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

Fall 2023, Spring 2024, Fall 2024, Spring 2025

Requirements

DED

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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

Fall 2023, Spring 2024, Fall 2024, Spring 2025

Requirements

DED

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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

Fall 2023, Fall 2024

Requirements

DED

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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

Fall 2023, Spring 2024, Fall 2024, Spring 2025

Requirements

DED

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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

Fall 2024

Requirements

DED

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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

Fall 2023, Spring 2024, Fall 2024, Spring 2025

Requirements

DED

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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

Spring 2024, Spring 2025

Requirements

DED

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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

Spring 2025

Requirements

DED

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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

Fall 2023

Requirements

DED

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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

Spring 2024, Fall 2024, Winter 2025, Spring 2025

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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

Fall 2024

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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

Spring 2025

Requirements

DED

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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

Spring 2024

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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

Winter 2024, Winter 2025

Requirements

DED, SCI, WTR

View in Course Catalog