Carleton’s Mathematics and Statistics department offers two majors and minors. The mathematics curriculum provides essential skills for students across many disciplines, and instills majors with a deep understanding of the history and current practice of mathematics. The statistics curriculum teaches the science of collecting and analyzing data. Students engage with statistical theory and computational methods, as well as interdisciplinary applications, exploring the full statistical analysis cycle.
About Mathematics and Statistics
Mathematics is an art, a pure science, a language, and an analytical tool for the natural and social sciences, a means of exploring philosophical questions, and a beautiful edifice that is a tribute to human creativity. The mathematics curriculum is designed to provide essential skills for students in a variety of disciplines and to provide mathematics majors with a deep understanding of mathematics as it has evolved over the past two thousand years and how it is practiced today.
Statistics is the science of giving meaning to data in the context of uncertainty. Statisticians are involved in data collection and study design, data analysis, and the communication of information to a broad audience. The statistics curriculum is designed to balance both statistical theory and application, and will provide students the opportunity to work on real world data problems and enhance their communication skills.
Students who wish to major in both Mathematics and Statistics should note the College policy that double majors may count no more than four courses toward both majors. Courses for which a student earns AP Credit, such as calculus, are included among these four courses.
Math Skills Center
The Math Skills Center supports all Carleton students in any mathematics or mathrelated course they are taking. The center’s tutors help students with mathematical concepts and with the mathematical tools needed to succeed in their courses.
Requirements for the Mathematics Major
The Mathematics major requires 72 credits:
 A. Required Core Courses (take either MATH 101 or MATH 111 and either MATH 210 or MATH 211 and all of remaining courses listed):
 MATH 101: Calculus with Problem Solving
 MATH 111: Introduction to Calculus
 MATH 120: Calculus 2
 MATH 134: Linear Algebra with Applications
 MATH 210: Calculus 3
 MATH 211: Introduction to Multivariable Calculus
 MATH 232: Linear Algebra
 MATH 236: Mathematical Structures
 B. Electives (36 credits): Six courses from among:
 CS 252: Algorithms
 CS 254: Computability and Complexity
 CS 352: Advanced Algorithms · not offered in 202425
 MATH 240: Probability
 MATH 241: Ordinary Differential Equations
 MATH 244: Geometries · not offered in 202425
 MATH 251: Chaotic Dynamics
 MATH 271: Optimization
 MATH 282: Number Theory · not offered in 202425
 MATH 295: Numerical Differential Equations
 MATH 321: Real Analysis I
 MATH 331: Real Analysis II
 MATH 332: Advanced Linear Algebra · not offered in 202425
 MATH 333: Combinatorial Theory
 MATH 341: Partial Differential Equations
 MATH 342: Abstract Algebra I
 MATH 344: Differential Geometry
 MATH 349: Methods of Teaching Mathematics · not offered in 202425
 MATH 352: Galois Theory · not offered in 202425
 MATH 354: Topology · not offered in 202425
 MATH 361: Complex Analysis · not offered in 202425
 MATH 395: Introduction to Analytic Number Theory
 STAT 250: Introduction to Statistical Inference
 STAT 320: Time Series Analysis
 STAT 340: Bayesian Statistics · not offered in 202425
At least four of these electives must be Carleton courses with a MATH designation. At least three of the following five areas of mathematics must be represented by the six electives (36 credits).
 Algebra:
 MATH 282: Number Theory · not offered in 202425
 MATH 332: Advanced Linear Algebra · not offered in 202425
 MATH 342: Abstract Algebra I
 MATH 352: Galois Theory · not offered in 202425
 Analysis:
 MATH 251: Chaotic Dynamics
 MATH 321: Real Analysis I
 MATH 331: Real Analysis II
 MATH 361: Complex Analysis · not offered in 202425
 MATH 395: Introduction to Analytic Number Theory
 Applied Mathematics:
 MATH 240: Probability
 MATH 241: Ordinary Differential Equations
 MATH 271: Optimization
 MATH 295: Numerical Differential Equations
 MATH 341: Partial Differential Equations
 STAT 250: Introduction to Statistical Inference
 STAT 320: Time Series Analysis
 STAT 340: Bayesian Statistics · not offered in 202425
 Discrete Structures:
 CS 252: Algorithms
 CS 254: Computability and Complexity
 CS 352: Advanced Algorithms · not offered in 202425
 MATH 333: Combinatorial Theory
 Geometry and Topology:
 MATH 244: Geometries · not offered in 202425
 MATH 344: Differential Geometry
 MATH 354: Topology · not offered in 202425
Of the six advanced courses, at least four must be Carleton courses with a Mathematics designation. Advanced courses substituted for MATH 232 or MATH 236 must also be Carleton courses with a Mathematics designation.
In addition, each senior major must complete an integrative exercise. Normally, that integrative exercise is a twoterm group project. At the department’s discretion, a oneterm independent project may be available. The group project would be MATH 399: Senior Seminar (6 credits) and MATH 400: Integrative Exercise (3 credits). The independent project would be MATH 400 (6 credits).
Majors must also accumulate eight talk credits during their junior and senior year by attending colloquia and the comps talks of their fellow mathematics or statistics majors. Students who major in both Mathematics and Statistics must accumulate a total of thirteen talk credits. We encourage majors to participate in the numerous activities that take place in the department.
Potential majors with especially strong preparation may petition the department for permission to substitute an advanced course for MATH 232 and/or for MATH 236. Advanced courses substituted for MATH 232 or MATH 236 must also be Carleton courses with a Mathematics designation.
There are many patterns of courses for the major depending upon a student’s mathematical interests and career goals. A guide for majors, which supplies information about suitable patterns of courses, is available on the Mathematics and Statistics Department website.
Major under Combined Plan in Engineering:
In addition to completing requirements for the mathematics major listed above including Mathematics 241 and 341, the student should take the following courses required for admission to engineering schools: Two terms of 100level Physics, CHEM 123, CHEM 224, and CS 111.
Requirements for the Statistics Major
The requirements for the Statistics Major are 74 credits:
 A. Supporting Courses (30 credits) Take either MATH 101 or MATH 111, either MATH 210 or MATH 211 and either MATH 134 or MATH 232 and all of remaining courses listed:
 CS 111: Introduction to Computer Science
 MATH 101: Calculus with Problem Solving
 MATH 111: Introduction to Calculus
 MATH 120: Calculus 2
 MATH 134: Linear Algebra with Applications
 MATH 210: Calculus 3
 MATH 211: Introduction to Multivariable Calculus
 MATH 232: Linear Algebra
 B. Required Core (18 credits): All of the following, of which at least two must be taken at Carleton
 MATH 240: Probability
 STAT 230: Applied Regression Analysis
 STAT 250: Introduction to Statistical Inference
 C. Electives (18 credits): Three electives, of which at least two must be Carleton courses with a Statistics designation. One of the three electives must be a 300level course with a Statistics designation.
 CS 314: Data Visualization
 CS 320: Machine Learning
 CS 362: Computational Biology · not offered in 202425
 MATH 271: Optimization
 STAT 220: Introduction to Data Science
 STAT 260: Introduction to Sampling Techniques · not offered in 202425
 STAT 270: Statistical Learning
 STAT 310: Spatial Statistics · not offered in 202425
 STAT 320: Time Series Analysis
 STAT 330: Advanced Statistical Modeling
 STAT 340: Bayesian Statistics · not offered in 202425
 D. Statistical Practice (2 credits):
 STAT 285 Statistical Consulting
In addition, each senior major must complete an integrative exercise. This is a twoterm group project. There is no independent comps in the statistics major. Each senior will first enroll in STAT 399: Senior Seminar (6 credits); the following term they will complete their comps in STAT 400: Integrative Exercise (3 credits).
Majors must accumulate eight talk credits during their junior and senior year by attending department colloquia and the comps talks of their fellow mathematics or statistics majors. Students who major in both Mathematics and Statistics must accumulate a total of thirteen talk credits. We encourage majors to participate in the numerous activities that take place in the department.
We recommend statistics majors also take courses in a discipline in which statistics can be applied. Students interested in data science should consider taking additional computer science courses.
Students considering graduate school in statistics or biostatistics are strongly encouraged to take Mathematics 236 (Mathematical Structures) and Mathematics 321 (Real Analysis). Consult a statistics faculty member for more information specific to your choice of program.
Requirements for the Mathematics Minor
To earn a minor in Mathematics, a student must earn 42 credits from courses taken in the Department of Mathematics and Statistics at Carleton. (Students who place out of courses based on work done outside of Carleton are still required to earn 42 credits from courses taken in the Department of Mathematics and Statistics at Carleton.) At least 36 of the required 42 credits must come from courses with a Mathematics designation. In addition, the only Statistics courses which can be counted toward the Mathematics minor are Statistics 250, 320 and 340.
Students who wish to major in Statistics and minor in Mathematics should note the College policy that a student may not fulfill more than half the credits for a minor from the courses counted toward their major or majors.
Requirements for the Statistics and Data Science Minor
The Statistics and Data Science minor requires 42 credits. Courses must be taken from the approved list of Carleton courses and must satisfy the following requirements:
A. STAT requirement: (18 credits)
 STAT 120: Introduction to Statistics
 STAT 220: Introduction to Data Science
 STAT 230: Applied Regression Analysis
A student may choose to replace STAT 120 with any STAT course from the list of approved elective courses.
B. CS Requirement: (6 credits)
One computer science course (6 credits) taken at Carleton numbered CS 111 or higher.
C. Electives: (18 credits)
Three additional 6 credit courses taken at Carleton from the approved list of courses shown below. At least one of these courses must be taken outside the departments of Mathematics and Statistics and Computer Science. At least two of these courses must be 200level or above.
Courses from the Mathematics and Statistics Department:
 MATH 240: Probability
 MATH 271: Optimization
 STAT 250: Introduction to Statistical Inference
 STAT 260: Introduction to Sampling Techniques · not offered in 202425
 STAT 270: Statistical Learning
 STAT 310: Spatial Statistics · not offered in 202425
 STAT 320: Time Series Analysis
 STAT 330: Advanced Statistical Modeling
 STAT 340: Bayesian Statistics · not offered in 202425
Courses from the Computer Science Department:
 CS 252: Algorithms
 CS 257: Software Design
 CS 314: Data Visualization
 CS 320: Machine Learning
 CS 321: Making Decisions with Artificial Intelligence
 CS 322: Natural Language Processing
 CS 334: Database Systems · not offered in 202425
 CS 344: HumanComputer Interaction
 CS 348: Parallel and Distributed Computing
 CS 352: Advanced Algorithms · not offered in 202425
 CS 362: Computational Biology · not offered in 202425
Courses from other departments:
 ARCN 246: Archaeological Methods & Lab
 BIOL 224: Landscape Ecology · not offered in 202425
 BIOL 321: Ecosystem Ecology · not offered in 202425
 BIOL 338: Genomics and Bioinformatics
 BIOL 352: Population Ecology
 CHEM 348: Introduction to Computational Chemistry
 DGAH 210: Spatial Humanities · not offered in 202425
 ECON 241: Growth and Development · not offered in 202425
 ECON 285: Computational Economics
 ECON 329: Econometrics
 ENTS 120: Introduction to Geospatial Analysis & Lab · not offered in 202425
 ENTS 254: Topics in Landscape Ecology · not offered in 202425
 GEOL 135: Introduction to Climate Science & Lab · not offered in 202425
 GEOL 340: Hydrogeology: Groundwater & Lab · not offered in 202425
 HIST 231: Mapping the World Before Mercator
 HIST 338: Digital History, Public Heritage & Deep Mapping · not offered in 202425
 LING 318: Laboratory Phonology · not offered in 202425
 MUSC 204: Theory II: Musical Structures
 MUSC 227: Perception and Cognition of Music
 MUSC 228: Perception and Cognition of Music Lab
 PHIL 213: Ethics
 PHYS 234: Computer Simulations in Complex Physical Systems
 POSC 230: Methods of Political Research
 PSYC 200: Measurement and Data Analysis in Psychology
 RELG 121: Introduction to Christianity
 RELG 155: Hinduism: An Introduction
 RELG 274: Religion and Biomedical Ethics · not offered in 202425
 SOAN 240: Methods of Social Research
The presence of a course on this list does not guarantee that it will be offered while you are completing your minor. Please check each department’s website for course descriptions and to determine when the course will be offered. A minor may petition for a course not on the approved list to count towards the required electives. See the minor website for more information about this process.
For computer science majors: A maximum of one elective can be a CS course.
For mathematics majors: A maximum of one elective can be a MATH course.
For majors outside computer science and mathematics: At most three courses (18 credits) may overlap with major requirements.
Statistics majors cannot earn this minor.
Mathematics Courses

MATH 100 Exploring Climate through Data and Models
Climate change is a complex process that spans multiple scales of time and space, from local extreme weather events lasting a few days to global glacial cycles that unfold over one hundred thousand years. Given this complexity, how do we quantify, understand, and predict Earth’s changing climate? Students in this course will build skills in analyzing datasets and mathematical models as we explore this question. Activities will include calculationbased problems that use algebra and spreadsheets, readings with discussion, and training in writing for both technical and broad audiences.
 Fall 2024
 6
 AI/WR1, Argument & Inquiry/WR1 QRE, Quantitative Reasoning

Student is a member of the First Year First Term class level cohort and is enrolled in the FOCUS Colloquium. Students are only allowed to register for one A&I course at a time. If a student wants to change this A&I course they must contact the Registrar's Office.
 IDSC 198
 Kate Meyer 🏫 👤

MATH 101 Calculus with Problem Solving
An introduction to the central ideas of calculus with review and practice of those skills needed for the continued study of calculus. Problem solving strategies will be emphasized. In addition to regular MWF class time, students will be expected to attend two problemsolving sessions each week, one on Monday or Tuesday, and one on Wednesday or Thursday. Details will be provided on the first day of class.
 Fall 2024, Winter 2025
 6
 FSR, Formal or Statistical Reasoning

Student has received a score of 101 on the Carleton Math Placement exam. Not open to students who have received credit for Mathematics 111. For more information, see the Mathematics' web page.
 Deanna Haunsperger 🏫 👤

MATH 106 A Tour of Mathematics and Statistics
The tour consists of a series of eight presentations given by a variety of Mathematics and Statistics department faculty. The course is intended for first or secondyear students considering a Mathematics or Statistics major or minor. The emphasis of these talks will be on presenting engaging ideas and research in various areas of mathematics and statistics, rather than on developing extensive knowledge or techniques in any particular subject area.
 Winter 2025
 S/CR/NC
 1
 No Exploration
 Deanna Haunsperger 🏫 👤

MATH 111 Introduction to Calculus
An introduction to the differential and integral calculus. Derivatives, antiderivatives, the definite integral, applications, and the fundamental theorem of calculus.
 Fall 2024, Winter 2025, Spring 2025
 6
 FSR, Formal or Statistical Reasoning

Student has received a score of 111 on the Carleton Math Placement exam. Not open to students who have received credit for Mathematics 101 or received a score of 4 or better on the Calculus AB AP exam or received a score of 4 or better on the Calculus BC AP exam or received a score of 5 or better on the Calculus IB exam. For more information, see the Mathematics' web page.
 Corey Brooke 🏫 👤 · Rebecca Terry 🏫 👤 · Joseph Johnson 🏫 👤 · Rob Thompson 🏫 👤

MATH 120 Calculus 2
Inverse functions, integration by parts, improper integrals, modeling with differential equations, vectors, calculus of functions of two independent variables including directional derivatives and double integrals, Lagrange multipliers.
 Fall 2024, Winter 2025, Spring 2025
 6
 FSR, Formal or Statistical Reasoning

Student has completed any of the following course(s): MATH 101 – Calculus with Problem Solving or MATH 111 – Introduction to Calculus with a grade of C or better or received a scored of 4 or better on AP Calculus AB test or received a scored of 5 or better on Calculus IB test or placement exam. Not open to students who received a scored of 4 or better on the AP Calculus BC test or completed MATH 211 with a grade of C or better.
 Rafe Jones 🏫 👤 · Corey Brooke 🏫 👤 · Rebecca Terry 🏫 👤 · Mike Adams 🏫 👤

MATH 134 Linear Algebra with Applications
Linear algebra centers on the geometry, algebra, and applications of linear equations. It is pivotal to many areas of mathematics, natural sciences, computer science, and engineering. To study linear equations, we will develop concepts including matrix algebra, linear independence, determinants, eigenvectors, and orthogonality. Students will use these tools to model real world problems and solve these problems using computational software.
 Fall 2024, Spring 2025
 6
 FSR, Formal or Statistical Reasoning

Not open to students who have taken MATH 232 – Linear Algebra or equivalents.
 Josh Davis 🏫 👤 · Rob Thompson 🏫 👤

MATH 210 Calculus 3
Vectors, curves, calculus of functions of three independent variables, including directional derivatives and triple integrals, cylindrical and spherical coordinates, line integrals, Green's theorem, sequences and series, power series, Taylor series. This course cannot be substituted for MATH 211.
 Winter 2025, Spring 2025
 6
 FSR, Formal or Statistical Reasoning

Student has completed any of the following course(s): MATH 120 – Calculus 2 with a grade of C or better. Students who have received a score of 4 or greater on the AP Calculus BC exam should register for MATH 211 – Multivariable Calculus.
 Corey Brooke 🏫 👤 · Caroline TurnageButterbaugh 🏫 👤

MATH 211 Introduction to Multivariable Calculus
Vectors, curves, partial derivatives, gradient, multiple and iterated integrals, line integrals, Green’s theorem.
 Fall 2024, Winter 2025
 6
 FSR, Formal or Statistical Reasoning

Student has received a score of 4 or better on the AP Calculus BC exam or received a score of 211 on the Carleton Math Placement exam.
 Caroline TurnageButterbaugh 🏫 👤 · Sunrose Shrestha 🏫 👤 · Kate Meyer 🏫 👤

MATH 232 Linear Algebra
Linear algebra centers on the study of highly structured functions called linear transformations. Given the abundance of nonlinear functions in mathematics, it may come as a surprise that restricting to linear ones opens the door to a rich and powerful theory that finds applications throughout mathematics, statistics, computer science, and the natural and social sciences. Linear transformations are everywhere, once we know what to look for. They appear in calculus as the functions that are used to define lines and planes in Euclidean space. In fact, differentiation is also a linear transformation that takes one function to another. The course focuses on developing geometric intuition as well as computational matrix methods. Topics include kernel and image of a linear transformation, vector spaces, determinants, eigenvectors and eigenvalues.
 Fall 2024, Winter 2025, Spring 2025
 6
 FSR, Formal or Statistical Reasoning

Student has completed any of the following course(s): MATH 120 – Calculus 2 or MATH 211 – Introduction to Multivariable Calculus with a grade of C or better or equivalent.
 Rebecca Terry 🏫 👤 · Rafe Jones 🏫 👤 · MurphyKate Montee 🏫 👤 · Mike Adams 🏫 👤 · Corey Brooke 🏫 👤

MATH 236 Mathematical Structures
Basic concepts and techniques used throughout mathematics. Topics include logic, mathematical induction and other methods of proof, problem solving, sets, cardinality, equivalence relations, functions and relations, and the axiom of choice. Other topics may include: algebraic structures, graph theory, and basic combinatorics.
 Fall 2024, Winter 2025, Spring 2025
 6
 FSR, Formal or Statistical Reasoning

Student has completed any of the following course(s): MATH 134 – Linear Algebra with Applications or MATH 232 Linear Algebra AND MATH 210 – Calculus 3 or MATH 211 – Multivariable Calculus with a grade of C or better or equivalent.
 Sunrose Shrestha 🏫 👤 · Deanna Haunsperger 🏫 👤 · MurphyKate Montee 🏫 👤

MATH 240 Probability
Introduction to probability and its applications. Topics include discrete probability, random variables, independence, joint and conditional distributions, expectation, limit laws and properties of common probability distributions.
 Fall 2024, Winter 2025
 6
 FSR, Formal or Statistical Reasoning

Student has completed any of the following course(s): MATH 120 – Calculus 2 or MATH 211 – Introduction to Multivariable Calculus or greater with a grade of C or better or received a score of 4 or better on the Calculus BC AP exam or equivalent.
 Andy Poppick 🏫 👤 · Katie St. Clair 🏫 👤 · Adam Loy 🏫 👤

MATH 241 Ordinary Differential Equations
Ordinary differential equations are a fundamental language used by mathematicians, scientists, and engineers to describe processes involving continuous change. In this course we develop ordinary differential equations as models of real world phenomena and explore the mathematical ideas that arise within these models. Topics include separation of variables; phase portraits; equilibria and their stability; nondimensionalization; bifurcation analysis; and modeling of physical, biological, chemical, and social processes.
 Fall 2024, Winter 2025, Spring 2025
 6
 FSR, Formal or Statistical Reasoning

Student must have completed any of the following course(s): MATH 134 – Linear Algebra with Applications or MATH 232 – Linear Algebra AND MATH 120 – Calculus 2 or MATH 211 – Multivariable Calculus with a grade of C or better or equivalents.
 Kate Meyer 🏫 👤 · Joseph Johnson 🏫 👤 · Rebecca Terry 🏫 👤

MATH 244 Geometries
Euclidean geometry from an advanced perspective; projective, hyperbolic, inversive, and/or other geometries. Recommended for prospective secondary school teachers.
Not offered in 202425
 6
 FSR, Formal or Statistical Reasoning

Student has completed any of the following course(s): MATH 236 – Mathematical Structures with a grade of C or better.

MATH 251 Chaotic Dynamics
Dynamics is the branch of mathematics that deals with the study of change. In this course we will focus on simple discrete nonlinear dynamical systems that produce astoundingly rich and unpredictable behavior — something that is colloquially referred to as "chaos". Topics will include one dimensional dynamics (including fixed points and their classifications), Sharkovsky's Theorem, a careful formulation/definition of "chaos", symbolic dynamics, complex dynamics (including Julia and Mandelbrot sets), iterated function systems, fractals and more.
 Winter 2025
 6
 FSR, Formal or Statistical Reasoning

Student has completed any of the following course(s): MATH 236 – Mathematical Structures with a grade of C or better or equivalent.
 Sunrose Shrestha 🏫 👤

MATH 271 Optimization
Optimization is all about selecting the "best" thing. Finding the most likely strategy to win a game, the route that gets you there the fastest, or the curve that most closely fits given data are all examples of optimization problems. In this course we study linear optimization (also known as linear programming), the simplex method, and duality from both a theoretical and a computational perspective. Applications will be selected from statistics, economics, computer science, and more. Additional topics in nonlinear and convex optimization will be covered as time permits.
 Spring 2025
 6
 FSR, Formal or Statistical Reasoning

Student must have completed any of the following course(s): MATH 134 – Linear Algebra with Applications or MATH 232 – Linear Algebra AND MATH 120 – Calculus 2 or MATH 211 – Multivariable Calculus with a grade of C or better or equivalents.
 Rob Thompson 🏫 👤

MATH 282 Number Theory
A first course in number theory, covering properties of the integers. Topics include the Euclidean algorithm, prime factorization, Diophantine equations, congruences, divisibility, Euler’s phi function and other multiplicative functions, primitive roots, and quadratic reciprocity. Along the way we will encounter and explore several famous unsolved problems in number theory. If time permits, we may discuss further topics, including integers as sums of squares, continued fractions, distribution of primes, Mersenne primes, the RSA cryptosystem.
Not offered in 202425
 6
 FSR, Formal or Statistical Reasoning

Student has completed any of the following course(s): MATH 236 – Mathematical Structures with a grade of C or better or equivalent.

MATH 294 Directed Research in Mathematics
Students work on a research project related to a faculty member's research interests, and directed by that faculty member. Student activities vary according to the field and stage of the project. The longrun goal of these projects normally includes dissemination to a scholarly community beyond Carleton. The faculty member will meet regularly with the student and actively direct the work of the student, who will submit an endofterm product, typically a paper or presentation.

MATH 295 Numerical Differential Equations
An introduction to numerical methods to compute approximate solutions of differential equations. Material will be selected from a range of topics such as error analysis, numerical differentiation, Euler and RungeKutta methods, predictorcorrector methods, boundary value problems, and curve fitting. Applications to other subjects such as physics, chemistry, ecology, epidemiology and neuroscience will be covered. Programming experience is not required.
 Fall 2024
 6
 FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning

Student has completed any of the following course(s): MATH 134 – Linear Algebra with Applications or MATH 232 – Linear Algebra with a grade of C or better or equivalent.
 Joseph Johnson 🏫 👤

MATH 321 Real Analysis I
A systematic study of singlevariable functions on the real numbers. This course develops the mathematical concepts and tools needed to understand why calculus really works: the topology of the real numbers, limits, differentiation, integration, convergence of sequences, and series of functions.
 Winter 2025
 6
 FSR, Formal or Statistical Reasoning

Student has completed any of the following course(s): MATH 236 – Mathematical Structures AND MATH 210 – Calculus 3 or MATH 211 – Multivariable Calculus with a grade of C or better or equivalents.
 Kate Meyer 🏫 👤

MATH 331 Real Analysis II
Further topics in analysis such as measure theory, Lebesgue integration or Banach and Hilbert spaces.
 Spring 2025
 6
 FSR, Formal or Statistical Reasoning

Student has completed any of the following course(s): MATH 321 – Real Analysis I with a grade of C or better.
 Sunrose Shrestha 🏫 👤

MATH 332 Advanced Linear Algebra
Selected topics beyond the material of Mathematics 232. Topics may include the CayleyHamilton theorem, the spectral theorem, factorizations, canonical forms, determinant functions, estimation of eigenvalues, inner product spaces, dual vector spaces, unitary and Hermitian matrices, operators, infinitedimensional spaces, and various applications.
Not offered in 202425
 6
 FSR, Formal or Statistical Reasoning

Student has completed any of the following course(s): MATH 236 – Mathematical Structures with a grade of C or better.

MATH 333 Combinatorial Theory
The study of structures involving finite sets. Counting techniques, including generating functions, recurrence relations, and the inclusionexclusion principle; existence criteria, including Ramsey’s theorem and the pigeonhole principle. Some combinatorial identities and bijective proofs. Other topics may include graph and/or network theory, Hall’s (“marriage”) theorem, partitions, and hypergeometric series.
 Winter 2025
 6
 FSR, Formal or Statistical Reasoning

Student has completed any of the following course(s): MATH 236 – Mathematical Structures with a grade of C or better or equivalent.
 Mike Adams 🏫 👤

MATH 341 Partial Differential Equations
An introduction to partial differential equations with emphasis on the heat equation, wave equation, and Laplace’s equation. Topics include the method of characteristics, separation of variables, Fourier series, Fourier transforms and existence/uniqueness of solutions.
 Spring 2025
 6
 FSR, Formal or Statistical Reasoning

Student has completed any of the following course(s): MATH 241 – Ordinary Differential Equations with grade of C or better.
 Joseph Johnson 🏫 👤

MATH 342 Abstract Algebra I
Introduction to algebraic structures, including groups, rings, and fields. Homomorphisms and quotient structures, polynomials, unique factorization. Other topics may include applications such as Burnside’s counting theorem, symmetry groups, polynomial equations, or geometric constructions.
 Fall 2024, Spring 2025
 6
 FSR, Formal or Statistical Reasoning

Student has completed any of the following course(s): MATH 236 – Mathematical Structures with a grade of C or better or equivalent.
 MurphyKate Montee 🏫 👤 · Rafe Jones 🏫 👤

MATH 344 Differential Geometry
Differential geometry is the study of shapes (like curves and surfaces) using tools from linear algebra and calculus. In this course we focus on the differential geometry of curves and surfaces and the concepts of curvature, geodesics, and first and second fundamental forms. These concepts will lead us to remarkable results like the Theorem Egregium and the GaussBonnet Theorem, which relate the ways that curvature and shape interact.
 Fall 2024
 6
 FSR, Formal or Statistical Reasoning

Student has completed any of the following course(s): MATH 236 – Mathematical Structures with a grade of C or better or equivalent.
 Rob Thompson 🏫 👤

MATH 349 Methods of Teaching Mathematics
Methods of teaching mathematics in grades 712. Issues in contemporary mathematics education. Regular visits to school classrooms and teaching a class are required.
Not offered in 202425

MATH 352 Galois Theory
In the nineteenth century, Évariste Galois discovered a deep connection between field theory and group theory. Now known as Galois theory, this led to the resolution of several centuriesold problems, including whether there is a version of the quadratic formula for higherdegree polynomials, and whether the circle can be squared. Today Galois theory is a fundamental concept for many mathematical fields, from topology to algebra to number theory. This course develops the theory in a modern framework, and explores several applications. Topics include field extensions, classical constructions, splitting fields, the Galois correspondence, Galois groups of polynomials, and solvability by radicals.
Not offered in 202425
 6
 FSR, Formal or Statistical Reasoning

Student has completed any of the following course(s): MATH 342 – Abstract Algebra I with grade of C or better.

MATH 354 Topology
An introduction to the study of topological spaces. We develop concepts from pointset and algebraic topology in order to distinguish between different topological spaces up to homeomorphism. Topics include methods of construction of topological spaces; continuity, connectedness, compactness, Hausdorff condition; fundamental group, homotopy of maps.
Not offered in 202425
 6
 FSR, Formal or Statistical Reasoning

Student has completed any of the following course(s): MATH 236 – Mathematical Structures with a grade of C or better or equivalent.

MATH 361 Complex Analysis
The theoretical foundations for the calculus of functions of a complex variable.
Not offered in 202425
 6
 FSR, Formal or Statistical Reasoning

Student has completed any of the following course(s): MATH 321 – Real Analysis I with a grade of C or better.

MATH 394 Directed Research in Mathematics
Students work on a research project related to a faculty member's research interests, and directed by that faculty member. Student activities vary according to the field and stage of the project. The longrun goal of these projects normally includes dissemination to a scholarly community beyond Carleton. The faculty member will meet regularly with the student and actively direct the work of the student, who will submit an endofterm product, typically a paper or presentation.

MATH 395 Introduction to Analytic Number Theory
An introduction to the techniques and principles of analytic number theory. Topics covered include arithmetical functions, Dirichlet multiplication, averages of arithmetical functions, elementary theorems on the distribution of the primes, and Dirichlet's theorem on primes in arithmetic progressions.
 Winter 2025
 6
 FSR, Formal or Statistical Reasoning

Student has completed the following course(s): MATH 321 – Real Analysis I and MATH 342 – Abstract Algebra I with a grade of C or better.
 Caroline TurnageButterbaugh 🏫 👤

MATH 399 Senior Seminar
As part of their senior capstone experience, majors will work together in teams to develop advanced knowledge in a facultyspecified area or application of mathematics, and to design and implement the first stage of a project completed the following term.

MATH 400 Integrative Exercise
Either a supervised smallgroup research project or an individual, independent reading. Required of all senior majors.
 Fall 2024, Winter 2025, Spring 2025
 S/NC
 3 – 6

Student is in the MATH program of study and has Senior Priority and has completed any of the following course(s): MATH 236 – Mathematical Structures or equivalent AND three courses from any Math course higher than MATH 236, CS 252 or equivalent, CS 254, CS 352, STAT 250, STAT 320 or STAT 340 with a grade of C or better.
 Deanna Haunsperger 🏫 👤 · Katie St. Clair 🏫 👤 · Rafe Jones 🏫 👤 · MurphyKate Montee 🏫 👤 · Kate Meyer 🏫 👤 · Joseph Johnson 🏫 👤
Statistics Courses

STAT 120 Introduction to Statistics
Introduction to statistics and data analysis. Practical aspects of statistics will be emphasized, including extensive use of programming in the statistical software R, interpretation and communication of results. Topics include: exploratory data analysis, correlation and linear regression, design of experiments, the normal distribution, randomization approach to inference, sampling distributions, estimation, and hypothesis testing. Students who have taken Mathematics 211 are encouraged to consider the more advanced Mathematics 240/Statistics 250 Probability/Statistical Inference sequence.
 Fall 2024, Winter 2025, Spring 2025
 6
 FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning

Not open to students that have taken PSYC 200 – Measurement and Data Analysis in Psychology, PSYC 201 – Measurement and Data Analysis Lab , SOAN 239 – Social Statistics or STAT 250 – Introduction to Statistical Inference.
 Amanda Luby 🏫 👤 · Katie St. Clair 🏫 👤 · Andy Poppick 🏫 👤 · Rebecca Terry 🏫 👤 · Spencer Wadsworth 🏫 👤 · Claire Kelling 🏫 👤

STAT 220 Introduction to Data Science
This course will cover the computational side of data analysis, including data acquisition, management, and visualization tools. Topics may include: data scraping, data wrangling, data visualization using packages such as ggplots, interactive graphics using tools such as Shiny, an introduction to classification methods, and understanding and visualizing spatial data. We will use the statistics software R in this course.
 Fall 2024, Winter 2025, Spring 2025
 6
 FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning

Student has completed any of the following course(s): STAT 120 – Introduction to Statistics or STAT 230 – Applied Regression Analysis, or STAT 250 – Introduction to Statistical Inference with a grade of C or better.
 Claire Kelling 🏫 👤 · Amanda Luby 🏫 👤

STAT 230 Applied Regression Analysis
A second course in statistics covering simple linear regression, multiple regression and ANOVA, and logistic regression. Exploratory graphical methods, model building and model checking techniques will be emphasized with extensive use of statistical software R to analyze reallife data.
 Fall 2024, Winter 2025, Spring 2025
 6
 FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning

Student has completed any of the following course(s): STAT 120 – Introduction to Statistics or STAT 250 – Introduction to Statistical Inference or PSYC 200 – Measurement & Data Analysis or SOAN 239 – Social Statistics with a grade of C or better or received a score of 4 or better on the Statistics AP exam.
 Claire Kelling 🏫 👤 · Andy Poppick 🏫 👤

STAT 250 Introduction to Statistical Inference
Introduction to modern mathematical statistics. The mathematics underlying fundamental statistical concepts will be covered as well as applications of these ideas to reallife data. Topics include: resampling methods (permutation tests, bootstrap intervals), classical methods (parametric hypothesis tests and confidence intervals), parameter estimation, goodnessoffit tests, regression, and Bayesian methods. The statistical package R will be used to analyze data sets.
 Winter 2025, Spring 2025
 6
 FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning

Student has completed any of the following course(s): MATH 240 – Probability with a grade of C or better.
 Amanda Luby 🏫 👤 · Adam Loy 🏫 👤

STAT 260 Introduction to Sampling Techniques
Covers sampling design issues beyond the basic simple random sample: stratification, clustering, domains, and complex designs like twophase and multistage designs. Inference and estimation techniques for most of these designs will be covered and the idea of sampling weights for a survey will be introduced. We may also cover topics like graphing complex survey data and exploring relationships in complex survey data using regression and chisquare tests.
Not offered in 202425
 6
 FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning

Student has completed any of the following course(s): STAT 120 – Introduction to Statistics or STAT 230 – Applied Regression Analysis, or STAT 250 – Introduction to Statistical Inference with a grade of C or better.

STAT 270 Statistical Learning
Statistical learning (sometimes called statistical machine learning) centers on the discovery of structural patterns and making predictions using complex data sets. This course explores supervised and unsupervised statistical learning methods, and the ethical considerations of their use. Topics may include nonparametric regression, classification, cross validation, linear model selection techniques and regularization, and clustering. Students will implement these concepts using opensource computational tools, such as the R language.
 Fall 2024
 6
 FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning

Student has completed any of the following course(s): STAT 230 Applied Regression Analysis with a grade of C or better and has NOT taken CS 320 – Machine Learning
 Adam Loy 🏫 👤

STAT 285 Statistical Consulting
Students will apply their statistical knowledge by analyzing data problems solicited from the Northfield community. Students will also learn basic consulting skills, including communication and ethics.
 Fall 2024, Winter 2025, Spring 2025
 S/CR/NC
 2
 FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning

Student has completed the following course(s): STAT 230 – Applied Regression Analysis with a grade of C or better.
 Katie St. Clair 🏫 👤

STAT 294 Directed Research in Statistics
Students work on a research project related to a faculty member's research interests, and directed by that faculty member. Student activities vary according to the field and stage of the project. The longrun goal of these projects normally includes dissemination to a scholarly community beyond Carleton. The faculty member will meet regularly with the student and actively direct the work of the student, who will submit an endofterm product, typically a paper or presentation.
 Fall 2024, Fall 2024, Winter 2025, Spring 2025
 S/CR/NC
 1 – 6
 No Exploration
 Adam Loy 🏫 👤 · Claire Kelling 🏫 👤

STAT 310 Spatial Statistics
Spatial data is becoming increasingly available in a wide range of disciplines, including social sciences such as political science and criminology, as well as natural sciences such as geosciences and ecology. This course will introduce methods for exploring and analyzing spatial data. Methods will be covered to describe and analyze three main types of spatial data: areal, point process, and pointreferenced (geostatistical) data. The course will also extensively cover tools for working with spatial data in R. The goals are that by the end of the course, students will be able to read, explore, plot, and describe spatial data in R, determine appropriate methods for analyzing a given spatial dataset, and work with their own spatial dataset(s) in R and derive conclusions about an application through statistical inference.
Not offered in 202425
 6
 FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning

Student has completed any of the following course(s): STAT 230 – Applied Regression Analysis and STAT 250 – Introduction to Statistical Inference with a grade of C or better.

STAT 320 Time Series Analysis
Models and methods for characterizing dependence in data that are ordered in time. Emphasis on univariate, quantitative data observed over evenly spaced intervals. Topics include perspectives from both the time domain (e.g., autoregressive and moving average models, and their extensions) and the frequency domain (e.g., periodogram smoothing and parametric models for the spectral density). Exposure to matrix algebra may be helpful but is not required.
 Spring 2025
 6
 FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning

Student has completed any of the following course(s): STAT 230 – Applied Regression Analysis and STAT 250 – Introduction to Statistical Inference with a grade of C or better.
 Andy Poppick 🏫 👤

STAT 330 Advanced Statistical Modeling
Topics include linear mixed effects models for repeated measures, longitudinal or hierarchical data and generalized linear models (of which logistic and Poisson regression are special cases) including zeroinflated Poisson models. Depending on time, additional topics could include survival analysis or generalized additive models.
 Winter 2025
 6
 FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning

Student has completed any of the following course(s): STAT 230 – Applied Regression Analysis and STAT 250 – Introduction to Statistical Inference with a grade of C or better and has completed or is in the process of completing MATH 134 – Linear Algebra with Practical Applications or MATH 232 – Linear Algebra with a grade of C or better or equivalents.
 Katie St. Clair 🏫 👤

STAT 340 Bayesian Statistics
An introduction to statistical inference and modeling in the Bayesian paradigm. Topics include Bayes’ Theorem, common prior and posterior distributions, hierarchical models, Markov chain Monte Carlo methods (e.g., the MetropolisHastings algorithm and Gibbs sampler) and model adequacy and posterior predictive checks. The course uses R extensively for simulations.
Not offered in 202425
 6
 FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning

Student has completed any of the following course(s): STAT 250 – Introduction to Statistical Inference with a grade of C or better.

STAT 394 Directed Research in Statistics
Students work on a research project related to a faculty member's research interests, and directed by that faculty member. Student activities vary according to the field and stage of the project. The longrun goal of these projects normally includes dissemination to a scholarly community beyond Carleton. The faculty member will meet regularly with the student and actively direct the work of the student, who will submit an endofterm product, typically a paper or presentation.
 Fall 2024, Fall 2024, Winter 2025, Spring 2025
 S/CR/NC
 1 – 6
 No Exploration
 Claire Kelling 🏫 👤 · Katie St. Clair 🏫 👤

STAT 399 Senior Seminar
As part of their senior capstone experience, majors will work together in teams to develop advanced knowledge in a facultyspecified area or application of statistics, and to design and implement the first stage of a project completed the following term.
 Fall 2024, Winter 2025
 6
 No Exploration

Students have completed any of the following course(s): STAT 230 – Applied Regression Analysis and STAT 250 – Introduction to Statistical Inference with a grade of C or better and has a Statistics Program of Study and senior class standing.
 Adam Loy 🏫 👤 · Amanda Luby 🏫 👤

STAT 400 Integrative Exercise
Either a supervised smallgroup research project or an individual, independent reading. Required of all senior majors.
 Fall 2024, Winter 2025, Spring 2025
 S/NC
 3 – 6
 Katie St. Clair 🏫 👤 · Adam Loy 🏫 👤 · Amanda Luby 🏫 👤