two students look at a mathematical proof on a chalkboard

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.

two students look at a mathematical proof on a chalkboard

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 calculus and linear algebra courses. 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

Major Requirements – 72-75 Total Credits

Core Courses – Required 30 Credits

Elective Courses – Required 36 credits

Six courses from among:

Elective Requirements

Of the six advanced courses, at least four must be Carleton courses with a Mathematics designation. At least three of the following five areas of mathematics must be represented by the six electives (36 credits).

Algebra

Analysis

Applied Mathematics

  • MATH 240: Probability
  • MATH 241: Ordinary Differential Equations
  • MATH 271: Optimization
  • MATH 334: Computational Linear Algebra (not offered 2025-26)
  • MATH 341: Partial Differential Equations
  • STAT 250: Introduction to Statistical Inference
  • STAT 320: Time Series Analysis (not offered 2025-26)
  • STAT 340: Bayesian Statistics

Discrete Structures

  • CS 252: Algorithms
  • CS 254: Computability and Complexity
  • MATH 333: Combinatorial Theory (not offered 2025-26)

Geometry and Topology

Advanced courses substituted for MATH 232: Linear Algebra or MATH 236: Mathematical Structures must also be Carleton courses with a Mathematics designation.

Senior Seminar and Senior Integrative Exercise – Required 6 or 9 credits

In addition, each senior major must complete an integrative exercise. Normally, that integrative exercise is a two-term group project. At the department’s discretion, a one-term independent project may be available. The group project would be MATH 399: Senior Seminar: Senior Seminar (6 credits) and MATH 400: Integrative Exercise: Integrative Exercise (3 credits). The independent project would be MATH 400: Integrative Exercise (6 credits).

Math Talk 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.

Additional Departmental Notes

Normally, a mathematics major must be declared by the last day of finals in the winter term of a student’s junior year.

Potential majors with especially strong preparation may petition the department for permission to substitute an advanced course for MATH 232: Linear Algebra and/or for MATH 236: Mathematical Structures. Advanced courses substituted for MATH 232: Linear Algebra or MATH 236: Mathematical Structures 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 100-level Physics, CHEM 123: Principles of Chemistry I & Lab, CHEM 224: Principles of Chemistry II & Lab, and CS 111: Introduction to Computer Science.

Requirements for the Statistics Major

Major Requirements – 77 Total Credits

Supporting Courses – Required 30 credits

Core Courses – Required 18 credits

All of the following, of which at least two must be taken at Carleton

Elective Courses – Required 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 300-level course with a Statistics designation.

  • CS 314: Data Visualization (not offered 2025-26)
  • CS 314*: Data Visualization (*=Junior Seminar)
  • CS 320: Machine Learning
  • CS 320*: Machine Learning (*=Junior Seminar) (not offered 2025-26)
  • CS 362: Computational Biology
  • MATH 271: Optimization
  • STAT 220: Introduction to Data Science
  • STAT 260: Introduction to Sampling Techniques
  • STAT 270: Statistical Learning (not offered 2025-26)
  • STAT 310: Spatial Statistics (not offered 2025-26)
  • STAT 320: Time Series Analysis (not offered 2025-26)
  • STAT 330: Advanced Statistical Modeling
  • STAT 340: Bayesian Statistics

Statistical Practice – Required 2 credits

Senior Seminar and Senior Integrative Exercise – Required 9 credits

In addition, each senior major must complete an integrative exercise. This is a two-term group project. There is no independent comps in the statistics major. Each senior will first enroll in STAT 399: Senior Seminar: Senior Seminar (6 credits); the following term they will complete their comps in STAT 400: Integrative Exercise: Integrative Exercise (3 credits).

  • STAT 399: Senior Seminar (6 credits)
  • STAT 400: Integrative Exercise (3 credits)

Statistics Talk 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.

Additional Departmental Notes

Normally, a statistics major must be declared by the last day of finals in the winter term of a student’s junior year.

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

Minor Requirements – 42 Total Credits

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.)

MATH Designated Courses – Required Minimum 36 credits

At least 36 of the required 42 credits must come from courses with a Mathematics designation.

STAT Courses – Maximum 6 credits

In addition, the only Statistics courses which can be counted toward the Mathematics minor are Statistics 250, 320 and 340.

Additional Departmental Notes

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

Minor Requirements – 42 Total Credits

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:

STAT Courses – Required 18 credits

A student may choose to replace STAT 120: Introduction to Statistics with any STAT course from the list of approved elective courses.

CS Course – Required 6 credits

One computer science course (6 credits) taken at Carleton numbered CS 111: Introduction to Computer Science or higher.

Elective Courses – Required 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 subject areas of Mathematics and Statistics and Computer Science. At least two of these courses must be 200-level or above. No more than two of these courses can come from the same subject area.

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
  • STAT 270: Statistical Learning (not offered 2025-26)
  • STAT 310: Spatial Statistics (not offered 2025-26)
  • STAT 320: Time Series Analysis (not offered 2025-26)
  • STAT 330: Advanced Statistical Modeling
  • STAT 340: Bayesian Statistics

Courses from the Computer Science Department

  • CS 252: Algorithms
  • CS 257: Software Design
  • CS 314: Data Visualization (not offered 2025-26)
  • CS 314*: Data Visualization (*=Junior Seminar)
  • CS 320: Machine Learning
  • CS 320*: Machine Learning (*=Junior Seminar) (not offered 2025-26)
  • CS 321: Making Decisions with Artificial Intelligence (not offered 2025-26)
  • CS 322: Natural Language Processing
  • CS 334: Database Systems
  • CS 344: Human-Computer Interaction
  • CS 348: Parallel and Distributed Computing (not offered 2025-26)
  • CS 362: Computational Biology

Courses from other Departments

Students who elect to take PSYC 234 must also take PSYC 235 to satisfy one of the elective course requirements.

  • ARCN 246: Archaeological Methods & Lab
  • BIOL 224: Landscape Ecology (not offered 2025-26)
  • BIOL 321: Ecosystem Ecology (not offered 2025-26)
  • BIOL 338: Genomics and Bioinformatics
  • BIOL 352: Population Ecology
  • CGSC 232: Cognitive Processes
  • CGSC 233: Laboratory in Cognitive Processes
  • CHEM 348: Introduction to Computational Chemistry (not offered 2025-26)
  • DGAH 210: Spatial Humanities (not offered 2025-26)
  • ECON 241: Macroeconomic Growth and Development
  • ECON 269: Economics of Climate Change (not offered 2025-26)
  • ECON 285: Computational Economics (not offered 2025-26)
  • ECON 329: Econometrics
  • ENTS 120: Introduction to Geospatial Analysis & Lab
  • ENTS 254: Topics in Landscape Ecology (not offered 2025-26)
  • GEOL 210: Geomorphology and Lab
  • GEOL 215: Paleoclimate & Lab
  • GEOL 340: Hydrogeology: Groundwater & Lab
  • HIST 231: Mapping the World Before Mercator (not offered 2025-26)
  • HIST 338: Digital History, Public Heritage & Deep Mapping
  • MUSC 227: Perception and Cognition of Music (not offered 2025-26)
  • MUSC 228: Perception and Cognition of Music Lab (not offered 2025-26)
  • PHIL 116: Sensation, Induction, Abduction, Deduction, Seduction (not offered 2025-26)
  • PHIL 123: Topics in Medical Ethics (not offered 2025-26)
  • PHIL 213: Ethics
  • PHYS 234: Computer Simulations in Complex Physical Systems (not offered 2025-26)
  • POSC 230: Methods of Political Research
  • PSYC 200: Measurement and Data Analysis in Psychology
  • PSYC 232: Cognitive Processes
  • PSYC 233: Laboratory in Cognitive Processes
  • PSYC 234: Psychology of Language (not offered 2025-26)
  • PSYC 235: Psychology of Language Laboratory (not offered 2025-26)
  • RELG 155: Hinduism: An Introduction (not offered 2025-26)
  • 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.

Other Elective Requirements

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.

Additional Departmental Notes

For majors outside computer science and mathematics: A maximum of 3 courses may be applied from a student’s major(s) towards the minor.

For students who are double majors: No more than 3 courses from your combined majors may be applied toward the minor.

Statistics majors cannot earn this minor.

Mathematics Courses

  • 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 problem-solving sessions each week, one on Monday or Tuesday, and one on Wednesday or Thursday. Details will be provided on the first day of class.

  • MATH 106 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 second-year 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.

  • 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.

  • 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.

  • 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. 

  • 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.

  • MATH 211 Introduction to Multivariable Calculus

    Vectors, curves, partial derivatives, gradient, multiple and iterated integrals, line integrals, Green’s theorem.

  • 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.

  • 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.

  • 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.

  • 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; non-dimensionalization; bifurcation analysis; and modeling of physical, biological, chemical, and social processes.

  • MATH 244 Geometries

    Euclidean geometry from an advanced perspective; projective, hyperbolic, inversive, and/or other geometries. Recommended for prospective secondary school teachers.

  • 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 non-linear 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. 

    Not offered in 2025-26

  • 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.

  • 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.

  • MATH 285 Mathematics Practicum

    This class is a collaborative research project culminating in a written report or paper. Students will use predictive modeling, computer simulations, visualization, and data management to analyze and provide insight into a problem coming from an external community partner.

    Not offered in 2025-26

    • S/CR/NC
    • No Exploration QRE, Quantitative Reasoning

    • Student has completed any of the following course(s): MATH 101 or MATH 111 or greater with a grade of C- or better 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 Mathematics IB exam or received a score of 3 on the Calculus BC AP exam with a Calculus AB subscore of 4 or received a Carleton Math 111 or better Requisite Equivalency.
    • CL: 200 level

  • 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 long-run 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 end-of-term product, typically a paper or presentation.

  • MATH 295.01 Tessellation

    This course explores a particularly visual sort of mathematical pattern: a tessellation. A tessellation is a way of covering the plane with shapes (called “tiles”) that don’t overlap. This class will explore questions like: Is it possible to make a tessellation out of a given set of tiles? How many different tessellations can I create from this set of tiles? We’ll cover both classical results (it is impossible to tile the plane with heptagons!), and the 2023 construction of the “Einstein tile”: the first known polygon that tiles the plane but never periodically. Links will be made with graph theory, topology, and geometry.

    Repeatable: This course is repeatable provided the topics are different.

  • MATH 297 Assessment and Communication of External Mathematical Activity

    An independent study course intended for students who have completed an external activity related to the mathematics major (for example, an internship or an externship) to communicate (both in written and oral forms) and assess their mathematical learning from that activity.

  • MATH 321 Real Analysis I

    A systematic study of single-variable 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.

  • MATH 331 Real Analysis II

    Further topics in analysis such as measure theory, Lebesgue integration or Banach and Hilbert spaces.

    Not offered in 2025-26

  • MATH 332 Advanced Linear Algebra

    Selected topics beyond the material of Mathematics 232. Topics may include the Cayley-Hamilton theorem, the spectral theorem, factorizations, canonical forms, determinant functions, estimation of eigenvalues, inner product spaces, dual vector spaces, unitary and Hermitian matrices, operators, infinite-dimensional spaces, and various applications.

  • MATH 333 Combinatorial Theory

    The study of structures involving finite sets. Counting techniques, including generating functions, recurrence relations, and the inclusion-exclusion 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.

    Not offered in 2025-26

  • MATH 334 Computational Linear Algebra

    Computational linear algebra is full of ideas that are useful when interpreting linear algebra objects as data. This course develops these ideas with a balance of theory, applications, and algorithms. Topics will be selected from singular value decomposition, LU and QR factorization, orthogonal computation, conditioning, numerical stability, eigenvalue approximation and iterative methods. Applications include interpolation, least squares, low rank approximation, principal component analysis, regularization, data classification, image processing, and selected topics from machine learning.

    Not offered in 2025-26

  • 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.

  • 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.

  • 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 Gauss-Bonnet Theorem, which relate the ways that curvature and shape interact.

    Not offered in 2025-26

  • MATH 349 Methods of Teaching Mathematics

    Methods of teaching mathematics in grades 7-12. Issues in contemporary mathematics education. Regular visits to school classrooms and teaching a class are required.

  • 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 centuries-old problems, including whether there is a version of the quadratic formula for higher-degree 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.

  • MATH 354 Topology

    An introduction to the study of topological spaces. We develop concepts from point-set 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.

  • MATH 361 Complex Analysis

    The theoretical foundations for the calculus of functions of a complex variable.

  • MATH 362 Representation Theory of Finite Groups

    Representation theory is the study of mathematical structures via the tools of linear algebra. The first objects to be studied in this way were finite groups at the end of the nineteenth century, motivated by the powerful framework of characters in number theory, but the field has generalized incredibly due to the prevalence of symmetry throughout mathematics, physics, and beyond. In this course the focus is on finite groups. Topics include Maschke’s theorem, complete reducibility, and Schur’s lemma; characters, orthogonality relations, and character tables; Fourier transformations and random walks. Additional topics may include Burnside’s Lemma, Frobenius reciprocity, and an exploration of representations of infinite groups.

  • MATH 372 Topics in Group Theory

    This course will build on the introduction to groups established in Math 342. Specific topics will vary by instructor, but may include the Sylow theorems and applications, finite simple groups, permutation groups, classification of groups of small order, finite abelian groups, solvable and nilpotent groups, the Jordan-Holder theorem, group actions on geometric spaces, group presentations, automorphism groups, and semi-direct products.

    Not offered in 2025-26

  • 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 long-run 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 end-of-term product, typically a paper or presentation.

  • MATH 399 Senior Seminar

    As part of their senior capstone experience, majors will work together in teams to develop advanced knowledge in a faculty-specified 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 group project or an individual, independent project. Required of all senior majors.

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.

  • 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.

  • 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 real-life data.

  • 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 real-life data. Topics include: resampling methods (permutation tests, bootstrap intervals), classical methods (parametric hypothesis tests and confidence intervals), parameter estimation, goodness-of-fit tests, regression, and Bayesian methods. The statistical package R will be used to analyze data sets.

  • STAT 260 Introduction to Sampling Techniques

    Covers sampling design issues beyond the basic simple random sample: stratification, clustering, domains, and complex designs like two-phase 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 chi-square tests.

  • 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 open-source computational tools, such as the R language.

    Not offered in 2025-26

  • 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.

  • 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 long-run 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 end-of-term product, typically a paper or presentation.

  • STAT 297 Assessment and Communication of External Statistical Activity

    An independent study course intended for students who have completed an external activity related to the statistics major (for example, an internship or an externship) to communicate (both in written and oral forms) and assess their statistical learning from that activity.

  • 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 point-referenced (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 2025-26

  • 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.

    Not offered in 2025-26

  • 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 zero-inflated Poisson models. Depending on time, additional topics could include survival analysis or generalized additive models. 

  • STAT 340 Bayesian Statistics

    The Bayesian approach to statistics provides a powerful framework for incorporating prior knowledge into statistical analyses, updating this knowledge with data, and quantifying uncertainty in results. This course serves as a comprehensive introduction to Bayesian statistical inference and modeling, an alternative to the frequentist approach to statistics covered in previous classes. Topics include: Bayes’ Theorem; prior and posterior distributions; Bayesian regression; hierarchical models; and model adequacy and posterior predictive checks. Computational techniques will also be covered, including Markov Chain Monte Carlo methods, and modern Bayesian modeling packages in R.

  • 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 long-run 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 end-of-term product, typically a paper or presentation.

  • STAT 399 Senior Seminar

    As part of their senior capstone experience, majors will work together in teams to develop advanced knowledge in a faculty-specified area or application of statistics, and to design and implement the first stage of a project completed the following term.

  • STAT 400 Integrative Exercise

    A supervised group project. Required of all senior majors.