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 any mathematics or math-related 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: Calculus with Problem Solving or MATH 111: Introduction to Calculus and either MATH 210: Calculus 3 or MATH 211: Introduction to Multivariable Calculus and either MATH 134: Linear Algebra with Applications or MATH 232: Linear Algebra and all of remaining courses listed):
  •  B. Electives (36 credits): Six courses from among:
  • CS 252: Algorithms
  • CS 254: Computability and Complexity
  • CS 352: Advanced Algorithms (not offered 2024-25)
  • MATH 240: Probability
  • MATH 241: Ordinary Differential Equations
  • MATH 244: Geometries (not offered 2024-25)
  • MATH 251: Chaotic Dynamics
  • MATH 271: Optimization
  • MATH 282: Number Theory (not offered 2024-25)
  • MATH 295.00: Numerical Differential Equations (.24/FA)
  • MATH 321: Real Analysis I
  • MATH 331: Real Analysis II
  • MATH 332: Advanced Linear Algebra (not offered 2024-25)
  • 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 2024-25)
  • MATH 352: Galois Theory (not offered 2024-25)
  • MATH 354: Topology (not offered 2024-25)
  • MATH 361: Complex Analysis (not offered 2024-25)
  • MATH 362: Representation Theory of Finite Groups (not offered 2024-25)
  • MATH 395.01: Introduction to Analytic Number Theory (.25/WI)
  • STAT 250: Introduction to Statistical Inference
  • STAT 320: Time Series Analysis
  • STAT 340: Bayesian Statistics (not offered 2024-25)

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 2024-25)
  • MATH 332: Advanced Linear Algebra (not offered 2024-25)
  • MATH 342: Abstract Algebra I
  • MATH 352: Galois Theory (not offered 2024-25)
  • MATH 362: Representation Theory of Finite Groups (not offered 2024-25)
  • MATH 395: Introduction to Analytic Number Theory
  • Analysis:
  • Applied Mathematics:
  • Discrete Structures:
  • CS 252: Algorithms
  • CS 254: Computability and Complexity
  • CS 352: Advanced Algorithms (not offered 2024-25)
  • MATH 333: Combinatorial Theory
  • Geometry and Topology:
  • MATH 244: Geometries (not offered 2024-25)
  • MATH 295: Numerical Differential Equations
  • MATH 344: Differential Geometry
  • MATH 354: Topology (not offered 2024-25)

Of the six advanced courses, at least four must be Carleton courses with a Mathematics designation. Advanced courses substituted for MATH 232: Linear Algebra or MATH 236: Mathematical Structures 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 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).

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: 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

The requirements for the Statistics Major are 74 credits:

  • A.  Supporting Courses (30 credits) Take either MATH 101: Calculus with Problem Solving or MATH 111: Introduction to Calculus, either MATH 210: Calculus 3 or MATH 211: Introduction to Multivariable Calculus and either MATH 134: Linear Algebra with Applications or MATH 232: Linear Algebra and all of remaining courses listed:
  • B.  Required Core (18 credits): All of the following, of which at least two must be taken at Carleton
  • 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 300-level course with a Statistics designation.
  • CS 314: Data Visualization
  • CS 314*: Data Visualization (*=Junior Seminar) (not offered 2024-25)
  • CS 320: Machine Learning
  • CS 362: Computational Biology (not offered 2024-25)
  • MATH 271: Optimization
  • STAT 220: Introduction to Data Science
  • STAT 260: Introduction to Sampling Techniques (not offered 2024-25)
  • STAT 270: Statistical Learning
  • STAT 310: Spatial Statistics (not offered 2024-25)
  • STAT 320: Time Series Analysis
  • STAT 330: Advanced Statistical Modeling
  • STAT 340: Bayesian Statistics (not offered 2024-25)
  • D. Statistical Practice (2 credits):
    • STAT 285: Statistical Consulting Statistical Consulting 

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).

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)

A student may choose to replace STAT 120: Introduction to Statistics 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: Introduction to Computer Science 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 200-level 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 2024-25)
  • STAT 270: Statistical Learning
  • STAT 310: Spatial Statistics (not offered 2024-25)
  • STAT 320: Time Series Analysis
  • STAT 330: Advanced Statistical Modeling
  • STAT 340: Bayesian Statistics (not offered 2024-25)

Courses from the Computer Science Department:

  • CS 252: Algorithms
  • CS 257: Software Design
  • CS 314: Data Visualization
  • CS 314*: Data Visualization (*=Junior Seminar) (not offered 2024-25)
  • CS 320: Machine Learning
  • CS 321: Making Decisions with Artificial Intelligence
  • CS 322: Natural Language Processing
  • CS 334: Database Systems (not offered 2024-25)
  • CS 344: Human-Computer Interaction
  • CS 348: Parallel and Distributed Computing
  • CS 352: Advanced Algorithms (not offered 2024-25)
  • CS 362: Computational Biology (not offered 2024-25)

Courses from other departments:

  • ARCN 246: Archaeological Methods & Lab
  • BIOL 224: Landscape Ecology (not offered 2024-25)
  • BIOL 321: Ecosystem Ecology (not offered 2024-25)
  • BIOL 338: Genomics and Bioinformatics
  • BIOL 352: Population Ecology
  • CHEM 348: Introduction to Computational Chemistry
  • DGAH 210: Spatial Humanities (not offered 2024-25)
  • ECON 241: Growth and Development (not offered 2024-25)
  • ECON 285: Computational Economics
  • ECON 329: Econometrics
  • ENTS 120: Introduction to Geospatial Analysis & Lab
  • ENTS 254: Topics in Landscape Ecology (not offered 2024-25)
  • GEOL 135: Introduction to Climate Science & Lab (not offered 2024-25)
  • GEOL 340: Hydrogeology: Groundwater & Lab (not offered 2024-25)
  • HIST 231: Mapping the World Before Mercator
  • HIST 338: Digital History, Public Heritage & Deep Mapping (not offered 2024-25)
  • LING 318: Laboratory Phonology (not offered 2024-25)
  • 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 2024-25)
  • 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 100.00 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 calculation-based problems that use algebra and spreadsheets, readings with discussion, and training in writing for both technical and broad audiences.

  • 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.

  • 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.

    Not offered in 2024-25

  • 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. 

  • 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.

    Not offered in 2024-25

  • 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 295.00 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 Runge-Kutta methods, predictor-corrector 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.

  • 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.

  • 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.

    Not offered in 2024-25

  • 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.

  • 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.

  • 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.

    Not offered in 2024-25

  • 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.

    Not offered in 2024-25

  • 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.

    Not offered in 2024-25

  • MATH 361 Complex Analysis

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

    Not offered in 2024-25

  • 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.

    Not offered in 2024-25

  • MATH 394 Directed Research in Mathematics

    The project examines the intersection between Biology and Mathematics. The project aims to elucidate the geometry of the cellular structures of various leafy greens, we’ll be examining the structure of curly kale cells and attempting to use local cell structure to show hyperbolicity in global cell structure.

  • MATH 395.01 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.

  • MATH 399 Senior Seminar

    As part of their senior capstone experience, majors will work together in teams (typically three to four students per team) 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.

    • Fall 2024
    • S/CR/NC
    • 6
    • No Exploration

    • Student is a Mathematics major and has Senior Priority.
    • MurphyKate Montee 🏫 👤 · Rafe Jones 🏫 👤

  • MATH 400 Integrative Exercise

    Either a supervised small-group research project or an individual, independent reading. 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.

    Not offered in 2024-25

  • 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.

  • 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

    This is ongoing research investigating the decision-making and reporting styles of forensic scientists. In many forensic science disciplines, there is no objective way to determine whether two fingerprints, bullets, or handwritten documents come from the same person or not. Instead, it is the responsibility of each individual analyst to make a subjective decision and communicate their results to a judge or jury. Differences have been observed among examiners when analyzing the same piece of evidence: some examiners appear to be well-calibrated with each other and utilize the full range of possible outcomes, while other examiners are outliers. Recently, there have been proposals to shift from a 3-category scale (e.g., “match”, “non-match”, and “inconclusive”) to 5 or even 7 category scales (e.g., “strong support for match”, “moderate support for match”, “inconclusive”, “moderate support for non-match”, “strong support for non-match”). Since examiner conclusions can influence investigator, judge, and jury decisions, it is important to measure and understand the range of individual differences in reporting styles before adopting a more complicated scale. This project aims to make substantive recommendations to practitioners, develop software for fitting statistical models, and investigate the performance of models through simulation.

  • 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 2024-25

  • 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.

  • 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

    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 Metropolis-Hastings algorithm and Gibbs sampler) and model adequacy and posterior predictive checks. The course uses R extensively for simulations.

    Not offered in 2024-25

  • STAT 394 Directed Research in Statistics

    We will analyze a co-complaint network on police officers in Minneapolis and St Paul. In this network, police officers have a tie connecting them if they were listed on a civilian complaint together. This dataset has never been analyzed before, to our knowledge. The project will consist of conducting preliminary analysis on this network dataset and writing a literature review on the use of networks in the analysis of policing data. This work is in partnership with a national research group that Professor Kelling co-directs called the Data Science, Police Accountability, Community Empowerment (DSPACE) Group.

  • 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.

    • Fall 2024, Winter 2025
    • S/CR/NC
    • 6
    • No Exploration

    • Students have completed any of the following course(s): STAT 230 and STAT 250 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 small-group research project or an individual, independent reading. Required of all senior majors.