Our Statistics courses have been renumbered and changed to a STAT designation. Probability has a new Math course number. See a chart showing the old and new numbers.
F1 Visa Holders who participate in an offcampus internship must take a course related to the internship to satisfy the curricular credit requirement. Mathematics or statistics majors should follow the steps outlined on our CPT student resources page prior to the start of your offcampus internship.
For information about placement into Calculus or Statistics, please visit the Math/Stats Placement page.
Math  Stats
Mathematics
 2023–2024 Courses:
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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.
Prerequisites: Not open to students who have received credit for Mathematics 111. 6 credits; Formal or Statistical Reasoning; offered Fall 2023, Winter 2024 · 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. Prerequisites: Requires placement via the Calculus Placement Exam 1, see Mathematics web page. Not open to students who have received credit for Mathematics 101. 6 credits; Formal or Statistical Reasoning; offered Fall 2023, Winter 2024, Spring 2024 · Rebecca Terry, Joseph Johnson, Rob Thompson, Corey Brooke 
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.
Prerequisites: Mathematics 101, 111, score of 4 or 5 on Calculus AB Exam or placement via a Carleton placement exam. Not open to students who have received credit for Mathematics 211 or have a score of 4 or 5 on the AP Calculus BC exam 6 credits; Formal or Statistical Reasoning; offered Fall 2023, Winter 2024, Spring 2024 · Claudio GómezGonzáles, Corey Brooke, Sunrose Shrestha 
MATH 206: A Tour of Mathematics
A series of eight lectures intended for students considering a Mathematics major. The emphasis will be on presenting various striking ideas, concepts and results in modern mathematics, rather than on developing extensive knowledge or techniques in any particular subject area. 1 credit; S/CR/NC; Does not fulfill a curricular exploration requirement; offered Winter 2024 
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.
Prerequisites: Mathematics 120. This course cannot be substituted for Mathematics 211 6 credits; Formal or Statistical Reasoning; offered Winter 2024, Spring 2024 · Corey Brooke, Caroline TurnageButterbaugh 
MATH 211: Introduction to Multivariable Calculus
Vectors, curves, partial derivatives, gradient, multiple and iterated integrals, line integrals, Green’s theorem. Prerequisites: Score of 4 or 5 on the AP Calculus BC exam, or placement via Calculus Placement Exam #3 6 credits; Formal or Statistical Reasoning; offered Fall 2023, Winter 2024 · Rebecca Terry, Josh Davis, Mike Adams 
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.
Prerequisites: Mathematics 120 or Mathematics 211 6 credits; Formal or Statistical Reasoning; offered Fall 2023, Winter 2024, Spring 2024 · Rafe Jones, Mike Adams, Rebecca Terry 
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. Prerequisites: Mathematics 232 and either Mathematics 210 or Mathematics 211 6 credits; Formal or Statistical Reasoning; offered Fall 2023, Winter 2024, Spring 2024 · Caroline TurnageButterbaugh, Claudio GómezGonzáles, Deanna Haunsperger 
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.
Prerequisites: Mathematics 120 or Mathematics 211 6 credits; Formal or Statistical Reasoning; offered Fall 2023, Winter 2024 · Adam Loy, Katie St. Clair 
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.
Prerequisites: Mathematics 232 or instructor permission 6 credits; Formal or Statistical Reasoning; offered Winter 2024, Spring 2024 · Joseph Johnson, Rob Thompson 
MATH 244: Geometries
Euclidean geometry from an advanced perspective; projective, hyperbolic, inversive, and/or other geometries. Recommended for prospective secondary school teachers. Prerequisites: Mathematics 236 6 credits; Formal or Statistical Reasoning; offered Fall 2023 · Sunrose Shrestha 
MATH 251: Chaotic Dynamics
An exploration of the behavior of nonlinear dynamical systems. Topics include one and twodimensional dynamics, Sarkovskii’s Theorem, chaos, symbolic dynamics, and the Hénon Map.
Prerequisites: Mathematics 232 or instructor permission 6 credits; Formal or Statistical Reasoning; not offered 2023–2024 
MATH 261: Functions of a Complex Variable
Algebra and geometry of complex numbers, analytic functions, complex integration, series, residues, applications. Not open to students who have already received credits for Mathematics 361. Prerequisites: Mathematics 210 or Mathematics 211 6 credits; Formal or Statistical Reasoning; not offered 2023–2024 
MATH 271: Computational Mathematics
An introduction to mathematical ideas from numerical approximation, scientific computing, and/or data analysis. Topics will be selected from numerical linear algebra, numerical analysis, and optimization. Theory, implementation, and application of computational methods will be emphasized.
Prerequisites: Mathematics 232 6 credits; Formal or Statistical Reasoning; offered Winter 2024 · Rob Thompson 
MATH 282: Elementary Theory of Numbers
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.
Prerequisites: Mathematics 236 or instructor permission 6 credits; Formal or Statistical Reasoning; offered Winter 2024 · Rafe Jones 
MATH 295: Introduction to Computational Algebraic Geometry
Classical algebraic geometry is the study of geometric objects defined by polynomial equations. This course will cover fundamental concepts and techniques—varieties, ideals, and Gröbner bases, to name a few—as well as algorithms for solving equations and computing intersections of curves and surfaces. Ultimately, this course will build towards several beautiful results: the 27 lines on a cubic surface, the 28 bitangents on a planar quartic, and the construction of regular polygons. Students will learn to use software such as SageMath to perform computations and practice visualization. While familiarity with Python would be helpful, it is by no means required!
Prerequisites: Mathematics 236 or instructor permission 6 credits; Formal or Statistical Reasoning; offered Spring 2024 · Claudio GómezGonzáles 
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. Prerequisites: Permission of department chair and homework in advance of the external mathematical activity 1 credit; S/CR/NC; Does not fulfill a curricular exploration requirement; offered Fall 2023, Winter 2024, Spring 2024 · Rafe Jones 
MATH 321: Real Analysis I
A systematic study of concepts basic to calculus, such as topology of the real numbers, limits, differentiation, integration, convergence of sequences, and series of functions. Prerequisites: Mathematics 236 or instructor permission 6 credits; Formal or Statistical Reasoning; offered Fall 2023, Spring 2024 · Caroline TurnageButterbaugh, 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. Prerequisites: Mathematics 236 or instructor permission 6 credits; Formal or Statistical Reasoning; offered Fall 2023 · Rob Thompson 
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. Prerequisites: Mathematics 236 or instructor permission 6 credits; Formal or Statistical Reasoning; not offered 2023–2024 
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.
Prerequisites: Mathematics 241 6 credits; Formal or Statistical Reasoning; offered Spring 2024 · 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. Prerequisites: Mathematics 236 or instructor permission 6 credits; Formal or Statistical Reasoning; offered Winter 2024 · Claudio GómezGonzáles 
MATH 344: Differential Geometry
Local and global theory of curves, Frenet formulas. Local theory of surfaces, normal curvature, geodesics, Gaussian and mean curvatures, Theorema Egregium. Prerequisites: Mathematics 236 or permission of the instructor. 6 credits; Formal or Statistical Reasoning; not offered 2023–2024 
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. Prerequisites: Junior or senior standing and instructor permission 6 credits; Does not fulfill a curricular exploration requirement; offered Fall 2023 · Deanna Haunsperger 
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.
Prerequisites: Mathematics 342 6 credits; Formal or Statistical Reasoning; offered Spring 2024 · Rafe Jones 
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.
Prerequisites: Mathematics 236 or instructor permission 6 credits; Formal or Statistical Reasoning; offered Winter 2024 · Josh Davis 
MATH 361: Complex Analysis
The theoretical foundations for the calculus of functions of a complex variable.
Prerequisites: Mathematics 321 or instructor permission. Students who have already received credit for Mathematics 261 may only take this course with instructor permission 6 credits; Formal or Statistical Reasoning; offered Winter 2024 · Caroline TurnageButterbaugh 
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.
Prerequisites: Mathematics 342 6 credits; not offered 2023–2024 
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.
Prerequisites: Mathematics 282 or Mathematics 342 6 credits; Formal or Statistical Reasoning; not offered 2023–2024 
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 facultyspecified area or application of mathematics, and to design and implement the first stage of a project completed the following term.
Prerequisites: Open only to senior Math majors 6 credits; S/CR/NC; Does not fulfill a curricular exploration requirement; offered Fall 2023 · Rob Thompson 
MATH 400: Integrative Exercise
Either a supervised smallgroup research project or an individual, independent reading. Required of all senior majors.
Prerequisites: Mathematics 236 and successful completion of three courses from among: Mathematics courses numbered above 236, Computer Science 252, Computer Science 254, Computer Science 352, Statistics 250, Statistics 320, Statistics 340 3 credits; S/NC; offered Fall 2023, Winter 2024, Spring 2024 · Deanna Haunsperger, Caroline TurnageButterbaugh, Rob Thompson, Rafe Jones, Sunrose Shrestha
Math  Stats
Statistics
 2023–2024 Courses:
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STAT 120: Introduction to Statistics
Introduction to statistics and data analysis. Practical aspects of statistics, including extensive use of the statistical software R, interpretation and communication of results, will be emphasized. Topics include: exploratory data analysis, correlation and linear regression, design of experiments, basic probability, the normal distribution, randomization approach to inference, sampling distributions, estimation, hypothesis testing, and twoway tables. Students who have taken Mathematics 211 are encouraged to consider the more advanced Mathematics 240/Statistics 250 Probability/Statistical Inference sequence.
Prerequisites: Not open to students who have already received credit for Psychology 200/201, Sociology/Anthropology 239 or Statistics 250 6 credits; Formal or Statistical Reasoning, Quantitative Reasoning Encounter; offered Fall 2023, Winter 2024, Spring 2024 · Deepak Bastola, Andy Poppick, Claire Kelling, Katie St. Clair, Adam Loy 
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, supervised and unsupervised classification methods, and understanding and visualizing spatial data. We will use the statistics software R in this course.
Prerequisites: Statistics 120, Statistics 230 or Statistics 250 6 credits; Formal or Statistical Reasoning, Quantitative Reasoning Encounter; offered Fall 2023, Winter 2024, Spring 2024 · Claire Kelling, Deepak Bastola 
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 to analyze reallife data.
Prerequisites: Statistics 120, Statistics 250, Psychology 200, or AP Statistics Exam score of 4 or 5. 6 credits; Formal or Statistical Reasoning, Quantitative Reasoning Encounter; offered Fall 2023, Winter 2024, Spring 2024 · Claire Kelling, Adam Loy, 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.
Prerequisites: Mathematics 240 Probability 6 credits; Formal or Statistical Reasoning, Quantitative Reasoning Encounter; offered Winter 2024, Spring 2024 · Andy Poppick, Katie St. Clair 
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.
Prerequisites: Statistics 120, Statistics 230, or Statistics 250 6 credits; Formal or Statistical Reasoning, Quantitative Reasoning Encounter; offered Winter 2024 · Katie St. Clair 
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.
Prerequisites: Statistics 230 and instructor permission 2 credits; S/CR/NC; Formal or Statistical Reasoning, Quantitative Reasoning Encounter; offered Fall 2023, Winter 2024, Spring 2024 · Adam Loy 
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.
Prerequisites: Permission of department chair and homework in advance of the external statistical activity 1 credit; S/CR/NC; offered Fall 2023, Winter 2024, Spring 2024 · Rafe Jones 
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.
Prerequisites: Statistics 230 and Statistics 250 6 credits; Formal or Statistical Reasoning, Quantitative Reasoning Encounter; offered Spring 2024 · Claire Kelling 
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).
Prerequisites: Statistics 230 and 250. Exposure to matrix algebra may be helpful but is not required 6 credits; Formal or Statistical Reasoning, Quantitative Reasoning Encounter; offered Fall 2023 · 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, generalized additive models or models for spatial data.
Prerequisites: Statistics 230 and 250 or permission of the instructor 6 credits; Formal or Statistical Reasoning, Quantitative Reasoning Encounter; not offered 2023–2024 
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.
Prerequisites: Statistics 250 6 credits; Formal or Statistical Reasoning, Quantitative Reasoning Encounter; not offered 2023–2024 
STAT 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 facultyspecified area or application of statistics, and to design and implement the first stage of a project completed the following term.
Prerequisites: Senior standing and instructor permission. Students are required to take Statistics 230 and Statistics 250 before enrolling 6 credits; Does not fulfill a curricular exploration requirement; offered Winter 2024 · Andy Poppick 
STAT 400: Integrative Exercise
Either a supervised smallgroup research project or an individual, independent reading. Required of all senior majors.
Prerequisites: Senior Statistics major. Students are strongly encouraged to complete Statistics 230 and Statistics 250 before starting this course 3 credits; S/NC; offered Fall 2023, Winter 2024, Spring 2024 · Deanna Haunsperger, Claire Kelling, Adam Loy, Andy Poppick