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 off-campus 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 off-campus internship.

For information about placement into Calculus or Statistics, please visit the Math/Stats Placement page.

Math | Stats

## Mathematics

• ### 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.

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, Fall 2023, 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, Fall 2023, Fall 2023, Fall 2023, Winter 2024, Winter 2024, Winter 2024, Spring 2024 · Claudio Gomez-Gonzales, 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 · Claudio Gomez-Gonzales
• ### 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, Winter 2024, Spring 2024 · Corey Brooke, Caroline Turnage-Butterbaugh
• ### 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, Fall 2023, Fall 2023, Winter 2024 · Rebecca Terry, Josh Davis, Mike Adams
• ### MATH 215: Introduction to Statistics

Introduction to statistics and data analysis. Practical aspects of statistics, including extensive use of statistical software, 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 two-way tables. Students who have taken Mathematics 211 are encouraged to consider the more advanced Mathematics 265-275 Probability-Statistics sequence.

Prerequisites: Not open to students who have already received credit for Psychology 200/201, Sociology/Anthropology 239 or Math 275. not offered 2023–2024
• ### 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, Fall 2023, Winter 2024, Winter 2024, Spring 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, Spring 2024 · Caroline Turnage-Butterbaugh, Claudio Gomez-Gonzales, 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, 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; non-dimensionalization; 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 245: 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 real-life data.

Prerequisites: Statistics 120 or Statistics 250 (formerly Mathematics 215 or 275) not offered 2023–2024
• ### MATH 251: Chaotic Dynamics

An exploration of the behavior of non-linear dynamical systems. Topics include one and two-dimensional dynamics, Sarkovskii’s Theorem, chaos, symbolic dynamics,and the Hénon Map.

Prerequisites: Mathematics 236 or instructor permission 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 not offered 2023–2024
• ### MATH 265: 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 211 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 275: 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.

Prerequisites: Mathematics 265 not offered 2023–2024
• ### MATH 280: 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: Mathematics 245 and instructor permission not offered 2023–2024
• ### 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 285: 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, clean up and manipulation, data visualization using packages such as ggplots, understanding and visualizing spatial and network data, and supervised and unsupervised classification methods. We will use the statistics software R in this course.

Prerequisites: Mathematics 215 or Mathematics 275 not offered 2023–2024
• ### 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 Gomez-Gonzales
• ### MATH 312: Elementary Theory of Numbers

Properties of the integers. Topics include the Euclidean algorithm, classical unsolved problems in number theory, prime factorization, Diophantine equations, congruences, divisibility, Euler’s phi function and other multiplicative functions, primitive roots, and quadratic reciprocity. Other topics may include integers as sums of squares, continued fractions, distribution of primes, integers in extension fields, p-adic numbers.

Prerequisites: Mathematics 236 or instructor permission not offered 2023–2024
• ### MATH 315: Topics Probability/Statistics: 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.

Prerequisites: Mathematics 275 not offered 2023–2024
• ### 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: math.236 or math.236p 6 credits; Formal or Statistical Reasoning; offered Fall 2023, Spring 2024 · Caroline Turnage-Butterbaugh, Sunrose Shrestha
• ### MATH 331: Real Analysis II

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

Prerequisites: Mathematics 321 or instructor permission not offered 2023–2024
• ### 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. 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 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.

Prerequisites: Mathematics 236 or instructor permission 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 Gomez-Gonzales
• ### 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. not offered 2023–2024
• ### MATH 345: 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, generalized additive models or models for spatial data.

Prerequisites: Mathematics 245 and Mathematics 275 or permission of instructor. Familiarity with matrix algebra helpful but not required not offered 2023–2024
• ### 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. 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 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.

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 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.

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 Turnage-Butterbaugh
• ### MATH 395: Algebraic Geometry Seminar

An exploration of topics in algebraic geometry and related commutative algebra. Participants will each give at least one substantive presentation at the blackboard. Topics will definitely include the Hilbert basis theorem and the Nullstellensatz, but beyond that substantial variation is possible, depending on the interests and mathematical backgrounds of the participants.

Prerequisites: Mathematics 342 or instructor consent 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 faculty-specified 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 | Stats

## Statistics

• ### 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 two-way 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, Fall 2023, Fall 2023, Winter 2024, Winter 2024, Winter 2024, Spring 2024, Spring 2024, Spring 2024, Spring 2024 · Deepak Bastola, Claire Kelling, Katie St. Clair, Adam Loy, Andy Poppick
• ### 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 · Deepak Bastola, Claire Kelling
• ### 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 real-life 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 · Adam Loy, Andy Poppick, Claire Kelling
• ### 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.

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 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.

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 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.

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

(Formerly MATH 315) 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, generalized additive models or models for spatial data.

Prerequisites: Statistics 230 and 250 or permission of the instructor not offered 2023–2024
• ### STAT 340: Bayesian Statistics

Formerly MATH 315) 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.

Prerequisites: Statistics 250 not offered 2023–2024