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 100: How Chance Changes the World

    The modern world is dominated by chance; we walk through life speaking of hopes, fears, failures, and more in the language of statistics. In this course, we will explore fundamental concepts in probability with an emphasis on computational examples, from apartment hunting to computer-generated art. We’ll look at the human history of chance—especially over the 19th and 20th centuries—to think about how we got here. We’ll see that, in a life of finite spacetime but infinitely complex problems, sometimes embracing randomness can be just what we need. But what is chance, how do we understand it, and why?

    Prerequisites: Concurrent registration in IDSC 198 6 credits; Argument and Inquiry Seminar, Writing Requirement, Quantitative Reasoning Encounter; offered Fall 2022 · Claudio Gómez-Gonzáles
  • 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 2022, Winter 2023 · 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 2022, Winter 2023 · McCleary Philbin, Kate Meyer
  • 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 2022, Winter 2023, Spring 2023 · MurphyKate Montee, Sunrose Shrestha, Steve Scheirer, McCleary Philbin, Rafe Jones
  • 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 2023
  • 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 2023, Spring 2023 · Caroline Turnage-Butterbaugh, Rob Thompson, Steve Scheirer
  • 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 2022, Winter 2023 · Joseph Johnson, Rob Thompson, Deanna Haunsperger
  • 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 2022, Winter 2023, Spring 2023 · Caroline Turnage-Butterbaugh, Steve Scheirer, MurphyKate Montee, Kate Meyer
  • 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 2022, Winter 2023, Spring 2023 · Deanna Haunsperger, Caroline Turnage-Butterbaugh, Claudio Gómez-Gonzáles, Sunrose Shrestha
  • MATH 240: Probability

    (Formerly Mathematics 265) 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 2022, Winter 2023 · Katie St. Clair, Laura Chihara
  • MATH 241: Ordinary Differential Equations

    An introduction to ordinary differential equations, including techniques for finding solutions, conditions under which solutions exist, and some qualitative analysis. Prerequisites: Mathematics 232 or instructor permission 6 credits; Formal or Statistical Reasoning; offered Fall 2022, Winter 2023, Spring 2023 · Kate Meyer, 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; not offered 2022–2023
  • 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 232 or instructor permission 6 credits; Formal or Statistical Reasoning; offered Winter 2023 · Sunrose Shrestha
  • 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; offered Spring 2023
  • 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 2023 · Rob Thompson
  • MATH 282: Elementary Theory of Numbers

    A first course in number 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 Fall 2022 · Caroline Turnage-Butterbaugh
  • MATH 295: Mathematics and Democracy

    In a democratic society we are confronted with problems of implementing fairness. How can we build a representative government, measure society’s preferences, or fairly divide power? Many of these problems are amenable to mathematical analysis and, in many cases, there exist deep theories and rich historical narratives of attempts at solution. We will study three such problems all of current political and mathematical interest: apportionment of representation, voting, and gerrymandering. We will approach these problems by considering what abstract properties a “fair” solution should have then attempting to construct and analyze procedures that maximize our measures of fairness.

    Prerequisites: Mathematics 232 or Mathematics 236 6 credits; Does not fulfill a curricular exploration requirement; not offered 2022–2023
  • MATH 295: Mathematics of Climate

    An introduction to mathematical methods for studying planetary climate. The focus will be on low-dimensional models, whose simplicity allows insight into fundamental mechanisms of climate change. We will use tools from algebra, geometry, and calculus to study topics including energy balance, greenhouse gas forcing, and ice-albedo feedback. This course will count towards the Applied Math area of the math major.

    Prerequisites: Mathematics 120 or 211 6 credits; Formal or Statistical Reasoning; not offered 2022–2023
  • 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 2022, Winter 2023, Spring 2023 · Katie St. Clair
  • 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 Winter 2023 · Kate Meyer
  • 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 6 credits; Formal or Statistical Reasoning; offered Spring 2023 · Rafe Jones
  • 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; not offered 2022–2023
  • 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 6 credits; Formal or Statistical Reasoning; not offered 2022–2023
  • 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 2023 · 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 Fall 2022, Spring 2023 · Claudio Gómez-Gonzáles, MurphyKate Montee
  • 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; offered Fall 2022 · Rob Thompson
  • 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; not offered 2022–2023
  • MATH 352: Topics in Abstract Algebra

    An intensive study of one or more of the types of algebraic systems studied in Mathematics 342. Prerequisites: Mathematics 342 6 credits; Formal or Statistical Reasoning; offered Winter 2023 · Claudio Gómez-Gonzáles
  • 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; not offered 2022–2023
  • 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; not offered 2022–2023
  • MATH 395: Geometric Group Theory

    Geometric group theory is the study of (infinite) groups using geometric tools. The underlying principle of geometric group theory is that if a group G acts “nicely” on a space, then information about that space tells us information about the group. This class will introduce tools from topology, graph theory, and geometry and use them to study groups. Topics will include groups acting on trees and (more generally) hyperbolic groups. This course counts toward the Algebra area of the math major.

    Prerequisites: Mathematics 342 or instructor consent 6 credits; Formal or Statistical Reasoning; offered Fall 2022 · MurphyKate Montee
  • 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 (formerly MATH 312) or Mathematics 342 6 credits; Formal or Statistical Reasoning; offered Spring 2023 · Caroline Turnage-Butterbaugh
  • MATH 400: Integrative Exercise

    Either a supervised small-group 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 2022, Winter 2023, Spring 2023 · Deanna Haunsperger, Rob Thompson, Caroline Turnage-Butterbaugh, Claudio Gómez-Gonzáles, Joseph Johnson, Sunrose Shrestha

Math | Stats

Statistics

  • STAT 120: Introduction to Statistics

    (Formerly MATH 215) 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 240/Statistics 250 (formerly Mathematics 265 and 275) Probability/Statistical Inference sequence.

    Prerequisites: Not open to students who have already received credit for Psychology 200/201, Sociology/Anthropology 239 or Statistics 250 (formerly Mathematics 275). 6 credits; Formal or Statistical Reasoning, Quantitative Reasoning Encounter; offered Fall 2022, Winter 2023, Spring 2023 · Andy Poppick, Claire Kelling, Deepak Bastola, Katie St. Clair, Adam Loy
  • STAT 220: Introduction to Data Science

    (Formerly Mathematics 285) 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 (formerly Mathematics 215), Statistics 230 (formerly Mathematics 245) or Statistics 250 (formerly Mathematics 275) 6 credits; Formal or Statistical Reasoning, Quantitative Reasoning Encounter; offered Fall 2022, Winter 2023, Spring 2023 · Deepak Bastola, Adam Loy
  • STAT 230: Applied Regression Analysis

    (Formerly Mathematics 245) 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 (formerly Mathematics 215), Statistics 250 (formerly Mathematics 275), Psychology 200, or AP Statistics Exam score of 4 or 5. 6 credits; Formal or Statistical Reasoning, Quantitative Reasoning Encounter; offered Fall 2022, Winter 2023, Spring 2023 · Adam Loy, Claire Kelling, Laura Chihara
  • STAT 250: Introduction to Statistical Inference

    (Formerly Mathematics 275) 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 (formerly Mathematics 265) 6 credits; Formal or Statistical Reasoning, Quantitative Reasoning Encounter; offered Winter 2023, Spring 2023 · Katie St. Clair, Andy Poppick
  • STAT 260: Introduction to Sampling Techniques

    (Formerly MATH 255) 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 (formerly Mathematics 215), Statistics 230 (formerly Mathematics 245), or Statistics 250 (formerly Mathematics 275) 6 credits; Formal or Statistical Reasoning, Quantitative Reasoning Encounter; not offered 2022–2023
  • STAT 285: Statistical Consulting

    (Formerly MATH 280) 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 (formerly Mathematics 245) and instructor permission 2 credits; S/CR/NC; Formal or Statistical Reasoning, Quantitative Reasoning Encounter; offered Fall 2022, Winter 2023, Spring 2023 · Andy Poppick
  • 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 2022, Winter 2023 · Katie St. Clair
  • 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 (formerly MATH 245) and Statistics 250 (formerly MATH 275) 6 credits; Formal or Statistical Reasoning, Quantitative Reasoning Encounter; offered Spring 2023 · Claire Kelling
  • STAT 320: Time Series Analysis

    (Formerly MATH 315) 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 (formerly Mathematics 245 and 275). Exposure to matrix algebra may be helpful but is not required 6 credits; Formal or Statistical Reasoning, Quantitative Reasoning Encounter; not offered 2022–2023
  • 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 (formerly Mathematics 245 and 275) or permission of the instructor 6 credits; Formal or Statistical Reasoning, Quantitative Reasoning Encounter; offered Winter 2023 · Laura Chihara
  • 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 (formerly Mathematics 275) 6 credits; Formal or Statistical Reasoning, Quantitative Reasoning Encounter; offered Fall 2022 · Adam Loy
  • STAT 400: Integrative Exercise

    Either a supervised small-group research project or an individual, independent reading. Required of all senior majors.

    Prerequisites: Senior Statistics major. Students are strongly encouraged to complete Statistics 230 (formerly Mathematics 245) and Statistics 250 (formerly Mathematics 275) before starting this course 3 credits; S/NC; offered Fall 2022, Winter 2023, Spring 2023 · Deepak Bastola, Katie St. Clair, Claire Kelling, Adam Loy