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. For mathematics or statistics majors, the course is Math 297. Please read the full description of the course: Math 297 Assessment and Communication of External Mathematical Activity.
For information about placement into Calculus or Statistics, please visit the Math/Stats Placement page.
Math  Stats
Mathematics
 2020–2021 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 2020 · 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 2020, Winter 2021 · Kate Meyer, Caroline TurnageButterbaugh 
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, score of 5, 6, or 7 on Math IB 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 ex 6 credits; Formal or Statistical Reasoning; offered Fall 2020, Winter 2021, Spring 2021 · Steve Scheirer, MurphyKate Montee, Rafe Jones, Owen Biesel 
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 2021 · Kate Meyer 
MATH 207: Communicating Mathematics
An introduction to communicating mathematics to a general audience in both writing and speaking. Students will gain practice in presenting their ideas and receive feedback. Students will use LaTeX and Beamer.
Prerequisites: Mathematics 236 or 240 (formerly Mathematics 265) or instructor permission 2 credits; Does not fulfill a curricular exploration requirement; not offered 2020–2021 
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 Fall 2020, Winter 2021, Spring 2021 · Alex Barrios, Alexander Garver, Rob Thompson, Caroline TurnageButterbaugh 
MATH 211: Introduction to Multivariable Calculus
Vectors, curves, partial derivatives, gradient, multiple and iterated integrals, line integrals, Green’s theorem. Prerequisites: Mathematics 121, 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 2020, Winter 2021, Spring 2021 · Alexander Garver, Eric Egge, Owen Biesel 
MATH 232: Linear Algebra
Vector spaces, linear transformations, determinants, inner products and orthogonality, eigenvectors and eigenvalues. Prerequisites: Mathematics 120 or Mathematics 211 6 credits; Formal or Statistical Reasoning; offered Fall 2020, Winter 2021, Spring 2021 · Rafe Jones, Caroline TurnageButterbaugh, Alexander Garver 
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 2020, Winter 2021, Spring 2021 · Deanna Haunsperger, MurphyKate Montee, Alex Barrios 
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 2020, Winter 2021 · Adam Loy, Josh Davis, Alexander Garver 
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 Winter 2021, Spring 2021 · Rob Thompson, Kate Meyer 
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 2020–2021 
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 2021 · Mark Krusemeyer 
MATH 295: Combinatorial Games
An introduction to the theory and practice of combinatorial games, which are twoplayer games in which players take turns, both players have complete information about the state of the game at all times, and there is no chance involved. Topics may include impartial games, a complete solution to nim, nim’s relationship with other impartial games, the correspondence between games and numbers, sums of games, birthdays of games, hot games, and thermographs of games. Specific games will be studied as examples of the general theory, possibly including hackenbush, domineering, amazons, chomp, the octal games, and variations of these games.
Prerequisites: Mathematics 236 or instructor permission 6 credits; Formal or Statistical Reasoning; offered Winter 2021 · Eric Egge 
MATH 295: Numerical Analysis
Methods of numerical appoximation and applications to scientific computing and data analysis. Topics will be selected primarily frm numerical linear algebra and optimization. Theory, implementation and application of numerical algorithms will be emphasized.
Prerequisites: Mathematics 232 6 credits; Formal or Statistical Reasoning; offered Fall 2020 · Rob Thompson 
MATH 295: Seminar in Set Theory
Introduction to settheoretic foundations of mathematics. The axiom system of ZermeloFraenkel, cardinal and ordinal numbers, and the Axiom of Choice. As time permits, additional topics may include construction of the real number, transfinite induction, or consistency/independence proofs.
Prerequisites: Mathematics 236 or instructor permission 6 credits; Formal or Statistical Reasoning; not offered 2020–2021 
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 2020, Winter 2021, Spring 2021 · Katie St. Clair 
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, padic numbers.
Prerequisites: Mathematics 236 or instructor permission 6 credits; Formal or Statistical Reasoning; offered Winter 2021 · Alex Barrios 
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 2020, Winter 2021 · Caroline TurnageButterbaugh, 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 2021 · Rafe Jones 
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; not offered 2020–2021 
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; offered Spring 2021 · Eric Egge 
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 2021 · Rob Thompson 
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 2020, Spring 2021 · Eric Egge, 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 2020 · Josh Davis 
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; not offered 2020–2021 
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 2021 · Mark Krusemeyer 
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; not offered 2020–2021 
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 2020–2021 
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 312 or instructor permission 6 credits; Does not fulfill a curricular exploration requirement; offered Spring 2021 · Caroline TurnageButterbaugh 
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 2020, Winter 2021, Spring 2021 · Andy Poppick, Caroline TurnageButterbaugh, Rafe Jones, Rob Thompson, Alex Barrios, Steve Scheirer, Alexander Garver, Kate Meyer, Mark Krusemeyer, MurphyKate Montee
Math  Stats
Statistics
 2020–2021 Courses:
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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 twoway 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 2020, Winter 2021, Spring 2021 · Andy Poppick, Samuel Ihlenfeldt, Owen Biesel, Steve Scheirer 
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, 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: Statistics 120 (formerly Mathematics 215) or Statistics 250 (formerly Mathematics 275) 6 credits; Formal or Statistical Reasoning, Quantitative Reasoning Encounter; offered Winter 2021, Spring 2021 · Katie St. Clair 
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 reallife data.
Prerequisites: Statistics 120 (formerly Mathematics 215) or 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 2020, Winter 2021, Spring 2021 · 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 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 (formerly Mathematics 265) 6 credits; Formal or Statistical Reasoning, Quantitative Reasoning Encounter; offered Winter 2021, Spring 2021 · Andy Poppick, Laura Chihara 
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 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 (formerly Mathematics 215) or Statistics 250 (formerly Mathematics 275) 6 credits; Formal or Statistical Reasoning, Quantitative Reasoning Encounter; offered Fall 2020 · Katie St. Clair 
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 2020, Winter 2021, Spring 2021 · Katie St. Clair 
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 2020, Winter 2021, Spring 2021 · Katie St. Clair 
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; offered Spring 2021 · Andy Poppick 
STAT 330: Advanced Statistical Modeling
(Formerly MATH 345) 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 (formerly Mathematics 245 and 275) or permission of the instructor 6 credits; Formal or Statistical Reasoning, Quantitative Reasoning Encounter; offered Winter 2021 · 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 MetropolisHastings algorithm and Gibbs sampler) and model adequacy and posterior predictive checks. The course uses R extensively for simulations.
Prerequisites: Statistics 250 (formerly Mathematics 275) not offered 2020–2021 
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 (formerly Mathematics 245) and Statistics 250 (formerly Mathematics 275) before starting this course 3 credits; S/NC; offered Fall 2020, Winter 2021, Spring 2021 · Andy Poppick, Katie St. Clair, Rob Thompson