Carleton’s Mathematics and Statistics department offers two majors and a minor. The mathematics curriculum provides essential skills for students across many disciplines, and instills majors with a deep understanding of the history and current practice of mathematics. Statistics focuses on organizing and analyzing data. Students gain experience with statistical software and learn to apply numbers to realworld problems.
About Mathematics and Statistics
Mathematics is an art, a pure science, a language, and an analytical tool for the natural and social sciences, a means of exploring philosophical questions, and a beautiful edifice that is a tribute to human creativity. The mathematics curriculum is designed to provide essential skills for students in a variety of disciplines and to provide mathematics majors with a deep understanding of mathematics as it has evolved over the past two thousand years and how it is practiced today.
Statistics is the science of giving meaning to data in the context of uncertainty. Statisticians are involved in data collection and study design, data analysis, and the communication of information to a broad audience. The statistics curriculum is designed to balance both statistical theory and application, and will provide students the opportunity to work on real world data problems and enhance their communication skills.
Students who wish to major in both Mathematics and Statistics should note the College policy that double majors may count no more than four courses toward both majors. Courses for which a student earns AP Credit, such as calculus, are included among these four courses.
Math Skills Center
The Math Skills Center supports all Carleton students in any mathematics or mathrelated course they are taking. The center’s tutors help students with mathematical concepts and with the mathematical tools needed to succeed in their courses.
Requirements for the Mathematics Major
The Mathematics major requires 72 credits:
 A. Required Core Courses (take either Mathematics 101 or 111 and either Mathematics 210 or 211 and all of remaining courses listed):
 MATH 101: Calculus with Problem Solving
 MATH 111: Introduction to Calculus
 MATH 120: Calculus 2
 MATH 210: Calculus 3
 MATH 211: Introduction to Multivariable Calculus
 MATH 232: Linear Algebra
 MATH 236: Mathematical Structures
 B. Electives (36 credits): Six courses from among:
 CS 252: Algorithms
 CS 254: Computability and Complexity
 CS 352: Advanced Algorithms · not offered in 202324
 MATH 240: Probability
 MATH 241: Ordinary Differential Equations
 MATH 244: Geometries
 MATH 251: Chaotic Dynamics · not offered in 202324
 MATH 261: Functions of a Complex Variable · not offered in 202324
 MATH 265: Probability · not offered in 202324
 MATH 271: Computational Mathematics
 MATH 275: Introduction to Statistical Inference · not offered in 202324
 MATH 282: Elementary Theory of Numbers
 MATH 295: Introduction to Computational Algebraic Geometry
 MATH 312: Elementary Theory of Numbers · not offered in 202324
 MATH 315: Topics Probability/Statistics: Bayesian Statistics · not offered in 202324
 MATH 321: Real Analysis I
 MATH 331: Real Analysis II · not offered in 202324
 MATH 332: Advanced Linear Algebra
 MATH 333: Combinatorial Theory · not offered in 202324
 MATH 341: Partial Differential Equations
 MATH 342: Abstract Algebra I
 MATH 344: Differential Geometry · not offered in 202324
 MATH 349: Methods of Teaching Mathematics
 MATH 352: Galois Theory
 MATH 354: Topology
 MATH 361: Complex Analysis
 MATH 395: Algebraic Geometry Seminar · not offered in 202324
 STAT 250: Introduction to Statistical Inference
 STAT 320: Time Series Analysis
 STAT 340: Bayesian Statistics · not offered in 202324
At least four of these electives must be Carleton courses with a MATH designation. At least three of the following five areas of mathematics must be represented by the six electives (36 credits).
 Algebra:
 MATH 282: Elementary Theory of Numbers
 MATH 312: Elementary Theory of Numbers · not offered in 202324
 MATH 332: Advanced Linear Algebra
 MATH 342: Abstract Algebra I
 MATH 352: Galois Theory
 MATH 395: Geometric Group Theory · not offered in 202324
 Analysis:
 MATH 251: Chaotic Dynamics · not offered in 202324
 MATH 261: Functions of a Complex Variable · not offered in 202324
 MATH 321: Real Analysis I
 MATH 331: Real Analysis II · not offered in 202324
 MATH 361: Complex Analysis
 MATH 395: Introduction to Analytic Number Theory · not offered in 202324
 Applied Mathematics:
 MATH 240: Probability
 MATH 241: Ordinary Differential Equations
 MATH 265: Probability · not offered in 202324
 MATH 271: Computational Mathematics
 MATH 275: Introduction to Statistical Inference · not offered in 202324
 MATH 295: Mathematics of Climate · not offered in 202324
 MATH 315: Topics Probability/Statistics: Bayesian Statistics · not offered in 202324
 MATH 341: Partial Differential Equations
 STAT 250: Introduction to Statistical Inference
 STAT 320: Time Series Analysis
 STAT 340: Bayesian Statistics · not offered in 202324
 Discrete Structures:
 CS 252: Algorithms
 CS 254: Computability and Complexity
 CS 352: Advanced Algorithms · not offered in 202324
 MATH 333: Combinatorial Theory · not offered in 202324
 Geometry and Topology:
 MATH 244: Geometries
 MATH 295: Introduction to Computational Algebraic Geometry
 MATH 344: Differential Geometry · not offered in 202324
 MATH 354: Topology
Of the six advanced courses, at least four must be Carleton courses with a Mathematics designation. Advanced courses substituted for Mathematics 232 or Mathematics 236 must also be Carleton courses with a Mathematics designation.
In addition, each senior major must complete an integrative exercise, Mathematics 400 (6 credits) which can be either a group or individual project. Majors must also accumulate eight talk credits during their junior and senior year by attending colloquia and the comps talks of their fellow mathematics or statistics majors. Students who major in both Mathematics and Statistics must accumulate a total of thirteen talk credits. We encourage majors to participate in the numerous activities that take place in the department.
Potential majors with especially strong preparation may petition the department for permission to substitute an advanced course for Mathematics 232 and/or for Mathematics 236. Advanced courses substituted for Mathematics 232 or Mathematics 236 must also be Carleton courses with a Mathematics designation.
There are many patterns of courses for the major depending upon a student’s mathematical interests and career goals. A guide for majors, which supplies information about suitable patterns of courses, is available on the Mathematics and Statistics Department website.
Major under Combined Plan in Engineering:
In addition to completing requirements for the mathematics major listed above including Mathematics 241 and 341, the student should take the following courses required for admission to engineering schools: Two terms of 100level Physics, Chemistry 123, 224, and Computer Science 111.
Requirements for the Statistics Major
The requirements for the Statistics Major are 74 credits:
 A. Supporting Courses (30 credits) Take either Mathematics 101 or 111 and either Mathematics 210 or 211 and all of remaining courses listed:
 CS 111: Introduction to Computer Science
 MATH 101: Calculus with Problem Solving
 MATH 111: Introduction to Calculus
 MATH 120: Calculus 2
 MATH 210: Calculus 3
 MATH 211: Introduction to Multivariable Calculus
 MATH 232: Linear Algebra
 B. Required Core (18 credits): All of the following, of which at least two must be taken at Carleton
 MATH 240: Probability
 MATH 245: Applied Regression Analysis · not offered in 202324
 MATH 265: Probability · not offered in 202324
 MATH 275: Introduction to Statistical Inference · not offered in 202324
 STAT 230: Applied Regression Analysis
 STAT 250: Introduction to Statistical Inference
 C. Electives (18 credits): Three electives, of which at least two must be Carleton courses with a Statistics designation
 CS 314: Data Visualization
 CS 320: Machine Learning
 CS 362: Computational Biology
 MATH 271: Computational Mathematics
 MATH 285: Introduction to Data Science · not offered in 202324
 MATH 295: Numerical Analysis · not offered in 202324
 MATH 315: Topics Probability/Statistics: Bayesian Statistics · not offered in 202324
 MATH 345: Advanced Statistical Modeling · not offered in 202324
 STAT 220: Introduction to Data Science
 STAT 260: Introduction to Sampling Techniques
 STAT 310: Spatial Statistics
 STAT 320: Time Series Analysis
 STAT 330: Advanced Statistical Modeling · not offered in 202324
 STAT 340: Bayesian Statistics · not offered in 202324
 D. Statistical Practice (2 credits):
 STAT 285 Statistical Consulting
In addition, each senior major must complete an integrative exercise. Statistics 400 (6 credits), which can be either a group or individual project. Majors must accumulate eight talk credits during their junior and senior year by attending department colloquia and the comps talks of their fellow mathematics or statistics majors. Students who major in both Mathematics and Statistics must accumulate a total of thirteen talk credits. We encourage majors to participate in the numerous activities that take place in the department.
We recommend statistics majors also take courses in a discipline in which statistics can be applied. Students interested in data science should consider taking additional computer science courses.
Students considering graduate school in statistics or biostatistics are strongly encouraged to take Mathematics 236 (Mathematical Structures) and Mathematics 321 (Real Analysis). Consult a statistics faculty member for more information specific to your choice of program.
Requirements for the Mathematics Minor
To earn a minor in Mathematics, a student must earn 42 credits from courses taken in the Department of Mathematics and Statistics at Carleton. (Students who place out of courses based on work done outside of Carleton are still required to earn 42 credits from courses taken in the Department of Mathematics and Statistics at Carleton.) At least 36 of the required 42 credits must come from courses with a Mathematics designation. In addition, the only Statistics courses which can be counted toward the Mathematics minor are Statistics 250, 320 and 340.
Students who wish to major in Statistics and minor in Mathematics should note the College policy that a student may not fulfill more than half the credits for a minor from the courses counted toward their major or majors.
Mathematics Courses

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.
 Fall 2023, Winter 2024
 6
 Formal or Statistical Reasoning
 Not open to students who have received credit for Mathematics 111.
 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.
 Fall 2023, Winter 2024, Spring 2024
 6
 Formal or Statistical Reasoning
 Requires placement via the Calculus Placement Exam 1, see Mathematics web page. Not open to students who have received credit for Mathematics 101.
 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.
 Fall 2023, Winter 2024, Spring 2024
 6
 Formal or Statistical Reasoning
 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
 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.
 Winter 2024
 S/CR/NC
 1
 Does not fulfill a curricular exploration requirement
 Claudio GómezGonzáles 🏫 👤

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.
 Winter 2024, Spring 2024
 6
 Formal or Statistical Reasoning
 Mathematics 120. This course cannot be substituted for Mathematics 211
 Corey Brooke 🏫 👤 · Caroline TurnageButterbaugh 🏫 👤

MATH 211 Introduction to Multivariable Calculus
Vectors, curves, partial derivatives, gradient, multiple and iterated integrals, line integrals, Green’s theorem.
 Fall 2023, Winter 2024
 6
 Formal or Statistical Reasoning
 Score of 4 or 5 on the AP Calculus BC exam, or placement via Calculus Placement Exam #3
 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 twoway tables. Students who have taken Mathematics 211 are encouraged to consider the more advanced Mathematics 265275 ProbabilityStatistics sequence.
Not offered in 202324
 6
 Formal or Statistical Reasoning Quantitative Reasoning Encounter
 Not open to students who have already received credit for Psychology 200/201, Sociology/Anthropology 239 or Math 275.

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.
 Fall 2023, Winter 2024, Spring 2024
 6
 Formal or Statistical Reasoning
 Mathematics 120 or Mathematics 211
 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.
 Fall 2023, Winter 2024, Spring 2024
 6
 Formal or Statistical Reasoning
 Mathematics 232 and either Mathematics 210 or Mathematics 211
 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.
 Fall 2023, Winter 2024
 6
 Formal or Statistical Reasoning
 Mathematics 120 or Mathematics 211
 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.
 Winter 2024, Spring 2024
 6
 Formal or Statistical Reasoning
 Mathematics 232 or instructor permission
 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.
 Fall 2023
 6
 Formal or Statistical Reasoning
 Mathematics 236
 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 reallife data.
Not offered in 202324
 6
 Formal or Statistical Reasoning Quantitative Reasoning Encounter
 Statistics 120 or Statistics 250 (formerly Mathematics 215 or 275)

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.
Not offered in 202324
 6
 Formal or Statistical Reasoning
 Mathematics 236 or instructor permission

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.
Not offered in 202324
 6
 Formal or Statistical Reasoning
 Mathematics 210 or Mathematics 211

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.
Not offered in 202324
 6
 Formal or Statistical Reasoning
 Mathematics 120 or 211

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.
 Winter 2024
 6
 Formal or Statistical Reasoning
 Mathematics 232
 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 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.
Not offered in 202324
 6
 Formal or Statistical Reasoning Quantitative Reasoning Encounter
 Mathematics 265

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.
Not offered in 202324
 S/CR/NC
 2
 Formal or Statistical Reasoning Quantitative Reasoning Encounter
 Mathematics 245 and instructor permission

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.
 Winter 2024
 6
 Formal or Statistical Reasoning
 Mathematics 236 or instructor permission
 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.
Not offered in 202324
 6
 Formal or Statistical Reasoning Quantitative Reasoning Encounter
 Mathematics 215 or Mathematics 275

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!
 Spring 2024
 6
 Formal or Statistical Reasoning
 Mathematics 236 or instructor permission
 Claudio GómezGonzáles 🏫 👤

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.
Not offered in 202324
 6
 Formal or Statistical Reasoning
 Mathematics 236 or instructor permission

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 MetropolisHastings algorithm and Gibbs sampler) and model adequacy and posterior predictive checks. The course uses R extensively for simulations.
Not offered in 202324
 6
 Formal or Statistical Reasoning Quantitative Reasoning Encounter
 Mathematics 275

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.
 Fall 2023, Spring 2024
 6
 Formal or Statistical Reasoning
 math.236 or math.236p
 Caroline TurnageButterbaugh 🏫 👤 · Sunrose Shrestha 🏫 👤

MATH 331 Real Analysis II
Further topics in analysis such as measure theory, Lebesgue integration or Banach and Hilbert spaces.
Not offered in 202324
 6
 Formal or Statistical Reasoning
 Mathematics 321 or instructor permission

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.
 Fall 2023
 6
 Formal or Statistical Reasoning
 Mathematics 236 or instructor permission
 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.
Not offered in 202324
 6
 Formal or Statistical Reasoning
 Mathematics 236 or instructor permission

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.
 Spring 2024
 6
 Formal or Statistical Reasoning
 Mathematics 241
 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.
 Winter 2024
 6
 Formal or Statistical Reasoning
 Mathematics 236 or instructor permission
 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.
Not offered in 202324
 6
 Formal or Statistical Reasoning
 Mathematics 236 or permission of the instructor.

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 zeroinflated Poisson models. Depending on time, additional topics could include survival analysis, generalized additive models or models for spatial data.
Not offered in 202324
 6
 Formal or Statistical Reasoning Quantitative Reasoning Encounter
 Mathematics 245 and Mathematics 275 or permission of instructor. Familiarity with matrix algebra helpful but not required

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.
 Fall 2023
 6
 Does not fulfill a curricular exploration requirement
 Junior or senior standing and instructor permission
 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.
 Spring 2024
 6
 Formal or Statistical Reasoning
 Mathematics 342
 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.
 Winter 2024
 6
 Formal or Statistical Reasoning
 Mathematics 236 or instructor permission
 Josh Davis 🏫 👤

MATH 361 Complex Analysis
The theoretical foundations for the calculus of functions of a complex variable.
 Winter 2024
 6
 Formal or Statistical Reasoning
 Mathematics 321 or instructor permission. Students who have already received credit for Mathematics 261 may only take this course with instructor permission
 Caroline TurnageButterbaugh 🏫 👤

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.
Not offered in 202324
 6
 Formal or Statistical Reasoning
 Mathematics 342 or instructor consent

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.
 Fall 2023
 S/CR/NC
 6
 Does not fulfill a curricular exploration requirement
 Open only to senior Math majors
 Rob Thompson 🏫 👤

MATH 400 Integrative Exercise
Either a supervised smallgroup research project or an individual, independent reading. Required of all senior majors.
 Fall 2023, Winter 2024, Spring 2024
 S/NC
 3
 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
 Deanna Haunsperger 🏫 👤 · Caroline TurnageButterbaugh 🏫 👤 · Staff Rob Thompson 🏫 👤 · Rafe Jones 🏫 👤 · Sunrose Shrestha 🏫 👤
Statistics Courses

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.
 Fall 2023, Winter 2024, Spring 2024
 6
 Formal or Statistical Reasoning Quantitative Reasoning Encounter
 Not open to students who have already received credit for Psychology 200/201, Sociology/Anthropology 239 or Statistics 250
 Staff 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.
 Fall 2023, Winter 2024, Spring 2024
 6
 Formal or Statistical Reasoning Quantitative Reasoning Encounter
 Statistics 120, Statistics 230 or Statistics 250
 Staff 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 reallife data.
 Fall 2023, Winter 2024, Spring 2024
 6
 Formal or Statistical Reasoning Quantitative Reasoning Encounter
 Statistics 120, Statistics 250, Psychology 200, or AP Statistics Exam score of 4 or 5.
 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 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.
 Winter 2024, Spring 2024
 6
 Formal or Statistical Reasoning Quantitative Reasoning Encounter
 Mathematics 240 Probability
 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.
 Winter 2024
 6
 Formal or Statistical Reasoning Quantitative Reasoning Encounter
 Statistics 120, Statistics 230, or Statistics 250
 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.
 Fall 2023, Winter 2024, Spring 2024
 S/CR/NC
 2
 Formal or Statistical Reasoning Quantitative Reasoning Encounter
 Statistics 230 and instructor permission
 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 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.
 Spring 2024
 6
 Formal or Statistical Reasoning Quantitative Reasoning Encounter
 Statistics 230 and Statistics 250
 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).
 Fall 2023
 6
 Formal or Statistical Reasoning Quantitative Reasoning Encounter
 Statistics 230 and 250. Exposure to matrix algebra may be helpful but is not required
 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 zeroinflated Poisson models. Depending on time, additional topics could include survival analysis, generalized additive models or models for spatial data.
Not offered in 202324
 6
 Formal or Statistical Reasoning Quantitative Reasoning Encounter
 Statistics 230 and 250 or permission of the instructor

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.
Not offered in 202324
 6
 Formal or Statistical Reasoning Quantitative Reasoning Encounter
 Statistics 250

STAT 400 Integrative Exercise
Either a supervised smallgroup research project or an individual, independent reading. Required of all senior majors.
 Fall 2023, Winter 2024, Spring 2024
 S/NC
 3
 Senior Statistics major. Students are strongly encouraged to complete Statistics 230 and Statistics 250 before starting this course
 Deanna Haunsperger 🏫 👤 · Staff Claire Kelling 🏫 👤 · Andy Poppick 🏫 👤