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Your search for courses · during 2025-26 · tagged with MATH Electives · returned 19 results
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CS 252 Algorithms 6 credits
A course on techniques used in the design and analysis of efficient algorithms. We will cover several major algorithmic design paradigms (greedy algorithms, dynamic programming, divide and conquer, and network flow). Along the way, we will explore the application of these techniques to a variety of domains (natural language processing, economics, computational biology, and data mining, for example). As time permits, we will include supplementary topics like randomized algorithms, advanced data structures, and amortized analysis.
- Fall 2026, Winter 2027, Spring 2027
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): CS 200 or CS 201 with a grade of C- or better or received a Carleton Computer Science 200 Requisite Equivalency AND CS 202 or MATH 236 with a grade of C- or better or received a Carleton Computer Science 202 Requisite Equivalency or received a Carleton Math 236 Requisite Equivalency. MATH 236 will be accepted in lieu of CS 202.
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CS 252.01 Fall 2026
- Faculty: Sneha Narayan 🏫 👤
- Size:28
- M, WWillis 204 12:30pm-1:40pm
- FWillis 204 1:10pm-2:10pm
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19 Seats held for CS Match until the day after rising sophomore priority registration.
Anticipated prefect-supported section.
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CS 252.01 Winter 2027
- Faculty: Eric Alexander 🏫 👤
- Size:28
- M, WHulings 316 9:50am-11:00am
- FHulings 316 9:40am-10:40am
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x Seats held for CS Match until the day after X priority registration.
Anticipated prefect-supported section.
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CS 252.01 Spring 2027
- Faculty: Sneha Narayan 🏫 👤
- Size:28
- M, WAnderson Hall 329 1:50pm-3:00pm
- FAnderson Hall 329 2:20pm-3:20pm
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x Seats held for CS Match until the day after X priority registration.
Anticipated prefect-supported section.
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CS 252.02 Spring 2027
- Faculty: Chelsey Edge 🏫 👤
- Size:28
- M, WLanguage & Dining Center 104 9:50am-11:00am
- FLanguage & Dining Center 104 9:40am-10:40am
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x Seats held for CS Match until the day after X priority registration.
Anticipated prefect-supported section.
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CS 254 Computability and Complexity 6 credits
An introduction to the theory of computation. What problems can and cannot be solved efficiently by computers? What problems cannot be solved by computers, period? Topics include formal models of computation, including finite-state automata, pushdown automata, and Turing machines; formal languages, including regular expressions and context-free grammars; computability and uncomputability; and computational complexity, particularly NP-completeness.
- Fall 2026, Winter 2027, Spring 2027
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): CS 200 or CS 201 with a grade of C- or better or received a Carleton Computer Science 200 Requisite Equivalency AND CS 202 or MATH 236 with a grade of C- or better or received a Carleton Computer Science 202 Requisite Equivalency or received a Carleton Math 236 Requisite Equivalency. MATH 236 will be accepted in lieu of CS 202.
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CS 254.01 Fall 2026
- Faculty: Chelsey Edge 🏫 👤
- Size:28
- M, WAnderson Hall 036 8:30am-9:40am
- FAnderson Hall 036 8:30am-9:30am
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7 Seats held for CS Match until the day after rising junior priority registration.
Anticipated prefect-supported section.
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CS 254.01 Winter 2027
- Faculty: Josh Davis 🏫 👤
- Size:28
- M, WWillis 204 1:50pm-3:00pm
- FWillis 204 2:20pm-3:20pm
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x Seats held for CS Match until the day after X priority registration.
Anticipated prefect-supported section.
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CS 254.01 Spring 2027
- Faculty: Layla Oesper 🏫 👤
- Size:28
- M, WHulings 316 12:30pm-1:40pm
- FHulings 316 1:10pm-2:10pm
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x Seats held for CS Match until the day after X priority registration.
Anticipated prefect-supported section.
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MATH 240 Probability 6 credits
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 2026, Winter 2027
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): MATH 120 or MATH 211 or greater with a grade of C- or better or received a Carleton MATH 211 or better Requisite Equivalency or equivalent.
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MATH 241 Ordinary Differential Equations 6 credits
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.
- Fall 2026, Winter 2027, Spring 2027
- FSR, Formal or Statistical Reasoning
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Student must have completed any of the following course(s): MATH 134 or MATH 232 AND MATH 120 or MATH 211 with a grade of C- or better or equivalents.
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MATH 251 Chaotic Dynamics 6 credits
Dynamics is the branch of mathematics that deals with the study of change. In this course we will focus on simple discrete non-linear dynamical systems that produce astoundingly rich and unpredictable behavior — something that is colloquially referred to as "chaos". Topics will include one dimensional dynamics (including fixed points and their classifications), Sharkovsky's Theorem, a careful formulation/definition of "chaos", symbolic dynamics, complex dynamics (including Julia and Mandelbrot sets), iterated function systems, fractals and more.
- Winter 2027
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): MATH 236 with a grade of C- or better or received a Carleton Mathematics 236 Requisite Equivalency.
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MATH 271 Optimization 6 credits
Optimization is all about selecting the "best" thing. Finding the most likely strategy to win a game, the route that gets you there the fastest, or the curve that most closely fits given data are all examples of optimization problems. In this course we study linear optimization (also known as linear programming), the simplex method, and duality from both a theoretical and a computational perspective. Applications will be selected from statistics, economics, computer science, and more. Additional topics in nonlinear and convex optimization will be covered as time permits.
- Spring 2027
- FSR, Formal or Statistical Reasoning
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Student must have completed any of the following course(s): MATH 134 or MATH 232 AND MATH 120 or MATH 211 with a grade of C- or better or equivalents.
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MATH 295 Error-Correcting Codes 6 credits
This course explores the mathematics behind error-correcting codes – the science of transmitting information reliably over noisy channels. How can a message be recovered after it has been corrupted in transit? How much redundancy must be introduced to guarantee accurate transmission? A "code" here refers to a carefully designed set of codewords, strings of symbols built to withstand errors. Codes of this kind are everywhere: they underpin QR codes, ISBN numbers, and solid-state drives. We begin with the fundamental ideas of error detection and correction before developing the theory of linear codes, the central objects of study, with examples including Hamming, Golay, and Reed-Muller codes. The course is proof-based, and all necessary background in finite fields and linear algebra is developed within the course.
Repeatable: Course is repeatable provided the topics are different.
- Winter 2027
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): MATH 236 with a grade of C- or better or received a Carleton Mathematics 236 Requisite Equivalency.
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MATH 321 Real Analysis I 6 credits
A systematic study of single-variable functions on the real numbers. This course develops the mathematical concepts and tools needed to understand why calculus really works: the topology of the real numbers, limits, differentiation, integration, convergence of sequences, and series of functions.
- Winter 2027
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): MATH 236 AND MATH 210 or MATH 211 with a grade of C- or better or equivalents.
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MATH 331 Functional Analysis 6 credits
Further topics in analysis such as measure theory, Lebesgue integration or Banach and Hilbert spaces.
Repeatable: Course is repeatable provided the topics are different.
- Spring 2027
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): MATH 321 with a grade of C- or better.
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MATH 334 Computational Linear Algebra 6 credits
Computational linear algebra is full of ideas that are useful when interpreting linear algebra objects as data. This course develops these ideas with a balance of theory, applications, and algorithms. Topics will be selected from singular value decomposition, LU and QR factorization, orthogonal computation, conditioning, numerical stability, eigenvalue approximation and iterative methods. Applications include interpolation, least squares, low rank approximation, principal component analysis, regularization, data classification, image processing, and selected topics from machine learning.
Not open to students who have taken MATH 332 – Advanced Linear Algebra Fall 2023 or Fall 2025.
- Fall 2026
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): MATH 236 with a grade of C- or better or received a Carleton Mathematics 236 Requisite Equivalency. NOT open to students who have taken MATH 332 – Advanced Linear Algebra Fall 2023 or Fall 2025.
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MATH 341 Partial Differential Equations 6 credits
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 2027
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): MATH 241 with grade of C- or better.
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MATH 342 Introduction to Groups, Rings, and Fields 6 credits
Groups, rings, and fields are basic algebraic structures that appear throughout mathematics. Topics in group theory include subgroups, cosets, homomorphism theorems, and quotient groups. Topics in ring and field theory include ideals, homomorphism theorems, quotient rings, integral domains, and finite fields.
- Fall 2026, Spring 2027
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): MATH 236 with a grade of C- or better or received a Carleton Mathematics 236 Requisite Equivalency.
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MATH 344 Differential Geometry 6 credits
Differential geometry is the study of shapes (like curves and surfaces) using tools from linear algebra and calculus. In this course we focus on the differential geometry of curves and surfaces and the concepts of curvature, geodesics, and first and second fundamental forms. These concepts will lead us to remarkable results like the Theorem Egregium and the Gauss-Bonnet Theorem, which relate the ways that curvature and shape interact.
- Fall 2026
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): MATH 236 with a grade of C- or better or received a Carleton Mathematics 236 Requisite Equivalency.
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MATH 352 Galois Theory 6 credits
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.
This course can be repeated only by students who took MATH 352 22-23
- Spring 2027
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): MATH 342 with grade of C- or better.
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MATH 354 Topology 6 credits
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.
- Winter 2027
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): MATH 236 with a grade of C- or better or received a Carleton Mathematics 236 Requisite Equivalency.
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MATH 372 Topics in Group Theory 6 credits
This course will build on the introduction to groups established in Math 342. Specific topics will vary by instructor, but may include the Sylow theorems and applications, finite simple groups, permutation groups, classification of groups of small order, finite abelian groups, solvable and nilpotent groups, the Jordan-Holder theorem, group actions on geometric spaces, group presentations, automorphism groups, and semi-direct products.
- Winter 2027
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): MATH 342 with grade of C- or better.
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MATH 395 Introduction to Ergodic Theory 6 credits
This course is an introduction to measures and ergodic theory. Measure theory provides a rigorous way to generalize the notion of length and area, extending such familiar ideas to more general/abstract settings (ex: probability spaces). The course will cover the construction of Lebesgue measure. Ergodic theory studies the probabilistic behavior of measure-preserving dynamical systems as they evolve through time. The course will cover basic dynamic notions like ergodicity and recurrence. Emphasis will be on specific examples like circle rotations, the doubling map, the dyadic odometer, and symbolic dynamics. Additional topics can include the ergodic theorem, its applications and mixing.
Repeatable: Course is repeatable provided the topics are different.
- Spring 2027
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): MATH 321 with a grade of C- or better.
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STAT 250 Introduction to Statistical Inference 6 credits
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.
- Winter 2027, Spring 2027
- FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning
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Student has completed any of the following course(s): MATH 240 with a grade of C- or better.
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STAT 340 Bayesian Statistics 6 credits
The Bayesian approach to statistics provides a powerful framework for incorporating prior knowledge into statistical analyses, updating this knowledge with data, and quantifying uncertainty in results. This course serves as a comprehensive introduction to Bayesian statistical inference and modeling, an alternative to the frequentist approach to statistics covered in previous classes. Topics include: Bayes’ Theorem; prior and posterior distributions; Bayesian regression; hierarchical models; and model adequacy and posterior predictive checks. Computational techniques will also be covered, including Markov Chain Monte Carlo methods, and modern Bayesian modeling packages in R.
- Winter 2027
- FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning
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Student has completed the following course(s): STAT 230 and STAT 250 with a grade of C- or better.