Search Results
Your search for courses · during 25FA, 26WI, 26SP · 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 2025, Winter 2026, Spring 2026
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): CS 200 with a grade of C- or better or CS 201 with a grade of C- or better or received a Carleton Computer Science 200 Requisite Equivalency AND CS 202 with a grade of C- or better or received a Carleton Computer Science 202 Requisite Equivalency or MATH 236 with a grade of C- or better 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 2025
- Faculty:Sneha Narayan 🏫 👤
- Size:28
- M, WAnderson Hall 329 1:50pm-3:00pm
- FAnderson Hall 329 2:20pm-3:20pm
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21 seats held for CS Match until the day after rising sophomore (only) priority registration.
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CS 252.01 Winter 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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24 seats held for CS Match until the day after Sophomore Only priority registration.
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CS 252.01 Spring 2026
- Faculty:Eric Alexander 🏫 👤
- Size:28
- M, WAnderson Hall 329 9:50am-11:00am
- FAnderson Hall 329 9:40am-10:40am
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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 2025, Winter 2026, Spring 2026
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): CS 200 with a grade of C- or better or CS 201 with a grade of C- or better or received a Carleton Computer Science 200 Requisite Equivalency AND CS 202 with a grade of C- or better or received a Carleton Computer Science 202 Requisite Equivalency or MATH 236 with a grade of C- or better 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 Winter 2026
- Faculty:Josh Davis 🏫 👤
- Size:28
- M, WHulings 316 1:50pm-3:00pm
- FHulings 316 2:20pm-3:20pm
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22 seats held for CS Match until the day after First Year priority registration.
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CS 254.01 Spring 2026
- Faculty:Chelsey Edge 🏫 👤
- Size:28
- M, WLanguage & Dining Center 104 12:30pm-1:40pm
- FLanguage & Dining Center 104 1:10pm-2:10pm
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CS 254.02 Spring 2026
- Faculty:Anna Rafferty 🏫 👤
- Size:28
- M, WLeighton 305 9:50am-11:00am
- FLeighton 305 9:40am-10:40am
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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 2025, Winter 2026
- 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 2025, Winter 2026, Spring 2026
- 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 244 Geometries 6 credits
Euclidean geometry from an advanced perspective; projective, hyperbolic, inversive, and/or other geometries. Recommended for prospective secondary school teachers.
- Winter 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.
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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 2026
- 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 282 Number Theory 6 credits
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 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 Math 236 Requisite Equivalency exam.
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MATH 295 Tessellation 6 credits
This course explores a particularly visual sort of mathematical pattern: a tessellation. A tessellation is a way of covering the plane with shapes (called “tiles”) that don’t overlap. This class will explore questions like: Is it possible to make a tessellation out of a given set of tiles? How many different tessellations can I create from this set of tiles? We’ll cover both classical results (it is impossible to tile the plane with heptagons!), and the 2023 construction of the “Einstein tile”: the first known polygon that tiles the plane but never periodically. Links will be made with graph theory, topology, and geometry.
Repeatable: This course is repeatable provided the topics are different.
Sophomore Priority
- Spring 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 Math 236 Requisite Equivalency exam.
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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.
- Fall 2025, Spring 2026
- 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 332 Advanced Linear Algebra 6 credits
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.
- Fall 2025
- 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.
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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 2026
- 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 Abstract Algebra I 6 credits
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 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 Math 236 Requisite Equivalency exam.
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MATH 349 Methods of Teaching Mathematics 6 credits
Methods of teaching mathematics in grades 7-12. Issues in contemporary mathematics education. Regular visits to school classrooms and teaching a class are required.
- Fall 2025
- No Exploration
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This course requires permission from the instructor.
To request permission, follow the instructions for requesting a prerequisite override.
Please note: the link will open in a new window. Once you have received permission from the instructor, you will be able to return to this page to register for the course.
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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 2026
- 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 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 Math 236 Requisite Equivalency exam.
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MATH 361 Complex Analysis 6 credits
The theoretical foundations for the calculus of functions of a complex variable.
- Winter 2026
- 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 362 Representation Theory of Finite Groups 6 credits
Representation theory is the study of mathematical structures via the tools of linear algebra. The first objects to be studied in this way were finite groups at the end of the nineteenth century, motivated by the powerful framework of characters in number theory, but the field has generalized incredibly due to the prevalence of symmetry throughout mathematics, physics, and beyond. In this course the focus is on finite groups. Topics include Maschke’s theorem, complete reducibility, and Schur’s lemma; characters, orthogonality relations, and character tables; Fourier transformations and random walks. Additional topics may include Burnside’s Lemma, Frobenius reciprocity, and an exploration of representations of infinite groups.
- Spring 2026
- 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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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 2026, Spring 2026
- 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.
- Fall 2025
- FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning
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Student has completed any of the following course(s): STAT 230 and STAT 250 with a grade of C- or better.