Search Results
Your search for courses · during 24FA, 25WI, 25SP · tagged with MATH Electives · returned 16 results
-
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 2024, Winter 2025, Spring 2025
- FSR, Formal or Statistical Reasoning
-
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.
-
CS 252.00 Fall 2024
- Faculty:Layla Oesper 🏫 👤
- Size:34
- M, WAnderson Hall 329 12:30pm-1:40pm
- FAnderson Hall 329 1:10pm-2:10pm
-
29 spots held for students in CS Match until 9:00 a.m. May 24
-
CS 252.02 Winter 2025
- Faculty:Sneha Narayan 🏫 👤
- Size:34
- M, WAnderson Hall 329 11:10am-12:20pm
- FAnderson Hall 329 12:00pm-1:00pm
-
CS 252.00 Spring 2025
- Faculty:Eric Alexander 🏫 👤
- Size:34
- M, WLanguage & Dining Center 104 9:50am-11:00am
- FLanguage & Dining Center 104 9:40am-10:40am
-
34 – reserved for REQ: CS 252 Match (Condition Rule) until 3/5/2025
-
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 2024, Winter 2025, Spring 2025
- FSR, Formal or Statistical Reasoning
-
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.
-
CS 254.00 Fall 2024
- Faculty:Chelsey Edge 🏫 👤
- Size:34
- M, WLanguage & Dining Center 104 11:10am-12:20pm
- FLanguage & Dining Center 104 12:00pm-1:00pm
-
34 spots held for students in CS Match until 9:00 a.m. May 24
-
CS 254.00 Winter 2025
- Faculty:Chelsey Edge 🏫 👤
- Size:34
- M, WWeitz Center 132 11:10am-12:20pm
- FWeitz Center 132 12:00pm-1:00pm
-
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 2024, Winter 2025
- FSR, Formal or Statistical Reasoning
-
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.
-
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 2024, Winter 2025, Spring 2025
- FSR, Formal or Statistical Reasoning
-
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.
-
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 2025
- FSR, Formal or Statistical Reasoning
-
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.
-
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 2025
- FSR, Formal or Statistical Reasoning
-
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.
-
MATH 295 Numerical Differential Equations 6 credits
An introduction to numerical methods to compute approximate solutions of differential equations. Material will be selected from a range of topics such as error analysis, numerical differentiation, Euler and Runge-Kutta methods, predictor-corrector methods, boundary value problems, and curve fitting. Applications to other subjects such as physics, chemistry, ecology, epidemiology and neuroscience will be covered. Programming experience is not required.
- Fall 2024
- FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning
-
Student has completed any of the following course(s): MATH 134 or MATH 232 with a grade of C- or better or received a score of 232 or better on the Carleton Math Requisite Equivalency exam.
-
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 2025
- FSR, Formal or Statistical Reasoning
-
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.
-
MATH 331 Real Analysis II 6 credits
Further topics in analysis such as measure theory, Lebesgue integration or Banach and Hilbert spaces.
- Spring 2025
- FSR, Formal or Statistical Reasoning
-
Student has completed any of the following course(s): MATH 321 with a grade of C- or better.
-
MATH 333 Combinatorial Theory 6 credits
The study of structures involving finite sets. Counting techniques, including generating functions, recurrence relations, and the inclusion-exclusion principle; existence criteria, including Ramsey’s theorem and the pigeonhole principle. Some combinatorial identities and bijective proofs. Other topics may include graph and/or network theory, Hall’s (“marriage”) theorem, partitions, and hypergeometric series.
- Winter 2025
- FSR, Formal or Statistical Reasoning
-
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.
-
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 2025
- FSR, Formal or Statistical Reasoning
-
Student has completed any of the following course(s): MATH 241 with grade of C- or better.
-
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.
- Fall 2024, Spring 2025
- FSR, Formal or Statistical Reasoning
-
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.
-
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 2024
- FSR, Formal or Statistical Reasoning
-
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.
-
MATH 395 Introduction to Analytic Number Theory 6 credits
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.
- Winter 2025
- FSR, Formal or Statistical Reasoning
-
Student has completed the following course(s): MATH 321 and MATH 342 with a grade of C- or better.
-
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 2025, Spring 2025
- FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning
-
Student has completed any of the following course(s): MATH 240 with a grade of C- or better.
-
STAT 320 Time Series Analysis 6 credits
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). Exposure to matrix algebra may be helpful but is not required.
- Spring 2025
- FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning
-
Student has completed any of the following course(s): STAT 230 and STAT 250 with a grade of C- or better.