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Your search for courses · during 25SP · tagged with MATH Electives · returned 9 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.
- Spring 2025
- 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 252.00 Spring 2025
- Faculty: Eric Alexander 🏫 👤
- Size:34
- M, WLanguage & Dining Center 104 9:50am-11:00am
- FLanguage & Dining Center 104 9:40am-10:40am
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34 – reserved for REQ: CS 252 Match (Condition Rule) until 3/5/2025
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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.
- Spring 2025
- 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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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.
- Spring 2025
- 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 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
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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 331 Real Analysis II (Measure Theory) 6 credits
Further topics in analysis such as measure theory, Lebesgue integration or Banach and Hilbert spaces.
- Spring 2025
- 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 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
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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.
- Spring 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 or received a Carleton Mathematics 236 Requisite Equivalency.
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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.
- Spring 2025
- 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 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
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Student has completed the following course(s): STAT 230 and STAT 250 with a grade of C- or better.