Search Results
Your search for courses · during 25WI · 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.
- Winter 2025
- 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 252.02 Winter 2025
- Faculty:Sneha Narayan 🏫 👤
- Size:34
- M, WAnderson Hall 329 11:10am-12:20pm
- FAnderson Hall 329 12:00pm-1:00pm
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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.
- Winter 2025
- 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 254.00 Winter 2025
- Faculty:Chelsey Edge 🏫 👤
- Size:34
- M, WWeitz Center 132 11:10am-12:20pm
- FWeitz Center 132 12:00pm-1:00pm
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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.
- Winter 2025
- 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.
- Winter 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 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
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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.
- Winter 2025
- 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 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
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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 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
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Student has completed the following course(s): MATH 321 and MATH 342 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 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.