Search Results
Your search for courses · during 2023-24 · tagged with MATH Electives · returned 18 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 2023, Winter 2024, Spring 2024
- Formal or Statistical Reasoning
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Computer Science 200 or 201 and Computer Science 202 (Mathematics 236 will be accepted in lieu of Computer Science 202)
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CS 252.00 Winter 2024
- Faculty:Eric Alexander 🏫 👤
- Size:28
- M, WAnderson Hall 329 12:30pm-1:40pm
- FAnderson Hall 329 1:10pm-2:10pm
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CS 252.02 Spring 2024
- Faculty:Jeff Ondich 🏫 👤
- Size:28
- M, WLanguage & Dining Center 104 9:50am-11:00am
- FLanguage & Dining Center 104 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.
- Winter 2024, Spring 2024
- Formal or Statistical Reasoning
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Computer Science 200 or 201 and Computer Science 202 (Mathematics 236 will be accepted in lieu of Computer Science 202)
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CS 254.00 Winter 2024
- Faculty:Anna Rafferty 🏫 👤
- Size:34
- M, WLeighton 305 9:50am-11:00am
- FLeighton 305 9:40am-10:40am
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CS 254.00 Spring 2024
- Faculty:Josh Davis 🏫 👤
- Size:34
- M, WLeighton 305 1:50pm-3:00pm
- FLeighton 305 2:20pm-3:20pm
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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 2023, Winter 2024
- Formal or Statistical Reasoning
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Mathematics 120 or Mathematics 211
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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 2024, Spring 2024
- Formal or Statistical Reasoning
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Mathematics 232 or instructor permission
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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.
- Fall 2023
- Formal or Statistical Reasoning
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Mathematics 236
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MATH 271 Computational Mathematics 6 credits
An introduction to mathematical ideas from numerical approximation, scientific computing, and/or data analysis. Topics will be selected from numerical linear algebra, numerical analysis, and optimization. Theory, implementation, and application of computational methods will be emphasized.
Not open to students who have already received credit for Mathematics 295 Numerical Analysis
- Winter 2024
- Formal or Statistical Reasoning
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Mathematics 232
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MATH 282 Elementary Theory of Numbers 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.
Formerly Math 312
- Winter 2024
- Formal or Statistical Reasoning
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Mathematics 236 or instructor permission
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MATH 295 Introduction to Computational Algebraic Geometry 6 credits
Classical algebraic geometry is the study of geometric objects defined by polynomial equations. This course will cover fundamental concepts and techniques—varieties, ideals, and Gröbner bases, to name a few—as well as algorithms for solving equations and computing intersections of curves and surfaces. Ultimately, this course will build towards several beautiful results: the 27 lines on a cubic surface, the 28 bitangents on a planar quartic, and the construction of regular polygons. Students will learn to use software such as SageMath to perform computations and practice visualization. While familiarity with Python would be helpful, it is by no means required!
Sophomore Priority
- Spring 2024
- Formal or Statistical Reasoning
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Mathematics 236 or instructor permission
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MATH 321 Real Analysis I 6 credits
A systematic study of concepts basic to calculus, such as topology of the real numbers, limits, differentiation, integration, convergence of sequences, and series of functions.
- Fall 2023, Spring 2024
- Formal or Statistical Reasoning
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math.236 or math.236p
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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 2023
- Formal or Statistical Reasoning
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Mathematics 236 or instructor permission
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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 2024
- Formal or Statistical Reasoning
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Mathematics 241
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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 2024
- Formal or Statistical Reasoning
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Mathematics 236 or instructor permission
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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 2023
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Junior or senior standing and instructor permission
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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 2024
- Formal or Statistical Reasoning
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Mathematics 342
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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 2024
- Formal or Statistical Reasoning
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Mathematics 236 or instructor permission
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MATH 361 Complex Analysis 6 credits
The theoretical foundations for the calculus of functions of a complex variable.
- Winter 2024
- Formal or Statistical Reasoning
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Mathematics 321 or instructor permission. Students who have already received credit for Mathematics 261 may only take this course with instructor permission
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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 2024, Spring 2024
- Formal or Statistical Reasoning Quantitative Reasoning Encounter
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Mathematics 240 Probability
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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).
- Fall 2023
- Formal or Statistical Reasoning Quantitative Reasoning Encounter
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Statistics 230 and 250. Exposure to matrix algebra may be helpful but is not required