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Mathematics 360: Graph Theory
4.00 Credits
Allegheny College
An introduction to the theory of undirected and directed finite graphs. Topics include the Konigsberg Bridge Problem, planar and non-planar graphs, the five-color theorem and the four-color theorem, Hamiltonian circuits, shortest path algorithms, and problems of network flow. This course may be applied toward the Mathematics requirement for a major in Computer Science. Prerequisite: Mathematics 205 or permission of instructor.
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Mathematics 360 - Graph Theory
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Mathematics 365: Combinatorics and Discrete Models
4.00 Credits
Allegheny College
The study of topics from combinatorics and discrete mathematical models including the pigeonhole principle, permutations and combinations of finite sets and multisets, binomial and multinomial coefficients, the inclusion-exclusion principle, recurrence relations, and generating functions. This course may be applied toward the Mathematics requirement for a major in Computer Science. Prerequisite: Mathematics 205 or permission of instructor.
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Mathematics 365 - Combinatorics and Discrete Models
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Mathematics 380: Optimization
4.00 Credits
Allegheny College
A study of the theory and techniques of mathematical optimization with application to economics, scheduling problems, and other areas of interest to the class. Techniques may include linear, integer, and dynamic programming. This course may also be of interest to students majoring in Economics and Computer Science. Prerequisites: Mathematics 320 or permission of instructor.
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Mathematics 380 - Optimization
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Mathematics 400: Topology
4.00 Credits
Allegheny College
A study of topological spaces and continuous maps, separation axioms, compactness, metric spaces, product spaces, connectedness and fixed point theorems. Proof techniques are emphasized. The course material ties together some ideas presented in the basic Mathematics courses. Prerequisite: Mathematics 340.
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Mathematics 400 - Topology
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Mathematics 425: Algebraic Structures II
4.00 Credits
Allegheny College
A study of rings and fields, including integral domains, polynomial rings, ideals, homomorphisms, and irreducibility of polynomials over prime fields. Other topics may include unique factorization domains, Euclidean domains, extension fields, automorphisms of fields and Galois theory, additional algebraic structures, or advanced topics in group theory. Prerequisite: Mathematics 325.
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Mathematics 425 - Algebraic Structures II
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Mathematics 440: Real Analysis
4.00 Credits
Allegheny College
An extension of the material introduced in Mathematics 340. Topics may include sequences and series of functions, uniform convergence, power series and Taylor's theorem, the topology of Euclidean space, the foundations of the calculus of several variables, the implicit function theorem, the inverse function theorem, and the Lebesgue integral. Prerequisite: Mathematics 340.
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Mathematics 440 - Real Analysis
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Mathematics 500: Undergraduate Internship
4.00 Credits
Allegheny College
Undergraduate Internship
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Mathematics 500 - Undergraduate Internship
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Mathematics 585: Junior Seminar
4.00 Credits
Allegheny College
Seminar discussion of selected topics in mathematics. Students read and present articles from mathematical journals and conduct preliminary research on potential senior project topics. The writing and presentation of mathematics is emphasized. Prerequisite: Mathematics 205 or permission of instructor.
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Mathematics 585 - Junior Seminar
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Mathematics 590: Independent Study
4.00 Credits
Allegheny College
Credit: Variable.
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Mathematics 590 - Independent Study
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Mathematics 620: Senior Project
4.00 Credits
Allegheny College
The student completes research and writing for the Senior Project and gives an oral defense. Prerequisite: Permission of instructor.
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Mathematics 620 - Senior Project
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