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MATH 351: Introduction to Real Analysis I
3.00 Credits
Loyola University Chicago
Prerequisite: MATH 201 and 212 This course provides a rigorous treatment of the real numbers and real-valued functions of a real variable, including sequences, the Bolzano-Weierstrass and Heine-Borel theorems, topology, uniform continuity, fixed-point theorems, derivatives, and other selected topics. Outcome: Students will obtain an understanding of the fundamentals of real analysis that will prepare them for advanced work in mathematics.
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MATH 351 - Introduction to Real Analysis I
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MATH 352: Introduction to Real Analysis II
3.00 Credits
Loyola University Chicago
Prerequisite: MATH 351 This course, a continuation of Mathematics 351, provides the theoretical background for differentiability and integrability on R and Rn and Taylor's theorem, the change of variable theorem, the inverse and implicit function theorems, Lebesgue integration, and other selected topics. Outcome: Students will obtain an understanding of topics in advanced analysis that will prepare them for graduate level work in mathematics.
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MATH 352 - Introduction to Real Analysis II
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MATH 353: Introductory Complex Analysis
3.00 Credits
Loyola University Chicago
Prerequisite: MATH 264 and 351 This course provides an introduction to the theory of functions of a complex variable, including analytic functions, contour integrals, the Cauchy integral formula, harmonic functions, Laurent series, residues and poles, conformal mapping, and other selected topics. Outcome: Students will obtain an understanding of the fundamentals of complex analysis that will prepare them for advanced work in mathematics.
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MATH 353 - Introductory Complex Analysis
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MATH 355: Methods of Applied Mathematics
3.00 Credits
Loyola University Chicago
Prerequisite: MATH 264 Vector calculus, linear transformations, matrices, series solutions of differential equations, special functions; Fourier series, Fourier and Laplace transforms; Partial differential equations and topics from complex analysis, Green's functions, integral equations, the calculus of variations. Outcome: Facility with mathematical methods used in sciences and engineering.
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MATH 355 - Methods of Applied Mathematics
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MATH 358: Methods in Operations Research
3.00 Credits
Loyola University Chicago
Prerequisite: MATH 212; STAT 203 or 335 This course provides an introduction to linear, integer, and non-linear programming, queuing theory, and game theory, with emphasis on applying the associated mathematical models to problems in economics, business, finance, and the behavioral sciences. Outcome: Students will obtain a broad background in the methods of operations research that will allow them to apply these methods in a variety of areas.
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MATH 358 - Methods in Operations Research
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MATH 360: Introduction to Game Theory
3.00 Credits
Loyola University Chicago
The noncooperative and cooperative theories of games. Two person zero sum matrix games, nonzero sum N-person games, Nash equilibria of games with a continuum of strategies, auctions, duels. Cooperative game theory, including the theory of bargaining, the theory of fair allocation of rewards using the nucleolus and using the Shapley value.
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MATH 360 - Introduction to Game Theory
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MATH 386: Introduction to Topology
3.00 Credits
Loyola University Chicago
Prerequisite: MATH 351 This first course in topology discussed topological spaces, continuity, connectedness, path-connectedness, compactness, product spaces, quotient spaces, Tychonoff's theorem, the Baire category theorem, and other selected topics. Outcome: Students will obtain a background in topology that will allow them to apply this topic to other areas of mathematics or to pursue graduate studies.
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MATH 386 - Introduction to Topology
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MATH 388: Special Topics in Mathematics
1.00 - 3.00 Credits
Loyola University Chicago
This course covers advanced topics in mathematics, including analysis, topology, algebra, applied mathematics, and logic. Outcome: Students will obtain an understanding of an advanced topic in their major.
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MATH 388 - Special Topics in Mathematics
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MATH 398: Independent Study
1.00 - 6.00 Credits
Loyola University Chicago
This course allows students to engage in independent study on selected topics in mathematics under the supervision of a faculty member. Outcome: Students will obtain an understanding of an advanced topic in their major.
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MATH 398 - Independent Study
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MATH 399: Honors Tutorial
1.00 - 3.00 Credits
Loyola University Chicago
No course description available.
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MATH 399 - Honors Tutorial
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