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MAT 380: Geometry
3.00 Credits
Allen University
Prerequisite: MAT 350 This course covers the axiomatic foundation of Euclidean geometry; the Parallel Postulate and attempts to prove it or replace it; and non-Euclidean Geometry.
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MAT 380 - Geometry
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MAT 403: Differential Equations
3.00 Credits
Allen University
This course topic includes exact differential.
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MAT 403 - Differential Equations
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MAT 404: Partial Differential Equations
3.00 Credits
Allen University
Prerequisites: MAT 403 The subject matter of this course includes waver and heat equations.
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MAT 404 - Partial Differential Equations
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MAT 406: Topology
3.00 Credits
Allen University
Prerequisites: MAT 305 and MAT 301 This is an introductory course on General Topology. It covers the naive set theory, the definition and constructions of topological spaces, base and subbase for a topology, the first and second countabilities, the separation axioms, the connectedness and the compactness. The metric spaces, with an emphasis of the Euclidean n-spaces, are treated as examples through the course. The product spaces are also covered if time allows.
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MAT 406 - Topology
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MAT 441: Real Analysis
3.00 Credits
Allen University
Prerequisites: MAT 228, MAT 301, MAT 304, and MAT 305 This course addresses the method and technique of Mathematical Analysis, through a study of the concepts of sets, the properties of real numbers, properties and convergences of sequences and series, continuities, differentiabilities and integrabilities of functions. Many concepts and theorems in Calculus are made clear and gaps are filled here.
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MAT 441 - Real Analysis
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MAT 442: Real Analysis I
3.00 Credits
Allen University
Prerequisite: MAT 350 This course covers the foundation of the real-number system, sequences and Cuchy sequences, convergence, limits, continuity, derivatives and Riemann integration.
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MAT 442 - Real Analysis I
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MAT 444: Real Analysis II
3.00 Credits
Allen University
Prerequisites: MAT 202 and MAT 442 This course is a continuation of MAT 442.
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MAT 444 - Real Analysis II
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MAT 445: Complex Variables
3.00 Credits
Allen University
Prerequisite: MAT 201 The topics covered in this course include elementary functions of one complex variable, differentiation and integration of complex functions, line integrals, and power series.
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MAT 445 - Complex Variables
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MAT 450: Set Theory And Logic
3.00 Credits
Allen University
Prerequisite: MAT 350 This course teaches the Zermelo Fraenkel set theory as a foundation of mathematics.
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MAT 450 - Set Theory And Logic
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MAT 495: Mathematics Seminar
1.00 Credits
Allen University
Prerequisite: Senior Standing This course enhances the growth of research and communication skills of students. It consists of reporting and readings assigned by the instructor.
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MAT 495 - Mathematics Seminar
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