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MATH 410: Introduction to Analysis
3.00 Credits
University of Southern Indiana
A study of the real number system as a complete ordered field, completeness properties and their equivalences, function of a single real variable, continuity differentiability, uniform continuity, and Riemann integral. Prereq: MATH 335.
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MATH 410 - Introduction to Analysis
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MATH 411: Theory of Numbers
3.00 Credits
University of Southern Indiana
The transition between problem-solving mathematics and mathematics which develops a theory. This course is rich in material useful for the secondary and elementary teacher. Prereq: 15 hours of mathematics or consent of instructor.
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MATH 411 - Theory of Numbers
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MATH 412: Modern Abstract Algebra I
3.00 Credits
University of Southern Indiana
Sets, functions, relations, number systems, theory of groups, including discussion of morphisms, quotient groups, and solvable groups. Prereq: 15 hours of mathematics or consent of instructor. F
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MATH 412 - Modern Abstract Algebra I
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MATH 413: Linear Algebra
3.00 Credits
University of Southern Indiana
Systems of linear equations, vector spaces, basic properties of matrices and determinants, linear transformations on a vector space, and canonical representations of a linear transformation. Prereq: 15 hours of mathematics or consent of instructor. Sp
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MATH 413 - Linear Algebra
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MATH 414: Modern Abstract Algebra II
3.00 Credits
University of Southern Indiana
Rings, integral domains, fields, quaternions, including discussions of characterizations of integers, embedding theorems, polynomials, and extension fields. Prereq: MATH 412.
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MATH 414 - Modern Abstract Algebra II
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MATH 426: Point Set Topology
3.00 Credits
University of Southern Indiana
Definition and properties of a topological space; continuous functions, and homeomorphisms, various topological properties such as compactness, separation, and connectedness; metric spaces. Prereq: 15 hours of mathematics or consent of instructor.
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MATH 426 - Point Set Topology
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MATH 432: Advanced Calculus
3.00 Credits
University of Southern Indiana
Functions of several variables, transformations, multiple integrals, line and surface integrals, infinite series. Prereq: MATH 335.
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MATH 432 - Advanced Calculus
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MATH 433: Differential Equations
3.00 Credits
University of Southern Indiana
Solutions to and applications of linear differential equations of order n and linear systems of differential equations. Prereq: MATH 335 (may be taken concurrently). Sp
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MATH 433 - Differential Equations
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MATH 434: Advanced Differential Equations
3.00 Credits
University of Southern Indiana
Solutions to non-linear and partial differential equations with an emphasis on numerical methods and techniques utilizing orthogonal functions. Prereq: MATH 433.
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MATH 434 - Advanced Differential Equations
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MATH 437: Numerical Analysis
3.00 Credits
University of Southern Indiana
A survey of current methods in numerical analysis. Topics will include polynomial approximation and interpolation, numerical differentiation and integration, numerical solutions of differential equations, functional approximation, solution of linear and nonlinear equations, and matrix methods for inverse and eigenvalue problems. Prereq: MATH 335.
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MATH 437 - Numerical Analysis
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