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MAT 402: Differential Equations II
3.00 Credits
St. Francis College
Series solution of differential equations. Lengendre's and Bessel's equation. Fourier series, Fourier and Laplace transforms. Partials differential equations. Prerequisite: MAT 401 3 credit.s Fall semester; day.
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MAT 402 - Differential Equations II
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MAT 403: Advanced Calculus I
3.00 Credits
St. Francis College
Axiom of continuity, least upper bounds, and greatest lower bounds; open and closed sets; continuity differentiation; maxima and minima for functions of two or more variables; the method of Lagrange; implicit function theorems; and general theorems of partial differentiation. Prerequisite: MAT 304. 4 credits. Fall semester; day.
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MAT 403 - Advanced Calculus I
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MAT 404: Advanced Calculus II
3.00 Credits
St. Francis College
Transformations and mappings, point set theory, uniform continuity, and fundamental theorems of continuous functions, the theory of Riemann integration, infinite series and uniform convergence, power series, improper integrals, and a study of the gamma functions. Prerequisite: MAT 403. 4 credits. Spring semester; day.
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MAT 404 - Advanced Calculus II
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MAT 406: Theory of Numbers
3.00 Credits
St. Francis College
An introductory course dealing with divisibility, number theorems, theory and congruences, quadratic residues, and Diophantine equations. Quadratic residues and quadratic reciprocity law. Fermat's theory, Chinese remainder theorem, Euler's theorem,and Wilson's theorem. Prerequisite: MAT 202. 3 credits. Offered as needed; day.
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MAT 406 - Theory of Numbers
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MAT 408: Numerical Analysis
3.00 Credits
St. Francis College
Numerical solutions of equations, difference tables, operator methods; numerical differentiation and integration; numerical solution of ordinary differential equations; systems of linear equations; solutions by iterative methods. Prerequisite: MAT 304 or MAT 401. 3 credits. Offered as needed; day.
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MAT 408 - Numerical Analysis
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MAT 409: Modern Algebra
3.00 Credits
St. Francis College
Sets and mappings; theory of groups, rings, and fields; homomorphisms, isomorphisms, and the first isomorphism theorem for groups and rings; the field of real/ complex numbers. Polynomials. Prerequisite: MAT 304. 3 credits. Every semester; day.
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MAT 409 - Modern Algebra
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MAT 410: Functions of a Complex Variable
3.00 Credits
St. Francis College
Complex numbers and the topology of the complex plane; analytic and elementary functions, contour integrals, conformal mappings, power series, Laurent series, Cauchy-Riemann partial differential equations; Cauchy-Goursat theorem. Prerequisite: MAT 304. 3 credits. Offered as needed; day.
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MAT 410 - Functions of a Complex Variable
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MAT 411: Introduction to Real Analysis
3.00 Credits
St. Francis College
Families of sets, countable and uncountable sets, metric spaces, the space of continuous functions on a compact set, the Stone- Weirstrass theorem, measure and measurable functions, the Lebesgue Integral, and dominated and monotone convergence theorem, Lp spaces. Prerequisite: MAT 404. 3 credits. Offered as needed; day.
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MAT 411 - Introduction to Real Analysis
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MAT 413: Advanced Linear Algebra
3.00 Credits
St. Francis College
Advanced course in linear algebra examining linear transformations and matrices, the characteristics and minimal polynomials, Caley-Hamilton theorem, diagonalization, unitary spaces, selfadjoint, normal matrices and the spectral theorem, Jordan ca- nonical form, and quadratic form. Prerequisites: MAT 312. 3 credits. Offered as needed; day.
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MAT 413 - Advanced Linear Algebra
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MAT 414: General Topology
3.00 Credits
St. Francis College
Set-theoretic preliminaries, metric spaces, topological spaces, continuity and homomorphism, compactness and connectedness, separation axioms, complete metric spaces, and covering spaces. Prerequisite MAT 403. 3 credits. Offered as needed.
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MAT 414 - General Topology
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