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Course Criteria
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4.00 Credits
Introduction to rudimentary set theory, the algebra of sets, systems of linear equations, linear transformations, matrix algebra, vector spaces, and determinants.
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4.00 Credits
Machine representation of the real number field and its consequences. Elements of error analysis. Introduction to the design, analysis and stability of algorithms. Well/ill-conditioned problems. Programming, graphics, numeric and symbolic computations in MATLAB (a high level programming environment). Examples and applications in mathematics, science and engineering.
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1.00 Credits
See depatment for course description.
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4.00 Credits
Properties of the real numbers, introduction to metric spaces, Euclidean spaces, functions of a real variable, limits, continuity, the extreme and intermediate value theorems, sequences.
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4.00 Credits
Topics in matrix algebra, determinants, systems of linear equations, eigenvalues, eigenvectors, and linear transformations. Selected applications from science, engineering, computer science, and business.
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4.00 Credits
Groups, homomorphisms, factor groups. Selected applications from geometry, combinatorics, computer science, chemistry.
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4.00 Credits
A presentation of the properties of numbers as found in the theory of divisibility, congruence, diophantine equations, continued fractions, and algebraic numbers.
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3.00 Credits
See department for course description.
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3.00 Credits
Sequences and series of functions; Lebesgue measure and integration; the Stone-Weierstrass and Baire category theorems; Fourier Series; elements of functional analysis. Courses must be taken in sequence.
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3.00 Credits
Solution techniques, qualitative analysis and applications: separation of variables, eigenfunction expansion, Sturm-Liouville problems, Green's functions, Fourier transform solutions, finite difference and finite element methods. Courses must be taken in sequence.
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