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Course Criteria
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3.00 Credits
In combinatorial theory the course will discuss the basic counting principles, arrangements, distributions of objects, combinations, and permutations. Considerable attention will be given to ordinary and exponential generating functions. Also to be covered will be the standard counting techniques of recurrence, inclusion-exclusion, Burnside's Theorem, and Polya's Enumeration Formula. In graph theory the course will cover the basic theory of graphs. Also covered will be graph isomorphism, planar graphs, Euler and Hamiltonian circuits, trees, and graph colorings
Prerequisite:
MATH 203
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3.00 Credits
In-depth study of an area of interest in mathematics. Different areas of study will be offered.
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3.00 Credits
Major topics covered include sums, recurrences, relations and functions including integer functions (mod, floor, ceiling), elementary number theory, binomial coefficients, discrete probability, and graphs. Additional topics may be chosen from generating functions (solving recurrences, convolutions), special numbers (e.g., Stirling, Bernoulli, Fibonacci), and asymptotics (O notation, manipulation, and summation formulas).
Prerequisite:
MATH 230 OR MATH 311
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3.00 Credits
Topics include the elements of plane geometry, up to and including congruence, parallelism and similarity, area and volume, ruler and compass constructions, other geometries and transformations. This course includes topics from the history of mathematics.
Prerequisite:
MATH 230 OR MATH 311 OR MATH 370
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3.00 Credits
Intuitive development of geometric shapes in two- and three-dimensional space. Concepts of congruence, parallelism, perpendicularity, symmetry, transformations, measurement (English and metric systems as well as estimation skills), right angle trigonometry, and coordinate geometry are considered. Mathematics 370 is for students seeking South Carolina Teacher Licensure in early childhood education or in elementary education or a B.G.S. in Educational Studies.
Prerequisite:
MATH 202 OR MATH 270
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3.00 Credits
An apprenticeship offered in the freshman mathematics program. Each student will work under the careful supervision of a mathematics faculty member who will assign outside reading as well as evaluate performance in both oral and written examinations.
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3.00 Credits
Introduction to the terminology and basic properties of algebraic structures, such as groups, rings, and fields. The course includes topics from the history of mathematics.
Prerequisite:
MATH 311 OR (MATH 306 AND MATH 230)
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3.00 Credits
At the intermediate-level covers the following topics: Cauchy sequences and the construction of real numbers, sequences and series of real numbers, the real line as a metric space, continuity and uniform continuity, derivatives of real-valued functions of one real variable, spaces of continuous functions, Lebesgue measure and the Lebesgue integral, and Fourier series.
Prerequisite:
MATH 311 OR (MATH 306 AND MATH 230)
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3.00 Credits
Complex numbers and functions, derivatives and integrals of complex functions, the Cauchy integral theorem and its consequences, residue theory, and conformal mapping. Additional topics as time permits.
Prerequisite:
MATH 311 OR (MATH 306 AND MATH 230)
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3.00 Credits
Introduction to Point Set Topology including discussion of limit points, continuity, compactness, connectedness, metric spaces, locally compact spaces, locally connected spaces, and the Baire Category Theorem.
Prerequisite:
MATH 311 OR (MATH 306 AND MATH 230)
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