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Course Criteria
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3.00 Credits
3 hours; 3 credits This course covers basic topics and techniques of combi - natorics, including mathematical induction, the pigeonhole principle, permutations, combinations, distributions, binomial coefficients, generating functions, partitions, recurrence relations, inclusion-exclusion, block designs, and finite projective planes. Prerequisite: MTH 3006 or 3010.
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3.00 Credits
3 hours; 3 credits Topics to be included are divisibility, primes, unique factorization, arithmetic functions, perfect numbers, linear and quadratic congruences, primitive roots, quadratic reciprocity, and diophantine equations. Prerequisite: MTH 3006, 3010, or 3030.
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3.00 Credits
3 hours; 3 credits Topics to be included are rings, groups, integral domains, fields, vector spaces, axiomatic development of rational and complex numbers, equivalence relations, isomorphisms, mathematical induction, divisibility, congruence, and fundamental theorem of arithmetic. Prerequisite: MTH 3020 or 3030 or either 3006 or 3010, the last two requiring departmental permission.
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3.00 Credits
3 hours; 3 credits This course surveys the evolution of mathematical ideas from ancient times to the present by working on actual problems posed by historical mathematicians. From the ancient period, mathematical contributions of Mesopotamian, Egyptian, Greek, Chinese, Indian, and Arab mathematicians will be sampled. Subsequent topics will illustrate the re-emergence of mathematics in Europe in the late Middle Ages; the role of mathematics in the scientific revolution of the 17th century; the history of the calculus; and a brief discussion of the diver - sification of mathematics in the 19th and 20th centuries. Prerequisites: MTH 3006 or MTH 3010, and at least one other 3000-level or higher mathematics course.
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3.00 Credits
3 hours; 3 credits This course is an introduction to the basic concepts in differential geometry. The topics to be discussed are the local and the global geometric properties of curves and of surfaces in three-dimensional Euclidean space: parametric representation of curves and surfaces, curvature, the normal, the tangent, and the binomial vectors of a curve, orientation, Jacobian matrix, the four-vertex problem, the index number, Gaussian curvature of a surface, and the Gauss map. Prerequisites: MTH 3020 and 4100 or departmental permission.
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4.00 Credits
4 hours; 3 credits The objectives of this second course are to provide a fuller understanding of computer organization and operation, to introduce assembly language programming, and to apply algorithm development techniques at the machine language level. Topics to be covered include computer structure and machine language, data representation, symbolic coding and assembly systems, macros, program segmentation and linkage, and applications. Although System/370 will be studied in detail, concepts and techniques that apply to a broad range of computers will be emphasized. (Not open to students who have completed CIS [STA] 3363.) Prerequisite: MTH 3300 or departmental permission.
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4.00 Credits
4 hours; 3 credits This course will introduce the student to the basic notions of mathematical logic. Topics to be covered include the syntax and semantics of propositional and first-order logic, the completeness and compactness theorems, computability theory (including the unsolvability of the halting problem and the concept of recursive function), and the G del incompleteness theorems. Time permitting, some elementary set theory will also be discussed. Prerequisite: MTH 3020 or 3030 or either 3006 or 3010, the last two requiring departmental permission.
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4.00 Credits
4 hours; 3 credits This course covers basic combinatorial procedures used in various applications of computer science. Some of these are searching (sequential, binary), sorting (bubble, quick, Shell, bucket, heap), and merging of files. These are followed by computer representations and traversing of graphs, spanning trees, minimal path, and Hamiltonian circuits. For each topic an algorithm will be designed, programmed, and run on the computer. The results will be analyzed in terms of efficiency. Prerequisites: MTH 3300 (STA 3300) or CIS (STA) 2359 and CIS (STA) 3362.
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4.00 Credits
4 hours; 4 credits This course develops the theory of finite differences methods. Topics to be included are interpolations with equal and unequal intervals, Sheppard's Rules, interpolation of functions of several variables, central difference formulas, summation, approximate differentiation and integration with equal and unequal intervals, difference equations, iteration, and systems of equations. (Not open to students who have completed MTH 4310.) Corequisite: MTH 3020 or 3030.
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4.00 Credits
4 hours; 4 credits Topics to be discussed include summation operator, summation by parts; measurements of interest, forces of interest and discount; fixed and varying annuities; bonds, serial bonds; installment loans; depreciation, depletion, and capitalized cost. Prerequisite: MTH 3006 or 3010.
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