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Course Criteria
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6.40 Credits
Problem solving and mathematical reasoning; sets and set operations; functions; numeration systems; the systems of whole numbers, integers, and rational numbers; algorithms; mental computation; elementary number theory; teaching strategies, materials, and technologies for these topics in grades pre K-6. 4 credits.
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3.00 Credits
Prerequisite: MTH-301 Decimals and percents; elementary probability; descriptive statistics; geometry of shapes in two and three dimensions; congruence and similarity; measurement; geometric transformations; teaching strategies, materials, and technologies for these topics in grades pre K-6 and fieldbased experiences in area schools. 4 credits.
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3.00 Credits
Prerequisite: MTH-260 Introduction to the arithmetic properties of the integers including divisibility, congruences, diophantine equations, primes and their distribution, quadratic forms and quadratic reciprocity. Additional topics will be chosen from continued fractions, cryptography, partitions, elliptic curves, modular forms and number fields. 4 credits.
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3.00 Credits
Prerequisite: MTH-260 Development of Euclidean and non-Euclidean geometries. Topics include axiom systems, models, congruence theorems, parallel postulates, and the philosophical and historical background to geometry. 4 credits.
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3.00 Credits
Prerequisite: MTH-260 A study of the primary methods and fundamental ideas of combinatorics and graph theory. Topics covered include generating functions, set partitions, recurrence relations, inclusion-exclusion, trees, graph connectivity, independence, and graph colorings. Additional topics will be chosen from Ramsey theory, set systems, planarity, directed graphs, matchings, and Hamiltonian and Eulerian graphs. 4 credits.
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3.00 Credits
Prerequisite: MTH-250 and 255 A selection of mathematical models using various continuous and discrete methods and having applications in business and the social and biological sciences. Included are ecological models, epidemic models, Richardson's arms race model, and population growth models. Other topics discussed are linear programming, voting problems, and Markov chains. 4 credits.
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3.00 Credits
Prerequisite: MTH-250 Calculus-based course in probability, covering counting, discrete and continuous probability, random variables, important probability distributions, joint distributions, expectation, moment generating functions, and applications of probability. 4 credits.
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3.00 Credits
Prerequisite: MTH-340 Calculus based course in statistics covering sampling, estimation, hypothesis testing, chi-square tests, regression, correlation, analysis of variance, experimental design, and nonparametric statistics. 4 credits.
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3.00 Credits
Prerequisite: MTH-250 Study of the complex plane and the calculus of functions of a complex variable. Topics to be considered include the algebra and geometry of complex numbers, limits and derivatives of functions of a complex variable, the Cauchy- Riemann equations, contour integrals, Taylor and Laurent series, and residues. 4 credits.
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3.00 Credits
Prerequisite: MTH-160 and 260 Study of finite dimensional real vector spaces, linear transformations, determinants, inner product spaces, eigenvalues and eigenvectors. 4 credits.
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