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Course Criteria
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3.00 Credits
Combines theory and practice of teaching middle school mathematics. A deeper investigation into student learning and the development of mathematical concepts and procedures. Class ideas applied in teaching situations. Prerequisite: MATHS 250, 393; a minimum grade-point average of 2.5 in all mathematics courses in the major; admission to Teacher Education; permission to enroll in 300/400-level professional education courses. Parallel: EDJHM 385.
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3.00 Credits
The theory of groups, including subgroups, cyclic groups, normal subgroups, cosets, Lagrange’s Theorem, quotient structures, homomorphisms, automorphisms, group actions, Sylow’s Theorems, structure of finite abelian groups, generators and relations. Prerequisite: MATHS 311 or permission of the department chairperson.
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3.00 Credits
An introduction to the theory of rings, including integral domains, division rings, and fields. Quotient fields of integral domains. Homomorphisms, ideals, and quotient structures. Factorization in commutative rings. Polynomial rings and field extensions. Aspects of Galois theory. Prerequisite: MATHS 411 or permission of the department chairperson.
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3.00 Credits
Exploration of applications of number theory, group theory, and linear algebra to areas such as cryptography and error-correcting codes; applications of graph theory to resource allocation and route planning; other possible topics selected by the instructor. Prerequisite: MATHS 311 or permission of the department chairperson.
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3.00 Credits
Topics include the division algorithm; positional notation; divisibility; primes; congruences; divisibility criteria; the sigma, divisor, and phi functions; diophantine equations; linear, polynomial, and simultaneous congruences; theorems of Fermat, Euler, Lagrange, and Wilson; quadratic reciprocity. Prerequisite: MATHS 215 or permission of the department chairperson.
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3.00 Credits
Survey designs; simple random, stratified, cluster, and systematic sampling; ratio estimates; regression estimates; cost and variance functions. Prerequisite: MATHS 321 or its equivalent.
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3.00 Credits
Addresses regression topics that include simple and multiple linear regression, polynomial regression, regression diagnostics, and forecasting. Introduces time series topics that include exponential smoothing, auto-regressive, integrated, moving average (ARIMA) models, and forecasting. Prerequisite: MATHS 321 or equivalent.
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3.00 Credits
Multivariate normal distribution; quadratic forms; linear models; simple random, randomized block, Latin squares, factorial, split-plot, balanced incomplete block design; analysis of covariance; confounding; multiple comparison tests. Prerequisite: MATHS 321 or its equivalent.
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3.00 Credits
Introduction to geometric topology, including piecewise linear structures, Euler's formula, surfaces and solids, knots, graphs, and other topics. Prerequisite: MATHS 217, 267; or permission of the department chairperson.
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3.00 Credits
Fundamentals of differential geometry, as an extensive study of curves and surfaces in 3-space. Includes the use of computer visualization and emphasizes the importance of differential geometry in areas like relativity theory and modern physics. Prerequisite: MATHS 267 or permission of the department chairperson.
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