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Course Criteria
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3.00 Credits
A course designed to offer selected topics in mathematics related to K-12 education. The specific topic or topics will be announced together with the prerequisites each term. Course may be repeated for credit when specific topics differ. (OC). 1.000 TO 3.000 Credit hours 1.000 TO 3.000 Lecture hours Levels: Undergraduate Schedule Types: Seminar Mathematics Department Course Attributes: Upper Division
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1.00 - 3.00 Credits
Topic: Number and Proportional Reasonning in Middle School Mathematics Teachers. This course is designed to deepen the teachers of middle school mathematics understanding of the rational number system and its extension to the real number system in a way that models appropriate pedagogy and raises curriculum issues relevant to teaching number concepts for conceptual understanding and computation fluency. A particular emphasis will be on understanding and applying concepts of proportional reasoning. Topics related to this emphasis include analyzing connections between fraction concepts and ratios and proportions; describing the relationship between proportions and direct and indirect variation; analyzing and applying the connections between proportions and similar figures, probability and sampling; and modeling and solving problems involving rations and proportions. Other major topics incude analyzing number theoretic concepts such as prime numbers and divisibility; and comparing and contrasting models of operations across number systems. Calculator and computer technology will be used as problem solving tools and for support in conceptual understanding. Curriculum resources and materials that support conceptual understanding are considered. 1.000 TO 3.000 Credit hours 1.000 TO 3.000 Lecture hours Levels: Undergraduate Schedule Types: Lecture Mathematics Department Course Attributes: Upper Division
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3.00 Credits
Properties of the integers, the division algorithm, Euclid's algorithm, Fermat's theorems, unique factorization of integers into primes, congruences, arithmetic functions, Diophantine equations, continued fractions, quadratic reciprocity. (W). 3.000 Credit hours 3.000 Other hours Levels: Undergraduate Schedule Types: Recitation Mathematics Department Course Attributes: Upper Division
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1.00 - 3.00 Credits
Independent study in mathematics for topics at the junior level. Topics and objectives chosen by agreement between student and instructor. 1.000 TO 3.000 Credit hours 1.000 TO 3.000 Other hours Levels: Undergraduate Schedule Types: Independent Study Mathematics Department Course Attributes: Upper Division
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3.00 Credits
The aim of this course is to survey the standard types of differential equations. This includes systems of differential equations, and partial differential equations, including for each type, a discussion of the basic theory, examples of applications, and classical techniques of solutions with remarks about their numerical aspects. Also included are autonomous and periodic solutions, phase space, stability, perturbation techniques and Method of Liapunov. Students cannot receive credit for both MATH 404 and MATH 504. (AY). 3.000 Credit hours 3.000 Lecture hours Levels: Undergraduate Schedule Types: Lecture Mathematics Department Course Attributes: Upper Division
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3.00 Credits
Origin and classification of integral equations, connections with differential equations, integral equations of convolution type, method of successive approximations, single kernels, elements of Hilbert space, linear operators, resolvents, Fredholm theory and Hilbert-Schmidt theory. Students cannot receive credit for both MATH 405 and MATH 505. (OC). 3.000 Credit hours 3.000 Lecture hours Levels: Undergraduate Schedule Types: Lecture Mathematics Department Course Attributes: Upper Division
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3.00 Credits
Introduction to groups, subgroups, group homomorphisms, factor groups, simple groups, cyclic groups. Sylow theorems, rings, ideals, integral domains, fields, polynomial rings, Kronecker's theorem, also properties of the integer, rational, real, and complex numbers. Students cannot receive credit for both MATH 412 and MATH 512. (W). 3.000 Credit hours 3.000 Other hours Levels: Undergraduate Schedule Types: Recitation Mathematics Department Course Attributes: Upper Division
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3.00 Credits
Vector spaces, linear transformations and matrices, determinants, inner product spaces, bilinear and quadratic forms, Hamilton-Cayley theorem, eigenvalues and eigenvectors, and spectral theorem. Students cannot receive credit for both MATH 413 and MATH 513. (F) 3.000 Credit hours 3.000 Lecture hours Levels: Undergraduate Schedule Types: Lecture Mathematics Department Course Attributes: Upper Division
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3.00 Credits
Review of distribution theory. Introduction to stochastic processes, Markov chains and Markov processes, counting, and Poisson and Gaussian processes. Applications to queuing theory. Students cannot receive credit for both MATH 420 and MATH 520. (AY,W). 3.000 Credit hours 3.000 Lecture hours Levels: Undergraduate Schedule Types: Lecture Mathematics Department Course Attributes: Upper Division
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3.00 Credits
Interval estimation and pivotal quantities, maximum likelihood estimation, hypothesis tests, linear models and analysis of variance, bivariate normal distribution, regression and correlation analysis, and nonparametric methods. Students cannot receive credit for both MATH 425 and MATH 525. (AY,S). 3.000 Credit hours 3.000 Other hours Levels: Undergraduate Schedule Types: Recitation Mathematics Department Course Attributes: Upper Division
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