<\/p>\n
MAT 505 Mathematical Logic<\/strong><\/span><\/td>\n| \u00a0\u00a0 3 SH<\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n | An introduction to mathematical logic, including sentential logic and first-order logic. Soundness, completeness, and compactness of sentential and first-order logic. Expressing properties of various mathematical structures with first-order languages. Applications of compactness. Prerequisite: MAT 375 or equivalent<\/span><\/p>\n Topics will be taken from both descriptive and inferential statistics. These include estimation, hypothesis testing, simple- and multiple-regression analysis, analysis of variance, and one or more multivariate techniques such as factor, cluster, discriminant, or principal components analysis. Applications from a range of subject areas from the behavioral to the physical sciences will be given. Computer statistical packages will be used throughout both semesters. Prerequisite<\/em>: MAT 120 or equivalent.<\/span><\/p>\n Groups are one of the fundamental mathematical objects that help us to understand how and why things work as they do in mathematics. They are significant in their own right, but are also important in applications of mathematics to physics, chemistry, and information security. As such, students can greatly benefit from a clear understanding of their properties and structures. Prerequisite: MAT 375: Algebraic Structures, or equivalent.<\/span><\/p>\n In this course, we examine rings, fields, field extensions, and vector spaces. Using these, we will study the Fundamental Theorem of Galois Theory in order to why some polynomials admit general solutions while others do not. Along the way we will also examine, rational, irrational, transcendental, constructible, and non-constructible numbers. Prerequisite: MAT 512: Group Theory or equivalent.<\/span><\/p>\n A first graduate course in Real Analysis. General theory of measure and Lebesgue integration, and Lp-spaces. Prerequisite: MAT 383 or equivalent<\/span><\/p>\n Complex number systems and properties of such, continuity, differentiability, analyticity, line integration, and power series. Residues and poles, conformal mapping, analytic continuation and the well-known classical theorems associated with the theory of complex analysis.<\/span><\/p>\n A second course in geometry focusing on axiomatic systems and non-Euclidean geometric systems. Topics covered include finite geometry, affine geometry, transformational geometry, analytic geometry, hyperbolic geometry and projective geometry. Proof and explanation are emphasized throughout. Prerequisite: Admission to MA program in Mathematics, MAT 207 and MAT 3xx or equivalent. Offered spring semester in odd years. Prerequisites: Admission to the MA Program in Mathematics, MAT 207 and MAT 3xx Axiomatic Geometry (or equivalent) or permission of the instructor.<\/span><\/p>\n This course will give a broad overview of the fundamental ideas in number theory and examine a handful of applications.<\/span><\/p>\n In this course we will examine significant moments in the development of key areas of mathematics. Particular emphasis will be placed on understanding contributions from a variety of cultures and time periods, as well as from significant individuals. Prerequisite: Successful completion of at least one 200-level math class or Equivalent, this course is not open to students who have completed MAT 429.<\/span><\/p>\n This course offers an opportunity for students to pursue in greater depth topics introduced in other courses or topics not included in other courses. The topic varies from year to year and from student to student. Typical subjects might include mathematical models, combinatorics, field theory, algebraic topology, decision theory, and harmonic analysis or applications.<\/span><\/p>\n This course is a comprehensive introduction to solution methods for partial differential equations. Advanced solution methods for ordinary differential equations, primarily for use in constructing solutions to partial differential equations, will also be discussed. Students will be introduced to a variety of partial differential equations of various orders and types. Fundamental analytical solution methods for partial differential equations will be discussed. Students will also be exposed to the occurrence and use of partial differential equations in various real-world applications. Appropriate technology will be used throughout the course as an aid in visualizing solutions, and to reinforce material learned in the course. Prerequisite(s): MAT 281 and MAT 282 with a grade of C or better. MAT 383 highly recommended.<\/span><\/p>\n The course will cover the development, analysis, and application of efficient and stable numerical methods to ordinary and partial differential equations that arise in a wide range of science, including meteorology; business; and engineering applications. Prerequisite(s): MAT 281 and MAT 282 with a grade of C or better.<\/span><\/p>\n The study of various transforms and their use in wavelet analysis and machine learning. This course will provide a foundation for wavelet analysis and machine learning techniques. The purpose of this course is to prepare students to apply relevant tools from wavelet analysis and machine learning to a variety of real-world problems and to prepare them to apply these tools for future use in their career, for instance, in graduate school \/ industry. Prerequisite(s): MAT 332 with a grade of C or better.<\/span><\/p>\n This course provides a thorough introduction to the foundations of functional analysis in normed linear spaces. The course will include a treatment of both Banach and Hilbert spaces. Fundamental theorems including but not limited to the \u201cBig theorems\u201d of functional analysis such as the Hahn-Banach theorem, Baire category theorem, uniform boundedness theorem, open mapping theorem, and closed graph theorem as well as their applications will be discussed. Linear operators including bounded, compact, and self-adjoint operators will be defined and their spectral properties will be explored. Prerequisite(s): MAT 272 and MAT 383 with a grade of C or better.<\/span><\/p>\n This course is designed for students fulfilling the thesis requirements for the M.A. in Mathematics degree. The submitted topic and outline for the thesis must be approved by the adviser, the department graduate committee, and the Dean of\u00a0Arts and Sciences\u00a0prior to registration for the course. The student will be required to work independently on the thesis research and writing. Credit for the thesis will be awarded upon the submission of one copy of the approved final draft of the thesis and thesis abstract. Prerequisite<\/em>:s ED 501 and permission of the department and the\u00a0Dean of Arts and Sciences.<\/span><\/p>\n This course is designed for the student fulfilling the requirements for the Master of Arts in Mathematics. The student must submit an acceptable thesis topic and outline in mathematics, and the student will be required to work independently on the thesis research and writing in consultation with the thesis advisor. Credit for the thesis will be awarded upon the submission of one copy of the approved thesis and abstract. Prerequisite<\/em>: permission of the thesis adviser and the Dean of Arts and Sciences.<\/span><\/p>\n MAT 598 Faculty-Developed Course <\/strong><\/span><\/p>\n This experimental course is offered by the Mathematics Department as a means of determining its value to the total department program or in response to a particular request from a group of students.<\/span><\/p>\n MAT 599 Student-Developed Study <\/strong><\/span><\/p>\n This vehicle is designed to provide the student with an opportunity to develop his\/her own learning experience. A student will design a project and secure a faculty sponsor. The vehicle may be utilized more than once. Prerequisite<\/em>: written permission of faculty sponsor and department. Registration through the Division of Graduate Studies Office\u00a0is required.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":" MAT 505 Mathematical Logic \u00a0\u00a0 3 SH An introduction to mathematical logic, including sentential logic and first-order logic. Soundness, completeness, and compactness of sentential and first-order logic. Expressing properties of various mathematical structures with first-order languages. 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