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Course Criteria
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3.00 Credits
This course examines the set of real numbers as a complete, ordered, archimedean field; R as a linear vector space equipped with inner product and norm; metrics, particularly Euclidean, on R, topological concepts: continuity, connectedness, and compactness; the intermediate value, extreme value, monotone convergence, Bolzano/Weierstrass and Heine/Borel theorems; convergence and uniform convergence of sequences of continuous functions; differentiation: the mean value, implicit and inverse function theorems.(Prerequisites: MA 231 and MA 272 or permission of the department chair) Three credits.
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3.00 Credits
Topics in this course include algebra of complex numbers, Cauchy-Riemann equations and analytic functions, complex differentiation, integration in the complex plane, Cauchy's Theorem and integral formula, conformal mapping, Laurent series and residue theory, and applications.(Prerequisite: MA 371 or permission of the department chair) Three credits.
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3.00 Credits
This course investigates computer arithmetic, round-off errors, the solution of nonlinear equations, polynomial approximation, numerical differentiation and integration, and the solution of systems of linear equations via student-written code to implement the algorithms and/or the use of available software.Also listed as CS 377.(Prerequisites: MA 172, MA 235 and proficiency in a computer language, or permission of the department chair) Three credits.
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3.00 Credits
Topics in this course include: foundation for plane geometries; theorems of Menelaus, Ceva, Desargues, Pascal, Brianchon, and Feuerbach; inversion and reciprocation transformations; projective, Riemannian and Lobachevskian geometries; and Poincarè model.(Prerequisites: MA 231 and MA 235 or permission of the department chair) Three credits.
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3.00 Credits
This course considers topological spaces, continuous functions; product, metric, and quotient spaces; countability and separation axioms; existence and extension of continuous functions; compactification; metrization theorems and complete metric spaces.(Prerequisite: MA 371 or permission of the department chair) Three credits.
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3.00 Credits
Participation is open to senior mathematics majors with a 3.50 or higher GPA in mathematics and invited junior and senior mathematics majors with demonstrated ability who have been recommended by the mathematics faculty.This seminar provides talented students with an opportunity to undertake individualized study under faculty direction.Participants present several reports on their findings before a group of peers.The seminar's subject matter varies each semester.Three credits.
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10.00 Credits
The internship program provides senior mathematics majors with opportunities to gain practical, career-related experience in a variety of supervised field settings.Student interns select from a variety of placements, especially those requiring applications of mathematics, numerical methods, and statistics.Interns spend a minimum of 10 hours per week working at the placement site and complete the required academic component specified by their faculty advisor.Internship credits vary; interns may register for a summer session and/or one or two semesters for an overall maximum of six credits.In addition, an internship must satisfy the requirements outlined in the University Internship Policy, which is available from the Career Planning Center.An internship may not take the place of a mathematics elective.(Prerequisites: senior standing, completed application form, acceptance by the field placement supervisor, and approval by the Department of Mathematics and Computer Science.) One to three credits per semester/session.
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3.00 Credits
Independent study provides students with the opportunity to examine areas not covered in the undergraduate curriculum.Under the guidance of a faculty member, advanced students learn about an area in mathematics through reading and research.Independent study includes written work in the form of exercises or papers.Students apply to a professor under whose direction they wish to study and obtain the approval of the department chair.This course may not replace a mathematics elective to fulfill the requirements for the major, unless special permission is given by the department chair.Three credits.
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3.00 Credits
This course covers basic engineering vibration analysis with application to control systems including free-damped and undamped vibration of one degree of freedom systems, forced vibration, response, shock excitation, harmonic analysis, and random vibration, multi-degree of freedom systems, Lagrange equation, and vibration of systems with distributed mass and elasticity.Automatic control system topics include the simple hydraulic servo, open loop and closed loop systems, root locus, Routh-Hurwitz criterion, Nyquist criterion, and Bode analysis.The course includes applications and case studies, and integrates computer-aided analysis and design tools (MATLAB and Working Model) to ensure relevance to the design and analysis of real-world engineering dynamic and control system problems.(Prerequisites: MA 321, ME 203) Three credits.
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3.00 Credits
This course emphasizes analysis and synthesis of closed-loop control systems using classical and state-space approaches with an emphasis on electro-mechanical systems.The mathematical requirements include the Laplace transform methods of solving differential equations, matrix algebra, and basic complex variables.Discussion of classical control-system design includes modeling of dynamic systems, block diagram representation, time and frequency domain methods, transient and steady state response, stability criteria, controller action (proportional; proportional and integral; proportional, integral, and derivative; and pseudo-derivatives feedback), root locus methods, the methods of Nyquist and Bode, and dynamics compensation techniques.Discussion of state-space methods includes formulation and solution (analytical and computer-based) of state equations, and pole-placement design.The course integrates computer-aided analysis and design tools (MATLAB and Working Model) to ensure relevance to the design of real-world controlled electro-mechanical systems.The course also includes lab (hardware-based) exercises.(Prerequisites: MA 321, ME 203, and EE 213) Three credits.
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