Class Periods: 11:00pm-11:50pm MWF
Classroom: Thompson Hall 303
Instructor: Mei Q. Chen
Office: Thompson Hall 328
E-mail:
Phone: (843) 953-7896 (office)
URL: http://macs.citadel.edu/chenm/495.dir/08fal.dir/syl.html
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Course Outline/Lecture Notes Homework assignments and exams
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1. Introduction to
Complex Variables.
Chapters 2-5 of the Textbook “The Fundamental Theorem of Algebra” written by Benjamin Fine and Gerhard Rosenberger, 1997, will be covered. Main topics are complex numbers, complex polynomials and properties, complex analysis, differentiation in complex variable, analytic functions, and complex integration. Two proofs of the Fundamental Theorem of Algebra will be studied. One proof is based on calculus and the other uses Liouville’s theorem in complex analysis. Click here for details.
2. Major
Field Test in Mathematics.
The Major Field Test in Mathematics is a two-hour exam given by the Educational Testing Service. It is designed to assess mastery of concepts, principles and knowledge in mathematics expected of a mathematics major. It is required by the Department of Mathematics and Computer Science at The Citadel. Topics covered in this test are calculus, linear algebra, abstract algebra, real analysis, graph theory, combinatorics, probability, statistics, dynamical systems, differential equations, geometry, numerical analysis and complex analysis. Some of these topics will be reviewed through the introduction to complex variables and the term project. Click here for more information and click here to see some sample problems.
Tentatively, the test is scheduled on Wednesday, November 12 (right after the election day).
3. Term Project.
Each student is required to complete a research project. Research results will be reported in a well-written paper and presented to students and faculty at a departmental seminar. Some suggested topics are listed below. Click on the title to see detailed description.
(1) Eigenvalues and Eigenvectors of Matrices over a Finite Field
(2) Properties of Special Square Matrices over a Finite Field
(3) Inverse Eigenvalue Problems Arising in Population Models
Presentations are tentatively scheduled during the class period on the last day of classes: Monday, December 8. Due days for the 1st, and the last drafts of the paper are Dec 1 and Dec 15, respectively. Every week, each student will present part of his paper.
Papers for previous year’s term projects are posted at:
http://macs.citadel.edu/chenm/495.dir/08fal.dir/papers_07fal.html
http://macs.citadel.edu/chenm/495.dir/07fal.dir/papers_07sp.html
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Hard copies are placed on a bookshelf in 309 Thompson.
The final grade for the course is based on:
(1) collected homework assignments and two hour exams on complex variables; (40%)
(tentatively, hour exams are on Sept 24 and Oct 29, relatively)
(2) the Major Field Test in Mathematics (20%); and
(tentatively, it will be on Nov 12, right after the Election Day)
(3) a term project including an oral presentation and a well-written paper to report research results. (40%).
(tentatively, oral presentation is on Dec 8, last day of classes)
Office Hours/ESP Study/Help Sessions
(1) Office Hours: 2:30-4:00pm,
MTWF, TH 328 or by appointment
(2) ESP Study/Help
Sessions: 8:00pm-9:30pm MR, TH 319
Last updated: August 26, 2008