Senior Seminar in Mathematics Math 495 Course Syllabus Class Periods: 2:30pm-3:45pm TR Classroom: Thompson Hall 303 Instructor: Mei Q. Chen, Thompson Hall Phone: (843) (office)

Math 495 Course Syllabus Task 1: Introduction to Complex Variables Chapters 2-5 of “The Fundamental Theorem of Algebra” by B. Fine and G. Rosenberger, 1997 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. Two hour exams: Sept 18 & Oct 18, Homework Homework

Math 495 Course Syllabus Task 2: Major Field Test in Mathematics Thur, Nov 15 A two-hour exam (given by ETS) required by the Dept More information More information Sample problems Sample problems

Math 495 Course Syllabus Task 3: Term Project Suggested topics: (1) Eigenvalues and Eigenvectors of Matrices over a Finite Field Eigenvalues and Eigenvectors of Matrices over a Finite FieldEigenvalues and Eigenvectors of Matrices over a Finite Field (2) The Minimum Rank of a Sign Pattern Matrix Over a Field The Minimum Rank of a Sign Pattern Matrix Over a FieldThe Minimum Rank of a Sign Pattern Matrix Over a Field (3) Solving Systems of Linear Equations in a Finite Field Solving Systems of Linear Equations in a Finite FieldSolving Systems of Linear Equations in a Finite Field (4) Stochastic Matrices Over a Field Stochastic Matrices Over a FieldStochastic Matrices Over a Field (5) Properties of Special Square Matrices over a Field Properties of Special Square Matrices over a FieldProperties of Special Square Matrices over a Field Presentations: Tuesday, December 4 Papers: 1 st draft/Nov 8, 2 nd draft/Dec 4, last draft/Dec 5-11 PapersPapers from Spring, 2007 Papers

Math 495 Course Syllabus Grading Policy: (1) Introduction to Complex Variables – 40% (2) Major Field Test in Mathematics – 20% (3) Term Project - 40%

Calculus I – Course Syllabus Office Hours/ESP Study Sessions (1) Office Hours: (1) Office Hours: 1:30-3:00pm, MWF 1:30-3:00pm, MWF 1:15pm-2:15pm TR 1:15pm-2:15pm TR TH328 TH328 (2) ESP Study/Help Sessions 8:00pm-9:30pm MR TH 319 or TH 328 TH 319 or TH 328