Senior Seminar in MathematicsSenior Seminar in MathematicsMath 495 Course SyllabusMath 495 Course Syllabus

Class Periods: 11:90pm-11:50pm MWF Class Periods: 11:90pm-11:50pm MWF

Classroom: Thompson Hall 303Classroom: Thompson Hall 303

Instructor: Mei Q. ChenInstructor: Mei Q. Chen, , Thompson Hall 328 Thompson Hall 328

E-mail: chenm@citadel.edu E-mail: chenm@citadel.edu

Phone: (843) 953-7896 (office)Phone: (843) 953-7896 (office)

http://macs.citadel.edu/chenm/495.dir/08fal.dir/syl.htmlhttp://macs.citadel.edu/chenm/495.dir/08fal.dir/syl.html

Math 495 Course SyllabusMath 495 Course Syllabus

Task 1: Introduction to Complex VariablesTask 1: Introduction to Complex Variables

Chapters 2-5 of “Chapters 2-5 of “The Fundamental Theorem of The Fundamental Theorem of AlgebraAlgebra” by B. Fine and G. Rosenberger, 1997 ” by B. Fine and G. Rosenberger, 1997

Main topics are complex numbers, complex Main topics are complex numbers, complex polynomials and properties, complex polynomials and properties, complex analysis, differentiation in complex variable, analysis, differentiation in complex variable, analytic functions, and complex integration. analytic functions, and complex integration.

Two proofs of the Fundamental Theorem of AlgebraTwo proofs of the Fundamental Theorem of Algebrawill be studied. One proof is based on calculus and will be studied. One proof is based on calculus and the other uses Liouville’s theorem in complex the other uses Liouville’s theorem in complex analysis. analysis.

Two hour exams: Sept 24 & Oct 29, Two hour exams: Sept 24 & Oct 29, HomeworkHomework

Math 495 Course SyllabusMath 495 Course SyllabusTask 2: Task 2: Major Field Test in MathematicsMajor Field Test in MathematicsWednesday, Nov 12Wednesday, Nov 12

A two-hour exam (given by ETS)A two-hour exam (given by ETS)required by the Deptrequired by the Dept

More information More information

Sample problemsSample problems

Math 495 Course SyllabusMath 495 Course SyllabusTask 3: Term ProjectTask 3: Term Project

Suggested topics:Suggested topics:

(1) Eigenvalues and Eigenvectors of Matrices over (1) Eigenvalues and Eigenvectors of Matrices over a Finite Fielda Finite Field

(2) Properties of Special Square Matrices over a (2) Properties of Special Square Matrices over a Finite FieldFinite Field

(3) Inverse Eigenvalue Problems Arising in (3) Inverse Eigenvalue Problems Arising in Population ModelsPopulation Models

Presentations: Monday, December 8 Presentations: Monday, December 8

Papers: 1Papers: 1stst draft/Dec 1, and 2nd draft/Dec 15 draft/Dec 1, and 2nd draft/Dec 15

PapersPapers from Spring, 2007 from Spring, 2007Papers from Fall, 2007 Papers from Fall, 2007

Math 495 Course SyllabusMath 495 Course Syllabus

Grading Policy: Grading Policy:

(1)(1) Introduction to Complex Introduction to Complex VariablesVariables – – 40%40%

(2) Major Field Test in (2) Major Field Test in MathematicsMathematics – – 20%20%

(3) Term Project(3) Term Project - - 40%40%

Math 495 – Course SyllabusMath 495 – Course Syllabus

Office Hours/ESP Study Sessions Office Hours/ESP Study Sessions

(1) Office Hours:   (1) Office Hours:  

2:30-4:00pm, MRWF2:30-4:00pm, MRWF

TH328TH328

(2) ESP Study/Help Sessions (2) ESP Study/Help Sessions     8:00pm-9:30pm MR8:00pm-9:30pm MR

TH 319TH 319