Math 7900 Syllabus  (Fall 2006)

 

Topic:  Foundations of Graduate Mathematics

Room: Grad Studies  410

Call Number:    Math 7900    03-153

6th Period:     1:25-2:15 MWF

                           

Instructor:  Dr. Robert Rumely           

E-mail: rr@math.uga.edu

Office:   437 Grad Studies      

Office:  (706)-542-2630

Home:  1081 Twin Lakes Rd, Athens, Ga 30606  Home: (706)-543-0443

 

Office Hours:    To be arranged.  There may also be an extra recitation scheduled, if the class desires.

 

Required Text:   None.  Selections will be made from various texts. 

 

Purpose:    I envision this course as covering basic logic, along with material in Calculus and Linear Algebra that is often not covered well in undergraduate classes, using those topics as a vehicle to work on proof-making skills.  Among the topics in Calculus I would like  to cover are the basic limit laws, L'Hopital's rule, Taylor's theorem, Green's theorem and various forms of Stokes' Theorem, the change of variables theorem for integration, "standard" examples and counterexamples for continuity and differentiability, and possibly the inverse and implicit function theorems.  In Linear algebra, I would like to cover abstract vector spaces, row rank equals column rank, dual spaces, the Spectral theorem, and maybe Jordan canonical form.  However the exact choice of topics will be made in consultation with the students in the course, and the list above is by itself much too ambitious.  I would rather cover a few things well, than many things poorly.   

              I expect to lecture about most topics, but the course will involve considerable student participation, with students presenting some solutions to problems and critiquing solutions given, and possibly lecturing on some topics.   

 

Grades:     Grades will be based on homework, to be assigned and collected weekly;   two in-class exams;  and a comprehensive Final Exam.   The Final Exam is scheduled for Friday, December 8, from 12:00-3:00 P.M.   Grades will be weighted as follows: 

 

                     Homework/Class work:             40%                                  

                     In-class exams:                            20%   each                       

                     Final exam:                                  20%                                  

                      

Deviations:   This course syllabus is a general plan for the course;  deviations announced

            in class by the instructor may be necessary.

 

Academic Honesty:   This course will operate in accordance with UGA’s academic 

           honesty policy   (http://www.uga.edu/ovpi).  All academic work must meet the

           standards contained in “A Culture of Honesty”.  Students are responsible for

           informing themselves of these standards before performing any academic work.