Mathematics 510 Modern Analysis Summer  2023

David Carothers

Roop 105

568 2817    

carothdc at jmu dot edu

ZOOM:   Zoom link here  

Asynchronous vs. Synchronous:  This class is the "former" in the sense that you can manage all requirements without necessarily attending a specific online meeting.  But we qualify that as follows:

1. There is a scheduled weekly ZOOM meetings Mondays and Thursdays at 4:30 PM (eastern daylight time).  This is intended for questions and discussion about the assignment.   Individual schedules and obligations make it impossible that everyone can make these sessions.   We hope that you will attend when this is not terribly inconvenient, and when unable to attend that you will review a video of the session. 

2. There is a schedule of topics, with due dates for specific assignments.  You may be able to work ahead a few assignments at any point. 

3. Assignment due dates are meant to be taken seriously.  Stuff happens, of course - but any departure from the specified due dates because of illness or other unavoidable circumstances should be cleared with me ahead of the due date.

 

Office Hours: An "office" link is set up on ZOOM.  We can make an appointment with me outside of the Monday/Thursday meeting times.  OR ...you may arrange to meet classmates there at any time, if you are into that "study group" sort of thing. 

Text: A Radical Approach to Real Analysis, 2nd ed.  David Bressoud

Software: Mathematica  visit here and scroll down to "student personally owned machines"  in order to download a copy on your computer.

Course information, including this page: http://educ.jmu.edu/~carothdc/math510summer23/

 Grading:  Grading will be based on the assignments listed at 

http://educ.jmu.edu/~carothdc/math510summer23/assignments 

as well as the video "quizzes" which will count as one additional assignment.  Note that "points" are assigned to individual problems, so that assignments have varying values.

The table below is a rough outline. The assignments associated with each entry are at the link above.

Begin on or before:	Topics	Text sections
May 22	Historical background, a little Mathematica and Wolfram Alpha practice	Chapter 1
May 24	Convergent series, Geometric. etc.	Chapter 2.1-2.2
May 27	Taylor Series	Chapter 2.3-2.5
May 31	Derivative, Continuity, MVT	Chapter 3.1-3-3
June 3	Derivative, Continuity, MVT	Chapter 3.2-3.4
June 7	Continuity and MVT	Chapter 3.3-3.5
June 10	Convergence Tests	Chapter 4.1-4.2
June 14	Power series, Fourier Series	Chapter 4.3-4.4
June 17	Groupings, Rearrangements, Continuity of Series	Chapter 5.1-5.2
June 21	Differentiation, Integration of Series, Uniform convergence	Chapter 5.3-5.4
June 24	Finishing ideas?	Chapter 6?

 

Academic Honesty: Strict adherence to the JMU Honor Code is expected. Further information may be found at www.jmu.edu/honor

Goals of the Course

1.  Students will understand the theoretical underpinning of calculus and real analysis.

2.   Students will develop skill in modeling, problem solving, and proof. 

3.  Student will learn about the historical development and motivation for fundamental notions such as function, convergence, and the real number system. 

 

 Additional  university  information:  

 www.jmu.edu/syllabus

 

 

Catalog

MATH 510. Modern Analysis 3 credits. 

Applications of concepts such as limits, continuity, differentiation and integration. May be taken for graduate credit and for certificate renewal by secondary school teachers.