Math 3210¤1     Foundations of Analysis I Sept. 1, 2000

MWF 8:35-9:25 in JTB 320
        
Instructor:      A. Treibergs, JWB 224, 581-8350.  
                 E-mail: treiberg@math.utah.edu.  
                 Web page: http://www.math.utah.edu/~treiberg/M3210.html
                 Office Hours: 10:40-11:30 MWF (tent.) & by appt.

Texts:           William R. Wade, An Introduction to Analysis 2nd. Ed.,
                 Prentice Hall, 2000. (Optional supplementary text, 
                 Kenneth A. Ross, Elementary Analysis: The Theory of 
                 Calculus, Springer, 1980.)
Grading

   Homework:     To be assigned weekly. You will be responsible for all 
                 assigned problems. You will be asked to write up and 
                 hand in some of these. Homework that is handed in one 
                 week or less after the due date will receive full 
                 credit. Homework that is more than one week late but 
                 not more than two weeks late will receive 50% of the 
                 credit. Homework that is turned in more than two weeks
                 late will receive no credit.

   Reader:       Inbo Sim, JWB 214, sim@math.utah.edu
                 You may turn late papers into Mr. Sim's mailbox in the
                 math department.               

   Midterms:     There will be three midterm exams on Sept. 20, Oct. 18 
                 and Nov. 15. Questions will be modifications of home-
                 work problems. 

   Final exam:   Fri., Dec. 15, 7:00-9:00am. Half of the final will be 
                 devoted to material covered after the third midterm 
                 exam. The other half will be comprehensive. Students 
                 must take the Ūnal to pass the course. 

   Course grade: Based on the best two of three midterm scores 37%, plus
                 homework 38% plus final 25%. 

   Withdrawals:  Until Oct. 20 you can withdraw from the class with no 
                 approval at all. After that date you must petition your
                 dean's office to be allowed to withdraw.

 ADA:            The Americans with Disability Act requires that reason-
                 able accommodations be provided for students with cog-
                 nitive, systemic, learning and psychiatric disabilities.
                 Please contact me at the beginning of the quarter to 
                 discuss any such accommodations you may require for 
                 this course.




Math 3210¤1     Foundations of Analysis I   Į Syllabus Č  


   Objectives:   There are two objectives for the course. The first is to
                 cover the concepts and theorems fundamental to calculus.
                 The second is to develop the students ability to do 
                 proofs and communicate mathematics rigorously.

   Topics:       Math 3210 shall cover the following chapters of text.

        Chapter 1.      Set theory. Real numbers. Completeness.
        Chapter 2.      Sequences of numbers. Limits. Cauchy sequences.
        Chapter 3.      Continuity, uniform continuity
        Chapter 4.      Differentiability. Mean value theorem. Inverse 
                        function theorem.
        Chapter 6.      Infinite sums. Convergence. Tests of convergence.
        Chapter 7.      Series of functions. Uniform convergence. Power 
                        series.
        Chapter 5.      (If time permits) Riemann integral. Fundamental 
                        theorem of Calculus.