Introduction to Real Variables – Math 4341

Syllabus for Spring 2007

Professor:  Dr. Jennifer McLoud

Office:  HPR 109

Phone:  903-565-5625

Email:  jmcloud@uttyler.edu  

Webpage:   http://math.uttyler.edu/jmcloud  

Office Hours:

I will be in my office from 10:00-10:50 MWF and 11:00-11:50 TR barring an emergency.  I have an open door policy with my students.  That is, if my door is open, then come on in and if it is closed, then I am probably busy so check back later.  Mornings are best to meet with me if I am not in class.  Afternoons will be used for my personal research time, however, appointments can be made if you are not able to make it to my regular office hours, just let me know.

Prerequisites:  Math 3345

Text: An Introduction to Analysis (Third Edition) by William R. Wade

Course Material:  The following is a detailed list of the topics that will be covered this semester.

            Chapter 5:  Integrability on R

5.1  Riemann integral

5.2  Riemann sums

5.3 Fundamental Theorem of Calculus

5.4 Improper Riemann integration

Chapter 6:  Infinite Series of Real Numbers

6.1  Introduction

6.2 Series with nonnegative terms

6.3 Absolute convergence

6.4 Alternating series

Chapter 7:  Infinite Series of Functions

7.1  Uniform convergence of sequences

7.2 Uniform convergence of series

7.3 Power series

7.4 Analytic functions

Chapter 8:  Euclidean Spaces

8.1  Algebraic structure

8.2 Planes and linear transformations

Chapter 10:  Metric Spaces

10.1  Introduction

10.2  Limits of functions

10.3  Interior, closure, and boundary

10.4  Compact sets

10.5  Connected sets

10.6  Continuous functions

Important Dates:

Monday, March 12 thru Friday, March 16 – Spring Break

Thursday, March 29 – Last Day to Drop with an Automatic “W”

Friday, May 11  – Comprehensive Final Exam

Blackboard Setup: 

This semester almost all of your grades, assignments, and handouts will be posted on Blackboard.  You will need to enroll in this course on your blackboard account.  Go to the UT Tyler website, click on the Blackboard link (at the bottom of the page), and then follow the instructions.  If you have a difficult time, then come to my office and I will make sure that you get into the system.

Evaluation:

· Homework (20% of grade) –  Homework will be taken up on a daily basis.  You are encouraged to share ideas on your homework through conversations but word-for-word copying is strictly prohibited.  The bulk of learning in a proofs course comes from the work done on homework assignments.  I warn you to not come too dependent on classmates’ ideas and hints as this can harm you when it comes time for the tests.

· Exams (50% of grade) –  There will be two in-class exams.  Exams will be announced at least one week in advance.  Tentative exam dates are Wednesday, October 4 and Wednesday, November 15.

· Final Exam (30% of grade) -- The comprehensive final exam will be held on Friday, May 11 from 8 a.m. -10 a.m.  

Make-ups:  If you know that you will be absent, then turn in your homework assignment early.  Otherwise a homework assignment turned in before the next class time will be given half credit.  After the next class period you will receive a zero.  Athletes and other students involved in extensive university activities should schedule a meeting in my office during the first two weeks of class to discuss this further.

ADA Compliance: 

If you have a disability, including a learning disability, for which you request disability support services/accommodation, please contact Ida MacDonald in the Disability Support Services office so that the appropriate arrangements may be made.  In accordance with federal law, a student requesting disability support services/accommodation must provide documentation of his/her disability to the Disability Support Services counselor.  For more information, call or visit the Student Services Office located in the University Center, Room 282.  The telephone number is 566-7079 (TDD 565-5579).

Social Security Statement: 

It is the policy of The University of Texas at Tyler to protect the confidential nature of social security numbers.  The University has changed its computer programming so that all students have an identification number.

Note Regarding Student Absence Due to Religious Observance:

Students who anticipate being absent from class due to a religious observance are requested to inform the instructor by the second class meeting of such absences.

Grade Replacement:

If you are repeating this course for a grade replacement, you must file an intent to receive grade forgiveness with the registrar by the 12^th day of class.  Failure to file an intent to use grade forgiveness will result in both the original and repeated grade being used to calculate your overall grade point average.  A student will receive grade forgiveness (grade replacement) for only three (undergraduate student) or two (graduate student) course repeats during his/her career at UT Tyler.  (2006-2008 Catalog, p. 35)