MATHEMATICS 501-Fall, 2009

Real Analysis

Carver 2  (basement)

Instructor: Howard A. Levine , Department of Mathematics, 410 Carver

Office Hours: MWF 9:30-10:50  or by appointment

Phone 515-294-8145, e-mail: halevine@iastate.edu

Textbook:  Principles of Real Analysis by Walter Rudin

Suggested alternate reading (in no particular order)

Manfred Stoll,  Real Analysis
Russel l A. Gordon,   Real Analysis,  A First Course
William R. Wade,  An introduction to Analysis
Robert Bartle and Donald Sherbert,  Introduction to Real  Analysis

Grading: Homework: 40%, Midterm 20% and Final: 40%

The grade will be determined from, homework, (200 pts.) the mid term, (100 pts.) and the in class final (200 pts.) . (There will be seven such assignments each consisting of roughly ten problems.)   Problems will be of varying difficulty and will be weighted accordingly and scaled to 200 pts at the end of term (40% of the grade).   You may consult with your fellow students  but the solutions you turn in must be written in your own words!

NOTE:  The homework problems will generally be a subset of those problems found at the end of each chapter in the text.   A  subset of the problems from each set will be graded.  

While I do not require the homework to be typed up in tex or some other text editing program, I do expect them to legible and written in clear English, otherwise I will penalize you 25% .

Course Lectures:   I will follow the textbook, but not slavishly.   You are expected to read and understand the material  and fill in the gaps that I will sometimes (deliberately) leave in the proofs I give in class or that the text omits.

Syllabus:

1. Chapter 1, Real and Complex Number Systems, all sections and the appendix.
2. Chapter 2,  Basic Topology,  all sections
3. Chapter 3,  Numerical Sequences and Series,  all sections.
4. Chapter 4,  Continuity, all sections.
5. Chapter 5,   Differentiation,  all sections.
6. Chapter 6,  The Riemann-Stieljes Integral  all sections.
7. Chapter 7,   Sequences and Series of  Functions,  all sections.


Homework problem sets are given below. . Due dates for each set are at the top of each page.  Late homeworks carry a 20% penalty.

Problem sets will be added to the list from time to time. Check back frequently.


Problem Set I,  Page 22 of text :  2, 3, 5, 6, 7, 8 , 13,  16, 19
    Also show that the set of rational numbers  whose cube is smaller than 3, defines a  Dedikind cut.  
Set I is due on September 7, 2009.

Problem Set II.  Page 43 of text: 1, 2, 6,7, 8, 11, 12, 17, 21, 23,.   Set II is due on  September 25, 2009.

Problem Set III.  Page 78 of  text.  3, 4, 6, 7,  8, 9, 10,  11,  12.   Set  III is due on  October 14,  2009

Problem  Set IV  Page  80  of  text.   13, 14 (a-d only) 16, 17, 18, 23    Set IV is due on October 23, 2009

Problem  Set V  Page  98 of  text.  3,  4, 6, 7, 8, 14,  18, 20, 21, 23.   Set V is due on  November 4, 2009

Problem Set VI  Page  114 of text .  2, 6, 8,  9, 11, 13, 14,  15,  25,  Set VI is due on November 16, 2009

Problem Set VII  Page  138  of text. 3, 4, 5,  ,6,   8,  9,  10,  13, 15     Set VII  is due on November 30, 2009

Problem Set VIII  Page  165 of text . 2,  3,  4,   6,  7,  9,  11,  15, 16, 18   Set VIII is due on December 11, 2009


MIDTERM EXAMINATION INFORMATION:


Midterm examination will be on  October 19.  It will cover the material from Chapter 1 through  Chapter 3 (except as noted in a recent e-mail).
 

FINAL EXAMINATION INFORMATION:

The Final exam will be based on Chapters 4-7.
Carver   2WednesdayDec. 169:45 a.m. - 11:45pm