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FOUNDATIONS OF REAL ANALYSIS
(MATH 6101-090, Fall 2004)

Instructor: Gábor Hetyei
Office: Fretwell 335F, Phone: 867-2543, E-mail: ghetyei@uncc.edu
Office hours: M 4:00-5:00pm, WF 2:00-3:00 pm, or by appointment.
Text:
  1. Foundations of Analysis by Edmund Landau, third Ed., American Mathematical Society, AMS Chelsea Publishing Series, 1966.
  2. Elementary Analysis, The Theory of Calculus by Kenneth A. Ross, first Ed., Springer Verlag, Undergraduate Texts in Mathematics, 1980. (We will keep using this book in MATH 6102 in Spring 2005.)
Prerequisite: MATH 6100 with a grade of C or better or consent of the department.
Topics:
From your notes during the first lecture and handouts:
Set theory.
From Landau's book:
  1. Natural Numbers (1.1 Axioms; 1.2 Addition; 1.3 Ordering; 1.4 Multiplication)
  2. Fractions (2.1 Definition and equivalence; 2.2 Ordering; 2.3 Addition; 2.4 Multiplication; 2.5 Rational numbers and integers)
  3. Cuts (3.1 Definition; 3.2 Ordering; 3.3 Addition; 3.4 Multiplication; 3.5 Rational cuts and integral cuts)
  4. Real Numbers: (4.1 Definition; 4.2 Ordering; 4.3 Addition; 4.4 Multiplication; 4.5 Dedekind's fundamental theorem)
From Ross' book:
1. Introduction; 2. Sequences.
Test dates:
Midterm: Monday October 18, 6:00-7:20 pm.
Final Exam: Monday December 13 2004, 7:00 pm - 10:00 pm
(Double-check in the UNCC Exam schedule !)
The final exam will be cumulative, consisting of two parts. The first part will be mandatory, covering only material taught after the midterm. The second half will contain questions reviewing the material taught before the midterm. This part will be optional, if left unanswered, I will substitute your midterm score.
Homework: Homework will be assigned every week, some to be turned in in writing, most will be presented by a randomly selected student in class. Since we meet only once per week, you should be planning on attending all lectures. If you are unable to come to a class you have to turn in all homework assigned for oral presentation on that day. I will make an effort to regularly post the homework on the webpage
http://www.math.uncc.edu/~ghetyei/courses/6101/hw.html.
In case of discrepancy, what I said in class is "official".
Evaluation: Grades will be based on: 34% for the homework, 33% for the midterm, and 33% for the final (22% for the mandatory part, 11% for the optional part).
Class meeting: M 6:00-8:50 pm in Gymns 232.
Homepage: http://www.math.uncc.edu/~ghetyei/courses/6101/index.html