MATH 6131-001: Introduction to Real Analysis
Fall 1996, University of Colorado at Denver
PREREQUISITES: MATH 4320 (Advanced Calculus II) or MATH
5070 (Applied Analysis). Students are assumed to be comfortable with
the concepts of proof, real numbers, and elementary point-set topology.
HOURS AND LOCATION: TR 4:00-5:15 pm, TE 110
INSTRUCTOR: Jan Mandel
Office: CU Bldg 620K. Phone: 556-4475
Office hours: Tuesday and Thursday 2:15-3:45
WWW:
http://www-math.cudenver.edu/~jmandel
Email: jmandel@math.cudenver.edu
TEXTBOOK:
H.L. Royden, REAL ANALYSIS, Macmillan, 1988
FORMAT:
Lectures and problem solution
CONTENTS:
- Ch. 1: Set theory (quick review)
- Ch. 2: Real number system (independent reading, except 2.7 - Borel sets
in class)
- Ch. 3: Lebesgue measure
- Ch. 4: The Lebesgue integral
- Ch. 5: Differentiation and Integration
- Ch. 6: Classical Banach spaces
- If time allows: Ch. 7 Metric spaces (review), Ch. 8 Topological spaces
(Sec. 1-5 only), maybe even selected parts from Ch. 10 Banach spaces, esp.
topological vector spaces
HOMEWORKS: Homeworks will require a substantial effort. There will be
about 5 throughout the semester.
GRADING: Homeworks: 1/3, Test 1 (take-home): 1/3, Test 2 (in class,
DEcember 17): 1/3. System: A=4 points=100% all fine, B=3 points=75% some
minor problem, C=2 points=50% still a substantial progress.