PREREQUISITE:
MATH 4320: ADVANCED CALCULUS II
HOURS: MW 6:55-8:10 pm (SO 102)
INSTRUCTOR:
Prof. Andrew Knyazev
Office: CU (Dravo Bldg) 620G. Phone: 556-8102.
Office hours: Tue 3pm - 6pm, or by appointment
WWW:
http://www-math.cudenver.edu/~aknyazev
TEXTBOOK:
Elementary Real and Complex Analysis, G.E. Shilov,
revised English edition translated from Russian and edited by R. A. Silverman,
Dover Publications, INC., New York $12.95
From the Dover's introduction:
"... the present work is specially designed for undergraduates
in mathematics, science and engineering. A high level of
mathematical sophistication is not required."
From the author's preface:
"... the reader of my course is invited to climb with me
from the foothills of elementary topics to successive levels
of abstraction and then look down from above on the various valleys which now come into his field of view.
Perhaps this approach is thornier, but in any event the mathematical
traveler will thereby acquire the training needed for furver exploration
on his own."
This testbook has been never used in CU-Denver before. I hope students will like the book as much as I do.
SUBJECT:
Introduction to real analysis, fundamentals of logic and
theorem prooving.
The course will not require any knowledge in math, all the theory will be built from a scratch. Instead, some abstract thinking is necessary. Students are assumed to be able to reason logically and to be ready to prove, based on definite axioms, many statements which seem to be obvious from a practical point of view.
CONTENTS:
The class will follow the outline below, touching on each major
topic in a depth that will be determined by the pace of the class.