Real Analysis I
Grades of C or better in MATH 228 and MATH 301.
Text and Materials:
Basic Elements of Real Analysis
by Murray H. Protter, Springer ISBN 0-387-
Supplementary Notes by the instructor, posted on iLearn
This course provides the foundations for and rigorous treatment of the
topics found in a first semester calculus course: an axiomatic development of the real
number system, limits of sequences, cluster points, limist superior inferior, the Bolzano-
Weierstrass Theorem, limits of functions, continuity, uniform continuity, differentiability,
the Intermediate Value Theorem, the Mean Value Theorem, L'Hôpital's Rule, the Inverse
Function Theorem, and the Riemann integral.
Students should learn the principal elementary concepts, definitions,
and theorems of single variable real analysis. They should also master a body of
illustrative examples. Competency will be demonstrated by being able to investigate
specific examples as well as general questions. Solutions to questions usually involve the
citation of appropriate theorems, construction of counter-examples, or proofs written in
correct mathematical English.
To a large extent, this course is about organizing and
writing cogent proofs and solutions.
There will be reading, weekly homework assignments, a midterm exam and a
final exam. Homework counts 40%, the exams count 30% each.