SYLLABUS
FOR MATHEMATICS 117: SUMMER 2013
MTuWTh 12:30-1:35, Girvetz 2108
Professor: John Douglas Moore, MTuW 1:45 or by
appointment, SH6714
Email: moore @ math.ucsb.edu
Web page: http://math.ucsb.edu/~moore/117Syllabus2013.htm
Text: Lay, Analysis,
Pearson Prentice-Hall, 2005
Tentative Grading Policy: Final 45%, Midterm 30%, quizzes 15%, homework
10%
Outline
of course:
The purpose of this course is to develop
techniques for proving theorems about the functions one encounters in
calculus. The course will be mostly
based upon Chapters 3-5 of the text. It is an introduction to real analysis which is treated in
more detail in Mathematics 118ABC.
A prerequisite for this course is Math 8, which
introduces the basic ideas of mathematical proof, and the theory of sets and
functions. Mathematical proof is
reviewed in Chapter 1 of the text, while set theory is reviewed in Chapter
2. We will give a brief review of
set theory and functions during the first week of the course.
Homework:
Homework will usually be assigned on Tuesdays and Thursdays.
Quizzes: Several
practice quizzes and pop quizzes may be given at various times throughout the session.
Monday August 5: Notation of set theory and
functions (Sections 5-7 in text)
Tuesday, August 6: Cardinality (8)
Wednesday, August 7: Induction, ordered fields I (10,11)
Thursday, August 8: Induction, ordered fields I
(10,11)
Monday August 11: Completeness (12)
Tuesday, August 12: Topology of the real numbers
(13)
Wednesday, August 13: Compactness I (14)
Thursday, August 14: Compactness II (14)
Monday August 19: Metric spaces (15)
Tuseday, August 20 Convergence of sequences I (16)
Wednesday, August 21: Convergence of sequences II (16)
Thursday, Autust 22: Midterm
Monday August 26: Limit theorems (17)
Tuseday, August 27: Monotone sequences (18)
Wednseday, August 28: Subsequences I (19)
Thursday, August 29: Subsequences II (19)
Monday September 2: Limits of functions (20)
Tuesday, September 3: Continuous functions I (21)
Wednesday, September 4: Continuous functions II
(21)
Thursday, September 5: Properties of continuous
functions (22)
Monday September 9: Uniform continuity (23)
Tuesday, September 10: Continuity in metric spaces
I (24)
Wednesday, September 11: Continuity in metric
spaces II (24)
Thursday, September 12: FINAL