This is a course in the theory of calculus with a radically different style from the 100-300 level calculus courses. The emphasis is on proving theorems, not on calculation techniques or applications of calculus to other quantitative disciplines. The homework and exams will be heavily slanted toward providing proofs of various statements with very few "routine calculation" problems. It's not assumed that students have had prior experience with devising proofs. To the contrary, one of the goals of the course is to help students develop proof skills. Although the lectures will try to provide examples illustrating various theoretical ideas, the bulk of class time will be the proverbial repitition of definition, theorem statement, proof, next definition, statement, proof,...
Time and Place: Tuesday, Thursday, 10:00-11:30 a.m., in Room 215, Cupples I
Instructor: Edward
N. Wilson
Office: Cupples I, Room 18 (in the basement)
Tentative Office Hours: MWF 1:00-2:00 and by appointment
Office Tel: 935-6729 (has voice-mail)
E-mail: enwilson@math.wustl.edu
Prerequisites: Math 233 is a hard and fast requirement. Math 309 is very strongly advisable as is some prior exposure to theoretical ideas in mathematics (outside reading, freshman seminar, Math 310,...)
Textbook: Introduction to Analysis, Maxwell Rosenlicht, Dover paperback edition, 1968.
Topic Outline: We'll
go through Rosenlicht's book fairly sytematically, i.e., without much hopping
around from one chapter to a later chapter. The hope will be to get
through essentially the entire book (248 pages) by the end of the semester.
When we get to the later chapters, we'll use linear algebra notation rather
than Rosenlicht's contorted notations avoiding linear algebra. This
is the place where prior experience with matrix algebra will be especially
important.
Exams/Homework: There will be an in-class exam at the end of September, either an in-class exam or a take-home exam in early November, and a take-home final exam during finals week. There will usually be a homework assignment to be handed in each week.
Grading: Final
averages will be determined by the following formula:
Final average = .25E1 + .25E2 + .30FinE +.2HW
Thus, each of the mid-semester
exams will be 25% of the final average, the final exam 30%, and homework
20%. That said, a different formula giving the final exam higher
weight will be used for those who do poorly on either of the mid-semester
exams, work hard on homework, and show improvement on the final.
Also, the process of converting final averages to letter grades won't,
from a student's point of view, be any worse than the traditional 90-100
A, 80-90 B, 70-80 C scale but might well be better, i.e., more generous.
Academic Integrity:
As
with all Washington University courses, cheating on exams will be
taken very seriously
with evidence supporting a cheating allegation forwarded to the Arts
and Sciences Integrity
Committee for adjudication. When the Committee concludes that a
student cheated on an
exam, it normally directs the instructor to assign the student a
failing grade for the
course.
Cheating on homework consists of either blindly copying off someone else's
solutions
or not acknowledging
the receipt of assistance from others in completing the assignment.
It's not anticipated
that students will work in isolation on homework problems. To the
contrary, discussing
problems with others is often a way to avoid frustration and gain
useful insight. However,
all students are expected to write up their own assignments and
to indicate in a short
note at the top of the first page the names of any people (other
than the instructor)
with whom they discussed the problems or from whom they received some
hints. Violation
of these requests will result in an instructor-imposed penalty (e.g.,
something like half
credit for the assignment) but won't be treated as a "hanging"
offense--in particular,
won't be brought to the attention of the Arts and Sciences
Integrity Committee.