Mathematics 2283 - Sequences, Series and Foundations



Instructor: W. Messing
Office: 257 Vincent Hall
Telephone: (612) 625-0735
Office Hours:  Monday 12:20 - 1:10, Thursday 1:25 - 2:15 (or by appointment)

Teaching Assistant: M Dobson

Text: Richter, Sequences, Series and Foundations (available at Alpha 
Print in Dinkytown)

The aim of this course is to introduce the student to certain 
theoretical ideas and techniques that underlie the techniques and 
rules that are studied in elementary Calculus.  In principle these 
could and should have been taught during the Calculus course.  Why 
weren't they?  There are two answers to this question.  Firstly other 
disciplines require that one be able to use the techniques of 
Calculus and be formally familiar with the symbolism of Calculus. 
These disciplines have different standards of rigor and different 
views as to what is an adequate conceptual basis than does 
Mathematics.  Consequently the "service course" manner of teaching 
Calculus downplays the theoretical aspects of the subject in order to 
"cover enough material" to placate other departments.  Secondly it is 
a common view, although not shared by your instructor, that the 
theoretical aspects of Calculus are "too difficult" to teach to first 
year University students.  This was not always the case, but the 
steady deterioration in the quality of High School mathematics 
programs has no doubt exacerbated the difficulties that students 
experience at the University level.  In order to minimize this 
"problem" the Calculus course has been "watered down".

Thus this course endeavors to revisit material with which you 
have some familiarity and to put it on a solid conceptual basis.  The 
primary objects studied in Calculus are functions of a real variable. 
To understand these it is necessary to UNDERSTAND what the real 
number system is.  That is one needs to understand the properties of 
numbers.  Only then can one understand functions of numbers.

Course Expectations:  The student is expected to achieve conceptual 
understanding of the real number system and of functions of a real 
variable.  This will be demonstrated by handing in precisely and 
clearly written homework and examination papers.

Homework will be assigned one week before it is due.  Late homework 
will be accepted ONLY if there is a COMPELLING justification.

There will be no make up exams.  Students who miss an exam under 
COMPELLING circumstances will have the remainder of their exams 
weighed more heavily and hence will not be penalized.  Requests for 
permitted absence from an exam should be made PRIOR to the exam (and, 
if possible, long prior to the exam).  Only emergency absences will 
not be penalized if prior notification has not been given.

Examination Schedule: October 2, October 23,  November 20
Final Exam: Thursday, December 18, 8 - 10 AM

Calculators: The use of calculators is permitted even though for 99 % 
of the material discussed in the course they are of no use.

Grades:  Homework 25 %, each of the midterm exams 15 %, Final Exam 30 %

Course Web Site:  The teaching assistant, Mr. Dobson, has generously 
offered to maintain a course web site.  On this site you will find a 
copy of this syllabus, the homework assignments and possibly other 
course related material.