MATH 2080 Introduction to Real Analysis F18

Office hours this term:  Tuesday 2:30 - 4:20, Wednesday 9:30 - 10:20 or by appointment  (NOTE: not applicable during exam period, see below)
e-mail:  eric_schippers@umanitoba.ca
office: 528 Machray Hall

Math Help Centre: 412 Machray Hall

General Information

syllabus (MUST READ)
Resources for Students (scheduleA)

Final Exam Information

Date, Time, and Location  (the location sometimes changes; please check again before the exam).
Office hours during exam period:  Thursday, Dec 13th 12:30 - 3:00 pm and Friday, Dec 14th 1:30 - 4:30 pm.  

FAQ

Q. Will the exam be cumulative?
A.  Yes.

Q. Will the exam emphasize material not covered on the midterm?
A.  Yes.  There will be a few questions from material covered on the midterm, but more on material since the midterm.

Q.  What topics am I responsible for?
A.  You're responsible for all sections listed under "suggested exercises" below (however, see the next question).

Q.  You didn't cover X in class.  Am I responsible for it?
A.   There were a few topics which I did not cover.  A complete list is below under "exceptions".  If it's on that list, you don't need to worry about it.  Otherwise you do.  

Q.  How should I study?
A.  Read the text.  Look over examples in the text and ones which I gave in class.  Solve suggested exercises.  Read the printed solutions to the assignments and midterm.

Material covered on final exam:

You are responsible for all sections listed below under "suggested exercises", as well as prerequisite material.  Section 5.4 is not on the final exam. 

Exceptions:

There are a few topics in these sections which you are NOT responsible for:

Section 2.5, Binary and decimal representations, periodic decimals, Cantor's second proof. 

Section 3.3  Euler's number.  

Section 3.4  Existence of monotone subsequences.  limit superior and limit inferior.  You ARE responsible for the Bolzano-Weierstrass theorem. 

Section 3.5 Contractive sequences (starting at the bottom of page 88). 

Midterm Information

date and time: Wednesday, October 31st, 5:45 to 7:00 pm
location: 204 Armes

The midterm will cover material up to and including Section 3.2.  

Assignments

Assignment 1
Assignment 2
Assignment 3 (please note: there is a typo on the printed version, which is corrected in the linked pdf file.  In the definition of the sequence in Question 2, it should read n >= 1, not n >= 2.)
Assignment 4 (please note: there is a mistake on the printed version.  In question 5, the limit should be 11/8, not 7/8.)

Tips

Worked Examples of Direct and Inverse Images
Worked Example of Solving an Inequality
Worked Example: Finding a Bound Using Triangle Inequality

Suggested Problems

Section 1.1   (review) all
Section 1.3   (review) all
Section 2.1   1 - 15, 16 - 21.
Section 2.2   1 - 17, 18 (b).
Section 2.3    all
Section 2.4    all
Section 2.5   1-11
Section 3.1    all
Section 3.2   1 - 14, 16, 17, 21.  
Section 3.3   1 - 5, 8, 9, 11, 12.
Section 3.4   1 - 4, 7 - 12, 15, 16, 18, 19 (note: 17, 18, and 19 are on lim sup and lim inf, which we have not yet covered).
Section 3.5   1 - 5, 7 - 9.
Section 4.1   all
Section 4.2   1 - 11, 13, 14.  
Section 5.1   1 - 5, 7 - 13.  
Section 5.2   1 - 3, 5, 7, 8, 10, 12.  
Section 5.3   1 - 4, 5 (just the first part: show existence of two roots), 6, 7 (just the first part: not the bisection method), 11, 15.