Math 425/825 Exam I Policies

When:

Wednesday October 4, 6p.m. to 8p.m.

Where:

Oldfather 304.

What will it cover?

Everything we talked about in class up to the end of Chapter 3 (closed sets is the last section) or the end of class, Friday September 29, whichever comes first.

Format:

There will be five questions, each of which will probably have several parts. These will fall into three camps: quiz-style, homework-style and bookwork. In quiz-style questions I'll be asking you to state definitions and theorems from the book and class notes. Homework-style questions will ask you to solve a new problem. They will be as hard as the easy-to-medium homework questions, or the Analysis Lab questions.

Book-Work:

You will be asked to prove one or two of the following:

1. 
Proposition 2.3	Archimidean Property
2. 
Corollary 2.4	Density of the rationals
3. 
Proposition 2.6	"greatest lower bounds exist"
4. 
Proposition 2.7	"unions of open sets are open"
5. 
Lemma 3.4		"properties of sequences which converge to zero"
6. 
Lemma 3.6		"convergent sequences are bounded"	
7. 
Theorem 3.10		"n-th roots of positive real numbers"
8. Theorem 3.12		Monotone convergence theorem

The aim of this type of question is to give you the opportunity of writing clear, correct mathematical arguments about substantial results. So I encourage you to phrase the arguments in your own words. If possible improve on the wording you got from the notes/WebNotes/Rudin!

Also, feel free to come and show me drafts of alternate wordings of these proofs to get my feedback.

"What should I do to prepare?":

Learn the bookwork that I set above.
Learn all the definitions and statements of theorems. ("Theorems" inlcudes lemmas, propositions and corollaries!) Theorems which have names are (i) really important (that's why they have names) and (ii) really easy to ask in questions (because they have names). Take a look at the index of theorems to see some names.
For the homework-style questions, the best revision you can do is make sure you can do all the homework problems. Of course you have a week to do the homework and only two hours for the exam, so I'll set easier questions, but you'll need the same ideas. Also look at the problems I set in the Analysis Lab, and the solutions that I came up with. Look at the homework solutions and the Analysis Lab solutions.

Go to the home page

Analysis WebNotes by John Lindsay Orr.
Comments to the author: jorr@math.unl.edu

Last modified: June 13, 1995