math 331
day 5
Math 331 Homework: Day 5
Practice and Reading
Reread Section 1.3 carefully. This section should be more familiar to you than cuts.
Hand In Wednesday: The nal part of the assignment
1. (a) Problem 1.3.5. Just list which of Axioms 111 fail (i
Topics for Test 1
Here is a list of some major topics with which every student in Math 331 should be familiar. The list is not
exhaustive, but if you know all of this material you are well on your way to doing a good job on the exam.
1. a) Denitions: Rati
Math 331 Homework: Day 16
Practice and Reading
1. The next big idea: uniform continuity. Read Section 2.6 carefully. Least upper bounds turn up again in the
intermediate value and max-min theorems. Do the Preparation on the back of the sheet.
2. Practice:
Math 331 Homework: Day 14
Reading and Preparation for Discussion Next Class.
Read Sections 2.3 and 2.4, and look ahead to Section 2.5.
1. a) Assume that g is a bounded function for all x = 0, that is, |g(x)| < B for all x = 0. Prove that
limx0 xg(x) = 0.
Math 331 Homework: For Day 10
Quote of the Day
One magnitude is said to be the limit of another magnitude when the second may approach the
rst within any given magnitude, however small, though the rst magnitude may never exceed
the magnitude it approaches
Math 331: Days 11 and 12
Class and Journal: Working with Limits
Last time we did #1 (a,b). The other easy ones are #2, 3 and 4. Any that we dont nish today we will
work on next time in class. Try at least a few of these before class and be prepared to dis
Math 331 Homework: Day 7
Note of the Day
Bernhard Bolzano: Lived from 1781 to 1848. Bolzano is said to have successfully freed calculus
from the concept of the innitesimal. He also gave examples of one-to-one correspondences
between the elements of an inn
Math 331: Day 9
Read Section 2.1 (including the problems) on functions, which should largely be review. We will not cover
this in class. Read Section 2.2 on limits. Pay particular to Denition 2.2.1 (memorize) and Examples 2.2.16.
Be prepared to discuss th
Math 331: Day 8
Group Work Session Today at 3:00 in Lansing 3:10. Get help on homework!
Classwork and Journal Work
Reread Section 1.4. And begin Section 2.1 which should be very familiar.
1. Determine which of these sets are bounded. Which are bounded abo
Math 331 Homework: Day 1
1. a) Review the syllabus. Make sure your understand how you will be assessed.
b) Read: Chapter 1 pages 115. Key terms in this reading: commensurable and incommensurable, rational
and irrational, and prime. You should be able to d
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Math 331: Day 3
Reading, Practice, and Journal Work
This is material we will be working on today and the next few days.
1. Reread Section 1.2 and review partially ordered sets from Math 135, as needed. H
Math 331 Homework: Day 4
Quote of the Day
For brevity and in order not to weary the reader I suppress the proofs of these theorems which
follow immediately from the denitions of the previous section.
Dedekind
Review Section 1.2. Make sure to memorize the
Math 331 Homework: Day 6
Practice and Reading
Reread Section 1.3 carefully. This section should be more familiar. Look ahead to Section 1.4 which
discusses the Heine-Borel Theorem and the Balzano-Weierstrass Theorem. The names are those of great
mathemati
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Math 331 Homework: Day 2
Quote of the Day
The Greeks reportedly suered some intellectual indigestion when they discovered the irrationality of
square roots, and with good reason: putting the theory of ir
Math 331 Day 15
1
Math 331 Day 15
Reading and Preparation for Discussion Next Class.
Re-read Section 2.4, and look ahead to Section 2.5 on Continuity. For pleasure, keep reading in A Tour of the
Calculus chapters 1214, p. 92128.
Limit Summary. Assume that