MATH 314 004 (70827) Assignment Page -- Fall 2006

Rev1 has Gone Live
Posted: Sun Sep 17 20:16:52 MDT 2006

Clicking the Rev1 button in the link strip above will whisk you off to an evolving list of review problems and suggestions for preparations for Test #1, Friday, 9/29/06.

Assignment #6 (Due Friday, 9/22/06)
Posted: Mon Sep 18 10:41:57 MDT 2006
Comment added at very end: Mon Sep 18 11:31:01 MDT 2006

• 4.8
  1. As before, write so as to show readers that you know the definitions of the items in play. This needs a little art: don't just copy a definition into your submission, rather, cite it at the point of your argument where it becomes relevant.
  2. Angela knows: if you write a proof by contradiction, bring it to a fine point (last week we had a > a, for instance). Maybe disengage from your solution writing for several hours (or days), then return to it and see if you can't improve or sharpen things.
  3. Part (a) says to "Observe" something. This means you need to write brief prose as to why the "Observed" assertion is true.
  4. For part (b), do not assume any more than the given hypotheses. Do not, for instance, assume that sets S and T are finite. Do not assume that max(S) exists. Do not assume that min(T) exists.
  5. Problem 4.8 probably doesn't require the density of the rationals in the reals...
• A formal rising-chain proof for the limit of the sequnce in 7.3(s).
  1. Keep the scratch-paper aspect of this work out of my sight.
  2. Annotate each step.
  3. Click here for a rising-chain example.
  4. As of Monday, 9/18/06, we have proved theorems (such as lemma 9.5, for instance) that obviate the basic-definition "epsilon-N" proof. But this assignment is to go directly from the basic definition.

Assignment #5 (Due Friday, 9/15/06)
Posted: Thu Sep 7 17:01:03 MDT 2006

• 4.6, 4.7 (write so's the reader can tell you know sup and inf definitions)
• 7.5 (Hint: check out the ancient algebra tricks in example 5, section 8)
• 8.1 (Formal proof, preferably using annotated rising chains. As in PMI proofs, we are trying to prove an implication, so we must be wary of the Circ Police.)

Assignment #4 (Due Friday, 9/8/06)
Posted: Thu Sep 7 10:14:51 MDT 2006

From the end of class on Wednesday: write up the following in such a manner as to avoid the attention of the Circular-Reasoning Police.

• Write a formal Mathematical-Induction proof that

  ∀ n ((n is a natural number ≥ 10) ⇒ 2ⁿ > n³).

• 3.8, the problem we started in class.

Scholarship??
Posted: Wed Aug 30 06:16:50 MDT 2006

Check in with Dr Margaret Kinzel (kinzelATmathDOTboisestateDOTedu) if the following part of her grant project might apply to YOU:

The grant will award scholarships to math, science, or engineering students who elect to go into education. Essentially, the grant will pay $10,000 a year for the final two years of school, with the obligation that the student teach in a high need district for 2 years for each year the scholarship was awarded. There is a graduate component that will start summer 2007: graduate students working towards initial teaching certification may receive the award for one year (with the 2-year teaching obligation).

Assignment #3 (Due Friday, 9/1/06)
Posted: Mon Aug 28 10:42:31 MDT 2006

• Show steps in computing the greatest common divisor of 5280 and 1812. As a by-product of this computation, find the integers x and y such that

  5280x + 1812y = GCD(5280, 1812).

  The Maple igcd command might be of help.
• 1.9
• 2.6
• 3.3
• 3.6

Stuff may be added. Yeah, right.

Assignment #2 (Due Wednesday, 8/23/06)
Posted: Mon Aug 21 15:01:00 MDT 2006

Complete the web-site quiz handed out in class on Monday, 8/21.

Click here if you need a copy.

Assignment #1 (Due Friday, 8/25/06)
Posted: Mon Aug 21 11:20:55 MDT 2006

• 1.7, 1.8 (write up nice PMI proofs)
• More problems to be announced.

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