June 9, 2016
The final exam and solutions are in the exam archive.
The archived version has two minor changes from the one given.
In problem 1(b), I removed the condition that the sets were families. It had no effect on the problem.
Also, I changed the "3" in problem 4 to a "6", as this makes the problem very slightly more interesting for future practice.
June 9, 2016
A histogram of final exam scores.
June 4, 2016
A histogram of homework 7 scores.
June 3, 2016
To study for the final exam, I recommend that you work problems on the final exams in my exam archive.
All old final problema are worth doing, except #2(b) from Spring 2013 B, #7 on Winter 2013, and #6 from Spring 2012.
May 28, 2016
A histogram of homework 6 scores.
May 21, 2016
A histogram of midterm 2 scores. The maximum possible score was 40.
May 16, 2016
Here are solutions to the practice problems for exam 2.
May 15, 2016
A histogram of homework 5 scores (the one zero score was for one student who did not turn the homework in).
May 13, 2016
Here is a set of practice problems for the second midterm. Note that problem 4 involves function composition, which will not be on the exam, but it is a good problem for practicing working with functions anyway.
I'll post answers/solutions some time on Monday.
May 10, 2016
A histogram of homework 4 scores (all the zeros were from people who did not turn the homework in).
May 1, 2016
A histogram of homework 3 scores (all the zeros were from people who did not turn the homework in).
April 27, 2016
Midterm 1 answers are posted in the exam archive.
Midterm 1 stats: low=9=; median=25; max=39 (out of 40).
Here is a histogram of scores from the first midterm exam.
April 18, 2016
Here are solutions to the review problems.
April 15, 2016
Here is a set of review problems for the first midterm exam.
Work on these, and bring questions to class on Monday.
Also, the first three problems on the first exam from Spring 2015 (in the Exam Archive, link at right) are worth doing. You can do the other two problems, too, but I won't ask you anything about power sets on this exam.
I will post answers to the review problems on Monday after class.
April 12, 2016
Here is a useful theorem regarding divisibility. Feel free to use this result as needed.
Also, note how contradiction is used to prove statements within the proof.
April 11, 2016
Some comments on homework.
- Suppose versus If. Very often, we wish to set some condition on a variable x. For instance, we may want to treat a case where x is positive, and other case when it is not. To start such a case, you should write a sentence: "Suppose x>0." This is better than saying "If x>0, then .... " because the "If" condition only applies for that one sentence. If you need several sentences of argument for the x>0 case, then you must use "Suppose x>0." to start it off.
-
Since. A statement of the form "Since X." is not a sentence. In fact, it is not
even a statement! Whenever you use the word "since" to give a justification, it must be used
in sentences of the form "Since X, Y", or "Y since X". Note that "since" takes no "then":
we say "Since I am hungry, I will eat.", not "Since I am hungry, then I will eat".
The common form "Since X, Y" means that Y is true because X is true: Y is the justification for X, (or Y imples X).
Also, if you have several components in a "since" phrase, you MUST use an "and".
For example, consider the sentence "Since x>0,y>0,x+y>0." Without an "and" this is ambiguous. Do we mean x>0 implies y>0 and x+y>0, or do we mean x>0 and y>0, and these two imply x+y>0? These are quite different statements, so be sure to use "and" to make it clear. Either "Since x>0, y>0 and x+y>0" or "Since x>0 and y>0, x+y>0".
- Please try to keep you proofs on a single page. This may require starting new pages for each theorem: that is perfectly okay. This will help you see your proofs in their entirety more easily. We will rarely have proofs that take more than one page.
April 10, 2016
A histogram of the scores from Homework #1.
March 25, 2016
Welcome to Math 300 C, Spring Quarter 2016.
The course discussion board is availble (link at right). Please take advantage of it to ask questions about homework problems or course topics. You might also use it as a way to arrange study groups. I will get immediate emails when posts are added to the board, so this is as good a way to contact me as email, but allows everyone to see my response.
Be sure to read the Homework Guidelines pdf before you start thinking about writing up the first homework assignment.
The first homework assignment will be posted soon.
In weeks when homework is due, we will meet on Thursdays from 5:30 to about 7:30 PM in PDL C-401 to discuss the homework. This is optional, but highly encouraged, and you may come for all or part of the time.