SUNY Geneseo Department of Mathematics
Friday, January 25
Math 239 01
Spring 2019
Prof. Doug Baldwin
Math Olympiad (formally, the 13th University of Rochester Math Olympiad)
A college-level regional math competition
Saturday, February 9
Contact Prof. Towsley for more information or if interested in participating.
Probably the most shockingly weird aspect of how I teach.
Suppose you get a grade of 70% on an exam. Roughly what letter grade is that? It’s a B. See the grades section of the syllabus
Also see the representative grade distribution, based on last time I taught this course.
Which of these are mathematical statements? Why or why not? If they are, are they true or false?
7 + 3 = 10. Statement: you can definitively tell whether it’s true or false (true in this case).
7 + 3 = 11. Statement: you can tell it’s false, but as long as you can make a true vs false determination, it doesn’t matter whether the statement is true or false.
x + 3 = 10. Not a statement: you can’t tell whether it’s true or false without knowing x.
If x and y are real numbers such that x < y, then x+1 < y+1. Statement: The “if” part provides the information you need about the variables, then you can show that it’s always true by algebra.
If x and y are real numbers, then xy > 0. Statement, but false because “if” statements in this form are implicitly about all things described in the “if” (in this case, all real numbers, but not all pairs of reals have products greater than 0).
Some roses are red. Statement: even though “some” is vague as to the exact number, it’s sufficient to tell you that you just need to know if there are one or more red roses. There are, so the statement is true.
This statement is false. Not a statement: this is a paradox that can be neither true nor false.
Fluffy is a rabbit. Not a statement: you need to know what “Fluffy” is, just as you need to know what variables represent in more classically mathy examples.
If today is Saturday, then sleep in. Not a statement: this is a command, not a assertion of fact. But you could make a similar statement, for instance “If today is Saturday, then you may sleep in.”
Today is a beautiful day. Not a statement: this relies on opinion so you can’t “definitively tell” whether it’s true or false.
Wow! Not a statement: it’s an exclamation, with no notion of truth or falsehood.
See handout for details.
Note on turning it in and grading it: those things happen during a face-to-face meeting with me. Nominally meet sometime next Thursday or Friday; in no case later than Friday, but earlier than Thursday if you’re done and want to meet earlier.
The easiest way to schedule the meeting is via Google calendar. This video from CIT shows you how, and I’ll be happy to demonstrate/explain as needed:
Evaluating how much your solution meets my expectations: notice the list of outcomes (things you should be able to do by the time you finish the problem set) in the “Purpose” section of the handout. That’s what I expect. When I grade, I’ll assign up to three “checkmarks” for each outcome:
You meet 3/4, 1/2, etc. of my expectations for the problem set according to what rounded fraction of the possible checkmarks you get. (Notice that exceeding my expectations is separate from this system.)
Conditional (“if-then”) statements.
Context: is the statement “if 1/2 is an integer, then pink elephants are dancing on the table in our classroom” true or false?
Read the rest of section 1.1 in the textbook (i.e., from “Conditional Statements” through the end — that’s more than just conditionals, but the “extra” material will be context for talking about statements and proving them).