SUNY Geneseo Department of Mathematics
Monday, January 28
Math 239 01
Spring 2019
Prof. Doug Baldwin
An annual event organized by the math department to give students a taste of doing mathematical research.
This year’s is next weekend (Feb. 1 - 2).
Leader: Dr. Elizabeth Cherry, RIT
Subject: Modeling the dynamics of the heart
Schedule:
If you want to participate in the weekend, apply through the department web site (www.geneseo.edu/math). Deadline to apply is Wednesday, Jan. 30. You need to have completed Math 230 and Math 233.
Anyone can go to the colloquium Friday afternoon.
I’ll give you up to 2 problem set points of extra credit if you go to the colloquium and write a paragraph or so about connections you make to the talk (e.g., ways you see it connecting to courses you have taken or are taking, ways it connects to your interests, other personal connections, etc.)
Would a demonstration of how to make appointments with it be helpful? Yes; said demonstration was given.
Also see CIT’s video tutorial on using Google calendar:
Part of section 1.1.
True or false: if 1/2 is an integer, then pink elephants are dancing on the table in our classroom.
This is true, because its hypothesis is false. Note that it does not mean that pink elephants are really dancing anywhere.
Give an example (not from the book) of a true conditional whose hypothesis and conclusion are both true: if 1 is a whole number, then 1 is an integer
Give an example (not from the book) of a true conditional whose hypothesis is true and whose conclusion is false: there’s no such thing! This (true hypothesis, false conclusion) is the one case in which a conditional is false.
Many, if not all, theorems can be posed as conditionals.
For example, “the set of rational numbers is closed under addition.” Some ideas about what this becomes as a conditional...
The second of these is particularly helpful for starting a proof, because it gives you some things to start with (2 rational numbers, named x and y), and a concrete thing to conclude (x+y is rational).
What is the only thing you need to show in order to prove this (i.e., in order to show that it is a true statement)? That x + y is rational whenever x and y are.
In other words, assume the hypothesis (i.e., x and y are rational), then show through logic, algebra, etc. that the conclusion is true (i.e., x + y is rational).
(That you only have this one thing to show is a very convenient consequence of the strange definition of truth of conditionals with false hypotheses.)
Do it:
Since we’re on the subject of proofs, we might as well start talking formally about them.
Read section 1.2.