MA 3260 Lecture 02 - Ands, Ors, and Nots
Thursday, August 30, 2012.
Objectives: Quantiers and other logical operators.
For convenience, well sometimes want to use shorthand symbols to represent statements. For example, we
might have
(1)
P (x) = The intege
MA 3260 Lecture 14 - Multiplication Principle, Combinations, and Permutation
Thursday, November 1, 2012.
Objectives: Basic counting formulas
Heres another way of looking at the fact that a set with n elements has 2n subsets.
If, for example, we have the s
MA 3260 Lecture 13 - Finite Counting Stu
Thursday, October 25, 2012.
Objectives: Basic counting formulas
We spent most of the class going over the Cantor set problem from the Homework. We discussed the
following.
0.9999 . . . = 1
We should occasionally re
MA 3260 Lecture 08 - The Conway Polynomial
Thursday, September 27, 2012.
Objectives: Dene the Conway Polynomial.
1. The Conway Polynomial
We can think of knots as coding information in a geometric manner. Wed like to be able to pull that
information out i
MA 3260 Lecture 10 - Boolean Algebras (cont.)
Thursday, October 4, 2012.
Objectives: Boolean algebras on cfw_ 0, 1 .
Before we move on, I wanted to give you a taste of what the connection between Boolean algebra and
computers might look like.
In simplisti
MA 3260 Lecture 12 - Some Uncountable Stu
Thursday, October 18, 2012.
Objectives: Example of an application of cardinality to continuous stu.
Whenever youre encountering a new concept, I think its a good idea to kind of step over to the other side,
and th
MA 3260 Lecture 09 - Boolean Algebras
Tuesday, October 2, 2012.
Objectives: Introduce binary operations on sets.
You may be familiar with taking the union and intersection of two sets. I would like to point out that union
and intersection are binary opera
MA 3260 Lecture 11 - Set Bigness
Tuesday, October 16, 2012.
Objectives: Introduce measure, probability, and cardinality.
Earlier in the semester, we briey discussed cardinality. Id like to go into this in a bit more detail now. In
particular, I want to lo
MA 3260 Lecture 07 - Binary Operations
Tuesday, September 25, 2012.
Objectives: Continue with binary operations.
Binary Operations
Given a set A, a binary operation is a function from the ordered pairs of elements from A back to A. In
particular, a binary
MA 3260 Lecture 05 - More stu about numbers
Tuesday, September 11, 2012.
Objectives: Investigate basic properties of numbers.
We started talking about linear combinations last time, and given integers a and b, I told you that the
GCD(a, b) is equal to the
MA 3260 Lecture 06 - Clock Arithmetic and Binary Operations
Thursday, September 13, 2012.
Objectives: Introduce binary operations through clock arithmetic.
Quiz 06A
We have a machine that is set to run for x hours, turn itself o for 3 hours, and then rest
MA 3260 Lecture 04 - Stu about numbers
Thursday, September 6, 2012.
Objectives: Investigate basic properties of numbers.
Let me start by naming our basic sets of numbers. In the context of sets, x A will mean that x is an
element of the set A.
Natural/Cou
MA 3260 Lecture 01 - If . . ., then . . . Statements
Tuesday, August 28, 2012.
Objectives: Warm up to thinking about logical statements.
True and False Statements
In some sense, mathematics is a study of statements and whether these statements are true or
MA 3260 Lecture 03 - Little Proofs
Tuesday, September 4, 2012.
Objectives: Proving .
Whats a proof?
Roughly, a proof is a demonstration that a statement is True (or False) based on the assumption that
certain basic statements are True. In other words, a p
MA 3260 Lecture 15 - Fibonacci Sequence
Tuesday, November 13, 2012.
Objectives: Introduce recurrence relations via the Fibonacci sequence.
Heres a problem:
We have this robot soldier that is programmed to build a workstation for itself (this will
take one