Reading and Homework Assignments MATH110-05

Chapters 3 and 4 on Probability and Statistics follow chapter 1on Permutation, Combinations and Pacsal's Triangle more naturally. I'd prefer to develop the material in Chapter 2 (logic) without interrupting the flow from chapters 1, 3 and 4.

Note: check this page frequently as assignments will change after each class depending on what we cover and the amount of time we need for questions.

At this early stage, I will frequently point to later sections that use what we are doing now. This will give you an idea of where we are going as well as give you some additional material that they may want to look over. For example, section 1.3 serves as an introduction to Statistical Analysis which is cover in Chapter 4 while section 1.4 servers as an introduction to Probability which is covered in Chapter 3.

Read the material before class and try some of the problems at the end of the sections. This will give you some idea of the areas that you need to focus in on in class. Do as many problems as you feel you need to do to understand the material. If you haven't looked over the material ahead of time, it will be hard to follow the class discussion.

After class, look over your notes and reread the sections to clarify any points that you still don't follow.

If there are concepts that you don't understand or questions that I haven't gotten to in class, e-mail me.

Date	Topic	Reading	HW	Comments
9/7	Sample applications: puzzles as solutions to real world problems			Overview of course; Some examples of mathematical modeling: Parking lots at WPU: Euler paths; Survivor and the Prisoner's dilemma problem.
9/12	Problem Solving; Pattern Recognition	Read Chapter 1. 1.1/1.2	Ex: 1.1, 1.2	Going from observations to generalization; Inductive Reasoning. Practical Application: We observe many things that look like they follow a pattern. What we want to do sometimes is to write a formal description of the pattern.
9/14 9/19	Pascal's Triangle; Counting Methods	Read Chapter 1. 1.3/1.4/1.5 (You may also want to glance at Chapter 3 section 1 which covers some of the same ideas as 1.4)	Ex 1.3,1.4,1.5	This section talks about ways in which we can count things. How many way can we do something? How many ways lead to success? What is the probability of success? Section 1.4 is one of the most important sections since it forms the basis of probability. You may want to look at section 3.1 to see where we are going. Practical Applications: How many ways can you pair people up? How many ways can you for committees/teams? Determining the odds in the lottery. Section 1.3 introduces you to Pascal's Triangle and binomial expansion: If you graph Pascal's triangle for a large number, you get the probability curve. This forms the basis for making statistical decisions. This forms the basis of the discussion in chapter 4. Go over HW from sections 1.1 and 1.2 at beginning and/or end of class. Go over questions from section 1.3 and 1.4 and answer questions about the first project in class (Depending on what we cover, I may need to revise the schedule of the next week: check here after Thursday's class.)
9/21	quiz	Read section 3.1	Do ex 3.1	I am having you read section 3.1 after chapter 1 to show you the connection between what we have done in chapter 1 and its relation to probability.
9/26	Presentations of Project 1		PROJECT 1 DUE; Project #1 is question 2 on page 43; You may work in groups up to 3.	You will hand in project 1 and be prepared to make a 5 minute presentation.
9/28	Probability and Conditional Probability	Read sections 3.2-2.3	Do ex 3.2-3.3	This section gives you a way of looking at probabilities when selections are made before sampling. We will look at how wording of statements changes their meaning (see below). Practical use: To solve problems such as "Of the tires on Ford Explorers X% are likely to fail." (contrast this with X% of tires are likely to fail.)
10/3	Expectation	read sections 3.4	Do ex 3.4	This section gives you techniques to evaluate the long term most likely outcome. (This is the same as the mean or average, but looked at in a different way.) Practical use: Calculation of return on investment; Calculating long term effects.
10/5	quiz	Section 4.1	Ex 4.1	This section show how you can apply what you learned in chapter 1 and 2 to probability.
10/10	Presentation of Project 2		PROJECT 2 DUE; Project #2 is any question on p. 111. You may work in groups up to 3.	You will hand in project 1 and be prepared to make a 5 minute presentation.
10/12	Mean, Median and Standard Deviation	Read section 4.2	Do ex 4.2	Practical applications: To determine the average expected outcome and then determine the margin of error and confidence levels: To be able to evaluate a statement such as 47% with a 2% margin of error. One standard deviation from the mean means that 68% of the time, the observations will fall within one standard deviation. Standard deviation also gives us a way to measure risk.
10/17	The normal Curve	Section 4.3	Ex 4.3	Practical applications: determine the relationship between confidence ranges and probability: How far can I deviate from the mean and still be 95% sure of the mean. THIS IS ONE OF THE MOST IMPORTANT CONCEPTS FOR PEOPLE TODAY. IT PROVIDES A WAY TO DETERMINE THE CONFIDENCE WE HAVE IN REPORTED INFORMATION. IT IS ALSO A WAY TO DETERMINE SIGNIFICANCE. THIS IS EXTREMELY IMPORTANT IN ANY AREA OF SOCIAL OR SCIENTIFIC RESEARCH. IT IS ALSO IMPORTANT FOR ANY CITIZEN SINCE IT PROVIDES AWAY TO EVALUATE INFORMATION. The normal distribution cure is derived from the binomial distribution of (a+b)^N Where N gets very large.
10/19	Correlation	Section 4.4	Ex 4.4	This shows the relationship between data. Practical Applications: Is there a correlation between SAT scores and GPA?
10/24	quiz
10/26	Presentation of Project 3		PROJECT 3 DUE; Project #3 is any question EXCEPT 1 on p. 147 You may work in groups up to 3.

PROJECT 1:	#2	p.43	DUE THURS 9/26
PROJECT 2:	any question on	p. 111	DUE 10/10
PROJECT 3:	#2-#5	p. 147	DUE 10/26
PROJECT 4:
PROJECT 5:
Projects should be in the form of a 5-10 page essay, double-spaced with full references. On the dates listed below, you will we required to hand in your projects and be prepared to present them to the class in a 5 minute talk. You may work with up to 4 classmates and submit 1 paper.