Mathematics 3: Finite Mathematics
Fall 2009

Instructor: Jim Sauerberg

Class: MWF 9:10--10:10am, Galileo 105
Email: jsauerbe@stmarys-ca.edu
Office Phone: 631-4248
Office: Galileo 101
Office Hours: MWF 10:20-11:20, 12:40-3:30. T 9:30-11:10, 1:00-3:00. By appointment.

Information Sheet: The details of what and how.
Course Calendar: What are we doing when.
How to Survive: Tips (and more) about suriving (and thriving!)

FINAL EXAM: Wednesday December 9th, 4:30--6:30pm

Announcements

The Student Math Center (SMC) has begun. It is open Sunday, Monday, Tuesday and Wednesday evenings 7:00-9:00pm in Galileo 110. No appointment necessary -- just drop in, do your homework, ask your question.

Homework
Monday November 23rd Regular Markov Systems
Read pages 523-524. Do exercises 13, 23, 25, 29, 37, 41, 45.
Friday November 20th Section 7.7: Markov Systems
Read pages 517-521. HW is posted on Webassign.
The next three class sessions study increasingly complicated versions of today's material. As I'm sure you time is tight, I've assigned the bare minimum of HW. But I expect you to do it carefully.
Wednesday November 18th Section 7.6: Tree Diagrams
We will not worry about the formalism of "Bayes' Theorem." Instead, carefully read examples 1 and 2, and then see if you can do example 3 using out tree method. HW has been posted.
Monday November 16th Exam III
Friday November 13thReview for exam
Good problems include
Chapter 4 Review: 1-8, 28-31, 34
Chapter 6 Review: 10-12, 23-36
Chapter 7 Review: 7-9, 11, 13, 14, 37-43.
Wednesday November 11th Section 7.4: Conditional Probability
Read pages 491-495. Do exercises 49-56, 63-72 and 79-81. Don't hand it (see answers in back) but be prepared to do such problems on Monday's exam.
Monday November 9th Section 7.2, 7.3: Probability
Section 7.2: Example 4 is the key one. Review also the 'dark boxes' of theoretical things.
Section 7.3: Read all.
HW has been posted.
Friday November 6th Section 7.1: Words of Probability
Look at examples 1, 2, 4, 5. HW posted on Webassing.
Wednesday November 4th Counting
Read all of 6.3. Pay careful attention to the examples. HW is on Webassign.
If you need more, look at 1-4, 15, 16, 21-24, 29, 30, 36-42, 45, 46, 51, 57, 58, 65-68.
Monday November 2nd Cardinality
Read all of 6.2. HW is on Webassign
If you need more, 1-6 adn 15-58 are all good.
Friday October 30th Sets
Read pages 397-400. HW is on webassign.
If you need more, 3, 7, 17, 19, 21-33, 54?, 61-68, 71-74, 76, 81, 82 are all good.
Wednesday October 28th Solving Multi-variate LP Problems
See the page Solver for a 'getting started' guide to using Google Documents for solving Linear Programming problems. Here is an spreadsheet of that problem.
Here is a set of problems and answers to do with technology.
Those who wish to use Excel instead certainly may. Most of the steps should translate will little difficulty. The Excel sheet Loading Solver should help you install a needed program into your Excel. program. Download the sheet, open it with Excel, and follow the directions.
Monday October 26thHarder LP Problems
Be able to set up the objective function and constraints for problems like these..
Friday October 23rdSection 4.2: Solving LP problems graphically
HW on Wednesay was quite hard, with the method for entering solutions confusing. Don't worry about it (if you tried hard an struggled.) Feel a bit guilty with an increased desire to work hard (if you didn't really try hard).
Tonight's HW is important. Each of the problems is a bit lengthy, with numerous places to make small errors. However, it is crucial that you understand the process and the methods in these "2-dimensional" problems before we move onto the harder ones next week. HW has been posted.
Wednesday October 21st Section 4.1: Linear Inequalities
Read section 4.1 starting on the middle of page 261 to end.
See WebAssign for some HW.
Monday October 19th Exam II
The exam covers everything since the last exam, namely chapters 3 & 5. It'll be about six questions, probably multiple parts.
Friday October 16th Review for Exam
I'll be around some on Sunday. Most likely at the Math Center in the evening. Stop by if you have questions, or email.
Here is a sampler of extra problems and answer.
Wednesday October 14th Section 3.5: Input-Output Models
Read the whole section. Webassign HW has been posted.
Here is the example and solution and the handout and solutions
Wednesday's class will carefully explain the meaning of the technology matrix A and develop the formulas X-AX = D and X=(I-A)^-1 D. However, we won't spend time discussing how to move from an input-output matrix to A (just divide each entry in a column by its column total - see page 229), nor the meaning of the entries of (I-A)^-1 (they show how the production level must change when the demand changes - see page 232). The former is important, but don't worry about the latter.
Monday October 12th: Section 3.3. Inverses.
Read pages 202 (top half page) and most of page 203.
Do 3.3: 27, 29, 31, 33, 43, 45, 51, 52.
Friday October 9th:Applications of Matrix Operations
HW has been posted on WebAssign.
Wednesday October 7th: Matrices and Matrix Multiplication
Section 3.1: Read pages 174 - mid 179. Do book exercises 1-7 odd, 13-25 odd.
Section 3.2: Read pages 184 - 188. Do book exercises 1-25 odd.
On Friday we start using these matrices and their operations for applications. Before we get there it is important that you can confidently perform matrix addition and multiplication (especially multiplication). So carefully and completely do these exercises by then.
Monday October 5th: End of Interest
This is our last day on chapter 5. Here are a selection of problems to do. Some are standard, some are tricky, some are long, some are hard. ALL need to be understood.
Chapter 5 Review. Exercises 1-18, 29-41. These are good practice for the next exam.
Friday October 2nd: Section 5.3 Types of Annuities.
Think carefully about sinking funds vs. increasing annuities vs. decreasing annuities vs. 'saving money via small deposits' vs. 'paying back money vis small payments'.
HW has been posted.
It would be worthwhile doing a couple of the odd book problems and comparing your answer with the back of the book to make sure your calculator button-pushing is going well. See me if it is not.
Wednesday September 30th: Section 5.3 Annuities
Terminology: Book's "Sinking Fund" = Lecture's "Increasing Annuity". Formula is on page 361.
Book's "Annuity" = Lecture's "Decreasing Annuity". Formula is on page 364.
Read pages 360 to mid 365. HW has been posted.
If you feel you are doing the HW correctly but webassign never agrees, try being careful in rounding. That is, _dont_ round any of your answers until the very end. If you do (1+.03)^8 as part of the problem, don't round this to 1.27 or 1.267 but leave it as 1.26677. Usually you can do this by carefully ordering your calculator-typing so that you never have to re-enter a number.
Here are some quick hints on some of the hardest problems from Monday's HW.
Monday September 28th: Section 5.2 Compound Interest
Read all , but skip page 353. HW is posted.
Posted now are comments on exam 1.
Friday September 25th: Section 5.1 Simple Interest
Read all. There are examples very similar to each one we did in class.
Carefully read example 5 on page 346, as it discusses the pricing of T-bills. T-bills are 'priced' by listing the percentage discount rate- how much less than face value they are sold for. This "discount rate" is not the same as the rate of interest earned. Read this carefully
For a simple example -- suppose the discount rate on a 1-year $100 T-bill is 50%. Then you buy the bill for 10-10*.5 = $50. But over that year your $50 turns into $100, so your interest rate is 100%!
Conclusion: discount rate is not the same as interest rate.
HW has been posted.
Wednesday September 23rd: Exam
In class. Covers everything up to this point. Bring a calculator.
Monday September 21st: Review
Here are several sample problems to try.
Each chapter ends with a selection of review material. To help guide you, the most applicable to me seem to be:
Chapter 1 Review: 1-8, 14-22, 24-27.
Chapter 2 Review: 7-12, 19-32.
Friday September 18th: Section 2.3: Systems of more than two variables
Read all. We have skipped section 2.2, as you won't have to solve such problems by hand. Instead, use this calculator to solve the systems.
See Webassign for the HW.
Wednesday September 16th Section 2.1: Linear Systems
Read the whole section. It is clear and helpful.
HW has appeared on WebAssign.
Monday September 14th: Linear Regression II
Those with laptops, bring them to class!
Here are Google Spreadsheet hints
Here is the Project Assignment
Finally, here is the Sample Regression as Excel.
Friday September 11th: Linear Regression
Make sure to bring your calculator!!
Wednesday September 9th: Linear Models
Section 1.4. Read all. This section introduces a number of very important concepts (supply, demand, cost ...) and how to interpret mathematical models involving them. Here's the handout we'll be using. (Copies given in class.)
Homework on Linear Models has been posted on Webassign.
Friday September 4th: Section 1.3 Linear Functions
Reading: Read all of Section 1.3. This may be review, but is very important.
HW: Posted on WebAssign.
Wednesday September 2nd: Functions
Reading: Read all of section 1.1. Pay careful attention to the examples and to Table 1. Read pages 44-47 of section 1.2.
HW: (1) Sign up to your account on WebAssign. Use your email username (e.g. "jjs2") as Username, stmarysca as Institution and smc email address as password.
(2) Complete the hw assignments there.
Monday August 31st: Introduction to Finite Math