Math 10120 - Finite Mathematics

Spring 2013

Instructor: David Galvin

General course arrangements (textbook, syllabus, office hours, grade assignment, etc.) are detailed here. Note: this information is provisional until the first day of classes!

For grades, please log on to Concourse.

• Topics to be covered:
  1. Section 5.1 (Basics about sets; intersection, union, complement)
  2. Section 5.2 (Inclusion-exclusion, De Morgan's laws)
  3. Section 5.3 (Counting with Venn diagrams)
  4. Section 5.4 (Multiplication principle, tree diagrams)
  5. Section 5.5 (Permutations, combinations)
  6. Section 5.6 (Putting things from last two sections together for more complicated counting problems)
  7. Section 5.7 (Various formulas for C(n,r), binomial theorem)
  8. Section 6.1 (Basics about probability; experiments, outcomes, sample space, events)
  9. Section 6.2 (Assigning probabilities, calculating odds)
  10. Section 6.3 (Experiments with all outcomes equally likely)
  11. Section 6.4 (Conditional probability, independence, product rule for probability of intersection)
  12. Section 6.5 (Using tree diagrams to calculate probabilities)
  13. Section 6.6 (Bayes theorem, using tree diagrams to "turn around" conditional probabilities)
  14. Section 7.1 (Various ways to represent data visually; median and quartiles of a set of numbers)
  15. Section 7.2 (Frequency tables, probability distributions)
  16. Section 7.3 (Binomial trials)
  17. Section 7.4 (The mean of a probability distribution and the sample mean of a sample)
  18. Section 7.5 (Sample and population variance, variance of a probability distribution, Chebychev's inequality)
  19. Section 7.6 (The normal distribution, calculating standard normal probabilities, going back and forth between standard normal and general normal)
  20. Section 7.7 (Approximating binomial trials with normal distribution)
  21. Section 9.1 (Two-person, zero-sum games, finding optimal pure strategies, finding saddle points)
  22. Section 9.2 (Figuring out the expected value of mixed strategy play)
  23. Section 9.3 (Just setting up a linear program that players solve to find their optimal mixed strategies)
  24. Section 3.1 (The basic setup of linear programming problems)
  25. Section 3.2 (Solving a linear programming problem with two variables graphically)
• Format of the exam: Mostly multiple choice questions, but there may be a few free response questions, especially on linear programming.
• Office hours: I will have extra office hours in the time before the exam, as follows:
  1. Friday, 1-3.30, HH248
  2. Monday, 5-7, HH248
  3. Wednesday, 11-12, HH248
  4. Wednesday, 3-4, HH248
  5. Thursday, 1-3, HH248
• Practice exams and study aids: Here is a practice final that was given in a previous running of this course, and an actual final from another previous running. Different instructors sometimes cover slightly different topics, so some of the questions in these exams are about things that we did not cover; I've identified those question to ignore below. Solutions will be posted by Tuesday midday.
  1. A previous year's practice final (Ignore question 24 in this exam!!!). Here is a solution key (note that it includes answers to questions 25 through 28, that weren't part of the practice exam).
  2. A previous year's final (Ignore questions 20 and 21 in this exam!!!). Here is a solution key
  Here is a short collection of extra problems, that cover some topics that aren't on either of the exams above (again, solutions by Tuesday midday):
  1. Extra problems, and here are solutions.
  At the end of each of the five chapters that we have covered (3, 5, 6, 7 and 9) there is a Chaper Summary, a Review of Fundamental Concepts, a list of Key Formulas, a collection of Supplementary Exercises, and a further collection of problems under the heading Chapter Test. The first three of these sections are excellent to review, to make sure that you know the important points of each chapter, and the last two of these are a great source of practice problems. Feel free to ask me about any of them.
• Any questions?: Email me!

Here are the slides on the games from the last day of class

Here is the link to the Linear Programming Solver that I showed in class on April 22

Here are the slides on the optimal mixed strategy for R that we talked about on April 22

Here are the Bayes' theorem problems that we talked about on February 27/March 1

Here are the slides on the two boys paradox

Here is the anonymous birthday poll, from Monday, February 18. Here are the slides on the birthday problem

Here are the slides on the basics of probability

Here are the slides on when to add, when to multiply

Here are the counting questions from January 28

Here are the slides on the multiplication principle

Here are the slides on Russell's paradox (who shaves the barber?)

To help you prepare for the exam, here are some practice problems (and here is the normal table, if you choose to use it). Here are solutions to the practice problems.

There will be several sessions to help you prepare for the exam:

• Sunday, 5-7pm, DeBartolo 232: Tutorial session with Caroline Schuitema
• Monday, 12.30-class time, HH248: office hours
• Tuesday, 2-4pm, HH248: office hours
• Wednesday, 11-12noon, HH248: office hours
• Wednesday, 3-4pm, HH248: office hours
• Wednesday, in class: Detailed review of the practice exams
• Wednesday, 5-7pm, DeBartolo 232: Tutorial session with Caroline Schuitema

Here are the solutions to the third exam. Please check the solution key before bringing grading questions to me!

Exam 2: The second exam will be held on THURSDAY, MARCH 7, at 8AM in NIEU 118 (the usual meeting place for the class). It will cover all the material that we cover in class from Monday, February 4 through Friday, March 1. This is essentially Section 5.7 from the top of page 246, through the end of Section 6.7. The exam will last 75 minutes.

To help you prepare for the exam, here are two practice exams:

• Practice exam 1; solutions here
• Practice exam 2, but ignore questions 9,10 and 14; solutions here
.

There will be several sessions to help you prepare for the exam:

• Sunday, 5-7pm, DeBartolo 232: Tutorial session with Caroline Schuitema
• Monday, 4-6pm, Hayes-Healy 248: Office hours
• Wednesday, in class: Detailed review of the practice exams
• Wednesday, 4.30-6, room TBA: Office hours/review session
• Wednesday, 5-7pm, DeBartolo 232: Tutorial session with Caroline Schuitema
.

Here are the solutions to the second exam. Please check the solution key before bringing grading questions to me!

Exam 1: The first exam will be held on THURSDAY, FEBRUARY 7, at 8AM in NIEU 118 (the usual meeting place for the class). It will cover all the material that we cover in class up to and including Friday, February 1. This is essentially Sections 5.1 through 5.6, and Section 5.7 up to the bottom of page 245. The exam will last 75 minutes.

To help you prepare for the exam, here are two practice exams:

• Practice exam 1; solutions here
• Practice exam 2; solutions here
.

There will be several sessions to help you prepare for the exam:

• Sunday, 5-7pm, DeBartolo 232: Tutorial session with Caroline Schuitema
• Tuesday, 2.30-4pm, Hayes-Healy 248: Added office hours
.
• Wednesday, 9.30-11am, DeBartolo 244: Added office hours (Note: not the usual venue!)
.
• Wednesday, in class: Detailed review of Practice exam 2
• Wednesday, 5-7pm, DeBartolo 232: Tutorial session with Caroline Schuitema
.

Here are the solutions to the first exam. Please check the solution key before bringing grading questions to me!