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.
FINAL EXAM: Thursday, May 9, 4.15pm, in NIEU 118 (our usual room)
- Topics to be covered:
- Section 5.1 (Basics about sets; intersection, union, complement)
- Section 5.2 (Inclusion-exclusion, De Morgan's laws)
- Section 5.3 (Counting with Venn diagrams)
- Section 5.4 (Multiplication principle, tree diagrams)
- Section 5.5 (Permutations, combinations)
- Section 5.6 (Putting things from last two sections together for more complicated counting problems)
- Section 5.7 (Various formulas for C(n,r), binomial theorem)
- Section 6.1 (Basics about probability; experiments, outcomes, sample space, events)
- Section 6.2 (Assigning probabilities, calculating odds)
- Section 6.3 (Experiments with all outcomes equally likely)
- Section 6.4 (Conditional probability, independence, product rule for probability of intersection)
- Section 6.5 (Using tree diagrams to calculate probabilities)
- Section 6.6 (Bayes theorem, using tree diagrams to "turn around" conditional probabilities)
- Section 7.1 (Various ways to represent data visually; median and quartiles of a set of numbers)
- Section 7.2 (Frequency tables, probability distributions)
- Section 7.3 (Binomial trials)
- Section 7.4 (The mean of a probability distribution and the sample mean of a sample)
- Section 7.5 (Sample and population variance, variance of a probability distribution, Chebychev's inequality)
- Section 7.6 (The normal distribution, calculating standard normal probabilities, going back and forth between standard normal and general normal)
- Section 7.7 (Approximating binomial trials with normal distribution)
- Section 9.1 (Two-person, zero-sum games, finding optimal pure strategies, finding saddle points)
- Section 9.2 (Figuring out the expected value of mixed strategy play)
- Section 9.3 (Just setting up a linear program that players solve to find their optimal mixed strategies)
- Section 3.1 (The basic setup of linear programming problems)
- 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:
- Friday, 1-3.30, HH248
- Monday, 5-7, HH248
- Wednesday, 11-12, HH248
- Wednesday, 3-4, HH248
- 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.
- 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).
- 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):
- 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!
Supplemental course material:
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?)
Homework:
Homework is usually due on Fridays; homework 1 will be due on Friday, January 25. I will try to post homework assignments for each section on the day that section is covered in class, and sent out an email each week to indicate when the entire assignment is posted.
New homework:
Homework 10 [LAST ONE!] due in class, Monday April 29
- Section 9.2 (April 19): problems 2, 5, 6, 11
- Section 3.1 (April 22): problems 2, 5, 6, 10
- Section 3.2 (April 24): problems 2, 3, 7, 8, 9, 10, 14, 18, 21, 22, 28, 31, 35
Old homework:
Homework 1 due in class, Friday January 25
- Section 5.1 (January 16): problems 1, 7, 14, 15, 16, 17, 19, 21, 22, 23, 25, 43, 44, 46
- Section 5.2 (January 18): problems 2, 6, 10, 13, 14, 19, 20, 21, 25, 31, 32, 37, 48, 49
- Section 5.3 (January 21): problems 3, 7, 8, 10, 12, 15, 16, 23, 25, 35, 37, 38, 49, 50, 54
Homework 2 due in class, Friday February 1
- Section 5.4 (January 23): problems 1, 5, 11, 12, 16, 17, 20, 22, 23, 24, 32, 33, 39, 49, 50
- Section 5.5 (started January 25): problems 6, 19, 24, 26, 27, 28, 31, 32, 33, 34, 35, 36, 38, 39, 42
- Section 5.5 (finished January 28): problems 44, 47, 48, 54, 56, 61 (be careful!), 62, 65, 68, 69 (note that the suits are not specified!), 72
Homework 3 due in class, ***MONDAY*** February 11 (note new day)
- Section 5.6 (started January 30): problems 1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16
- Section 5.6 (finished February 1): problems 17, 18, 19, 20, 23, 24, 28, 29, 31, 32, 37, 38, 43
- Section 5.7 (February 4): problems 21, 29, 30, 31, 33, 35, 39, 41, 43
Homework 4 due in class, Monday February 18 (note new day)
- Section 6.2 (started February 8, finished February 11): problems 1,3, 4, 6, 8, 9, 11, 13, 17, 19
- Section 6.3 (started February 11): problems 1, 2, 3, 4, 6, 8, 10, 11, 12, 13, 14
- Section 6.3 (finished February 13): problems 16, 17, 18, 19, 21, 22, 23, 27, 28
Homework 5 due in class, Monday February 25 (note new day)
- Section 6.4 (started February 15): problems 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13
- Section 6.4 (finished February 18): problems 14, 15, 16, 17, 18, 20, 22, 24, 27, 30, 31
- Section 6.5 (started February 18, finished February 20): problems 1, 2, 5, 6, 7, 8, 9, 10, 12, 13, 15, 16, 17, 19, 23, 24, 32, 34, 35, 47, 49, 51
Homework 6 due in class, Monday March 4 (note new day)
- Section 6.6 (started February 22, continued February 25, finished February 27): problems 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 22, 24, 25, 29, 35
- Section 6.7 (March 1): problems 1, 3, 5, 9, 11
Note on Section 6.7: we didn't discuss the Bayes' theorem formula in class; but each of the assigned questions can easily be solved using tree diagrams (exactly as we solved th question about Senator Joe Donnelly in class on March 1).
Homework 7 due in class, Monday March 25 (note new day)
- Section 7.1 (March 4): problems 2, 6, 8, 12, 14, 15, 16, 19, 26
- Section 7.2 (March 18): problems 2, 4, 6, 10, 11, 12, 13, 16, 24, 28acefgj, 29
- Section 7.3 (March 20): problems 4, 6, 9, 10, 14, 15, 16, 23, 24,
25, 26, 28, 29, 30, 31, 32, 35, 37, 47, 55
Note on Section 7.3: assignment changed on March 20 to remove the struck out questions (25, 47, 55) and add the bolded ones (30, 32, 35).
Homework 8 due in class, Monday April 8 (note new day)
- Section 7.4 (Started March 22, finished March 25): problems 2, 5, 6, 9, 10 (a silver dollar is worth one dollar; a slug is worth no dollars), 11, 12, 13, 14, 15, 18, 19, 26
- Section 7.5 (Started March 27, finished April 3): problems 1, 2, 5, 6, 8, 9, 10, 11, 12, 15, 16, 17, 20, 21, 23, 24
- Section 7.6 (Started April 3, continued April 5): problems 1, 2, 3, 4, 8, 9, 10, 11, 12, 13, 14, 15, 16, 19, 20
Homework 9 due in class, Monday April 15 (if you want it back by Wednesday, before the exam) or Wednesday April 17 (otherwise)
- Section 7.6 (finished April 8): problems 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 37
- Section 7.7 (April 8): problems 1, 4, 7, 11, 16
- Section 9.1 (Started April 10, finished April 12): problems 3, 5, 8, 10, 12
Exams:
Exam 3: The third exam will be held on THURSDAY, APRIL 18, at 8AM in NIEU 118 (the usual meeting place for the class). It will cover Chapter 7 and Section 9.1. The exam will last 75 minutes.
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
Please make use of these resources!
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:
The practice exams are the same format (mix of multiple choice and free response questions) as the actual exam will be. I strongly encourage you to do at least one of this practice exams under exam conditions!
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
.
Please make use of these resources!
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:
The practice exams are the same format (mix of multiple choice and free response questions) as the actual exam will be. I strongly encourage you to do at least one of this practice exams under exam conditions!
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
.
Please make use of these resources!
Here are the solutions to the first exam. Please check the solution key before bringing grading questions to me!