Math 10120 - Finite Mathematics
Spring 2014, Section 01
Instructor: David Galvin
About the course
The course is broadly about chance and strategy.
We begin with probability, the mathematical language that allows us to talk precisely about experiments involving chance. We start with an exposition of some useful and efficient techniques for counting. Next we apply these techniques to the calculation of probabilities or the chances of various events occurring. Finally, we do a little bit of statistics: making sensible inferences about a whole population, when all we have to work with is information about a small sample.
We then move on to optimization, the study of what choices you should make to maximize some payoff (or minimize some payout), when various constraints are placed on the choices that you get to make. We start by examining systems of linear equations and their solutions. Matrices are introduced and we see how these can be used to solve systems of linear equations. We then look at optimization problems, which involve getting the most out of limited resources. Often such problems can be reduced to solving systems of linear equations.
We end with some game theory, or the mathematics of strategy. When you play a game with other players, you want to maximize your return, or minimize your loss, but you have to keep in mind that your opponents also have the same objectives. We use matrices, optimization and probability to find optimal strategies for some games.
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Basic information
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Tutorial
Twice weekly throughout the semester, there will be a (voluntary) two-hour tutorial led by Justin Vogt, (jvogt2 at nd.edu). The times for the tutorials have set as
The tutorials are a great opportunity to ask questions about anything in the course that is causing you trouble.
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Textbook options
You have two choices:
- EITHER Finite Mathematics (by H. Rolf) [hybrid edition with Enhanced WebAssign with EBook LOE Printed Access Card], ISBN 9781285084640, published by Cengage learning
- OR Enhanced WebAssign Access Card, ISBN 9781285858500, published by Cengage learning.
The first option ($115.50 from bookstore; $90 if purchased direct from the publisher here) gives you a hard-copy of the course textbook, and access to WebAssign, the online homework system that we will be using (see below). The second option ($79 from bookstore; $65 if purchased direct from the publisher here) just gives you access WebAssign, through which you can see an online copy of the book. Note that both options include access to WebAssign --- this is absolutely necessary.
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Weekly schedule
Here is an outline of what sections of Rolf's book we will be covering. It may change slightly as the semester progresses.
- Week 1 (January 15,17)
- Section 6.1 (Sets)
- Section 6.2 (Counting elements in a subset using a Venn diagram)
- Week 2 (January 20,22,24)
- Section 6.3 (Basic counting principles)
- Section 6.4 (Permutations)
- Section 6.5 (Combinations)
- Week 3 (January 27,29,31)
- Section 6.6 (A mixture of counting problems)
- Section 6.7 (Partitions)
- Week 4 (February 3,5,6,7)
- Section 7.1 (Introduction to probability)
- Review for exam 1
- Exam 1 (8am on Thursday, February 6)
- Section 7.2 (Equally likely events)
- Week 5 (February 10,12,14)
- Section 7.3 (Compound events)
- Section 7.4 (Conditional probability)
- Week 6 (February 17,19,21)
- Section 7.5 (Independent events)
- Section 7.6 (Bayes' rule)
- Week 7 (February 24,26,28)
- Section 8.1 (Frequency distributions)
- Section 8.2 (Measures of central tendency)
- Section 8.3 (Measures of dispersion)
- Week 8 (March 3,5,6,7)
- Section 8.4 (Random variables and probability distributions of discrete random variables)
- Review for exam 2
- Exam 2 (8am on Thursday, March 6)
- Week 9 (March 17,19,21)
- Section 8.5 (Expected value of a random variable)
- Section 8.6 (Bernoulli experiments and binomial distributions)
- Week 10 (March 24,26,28)
- Section 8.7 (Normal distribution)
- Section 2.1 (Systems of two equations)
- Section 2.4 (Matrix operations)
- Week 11 (March 31, April 2,4)
- Section 2.5 (Multiplication of matrices)
- Section 3.1 (Linear equalities in two variables)
- Week 12 (April 7,9,11)
- Section 3.2 (Solutions of systems of linear inequalities)
- Section 3.3 (Linear programming)
- Week 13 (April 14,16,17)
- Review for exam 3
- Exam 3 (8am on Thursday, April 17)
- Week 14 (April 23,25)
- Section 9.1 (Two-person games)
- Week 15 (April 28,30)
- Section 9.2 (Mixed strategy games)
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Assessment
You will be marked out of 600 points, with the specific breakdown as follows:
- Homework, 100 points: There will be online homework assigned for each section of the text that we cover, usually made available just before we cover the section, and due a few days after we finish it. The online homework system is WebAssign, and you must purchase assess to the WebAssign system to complete the homework (see below for more information). The homework for Sections 6.1 and 6.2 will each count for 0 points (to allow you some false starts getting used to the system!); after that, each homework will count, equally weighted, towards the 100 point total.
- Quizzes, 50 points: There will be five ten-minute in-class quizzes during the semester, which will each count, equally weighted, towards the 50 point total. Detailed information about each quiz (the material being covered, and when it will be given) will be announced in class a few days before each one.
- Mid-semester exams, 300 points: There are three mid-semester exams for this course. These have been scheduled by the registrar's office as follows:
- Thursday, February 6, 8am-9.15am
- Thursday, March 6, 8am-9.15am
- Thursday, April 17, 8am-9.15am.
Each will count, equally weighted, towards the 300 point total. Specific information about each mid-semester exam, such as exactly what material will be covered, where it will be held, and what to do in the case of a conflict with another class or exam scheduled at the same time, will be announced in class a week or so before each one.
- Final exam, 150 points: The (cumulative) final exam for this course will take place as follows:
- Wednesday, May 7, 1.45pm-3.45pm.
Specific information about the final exam, such as where it will be held, and what to do in the case of a conflict, will be announced in class during the final week of the semester.
Your marks on each of these components will be periodically updated on Sakai.
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Late assignments
All homework must be done by the due date to receive credit, and all quizzes and exams must be taken at the assigned times.
I will not consider requests for homework extensions --- the online homework system gives ample time after each section has been covered to complete each assignment, so if you have to be off-campus, I expect that you manage your travel time in such a way that you can complete your assignments in a timely manner, and if you have computer problems I expect you to go to a computer cluster on campus to complete your online homework.
I will not consider requests for make-up quizzes and/or exams, except in the case of legitimate, university-sanctioned conflicts. It is your responsibility to let me know the full details of these conflicts before they cause you to miss an assignment! Excepting university-sanctioned conflicts, it is your responsibility to be in class for all scheduled lectures and mid-semester exams; in particular, you should not plan travel on the morning of any of the Thursdays on which mid-semester exams are scheduled. [Note that this includes Holy Thursday.]
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WebAssign/Homework information
We are using WebAssign for online homework; there will be no paper homework.
- Getting started with WebAssign: The first thing you must do to use WebAssign is to enroll yourself in the class. This will involve setting up a WebAssign account (if you have not already done so), and entering something called a class key (not the same as the access code that you purchase with the text book). The full details on how to enroll, including the necessary class key for Section 01 (Professor Galvin) is available here. Note that our institution code is nd.
- Using WebAssign: The first assignment you will see when you enroll and login is entitled Entering Answers in EWA, and takes you through all the features of WebAssign that you should be aware of. The next assignment you will see is entitled Finite Mathematics Section 6.1 Sets; this is the first actual course assignment, and becomes visible early on the morning of Wednesday January 15, due early on the morning of Wednesday January 22. It, along with the section 6.2 assignment, counts for 0 points (to allow you to get used to the system), but you should still complete it since it is on examinable material. In general, new assignments will become available on the morning of the lecture on which we begin the section, and will be due one week later. You are responsible for noting the exact due dates for each assignment!
- Getting help: WebAssign has many built-in help tabs that you should use if you have any problems; you should also look over the following quick-start guide. There will be a help session on
- Saturday (January 18) from 2pm to 4pm in Hayes-Healy 117.
You can also bring up any WebAssign problems you have with me during office hours or after class.
- The access code: You must purchase an access code for this course (it comes with any of the book options listed above). You will only get free access to WebAssign until January 29; by then you will have to have entered your access code to ensure that you can continue using WebAssign.
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Quizzes
- Quiz 1 (January 31): Here. The correct answers were b) (for question 1) and e) (for question 2).
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Exams
Exam 2:
The second mid-semester exam will be held on
at
in
- DeBartolo 129 (NOT the usual class meeting room).
The exam will cover Sections 7.1 through 7.6, and 8.1, of the textbook. To help you prepare, here is a
that we will go over in class on Wednesday.
To help you prepare for the exam, there will be office hours as follows:
- Tuesday: 5-6pm, Hayes-Healy 248 (usual office hours)
- Wednesday: 5-6pm, Hayes-Healy 125 (note that this is a classroom, not my office).
Exam 1: Here is Exam 1, and here are solutions. The average for the exam (before the re-grading of question 15) was 82.4/100. Here are the grade boundaries:
- A/A-: 90+
- B-/B/B+: 80-89.5
- C-/C/C+: 65-79.5
Here is the re-do version of Question 15. If you did not get full marks on this question, you have the option to print out this page, re-do the question, and turn it in to me by Friday, February 14. Here is the solution to this question.
The first mid-semester exam will be held on
at
in
- DeBartolo 129 (NOT the usual class meeting room).
The exam will cover Sections 6.1 through 6.7 of the textbook. To help you prepare, here is a
which has the same format and length as the actual first exam (it is the first exam from last year's iteration of the course). We will go over the practice exam in class on Wednesday. There are two other practice exams you might look at here and here. Also, here are some problems that you might look at from Section 6.7 to help you prepare for possible questions from that section: Rolf Page 503, questions 21, 29, 33.
Solutions:
To help you prepare for the exam, there will be office hours as follows:
- Sunday: 6.30-8.30pm, Hayes-Healy 229 (tutorial session with J. Vogt)
- Tuesday: 5-6.30pm, Hayes-Healy 248 (office hours with D. Galvin)
- Wednesday: 5-5.50pm, Hayes-Healy 248 (office hours with D. Galvin).
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Supplementary material
Here is where I will post any supplementary material for the course, such as slides that I go over in class.
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Conduct
Honor code: You have all taken the Honor Code pledge, to not participate in or tolerate
academic dishonesty. For this course, that means that although you may discuss homework assignments
with your colleagues, you must complete each WebAssign assignment yourself, all work that you present in quizzes and exams must be your own, and you will adhere
to all announced exam policies.
Class conduct: The lecture room should be a place where you should feel free to engage in
lively discussion about the course topic; don't be shy! But non course related interruptions should
be kept to a minimum. In particular, you should turn off or switch to silent all phones, etc.,
before the start of class. If for some good reason you need to have your phone on during class, please
mention it to me in advance.
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