# Math 10120 - Finite Mathematics

## Spring 2017, Section 02

### Instructor: David Galvin

NOTE: all course policies announced here are subject to change up to the first day of semester!

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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

Four times weekly throughout the semester, there will be a (voluntary) two-hour tutorial led by Megan Donnelly and Lydia Liu, (mdonnel9 at nd.edu and jliu10 at nd.edu). The tutors will always be in 109 Pasquerilla Center. The times for the tutorials are as follows:

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

We will cover material from the book

Finite Mathematics, 8th Edition, Rolf (Hybrid Edition with access to online homework).

You may either

purchase a hard copy of this book along

or

and use the e-book that comes with it for reference.

Specifically, you have four purchasing options:

1. Direct from publisher: Hybrid book with access to online homework and e-book, \$129.95. The link is here.
2. ND Bookstore, option 1: Single Term Access code for online homework and e-book (Enhanced WebAssign Access), \$96. The link is here.
3. ND Bookstore, option 2: Hybrid book with access to online homework and e-book (new), \$139.75. The link is here.
4. Improvisational option: You may also purchase an access code online through WebAssign after you register for online homework, \$79 (this was the cost in spring of 2016; it may have now increased by a few dollars). This includes an electronic copy of the book. If you also want a hard copy you can easily purchase a second-hand copy online fairly cheaply. Keep in mind that used copies of the hybrid book will not have an access code, since access codes are not transferable. You may register for online homework as soon as semester starts (January 17) and you have roughly two weeks to purchase and enter an access code before your account (and whatever homework you have completed to date) is erased.

Note that all 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. Click on each section number to see the slides for that section. Note that the slides will only become available on the morning of the relevant lecture (before that you will hit dead links).

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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 will 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 six ten-minute in-class quizzes during the semester, which will each count, equally weighted, towards the 50 point total. The schedule for the quizzes in included in the syllabus (see above). Information about the material being covered will be announced in class a few days before each quiz.
• 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 9, 8am-9.15am
• Thursday, March 9, 8am-9.15am
• Thursday, April 20, 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:
• Monday, May 8, 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.

A total of 570 out of 600 points will earn you an A; 550 will earn you an A-; 530 a B+; 505 a B; 480 a B-; 455 a C+; 430 a C; and a total of 410 out of 600 points will earn you a C-.

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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.

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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.
• Go to WebAssign.
• Under the "STUDENTS" tab select "I have a class key".
• Enter the class key "nd" (first box) "7185" (second box) "7909" (third box) (no quotes in the class key).
• Verify that you are enrolling for "MATH 10120 --- Section 002".
• If you don't yet have a WebAssign account, you can now create one, with a user name and password of your choosing; then when you log in to WebAssign you will have immediate access to the class.
• 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 18, due early on the morning of Wednesday January 25. It 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
• Friday January 20 from TBA to TBA in TBA.
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 31; 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 6 was given on May 1. Here is the quiz, with solutions.

Quiz 5 was given on April 12. Here is the quiz, with solutions.

Quiz 4 was given on March 31. Here is the quiz, with solutions.

Quiz 3 was given on March 3. Here is the quiz, with solutions.

Quiz 2 was given on February 17. Here is the quiz, with solutions.

Quiz 1 was given on February 3. Here is the quiz, with solutions.

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Exams

The final exam will be on Monday May 8 at 1.45pm in 129 Hayes-Healy. It will last 2 hours. It will be cumulative, with 30 multiple choice questions, split roughly 8/8/8/6 between the material for each of the three midterms and the material we've covered since the last midterm. Here are some practice exams:

Here are some resources for help.
• Galvin's office hours Monday: 3pm to 4pm, HH132
• Help session with tutor Monday: 4pm-6pm, Pasquerilla 109
• Help session with tutor Tuesday: 5pm-7pm, Pasquerilla 109
• Review for final Wednesday: In class
• Help session with tutor Wednesday: 4pm-6pm, Pasquerilla 109
• Galvin's office hours Thursday: 2pm to 4pm, HH132
• Galvin's office hours Friday: 3.30pm to 5pm, HH132
• Galvin's office hours Sunday: 3.30pm to 5pm, Einstein Bros at the bookstore
• Galvin's office hours Monday: 9.30am to 11am, HH132

Exam 3 (click for copy with solutions) was on Thursday April 20, covering Sections 8.3 through 8.7 and 3.1 through 3.3. A practice exam is posted here (ignore question 10), with solutions here, and a second one is here, with solutions here. Please don't look at the solutions until you have spend a reasonable amount of time working on the exams! Here were some resources for help:

• Galvin's office hours Monday: NONE (university closed for Easter)
• Help session with tutor Monday: NONE (university closed for Easter)
• Galvin's office hours Tuesday: 4-5.30, Hayes-Healy 132
• Help session with tutor Tuesday: 5pm-7pm, Pasquerilla 109
• Galvin's office hours Wednesday: 12.00-12.50, Pasquerilla 109, and 3.10-4.30, Hayes-Healy 132
• Review of practice exam Wednesday: In class
• Help session with tutor Wednesday: 4pm-6pm, Pasquerilla 109

Exam 2 (click for copy with solutions) was on Thursday March 9, covering Chapter 7 and Sections 8.1 and 8.2. A practice exam is posted here (an actual exam from a previous running of this course), with solutions here, and a second one is here, with solutions here. Here are some resources for help:

• Galvin's office hours Monday: 12.20pm-12.50pm, Pasquerilla 112 and 5.15pm-5.55pm, Hayes Healy 132
• Help session with tutor Monday: 4pm-6pm, Pasquerilla 109
• Galvin's office hours Tuesday: 3.30pm-4.45pm, Hayes Healy 132
• Help session with tutor Tuesday: 5pm-7pm, Pasquerilla 109
• Galvin's extra office hours Wednesday: 12.10-12.50, Pasquerilla 109, and 3.30-4.45, Hayes Healy 132
• Review of practice exam Wednesday: In class
• Help session with tutor Wednesday: 4pm-6pm, Pasquerilla 109

Exam 1 (click for copy with solutions) was on Thursday February 9, covering Sections 6.1 through 6.7. Here is a practice exam (an actual exam from a previous running of this course). Solutions are here (note that the wording of Q15 in the solution write-up is slightly different from in the practice exam, but it is exactly the same question). Here were some resources for help:

• Galvin's office hours Monday: 12-12.40, outside the classroom in Pasquerilla, and 5-5.45, HH132
• Help session with tutor Monday: 4pm-6pm, Pasquerilla 109
• Help session with tutor Tuesday: 5pm-7pm, Pasquerilla 109
• Galvin's extra office hours Wednesday: 12-12.40, outside the classroom in Pasquerilla, and 5pm-6pm, HH132
• Review of practice exam Wednesday: In class
• Help session with tutor Wednesday: 4pm-6pm, Pasquerilla 109

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Supplementary material

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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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