Math 10120 - Finite Mathematics
Spring 2016, Section 02
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
- Meeting times: Monday, Wednesday, Friday, 12.50pm to 1.40pm, DeBartolo 117, January 13 to April 27.
- Instructor: David Galvin, 132 Hayes-Healy (dgalvin1 at nd.edu).
- Office hours:
- Tuesday: Noon-1pm, 132 Hayes-Healy
- Friday: 4pm-5pm, 132 Hayes-Healy.
- Tutorial times (see below):
- Tuesday: 3pm-5pm, Hayes-Healy 125
- Thursday: 3pm-5pm, Hurley 258.
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Tutorial
Twice weekly throughout the semester, there will be a (voluntary) two-hour tutorial led by Lydia Liu, (jimin.liu.155 at nd.edu). 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
with access to the e-book and online homework
or
purchase access to the online homework system
and use the e-book that comes with it for reference.
Specifically, you have four purchasing options:
- Direct from publisher: Hybrid book with access to online homework and e-book, $125. The link is here.
- ND Bookstore, option 1: Hybrid book with access to online homework and e-book (new), $139.70. The link is here.
- ND Bookstore, option 2: Single Term Access code for online homework and e-book (Enhanced Webassign Access), $96. The link is here.
- Improvisational option: You may also purchase an access code online through webassign after you register for online homework, $79. 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 12) 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.
- Week 1 (January 13,15)
- Section 6.1 (Sets)
- Section 6.2 (Counting elements of a set using Venn Diagrams, and Inclusion-exclusion principle)
- Week 2 (January 20,22 --- no class January 18, Martin Luther King, Jr. Day)
- Week 3 (January 25,27,29)
- Week 4 (February 1,3,4,5)
- Section 6.7 (Partitions)
- Review for exam 1
- Exam 1 (8am on Thursday, February 4)
- Section 7.1 (Introduction to probability)
- Week 5 (February 8,10,12)
- Section 7.2 (Equally likely outcomes)
- Section 7.3 (Compound events, Union, Intersections and Complements)
- Exam 1 add-on quiz on Wednesday February 10
- Week 6 (February 15,17,19)
- Section 7.4 (Conditional probability)
- Section 7.5 (Independent events)
- Quiz 2 (rescheduled) on Friday February 19
- Week 7 (February 22,24,26)
- Week 8 (February 29, March 2,3,4)
- Section 8.2 (Measures of central tendency)
- Review for exam 2
- Exam 2 (8am on Thursday, March 3)
- Section 8.3 (Measures of dispersion)
- Week 9 (March 14,16,18)
- Section 8.4 (Random variables and probability distributions of discrete random variables)
- Section 8.5 (Expected value of a random variable)
- Section 8.6 (Bernoulli experiments and binomial distributions)
- Week 10 (March 21,23 --- no class March 25, Good Friday)
- Section 8.7 (Normal distribution)
- Quiz 4 on Wednesday March 23
- Week 11 (March 30, April 1 --- no class March 28, Easter Monday)
- Week 12 (April 4,6,8)
- Section 3.2 (Solutions of systems of linear inequalities)
- Section 3.3 (Linear programming)
- Quiz 5 on Friday April 8
- Week 13 (April 11,13,14,15)
- Review for exam 3
- Exam 3 (8am on Thursday, April 14)
- Section 9.1a (Two-person games)
- Week 14 (April 18,20,22)
- Week 15 (April 25,27)
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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 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 4, 8am-9.15am
- Thursday, March 3, 8am-9.15am
- Thursday, April 14, 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:
- Friday, May 6, 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) "0020" (second box) "8592" (third box) (no quotes in the class key).
- Verify that you are enrolling for "MATH 10120 --- Section 002".
- If you already have a WebAssign account, you can now log on to WebAssign with your WebAssign user name and password (not your ND user name and password!), and you will have immediate access to the class.
- 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 13, due early on the morning of Wednesday January 20. 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
- Friday (January 15) from 5pm to 6.15pm in Hayes Healy 125.
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 27; 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 April 25. Here is the quiz, with solutions.
Quiz 5 was given on April 8. Here is the quiz, with solutions.
Quiz 4 was given on March 23. Here is the quiz, with solutions.
Quiz 3 was given on February 26. Here is the quiz, with solutions.
Quiz 2 was given on February 19. Here is the quiz, with solutions.
Quiz 1 was given on January 29. Here is the quiz, with solutions.
A supplementary quiz, part of Exam 1, was given on February 10. Here is the quiz. The answers were:
- Question 1: E (3 choices for first digit, then 5 for second, 4 for third, 3 for fourth)
- Question 2: A (8 sequences where first two are Heads, plus 8 where last two are, minus 2 where both first two and last two are --- HHHHH and HHTHH)
- Question 3: F
- Question 4: C (unordered partition of set of size 16 into eight unordered sets each of size 2)
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Exams
The final exam will be on Friday May 6, at 1.45pm, in 126 DeBartolo. 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 two practice
exams:
Here are the solutions to the first practice exam, and here are the solutions to the second practice exam.
Solutions to these exams will be posted by Tuesday afternoon. Here are some resources for help:
- Galvin's office hours Monday: 3.15pm to 4.45pm, HH132
- Galvin's office hours Tuesday: 4.15pm to 5.45pm, HH132
- Galvin's review session Wednesday: 4.00pm to 5.15pm, HH231
- Bhattacharya's review session Thursday: 4.00pm to 5.15pm, HH129
Exam 3 (click on link for solutions) was on Thursday April 14, 8.00am to 9.15am in 208 DeBartolo Hall (not the usual class meeting room). It covered Sections 8.3 through 8.7 and 3.1 through 3.3, including finding the intersection of two lines.
Here are two practice
exams:
Solutions to these exams are here (first practice exam) and here (second practice exam). Here were some resources for help:
- Galvin's office hours: Tuesday 11.25am-1.25pm, HH132 (note: extended at both ends)
- Help session with tutor: Tuesday 3pm-5pm, HH125
- Review of practice exam: In class on Wednesday
- Galvin's extra office hours: Wednesday 4.10pm-5.45pm, HH132
Exam 2 (click on link for solutions) was on Thursday March 3, 8.00am to 9.15am in 208 DeBartolo Hall (not the usual class meeting room). It covered Sections 7.1 through 8.2. Here is a practice exam (an actual exam from a previous running of this course). Solutions are here. Here were some resources for help:
- Galvin's office hours: Tuesday noon-1pm, HH132
- Help session with tutor: Tuesday 3pm-5pm, HH125
- Review of practice exam: In class on Wednesday
- Galvin's extra office hours: Wednesday 4.15pm-5.45pm, HH132
Exam 1 (click on link for solutions) was on Thursday February 4, 8.00am to 9.15am in 208 DeBartolo Hall (not the usual class meeting room). It covered Sections 6.1 through 6.7. Here is a practice exam (an actual exam from a previous running of this course). Solutions are here. Here were some resources for help:
- Galvin's office hours: Tuesday noon-1pm, HH132
- Help session with tutor: Tuesday 3pm-5pm, HH125
- Review of practice exam: In class on Wednesday
- Galvin's extra office hours: Wednesday 5pm-6pm, HH132
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Supplementary material
Here is where I will post any supplementary material for the course. Note that the slides that I go through in class are available by clicking on the relevant section number in the weekly schedule
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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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9.1a
9.1b
9.2a
9.2b