Math 461, Section G83
Probability & Mathematica
Fall 2012

Course Information

Piazza link
Professor:Kay Kirkpatrick
Office:334 Illini Hall
Contact:The way to get in touch with me is by email, kkirkpat(at)illinois.edu, with subject line "Math 461 ...", and with salutation "Dear Professor Kirkpatrick".
TA: Sishen Zhou, szhou15@illinois.edu, in the lab with us approximately two days per week. His office hours are Mondays from 2-3pm at B1 Coble Hall.
Time and place: MWF 3:00-3:50 pm (usually M&F in 24 Illini Hall lab, W in 245 Altgeld Hall classroom; locations subject to change). The first week we will meet IH 24. The second week we will meet in 245 AH on Wednesday and 24 IH on Friday.
Office hours: Mondays and Wednesdays, 4:00-4:50 pm, or by appointment. I would be happy to answer your questions in my office anytime as long as I'm not otherwise engaged, and before and after class are good times to catch me either in my office or in the classroom.
Syllabus and Text: Course topics: Introduction to mathematical probability: includes the calculus of probability, combinatorial analysis, random variables, expectation, variance, distribution functions, moment-generating functions, and the central limit theorem. Online syllabus at http://cm.math.uiuc.edu/461syl.php The textbook is Prob/Stat & Mathematica by Davis and Uhl at http://go.illinois.edu/NetMath461Courseware. There are ten chapters, with Basics, Tutorials, Give it a Try, and Literacy components. I will also be leading discussions to supplement the material. If you want to install Mathematica on your personal computer, go to http://webstore.illinois.edu, follow the link for "Personal Purchase," and search for Mathematica. If you have not signed up for it before, you have the option of adding MA290, which is an extra credit hour recognizing the fact that you are taking a Mathematica-based class. There will not be any extra work assigned for this credit, and the grade for it will be the same as your grade in the class. If you go to the Undergraduate Math Office in 313 Altgeld Hall, you can request to add 290.
Homework policy: There are two types of homework that will be assigned and collected regularly. The Mathematica homework is taken from the Give it a Try components of the lessons, and written problem sets will parallel the topics touched on in the lessons. You are encouraged to work together on the homework, and Mathematica homeworks may be submitted jointly, but written problem sets should be written up and turned in individually. Late homework will be corrected but not be graded, and if for some reason you've done a homework but can't turn it in in class, you should turn it in to my mailbox in 250 Altgeld Hall (importantly, not under my office door) before class, or ask a classmate to turn it in for you. Because of this strict policy on late homework, I will drop your two lowest homeworks of each type.
Homework philosophy: Mathematics is not a spectator sport, so this course based on Mathematica lends itself well to learning by doing. Doing homework problems and explaining them to each other is the best way to really learn the material, so I encourage you to work together on the homework. If, after thinking and talking about homework problems, you have questions or get stuck, I will be happy to help you. I also have the philosophy that you will learn the material best if you come to class and read the textbook before and/or after class, even if you can learn the material from the textbook alone. You can maximize your chances of doing well in this class by combining all of these resources: classes, textbook, homework, office hours, and discussions with classmates.
Exams: There will be two in-class midterm exams, scheduled at roughly 1/3 and 2/3 of the way through the semester. Each exam will be technically comprehensive, but emphasizing recent material. You will not be tested on Mathematica code, only probability content.

Tentative Midterm 1 date: Sept 28. Tentative Midterm 2 date: Nov 9. Midterms will cover material done in class up to the exam date, and homework content up through the most recent returned homeworks.
The final exam is: 7:00-10:00 pm, Thursday, Dec. 20th, location to be announced. It will cover the most important topics of the whole course, emphasizing recent material somewhat.
Exam policy: Make-up exams will be given only for medical or other serious reasons. If you discover that you cannot make it to an exam, please let me know as soon as possible, so that we can make other arrangements.
Grading policy: Mathematica homework: 10% of the course grade
Written problem sets: 10%
2 Midterms: 20% each
Final Exam: 40%
There will probably be a curve for the final letter grades, but at worst, 90% would be the highest cutoff for an A-, 80% for a B-, and so on.
Cheating: You may work together on doing your homework, but you must work completely on your own during midterm and final exams (and any quizzes, of which there may be a few). I've caught students cheating before, and they had to suffer the consequences, so just don't do it. On a more positive note, I make my exams fair and similar to homework, so as long as you make use of the resources provided, you should do fine. If you have difficulties of any kind or fall behind in the class, please come talk to me as soon as possible.

Schedule of material and location

Week 1: all week in IH 24

Monday 8/27, IH 24: Introduction, "Feel of Mathematica" on Moodle. Starting tips:
1. Double-click on the right-hand side of cells to expand them.
2. Instead of just Enter/Return, need to hit Shift-Return to evaluate a cell.
3. Always click Yes on the initialization box.

Wednesday 8/29, IH 24: From the "Course text for the first two weeks" on Moodle:
1. Start with Prob.01.1.Basics, especially the Uniform Distribution. You can refer back to Feel of Mathematica for coding questions.
2. GOAL #1: Adapt the Uniform Distribution to simulate the birthday problem.
3. Work through Prob.02 Data Analysis Basics and Tutorials
4. GOAL #2: Download HW1b from Moodle and start doing the first problem, 01.G.3) Random walks. There are hints along the way.
5. Turn in HW #0 if you wish (due Friday).

Friday 8/31, IH 24: To-do list:
1. Turn in HW #0, due by the end of class.
2. Download HW1b from Moodle and start doing the first problem, 01.G.3) Random walks. There are hints provided for a not-so-random walk through this important topic.
3. Start on the HW problems from Prob.02 Data Analysis, referring back to Basics and Tutorials and Feel of Mathematica as needed.

Week 2: Lesson 2 Data Analysis. Wed in AH 245 and Fri in IH 24. Details and the lessons are available on Moodle.

Week 3: I will be gone to a research conference, so the TA and CAs will be covering the class. Lesson 3 Probabilities.

Week 4: Lesson 4 MoreDataAnalysis. I will be back, and will hold individual office meetings with each one of you September 17-19.

Further updates are on Moodle and Piazza.
The rest of the lessons in the text are:
Prob.03.Probabilities
Prob.04.MoreDataAnalysis
Prob.05.NormalExponential
Prob.06.RandomVariables
Prob.07.JointConditional
Prob.08.CentralLimit
Prob.09.Counting
Prob.10.Statistics

Homework assignments

HW #0, due Friday, Aug. 31, in class: The handout from the first day of class.

HW #1a, written, due Friday, Sept. 7, in class: Handed out in class on Friday, Aug. 31. Resource for this (much of which will be covered in the class discussion on Sept. 5): Random variables, expectation, and variance. This HW is also similar to Lesson 2 Data Analysis, so doing the two in parallel is a good idea.

HW #1b, Mathematica, due Sunday, Sept. 9 at 5pm: Prob.01.3.G.3, 02.G.5, 02.G.6, available by logging into Moodle: https://learn.illinois.edu/ This website is where you will download and turn in your electronic homeworks, get back graded homeworks, and get some class announcements (many announcements will be made in class and not online).

HW #2a, written, due Friday, Sept. 14, in class: Available here. Resource here.

Further updates are on Moodle and Piazza.

Guidelines for the Mathematica homework

1) Make sure to put your name inside the Mathematica notebook in a text cell at the top of the notebook. If you are working in a group, make sure that all the names of the group are included in the text cell.
2) Highlight your answers to each question. The easiest way to do this is to use the PizzazButton located in the Feel of Mathematica tutorials on Moodle. This make it easier for the grader to distinguish your solution from the questions.
3) When working on a HW problem, you can use the Basics and Tutorials notebooks for that lesson as resources for code that you can cut/paste/modify to solve your problem. This is easier to do if you have gone through the Basics and Tutorials first! In any event, at some point during each lesson, you should work your way through the Basics and Tutorials to full engage the material covered. (Not everything you need to learn from each lesson is covered by a HW problem.)
4) Add text cells to your solutions to explain your thought process. Ideally, on a problem that requires multiple steps in the solution, you would intersperse text cells with calculations to indicate the flow of the solution. (i.e., don't have just one giant code cell with no text) The explanations should be clearly written to demonstrate your understanding, and that you didn't just cut and paste your way through.

Holidays

This semester we will not have classes on September 3 and November 19-23.

Why study probability?

Two main reasons: uncertainty and complexity. Uncertainty is all around us and is usefully modeled as randomness: it appears in call centers, electronic circuits, quantum mechanics, medical treatment, epidemics, financial investments, insurance, games (both sports and gambling), online search engines, for starters. Probability is a good way of quantifying and discussing what we know about uncertain things, and then making decisions or estimating outcomes. Some things are too complex to be analyzed exactly (like weather, the brain, social science), and probability is a useful way of reducing the complexity and providing approximations. And the reason I study probability: statistical mechanics, which combines both the uncertainty of quantum mechanics, and the complexity of zillions of particles interacting.