Math 30530 – Intro to Probability – Fall 18

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

Probability deals with occurrences that have some degree of randomness in their outcomes; in other words, just about everything, from calculating how likely it is that you win the lottery, to estimating how much longer until your computer’s hard-drive goes kaput. The mathematical study of probability creates a language and a framework within which we can talk sensibly about random phenomena, and make realistic predictions about them.

Official course description: An introduction to the theory of probability, with applications to the physical sciences and engineering. Topics include discrete and continuous random variables, conditional probability and independent events, generating functions, special discrete and continuous random variables, laws of large numbers and the central limit theorem. The course emphasizes computations with the standard distributions of probability theory and classical applications of them.

Objectives of the course: At the end of the semester, you will be able to

  • Define and distinguish between the basic objects of probability theory;

  • Compute the probability of events, given appropriate probability distributions;

  • Model the occurrence of events using appropriate probability distributions;

  • Apply the Central Limit Theorem when estimating probability distributions and determining sample size;

  • Prove facts from probability requiring techniques from calculus (i.e. series convergence and integration).

More generally, this course will prepare you for basic applications of probability theory including mathematical statistics and notions of randomness.

Basic information

  • Meeting times: Monday, Wednesday, Friday, 2.00pm to 2.50pm, Hayes Healy Center 229, August 27 to December 12.

  • Instructor: Abdul Basit, 248 Hayes-Healy (abasit@nd.edu).
    Note that while Sakai offers a “contact the instructor” option, you will have no success getting in touch with me through that, as I don’t check it with any regularity. I do, however, respond quickly to email sent to my nd.edu address.

  • Office hours: Tuesdays, 3.00pm — 5.00pm, or by appointment.

Textbook

We will be using the ebook

Notes on Elementary Probability, by L. Nicolaescu.

Professor Nicolaescu makes this book freely available to Notre Dame students taking this course.

Assessment

Your final grade in this class will be based on a combination of homework, quiz, midterm and final exam scores.

  • Homework: 100 out of 550 points

  • Quizzes: 100 out of 550

  • Two midterms: 100 out of 550 each

  • Final: 150 out of 550.

Scores will be recorded on Sakai. This is the only use I will make of Sakai; all other information about the course will be communicated either through email or through this website.

An average of 94% will earn you an A; of 90% an A-; 85% a B+; 80% a B; 75% a B-; 70% a C+; 65% a C; and 60% a C-.

Grading disputes: If you have any issue with the grading of your weekly assignments or with your midterm exams, you must let me know (in writing; email is fine) within seven days of receiving the work back; otherwise I can’t promise that I can consider the issue.

Homework

Homework will be announced most Fridays and posted on this website. It will be due at the beginning of class the following Friday.

Each assignment will involve some reading and some problems, possibly on an area not yet covered in lectures. Presented assignments should be neat and legible. Attach a cover sheet to your submission with your name, the course number and the assignment number. If you use more than one page, you should staple all your pages together. The grader reserves the right to leave ungraded any assignment that is disorganized, untidy or incoherent. No late assignments will be accepted. It is permissible (and encouraged) to discuss the assignments with your colleagues; but the writing of each assignment must be done on your own.

Quizzes

Roughly every second Wednesday there will be a quiz in class, on material covered in the previous three lectures.

Exams

There will be two in-class midterm exams, tentatively scheduled for:

  • Midterm 1: Monday, October 07.
    This will cover everything we have done from Chapter 1, and Chapter 2 up till the Binomial Distribution.
    Here is a practice exam. Solutions to the practice exam are here.
    Here are solutions to the actual exam.

  • Midterm 2: Monday, November 18
    This will cover Chapters 2 and 3 (up till covariance) from the text.
    Here is a practice exam. Solutions to the practice exam are here.
    Here are solutions to the actual exam.

Specific exam policies (such as format, which sections will be covered, et cetera) will be announced in class closer to the date.

There will also be a (cumulative) final exam:

  • Final exam: Thursday, December 19, 1.45pm — 3.45pm in 129 Hayes Healy.
    Here are are the topics that we have covered and some practice questions.
    Here is a practice exam. Solutions are here.

Getting help

Mathematics, like all the other sciences, is not a solitary discipline. It is a collaborative, communicative affair. Your mathematical skills will thrive by practicing talking mathematics. I encourage you to take every advantage of the opportunities available to you to do this. In particular, please contribute in class, and please come to office hours when you need to. I encourage you also to talk to each other. Share knowledge, share concerns, share questions.

Mathematics is also a cumulative subject. What we see for the first time one week, we will be building on the next week. It’s important to keep up with new material, because if you let one topic slide, you run the risk of not following any subsequent topic. I encourage you to bring up in office hours any difficulties you encounter, soon after you encounter them.

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.

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.