Math 30530 - Introduction to Probability

Spring 2019

Instructor: David Galvin


NOTE: all course policies announced here are subject to minor change as the semester progresses!

About the course

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

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

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Basic information

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Textbook and topics covered

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. We will cover all the material in the first 6 chapters of the book, except Sections 4.2, 4.4 and 5.3. For an exhaustive list of the topics covered during the semester, please see the section labelled ``Topics'' in the document here.

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

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.

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

  • Quiz 5 from April 12, solutions.
  • Quiz 4 from April 3, solutions.
  • Quiz 3 from March 19, solutions.
  • Quiz 2 from February 20, solutions.
  • Quiz 1 from February 13, solutions.

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    Solutions will be posted in a file here, updated week-by-week.

    Homework will be announced most Fridays and posted on the course 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. At the top of the first page, you should write 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.

    Homework 9, due in class Friday April 27:

    Homework 8, due in class Friday April 5:

    Homework 7, due in class Friday March 29:

    Homework 6, due in class Friday March 22:

    Homework 5, due in class Wednesday March 6:

    Homework 4, due in class Friday February 22:

    Homework 3, due in class Friday February 15:

    Homework 2, due in class Friday February 8:

    Homework 1, due in class Friday February 1: (Numbered problems are taken from the version of the textbook posted on this website)

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    The final will be on Tuesday morning May 7, at 8am. Detailed information, including a set of practice questions, and a list of office hours, is available here. Solutions to the practice problems can be found here.

    The second midterm exam will be in-class on Monday, April 15. It will cover what we have seen since the first midterm --- essentially, chapters 2 and 3 of the textbook.

    Some of the questions will be testing your knowledge of basic definitions/concepts. Other questions will be problems applying these principles.

    I'll have office hours as follows prior to the exam:

    The first midterm exam will be in-class on Monday, February 25. It will be on everything we have done this semester, up to (but not including) specific named discrete probability distributions (Section 2.2 of the text). Note than this does not include material from Section 2.1 on independence of random variables, which we will return to later.

    Some of the questions will be testing your knowledge of basic definitions/concepts (such as the rules of a probability function, definitions of concepts such as conditional probability and independence, and statements of principles such as law of total probability and Bayes' theorem). Other questions will be problems applying these principles.

    I'll have office hours as follows prior to the exam:

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

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

    There will also be a (cumulative) final exam:

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    Other material

    Here is where I will post any material other than homework, quizzes and exams that might be relevant for the class.

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    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.

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    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 (and should) discuss assignments with your colleagues, you must write the final version of each of your assignments on your own; if you use any external sources to assist you (such as other textbooks, computer programmes, etc.), you should cite them clearly; your work on the mid-semester exam and the final exam should be your own; and you will adhere to all announced exam and class 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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