Foundations of Probability & Statistics
General Information
Course OVERVIEW
COURSE DESCRIPTION
While the mathematical framework behind probability and statistics is relatively set and uncontroversial, the proper application and interpretation of this framework is a matter of longstanding, heated debate. Philosophical controversy permeates the very concept of probability and divides contemporary statisticians. In this course, we will discuss the most influential interpretations of probability (both throughout history and today), and we will examine how these determine the uses that the probability calculus may legitimately have. Along the way, students will develop a firm understanding of elementary probability theory and basic statistical reasoning. While our focus will mostly be on the philosophical issues that lay at the foundations of probability theory, we will also pay attention to some of probability's common philosophical applications. Specifically, we may discuss epistemological questions regarding testimony, scientific confirmation, and the problem of induction.
COURSE OBJECTIVES
By the end of this course and successful completion of all course requirements, the student will be able to do all of the following:
- list and explain the importance of all of the axioms and basic rules of probability theory,
- calculate the probabilities of various events and determine the probability distributions for random variables,
- compare and contrast the most prominent interpretations of probability, and explain how each of these affect probability theory's range of legitimate applications,
- summarize longstanding philosophical issues to which the probability theory has been applied, and evaluate the probabilistic approaches to these issues.
COURSE PREREQUISITES
Although this course does not have any official prerequisites, it does presuppose an acquaintance with both elementary symbolic logic and high school mathematics. Exams will include proofs and calculations as well as conceptual questions. Students who are unprepared to do this sort of work will not earn a passing grade and are strongly urged to take some other course.
Course Materials
METHOD OF INSTRUCTION
CLASSES: On Mondays and Wednesdays, we will focus our attention on learning new material in a discussion-based lecture format. I intend for these “lectures” to draw heavily upon student input and dialogue; ideally, these will look more like discussion sections than sit-and-listen lectures. Students will be expected to prepare well by doing the reading and homework carefully before classes and to participate throughout each class time.
LABS: Fridays are "lab days" devoted especially to answering student questions, reviewing or catching up on important concepts from the readings and lectures, and going over issues with the homework material (see below).
OPEN LEARNING INITIATIVE / HOMEWORK: Although we will be using the first few weeks of our course to go quickly through the basic mathematics of probability theory, students will be required to work more slowly and deeply through this material and to do a number of related homework assignments. For these purposes, we will be using Carnegie Mellon University's OLI course on "Probability and Statistics".
READINGS / CANVAS DISCUSSION BOARD: To keep up with this course and to get the most out of our class times, you must do the assigned reading slowly and carefully. I encourage you all to make use fo the CANVAS discussion board in order to ask each other questions and discuss the readings in preparing for class.
COURSE MATERIAL
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Carnegie Mellon University, Open Learning Initiative (OLI)
- Students must enroll with our class through the OLI in order to get credit for their work [Key: PHIL3210F13].
- Enrollment cost is $25 for the term.
- To register you will need to follow these instructions.
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Ian Hacking, An Introduction to Probability and Inductive Logic (Cambridge University Press, 2001).
CANVAS <http://utah.instructure.com>
- I will use this resource throughout the term to keep you updated on your
grades, for course communication, and for our course calendar. Class handouts and some readings may be posted here as well.
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COURSE Requirements
ATTENDANCE / PARTICIPATION
(10% of final grade)
Attendance is required for Monday and Wednesday classes, but not for Friday labs. By not coming to class, students will be hurting their own final course grades in several ways. Specifically, they will miss important course content, and consequently will not do as well on tests, assignments, or in class discussion.
OLI CHECKPOINTS / HOMEWORK
(30% of final grade)
The OLI component of this course (see above) includes several "checkpoint" assignments for you to complete and submit for grading online. See the course schedule or the OLI syllabus for assignments and due dates. OLI checkpoints must be completed and submitted by Friday, 5pm on those weeks that they are due. I will not accept any late homework, and I will not drop any scores at the end of the semester, so make sure that you finish all of your assignments and get them submitted on time. Your overall homework grade at the end of the term will be calculated as a straight average of all of your individual assignment grades throughout the term.
EXAMS
(2 x 30% = 60% of final grade)
Students will take a midterm and final exam. The final will be cumulative. I will verify the format of these later in the term, but they will most likely be in-class exams. The exams will cover students' knowledge of the probability theory as well as the philosophical ideas and arguments treated in the course -- those covered in the readings and espeically in class times. Check the schedule for exam details, once posted. Note that I do not allow students to make up missed exams. Some exceptions might be made in cases where students have a valid reason excusing them and evidence of that reason (e.g., sickness and a doctor’s note).
Grading
Final letter grades will follow a standard 10-point scale: 98-100 A+, 92-98 A, 90-92 A-, 88-90 B+, 82-88 B, 80-82 B-, etc. I will not be using a curve when calculating your grades.
Policies, etc.
MISSING AND LATE ASSIGNMENTS
Students will not be allowed to make up missed tests without a valid reason excusing them and evidence of that reason (e.g., sickness and a doctor’s note). Late homework will not be accepted in any case; the OLI system will not allow late submissions for students.
ELECTRONIC DEVICES
Please silence your electronic devices during class. This includes your phones, tablets, computers, etc. Also, please refrain from texting, surfing the web, social networking, etc. during class time. Phones should not be used at all during class; tablets and computers should only be used for relevant readings / note-taking.
HUMANITIES ACADEMIC MISCONDUCT POLICY
Academic misconduct includes cheating, plagiarizing, research misconduct, misrepresenting one’s work, and inappropriately collaborating. Definitions can be found in the Student Code.
If you are suspected of academic misconduct, the process proceeds according to the rules found in the Student Code, University Policy 6-400(V). According to that policy, after meeting with you, the instructor must determine whether academic misconduct has, in fact, occurred.
- If s/he determines that no academic misconduct has occurred, s/he will document that you are not responsible for any academic misconduct.
- If s/he determines academic misconduct has occurred and this is the first instance in which you have been alleged to have committed academic misconduct, s/he will take into account whether the act was intentional or a result of negligence in determining the appropriate sanction, which can be up to failing the course. The sanction will be noted in the resolution of the case and your right of appeal is as specified in Policy 6-400(V).
- If s/he determines academic misconduct has occurred, and you have previously been sanctioned for an act of academic misconduct, and the prior instance of misconduct resulted in a sanction less than failing the course, the department will follow the process to fail you for the course. If the prior sanction was failure of the course, your new act of misconduct will result in failure of the course and the department will also follow the process to seek your dismissal from the program and the University.
ADA STATEMENT
The University of Utah seeks to provide equal access to its programs, services and activities for people with disabilities. If you will need accommodations in the class, reasonable prior notice needs to be given to the Center for Disability Services, 162 Olpin Union Building, 581-5020 (V/TDD). CDS will work with you and the instructor to make arrangements for accommodations. All information in this course can be made available in alternative format with prior notification to the Center for Disability Services.
GENERAL EDUCATION STATEMENT
This course contributes to the University of Utah's Quantitative Reasoning and Quantitative Intensive requirements. For such courses, academic units must identify three essential learning outcomes (ELOs) that are relevant to university general education objectives. The ELOs for this course are: Inquiry and Analysis, Quantitative Literacy, and Foundations and Skills for Lifelong Learning.