Math 563 and Statistics 563 - Probability Math

Syllabus for MATH/STAT 563, Section 001, Fall 2022

Location and Times

This course meets MWF 11-11:50am, Env & Nat Rsrcs Phas2 (ENR2), Rm S395.

Course Description

Course Prerequisites or Co-requisites

1. MATH 523B, or MATH 527B, or consent of instructor.

Instructor and Contact Information

Information	Data
Instructor	Professor Marek Rychlik
Office	Mathematics 605
Telephone	1-520-621-6865
Email	rychlik@arizona.edu
Instructor Homepage/Web Server	http://alamos.math.arizona.edu
Course Homepage	http://alamos.math.arizona.edu/courses/math563
Course Homepage (Mirror)	http://marekrychlik.com/courses/math563

Course Format and Teaching Methods

The course format is that of a conventional lecture, with in-class discussion and additional web-delivered content. All lectures will be recorded and available on Zoom and Panopto.

Course Objectives

This course is a course in foundations of probability theory. Topics to be covered include most of the first four chapters of the textbook, including:

1. Measure Theory (random variables, expectation and integration, independence)
2. Laws of Large Numbers (Borell-Cantelli lemmas, strong law of large numbers)
3. Central Limit Theorems (notions of convergence, convergence in distribution, proofs, infinitely divisible distributions)
4. Conditional Expectation
5. Martingales
6. Markov Processes (light overview)
7. Brownian Motion (only basics)

Learning outcomes

The student will, upon completion of the course:

• gain understanding of the mathematical foundations of probability theory;
• understand and be able to reproduce the proofs of the fundamental theorems;
• acquire problem-solving skills necessary to solve advanced problems.

Absence and Class Participation Policy

Importance of attendance and class participation

Participating in course and attending lectures and other course events are vital to the learning process. As such, attendance is required at all lectures and discussion section meetings. Students who miss class due to illness or emergency are required to bring documentation from their healthcare provider or other relevant, professional third parties. Failure to submit third-party documentation will result in unexcused absences.

Missed Exams

Students are expected to be present for all exams. If a verifiable emergency arises which prevents you from taking an in-class exam at the regularly scheduled time, the instructor must be notified as soon as possible, and in any case, prior to the next regularly scheduled class. Make-up exams and quizzes will be administered only at the discretion of the instructor and only under extreme circumstances. If a student is allowed to make up a missed exam, (s)he must take it at a mutually arranged time. No further opportunities will be extended. Failure to contact your instructor as stated above or inability to produce sufficient evidence of a real emergency will result in a grade of zero on the exam. Other remedies, such as adjusting credit for other exams, may be considered.

COVID-19 related policies

As we enter the Fall semester, the health and wellbeing of everyone in this class is the highest priority. Accordingly, we are all required to follow the university guidelines on COVID-19 mitigation. Please visit http://www.covid19.arizona.edu for the latest guidance.

UA policies

The UA's policy concerning Class Attendance, Participation, and Administrative Drops is available at: http://catalog.arizona.edu/2015-16/policies/classatten.htm The UA policy regarding absences for any sincerely held religious belief, observance or practice will be accommodated where reasonable, http://policy.arizona.edu/human-resources/religious-accommodation-policy . Absences pre-approved by the UA Dean of Students (or Dean Designee) will be honored. See: http://uhap.web.arizona.edu/policy/appointed-personnel/7.04.02

Required Texts or Readings

Required Textbook

Probability: Theory and Examples Richard Durrett, Fifth Edition

Optional Reference Textbook

Introduction to probability theory. Hoel, Paul G., Stone, Charles J., Port, Sidney C.

Assignments and Examinations

Notes on exam administration

All examinations are planned to be administered during the class time, either in person or on Zoom.

If, due to unforseen circumstances, they cannot be held in person, they are held on Zoom using the "gallery view" mode.The exam papers for not in-person tests will be distributed on-line by D2L and collected electronically using D2L "dropbox" feature.

Exam/assignment listing with date and grade contribution

Exam or Assignment	Date	Grade contribution
Midterm 1	October 5 (Wednesday), 11:00am - 11:50am October 3 (Monday), 11:00am - 11:50am	20%
Midterm 2	November 7 (Monday), 11:00am - 11:00am	20%
Final Examination	December 12 (Monday), 10:30pm - 12:30pm	30%
Homework	See D2L	30%

Homework Assignments

Written homework consists of approximately twelve assignments equally contributing to the grade, each worth 30/12 = 2.5% of the grade. The assignments are posted on line at this link: Homework. The assignment papers are collected via Gradescope, which is cloud-based software for semi-automatic grading. Things to keep in mind:

• The student will submit all graded work through Gradescope.
• In addition, the student is required to submit to D2L the work that produced the answers submitted to Gradescope. The work should be clean and readable, but can be provided in the form of rough solutions ("scratchwork"). I will not grade the scratchwork submitted to D2L, but review it periodically to make sure that the student is following good practices, such as appropriate notation and problem methodology. Gradescope assignments, by their nature, are answer-oriented. To some degree the opportunity for partial credit is limited. Scratchwork shall be submitted to D2L "dropbox" (in 'Assignments' tab) which have the same name as the corresponsing Gradescope assignments.
• Homework must not be submitted through e-mail (no exceptions).
• The D2L "dropbox" will not be used for graded homework. You may submit a record of your work in D2L.
• Due dates will be adjusted in Gradescope as needed and the student is expected to check regularly for those adjustments.

Homework is assigned regularly throughout the semester, for a total of approximately 80 problems. Two types of homework will be assigned:

1. Homework which consists of selected exercises in the required textbook.
2. Custom homework problems composed by the instructor. Some of the custom problems will require programming.

Homework submission requirements

The main requirement is that the solutions must be structured in such a way that Gradescope can read them and that its 'AI' can interpret them. Your homework must be submitted as PDF, even if you use scanner or phone to capture images. Two typical workflows will be as follows:

1. Download the blank assignment (also called a 'template') from Gradescope.
2. Read and understand exactly what answers you need to provide. The space to enter the answer is a blue box, and marked with a label such as 'Q1.1' ("Question 1, part 1").
3. Work out the problem on "paper" (real or virtual), to obtain the answers. They must fit in the designated boxes in the 'template'. The size of the box is a hint from the instructor about the size of the answer (typically a number or a math formula) when entered by hand, using regular character size.
4. The recommended way to fill out the 'template' is paperless, by using suitable software and hardware (digital pen or tablet). I use a free program Xournal for this and it works great. You need to use it in combination with a digital pen or a tablet. It can produce a PDF easily, ready for submission to Gradescope.
5. You can also print the assignment on (real) paper, fill out the answers and scan the marked up document back to PDF format. However, the position of the boxes must be exactly (to a fraction of an inch) as in the original. Also, you may encounter a variety of "quality control" issues, especially if you are using a digital camera to scan the paper solution. All issues can be solved by a mix of the right hardware and software, but may not be the best time investment. The least troublesome way to scan is to use a real, flatbed scanner, e.g. in the library.
6. Upload the resulting document (a PDF of the 'template' marked up with your answers) to Gradescope. Your PDF must contain your name and student id in designated spaces. The Gradescope 'AI' will look for your name and student id, to properly associate it with your account.
7. After grading, the grade will be transmitted to D2L (Brightspace) and will be added to your 'Final Calculated Grade' automatically.
8. Some additional requirements:
   1. Do not reduce handwriting size! Reduce the size of your answer using
      • closed form expressions;
      • appropriate math functions, e.g., absolute value, min and max.
   2. Under no circumstances write outside the provided space (boxes). Gradescope, and the grader only considers the content of the designated boxes.
9. Written scratchwork must be submitted via D2L as instructed above.

Final Examination

The final examination is scheduled for: December 12 (Monday), 10:30pm - 12:30pm.

The time, data and general exam rules are set by the University and can be found at these links:

• Final Exam Regulations
• Final Exam Schedule

Grading Scale and Policies

The student in the class normally receives a letter grade A, B, C, D or E.

The cut-offs for the grades are:

Grade	% Range
A	90%+
B	80-90%
C	70-80%
D	60-70%
E	0-60%

Normally, individual tests and assignments will not be "curved". However, grade cut-offs may be lowered at the end of the semester (but not raised!) to reflect the difficulty of the assignments and other factors that may cause abnormal grade distribution.

The grade will be computed by D2L and the partial grade will be updated automatically by the system as soon as the individual grades are recorded.

General UA policy regarding grades and grading systems is available at https://catalog.arizona.edu/policy-type/grade-policies

Classroom Behavior Policy

To foster a positive learning environment, students and instructors have a shared responsibility. We want a safe, welcoming and inclusive environment where all of us feel comfortable with each other and where we can challenge ourselves to succeed. To that end, our focus is on the tasks at hand and not on extraneous activities (i.e. texting, chatting, reading a newspaper, making phone calls, web surfing, etc).

Threatening Behavior Policy

The UA Threatening Behavior by Students Policy prohibits threats of physical harm to any member of the University community, including to one's self. See: http://policy.arizona.edu/education-and-student-affairs/threatening-behavior-students .

Accessibility and Accommodations

Our goal in this classroom is that learning experiences be as accessible as possible. If you anticipate or experience physical or academic barriers based on disability, please let me know immediately so that we can discuss options. You are also welcome to contact Disability Resources (520-621-3268) to establish reasonable accommodations. For additional information on Disability Resources and reasonable accommodations, please visit http://drc.arizona.edu/ .

If you have reasonable accommodations, please plan to meet with me by appointment or during office hours to discuss accommodations and how my course requirements and activities may impact your ability to fully participate. Please be aware that the accessible table and chairs in this room should remain available for students who find that standard classroom seating is not usable. Code of Academic Integrity Required language: Students are encouraged to share intellectual views and discuss freely the principles and applications of course materials. However, graded work/exercises must be the product of independent effort unless otherwise instructed. Students are expected to adhere to the UA Code of Academic Integrity as described in the UA General Catalog. See: http://deanofstudents.arizona.edu/academic-integrity/students/academic-integrity http://deanofstudents.arizona.edu/codeofacademicintegrity .

UA Nondiscrimination and Anti-harassment Policy

The University is committed to creating and maintaining an environment free of discrimination, http://policy.arizona.edu/human-resources/nondiscrimination-and-anti-harassment-policy . Our classroom is a place where everyone is encouraged to express well-formed opinions and their reasons for those opinions. We also want to create a tolerant and open environment where such opinions can be expressed without resorting to bullying or discrimination of others.

Additional Resources for Students

UA Academic policies and procedures are available at: http://catalog.arizona.edu/2015-16/policies/aaindex.html Student Assistance and Advocacy information is available at: http://deanofstudents.arizona.edu/student-assistance/students/student-assistance

Confidentiality of Student Records

http://www.registrar.arizona.edu/ferpa/default.htm .

Subject to Change Statement

Information contained in the course syllabus, other than the grade and absence policy, may be subject to change with advance notice, as deemed appropriate by the instructor.

Significant Dates (from the Registrar's Website)

Graduate

      Date	Standard Class Dates: Fall 2022 - Graduate - Regular Academic Session
3/1/2022	Shopping Cart available
8/21/2022	Last day for students to add to or drop from a waitlist
8/22/2022	FIRST DAY OF CLASS

    UAccess still available for registration
    First day to add classes for audit; instructor signature is required 

8/29/2022	Last day to use UAccess for adding classes, changing classes, or changing sections
8/30/2022	Instructor approval required on a Change of Schedule form to ADD or CHANGE classes
9/4/2022	Last day for a refund
9/5/2022	Beginning today, students may completely withdraw from all classes in the term
9/5/2022	Labor Day, no classes
9/16/2022	Last day for department staff to add or drop in UAccess
9/16/2022	

    Last day to drop without a grade of W (withdraw)
    Classes dropped on or before this date will remain on your UAccess academic record with a status of dropped, but will not appear on your transcript
    Last day to change from credit to audit, or vice versa, with only an instructor's signature

9/16/2022	Last day to change from pass/fail to regular grading or vice versa with only instructor approval on a Change of Schedule form
9/17/2022	Instructor's and dean's signatures are required on a Change of Schedule form to change from pass/fail to regular grades or vice versa
9/17/2022	

    W period begins A penalty grade of W will be awarded for each withdrawal and the class(es) will appear on your transcript
    Beginning today, a change from credit to audit requires instructor approval on a Change of Schedule form

10/16/2022	Last day to make registration changes without the dean's signature
10/17/2022	Instructor's and dean's signatures are required on all Change of Schedule forms to ADD or CHANGE classes
10/30/2022	

    Last day for students to withdraw from a class online through UAccess
    Last day for students to change to/from audit with only instructor approval
    Last day for instructors to administratively drop students 

10/31/2022	

    Instructor's and Graduate College dean's permission required on a Change of Schedule form to withdraw from a class--penalty grade of W will be awarded and the class will appear on your transcript
    Instructor's and dean's permission required on a Change of Schedule form to change to/from audit

11/11/2022	Veteran's Day, no classes
11/24/2022	Thanksgiving recess begins today with no classes until Monday
12/7/2022	Last day of class--no registration changes can be made after the last day of class
12/8/2022	Reading day, no classes
12/9/2022	Final exams begin
12/15/2022	

    Final exams end
    Final grades are available in UAccess as soon as the instructor posts them
    Per Faculty Senate Policy, grades should be submitted within two business days after the final exam 

12/16/2022	Degree award date

    

Material Covered

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