• Welcome to choose this class~!
• The syllabus was created in April 2024 and it is subject to update.

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• Contacts
• Course description
• Textbook
• Coverage
• Prerequisite
• Obligations and tips
• Homework
• Test and exam
• Attendance
• Assessment
• Tentative schedule and slides
• Gradescope
• Honor code
• Accessibility
• Harassment and Discrimination
• Acknowledgment

Lecture Instructor	Dr. Le Chen	lzc0090@auburn.edu
Class Time and Room	TR, 2:00 PM -- 3:15 PM	Parker Hall 248
Office hours	TR, 1:00 PM -- 1:50 PM	Parker Hall 203

• When you send us emails, please do include the keyword Math 7800 or Math 7810 in the subject field of your email to ensure a timely response.
• In case you want to make an appointment with the instructor via Zoom, here is the link:
  https://auburn.zoom.us/j/8141875411

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Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. It has been widely used in areas of study such as statistics, finance, artificial intelligence, machine learning, game theory, mathematical physics, etc.

This course is the first course of the two-semester sequential courses -- Math 7800 and Math 7810. In Math 7800 -- Probability I, we will cover the standard materials for the measure-based probability theory, including measure theory, laws of large numbers, and central limit theorems. While in Math 7810 -- Probability II, we will cover some more advanced topics such as martingale theory, Brownian motion, stochastic differential equations, random matrices, etc. These topics may vary from year to year.

• "Probability and Measure", third edition, by Patrick, Billingsley.
• "Probability: Theory and Examples", 5th Edition, by Rick Durret
• 

Math 7800 will cover topics such as measure-theoretical probability theory, including strong and week laws of large numbers, characteristic functions, central limit theorems. We will follow mostly most parts of the first three chapters of the text book:

• Math 7800 -- Probability I
  • Chapter 1. Probability
    • Section 1. Borel's normal number theorem
    • Section 2. Probability measures
    • Section 3. Existence and extension
    • Section 4. Denumerable probabilities
    • Section 5. Simple random variables
    • Section 6. Law of large numbers
  • Chapter 2. Measure
    • Section 10. General measures
    • Section 11. Outer measure
    • Section 12. Measures in Euclidean space
    • Section 13. Measurable functions and mappings
    • Section 14. Distribution functions
  • Chapter 3. Integration
    • Section 15. The integral
    • Section 16. Properties of the integral
    • Section 17. The integral with respect to Lebesgue measure
    • Section 18. Product measure and Fubini's theorem
    • Section 19. The Lp spaces
  • Chapter 4. Random variables and expected values
    • Section 20. Random variables and distributions
    • Section 21. Expected values
    • Section 22. Sums of independent random variables

Math 7810 will cover more advanced topics, including convergence of distributions, conditional probability/expectations, and martingale theory. Depending on the request, we may also cover some materials from random matrices.

• Math 7810 -- Probability II
  • Chapter 5. Convergence of distributions
    • Section 25. Weak convergence
    • Section 26. Characteristic functions
    • Section 27. Central limit theorem
    • Section 30. The method of moments
  • Chapter 6. Derivatives and conditional probability
    • Section 31. Derivatives on the line
    • Section 32. The Radon-Nikodym theorem
    • Section 33. Conditional probability
    • Section 33. Conditional expectation
    • Section 34. Martingale

• Real analysis is not a prerequisite. We will cover some measure theory in the course. However,
  some exposure of real analysis before will be a big bonus.

This is a demanding course and it requires a great deal of work from your side. In order to successfully master the material and complete the course, you are expected to

• Read the textbook and attend lectures.
• Take the advantage of the office hours, which give you additional chance to interact with the
  instructor.
• Read solutions and any feedback you receive for each problem set.
• Complete and submit weekly homework through Gradescope.
• Complete both midterm test and the final exam.
• Use appropriate etiquette and treat other students with respect in all discussions.
• Do not hesitate to ask for help whenever needed.

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Note: The syllabus was created in April 2024, and it is subject to changes during the semester.

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• There will be about 5 homework assignments in each semester.
• No late homework will be accepted.
• You need to write full details of the problems and upload your solutions to gradescope.
  • Go to Canvas --> Find this course --> Click Gradescope on the left panel.
  • See below for more instructions on gradescope.
• We will randomly select a few problems to grade and the rest will be checked only for completion.

• There will be one midterm test during the class session:
• Final exam will be cumulative.

  	Date/Time	Coverage
  Midterm Test	TBA	TBA
  Final Exam	TBA	Comprehensive

• Please note down the above dates. No late exam/test will be given.
• Makeup exams will only be allowed in extreme circumstances. Exams cannot be made up without a
  university-approved excuse. Any excuse must be submitted by the date of exam to be considered.
  Please refer to the Tiger Cub for the list of acceptable reasons for being absent from an exam or
  a test. Makeup exam/test has to be scheduled and made up in a timely manner.
• More details will come during the semester.

• Notify the instructor if you are not able to participate in a lecture due to illness or some other emergency.
• Attendance will not be directly counted into your final score.
• But sufficient attendance will make your eligible for grade curving at the end of semester.

• The final score will be determined as follows:
• 
• Based on the final score (plus potential bonus points), the final letter grade will be
  determined as follows:

  Grade (+)		Grade		Grade (-)
  		A	92%-100%	A-	90%-91.9%
  B+	87%-89.9%	B	82%-86.9%	B-	80%-81.9%
  C+	77%-87.9%	C	72%-76.9%	C-	70%-71.9%
  D+	67%-67.9%	D	67%-67.9%	D-	60%-61.9%
  		F	0%-59.9%

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• Below is the tentative schedule that may change during the semester:

  	Tuesday	Slides or coverage	Thursday	Slides or coverage
  Week 1	08/20		08/22
  Week 2	08/27		08/29
  Week 3	09/03		09/05
  Week 4	09/10		09/12
  Week 5	09/17		09/19
  Week 6	09/24		09/26
  Week 7	10/01		10/04
  Week 8	(10/08)		--	Midterm Exam
  Week 9	10/15		10/17
  Week 10	10/22		10/24
  Week 11	10/29		10/31
  Week 12	11/05		11/07
  Week 13	11/12		11/14
  Week 14	11/19		11/21
  Week 15	11/26		11/28
  Week 16	11/33		12/05

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• We will use gradescope to handle submissions of homework, which allows
  us to provide fast and accurate feedback on your work.
• As soon as grades are posted, you will be notified immediately so that you can log in and see your
  grades and feedback.
• If you have any questions regarding Gradescope, please send your message to
  • help@gradescope.com
• Printer+scanner or tablet
  • The easiest way to submit the homework/tests/exams is the following steps:
    1. print the given template;
    2. complete the problem sets;
    3. scan the resulting paper (make sure it is legible);
    4. upload the scanned file to gradescope.
  • Alternatively, if you have a tablet that you can write on it, you may simply write on the
    template pdf file and upload the resulting file.
  • Make sure that you make the correct association of your solutions to the problems.
  • Double check your scan quality and make sure your solutions are legible.

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• Students should familiarize themselves with Auburn honor code here
  • https://www.auburn.edu/academic/provost/academic-honesty/.
• Students are encouraged to share ideas and solutions on problem sets and labs, but must
  express those ideas in their own words in their submitted work.
• Students are not authorized to view or use the work of another student during exams.

Your success in this class is important to me. We will all need accommodations because we all learn differently. If there are aspects of this course that prevent you from learning or exclude you, please let me know as soon as possible. Together we will develop strategies to meet both your needs and the requirements of the course.

I encourage you to visit the Office of Accessibility to determine how you could improve your learning as well. You can register and make a request for services from the Office of Accessibility. In this case, please do inform me of such requests. See the following link for more information:

• https://accessibility.auburn.edu/

• According to Auburn University policies: http://auburn.edu/administration/aaeeo/H&D.php

  
  Auburn University is committed to providing a working and academic environment free from prohibited
  discrimination and harassment and to fostering a nurturing and vibrant community founded upon the
  fundamental dignity and worth of all its members. Auburn University prohibits harassment of its
  students and employees based on protected classes and works to eliminate prohibited behavior from
  its academics and employment through corrective measures and education.
  
  The Office of AA/EEO oversees compliance with the Policy Prohibiting Harassment of Students, the
  Policy Prohibiting Harassment of Employees, and the Policy on Sexual and Gender-Based Harassment and
  Other Forms of Interpersonal Violence.
  
  Protected classes are race, color, sex (which includes sexual orientation, gender identity, and
  gender expression), religion, national origin, age, disability, protected veteran status, or genetic
  information.
  
  Auburn University also prohibits retaliation against any individual for opposing a practice he/she
  reasonably believed to be discriminatory; for filing an internal or external complaint, grievance,
  or charge; or for participating in any investigation or proceeding, in accordance with Auburn
  University's policies.
  

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