• Welcome to choose this class~!

---

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

Lecture Instructor	Dr. Le Chen	lzc0090@auburn.edu
Class Time and Room	TR, 12:30 AM -- 13:45 PM	Parker Hall 228
Office hours	TR, 15:00 PM -- 15:50 PM	Parker Hall 203

• When you send us emails, please do include the keyword 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

---

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 second course of the two-semester sequential courses -- Math 7800 and Math 7810. In Math 7800 -- Probability I, we have cover most materials in the 9 sections of Chapter one of Billingsley's book. In Math 7810 -- Probability II, we will cover quickly go over Chapters two and three for the Lebsgue measure and integration, and then focus on the rest of Chapters four, five and six.

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

This two-course sequence will cover topics such as measure-theoretical probability theory, including strong and week laws of large numbers, characteristic functions, central limit theorems. We will mostly cover the following three chapters of Billingsley's book:

• Math 7800 -- Probability I
  • Chapter 1. Probability
    • Section 1. Borel's normal number theorem
    • Section 2. Probability and measures
    • Section 3. Existence and extension
    • Section 4. Denumerable probabilities
    • Section 5. Simple random variables
    • Section 6. The law of large numbers
    • Section 7. Gambling system
    • Section 8. Markov chains
    • Section 9. Large deviations and the law of iterated logarithm
• Math 7810 -- Probability II
  • Chapter 4. Random variables and expected values
    • Section 20. Random variables and distributions
    • Section 21. Expected values
    • Section 22. Sums of independent random variables
    • Section 23. The Poisson process
    • Section 24. The Ergodic theorem
  • Chapter 5. Convergence in distributions
    • Section 25. Weak convergence
    • Section 26. Characteristic functions
    • Section 27. The central limit theorem
    • Section 28. Infinite divisible distribution
    • Section 30. The moment problem

• Department approval
• Math 7800

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.
• We will use Mathematica throughout the semester. Make
  sure to have the access to it (consult COSAM IT) and learn how to use it.
• 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.

---

Note: The syllabus was created in April 2022, and it is subject to changes during the semester.

---

• There will be about 4 - 7 homework assignments.
• 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.
• You may need to use Mathematica, or Matlab/Python//Sage, to assist you for the homework.

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

  	Date/Time	Coverage
  Midterm Test	Mar. 2rd, Thursday	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%

---

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

  	Tuesday -- Thursday	Coverage	Some Lecture Notes
  Week 1	--/-- -- 01/12	20
  Week 2	01/17 -- 01/19	20, 21	01/17 - Section 20 Example 20.4
  Week 3	01/24 -- 01/26	21	01/19 - Example of Two normals, Section 21 Example of covariance of two normals 01/24 Section 21
  Week 4	01/31 -- 02/02	22	01/26 Strong law of large number 01/31 Moment problem 02/02 Random series
  Week 5	02/07 -- 02/09	22, 14	02/07 Three series Theorem 02/09 Distribution functions
  Week 6	02/14 -- 02/16	25	02/15 Weak convergences 02/17 Weak convergences
  Week 7	02/21 -- 02/24	25	02/21 Weak convergences 02/23 Weak convergences
  Week 8	02/28 -- (03/02)	25, Midterm Exam	02/28 Weak convergences
  Week 9	03/14 -- 03/16	26	03/14 Characteristic functions 03/16 Characteristic functions
  Week 10	03/21 -- 03/22	26, 27	03/21 Characteristic functions 03/23 Central limit theorem
  Week 11	03/28 -- 03/30	30	03/28 Stein method 03/30 Method of moments
  Week 12	04/04 -- 04/06	30, 33	04/04 Method of moments 04/06 Conditional probability
  Week 13	04/11 -- 04/13	33, 34	04/11 Conditional probability 04/13 Conditional probability
  Week 14	04/18 -- 04/20	Reviews
  Week 15	04/25 -- 04/27	Reviews
  Week 16	05/01	Exam

---

• 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.
• The following short video (1 minutes 40 seconds) shows the basic usage of gradescope, which should
  explain everything you need to be able to do.

• More instruction will be available towards the Spring 2023.

---

• 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.
  
  

---

• Using stable diffusion model to generate images.
  1. AU Football in the space with an bald eagle
  2. AU football in Picasso style
  3. An elephant in the classroom with Von Gogh style

• The page is powered by VimWiki.