Math 411, Spring 2019: Probability
Meeting: MWF 9:10-10:00am (sects. 200, 501) and 10:20-11:20am (sect. 502)  BLOC 149
 Office hours: Wed. 2-3pm,  Thurs. 10-11am,    or by appointment
 
Instructor: Joseph (JM) Landsberg
office 601H.

  E-mail: jml@math.tamu.edu please include "411" in the subject line when emailing me
 

my cv

E-mail. I will be contacting the class though the TAMU e-mail system.


Course description
Probability theory is used in many fields, e.g. economics, computer science, statistics. We will learn the basic concepts of the theory and some elegant techniques:  Probability spaces, discrete and continuous random variables, special distributions, joint distributions, expectations, law of large numbers, the central limit theorem.   Honors students will be assigned supplementary material that will be optional for regular students,  and will have the opportunity to do a project associated to the course.

Prerequisite: MATH 148,or 152, or  172 or equivalent.


 
Textbook
The required textbook is Introduction to Probability, 2nd - Bertsekas, Tsitsiklis. Athena Scientific.
There is a texbook webpage: http://www.athenasc.com/probbook.html with plenty of supplementary information.

Grading System: Your grade will be based on three in-class tests, homework, and a final examination. Each in-class test will count for 20% of your grade, the homework for 10%, quizzes 10% and the final examination will count for the remaining 20%. 

Honors project: Honors students are required to read an article on an aspect of probability and write a 3-5 page report on it.
Preliminary draft due Wed. 4/10. Final version due Tues 4/30 (new due date). Students may select their own article, subject to my approval, or choose one from the following list (obtain the articles by clicking the titles, books):
Shannon's classic article A mathematical theory of communication (just read first half)
Alon, Noga(IL-TLAV); Spencer, Joel H.(1-NY-X)
The probabilistic method. 
Fourth edition. Wiley Series in Discrete Mathematics and Optimization. John Wiley & Sons, Inc., Hoboken, NJ, 2016. xiv+375 pp. ISBN: 978-1-119-06195-3 (just read first few chapters)
Aldous, David; Diaconis, Persi Shuffling cards and stopping times. Amer. Math. Monthly 93 (1986), no. 5, 333–348.
Billera, Louis J.; Brown, Kenneth S.; Diaconis, Persi Random walks and plane arrangements in three dimensions. Amer. Math. Monthly 106 (1999), no. 6, 502–524
Diaconis, Persi(1-HRV)
Group representations in probability and statistics. 
Institute of Mathematical Statistics Lecture Notes—Monograph Series, 11. Institute of Mathematical Statistics, Hayward, CA, 1988. vi+198 pp. ISBN: 0-940600-14-5 (just read part)
Hardy, Quantum theory from five reasonable axioms
Homework will be assigned each week. Some weeks quizzes will be given on days homework is
due. The quiz will consist of a single question taken from the homework and last 15 minutes.
Homework schedule will be posted here.
Supplementary homework problems for the book are available here
Tentative homework assignments: Warning - subject to change up until 1 week before due.
Due Friday Jan. 18, Problems Chap. 1: 1,2  from the text and supplementary
problems for chapter 1: 1,2,3   from the above webpage.
Due Friday Jan. 25: Problems Chap. 1:  5-10 from the text and supplementary
problems for chapter 1:  5,6,9 from the above webpage.
Due Friday Feb. 1: From book: Chap. 1: 14,15,19,25. From webpage: Chap 1: 13,15,16,17.
Due Friday Feb. 8: From book: Chap 1: 30,34,53,55. From webpage: Chap 1: 19,21,34,36
Honors homework due 2/8 click here (any student may hand in for extra credit)
Due Friday Feb. 15: From book: Chap 2: 3,7. From webpage: Chap 2: 2.
Due Friday, Feb. 22: From book: Chap 2: ,13,18,25,26 From webpage: Chap 2: 3,4,6,12,13
March 1: test, no homework
Due Friday, March 8: From book: Chap 2: 31,32,40,42 (c,d are extra credit!). From webpage: Chap 2: ,15,17,19,20
Honors homework: Due Monday March 18 here
Due Friday, March 22: From book: Chap 3: 1,2,7,8,13. From webpage: Chap. 3:1,2,3,5,6
Due Friday, March 29: From book: Chap 3: 15,16,19,21. From webpage: Chap. 3: 11,12,16,17
Due Wed. , April 10: From book: Chap 4: 1,2,6,12. From webpage: Chap. 4: 15, 16,17,18
Due Wed. April 17: From book: Chap 4: 9,17,19,23. From webpage: Chap 4: 21,23,24
Due Fri. April 26: From book: Chap 4: 29,30,34,36,41,43, Chap 5: 1. From webpage: Chap 4: 2,3,6,7.Chap 7: 2,3,4
Due Tues. April 30: Optional Extra credit homework assignment: From book Chap. 7:5,10,11

 

Tests

Quizzes will occasionally take place  on days homework is due (unannounced). There are no make-ups for quizzes.


Tentative schedule (subject to change!)
weeks 1-2:  intro, 1.1: sets, 1.2 probabilistic models, 1.3 conditional probability, 1.4 total probability theory and Bayes rule
week 3:   1.5 independence, 1.6 counting, 2.1 discrete random variables.
week 4:    2.2 probability mass functions, 2.3 functions of random variables, 2.4 expectation and variance.
week 5:   2.4 cont'd, 2.5 joint PMF's of multiple random variables
week 6:   2.6 conditioning, 2.7 independence,
week 7:    
week 8:     3.1 continous random variables and PDF's, 3.2 cumulative distribution functions, 3.3 normal random variables.
spring break! (3/11-15)
week 9:  3.4 Joint PDF's of multiple random variables, 3.5 conditioning,
week 10:  3.6, 4.1, review
week 11:   4.2, 4.3
week 12:     4.4
week 13:  4.5, 5.1,5.2,5.3
week 14:   5.4,5.5
week 15:   review.

Last lecture: Tues. April 30  (redefined day). 

 

TAMU policy statements
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This federal antidiscrimination statute provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe you have a disability requiring an accommodation, please contact Disability Services in Room B118 of Cain Hall, or call 979-845-1637. For additional information visit the website of Disability Services.
Attendance
See Student Rule 7.

 


Grade complaints: If you think a homework  was graded incorrectly you
have one week from the time the graded assignment was returned to you to bring the
issue to the instructor's attention. No complaints after that time will be considered.
  
 
 
Policy regarding absences related to injury or illness: All such absences will be excused
if sufficient documentation is provided as per University policy and
the instructor will help the student make up any missed material.
 

Americans with Disabilities Act (ADA) Policy Statement

The following ADA Policy Statement (part of the Policy on Individual Disabling Conditions) was submitted to the University Curriculum Committee by the Department of Student Life. The policy statement was forwarded to the Faculty Senate for information.

The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe you have a disability requiring an accommodation, please contact Disability Services, currently located in the Disability Services building at the Student Services at White Creek complex on west campus or call 979-845-1637. For additional information, visit http://disability.tamu.edu.

Academic Integrity Statement

“An Aggie does not lie, cheat, or steal or tolerate those who do.” All syllabi shall contain a section that states the Aggie Honor Code and refers the student to the Honor Council Rules and Procedures on the web http://www.tamu.edu/aggiehonor