Syllabus for Math 3100-002.

Introduction to Probability. Math 3100, Section 2. Spring 2016

TuTh 11am-12:15 pm, Gibson 211.

Instructor: Mikhail Ershov
Office: Kerchoff 302
e-mail: ershov at virginia dot edu
Office hours: 3 hrs TBA and by APPOINTMENT
Course webpage: http://people.virginia.edu/~mve2x/3100_Spring2016

References:

required text: Introduction to Probability, second edition, Dimitri Bertsekas and John Tsitsiklis
additional text (recommended): Elementary Probability for Applications, Rick Durrett
additional text (recommended): Probability, Jim Pitman

Prerequisites and expectations:

The official prerequisite for this course is Math 1320 Calculus II, and it is an essential prerequisite for two reasons. First Math 1320 is required to ensure that students taking 3100 have sufficient mathematical maturity. Second, Math 3100 uses a lot of concepts and techniques from calculus. These include basic properties of exponential and logarithmic functions (technically this is precalculus material, but it is often studied in calculus), integration techniques (mostly substitution and parts), basic techniques for computing limits and basic results on convergence of series and power series. If it has been a while since you have taken calculus, you are encouraged to review this material in the first few weeks (most of it will not be needed until the second half of the course). Important: If you have never taken Math 1320 (or equivalent), you should talk to me at the beginning of the semester to ensure that you have sufficient background for 3100.

It is not expected that you have taken a proof-based course prior to 3100 and this course will not emphasize abstract proofs, but there will be some theoretical questions in both exams and homeworks.

Reading assignments: There will be a required reading assignment before each class (usually from our main textbook), and I will expect that you have at least looked over that material before the class. This should allow us to save time on the theoretical part and spend more time on examples.

Very tentative schedule.

week	sections	topics
Jan 21	1.2	Probabilistic models.
Jan 26, 28	1.3, 1.4	Conditional Probability. Bayes' Rule
Feb 2, 4	1.5, 1.6	Independence. Counting.
Feb 9, 11	2.1, 2.2, 2.3	Discrete Random Variable. Probability Mass Functions (PMF). Functions of Random Variables.
Feb 16, 18	2.4, 2.5	Expectation, Mean and Variance. Joint PMFs
Feb 23, 25	2.6, 2.7	Conditioning and independence for discrete random variables.
Mar 1	3.1	Continuous Random Variables and PDFs.
Mar 15, 17	3.2, 3.3	Cumulative Distribution Functions. Normal Random Variables.
Mar 22, 24	3.4, 3.5	Joint PDFs and Conditioning for Continuous Random Variables.
Mar 29, 31	4.1, 4.2, 4.3	Derived Distributions. Covariance and Correlation. Conditional Expectation and Variance Revisited.
Apr 5,7	5.1, 5.2, 5.3	Markov and Chebyshev Inequalities. The Weak Law of Large Numbers. Convergence in Probability.
Apr 12,14	5.4, 5.5	The Central Limit Theorem. The Strong Law of Large Numbers.
Apr 19, 21	6.1	The Bernoulli Process.
Apr 26, 28	6.2	The Poisson Process.
May 3		Review.

Evaluation

The course grade will be based on homework homework, quizzes, one midterm and the final (all in-class), with weights distributed as follows:

homework: 15%
quizzes: 15%
midterm: 20%
final: 50%

Exams

The midterm date given below is tentative and may be changed later. The date and time of the final exam is determined by the registrar and cannot be changed.

Midterm exam: Thu, Mar 3rd
Final exam: Sat, May 7th, 9am-12pm

Homeworks and quizzes

Homework will be assigned weekly but only about half of the assignments will be collected
For homework assignments that will be collected 3-4 selected (but not announced in advance) problems will be graded for credit.
During most weeks when assigned homework will NOT be collected, a 15-25 minute long quiz will be given at the beginning of class on the day when homework is due (usually Thursday). Most quiz questions will either come directly from homework or will be similar to homework problems; however, I may also ask for formulations of definitions and theorems on the current material. Tentative quiz dates are Feb 4, Feb 25, Mar 24, Apr 7, Apr 21 and May 3 (all Thursdays except May 3).
Please STAPLE your homework.
No late homework will be accepted. However, the lowest homework score (out of about 6 assignments) will be dropped.
The lowest quiz score (out of about 6 quizzes) will be dropped.

Make-up policy

If you miss an exam or quiz without a compelling reason, you will be assigned the score of 0 on that exam/quiz.
If you miss an exam for a legitimate reason (and appropriate documentation is provided), a make-up will be arranged; however, you must obtain my permission for a make-up before the exam, except for emergencies
If you miss a quiz for a legitimate reason (and appropriate documentation is provided): for the first missed quiz no make-up will be given, but that quiz will not be counted towards your score; for subsequent misses the same rules as for exams will apply.
University regulations specifically prohibit early make-ups.

Collaboration policy on homework.

You are welcome (and even encouraged) to work on homework together, but you must write up solutions independently, in your own words. In particular, you should not be consulting others during the process of writing down your solution .

Announcements

Major announcements will be made in class and also posted on the course webpage. Some other announcements may only be made by e-mail, so check your e-mail account regularly.

Add/drop/withdrawal dates:

Monday, February 3 -- Last day to ADD a course, elect the audit option, change the grading option (grade or CR/NC), or establish an independent study
Tuesday, February 4 -- Last day to DROP a course (deletion from the transcript)
Wednesday, March 16 -- Last day to withdraw from a course

Special statement

All students with special needs requiring accommodations should present the appropriate paperwork from the Student Disability Access Center (SDAC). It is the student's responsibility to present this paperwork in a timely fashion and follow up with the instructor about the accommodations being offered. Accommodations for test-taking (e.g., extended time) should be arranged at least 5 business days before an exam.