Mathematical Theory of Probability (477)
In a nutshell
| Instructor: | Julia Wolf, Email: jwolf137 at math dot rutgers dot edu |
| Lectures: | Monday and Wednesday, 1:40-3:00pm, SEC-217, BUS. |
| Credits: | 3 credits (for at most one out of 01:640:477, 01:198:206, 01:960:381, or 14:330:349). |
| Prerequisites: | Math 251 (third semester multivariable calculus) |
| Links: | department course information |
| Textbook: | Sheldon Ross, A first course in probability, 7th Edition, Prentice-Hall. |
| Office hours: | Wednesday 3:30-4:30pm at Hill 432 and by appointment. |
Synopsis | Syllabus | Homework | Quizzes | Grading Information | Student Support | The Probability Challenge
Synopsis
If there were one mathematics course that should be made compulsory for ANYONE's education, this would be it. Apart from representing beautiful and elegant mathematics, probability is absolutely essential for being able to make sense of the world around you. In fields as diverse as politics, economics or the life sciences, probabilistic models are ubiquitous and extremely powerful. This course hopes to lay the foundations and provides you with the basic tools needed to make informed choices.
Syllabus
The following list of topics covered is tentative so please check back frequently. General course announcements will be made via the course's Sakai page.
| Wednesday | Sep 2 | 1.1 - 1.3 | introduction |
| Tuesday | Sep 8 | 1.4 - 1.5 | basic counting: permutations and combinations |
| Wednesday | Sep 9 | 2.1 - 2.3 | sample spaces, events and the axioms of probability |
| Monday | Sep 14 | 1.6, 2.4 | the inclusion-exclusion principle and some number theory |
| Wednesday | Sep 16 | 2.5 | uniform distributions and examples |
| Monday | Sep 21 | 3.1 - 3.3 | conditional probability and Bayes' formula |
| Wednesday | Sep 23 | 3.4 | independent events |
| Monday | Sep 28 | 3.4 - 3.5 | repeated independent trials |
| Wednesday | Sep 30 | 4.1 - 4.2 | random variables and distribution functions |
| Monday | Oct 5 | 4.3 - 4.5 | expectation and variance of discrete random variables |
| Wednesday | Oct 7 | 4.6 - 4.7 | the bernoulli, binomial and poisson distributions |
| Monday | Oct 12 | ***MIDTERM EXAM NO. 1*** | |
| Wednesday | Oct 14 | 4.8.1 - 4.8.3 | the negative binomial, geometric and hypergeometric distributions |
| Monday | Oct 19 | 5.1 - 5.2 | expectation and variance of continuous random variables |
| Wednesday | Oct 21 | 5.3 - 5.5 | the uniform, normal and exponential distributions |
| Monday | Oct 26 | 5.3 - 5.7 | more continuous distributions |
| Wednesday | Oct 28 | 6.1 | jointly distributed random variables |
| Monday | Nov 2 | 6.2 | independent random variables |
| Wednesday | Nov 4 | 6.3 | sums of independent random variables |
| Monday | Nov 9 | 6.4 - 6.5 | conditional distributions |
| Wednesday | Nov 11 | 7.1-7.4 | properties of expectation, covariance and correlation |
| Monday | Nov 16 | ***MIDTERM EXAM NO. 2*** | |
| Wednesday | Nov 18 | 7.5 | conditional expectation |
| Monday | Nov 23 | 7.7 | moment generating functions |
| Wednesday | Nov 25 | ***THANKSGIVING*** | |
| Monday | Nov 30 | 8.1 - 8.2 | markov and chebychev inequalities, the weak law of large numbers |
| Wednesday | Dec 2 | ***INSTRUCTOR AWAY*** | |
| Monday | Dec 7 | 8.3 | the central limit theorem |
| Wednesday | Dec 9 | review | |
| Friday | Dec 18 | ***FINAL EXAM*** |
There will be NO calculators in this class. I am hoping to teach you to use your brain instead.
Homework
Homework problems and grades will be announced on Sakai as we go along. You should expect to spend about 2 1/2 hours per lecture working on homework assignments and consolidating your knowledge of the material by re-reading your notes and following up with the textbook. Homework problems will be collected each Monday, and late homework will NOT be accepted.
Quizzes
There will be an average of one quiz per week of no more than 10 minutes' length. Occasionally these quizzes will be administered online via the Sakai website. You should be able to answer the questions without too much trouble if you pay attention in class and keep up with the homework. There will generally be NO opportunity to make up quizzes, so class attendance is crucial.
Grading information
A total of 500 points is available for this class, which will be allocated as follows.
| Final exam: | 200 |
| Midterm I: | 100 |
| Midterm II: | 100 |
| Homework: | 50 |
| Quizzes: | 50 |
| Total: | 500 |
Student support
What to do if you miss a class? You can look at the syllabus and work through the textbook sections indicated, talk to a friend and borrow their notes. In addition, we are going to set up a Course Diary section on Sakai. This means we need one volunteer per lecture to write a brief summary of what we did in class. The emphasis is on "brief", with references to relevant resources. When you write a summary, think about what you would like your friend to tell you if you had missed the lecture. Ten extra points will be added to your quiz score at the end of the semester if you volunteer and complete the task within 24h. Note that you can volunteer at most twice during the semester.
A note on the use of Sakai
While we try our best to accurately transfer your grades to the Sakai gradebook, mistakes do occur. It is your responsibility to check your grades and notify us of any errors no more than a week after they were first announced on Sakai.
The Probability Challenge
| Code name | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | Total |
| Bruce | x | x | 2 | ||||||||||
| yankees13 | x | x | 2 | ||||||||||
| Bonus | x | x | x | x | x | x | x | 7 | |||||
| 121003577 | x | x | x | x | x | x | x | x | x | x | x | 12 | |
| tnagy | x | x | x | 3 | |||||||||
| jbakker | x | x | x | x | x | 5 | |||||||
| mastermodi | x | 1 | |||||||||||
| 127001333 | x | x | x | 3 | |||||||||
| kjhorn | x | 1 | |||||||||||
| FetaCheese | x | x | 2 | ||||||||||
| mike... | x | 1 | |||||||||||
| wexlermi | x | 1 |
Congratulations to 121003577!
Each "x" is worth 1 point. I'll try and update this page after every round. Please let me know by email if you think there is a mistake in this table.