Mathematical Theory of Probability (477)


In a nutshell

Ross

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.

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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.

WednesdaySep 21.1 - 1.3 introduction
TuesdaySep 81.4 - 1.5 basic counting: permutations and combinations
WednesdaySep 92.1 - 2.3 sample spaces, events and the axioms of probability
MondaySep 141.6, 2.4 the inclusion-exclusion principle and some number theory
Wednesday Sep 162.5 uniform distributions and examples
Monday Sep 213.1 - 3.3 conditional probability and Bayes' formula
Wednesday Sep 233.4 independent events
Monday Sep 283.4 - 3.5 repeated independent trials
Wednesday Sep 304.1 - 4.2 random variables and distribution functions
Monday Oct 54.3 - 4.5 expectation and variance of discrete random variables
WednesdayOct 74.6 - 4.7 the bernoulli, binomial and poisson distributions
MondayOct 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
WednesdayOct 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
MondayNov 9 6.4 - 6.5 conditional distributions
WednesdayNov 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
WednesdayNov 25 ***THANKSGIVING***
MondayNov 30 8.1 - 8.2 markov and chebychev inequalities, the weak law of large numbers
Wednesday Dec 2 ***INSTRUCTOR AWAY***
Monday Dec 78.3 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.

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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.

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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.

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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

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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.

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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.

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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.

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This page was last updated 2nd September 2009.