Class
meetings: Tuesday
and Thursday 12:30 - 1:45, in Peabody 218.
Prerequisites:
A
good working knowledge of Mathematics 231-233 (calculus of
one and several variables) or equivalent. Students
will need some familiarity with manipulating single
and double sums and should be comfortable with standard mathematical
notation
for sums, products, unions, intersections, sets and so on. They
should be familiar with integration on the line (including the
integrals of exponential functions and polynomials) and with multiple
integrals in the plane. We will assume knowledge of some basic
facts like the binomial theorem, the geometric series, and the series
expansion of the exponential function.
Registration:
Enrollment
and registration for the course is handled by
Charlotte Rogers in the Department Statistics and Operations Research. Ms. Rogers can be reached at 962.2307,
or by email at crogers@email.unc.edu.
The instructor does not have control over the class rolls.
Though the first several lectures are often crowded, there is usually
space to accomodate students interested in taking the course.
Instructor:
Andrew
B. Nobel, Department of Statistics and Operations
Research
Office:
Hanes
308 Phone: 962-1352.
Office
Hours: Monday 2:30 - 3:30, Tuesday 4:15 - 5 and Thursday 1:45 -
2:30
Grader:
Zhitao
Zhang
Office:
B54 Hanes
Phone:
Email:
zhitaoz@email.unc.edu
Grader's
Office Hours: 12 - 1:30 Wednesdays
Textbook:
"A
First Course in Probabililty", Seventh Edition,
by Sheldon Ross.
Calculators:
You
will need a calculator that can compute exponentials and
factorials. Calculators should be
brought to exams.
Classroom
Protocol:
Please show up on time, as late arrivals tend to disturb folks
already present. Please refrain
from reading newspapers or using laptops during class.
Attendance is not taken in class. If you are unable to make a
lecture, see to it that you obtain the notes from someone else in the
class.
Homework
policy: Homework
assignments will be posted on the course web page
and will typically be due once a week. Assignments will be collected at
the
beginning of class on the day they are due. Each homework assignment
will be
graded: late/missed homeworks will receive a grade of zero. In computing a student's overall
homework score for the course, their two lowest homework scores will be
dropped. This latter provision is meant to cover exceptional situations
in
which a student is unable to turn in an assignment due to circumstances
beyond
his/her control. As a general
matter, students are expected to turn in every homework assignment.
To
receive full credit on the homework assignments, you must clearly label
each
problem, neatly show all your work (including written justifications of
your
mathematical arguments), circle or underline your final answers, and
staple
together the pages of each assignment in the correct order. Please
write your
name or initials on each page. You should give a clear account of your
reasoning in English, and use full sentences where appropriate.
You
are allowed to discuss the homework problems with other students, but
must
prepare each assignment by yourself. Copying of homework is not
allowed. Any
questions regarding the grading of homeworks should first be addressed
to the
TA. If you are absent from class when an assignment is returned, you
can get
your paper from the TA during their office hours.
Exams:
There
will be two in-class midterm exams, and a comprehensive
final examination that will also be in-class. All exams will be closed
book and
closed notes. Tentative exam dates are as follows. The final exam
will be given at the date and time specified in the official University
Final Exam Schedule.
|
Midterm1 |
23
September (Tentative) |
|
Midterm2 |
30 October (Tentative) |
|
Final |
See
University Timetable |
Grading:
The
overall course grade will be based on the homework
assignments and exams, and will be calculated as follows:
|
Homework |
15% |
|
Midterm 1 |
22% |
|
Midterm 2 |
22% |
|
Final |
41% |
Syllabus:
We
will cover selected material from Chapters 1 - 8 of the
text, with particular emphasis on the following topics:
Probability models for
random experiments
Conditional probabilities
and independence
Discrete and continuous
random variables
Important discrete and
continuous distributions
Jointly distributed random
variables
Definition and basic
properties of expectations
Laws of large numbers and
the central limit theorem
Basic inequalities for
probabilities and expectations
Conditional Expectations
(as time permits)
Other Texts: You should feel
free to consult other textbooks regarding the material in the course,
including a good calculus textbook. The books below are good
sources for some of the material in the course, though they are not
about probability per se.
``Concrete Mathematics'' by Graham, Knuth and
Patashnick. This book provides a very comprehensive treatment of
standard summation notation (chapter 2), and binomial coefficients
(chapter 5).
``The Cauchy-Schwartz Master Class'' by J.M. Steele. This book
provides a very readable introduction to basic inequalities. At
this writing, two chapters are available online free of charge.
Other probability textbooks that
may be useful are:
``Probability'' by Jim Pitman, published by Springer
``Introduction to Probability'' by Douglas G. Kelly, published by Macmillan
``Probability and Random Processes'' by G.R. Grimmett and D.R.
Stirzaker,
published by Oxford
Honor
Code: Students
are expected to adhere to the UNC honor code at all
times. Violations of the honor code will be prosecuted.
Study
tips:
1. Keep up with the
reading and homework assignments.
2. Look over the notes
from the lecture k before attending lecture k+1. This will
help keep you on top of the course material. Ideas from one
lecture
often carry over to the next: you will get much more out of the
material if you can maintain a sense of continuity.
3. Read the book
carefully *before* doing the homework. Trying to find the right
section for a particular problem often takes as much time, and tends to
create more confusion than it resolves.
4. Keep careful track of
any concepts and ideas that you are unclear about, and make efforts to
master these in a timely fashion, using the class notes, the text,
office hours, and outside reading if necessary.
5. One good way of seeing
if you understand an idea or concept: write down the associated
definitions and basic facts, without the aid of the book or your notes,
in full, grammatical sentences. Translating ideas from
mathematics to complete English sentences, and vice versa, is one
underlying theme of the course.
6. Carefully look over
your corrected homework assignments. Note and correct any
mistakes you made on the problems.
7. Begin studying for
exams one week before they are given. Look over your notes,
homework, and the text. Write up a study guide containing the
main concepts and definitions being covered, and use this to get a
clear picture of the overall landscape of the material.