|Office:||334 Illini Hall|
|Contact:||The way to get in
touch with me is by email, kkirkpat(at)illinois.edu, with
subject line "Math 461 ...", and with salutation "Dear
Professor Kirkpatrick". |
MWF 10:00-10:50 (347 Altgeld Hall)
||Mondays and Wednesdays, 11:00-11:50, or by appointment. I would be
happy to answer your questions in my office anytime as long as I'm not otherwise engaged,
and before and after class are good times to catch me either in my
office or in the classroom. Office hours the first two weeks
will be 1/18 & 1/20 at 11am, and 1/27 at 9am (and as announced by
the guest lecturer).|
Sheldon Ross, A First Course in Probability, 8th Edition. 2008,
Prentice Hall. (It is okay to use an old edition for studying, but
the homework problems will be from the 8th edition, and you can check
my textbook or a classmate's to make sure you're doing the right problems.)
Homework will be assigned regularly, and collected on Fridays in class.
You are encouraged to work together on the homework, but I ask that
you write up your own solutions and turn them in separately.
Late homework will not
be graded, and if for some reason you've done a homework but can't
turn it in in class, you should turn it in to my mailbox before
class, or ask a classmate to turn it in for you. Because of this
strict policy on late homework, I will drop your two lowest
Mathematics is not a spectator sport, so it is important that you do
the homework. Doing homework problems and explaining them to each
other is the best way to really learn the material, so I
encourage you to work together on the homework. If, after thinking and talking about homework problems, you have
questions or get stuck, I will be happy to help you in my office.
I also have the philosophy that you will learn the material best
if you come to class and read the textbook before
and/or after class, even if you can learn the material
from the textbook alone. (This textbook is full of examples, and
sometimes it's hard to figure out what is important.) You
can maximize your chances of doing well in this class by combining
all of these resources: lectures, textbook, homework, office hours,
and discussions with classmates.
There will be two in-class midterm exams, scheduled for February 24th
and tentatively April 6th. Each exam will be
technically comprehensive, but emphasizing recent material up to
the most recent graded and returned homework assignment, and exam problems will
be very similar to homework problems.
The final exam is: 8:00-11:00 AM, Tuesday, May 8th. It will cover the
most important topics of the whole course, emphasizing recent
Make-up exams will be given only for medical or other serious
reasons. If you discover that you cannot make it to an exam, please
let me know as soon as possible, so that we can make other
Homework: 10% of the course grade |
2 Midterms: 25% each
Final Exam: 40%
There will probably be a curve for the final letter grades,
but at worst, 93% would be the highest cutoff for an A, 90% for an A-, 87%
for a B+, and so on.
Homework assignments (to be updated)
HW #1, due Friday, January 20 before class: please send me an email
introducing yourself: for instance, your major, where you're from,
your hobbies, why you're interested in probability, what you hope to
get out of this class, or anything else you
want to share or have questions about.
HW #2, due Friday, January 27 in class: Ch. 1 (pp. 16-17): 4, 5, 7,
8, 11, 12, 18, 19, 20, 21, 24, 27, and Ch. 2 (pp. 50-51): 2, 3, 5, 6
HW #3, due Friday, February 3 in class: Ch. 2 (pp. 50-51): 7, 8, 9,
12, 17, 18, 20, 21, 25, 27, 28, 32, 37, 43
HW #4 due Friday, February 10 in class: Ch. 2 (pp. 50-51): 50,
53, 54, and Ch. 3 (pp. 102ff): 1, 5, 6, 9, 10, 20, 23, 30, 47, 51,
56, 57, 59.
Solutions to the Diagnostic
HW #5 due Friday, February 17 in class: Ch. 3 (pp. 107ff): 64, 66, 78,
81, 83, 84, and Ch. 4 (pp. 172ff): 1, 4, 5, 13, 14, 17, 19 (in
these last two problems, "distribution function" means cumulative
Friday, February 24: first exam in class (no HW due). Please
contact me asap if you are not able to attend the exam. There are
several things to help you study: HW
answers and the solutions to the Diagnostic above.
Also, what the exam will cover:
HW #2-5, and material from chapters 1 through 4, up through section
4.7, including definitions of
fundamental concepts, but not proofs. For the material of chapter 4 that is covered on the exam but hasn't been represented in the homework yet, you are responsible only for what we've done in class. Here's a sample
exam with solutions
, if that helps you study.
Caveat downloader: this is borrowed from
someone else, and my exam may be a bit different.
Midterm 1 with solutions
HW #6 due Friday, March 2 in class: Ch. 4 (pp. 172ff): 21, 23, 32, 35,
37, 38, 40, 42, 45, 48, 50.
HW #7 due Friday, March 9 in class: Ch. 4 (pp. 172ff): 55, 57, 59, 61,
63, 72, 73, 77, 78, 79, 84, 85. Ch. 5: 1, 2, 4, 5.
No HW due Friday, March 16
HW #8 due Friday, March 30 in class: Ch. 5: 6, 10, 12, 13, 15, 18,
21, 22, 23, 25, 28, 32, 33, 34, 37, 38, 40, 41. Ch 6: 2, 7, 8, 9,
Friday, April 6: second exam in class (no HW due). Here are some study tips from Richard Laugesen:
Make an outline, with the main definitions and methods from each
Review the summary sheets for
distributions, reminding yourself of their pmf/pdf formulas,
expectations, and variances. (The hypergeometric and Cauchy distributions are cool but not your responsibility.)
Review the physical/engineering interpretation of each random
variable (e.g., the waiting time for a Poisson event is an
After doing all that review, then you will benefit from re-working
homework problems and in-class examples, because then you will have an
improved mental framework to fit the problems into.
Work through the practice
keeping in mind that our exam will be different.
HW #9 due Friday, April 13 in class: Ch. 6: 11, 13, 14, 18,
20, 21, 22, 23, 27, 28, 29, 31, 33.
HW #10 due Friday, April 20 in class: Ch. 6: 38, 40, 41,
42, 48, and Ch. 7: 5, 6, 7, 8, 11, 18, 19, 21.
UPDATE: last HW #11 due Friday, April 27 in class: Ch. 7: 30, 31, 33,
38, 39, 41, 42, 50, 51, 56, 57.
Suggested homework problems not to be turned in, but as practice for
the final: Ch. 7: 75, Ch. 8: 1, 2, 4, 5.
Research opportunities announced in class: I'm open to Honors Credit
Learning Agreements involving projects connecting probability to the
real world and to your interests. Please email me if you're
Schedule of material covered (to be updated)
Week 1: Introduction, sections 1.2, 1.3, 1.4, 1.6
Week 2: Guest lectures Monday and Wednesday, sections 1.5, 2.2-2.5
Week 3: Sections 2.5, 3.2-3.4
Week 4: Sections 3.4, 4.1, 4.2, 4.10
Week 5: Guest lectures Monday and Wednesday, sections 4.3-4.6
Week 6: Sections 4.7, 4.8, Review, Exam #1 scheduled for Feb. 24
during the usual class time
(please contact me asap if you are not able to attend the exam).
Week 7: Sections 4.8-4.9, 5.1-5.3
Week 8: Sections 5.4-5.7
Week 9: Sections 5.7, 6.1
Week 10: (Spring break)
Week 11: Sections 6.2-6.5
Week 12: Section 6.5-6.6, review, and Exam #2 scheduled for Apr. 6. Please contact me
asap if you might not be able to attend the exam.
Week 13: Sections 7.2-7.4
Week 14: Sections 7.5-7.7
Week 15: Sections 7.7, 8.2-8.3
Week 16: Section 8.3 (last day of class: May 2)
Final exam: 8:00-11:00 AM, Tuesday, May 8th.
Outline of approximate time to spend on each chapter:
Chapter 1, Combinatorial Analysis, 4 hours
Chapter 2, Axioms of Probability (omit sections 2.6, 2.7), 4 hours
Chapter 3, Conditional Probability and Independence (omit section 3.5), 4 hours
Chapter 4, Random Variables (omit subsection 4.8.4), 6 hours
Chapter 5, Continuous Random Variables (omit subsections 5.5.1, 5.6.2, 5.6.4), 7 hours
Chapter 6, Jointly Distributed Random Variables (omit sections 6.6, 6.8), 5 hours
Chapter 7, Properties of Expectations (omit subsections 7.2.1, 7.2.2, 7.7.1, and section 7.9), 7 hours
Chapter 8, Limit Theorems (omit sections 8.4, 8.5, 8.6), 3 hours
Exams and leeway, 5 hours
We will use important topics from calculus, such as infinite series
with positive terms (most calculations involve the geometric series
and series derived from it), improper integrals and double integrals
(change of variables formula, manipulating Gaussian integrals).
This semester we will not have classes on March 19-23 (spring break).
Introduction to mathematical probability: includes the calculus of
probability, combinatorial analysis, random variables, expectation,
distribution functions, moment-generating functions, and the central limit
theorem. We will cover most of the material in the first eight
chapters of the textbook.
Why study probability?
Two main reasons: uncertainty and complexity.
Uncertainty is all around us and is usefully modeled as randomness: it appears in call centers,
electronic circuits, quantum mechanics, medical treatment,
epidemics, financial investments, insurance, games (both sports and
gambling), online search engines, for starters.
Probability is a good way of quantifying and discussing what we know
about uncertain things, and then making decisions or estimating
Some things are too complex to be analyzed exactly (like weather, the
brain, social science), and probability is a
useful way of reducing the complexity and providing approximations.
And the reason I study probability: statistical mechanics,
which combines both the uncertainty of quantum mechanics, and the
complexity of zillions of particles interacting.