Professor: Jill Pipher
Office: Chair's office: Kassar 104
Phone: (401) 863-3319
Fax: (401) 863-9013
Email: jpipher at math dot brown dot edu
Office Hours: Wed. 3-4, Thurs 1-2:30 and by appointment
Grades in the course are based on
weekly homework assignments (25%), one midterm (25%), and the final examination
(50%). The syllabus and
assignments will be posted on
this website, and updated
weekly. Homework is collected on Thursdays. Please turn in
the problems assigned on the Tuesday of that
same week, and the previous Thursday.
Who should take this course? This course has no advanced prerequisites,
but I'll assume you've had (or are taking now) a course in linear algebra
(52 or 54). The calculus requirement (equivalent of Math 180,
200 or 350) is a serious one.
We will use multivariable calculus in this course. Take the Calculus
review test if you have any doubts that you are properly placed.
Calculus Review Problems, by S.J.Miller
Extra help in math1610: There is
an undergraduate TA for this course who will be holding a weekly
recitation section. The recitation section is optional, not
mandatory, but I recommend that you attend if possible.
Your TA is Drew Parker
and you can contact him by email at William_Parker followed
by the usual Brown address. The recitation section meets
Wednesdays 5-6 in BH 159.
Undergraduates with an interest or major in mathematics can check out the
Mathematics Department undergraduate program website at
http://www.math.brown.edu/ugrad_prog.html and the links
there to the Math DUG and
WISE (Women in Science
and Engineering) groups.
LATEST NEWS:
Check out
http://site.ebrary.com/lib/brown for links to books
online. For example, the Schaum's outline series is available.
| Calendar | Material Covered | Homework Assignments |
| Sept. 6 | Introduction
Sample spaces, probability distributions | Read Chapter 0,
Do problems 6,9,12 p.48 |
| Sept. 11
Sept. 13 | Finish chapter 1, begin Chapter 2
Chapter 2: Conditional prob, independence | Read Chapter 1, Do #1,3,8 p. 76 (due 9/20)
Read Chapter 2, Do #14,34,35,36,43 (due 9/20) |
| Sept. 18
Sept. 20 | Counting! permutations, combinations
More counting | Start reading chapter 3, Do #1,4,6,14 p. 108 (due9/20)
Finish chapter 3 (& all examples) Do #8,13,27 p. 108 |
| Sept. 25
Sept. 27 | Random variables, expected value,
Variance, conditional distributions | start reading chapter 4, Do #2,5 p. 151 and Ex. 4.10.1, 4.10.2
Read chapter 4, Do #20,36 and Ex. 4.18.2. |
| Oct. 2
Oct. 4 | Finish chapter 4, conditional expectation, inequalities
Start Chap. 5, joint distribution functions | p. 151 #42, 46 (due Thurs. Oct 4)
Review Chapter 4, and sample problems |
| Oct. 9
Oct. 11 | Chap. 5, joint probability mass functions
>NO CLASS | p.226, #2,4,21
Study for exam, in class 10/16 |
| Oct. 16
Oct. 18 | Exam
covariance, begin Chapter 7 | p.206 Ex. 5.11 (3), (5)
Read 7.1, p. 334 #1,2,5 |
| Oct. 23
Oct. 25 | Sections 7.2 and 7.4
Continue 7.4 | Ex. 7.18.3, 7.18.6, p.334 #7,8,17,33
|
| Oct. 30
Nov. 1 | 7.5
Moment generating functions and Random selection | p. 334 #23, 24 (due Thursday Nov.8)
p. 325 Ex. 7.13.2, 7.13.3, 7.13.4 |
| Nov. 6
Nov. 8 | Joint density functions, vectors of random variables
Change of variable, section 8.2 | Read 8.1, Do #1,3,10 p.391
Read 8.2 |
| Nov. 13
Nov. 15 | Introduction to sums of rv's, conditional densities
Independence and sums of rv's | p. 327 Ex. 7.15.6, 7.15.7, p. 392 #5, 6
Ex. 8.11.3, 8.11.4, p. 392 #18, |
| Nov. 20. | Special topics (Markov chains, random walk) | |
| Nov. 27
Nov. 29 | Conditional expectation
Chebychev, Weak Law of Large Numbers | on handout
on handout |
| Dec.4
Dec. 6 | Central Limit Theorem
Strong Law of Large Numbers/Chernoff bounds | See homework handout on Thursday |
| Dec. 11
Last class - miscellaneous topics and review |