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Math 115 Summer 2008

'He who asks is a fool for five minutes, but he who does not ask remains a fool forever'.
--Chinese Proverb

My Office: 3C13
Office Phone: 215 898 2949
Email:

Office Hours:
Monday - Thursday 3:10pm - 4pm
By appointment.

Your homework assignment:

Note: There might be repetitions (or at least very similar problems) among the old exam problems. If you feel you know how to do the problem and you have done some problems of the same kind, skip the problem.

Assignment 1, week 1: F06: 7, 11; S06: 7, 8, 11; F05: 15; S05: 6, 8; F04: 9, 10; S04: 6, 8; S03: 16, 17; F02: 7, 9.
Answers: F06: E, B; S06: B, B, F; F05: C; S05: F, H; F04: F, B; S04: B, E; S03: H, C; F02: D, H.

Assignment 2, week 1: F06: 6, 8; S06: 6; F05: 14, 16; F04: 16; S04: 7, 9; F03: 7; S03: 15, 18; F02: 8.
Answers: F06: F, E; S06: A; F05: F, D; F04: E; S04: E, F; F03: F; S03: D, G; F02: F.

Assignment 3, week 2: F06: 13; S05: 7; S04: 10; F02: 10.
Answers: F06: C; S05: D; S04: F; F02: G.

Assignment 4, week 2: F06: 12; S06: 14; F05: 2; S05: 16; F04: 17; S04: 17; F03: 13; S03: 2.
Answers: F06: F, C; S06: H; F05: E; S05: D; F04: H; S04: C; F03: A; S03: B.

Assignment 5, week 3: F06: 9; S06: 9; F05: 1, 6; S05: 10; F04: 11, 18; S04: 12; F03: 9; S03: 1; F02: 11.
Answers: F06: C; S06: F; F05: C, C; S05: C; F04: C, C; S04: C; F03: D; S03: F; F02: D.

Assignment 6, week 4: F06: 10; F05: 5, 17; F04: 8; F03: 14; S03: 14; F04 Mk: 17, 18.
Answers: F06: H; F05: H, H; F04: B; F03: A; S03: C; F04 Mk: G, F.

Assignment 7, week 4: F06: 1, 2, 3, 4, 5, 14; S06: 1, 3, 4, 5; F05: 3, 7, 8, 10; S05: 1, 2, 3, 4, 5; F04: 1, 2,3, 4, 13, 14.
Answers: F06: D, F, B, G, D, D; S06: D, B, A, C; F05: C, D, A, D; S05: H, F, C, D, D; F04: F, D, B, C, F, F.

Assignment 8, week 5: F06: 15, 16; S06: 15, 16; F05: 9, 12, 13; S05: 13, 14; F04: 5, 7.
Answers: F06: D, A; S06: (0, infinity, 1, 0), E; F05: B, E, F; S05: (0, infinity, 0, 1), C; F04: B, B.

Assignment 9, week 5: S06: 10, 17; F05: 18; S05: 9, 18; F04: 12, 15; S04: 1, 2, 4, 5, 15, 18, 19; F03: 3, 5, 10, 11, 18; S03: 3, 5, 12; F02: 1, 4, 5, 12, 14, 16.
Answers: S06: D, F; F05: C; S05: D, A; F04: B, E; S04: E, C, B, E, A, D, E; F03: -; S03: G, E, A; F02: D, B, G, E, C, (infinity, 1, 0).

Tentative course schedule:

The sections below refer to the relevant sections in Probability and Matrices and Calculus. The probability theory will not be covered in strictly in this order, see material covered below.

Week 1 + 2

Definition of probability and discrete random variables.
Sections: 1.5, 1.6, 1.7, 1.8, 1.9, 1.10, 2.1, 2.2, 2.3, 3.1, 4.1, 4.2, 4.3, 5.2, 5.4.

Week 3

Continuous random variables.
Sections: 3.2, 3.3, 4.1, 4.2, 4.3, 5.6, 5.9
Exam 1

Week 4

Calculus.
Sections: 15.1, 15.2, 15.3, 15.4, 15.5, 15.7, 16.1, 16.2, 16.3.

Week 5

Linear Algebra.
Sections: 2.1, 2.2, 2.3, 2.4, 2.5, 2.6.

Week 6

Bivariate distribution, Markov chains, Least squares fit.
Sections: 3.4, 2.4, 1.3.
Exam 2.

Material Covered in Class:

The sections below refer to the relevant sections in "Probability and Matrices" [PB] and "Calculus" [C]. [R] refers to the supplementary book "A First Course in Probability Theory" by Ross.

Week 1

Monday:
[PB]: The counting and combinatorial methods in 1.7 and 1.8.
[R]: 1.1 - 1.4.
Tuesday:
[PB]: 1.5 - 1.10.
[R]: 1.5, 2.1 - 2.5.
Wednesday:
[PB]: The remaining part of sections 1.5 - 1.10.
[R]: Section 2.5.
Thursday:
[PB]: Section 2.1, 2.2.
[R]: Section 2.2 3.1 and 3.2.

Week 2

Note that we have only covered discrete random variables, the sections [PB] 4.1 - 4.3 cover both discrete and continuous random variables.

Monday:
[PB]: 2.2, 2.3, 3.1.
[R]: 3.2 3.3, 3.4, 4.1.
Tuesday:
[PB]: 3.1, 4.1, 4.2.
[R]: 4.1, 4.2, 4.3.
Wednesday:
[PB]: 4.3, 5.2.
[R]: 4.4, 4.5, 4.6, 4.6.1.
Thursday:
[PB]: 5.2, 5.4.
[R]: 4.6.1, 4.6.2.

Week 3

We covered almost all of the material on continuous random variables, including expectation and variance of continuous random variables and uniform and normal distributions.

Monday:
[PB]: 3.2, 4.1, 4.2.
[R]: 5.1, 5.2.
Tuesday:
Problems from the homework.
Wednesday:
[PB]: 4.2, 4.3.
[R]: 5.2, 5.3.
Thursday:
[PB]: 5.6.
[R]: 5.4, 8.3.

Week 4

Monday:
[PB]: 5.8.
[R]: 3.5
[S]: 15.1, 15.2
Tuesday:
[S]: 15.2, 15.3, 15.4, 15.5.
Wednesday:
[S]: 15.6, 15.7.
Thursday:
[S]: 16.1,16.2, 16.3.

Week 5

Monday:
[PB]: 2.1, 2.2, 2.3, 2.4, 2.5.
Tuesday:
[PB]: 2.6.
[R]: 6.1.
Wednesday:
Problems from the homework.
Thursday:
[R]: 6.1, 6.2.

Week 6

Monday:
[R]: 6.3.
Tuesday:

Wednesday:
Project presentation and problems from the homework.
Thursday:
Exam.

General Information

The lectures take place in DRL 4C6 on Monday, Tuesday, Wednesday and Thursday from 1:00pm to 3:10pm. There will be a 10min break at 2:00pm.

Email

I will send out general organizational information by email, so make sure you check your inbox at least every couple of days. I will answer questions received by email as soon as possible. I promise that you will have an answer within 24 hours.

Homework, Project, Tests and Possible Makeups

Homework: You are not required to hand in your homework. It is, however, vital that you do and understand the homework assignments; both for understanding the material and since the exam problems will essentially consist of homework problems. Homework will follow the lectures and will primarily consist of old exam problems. I will announce the relevant problems twice a week.

Quizzes: There is one quiz per week, typically an old exam problem in the material we covered that week. If you must miss a quiz, come see me during office hour for a makeup. In weeks with an exam there is no quiz.

The Project: You are supposed to write a short essay on one of the topics we will cover in probability theory. You will present this in class on the Monday before the second exam. The presentation will be about 10min long and you are expected to say a little about your essay. You will hand in the essay (due date to be decided) and I will check it before the presentation.

Exams: There will be two exams, one in week three and one in week six (Thursdays, first hour of class). The material on the first test will be everything we have covered in class before the exam. The second test will have an emphasis on the material covered in the last three weeks. This does not mean that the material covered in the first three weeks will be completely left out! If you know you are going to miss an exam, please let me know as soon as possible (office hours or email).

Grades will be posted on Blackboard.

Group Work

Working with other people on mathematics is not only allowable, but is highly encouraged and fun. You may work with anyone (other students in your section, in the course, not in the course, bums on the street) on your homework problems. If done right, you'll learn the material better and more efficiently working in groups.

I strongly encourage you to get together in small groups and work on the homework problems!

You should get used to writing up a final draft yourself. This is the only way to make sure that you really understood the solution your group came up with. If you cannot write it up you didn't understand it as well as you should have and you need to go back and look at it again, and ask your group. Nobody will be angry at you for asking; to explain it to others is actually a good way to learn the material.

Help Resources

It is important that you understand that our (my!) only objective is to help you understand the material. Period. So, if you have problems, for example if you are falling behind with homework, if you have difficulties understanding what is presented in the lectures or maybe you are simply getting worn down because of the general work load, there are several things you can and should do.

(1) Email me or come see me.

(2) Private tutoring is an excellent way to get rid of small (or big) misunderstandings. You pay an experienced graduate student (pick one from the 'approved by the department' tutor list here to teach you the fundamentals, to help you with the problems, or whatever way you would like it. You pay for it, the average salary is 40$ an hour.

Please do not hesitate to contact me if you have suggestions for ways to help you better succeed in this class!