Math 60850, Fall 2014

Pasquerilla Center 107: MW  12:30-1:45


Information on grading, tests, and homework  

Course Syllabus


Instructor: Andrew Sommese (Hurley 291).

Email: sommese@nd.edu

 

Office Hours: open door.


Handouts

Analysis of Craps (PDF file);

Markov Chains Applied to Craps (PDF of Maple Worksheet);

Markov Chain for Random Walk on Vertices of a Die (PDF of Maple Worksheet);

Markov Chain for Usual Random Walk with Barriers (PDF of Maple Worksheet);

rutherford.pdf, PDF of a Maple Worksheet on the Poisson distribution and the chi-square goodness-of-fit test: Rutherford's Geiger Count Data.

 


Exam Schedule

Exam 1: Wednesday, October 8 (take home due date).    Answers
Exam 2: Wednesday, November 19 (take home due date). Answers
       PDF of Maple Worksheet For Test 2
Final: December 17, 2014 (take home due date).  Answers


Homework

Homework 1 (Due Wednesday, September 3)    Answers

        pg 12  Problem 6 and 7.  For Problem 7, only do the case n = 4.

          pg 14  Problem 9.

          pg 21 (in Problem set 1.8) Problems 1 and 3.

          pg 22 Problem 11 (case n=3 only), 14, 16.

 

Homework 2 (Due Wednesday, September 10)    Answers

        pg 30 Problems 1, 2, and 3 of the Exercises for Section 2.1.

          pg 35 Problems 4 and 5 (part a) of the Exercises for Section 2.3.

          pg 38 Problems 1 (parts a, c, and e) and 2 of the Exercises for Section 2.4.

          pg 43-45 Problems 5, 6, 9, 18, and 19 (parts a and b) of the Exercises for Section 2.7.

 

Homework 3 (Due Wednesday, September 17)    Answers

        pg 47 Problems 1ad, 2 (only for a and d of Prob. 1), and 3 of the Exercises for Section 3.1.

          pg 49 Problems 2abc and 4 of the Exercises for Section 3.2.

          pg 55 Problems 1, 2, and 4 of the Exercises for Section 3.3.

          pg 59 Problem 1 of the Exercises for Section 3.4.

          pg 155 Problem 2 of the Exercises for Section 5.1.

 

Homework 4 (Due Wednesday, September 24)    Answers

        pg 62 Problem 2 of the Exercises for Section 3.5.

          pg 66 Problem 1 of the Exercises for Section 3.6.

          pg 69 Problems 1, 2, and 4 of the Exercises for Section 3.7.

          pg 71 Problem 5 of the Exercises for Section 3.8.

          pg 75 Problem 1 of the Exercises for Section 3.9.

 

Homework 5 (Due Wednesday, October 1)    Answers

        pg 91 Problem 1c (with n = 1) and 3 of the Exercises for Section 4.1 (for 3, Exercise 3 of 2.3 might be useful) .

          pg 92 Problem 1 of the Exercises for Section 4.2.

          pg 94 Problems 1a and 3 of the Exercises for Section 4.3 (for 3 assume that x^r*P(X > x) → infinity as x → infinity).

          pg 103 Problems 4, 7, 8 of the Exercises for Section 4.5.

          pg 107 Problem 8 of the Exercises for Section 4.6.

 

Homework 6 (Due Wednesday, October 29)    Answers

          pg 107 Problem 4 of the Exercises for Section 4.6.

          pg 192 Problems 1 and 3 of the Exercises for Section 5.9.

          pg 200 Problem 1a of the Exercises for Section 5.10.

          pg 206 The first half of Problem 37 (showing independence) of the Exercises of Problem Set 5.12.

          pg 219 Problems 1, 2a, and 9a of the Exercises for Section 6.1.

          pg 226 Problem 4ab of the Exercises for Section 6.3.

 

Homework 7 (Due Wednesday, November 5)    Answers

          pg 236 Problems 4 and 11a of the Exercises for Section 6.4.

          pg 242 Problem 1 of the Exercises for Section 6.6.

          pg 255 Problems 1 and 2 of the Exercises for Section 6.8.

          pg 264 Problem 1 of the Exercises of Exercises for Section 6.9.

 

Homework 8 (Due Wednesday, November 12)    Answers

          pg 255 Problem 5 of the Exercises for Section 6.8.

          pg 296ff Problems 1, 3 and 5 of the Problem Set 6.15.

          pg 338 Problems 1, 3, 4 of the Exercises for Section 7.7.    

 

Homework 9 (Due Monday, December 1)   Answers

          pg 475 Problems 1i and 2 of the Exercises for Section 12.1.

          pg 490 Problems 1, 2 and 7 of the Exercises for Section 12.4.

          pg 495 Problems 4 and 7 of the Exercises for Section 12.5.

          pg 525 Problem 9 of the Exercises for Section 13.3.

          pg 529 Problem 1 of the Exercises for Section 13.4.

 

Homework 10 (Due Monday, December 8)   Answers

          pg 544 Problems 1 and 5 from the Exercises for Section 13.8 (You may use Ito’s Formula).

          pg 547 Problems 2, 3,  4, and 5 from the Exercises for Section 13.9.

          pg 561 Problem 1ab from the Exercises for Section 13.12.


Lectures

Lecture 1 (Wednesday, August 27, 2014)

Lecture 2 (Monday, Sept 1, 2014)

Lecture 3 (Wednesday, Sept 3, 2014)

Lecture 4 (Monday, Sept 8, 2014)

Lecture 5 (Wednesday, Sept 10, 2014)

Lecture 6 (Monday, Sept 15, 2014)

Lecture 7 (Wednesday, Sept 17, 2014)

Lecture 8 (Monday, Sept 22, 2014)

Lecture 9 (Wednesday, Sept 24, 2014)  The alpha used in the problem has an extra N in the exponent.  Replacing the alpha used with the corrected N-th root of alpha does not affect the argument, i.e., alpha is still < 1.

Lecture 10 (Monday, Sept 29, 2014)

Lecture 11 (Wednesday, Oct 1, 2014)

Lecture 12 (Wednesday, Oct 8, 2014)

Lecture 13 (Monday, Oct 13, 2014)

Lecture 14 (Wednesday, Oct 15, 2014)

Lecture 15 (Monday, Oct 27, 2014)

Lecture 16 (Wednesday, Oct 29, 2014)

Lecture 17 (Monday, Nov 3, 2014)

Lecture 18 (Wednesday, Nov 5, 2014)

Lecture 19 (Monday, Nov 10, 2014)

Lecture 20 (Wednesday, Nov 12, 2014)

Lecture 21: (Notes from Nov 17 and 19, 2014)

Lecture 22 (Monday, Nov 24, 2014)

Lecture 23 (Monday, Dec 1, 2014)

Lecture 24 (Wednesday, Dec 3, 2014)

Lecture 25 (Monday, Dec 8, 2014)


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