Math 646 Applied Mathematics and Math Modeling

Instructor: Matthew Dobson
Class meeting: MWF 9:05am-9:55am LGRT 1322
Course Text: Applied Mathematics by David Logan (3rd edition preferred, others permitted).
Office hours: Mo 10:10-11:00am, Tu 3-4pm, Fr 11:10am-12pm or e-mail me to make an appointment.
Office: LGRT 1430 (Tower)
e-mail: dobson@math.umass.edu
Office phone: 545-7194

Course Structure and Grading Policies:

Reading Assignments

Week 1: Sections 1.3 and 2.1 (3rd edition) Sections 1.3 and 3.1 (4th edition). Send your questions to me by midnight on 1/25.

Week 2: Sections 2.2-2.5 (3rd edition) Sections 3.2-3.5 (4th edition). Send your questions to me by midnight on 2/1.

Week 3: Sections 3.1-3.3 (3rd edition) Sections 4.1-4.3 (4th edition). Send your questions to me by midnight on 2/8.

Week 4: Sections 3.4-3.5 (3rd edition) Sections 4.4-4.5 (4th edition). Send your questions to me by midnight on 2/15.

Week 5: Snowball Earth and Global Warming, from K. K. Tung's Topics in Mathematical Modeling. (Printed copy provided in class.) Send your questions to me by midnight on 2/22.

Week 6: Sections 5.1-5.3 (3rd edition) Sections 9.1-9.3 (4th edition). Send your questions to me by midnight on 2/29.

Week 7: Section 5.4 (3rd edition), Section 9.4 (4th edition). Also: An Algorithmic Introduction to SDEs by D. Higham. Send your questions to me by midnight on 3/7.

Week 8: Readings from Introduction to Stochastic Differential Equations for Finance by Andrew Papnicolaou
Chapter 1, Sections 2.1-2.3, Sections 3.1-3.5. Please send your questions by midnight on 3/22.

Week 9: Sections 6.1 and 6.2 (both editions). Please send your questions by midnight 3/31.

Week 10: Sections 6.3-6.6 (both editions). Please send your questions by midnight 4/4.

Week 11: Sections 7.1-7.2. Please send your questions by midnight 4/14.

Week 12: Chapter 8. Please send your questions by midnight 4/21.

Additional Resources

An additional resource on random walks: Durret, Probability: Theory and Examples

Demo code for March 25th:
Random Walk Codes. The code is written in Scilab, which is a free software alternative to Matlab. The syntax is similar to Matlab, so it should be easy to convert if you choose.
Demo code for March 27th:
Heat Map Generation.

Homework Assignments

Problem numbers are listed for each edition. Please carefully note the subsection and subsubsection number for each problem, since subsections can have multiple sets of exercises.

Homework 1: Due 2/10
Sec 1.1.4: 6, 11; Sec 1.2.3: 3; Sec 2.1.4: 2; Sec 2.2.3: 1a,c; Sec 2.3.4: 4. (3rd edition)
Sec 1.1.4: 6, 11; Sec 1.2.3: 3; Sec 3.1.4: 2; Sec 3.2.3: 1a,c; Sec 3.3.4: 4. (4th edition)


Homework 2: 2/26
Section 2.4.2: 4; Sec 2.5.2: 5; Sec 3.1.2: 2; Sec 3.2.3: 13; Sec 3.3.3: 13; 3.5.3: 3, 8. (3rd Edition)
Section 3.4.2: 4; Sec 3.5.2: 5; Sec 4.1.2: 2; Sec 4.2.3: 5; Sec 4.3.3: 13; 4.5.3: 3, 8. (4th edition)


Homework 3: 3/13
Tung Handout: 6, 9
Section 5.1.2: 5; Sec 5.3.2: 4, 5; 5.3.3: 3, 5. (3rd Edition)
Section 9.1.2: 4; Sec 9.3.2: 4, 5; 9.3.3: 3, 5. (4th Edition)

Homework 4: 4/3
Homework 4


Homework 5: 4/17
Section 6.1.1: 4, 6
Section 6.2.5: 3, 13
Section 6.3.2: 7 (There is a typo in both editions. Please take n = 3.)
Section 6.4.2: 1b
Section 6.6.2: 2, 3


Homework 6: 5/1
Section 7.1.2: 1; Section 7.2.1: 2; Section 8.1.4: 4,6; Section 8.3.3: 6, 20, 21, 22 (3rd Edition)
Section 7.1.1: 1; Section 7.2.1: 2; Section 8.1.2: 1, 11 Section 8.4.3: 6, 21, 22, 23 (4th Edition)