Math 56 - Modeling

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This is the home page for Math 56.

Here is the Markov Chain tool from class:

transitions1.xls

10/29/07: Here's homework 3:

56homework3.doc -- one-page Word document; due 10/30/07

10/9/07 - TaylorChapter4.pdf - That's a link to a scan (3MB+ pdf file) of Chapter 4, on Political Power, in Alan Taylor's book, Mathematics and Politics.

9/20/07 - Spreadsheet at end of class 9/20:

PopulationMatrix1.xls

9/20/07 - Solution sheet for homework 1:

56solutions1.doc (WORD document with a bit of MathType; 11 pages)

Your solutions were probably better.

9/19/07 - CORRECTION TO PROBLEM 3 in tomorrow's homework:

This may be too late to help, but

Equation (11) should be
r(t) = r_0 - a(t-t_0)

Equation (12) should be
x(t) = x_0 exp ( r_0(t-t_0) - [a(t-t_0)^2]/2 ).

(I'm using the TeX symbols _ for subscripts and ^ for superscripts. For example, t_0 means t-with-subscript-zero and ^2 means exponent 2.)

If you don't want to start the problem over with the correction, feel free to assume that t_0 = zero. With that assumption, the correction is unnecessary.

9/19/07 - As you may have noticed, there are errors in problem 3 of the homework, too. Some of the t's should be (t-t0)'s. And it may be worse than that---some of the integrals may depend on the correction. I'll try to post a full correction later; meanwhile, maybe the best way to deal with problem 3 is to assume that t0 is always 0, wherever it appears.

9/18/07 - Here is the spreadsheet from class 9/18 (very slightly cleaned up):

PopulationMatrix.xls

It uses these three tricks from Excel:

(1) Naming a block of cells...Highlight the block of cells (any rectangle), and then type a name into the "name box" (just above the upper-left corner of the spreadsheet). THEN HIT ENTER before going on. From then on, you can use that name in formulas to refer to that block of cells. (Names that can be confused with columns or cells, like A or A10, are very unlucky.)

(2) Array formulas...Highlight a block of cells, and then type a formula as if you were entering it into one cell. But, the formula gives an entire array as an answer, so it fills the array you have highlighted. When you're done typing the formula, DON'T JUST HIT ENTER. Hit Ctrl-shift-ENTER. That tells Excel that it's an array formula. Example: cells B9:B12 in the spreadsheet.

(3) The Matrix-Multiplication function: "=MMULT(array1, array2)". This is always an array formula.

9/18/07 - Homework for Thursday, with two corrections:

(WORD) 56homework1.doc

(web) 56homework1.htm

The corrections are, in problem 1, equation 4, exp(rt) becomes exp(r(t-t_0)), and in problem 2, equation 10, the left side is 1+R_k, not just R_k.

9/6/07 - Here's the spreadsheet from class (just as we left it, with no further editing): Population1.xls

9/4/07 - Well, I guess our little experiment in Social Choice turned out well. The winning topic (by number of mentions or subjective reading) was "Social Choice and Game Theory" --- and "Social Choice" and "Game Theory" would have been among the winners even if treated as two topics. These are among my favorite subjects, too, so I guess we'll look at Social Choice right after population models, probably starting with Maki-Thompson Section 2.3, and pick some other game-theoretical models, too.

On the other hand, the next five topics were all essentially tied: Reliability, Queueing, Cellular Automata, Search for Lost Objects, Regression and Curve Fitting.

Nobody mentioned linear programming, network flow, or graphs, and only a few people mentioned population models, presumably because I declared these things to be part of the course automatically.

9/4/07 - Links to: Louis J. Gross's home page --- His presentation on Florida (ppt link) --- Jennifer Tour Chayes's home page at Microsoft --- a paper by her with a large-graph model of a social network (pdf link, not the one on internet worms) --- Daniel Maki's home page

Also, the smiley faces.

9/2/07 - Here's the text:

Maki and Thompson, *Mathematical Modeling and Computer Simulation,* Thompson-Brooks/Cole, 2005, ISBN 0-534-38478-1.

After some introductory examples we'll start with population growth models, which are treated in section 2.2 of the text, and further in sections 2.5 and 2.6. An advocate said on TV yesterday that the increase in the U.S. population between now 2060 will be 167 million, two-thirds from immigration (mostly legal immigration). Is that right? Plausible? How would anyone know?

56homework3.doc -- one-page Word document; due 10/30/07

56homework2.doc --

56homework1.doc --

56Schedule.htm -- schedule (as of 9/2/07)

56Schedule.xls -- schedule (as of 9/2/07) (Excel version)

56CourseInfo.html -- syllabus (preliminary 9/2/07)

**Course info: (or see **syllabus**)**

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**Class:** Science Center 145, TT 11:20am-12:35pm

**Instructor:**
**Walter Stromquist**

Office: Science Center 159.

Office hours: Tu-Thur 1:30-3:30 or whenever.

Email: wstromq1@swarthmore.edu

Phone: Cell 610-220-4382 (ok to leave messages).

Office phone 610-690-6827 (please don't leave messages).

For snow emergencies on class days, call the office phone 610-690-6827 after 9:30am.

**Text:** Maki and Thompson, *Mathematical Modeling and Computer Simulation,* Thompson-Brooks/Cole, 2006, ISBN 0-534-38478-1.

**Web site:**
http://www.swarthmore.edu/NatSci/wstromq1/math56/index.html

**Course requirements:** Homework (30% of grade), class participation (10%), two interim exams (probably takehome, due about October 9 and November 13; 30% total), final project paper (30%), no final exam (0%).

**From the catalog:** "An introduction to the methods and attitudes of mathematical modeling. Because modeling in physical science and engineering is already taught in courses in those disciplines, applications in this course will be primarily to social and biological sciences. Various standard methods used in modeling will be introduced: differential equations, Markov chains, game theory, graph theory, and computer simulation. The emphasis, however, will be on how to apply these subjects to specific modeling problems, not on their systematic theory. The format of the course will include projects as well as lectures and problem sets."

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