Math 139A, Fall 2017

Applications of Mathematics 


Instructor                   John E. McCarthy
Class                           Tu 10.00-11.00 in 115 Cupples I

JM Office                   105 Cupples I
JM Office Hours       M 3.00-4.00, Tu 2.00-3.45, Th 10.00-11.30, and by appointment
Phone                          935-6753


Math 131, taken concurrently


Mathematics can often seem intimidatingly abstract.
"Why do we need to know this?" and "What is this good for?" are common
questions, which sometimes are not adequately answered. 
It is all very well to say that mathematics is needed for cell-phone design, or
to make ultrasound images, or for Google to calculate page-rank; but explaining
exactly how it is used in any of these applications takes a great deal ot time.

The purpose of this course is to give examples of how mathematics can be used to
understand real world problems. It is restricted to students enrolled in Calculus I, Math 131,
so we will start with problems that only need pre-calculus to solve, and work up to ones that use

Do I need to be a math wiz to take this course?
No. The course is for students who are curious about how mathematics is used in the modern
world, and like learning.



Here is a tentative schedule. The first seven do not use calculus, the next six do.
We may change some of these topics.

  1. Dimensional Analysis. How to guess plausible formulas.
  2. The mathematics of convoys. Are they a good idea? What are the pros and cons?
  3. Fibonacci Numbers. See this site for pictures
  4. The golden ratio
  5. Fractals I :  Coastlines
  6. Fractals II : what is dimension? 
  7. Linear regression I. Application: the Gutenberg-Richter law of earthquake magnitudes. How can we speak of a twenty thousand year event? Earthquakes
  8. Euclid's algorithm versus Stein's algorithm. Efficiency of algorithms.
  9. Network capacities. Braess's paradox - building extra roads can increase congestion.
  10. Linear Regression II: How to find the best line. Application: Metabolic rate versus animal size
  11. Fractals III: Blood flow.
  12. Should we all have the same mitochondrial DNA? Galton's approach to surnames.
  13. How genes spread through populations.
  14. Sigmoid curves for populations, and the logistic equation.
  15. SIR model of infectious diseases.


Basis for Grading

Grading will be based on classrooom participation, and a term paper.
The topic of the term paper should be chosen in consultation with the Instructor.
A preliminary draft should be handed in October 31st. This will be graded and returned,
and a final version should be handed in December 5th.

Classroom Participation (contribution to discussion): 20%
Term Paper - first draft: 30%
Term Paper - final draft: 50%




I do expect you to come to class every day, and to participate in class discussions.
I expect you to read the corresponding section in Korner's book. I may call on you at
any time to answer a question.


Texts           The Pleasures of Counting, by T.W. Korner  (Cambridge, 1996).
                    This is a lovely book. If you get bogged down in some section, it is okay to move on.