Dr. Sarah's What is a Mathematician?     A Teaching Assignment (Presentation and Worksheet)

In this segment we will examine the way that mathematicians do research and the kind of problems that they work on. While we will mainly focus on the mathematics, you should try and identify with the mathematicians and their struggles with mathematics and relate this to the way that you do mathematics. We will highlight the validity of diverse styles and diverse mathematical strengths and weaknesses. We will see that there are lots of different ways that people are successful in mathematics. We will also examine the changing roles of women and minority mathematicians over time.

In class on Thursday, groups will choose a mathematician (see below). Then, on your assigned day, you will present a PowerPoint presentation, and will create a classroom activity sheet to further engage the class.

I have worked hard to accumulate good references for you so that you won't have much research to do. I will give you both web and paper references. Your job is to learn the material and figure out how to teach it to the rest of the class. I am handing the assignment out early to give you plenty of time to examine the material and let it sink in and jell, and to allow you time to make it into office hours. This process is important for success on this topic, so do not leave this until the last minute! Instead, you should work on the mathematics a little bit at a time, reading and engaging it for about an hour or two, then putting it aside for a day or two, and then coming back to it and trying again and again and again.

Answer the Following Questions on the Mathematics that is Related to your Mathematician

Be sure that you include answers to the following questions about mathematics that is related to your mathematician in your presentation. Some answers may be brief so ask me if you are not sure of the expected depth. Be sure that you engage the class with the material in your worksheets, and that you explain the mathematics in your own words. I also recommend that you bring drafts into office hours and class to discuss them with me. You are responsible for the material from other people's presentations, worksheets and the material that Dr. Sarah highlights for WebCT quizzes and for the exam. Checklists for more pointers on the presentation and classroom worksheet that you will prepare will be handed out later.

Thomas Fuller (1710-1790) Speed of Mental Calculations, Calculator and Computer Time
  • How would we do Fuller's calculation of the number of seconds a man who is seventy years, seventeen days and twelve hours old has lived by hand?
  • What affects calculator and computer calculation time?
  • Compare Fuller's times to various calculator and computer times (the first calculator, the first computer, eniac, and modern calculators and computers).
  • Is there a limit to how fast a computer can calculate?

    Maria Agnesi (1718-1799) Witch of Agnesi and Calculus
  • What is the witch of Agnesi? How did it receive that (derogatory) name?
  • How do you construct it geometrically?
  • If the generating point is dragged far enough to the right, why won't the point generated on the curve be located at y=0?
  • How does it relate to Agnesi's mathematics?
  • How is it used in real life?
  • What are some of the applications of calculus to real-life?

    Sophie Germain (1776-1831) Sophie Germain Primes and RSA Coding
  • What is a Sophie Germain prime?
  • Why did she come up with Sophie Germain primes?
  • What is the largest Sophie Germain prime that has been found? How many digits does this have?
  • What is the definition of a mod b?
  • How do modular arithmetic and Sophie Germain primes relate to RSA coding?

    Carl Friedrich Gauss (1777-1855) Non-Euclidean Geometry
  • What is Euclid's 5th postulate?
  • What is the equivalent form of the 5th postulate that we learn in high school?
  • What is the negation of the 5th postulate?
  • What two geometry possibilities does this negation give rise to?
  • How does this relate to Gauss?

    Georg Cantor (1845-1918) The Size of Infinity
  • What are the natural numbers?
  • What are the real numbers?
  • Using ideas related to Dodgeball, why are there more real numbers than natural numbers?

    Srinivasa Ramanujan (1887-1920) Chebyshev's Theorem and Estimating the Number of Primes Less than a Given Number.
  • What is a prime number? Why are they of interest?
  • What is the statement of Chebyshev's Theorem? How does this relate to Ramanujan?
  • What were Gauss' estimates of the number of primes less than or equal to a given number? How does this relate to Ramanujan?

    Paul Erdos (1913-1996) The Party Problem
  • What is the statement of the party problem? How does this relate to Erdos?
  • Why does a 6 sided polygon colored red with a 6 sided embedded star with edges colored blue prove that 5 people at a dinner party is not enough to ensure that there are at least 3 people who are either complete strangers or acquaintances?
  • To show that if there are 6 people at a dinner party then there are at least 3 people who are either complete strangers or acquaintances, why can we reduce to looking at 4 of those people? How do you complete the argument from here?

    David Blackwell (1919-) What is Game Theory?
  • What is the prisoner's dilemma? How does this relate to what David Blackwell worked on?
  • What matrix of payoffs represents the prisoner's dilemma?
  • If a person is deciding what to do, why does it make sense (when looking at the possible cases) for him to confess?
  • What are the applications of game theory to real life?

    Mary Ellen Rudin (1924-) What is Topology?
  • What is topology? How is it different from geometry and projective geometry?
  • Why are a basketball and a football the same in topology?
  • Why are an iron and a mug with one handle the same in topology?
  • Why is a vest and a mug with two handles the same in topology?
  • Why are the above lines different from each other in topology?

    Frank Morgan (195?-) The Double Bubble Problem
  • Why is the sphere the least area way to enclose a given volume for a package?
  • If a sphere and a box have the same surface area, then which will have the largest volume?
  • What is the Double Bubble Problem?
  • What did Frank Morgan prove about it?
  • Did he have to check every possible double bubble?

    Ingrid Daubechies (1954-) Wavelets
  • How can images be stored on a computer?
  • What is image compression? Why do we need it?
  • How are wavelets related to image compression?
  • Why are wavelets better then JPEG?
  • What are other applications of wavelets to real life?
  • What do wavelets have to do with Ingrid Daubechies?

    Group Work

    Group work on major assignments will be self evaluated and that these evaluations will be taken into account in the determination of the final grade. So, your job is to make sure that you do your part to make sure you are working in a group effectively. Inequalities in group work WILL be addressed.