Project 2: What is a Mathematician?     (Presentation and Handout)

  • Step 1 The entire class will complete related readings due the day of your presentation
  • Step 2 Your PowerPoint presentations on influences, barriers, support, diversity issues and mathematical style, and a related classroom handout you create.
  • Step 3 Dr. Sarah will go over mathematics related to your mathematicians, along with select activities.
  • 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 and relate this to the way that you do mathematics, and you should also continue to think about what mathematics is, and the useful problem solving techniques that arise from its study. 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. I have worked hard to accumulate good references for you. I will give you both web and paper references.

    Step 2: 7 - 10 minute PowerPoint Presentation and Classroom Handout

    Prepare a PowerPoint presentation and classroom handout by using the related checklists. The presentation computer file (whatever.ppt) must be sent to Dr. Sarah as an attachment on WebCT before 3pm for a Monday presentation and 11:30am for a Tues/Thur presentation. It is your responsibility to make sure that this is received by Dr. Sarah and runs correctly. Do not expect to load your presentation from a disk - the computer does not have a disk drive - but do also have the presentation backed up on disk so that you could send it from school if necessary. Be sure to follow the presentation checklist and to prepare great presentations! Oral presentations my be summed up as follows: "Tell them what you're going to tell them. Tell them. Then tell them what you told them". Don't be scared of this repetition. Sometimes repetition is the only way to clarify misconceptions. Naturally, this means that you should repeat things in different ways, and not quote yourself verbatim. Bring copies of a related handout. These are DUE at the beginning of class on the day of your presentation, but I am happy to make the photocopies for you if the completed handout is given to me a day in ADVANCE during office hours. Otherwise you must make the copies yourself. Follow the handout checklist.

    Group Work Group work on major assignments will be self-evaluated and 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.

    Step 3: Dr. Sarah Will Answer the Following Questions on the Mathematics that is Related to your Mathematician

    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 form of the 5th postulate that we learn in high school? What is the negation? What two geometry possibilities does this negation give rise to?
  • How does this relate to Gauss?
  • What are some other areas Gauss worked on?

    Georg Cantor (1845-1918) The Size of Infinity
  • What are the natural numbers?
  • What are the real numbers?
  • Using an argument that is similar to Dodgeball, show 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?
  • Why are people still interested in Ramanujan's notebooks?

    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, once we reduce to just looking at 4 of those people (3 who all either know or don't know the first person), how do we 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?
  • Give an array of payoffs filled with numbers that represents the prisoner's dilemma, and explain how to read the array.
  • 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 some 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 objects with different number of holes 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?