Math E-320: Fall 2015

Teaching Math with a Historical Perspective

Mathematics E-320:

Instructor: Oliver Knill

Office: SciCtr 432

Email: knill@math.harvard.edu

If you have some ideas or drafts, you can bounce them by me any time. You are quite free but there are two constraints: The title of the project is fixed, the structure should look as follows. Each chapter is a short story (could be 2 pages with references). Its fine to restrict the topics to a particular field you care about, or to a particular time or take a particular point of view. Experience has shown however that narrowing the topics down can be hard. Here is an example of a title structure (which is on the very narrow side as it all deals with concepts Euler found):"Ten core concepts or ideas in mathematics".

Ten core concepts or ideas in mathematics ----------------------------------------- by Leonard Euler, October 19, 2015 1. The Euler pentagonal theorem 2. The Euler polyhedral formula 3. Euler's solution to the Basel problem 4. The Euler number 5. The Koenigsberg problem 6. The even perfect numbers 7. The concept of the number 1 8. The Euler step 9. The Euler equations in fluid dynamics 10. The Euler anglesHere is an example of a title structure, which is more global

Ten core concepts or ideas in mathematics ----------------------------------------- by Archimedes, October 19, 2015 1. The number system 2. The concept of a function 3. The concept of a limit 4. The idea of symmetry 5. Equations and their solutions 6. Inequalities 7. The idea of infinity 8. The concept of proof 9. The idea of prime numbers 10. The notion of integrability

- A) For bibliography, both web biography like links and non-internet bibliography like books and articles count. Citing sources is a bonus. Books and articles give more weight. If illustrations are used, also here, references are required.
- B) For Math and theme, it will be important how the concept is explained in own words. Following directly from a source scores less points. Of course, one can get inspired from sources. Selecting an important core point and focusing on is better than a laundry list. How do the 10 stories fit together? An optimal collection has each story of similar length and difficulty level.
- C) For clarity and style, we will look whether the statements make sense, whether the story is readable (where the level does not matter), whether the structure is thought through, whether the formulations fits together and how the overall structure is. Is it clear what the theorem is?
- D) For originality and freshness, an unusual approach can gain more points. Lower scores come from formulations which can be found in a similar way on popular sources like MacTutor or Wikipedia. It is possible to cite verbatim a sentence if necessary but it has to be clearly stated. A big impact can be made by telling something which is a bit harder to find or where I can learn something new.

Please send questions and comments to knill@math.harvard.edu