Math E-320: Fall 2017

Teaching Math with a Historical Perspective

Mathematics E-320:

Instructor: Oliver Knill

Office: SciCtr 432

Email: knill@math.harvard.edu

Here is a more detailed talk: write four short stories, each should deal with a major mathematical idea and each be connected to a major mathematician. One from -1000-0 AC, one from 0-1000 BC and one from 1000 to 2000 BC and one from 2000- to now. The format is pretty free. There are no formal requirements. It does not have to be long but there are no length restrictions. I expect 3-4 pages for each story. Here is an example of a structure. What I would like to see is to one side cover an important aspect of the mathematics of that millenium, on the other side to be personal if possible entertaining, some story you could tell to a student, if possible something inspiring. Here is an example of a structure:

Four millenia, four milestones, four lives ------------------------------------------ Project written by Leonard Euler 1. Antique: Hyppocrates 2. First Millenium: Thabit ibn Qurra 3. Second Millenium: Sofia Kovalevskaya 4. Modern time: Grigori PerelmannIn this course, I always have evaluated the projects with four numerical grades, then took the average.

1. Sources www sources are ok but count less than books or article bibliography 2. Content especially mathematical and historical accuracy, correctness, richness 3. Originality choice of topic, implementation, weaker are rewritings of well known things 4. Style clarity and readability, also the overall uniformity and how the 4 stories match or complementIn general, the level of mathematics or difficulty of topic should not matter. With more math content it is also reasonable to be more forgiving as writing about a difficult topic can be harder. Also writing about an more elementary topic should not be penalized. For style, also some structural things can matter. Having one story 10 pages and an other 2 pages is less good than a balanced essay with four stories each weighting about the same. I would be a bit careful about implementing too much constraints. One could for example make the restriction to have all 4 stories taking place in Greece or that all stories deal with Algebra. It has sometimes worked out to be more restrictive to get a "theme" but it also has turned out to be tougher to write. It is a good idea to start with the project early. Open a file and enter ideas while we go through the topics. Make 4 bins, through in ideas for each. Look for sources for each and see whether it is rich enough. Some topic might look good but is harder to implement. Inventing a fictional character like "anonymous Mayan Mathematician" could be challenging for example Let me know if you have questions. You can also bounce ideas with me if you like.

Audience: Put yourself in readers shoes Context: Use complete sentences, explain notation Formality: Avoid shorthand formal writing Etiquette: Conventions, define unfamiliar words Tone: Set an invitational tone Elegance: Highlight the important Structure: Use Paragraphs, split hard things Examples: Use good examples Clutter: Remove the unnecessary Simplify: Step back, streamline Culture: Observe norms, practice Enjoy: The art of writing

- 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