HISTORICAL ESSAY MAT390/HPS390 FALL TERM 2024

The following description outlines the three course components related to your historical essay:

DRAFT ESSAY: (5% of your total grade for this class, 3/3) A draft of your paper should be uploaded electronically to QUERCUS. Your draft essay will be graded based on the following (1 point for references/bibliography, 1 point for identifiable essay structure such as thesis statement introduction body and conclusion, 1 point for completeness in terms of length of the paper). If you don’tupload your draft essay to Quercus by the due date you will receive 0/3 on this component. No late submissions.

You also must upload your draft a second time to Peer Scholar. To do this, click on the Peer Scholar  exercise on our course page, load Peer Scholar in a new browser window, goto the Create phase of the activity and upload your draft document.

PEER SCHOLAR EXERCISE: (5% of your total grade for this class, 2/2) Using Peer Scholar you will be matched with two essays written by your peers in this class. You will be given the task of reading these essays and offering your feedback on them. You have already practiced applying criteria to evaluate the  quality of historical arguments in A2: Human and AI Generated Texts on History of Mathematics. You will apply similar skills here to essays composed by your current peers. The students whose work you comment on will then receive your feedback so they can revise their argument into something stronger. You must upload your drafts to Peer Scholar to participate and get marks for this activity!! NOTE:  While your peers will help you identify areas to revise before final submission, student feedback is independent of grades given to you by course staff on your draft and final essay submissions. The grade you are given for this activity is based on the quality of your written and evaluative feedback. You have   to complete all aspects of the “create” “assess” and “reflect” phases in Peer Scholar to get all points for the Peer Scholar activity. If you don’t finish all three phases you won’t get full marks. We will devote the activity period on Monday November 18 to completing the "assess" phase of the Peer scholar assignment.

FINAL ESSAY: (25% of your total grade for this class, 25/25) Uploaded electronically to QUERCUS. The essay should be 2000 words (papers accepted in the range of 1900-2200 words). LATE POLICY: There will be a deduction of 5% per day (including weekend days) on later papers.

This final essay is a major component of your grade for this course. It is recommended that a topic be chosen early and that your research and writing be underway by later October to early November. The essay should consist of your own work; it will be run through a standard database to verify that there has been no plagiarism from any source. In particular, do not cut and paste text from websites or Wikipedia articles into your essay. Do not plagiarize.

POLICY ON USE OF GENERATIVE AI:

This assignment is designed to be completed without the use of generative AI, using only concepts and   skills we have developed in activities and through discussion of our course readings. However, as stated in the course syllabus, you may choose to use generative AI tools like ChatGPT as a tool when working    on this assignment. We encourage you to review the section on generative AI tools in the course

syllabus before considering using such tools within this assignment. Excellent work can be produced

without the use of AI. The discussion we will have while completing A2: Human and AI Generated Texts on History of Mathematics will help us determine as a class, some ways generative AI can be useful and some of its pitfalls. Remember you are responsible for the final work you submit for this assignment.

If you choose to use generative AI tools while working on this assignment, you must acknowledge which tools you used and how you used them. It is an academic offence to not credit sources—including generative AI—in any work you submit for academic credit. This acknowledgment should take the form of an appendix and in-text citations. See below for details.

APPENDIX: Students who choose to use AI must submit an appendix with their historical essay. This

appendix should be titled “Appendix: Statement on Usage of Generative AI” . Underneath this title, you must provide links to the raw transcripts that record your interactions with the tool while working on the assignment, including prompts and responses. For example, you should create a subtitle in your appendix such as “Compose an opinion editorial about how great Newton's discovery of calculus is” prompt. ChatGPT 3.5, 25 Sept. version, OpenAI, 3 Oct. 2023, chat.openai.com/chat. Then paste the text that was generated on that date by this prompt, followed with the link to the transcript. For ChatGPT transcripts,use the “share” icon in the upper right hand corner. You can find out more how to create these citations herehttps://style.mla.org/citing-generative-ai/.

CITATION OF Appendix CONTENT PRODUCED BY GENERATIVE AI: Moreover, should content be produced, written or discovered through artificial intelligence and this research or text incorporated into the body text of the historical essay, students must cite that content. For all standard references in this assignment, Iamasking for those to be formatted in APA style. For your references that use information  gathered through AI prompts, you will reference that part of your Appendix that has compiled all your prompts and responses generated.

If you quote or paraphrase a passage from text generated by AI in response to a prompt, you should have already pasted the prompt and its associated text into your Appendix. Cite that output, signalling you arrivedata certain factor opinion or through your interaction with AI. You can do that by citing the Appendix using intext citation,e.g., place the citation (See Appendix: Statement on Usage of Generative AI, p. 13) at the end of the sentence of text in which you used those ideas gather from AI.

Your final paper will be evaluated out of 25 points according to the following grading rubric:

7.5 points Motivation/Arguments: The essay presents a concise, well-stated, interesting and non-trivial thesis that is argued for persuasively. Analysis of historical sources is demonstrated. Clear and deep understanding of topic and concepts investigated. Student expresses reasoned opinion about topic at hand. Topic of paper is within scope of the course.

5 points Structure : The paper has an introduction, body, conclusion, and well-written topic sentences and coherent transitions between paragraphs. Historical material is presented in a logically cohesive way. Conclusion follows from the thesis and supporting evidence. Word count within 1900-2200 range.

5 points Written Style: Sentence structure to the point, appropriate use of paragraphs and foot/endnotes, formal (academic) style in mostly the third person, capitalization of proper nouns [e.g.: names, places, book titles], use of italics, underline or boldface is appropriate.

2.5 points Sources : At minimum the essay demonstrates a thorough reading and analysis of at least eight different sources. At least six of these sources must be academic publications that can be found through the search function of the University of Toronto library system. Application of APA bibliographic style is clear and consistent for all citations. Quotations from sources are appropriate. Any usage of generative AI as a discovery tool within essay construction has been properly cited and documented within an Appendix according to the “ POLICY ON USE OF GENERATIVE AI” laid out in this document.

5 points Overall effort : Essay demonstrates original thinking, creative research skills and/or good overall effort. The essay led the student to consider new questions or state a novel perspective on their topic. A passionately argued essay using mathematical and/or historical evidence.

American Psychological Association (APA) bibliographic and citation conventions

Please apply APA style. for citations and references:

https://apastyle.apa.org/style-grammar-guidelines/references/examples

Where to get started?

The MacTutor website for the history of mathematics can be a starting place. If you goto the bottom of an article of interest, click >References >show to see the source list for links. This is a good way to start   finding sources for your research, depending on your topic. It can be a useful place (and a more rigorous/academic online source than Wikipedia) for history of mathematics:http://mathshistory.st- andrews.ac.uk/

Essay Topics

Your essay should develop a perspective upon (thesis) about your topic. General descriptive overviews are not useful. Evidence presented in the essay must always have relevance to your thesis claim. I also encourage you to express yourself in your writing. Connect yourself in some way with your topic – this makes your writing more meaningful. What interests you about the topic? Use this question as your

“way in” to finding a claim you want to make about it. What surprised you during your research?

Observations you make, that are unique to you, often lead you to the best thesis statements. Give us your take on this discovery. Although your essay will contain factual material, it should be focused, analytical and motivated by your argument about a particular view upon the given topic.

Is history just facts? No! It is interpretation of the facts that makes some historical essays exceptional!

HERE ARE THE TOPICS

ON QUERCUS ARE LINKS TO RESOURCES THAT MAY HELP YOU GET STARTED ON EACH TOPIC AREA

1.    Getting into their heads: What Babylonian mathematical artifacts tellus

2.    How Greek and Roman people told time: Ancient Sundials

3.   Are non-constructive proofs convincing? Archimedes’ proof of circular area

4.    Does the Ancient Greeks practice of geometrical construction prove the existence of

mathematical objects in Euclid’s Elements?

5.    Not a Computer: The Antikythera mechanism and ancient Greek astronomy

6.    How is the study of cosmic triangles in Ptolemy’s Almagest and Aryabhata’s Aryabhatiya,

different from, or similar to, techniques of modern trigonometry?

7.    In what ways was Japan’s wasan period of mathematics culturally distinct in style, practice,

and topics investigated as compared with other mathematical traditions?

8.   Transmission of knowledge or independent discovery? Pascal’s Treatise on the

Triangle and Zhu Shijie’s Precious Mirror of the Four Elements

9.    Differences and similarities between Francois Viète’s The Analytic Art and modern algebra

10. Simplifying calculation prior to the modern digital computer: Napier's invention of Logarithms

11. Logic of the highly improbable: How did Compte de Buffon, Blaise Pascal and Pierre de Fermat

justify the quantification of chance?

12. Why was Cavalieri accused of heresy for his method of indivisibles? Did Cavalieri's method

present a logically sound way of measuring areas and volumes?

13. Is mathematics invented or discovered? Solution to the Pell equation in India, China and Europe

14. "Recognize the lion by his claw": The role of competition in generating solutions to the

Brachistochrone problem

15. A precursor to Tartaglia and Cardano? Expanding concepts of algebra in the Islamic golden

age: the case of Omar Kayam and the cubic equation

16. A clock that keeps perfect time: Christian Huygens and the isochrone curve