|
Prof. Erin McNicholas
Office: Ford 211
emcnicho@willamette.edu
(503)370-6590
|
Class Meetings: MWF 10:20-11:20 am, Ford 201 Office Hours: Tuesday 1-2pm, Wednesday 3-4pm, Thursday 9-10am, and by appointment. Syllabus: http://willamette.edu/~emcnicho/courses/Syllabi/SyllabusMath399HistoryF17.pdf Our Blog Site: https://infinitelymanypigeons.wordpress.com/ |
| Due by: | Most Recent Assignment |
| Th (12/14) |
Final video project due 12/13. Viewing 8:30 am 12/14 Grade distribution Preference due 12/14 Winter Break Diversions: Read the blogs you haven't read yet Listen to the podcasts (sent out via email) Read the Quanta article on Minhyong Kim Watch Hidden Figures Watch video on Navajo Math Circles Watch The Proof (about Fermat's Last Theorem) |
| Day | Readings & Assignments |
| M (8/28) |
Read Drawbridge Up, watch PBS In My Humble Opinion Submit one or two questions based on the reading, bring a list of questions/themes you hope to explore this semester to class. |
| W (8/30) |
Read Chapter #1 of Burton, listen to Symmetry Podcast #6: Babylonian & Greek Mathematicians Do Assignment #1 Submit one discussion question to the chat room discussion |
| F (9/1) |
Read: 1. Sherlock Holmes in Babylon, 2. Neither Sherlock Holmes nor Babylon (pgs 167-174), 3. Words and Pictures (From the bottom of pg 15 - pg 20), 4. Neither Sherlock nor Babylon (pgs 183-186 & 202-2013) 5. Read Guardian article and watch embedded video Submit one discussion question to the chat room discussion Assignment #2 (due in-class Friday): 1. Use the method of multiplying by the reciprocal to find 4/29 divided by 18 (where numbers are in the Babylonian base 60 system, written in slash notation) 2. Write a response to the reading (no more than 1 page). What are the authors' main arguments? Are they convincing? Any other observations/response you care to share. |
| M (9/4) | Labor Day - No Class |
| W (9/6) |
Read: Euclid & the Quadratic (ME Section 5.2) Assignment #3 (due in-class Wednesday): Write a blog/podcast topic proposal. You are not committing to this topic, merely identifying a topic you think would be interesting to pursue and which is likely to have enough content for a blog entry or podcast. Your proposal must describe the mathematical content (though not in any detail - I just need to see that there is mathematical content) as well as the historic or sociological considerations you would consider. Identify at least one source you might use (i.e. do a quick internet search and make sure there's at least somewhere to start your research). Your proposal should be about a page long, typed. * Optional reading for those of you who can't get enough of Plimpton 322 |
| F (9/8) |
Assignment #4 (due Friday 9/8): 1. Before doing the reading(!!!!!) determine Diophantus' age at death from the following epigram: 'Here lies Diophantus,' the wonder behold. Through art algebraic, the stone tells how old: 'God gave him his boyhood one-sixth of his life, One twelfth more as youth while whiskers grew rife; And then yet one-seventh ere marriage begun; In five years there came a bouncing new son. Alas, the dear child of master and sage After attaining half the measure of his father's life chill fate took him. After consoling his fate by the science of numbers for four years, he ended his life.' (4th c.e. epigram) Show your work and turn it in on Friday. 2. Read Second Alexandrian School: Diophantus (Burton Ch. 5) 3. Do problems 7, 8, and 12 on page 251 of the reading (in the manner of Diophantus) |
| M (9/11) |
Assignment #5 (due Monday 9/11): 1. Read Mathematics in the Near and Far East, Burton pages 238-250 2. Post two discussion questions to the chat room by 8am Monday 3. Do problems 5.5/ 1d, 4, 6, 10 |
|
W (9/13) |
Assignment #6 (due Wednesday 9/13): 1. Read Mathematical Masterpieces, pages 83-96 2. Listen to podcast: My favorite Theorem, Ep 2: Dave Richeson 3. Post two discussion questions (on reading or podcast) to the chat room by 8am Wednesday 4. Do problems 2.2, 2.3, 2.4 |
| F (9/15) |
Assignment #7 (due Friday 9/15): 1. Listen to podcast: My favorite Theorem, Ep 1: Amie Wilkinson, (dedicated to Ashlyn) 2. Start reading Mathematics in the Near and Far East, Burton pages 251-269 3. Start working on your second blog proposal (it can be totally different than your first -probably should be). It does not have to connect to the content we've studied thus far. |
| M (9/18) |
Assignment #8 (due Monday 9/18): 1. Listen to podcast: My favorite Theorem, Ep 3: Emille Davie 2. Finish reading Mathematics in the Near and Far East, Burton pages 251-269 3. Post two discussion questions (on reading or podcast) to the chat room 4. Do problems 5.5/ 16a, 19b, 21 (due Monday) 5. Turn in your second blog proposal |
| W (9/20) |
Assignment (due Wednesday 9/20): 1. Read Journey Through Genius, pages 133-142 2. Listen to A short history of symmetry, ep 7, What is symmetry? 3. Work on blog post |
| F (9/22) |
Assignment (due Thursday 9/21 9pm): 1. Finish Chapter 6 of Journey Through Genius, pages 142-154 2. Listen to A short history of symmetry, ep 5, Competitive mathematics in Renaissance Italy 3. Work on blog post 4. Discussion Group 1, post 2 questions to the chat room by 9pm THURSDAY. |
| M (9/25) |
1. Work on blog post |
| W (9/27) |
1. Read Men of Mathematics, Ch. 10 Lagrange, A Lofty Pyramid 2. Discussion Group 2, post 2 questions to the chat room by 9pm TUESDAY. 3. Bring two copies of your rough draft blog post to class on Wednesday. If you do not have a complete rough draft, bring a rough draft of the first page or two and a complete outline of your post. |
| F (9/29) |
1. Read Mathematical Expeditions, 5.4 Lagrange, focusing on pages 236-246. Recall our translation between Cardano and Lagrange: Cardano x^3+mx=n, Lagrange x^3+nx+p=0. Thus Cardano's m is Lagrange's n and Cardano's n is Lagrange's -p. Furthermore, Cardano's t is Lagrange's y and Cadano's u is Lagrange's -z. Simple! 2. No discussion group assignment, but feel free to post questions about the math to the chat room and I will try to address them in class Friday. 3. Proof-read your 2 (possibly 1) blog post rough drafts. For each, write a paragraph to the author (due in-class Friday) giving suggestions. Things to look for/comment on: 1) Grammatical errors. You don't need to correct them, just make note if they are there. Grammatical errors are enough to make the post un-publishable. 2) Tone. Is the writing engaging/interesting or does it read like a DVD player instruction manual (I said VCR in class and you were probably terribly confused. Ah, youth). Similarly, does it seem forced or not genuine. 3) Reasoning and analysis. Are positions supported with well developed arguments and evidence? Are ideas meaningfully explored and explained? 4) Does it contain mathematical and historical (or sociological) content? 5) Who is the audience? Is it clear from the writing? The rubric is here if you want to reference it. |
| M (10/2) |
1. Upload your blog post to WISE under Assignments. Turn in a printed copy with your peer-reviewer feedback. This is technically due Monday, but you have a five day margin to work with for the blog and podcasts this semester (meaning you can turn in any of the blog/podcast assignments, other than the final project, late but the total number of days late added over all three assignments can not exceed 5). |
| W (10/4) |
1. Finish the Solution of the cubic handout and turn it in during Wednesday's class. I've posted the file under resources if you need another copy. 2. Review Mathematical Expeditions, 5.4 Lagrange, focusing on pages 236-246. Your goal is to fully understand Lagrange's derivation of the cubic solution (which is very similar to Cardano's and is covered in part 1 of section 1 (pgs. 236-237)). Do your best to follow the rest, making note of the mathematical innovations Lagrange uses that were not available to Cardano and getting a general sense of the structure of his argument. Recall our translation between Cardano and Lagrange: Cardano x^3+mx=n, Lagrange x^3+nx+p=0. Thus Cardano's m is Lagrange's n and Cardano's n is Lagrange's -p. Furthermore, Cardano's t is Lagrange's y and Cadano's u is Lagrange's -z. Simple! Please post math questions to the chat room. 3. Listen to podcast Who's Gerry and Why Is He So Bad at Drawing Maps? |
| F (10/6) |
1. Do the homework on Symmetric Polynomials and Roots of Unity 2. Get a head start on Monday's reading. |
| M (10/9) |
1. Read Cauchy's Math Part I and do the two homework questions embedded in that reading (to be turned-in on Monday) 2. Read Mathematics and Windmills. If you are in Discussion Group 3, post 2 questions to the chat room by 9pm Sunday. |
| W (10/11) |
1. Read Genius and Poverty and A Memoir on Algebraic Equations. If you are in Discussion Group 1, post 2 questions to the chat room by 9pm Tuesday. One of your questions may be a purely mathematical question, or not. |
| F (10/13) |
1. Finish Cauchy's Math Part II (to be turned-in on Friday) 2. Read Cayley's Math Part I and due the following problems: If you are in Abstract Algebra or have taken AA previously, do problems 2, 7, 8b, 9, 10, and 11 If you have not taken Abstract Algebra, read problem 1 and do problems 4, 5, 7, 8a, 9, 10, and 11 3. Look over the draft podcast assignment and begin thinking about who you might want to work with and what topic you would like to pursue. |
| M (10/16) |
1. Due Monday:
If you are in Abstract Algebra or have taken AA previously, do problems 12a, 13b, and read through page labeled "2" (i.e. page 3). If you have not taken Abstract Algebra, do problems 12b, 13a, and read through page labeled "2" (i.e. page 3).
2. Listen to the podcast A Brief History of Mathematics: Galois and watch the YouTube video Dance Your PhD: Representations of the Braid Group. For the YouTube video, pay attention to the mood of the presentation and how this interacts with the mathematical content. How do they create mood? Does it enhance/detract from understanding the mathematical concepts? If you are in Discussion Group 2, post 2 questions/observations regarding the podcast or video to the chat room by 9pm Sunday. |
| W (10/18) |
Read Galois Theory, sections 28, 29, 31, 32, 33, 34, 37 and highlighted portions of Galois's Letter to Auguste Chevalier Finish problems 15 and 16 of Cayley's Math Part II Instead took day to remember why we do this and watched Francis Su's Departing Address |
| F (10/20) | No Class: Mid-Semester Break |
| M (10/23) |
Read Bell's take on Galois. If you are in Discussion Group 3, post 2 questions/observations regarding the reading to the chat room by 9pm Sunday. Read Galois Theory, sections 28, 29, 31, 32, 33, 34, 37 and highlighted portions of Galois's Letter to Auguste Chevalier. Answer first page of reading guide questions |
| W (10/25) |
Read Galois Theory, sections 38, 40, 41, 43, 44, 45 Answer second page of reading guide questions |
| F (10/27) |
Turn-in a detailed outline of your podcast. Message to the Board in chatroom |
| M (10/30) |
Do problems 1, 2, and 3 from the Galois Theory Homework Read Niels Hendrick Abel and Equations of the Fifth Degree Answer question: Which food would you pair with Abstract Algebra? in the chatroom |
| W (11/1) |
Do problem 5 from the Galois Theory Homework (which will be collected Friday) Answer question: Which food would you pair with Abstract Algebra? in the chatroom Read the brief bio of Emmy Noether, listen to Stuff you Missed in History Class: Emmy Noether and A short history of symmetry, ep3 Physicists, Einstein and Symmetry. If you are in Discussion Group 1 or 2, post 1 questions/observation regarding the podcasts to the chat room by 9pm Tuesday. |
| F (11/3) |
Do problem 6 from the Galois Theory Homework Set. All problems except #4 due in-class Friday. In preparation for our celebration of Algebra and our wake for Mirzakhani, Noether, Cayley, Galois, Cauchy, Abel, Lagrange, Tartaglia, Cardano, Qin, Khayyam, Diophantus, and Euclid, please read the following blog posts (most of which are pretty short): http://www.lastwordonnothing.com/2013/04/01/guest-post-physicist-dies-made-great-chili/ https://blogs.scientificamerican.com/roots-of-unity/thank-you-sophie-and-im-sorry/ If you are in Discussion Group 2 or 3, post 1 question/observation regarding the reading to the chat room by 9pm Thursday. |
| M (11/6) |
Communication Norms in Mathematics Read the Abstract and Prologue and sections 1.1-1.2.2 of this unconventional thesis Read this Facebook conversation thread, as well as this article and discussion linked in the thread. Write a 1 page reflection on communicating mathematics (to be turned-in in-class Monday). The purpose of this writing assignment is to organize your thoughts before the class discussion. I will not be critically grading your writing on this assignment. Questions to consider: From the readings, podcasts, etc. for this class as well as your experiences in Foundations and other math classes, what are some examples of well communicated mathematics? What are some examples of poorly communicated mathematics? What are the norms in mathematics writing (as adopted by us, the society of mathematicians)? What are the motivations/sources/causes of these norms? Which of these norms improve mathematical communication, which impede it? Anything else you want to reflect on regarding the communication of mathematics and the art of proof writing. |
| W (11/8) | Read Archimedes Quadrature of the Parabola |
| F (11/10) |
Podcast Dialogue Due Finish Archimedes Quadrature of the Parabola Worksheet (except problem 3). Here is an updated version with problem 7b included, typo in problem 2 corrected, and source for problem 3 if you are interested in reading the proof. :) Read Archimedes Method |
| M (11/13) |
Turn in Archimedes' Quadrature of the Parabola Worksheet, and finish problem 1 of Archimedes' Method Worksheet. The linked worksheet has been updated to include sources if you'd like to learn more about the palatial properties of parabolas. Work on your Podcast. It's due Friday. Work on your blog re-writes. I will not accept any rewrites after 11/27 (as I won't have time to regrade them if they come in after that). |
| W (11/15) |
Finish Newton reading Listen to A Brief History of Mathematics, Ep1 Newton & Leibniz If you are in Discussion Group 1 or 3, post 1 question/observation regarding the reading or podcast to the chat room by 9pm Tuesday. |
| F (11/17) |
Read Leibniz reading If you are in Discussion Group 1 or 3 and didn't post a questions or observation from the Newton reading or Newton/Leibniz podcast, here's your second chance! Post a comment by 9pm Thursday. Finish the Newton handout (due in-class Friday) Podcast Due |
| 11/20-11/24 | Thanksgiving Break - No class |
| M (11/27) |
Read about the Bernoulli Brothers If you haven't already done so, Watch the YouTube video Dance Your PhD: Representations of the Braid Group. Check back for podcast assignment by Wednesday If you are in Discussion Group 1 or 2 post a questions or observation from reading, video, or podcasts by 9pm Sunday (11/26).
|
| W (11/29) |
Read Cauchy's Rigorization of Calculus, Listen to podcast on AlphaGo AI If you are in Discussion Group 2 or 3 post a questions or observation from reading, video, or podcasts by 9am Wednesday (11/29). |
| F (12/1) |
Read Robinson Resurrects Infinitesimals, read Jaime's blog post on the Intermediate Value Theorem, and listen to the podcasts on modular arithmetic and math in nature. If you are in Discussion Group 3 or 1 post a questions or observation from the reading or podcasts by 9pm Thursday (11/30). Final Video Project Proposal Due: Give names of group members, topic of video, and brief description of approach (human acted vs. mostly computer generated or Vi Hart like video). |
| M (12/4) |
Read Ideas of Calculus in Islam and India, Non-Deductive Proof in Ancient Chinese Mathematics, and Temple Geometry and Japanese Mathematics. If you are in Discussion Group 1 or 2 post a questions or observation from the readings by 9pm Sunday (12/3). Complete the Cauchy/Robinson handout started in-class on Friday (due in-class Wednesday) Think about the what you personally are taking away from this course. See `Final Reflection' under Assignments. Reflections will be due on Friday 12/8 |
| W (12/6) |
Read A Simplified Explanation of Godel's Incompleteness Theorem, listen to the Philosophy of Mathematics podcast If you are in Discussion Group 2 or 3 post a questions or observation from the reading or podcast by 9pm Tuesday (12/5). If you are in the class, post a food pairing for analysis (with justification) on the appropriate chat room by 9pm Wednesday (12/6). |
| F (12/8) |
Modern Math History: Quanta article on Kim If you are in the class, post a food pairing for analysis (with justification) on the appropriate chat room by 9pm Wednesday (12/6). Read Two blog posts you have not already read. Post comments/questions about each post on the comment section of the blog site. Final Reflection (see Wise Assignments for details) due |
| Th (12/14) | Final video project due 12/13. Viewing 8:30 am 12/14 |