What are Numbers? A Narrative of 30,000 years and counting...
Course: Math 3135, Spring 2017
Time & Place: MW 3:30 – 5:00 pm (SC 201)
Instructor: Jorge Basilio (jbasilio@sarahlawrence.edu)
Office Hours:
- By appointment
Handouts
Winger & Abbott's essays
- Winger’s “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”
- Abbott’s “The Reasonable Ineffectivenss of Mathematics”
On Reading Mathematics
Reaction/Reflection Pieces
Announcements
Final Conference Work Submission Instructions
It’s that exciting time of the semester where we are almost done and we get to compile our efforts into a final document. To guarantee the final submission looks professional, please follow these instructions. I can’t wait to read your work!- Final Due date: Tuesday, December 20, by 5 pm on your Google Drive submitted as a single PDF document (instructions may easily be found on the web).
-
What to submit:
Cover page
Table of Contents
A paragraph (or two) that explains what the conference project was, what we discussed in meetings, and why you chose this topic.
Main Work (this is your final paper)
References - Cover page: Please choose an appropriate title for your conference work. Please have me approve the title before the final submission. This is the title that I will submit in my evaluation. Please also include: Name, Date, Course Number, Course Name, Instructor
- The "Main Work" might have the same or a different title than the Conference Project.
- Format: Please write using 12 point font (either Georgia or Arial font), double-spaced, with 1 inch margins. Please include proper citations which you will include in the “References” page but you can follow any of the standard ways to do so (APA, MLA,...).
(i) Make sure that the font is the same for the entire document.
(ii) Typing this up using LaTeX is highly recommended, but I decided not to require it.
If you want info on LaTeX, see: Professor Ethan Bloch's LaTeX website
If you have any questions, please do not hesitate to ask!
Borges'
Readings added--see schedule for link!
Medieval Universe
Unknown artist. Read about it
Archimedes'
Sand Reckoner added--see schedule for link!
Ancient Number Systems
handouts added--see schedule link!
Videos & Readings
Videos & Readings for first day of class added to the schedule
Hello!
Welcome to "What are Numbers?"! I'll post important information here. I posted the course syllabus below--for students who have not taken a course with me please read it carefully. More info coming soon...
| Week | Class | Hand-in homework Due |
|---|---|---|
| 1 {1/23 & 1/25} | {M} Class introductions; Read this (Documentary of Number One) & watch this (Monty Python + Math + History = Awesome) This is a nice overview of basics Watch: What makes us human?; Watch: A Murder of Crows, TED talk shorter version; {W} Read [#] Ch 1, 2 | — |
| 2 {1/30 & 1/31} | {M} Read [#] Ch 3, 4; {W} Continue to discuss [#] Ch 3, 4 | — |
| 3 {2/7 & 2/9} | {M} Read [NoMath] Ch 1, 2; {W} Read [Civ] Ch 1 only 1.1-1.3! | — |
| 3 | HHW 1 | 2-8-17 @ 9 pm |
| 4 {2/21 & 2/23} | {M} Continue with ancient number systems: [No RP due today :P] Egyptian; Roman; Babylonian; Greek; {W} Read [Civ] Ch 1.4 | — |
| 5 {2/13 & 2/15} | {M} Read [Civ] Ch 1.5; {W} Read [Civ] Ch 1.6, 1.7; | — |
| 6 {2/28 & 3/2} | {M} Read [Civ] Ch 2; {W} Read [Civ] Ch 3 | — |
| 7 {3/6 & 3/8} | {M} Read [#] Ch 5. Also, some from [Civ] Ch 3; {W} Read [#] Ch 6 | — |
| 3 | HHW 2 | 3-8-17 @ 9 pm |
| 8 {3/27 & 3/29} | {M} Read [#] Ch 7, 8 {W} Read [#] Ch 9, 10 | — |
| 9 {4/3 & 4/5} | {M} Discussed complex numbers (some of Ch 10): visual and algebraic interpretations {W} Archimedes’ Sand Reckoner (or another link: this link has some commentary before the work) | — |
| 10 {4/10 & 4/12} | {M} Read [0]: Ch 0, 1, 2, 3; {W} Class canceled due to illness | — |
| 10 | HHW 3 | 4-10-17 @ 9 pm |
| 11 {4/17 & 4/19} | {M} Read [0]: Ch 4, 5; {W} Read [0]: Ch 6, 7, 8 | — |
| 12 {4/24 & 4/26} | {M} Read [0] Ch ∞, Appendices; {W} Bonus class on Cardinality and Sizes of Infinity (No RP due) | — |
| 13 {5/1 & 5/3} | {M} Borges readings: The Aleph & Library of Babel; {W} More discussion of Borges. Calculations from Library of Babel. | — |
| 13 | HHW 4 | 5-3-17 @ 9 pm |
| 14 {5/8 & 5/10} | {M} Winger’s “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” & Abbott’s “The Reasonable Ineffectivenss of Mathematics”; {W — Last day of class} Conference Project Presentations! Please prepare a 5 to 10 minute presentation that summarizes what your project was. | — |
| 14 | HHW 5 | 5-12-17 @ 9 pm |
Course Policies
Please consult the Course Syllabus for a more detailed description.
Prerequisites
High-school algebra and geometry is required; high-school trigonometry is recommended. Though curiosity and desire to learn are far more important.Hand-in Homework
There will be homework assignments consisting of various types of problems or tasks. Some might be straight-forward calculations, others might me short-essays and free-response. You are encouraged to work with other students in solving the homework problems, but you should write your own solutions, and you must acknowledge anyone that you work with. Your solutions should be written clearly and in complete sentences, with enough detail that another student in the class would be able to follow your reasoning.Required Texts
- [#] Number: The Language of Science, by Tobias Dantzig
- [Civ] Mathematics in Civilization, 3rd Edition, by H.L. Resniko & R.O. Wells, Jr.
- [0] Zero: The Biography of a Dangerous Idea, by Charles Seife
- [NoMath] Mathematics for the nonmathematician, by Morris Kline
- Library of Babel by Jorge Luis Borges (distributed in class)
- El Aleph by Jorge Luis Borges (distributed in class)