First Year Seminar – The Nature of Mathematics
Instructor:
 William T. Ross
 Jepson Hall, Room 212
 Office Hours: Stop on by anytime
Required Texts:
 K. Ferguson, The Music of Pythagoras, Walker, 2008.
 T. L. Heath, Archimedes, MacMillian, 1920 (Available only on web — or Kindle).
 T. L. Heath, A History of Greek Mathematics – Vol I, 1921 (Available in paperback)
 D. Richeson, Euler’s Gem, Princeton, 2008.
 S. Singh, Fermat’s Enigma, Walker, 1997.
 G. H. Hardy, A Mathematicians Apology, Cambridge University Press, Canto Edition, 1992.
Other readings:
 D. E. Joyce, Euclid’s Elements (online)
 The Republic, Plato (online)
 Allegory of the Cave, video by Bullhead Entertainment. (online)
 Fermat’s Last Theorem (video by Singh and Lynch, BBC TV 1996)
 P. B. Shelley, Ozymandias. (online)
 J. O’Connor and E. Robertson, MacTudor history of mathematics online archive (online)
 B. Russell, The teaching of Euclid, Mathematical Gazette, Vol 2, 1902, 165 – 167.
Assignments:
 Be ready for a short quiz at the beginning of every class (so don’t be late for class!)
 There will be many readings. The due dates for these readings are posted below on the detailed schedule. There will be a quiz on each one.
 There will be two short papers (3 pages) and two major research papers (8 pages) due at various times during the semester. Submit drafts of these papers to your writing fellow to receive feedback. Submit the draft as well as the final product to me for a grade.
 Due dates for papers:
 2/17 First opinion paper due (draft due to writing fellow 2/8)
 3/17 First research paper due (draft due to writing fellow 2/27)
 4/5 Second opinion paper due
 4/12 Second research paper due
Final Exam:
 There will be no semester exams (except for the short daily quizzes) but there will be an inclass written comprehensive final exam. The questions will be selected from a list you will receive the last day of class.
Grades:
 Daily quizzes 20%
 Short papers (10% each x 2) 20%
 Research papers (20% each x 2) 40%
 Final Exam 20%
 3 points off your final grade for each missed class (plus a zero on the daily quiz).
Miscellaneous:
 There will be a short daily quiz will be given at the beginning of class and there are no make ups.
 No laptops in class. Sure laptops are a great way to take notes but the call of email, Facebook, MLB, NBA, NFL, CNN, etc., is just too great. Plus, the Greeks managed to do some of the greatest mathematics without even proper writing instruments! Surely we can learn some of their ideas without computing. If we need to look something up. We all have smartphones.
 You are probably wondering: how is a mathematician going to judge writing? As it turns out, mathematics is not all about computing (calculus and statistics) but about communicating complex ideas and producing convincing arguments, i.e, proofs. Thus good writing is important. I write plenty of mathematics myself and work for various journal editors on judging the worthiness of papers for publication. So I have lots of mathematical writing experience. Do I know every silly rule of grammar (misplaced modifiers, dangling modifiers, etc..)? Certainly not. But I do know that when I’m reading a mathematics paper and I’m getting confused, it is poor writing. So, the writing fellow will help you with all the grammar rules and I will judge how well you can communicate.
General Schedule
 1/9 – 1/13
 M 1/9 Introduction (Read Chapter 4 of Heath’s A History of Greek Mathematics for 1/11)
 W 1/11 Thales
 F 1/13 Thales (Read Chapters 0 – 6 of Ferguson’s The Music of Pythagoras for 1/18)

1/16 – 1/20

M 1/16 MLK Day — no class

W 1/18 Pythagoras

F 1/20 Pythagoras (Read Chapter 11 of Heath’s A History of Greek Mathematics for 1/25)


1/23 – 1/27

M 1/23 Pythagoras

W 1/25 Euclid (Read Russel’s The Teaching of Euclid for 1/27)

F 1/27 Euclid (Read Heath’s Archimedes for 1/30)


1/30 – 2/3

M 1/30 Archimedes

W 2/1 Archimedes

F 2/3 Archimedes (Draft of first opinion paper due on 2/8)


2/6 – 2/10

M 2/6 Bisection and trisection

W 2/8 Bisection and trisection (Draft of first opinion paper due, Read Chapters 7 – 9 of Ferguson’s The Music of Pythagoras for 2/10, Read Plato’s The Allegory of the Cave and watch the online video for 2/10)

F 2/10 Plato (Read Chapters 1 – 15 of Richeson’s Euler’s Gem for 2/15, Read the online biography of Euler for 2/15, Meetings with writing fellow to consult about first opinion paper – final version due 2/17)


2/13 – 2/17

M 2/13 Library Lecture

W 2/15 Polyhedra

F 2/17 Polyhedra (Final version of first opinion paper due. Draft of first research paper due to writing fellow on 2/27)


2/20 – 2/24

M 2/20 Polyhedra (Read the online biography of Gauss for 2/22)

W 2/22 Prime number theorem

F 2/24 Prime number theorem (Start reading the Singh’s Fermat’s Enigma for 3/15)


2/27 – 3/3

M 2/27 The Goldbach conjecture (Draft of first research paper due. Meetings with writing fellow to discuss first research paper – final version due 3/17)

W 3/1 Four, five and six color theorems

F 3/3 Four, five, and six color theorems


3/6 – 3/10 (Spring Break)

3/13 – 3/17

M 3/13 Four, five, and six color theorems

W 3/15 Fermat’s last theorem

F 3/17 Fermat’s last theorem (Final version of first research paper due)


3/20 – 3/24

M 3/20 Fermat’s last theorem (Read the online biography of Cantor for 3/23)

W 3/22 Cantor

F 3/24 Cantor (Second opinion paper due on 4/5)


3/27 – 3/31

M 3/27 Cantor

W 3/29 Cantor

F 3/31 Axiom of choice (Read Hardy’s A Mathematician’s Apology for 4/10, Second research paper due on 4/12)


4/3 – 4/7

M 4/3 Axiom of choice

W 4/5 Continuum hypothesis (Second opinion paper due)

F 4/7 Gödel’s incompleteness theorem


4/10 – 4/14

M 4/10 Hardy’s Apology

W 4/12 Hardy’s Apology (Second research paper due)

F 4/14 Hardy’s Apology


4/17 – 4/21

M 4/17 Wrap up

W 4/19 Wrap up

F 4/21 Last Day of Class


Final Exam Wed, April 26, 9 AM – 12 N.