History of Mathematics

Fall 2018

Sarah Glaz

(click on link and remove end x)

Office: MONT 133
: (860) 486 1280

Office Hours
: Tuesday 2:00 - 3:00
Open Door Policy: You are welcome to drop by to discuss any aspect of the course, anytime on Tuesday -- the day I am on campus.

Class Meeting Times/Place and Course Website

Tuesday: 3:30 - 6:15pm (with a 15 minute break sometimes in the middle).
Classroom:  MONT 319
Course website: http://www.math.uconn.edu/~glaz/math2720f18

Catalog Course Description

A historical study of the growth of the various fields of mathematics.


Please purchase the two main textbooks (available new at UCONN Bookstore and, both new and used, at amazon.com)

In addition, we will use the following online resource (browse to become familiar with the many biographies and mathematics topics available at this website):

Click on the link below for a short list of recommended (but not required) reading:
Grading Policy

The course grade will be determined as follows:

The final version of each paper will be graded using the following grading scheme: 40% content (writing style, depth and elaboration of points, evidence of supporting research), 40% structure (organization and focus), 20% mechanics (grammar and citation style). For details see the Paper Grading Rubric.

According to UCONN policies for W courses, you cannot pass this course unless you receive a passing grade for its writing component (papers 1, 2, and 3).

Individual and Group-Work Assignments

Individual or group-work assignments, aimed at practicing mathematical concepts and writing techniques, will be given every week. Some of the assignments will be worked at during class-time; others will be given as homework. In all cases, assignments done in class (usually group-works) are due the same day, and assignments given as homework (usually individual) are due on the Tuesday after they were assigned. Each week's assignment will be graded on a scale of 0 to 10 (divided among the various components). For group-works: the group will submit one completed assignment and each member of the group will receive the grade awarded for this joint submission. Most group-works will be completed and collected during class, and absent students will not be able to receive credit for the group-work they missed, unless there is a serious reason for their absence for which proof is provided.

The Papers (1, 2 and 3)

Consult these links before starting to work on your first writing assignment.

UCONN policies for W courses require that the combined lengths of the three papers (papers 1, 2 and 3), excluding bibliography, is at least 15 pages. Page length assumes a 12-point Times New Roman font, double-spaced, 1" margin page. There are about 250 words per page. Since typing-software affect page length, please use word count when calculating the length of your paper.

NO LATE SUBMISSIONS of drafts or final versions of papers 1, 2 and 3 are accepted, unless there is a serious emergency for which you provide proof. Paper 3 is considered to be the final exam for this course and as such rescheduling its submission needs approval from UCONN's Dean of Students Office, see UCONN Final Exam Policy.

Paper Schedule
Paper Guidelines
(an active link to each paper guidelines will appear in the week before each paper is assigned)
Paper 1
Draft and Draft Cover Letter due: Tuesday, September 11
Final Version and Final Version Cover Letter due: Tuesday, September 25 
Paper 1
Draft Cover Letter Template (Word file)
Final Version Cover Letter Template (Word file)
Paper 2
Draft and Draft Cover Letter due: Tuesday, October 9
Final Version and Final Version Cover Letter due: Tuesday, October 23
Paper 2
Draft Cover Letter Template (Word file)
Final Version Cover Letter Template (Word file)
Paper 3
Draft and Draft Cover Letter due: Tuesday, November 13
Peer Review Forms due: Tuesday, November 27
Final Version and Final Version Cover Letter due: Tuesday, December 4
Paper 3
Draft Cover Letter Template (Word file)
Paper 3 Final Version Cover Letter Template (Word file)
Guidelines for Peer Review
Peer Review Form Template (Word file)
Peer Review Groups

Extra Help: UCONN Writing Center

I encourage you to come to my office for help during office hours, and I will be happy to find other times when we can meet if my office hours schedule does not fit your schedule. Since part of the purpose of this course is to help you learn how to write effectively, you may also wish to consult the tutors at the UCONN Writing Center.

Syllabus, Homework Assignments, and Reading Assignments

The actual pace of the course may be slightly different than listed in the syllabus below. It will depend on the students' response to the material. Individual homework assignments and in- class group-work will be given every week. Please check the course's website for updates on a weekly basis.

Notes: * Below we will denote by: D =  Journey through Genius by W. Dunham,  B&G = Math through the Ages (Expanded 2nd Edition) by W. P. Berlinghoff and F. Q. Gouvea,  MTM = The MacTutor History of Mathematics Archives.                                                                                  

Papers due dates
Reading for each week's topic
To be read before the Tuesday class of that week
Homework and Classwork
Homework is due on the Tuesday after they
were assigned, classwork is collected the day
they are done in class
Week 1: Aug 28

* Overviews of the history of mathematics
The history of numerals
The history of zero

* Important historical names, dates, and events
* Mathematical Periods
MTM: An overview of the history of mathematics
B&G: Sketch 1(p 67-72); Sketch 3 (p 81-84)
Individual Assignment:
* Math Autobiography (Guidelines)
* How to recognize plagiarism: Tutorial and test
(complete test and hand in
the signed, completed certificate)
Group-Work 1: Ancient Numerals
Week 2: Sep 4

* Babylonian mathematics
* Egyptian mathematics

An overview of Babylonian mathematics
An overview of Egyptian mathematics

The new Plimpton 322 controversy (Read for fun!)
* Mystery of the Babylonian Clay Tablet, Plimpton 322
* Don't Fall for Babylonian Trigonometry Hype
Individual Assignment:
Paper 1 draft and draft cover letter
(see guidelines in Papers section)
Group-Work 2: Eliminating Wordiness
(use Conciseness
and Active versus passive voice)
Week 3: Sep 11

Paper 1 draft:
Due Tue, Sept 11
* Early Greek mathematics
* Euclid's Elements: Geometry 
D: Chapter 1 (p 1-11)
D: Chapter 2 (p 27- 53, 
may skip the proof of book I:15, 16, 26, 27, 32, 41) 
Group-Work 3: Pythagoras Theorem
Week 4: Sep 18

Shorter class
* Euclid's Elements: Number theory

D:  Chapter 3 (p 68-75 and 81-83)

Individual Assignment:
Paper 1 final version and final version cover letter
(see guidelines in Papers section)

Week 5: Sep 25

Paper 1
final version:
Due Tue, Sept 25
* Archimedes and the circular area
* The history of  π
* Archimedes Cattle Problem
* TED Talk: Revealing the lost codex of Archimedes
 * The Mountains of Pi by Richard Preston
   (Not required. Check them all for fun!)
D: Chapter 4 (p 84-112, you may skip the proofs)
B&G: Sketch 7 (p 109-112)     
Group-Work 4: Comma Usage
(use Rules for using commas)
Week 6: Oct 2
* Greek mathematics after Archimedes
* Non-Euclidean geometries 
D: Chapter 2 (p 53-60, you may skip the proof of
Theorem AAA)
D: Chapter 5 (p 113-132, you may skip the proofs)
B&G: Sketch 19 (p 195-200)
* Non-Euclidean art:
Daina Taimina crocheted hyperbolic planes
Dick Termes painted termespheres
Individual Assignment:
Paper 2 draft and draft cover letter
(see guidelines in Papers section)
Group-Work 5: Late Greek Mathematics
Week 7: Oct 9

Paper 2 draft:
Due Tue, Oct 9
Arabic mathematics
*  The cossic art
 MTM:  An overview of Arabic mathematics
* Earliest Uses of Various Mathematical Symbols
    (Not required. Check for fun!)
 B&G: Sketch 8 (p 115-120)
Group-Work 6: Organization and Focus
(use: Structure of a general expository essay)
Week 8: Oct 16
* Renaissance: solutions to
   cubic and quartic equations
*  The quintic equation and group theory:
     Abel and Galois
B&G: Sketch 11 (p 135-138)
D: Chapter 6 (p 133-154)
MTM: A biography of Abel
           A biography of Galois
Individual Assignment:
Paper 2 final version and final version cover letter
(see guidelines in Papers section)
Group-Work 7: Cubic Equations

Week 9: Oct 23

Paper 2
final version:
Due: Tue, Oct 23
* Descartes, Fermat and a gem from Isaac Newton
* Fermat's last theorem
D: Chapter 7 (p 155-174 and 177-183)
* The enigmatic number e
   (Not required. Read for fun!)
* BBC-Horizon-1996: Fermat's Last Theorem
(Not required. Watch for fun this amazing
50 minute documentary directed by Simon Singh)
Group-Work 8: Common Mistakes
Week 10: Oct 30
* Calculus:
Newton, Leibniz, and the Bernoulli brothers
D: Chapter 8 (p 184-206)
B&G: Sketch 30 (p279-284)
Individual Assignment:
Paper 3 draft and draft cover letter
(see guidelines in Papers section)
Group-Work 9: Some Series of Newton and Leibniz
Week 11: Nov 6
* Euler and his legacy
D: Chapter 9 (p 207-222)
     Chapter 10 (p223-235,You may skip the proofs)
* An evening with Leonhard Euler, by William Dunham
   (Not required. Watch for fun!)
Group-Work 10: Euler's 7 Bridges of Konigsberg
Week 12: Nov 13

Paper 3 draft:
Due Tue, Nov 13
* From Gauss to Cantor
* Overview of 19 century mathematics
MTM: A biography of Gauss
B&G: Sketch 6 (p 103-106)
D: Chapter 11 (p 245-266)
* Weierstrass' continuous and nowhere differentiable function
   (Fun animation!) 
Individual Assignment:
Paper 3 Peer Review Forms
(see guidelines and the list of peer review groups
in Papers section)
Group-Work 11: Gauss' Congruent Integers
Nov 18 - 24
Enjoy and have fun!

Week 13: Nov 27

Peer Review

Due Tue, Nov 27
* The foundations of mathematics:
   Cantor, Hilbert, Russell, Goedel
* Mandatory Attendance:
   Peer-Review Workshop for Paper 3 
   (Counts as a Group-Work)
* Hilbert's Problems
* Goedel and the limits of logic
D: Chapter 12 (p 267-283)
B&G: Sketch 25 (p 239-244)
B&G: Sketch 29 (p271-276)
Individual Assignment:
Paper 3 final version and final version cover letter
(see guidelines in Papers section)
Group-Work 12: Peer-Review Workshop for Paper 3 
Week 14: Dec 4

Paper 3
final version:
Tue, Dec 4
* A brief look at today's mathematics.
Recommended reading (not required):
* Poetry Inspired by Mathematics:
    A brief journey through history
* List of Unsolved Problems in Mathematics
* Watch fractal art in action!
B&G: Sketch 23 (p225-230)
Group-Work 13: Map Coloring
Final Exams
Dec 10 - 16
Good Luck with all your finals!

No final Exam in this course.

Academic Integrity

A fundamental tenet of all educational institutions is academic honesty; academic work depends upon respect for and acknowledgment of the research and ideas of others. Misrepresenting someone else's work as one's own is a serious offense in any academic setting and it will not be condoned. Academic misconduct includes, but is not limited to, providing or receiving assistance in a manner not authorized by the instructor in the creation of work to be submitted for academic evaluation (e.g. papers, projects, and examinations); any attempt to influence improperly (e.g. bribery, threats)any member of the faculty, staff, or administration of the University in any matter pertaining to academics or research; presenting, as one's own,the ideas or words of another for academic evaluation; doing unauthorized academic work for which another person will receive credit or be evaluated; and presenting the same or substantially the same papers or projects in two or more courses without the explicit permission of the instructors involved. A student who knowingly assists another student in committing an act of academic misconduct shall be equally accountable for the violation, and shall be subject to the sanctions and other remedies described in The Student Code.

Student Support Services

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This page is maintained by Sarah Glaz                   
Last modified: Fall 2018