MATHEMATICS 320-01
International Studies in Mathematics History: Turkey
Spring 2011
Instructor: Dr. Sharon Emerson-Stonnell
Office Hours: M-F 9 – 10:30am
Office: Ruffner 333
Telephone: 434-395-2197
E-mail: emersonstonnellss@longwood.edu
Text: The History of Mathematics: An Introduction (Third Edition). Victor J. Katz. Addison-Wesley,
2009.
Course Description: The study of the mathematics of a particular culture with a focus on the historical
relevance of the culture’s mathematical results and its impact on later cultures. Course will provide a
short-term immersion in the country (at additional cost) where the relevant mathematical developments
took place. Prerequisite: MATH 260 or MATH 261. 3 credits.
Course Goals and Objectives:
Students will be able to demonstrate that they have learned:
1. how historical mathematical results were achieved by the culture being studied.
2. how later mathematicians from various cultures used these results and proved their accuracy.
This course will concentrate on the Turkish culture. As such, students will additionally be able to
demonstrate that they have learned:
1. the development of arithmetic from ancient Babylonian to Islamic mathematics;
2. how the study of solving quadratic equations that began geometrically with the Greeks was further
developed into higher degree equations and systems of equations in Islamic mathematics;
3. how the study of trigonometry in Hindu mathematics was further developed in Islamic
mathematics;
4. how spherical trigonometry was developed in Islamic mathematics for the purpose of determining
the direction of Mecca.
Grading Policy:
1. There will be two tests. Each test will be worth 100 points and will be 20% of your final grade.
2. Each student is expected to attend daily and actively participate in all class discussions during the
portion of the class held in Farmville, Virginia and during the portion of the class held in Turkey
and Greece. Participation will constitute 10% of your final grade.
3. Individual homework or group lab assignments will be assigned daily. Group lab assignments
must be done in groups of 2-3 students. Homework and labs will be collected daily and will
constitute 20% of your final grade.
4. Each student will be expected to give two presentations. One presentation will be on Thursday,
May 5 and will present aspects of modern day Turkey to prepare for travel to Turkey. The
presentation will be 15-20 minutes in length. Your topic must be approved by March 11. The
second presentation will occur in Turkey or Greece and will discuss the mathematics involved in
developments in ancient Babylon, at the House of Wisdom, or in the Islamic World. This
presentation will be 30-40 minutes. Your topic must be approved by February 11. Each
presentation will constitute a total of 12% of your final grade.
5. A final project must incorporate the experience in Turkey and its relationship to the mathematics
learned in this course. The final project will be worth 6% of your final grade and is due at 5pm on
Monday, June 6, 2011.
6. Make-up tests will be given only when the reason for missing the test meets the criteria for an
excused absence. Lack of preparation will not be considered an adequate reason for missing a test.
Make-up tests will always be more difficult than the regularly scheduled tests.
Grading Scale:
90-100 A
80-89 B
70 -79 C
60 – 69 D
0 – 59 F
Attendance Policy: Absences are excused only for illness, college sponsored activities and recognizable
emergencies. You must assume full responsibility for all material covered during your absence. A grade of
"0" will be assigned for all work missed due to unexcused absences.
Honor Code Statement: Students (whether working individually or in small groups) are expected to
conform to the Longwood University Honor System. All material handed in to me should be pledged.
Class Schedule:
January 17 - 19
Monday
No class
Wednesday 12 – 12:50pm
January 24 - 26
Monday
12 – 12:50pm
Wednesday 12 – 12:50pm
January 31 – February 2
Monday
12 – 12:50pm
Wednesday 12 – 12:50pm
February 7 - 9
Monday
12 – 12:50pm
Wednesday 12 – 12:50pm
February 14 - 16
Monday
12 – 12:50pm
Wednesday 12 – 12:50pm
February 21 - 23
Monday
12 – 12:50pm
Wednesday 12 – 12:50pm
February 28 – March 2
Monday
12 – 12:50pm
Wednesday 12 – 12:50pm
March 7 - 9
Monday
12 – 12:50pm
Wednesday 12 – 12:50pm
March 14 - 16
No class
Spring Break
March 21 - 23
Monday
12 – 12:50pm
Martin Luther King Day
2.1 Earliest Greek Mathematics
2.2.1 Euclid’s Elements
2.2.4 Euclid’s Elements
2.2.6 Euclid’s Elements
3.1 Archimedes
5.2, 6.2 Chinese and Indian Geometry
3.3 Greek Astronomy
6.5, 3.3.5 Indian Trigonometry and Greek Spherical Trig.
7.5 Trigonometry of Islam
7.5.2 Spherical Trigonometry of Islam
Chapter 15 Eighteenth Century Geometry
2.2.2 Euclid’s Elements (Geometric Algebra)
Chapter 4 Arithmetica
Test
5.3 – 5.5 Chinese Algebra
6.3, 7.2 Indian and Islamic Algebra
Wednesday
March 28 - 30
Monday
Wednesday
April 4 - 6
Monday
Wednesday
April 11 - 13
Monday
Wednesday
April 18 - 20
Monday
Wednesday
April 25 - 27
Monday
Wednesday
Week 16
Thursday
12 – 12:50pm
7.2.5, 8.3 Cubic Equation Solutions of Islam and Medieval Alg.
12 – 12:50pm
12 – 12:50pm
9.1, 10.1 Renaissance and Seventeenth Century Algebra
Chapter 14 Eighteenth Century Algebra
12 – 12:50pm
12 – 12:50pm
6.4, 7.3 Indian and Islamic Combinatorics
8.2, 10.3 European Combinatorics and Probability
12 – 12:50pm
12 – 12:50pm
Chapter 13 Eighteenth Century probability and Statistics
9.3 Logarithms
12 – 12:50pm
12 – 12:50pm
11.1 European Tangents and Extrema
Test
12 – 12:50pm
12 – 12:50pm
11.2 Areas
11.2 Volumes
11:30am – 2pm
Turkey Presentations
Turkey and Greece Travel:
Students will be expected to attend class one to two hours daily. Each student should be prepared to give
his or her presentation on any given day during the trip. Each presentation should be 30 – 40 minutes in
length. All presentations must be prepared and approved before the trip and include handouts,
illustrations, posters, etc.
May 21
Saturday
Dulles
5-6pm
7-8pm
8:45pm
Ancient Babylonian arithmetic presentation
Ancient Babylonian equations presentation
flight to Europe
May 22 - 28
Sunday
Istanbul
10:30am
4:20pm
5:30pm
8:30am
2pm
7am
8– 9am
10am
2pm
8am
2-3pm
3pm
9am
1pm
2pm
arrive in Europe
arrive in Istanbul
walking tour of Istanbul
tour Topkapi Palace and the Blue Mosque
Bosphorous cruise
ferry to Yalova
ibn al-Haytham presentation
Bursa tour
travel to Canakkale
Troy tour
Islamic sum of powers presentation
free time at the beach
Pergamon tour
House of Wisdom presentation
travel to Kusadasi
Monday
Istanbul
Tuesday
Canakkale
Wednesday
Canakkale
Thursday
Kusadasi
Friday
Kusadasi
Cruise
9am
4-5pm
8am
1-2pm
3pm
Ephasus tour
Islamic number theory presentation
Greek island cruise
Islamic trigonometry presentation
Patmos port of call
Saturday
May 29 – June 1
Sunday
Cruise
9am
Heraklion port of call
Tour of Knossos
Archimedes presentation
Santorini port of call
tour of Athens
Heron presentation
free time in Athens
Travel to Delphi
lunch and tour of Delphi
travel to Athens
travel to airport
Summary
flight
arrive in Dulles
Monday
Athens
Tuesday
Delphi
Wednesday
Athens
1-2pm
4pm
9 am
3-4pm
4pm
8am
12pm
3pm
11am
12-1pm
2pm
8:10pm
Guidelines for Behavior while in Turkey and Greece: Recall the “Conditions of Participation” that you
and your parents signed before being accepted into this course. This contract states that any student
whose behavior or health becomes detrimental will be sent home at their own expense, relinquishing
all money paid into the program and credits for the class. The following rules hold for all students
throughout the trip.
1. The syllabus contains a percentage of your grade based upon your participation. All of the
activities and tours are part of the class, and you will be responsible for the information given
during them.
2. Your behavior during the program includes how you treat others in the group. You may have
close friends in the group, but you must include others in your activities during the program, so
please make efforts to get to know others and to get along with them. No petty, rude, or
disrespectful behavior will be tolerated.
3. You should be back in your hotel room by 12am, so that you can get a good night’s sleep.
Each day is full, and you will need to be rested and alert to fully participate.
4. When staying at hotels or on the cruise ship, be respectful of other guests. This means all noise
should be contained to your room and should not be heard by other guests in their rooms or in
the hallways. Remember that many of the guests will be families with young children who
retire much earlier than college students.
5. You may never be out alone at any time during the trip. Always travel with at least one other
person; small groups are encouraged.
6. Respect the local customs. Turkey offers a unique cross between eastern and western cultures.
Enjoy this opportunity rather than behaving as an “American tourist.”
7. Bring snacks such as granola bars and bottled water to activities and tours; there may be long
intervals between meals. Do not eat or drink in museums or other indoor sites.
8. Students under 21 must have a signed Parental Approval for Alcohol Consumption form in
order to drink alcohol while in Turkey and Greece. Students over 21 and those with the
consent form will be allowed to consume small amounts of beer and wine at the hotel and
cruise ship after the day’s activities are completed. Drunkenness and consumption of hard
alcohol will not be tolerated during the trip. Students will not be allowed to frequent bars or
other establishments dedicated to alcohol consumption as these are designed for tourists.