THE MATHEMATICS OF ASIA


Organized by Victor J. Katz, Professor Emeritus, University of the District of Columbia

Historically, there was much mathematics developed in China, India, and the Islamic World in the time period from the beginning of our era through the fifteenth century.  Although some of these mathematical ideas were transmitted to Europe during that same time period, many other Asian mathematical accomplishments were not translated into any European language until the nineteenth or twentieth century.  But today, much of the corpus of Indian, Chinese, and Islamic mathematics is available in English translation.   And given the increasingly multicultural makeup of our student bodies, it is important that college teachers be familiar with these ideas so that they can use them in their teaching.  They will then not only understand that mathematical thinking has been a part of every literate culture of which we are aware, but also will be able to communicate to their students the worldwide nature of mathematics and how its history plays a vital role in its current use and future development. 

The goals of this workshop are for the participants to learn in some detail about the mathematics of China, India, and Islam, through lectures and through study of selected original sources, and then to produce some classroom materials that can be used in the teaching of various topics in the mathematics curriculum.  The subject matter to be discussed will include ideas from trigonometry, solutions to polynomial equations (both algebraic and numerical), synthetic geometry, calculus, linear algebra, and number theory.  The workshop will be led by Professor Katz, who will specifically discuss the mathematics of Islam, Frank Swetz, who will deal with Chinese mathematics, and Homer White and Kim Plofker, who will deal with Indian mathematics.

To prepare for the workshop, each participant will receive a copy of a new book, The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook, to be published in 2007 by Princeton University Press.   We will select specific sources to be read before the workshop, with some questions about each source for participants to consider.  Participants and organizers will be connected electronically so they can share the answers to the questions.

During the intensive part of the workshop we will have lectures on the civilizations of China, India, and Islam, the mathematical problems that were of interest in these civilizations, and some of the mathematical ideas that were developed.  We will have small group sessions to discuss some of the original sources read by the participants, under the guidance of one of the workshop leaders.  And the participants will work together on developing appropriate lesson materials that bring in the mathematics of the three civilizations.  We expect that at the end of the week in Washington, each participant will have at least one good classroom activity and will have started on others.  Then, during the following six months, we will continue the electronic connection so that participants can share their ideas as they work on other lesson materials.   We expect that some of these lesson materials will be presented at a Contributed Paper Session on Using Ideas from Asian Mathematics in the Classroom at the 2008 Joint Meetings in San Diego.

The Workshop is suitable for College level faculty, as well as secondary teachers.  The required background is the equivalent of a college mathematics major, as well as an interest in the history of mathematics. 


SPEAKERS

Victor J. Katz received his Ph.D. in mathematics from Brandeis University in 1968 and is now Professor Emeritus of Mathematics at the University of the District of Columbia.  He has long been interested in the history of mathematics and, in particular, in its use in teaching.  His well-regarded textbook, A History of Mathematics: An Introduction, won the Watson Davis Prize of the History of Science Society in 1995, a prize awarded annually to the best book on the history of science aimed at undergraduates.  Professor Katz has published many articles on the history of mathematics and its use in teaching and has edited two recent books dealing with this subject, Learn from the Masters (1994) and Using History to Teach Mathematics (2000).  He has also directed two NSF-sponsored projects which helped college teachers learn the history of mathematics and how to use it in teaching and also involved secondary school teachers in writing materials using history in the teaching of various topics in the high school curriculum.  These materials, Historical Modules for the Teaching and Learning of Mathematics, have now been published on a CD by the MAA.  Currently, Professor Katz is the editor of Convergence:  Where Mathematics, History and Teaching Interact, an online magazine of the MAA that publishes articles and reviews designed to help teachers of grades 9-14 mathematics use history in the classroom. 

Frank Swetz is Professor Emeritus of Mathematics and Education at The Pennsylvania State University.  His research interests have focused on societal impact in the development of mathematics and its teaching and learning. In particular, Dr. Swetz has investigated the historical development of mathematics in China.  His work in this area has resulted in numerous publications, principally: Was Pythagoras Chinese? An Investigation of Right Triangle Theory in China (1977); The Sea Island Mathematical Manual: Surveying and Mathematics in Ancient China (1992) and Legacy of the Luoshu (2002). He has taught, lectured and traveled widely in Asia.

Kim Plofker received her doctoral degree from the History of Mathematics Department at Brown University (USA), where she studied with the late David Pingree. She specializes in the history of Indian and Islamic mathematics and astronomy, and also works on early modern exact sciences in Latin. She has held various postdoctoral positions at Brown, at the Dibner Institute for the History of Science and Technology at MIT,and most recently at the Mathematics Institute of the University of Utrecht and the International Institute for Asian Studies in Leiden. In 1994--95 and 2003--04 she received grants from the American Institute for Indian Studies to research Sanskrit scientific manuscripts in India. Her book on the history of mathematics in India from 500 BCE to 1800 CE will be published shortly by Princeton University Press.

Homer White received an A.B. in philosophy from Princeton University and a Ph.D. in mathematics from the University of North Carolina at Chapel Hill.  His mathematical work focused on ergodic theory and dynamical systems, but recently he has been working in the history of mathematics, especially with a view to pedagogical applications.  In particular, using his knowledge of Sanskrit, he has been studying the mathematics of classical India.  He has used Indian material in his mathematics classes and has given several presentations on the subject at regional and national meetings.


SCHEDULE

The tentative schedule is as follows. More details will be posted later.

Sunday, June 10
6:00-8:00pm
 General introduction to the program; division of participants into three small groups for the group work of the program; light meal

Monday, June 11
8:30-10:00am
 Introduction to mathematics and computational techniques in China – Frank Swetz
10:00-10:30am
 Break
10:30-12:00n
 Overview of the role of mathematics in India – Kim Plofker
12:00-1:30pm
 Lunch
1:30-3:00pm
 Introduction to mathematics in Islam – Victor Katz
3:00-3:30pm
 Break
3:30-5:00pm
 Detailed reading of the three original sources in three separate small groups, each led by one of the staff members. The three groups will rotate through each of the staff members, so that each group will meet once with each staff member.

Tuesday, June 12
8:30-10:00am
 The Han period and the solving of equations – Frank Swetz
10:00-10:30am
 Break
10:30-12:00n
 Algebra in India – Kim Plofker
12:00-1:30pm
 Lunch
1:30-3:00pm
 Algebra in Islam – Victor Katz
3:00-3:30pm
 Break
3:30-5:00pm
 Detailed reading of the three original sources in three separate small groups, each led by one of the staff members

Wednesday, June 13
8:30-10:00am
 More on equation solving in China – Frank Swetz
10:00-10:30am
 Break
10:30-12:00n
 Detailed reading of the three original sources in three separate small groups, each led by one of the staff members
12:00-1:30pm
 Lunch
Afternoon Free

Thursday, June 14
8:30-10:00am
 Geometry in India – Kim Plofker
10:00-10:30am
 Break
10:30-12:00n
 Geometry and proof in Islamic mathematics – Victor Katz
12:00-1:30pm
 Lunch
1:30-3:00pm
 Advanced techniques in the Song dynasty – Frank Swetz
3:00-3:30pm
 Break
3:30-5:00pm
 Infinite series in Kerala – Homer White
5:15-6:00pm
 Introduction to development of classroom ideas using the mathematics of Asia – in three groups with staff members participating
6:30-8:00pm
 Conference dinner at Carriage House

Friday, June 15
8:30-10:00am
 Trigonometry in Islam – Victor Katz
10:00-10:30am
 Break
10:30-12:00n
 Work on classroom ideas in small groups
12:00-1:30pm
 Lunch
1:30-3:00pm
 Reports from participants on ideas for classroom materials
3:00-3:30pm
 Plans for future and farewell


TRAVEL AND HOUSING

You should arrange your travel to arrive in Washington early enough to come to the evening meeting on Sunday, June 10.  You should also note that the program will end in the middle of the afternoon on Friday, June 15, so should plan your departure with that in mind.

Accommodations will be in the dormitories of George Washington University Potomac House 2021 F St NW, Washington, DC 20052 (single units).

*Check-in June 10 starting from 3 PM
*Check-out June 15 in the evening. Since the workshop ends in the late afternoon on June 15, you are welcome to stay an extra night (with no extra cost for you) at the dorm and check out on June 16 before 11AM.

More info on the Potomac House at http://gwired.gwu.edu/hc/ViewResidenceHalls/ViewHall/merlin-cgi/building_id/90

Workshop will take place at MAA Carriage House 1529 18th street NW Washington, DC 20036. MAA is located close to the corner of the 18th street and Q street.


LOCATION OF THE MAA CARRIAGE HOUSE

Map of the MAA Carriage House Located at 1781 Church Street NW, Washington, DC 20036


DIRECTIONS FROM THE POTOMAC HOUSE TO MAA CARRIAGE HOUSE

1. You can take a brisk 30-minute walk from the dormitory to the conference center; directions can be found at Driving Directions from 2021 F St Nw, Washington, DC to 1781 Church St Nw, Washington, DC

2. You can use the metro (plan about 45 minutes for the walk to the metro, the ride, changing the lines, and the walk from the metro). Foggy Bottom Metro station (2301 I Street NW) is just a few blocks away from the dormitory. Take the orange line towards New Carrolton or blue line towards Largo Town Center. Ride three stops until the Metro Center and change to a red line (upstairs) towards Shady Grove. Ride two stops and exit at Dupont Circle. From there, the MAA Carriage House is just a few blocks away at the corner of the 18th street and Q street. The cost of the fare is $1.35 and you can buy farecards from every station. More information is available at http://www.wmata.com/metrorail/buyingfarecrd.cfm.

You can also choose Farragut West metro station (900 18th street) instead of Foggy Bottom and continue as previously described.

The link to the homepage of Metro http://www.wmata.com/default.cfm
The map of all the metro stations http://www.wmata.com/metrorail/systemmap.cfm


MEALS

Sunday, June 10

Dinner-Carriage House

Monday, June 11

Breakfast-at the dorm
Lunch-Carriage House
Dinner-at the dorm

Tuesday, June 12

Breakfast—at the dorm
Lunch-Carriage House
Dinner-at the dorm

Wednesday, June 13

Breakfast-at the dorm
Lunch-Carriage House
Afternoon free
Dinner-on your own; you will have a wonderful opportunity to explore the restaurants in downtown Washington D.C.

Thursday, June 14

Breakfast-at the dorm
Lunch and dinner-Carriage House

Friday, June 15

Breakfast-at the dorm
Lunch-Carriage House

 

READINGS

All participants will be expected to read some original sources from the three civilizations of China, India, and Islam before arriving in Washington, so they can be discussed during the workshop.  We will provide the list of readings by early May.  These readings will be included in the new book The Mathematics of Egypt, Mesopotamia, China, India, and Islam:  A Sourcebook, edited by Victor Katz, to be published soon by Princeton University Press.  At the moment, we are not certain whether the book will be available by the time of the workshop.  If it is not, we will provide you with copies of the appropriate page proofs, and you will receive a copy of the book itself as soon as it is published.