This document provides instructor notes for an 8-day lesson plan exploring the origins and developments of algebra, mathematics, and the number system within Islamic culture and the House of Wisdom in Baghdad. Some key points covered include: 1) Algebra originated from the first algebra book written by al-Kwarizmi in Baghdad in 780, which contained the word "al-jabr" in its title. 2) The House of Wisdom in Baghdad translated ancient Greek and Hindu mathematical texts into Arabic and advanced mathematical knowledge. 3) Al-Kwarizmi studied these translations and developed the Hindu-Arabic number system still used today based on the superior Hindu system.

1. Islam, Mathematics, and Culture Across the Curriculum
Instructor Notes
This is just one way to present the material. I realize that some of you know much more
about this than I do. My purpose here is to recreate what we did in the talk. There are
many ways to show this material. I give myself permission to use five minutes of any
class session for anything I choose. That is how I present the material below: five
minutes at a time. I have used italic type for what I say in class.
Day 1: Why do We Call it Algebra?
Show Transparency 1 We call it algebra because of this man, who wrote the first
algebra book in Baghdad around 780. Yes, that’s the same Baghdad we see in the news
everyday.
Show Transparency 2 Here is a page from that first algebra book. The title contains
the word “al-gabr” and this is where algebra comes from. Also, in the title, “balancing”
refers to the addition property and multiplication property of equality, the properties we
use to keep both sides of an equation “balanced.”
Show Transparency 3 You can see that what we have discovered about the word
algebra is common knowledge. It is in the dictionary.
Day 2: What was going on in Baghdad to cause the first algebra book to be written
there?
Show Time Line You can talk about as many of the things on the timeline as you like,
and then get into Baghdad: The House of Wisdom is established in Baghdad around 750.
All the ancient Greek and Hindu math texts are brought into the House of Wisdom and
translated into Arabic. Al-Kwarizmi studies these translations, extends what he has
learned, and then writes his algebra book.
Show Map Talk about the expansion of the Muslim Empire. Show where Euclid did his
work in Alexandria. All the ancient text lay unused and dormant. If it wasn’t for the
translations of these books into Arabic, they may have been lost forever. Remember, this
period of time is referred to as the Dark Ages in Europe. While education and
scholarship in Europe has stagnated, it is flourishing in the Muslim Empire.
Show Quote I think this is enough to get the point across that Islam values scholarship
highly, and this is why the House of Wisdom was established in the first place.
Day 3: Our number system comes from the House of Wisdom also.
Show Espana Postage Stamp When Al-Kwarizmi studied the Greek and Hindu texts he
realized that the Hindu number system was superior to what was being used at the time.
He included the details of the new number system in his algebra book and went to great

2. lengths to explain how to do arithmetic in this number system. As a result, the word
“algorithm” is used to acknowledge his contribution in this area. This stamp
commemorates the contribution of the Hindu-Arabic number system to mathematics.
There are many places to use this transparency; explaining how efficient our positional
notation number system is, or as an introduction or follow-up to scientific notation.
Show Dictionary Definition of Algorithm You can see Al Kwarizmi’s name in the
dictionary definition.
Day 4: Where did Fibonacci learn mathematics?
I have included a few transparencies connected with the Fibonacci. Of course there is
much more. All we need is an introduction so we can get back to the Map and Time Line
Show Cover of Liber Abaci You can read the quote from the MAA.
Show Map (and Time Line if you like) Fibonacci’s father worked for one of the
shipping companies that moved goods between Pisa and North Africa. Fibonacci went
to live and work with his father. He traveled through North Africa and was trained in
mathematics by the Muslim mathematicians. He read Al-Kwarizmi’s book.
The trade routes where the way in which information traveled between communities.
The initial spread of Islam was because of the Prophet Muhammad’s connection with the
trade routes. Al-Kwarizmi lived at the end of the Silk Route. Fibonacci traveled and
learned mathematics because his father worked for a shipping route.
Show Brochure for Silk Route Odyssey Read second to last paragraph.
Day 5: Completing the Square
The words are right from Al-Khwarizmi’s book. I like to point out that even though it
was an algebra book, there were no symbols like we use today. The equal sign is not
invented until hundreds of years later. For me, this shows how much more concentration
it takes to do algebra without symbols, and how wonderfully compact and efficient our
modern notation is.
I use this transparency for completing the square when solving quadratic equations, then
again when we complete the square to find the vertex of a parabola, and again when we
work with circles and conic sections. When I present something new in terms of
something they have seen before, it makes the new material seem familiar, even though it
is new.
Day 6: Pascal’s Triangle
I have included some introductory material that reinforces the ideas behind multiplying
polynomials, and then leads into Pascal’s triangle. Pascal and Descartes were

3. contemporaries. Descartes’ famous quote is “I think, therefore I am.” Pascal said “The
heart has it’s reasons, which reason does not know.”
Show Al-Samawal He describes how to create the third row of Pascal’s triangle. Point
out that he lived hundreds of years before Pascal.
Day 7: The Golden Rectangle
Some introductory material on the Pythagorean theorem that leads into the golden
rectangle. Can use some of these to talk about the Pythagoreans’ culture and beliefs.
Show Second Al-Samawal Transparency He gives the golden ratio in an unsimplified
form. Great transparency for reviewing all the procedures they have trouble with when
working with radicals. Could be a good group project.
Day 8: The Toledo School of Translation
Keith Devlin’s description explains what is happening. It is a model of three cultures
living in relative harmony, and collaborating on translation projects that have benefited
all educated people ever since.
End Notes
Remember, my target audience is just the students I have in class. I’m thinking of the
student, Muslim or not, who watches or reads the news and comes away with a sense of
hopelessness. Where is the model of peace and cooperation among the people at odds
with each other today? Then that student walks into their math class one day, and sees
the model we have just presented. I think it can ease their sense of hopelessness (it has
for me) and gives them a view of history and culture they may not get elsewhere.
This is a great time to be a math teacher!