Mathematics 390

Here is the full syllabus.

Here's my single favourite history of mathematics web site.  Look there for more information about the history of anything in mathematics.

First two chapters from our textbook.  I have also recalled the library's copy and placed it on 4-hour reserve at the library.  The entirety of the book may be viewed from the library online. 

Do we want to move the midterm to a Friday, either the one before or Spring Break?

Here's a place you may leave anonymous comments about the course.

Here's a list of resources that come to my mind quickly:
William Dunham's Journey through Genius is in Milne (QA21.D78 1990).
Ronald Calinger's A Contextual History of Mathematics is another book that connects history of mathematics with the rest of history.  It's also in Milne (QA21.C188 1999).
Browsing the library in the QA21 section in general is a good idea.  
Here are some other sources that I think highly of:
Morris Kline - Mathematical Thought from Ancient to Modern Times
Victor Katz - A History of Mathematics:  An Introduction
John Stillwell - Mathematics and Its History
Historia Mathematica
is a journal of history of mathematics - we have this in the library as well.
Ronald Calinger's Classics of Mathematics is a source book of original sources, as is Dirk Struik's Mathematical Source Book, along with Fauvel and Gray's History of Mathematics:  A Reader.  I believe all are in the library. 
Cajori, Florian, A history of mathematical notations.
I have several more sources, but this should be enough to get you started.  Tell me if you seek something.  

Here's a student-made timeline up to the end of the first millennium.  And here's a fun graphical-interactive timeline from someone online.  It doesn't follow our course precisely, but it's a good start and a place where you use to get going and then add in your own content.

Here's a website just of portraits of mathematicians.  Note that it says "Note that portraits of mathematicians from earlier than the fifteenth century are only suggestive."  Once we get ones that are contemporary (and I think we will somewhat before the 15th century), I'll start including them in my discussions. 

Here's an article about (and a link to) an online "exhibit" about history of mathematics at the wonderful Museum of Mathematics.  I have not dug through it, but I am certain there is good information here.


links by section:

§1.2

Course Theme Song

Opening Day Theme Music

Quick Answers text


The Rosetta Stone (Rosetta Stone details) - one message in hieroglyphic, demotic (later form of hieratic) and Greek.  From 196 BCE, discovered 1799 CE.  
The Reisner Papyrus (~2000 BCE) sections 
Here are some views of the Rhind Papyrus (~1650 BCE) - to give you a sense of what this relic actually is. 
Some values from and comments about the 2/n table 
The Moscow Papyrus
Here is a little bit from the Moscow Papyrus (the bit called problem 1.1 in our text).  (~1900 BCE) 
Some problems from the Rhind and Moscow - translated.  More detailed version


§1.2.2 and 1.3

Music for today

Quick Answers text

The Berlin Papyrus (~1800 BCE)

Some about Babylonian base 60 

A nice overview of Babylonian tablets.

Babylonian quadratic solution on copy of YBC 6967  Details of original solution. (~1800 BCE) 
Bablyonian square root of 2 on YBC 7289 (~ 1700 BCE)

Plimpton 322 and some commentary, and some other information also. (~1800 BCE)

§2.1 

Music for today

Quick Answers text 

Thales (~600 BCE), 
Pythagoras (~500 BCE) (tuning)

A monochord
On-line piano for interval demonstrations.  
Euclid's proof of the Pythagorean Theorem
Hippasus (golden irrational)
Hippocrates and the lune, (~425 BCE)
Hippias 
(some good quadratrix information), (~425 BCE)
Eudoxus, (~375 BCE)
Euclid (greatest common divisor, infinitely many primes), (~300 BCE)
Erastosthenes (here's a fun link to 
Carl Sagan on the old Cosmos show talking about him [start at 3:53]),(~250 BCE)
Apollonius (~225 BCE)


§2.2


Speculative ancient roman music

More Roman music.

Quick Answers text

Archimedes (~250 BCE)  circle formula, volumes, and pi, Hipparchus (134 BCE) (and the moon).  Roman calendars.  (45 BCE)
Heron's (~50 CE) formula.
Nicomachus (~100 CE), Menelaus (~100 CE) (planar version of theorem / sphere version),  Ptolemy, (~125 CE) Diophantus (~250 CE), Pappus (~325 CE), Hypatia (~400 CE), Proclus, Eutocius, Boethius


§3.1

Very old Chinese music
Annotated Bibliography assignment
Quick answers text

Outline of Chinese History.  Written Chinese numeration Image of Zhoubi suanjing (~100 BCE) 
An 
image of nine chapters Text from nine chapters.
Contents of nine chapters (excuse the Wikipedia link - I do have this in a print source but this way I don't need to scan it here).  (1000 BCE - 200 CE) 

Sun Zi (~450 CE) Chinese Remainder Theorem

Chang Ch'iu-Chien [Zhang Qiujian] (475 CE) indeterminant problem

Wang Hs'iao-T'ung [Wang Xiaotong] (625 CE) cubic problem

Li Zhi (1248 CE) quartic problem 

Yang Hui and Qin Jiushao (1247 CE) - Approximating quartics

Yang Hui's triangle  (1261 CE based on Jia Xian ~1050 CE) 


§3.2

Quick answers text

Baudhayana (~800 BCE) MCRTT

Vedic square doubling (-750 BCE)

Some Jain stories and many other links for multicultural mathematics. (< 500 BCE)

Son of Chajaka (~300 CE)

Bakshali Manuscript "controversy" NOVA about zero,  Anaysis videoAMS article.


Numerals (~ 850 CE)

indeterminate equations from Bakshali. 

Trig tables (499 [Aryabhata] & ~550 CE)
Varahamihira (~550 CE) Arithmetic triangle for combinatorics - perfumes made by choosing substances from a larger set

Brahmagupta (650 CE) Pulveriser (but reported in Bhaskara)
Lilavati contents (~1150 CE)
Details from Bhaskara (~1150 CE)


§4.1-2

Quick answers text 

An overview of "Arabic mathematics".

Some from al-jabr. (800) by al-Khwarizmi

further work from ibn Turk (830)

Early decimal point (952)

al-Haytham on geometry. (~1000)

Abu'l Wafa's finger reckoning (~975) was an influence on things like this.

al-Biruni's qibla problem (~1000)


§4.2

The Rubaiyat in Farsi with Persian classical music.

Quick answers text 

Lecture 

Great mosque - detail.  
Friday mosque
An article about al-Khayyami and the ring of four almonds.

al-Khayyami on the cubic (1100)



§4.3-4 next time

al Samawa'l (1175)

al-Mu'taman's (1082) work with circles and chords (long article)
ibn Mun'im's (1212) arithmetic triangle



§5.1

Quick answers text

Translators, Rabbits, Pisa, and more

If you want to know more (e.g. why 24?) about the Book of Squares problem, look here


§5.2

Quick answers text

Dionysius Exiguus 525

More on Bede. 725
Letters 
Alcuin Problems to Sharpen the Young 800
Pope Sylvester II 980
Sestina
Jordanus 1250


§5.3

Quick answers text 

1321 Levi ben Gerson justifies theory.  Induction

1328 Bradwardine

1340 Nicole Oresme, graphs and infinite series Harmonic diverges 

1484 Chuquet

§6.1

Quick answers text

Room of Masks (first century BC? - Rome)

Abraham with Angels (early christian 548 AD)
Annunciation - Simone Martini (14th century) attractive but not perspective 
Madonna in Majesty - Duccio (14th century), progress is being made Last Supper
1468 Paolo Uccello - Pawning of the Host more progress
1415 Filippo Brunelleschi - Peepshow
1435 Leon Battista Alberti
1460 Piero della Francesca - Flagellation
School of Athens
1494 Luca Pacioli - actual Summa excerpts from his Summa  diagams by da Vinci  Last Supper
1525 Albrecht Dürer - St. Jerome Designer of the sitting man, Designer of the lute.  Melancholia
Perspective Example

1545 Tartaglia notes on the controversy

(some of this will get pushed to next time)

1545 Cardano - Ars Magna (both his work and Ferrari's)
1572 Bombelli


§6.2

Quick answers text 

leftover from last time

1545 Cardano - Ars Magna (both his work and Ferrari's)
1572 Bombelli

1463 Regiomontanus - on triangles
1525 Rudolff's notation
1550 Riese Arithmetic book 
1553 Stifel's triangle
1514 Copernicus

1525 Albrecht Dürer  Some pictures to end the day.


§7.1

Quick answers text 

1582 Christoper Clavius (German working in Rome) last step to current calendar

1591 Viete  The Analytic Art

1650 Fermat - Last & Little, 1636 Coordinates, Areas

1650 Roberval works.

1650 Mersenne

The problem of points

1650 Pascal - Triangle (parallelogram visual), Conics (applet to visualise for circles - works for any conic section)



§7.2

Quick Answers text

1585 Simon Stevin - decimals different tunings 
1637 Rene Descartes - coordinates, normals/tangents
Rembrandt's painting
1659 Hudde & van Heuraet - works
Leibniz - 1684 derivatives, 1693 FTC

§7.3

Quick Answers text 


1557 Recorde - English arithmetic

1560s Gerardus Mercator - schematic map (straight cylindrical - not Mercator) - map projection - loxodrome vs. straight

\int_0^{\phi} \sec t dt = \ln(sec \phi + tan \phi).  (stretch vertical distances as much as horizontal)

1590 Harriot - equations with curious notation
1614 Napier - logarithms
~1614 Burgi
1656 Wallis
1670 Barrow - FTC
1687 / 1704 Newton - calculus, limits in principia




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