Bring a copy of this full syllabus
to class on Friday, January 22.
Here's my single favourite
mathematics web site. Look there for more
the history of anything in mathematics.
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
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
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-timeline up to the
end of the first millennium.
Here's a website just of portraits
Note that it says "Note that portraits of mathematicians from
earlier than the fifteenth century are only suggestive." Once
get ones that are contemporary (and I think we will somewhat before the
15th century), I'll start including them in my discussions.
links by section:
Quick answers for this section.
Stone schematic) - one message in hieroglyphic, demotic
(later form of hieratic) and Greek.
Here is a photograph of the Rhind
Papyrus - to give you a sense of what this relic actually is.
Here is a little bit from the Moscow
Papyrus (the bit called problem 1.1 in our text).
Some problems from the Rhind and
Moscow - translated. More
Here's a historical
map of the region.
Babylonian quadratic solution on copy of YBC
6967 Details of
Bablyonian square root of 2 on YBC
Thales, Pythagoras (tuning), Hippasus, Hippocrates lune
piano for interval demonstrations.
(and a cuter
Euclid's proof of the Pythagorean
Hippocrates and the cube, Hippias (some
good quadratrix information), Eudoxus, Euclid, Erastosthenes
(here's a fun link to Carl Sagan
on the old Cosmos show talking about him), Appolonius
Archimedes circle formula,
volumes, and pi, Hipparchus (and
the moon). Roman
old music for Friday
Annotated Bibliography assignment
of nine chapters, and another
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).
Early decimal point
Abu'l Wafa's finger reckoning was an influence on things
mosque - detail.
al-Khayyami on the cubic
al-Mun'im's arithemetic triangle
Translators, Rabbits, Pisa,
Letters and Sestina
Levi ben Gerson justifies theory.
of Masks (first century BC? - Rome)
with Angels (early christian)
- Simone Martini (14th century) attractive but not perspective
in Majesty - Duccio (14th century), progress is being made Last
Uccello - Pawning
of the Host more progress
Brunelleschi - Peepshow
della Francesca - Flagellation
Pacioli - excerpts
from his Summa
diagams by da Vinci Last
Dürer - St.
Jerome, Designer of the sitting man, Designer
of the lute. Melancholia
Tartaglia notes on the controversy
Cardano - Ars Magna (both his work and Ferrari's)
Regiomontanus - on triangles
Fermat - Last & Little, Coordinates
Pascal - Triangle, Conics (applet to visualise for circles - works for any conic section)
Simon Stevin - decimals
Rene Descartes - coordinates, normals/tangents
Hudde & van Heuraet - works
Leibniz - derivatives, FTC
Recorde - English arithmetic
Gerardus Mercator - schematic map (straight cylindrical - not Mercator) - map projection
Harriot - equations with curious notation
Napier - logarithms
Barrow - FTC
Newton - calculus
Berkeley - analyst
Johann Bernoulli - integrating rational functions
Maclaurin - calculus
Bernoulli family tree
Jakob Bernoulli - large numbers
Euler - trig & FLT
Lambert - irrational π
d'Alembert - limits
Brianchon - theorem
Cauchy - derivatives, FTC
Galois - and Berlioz
Abel - quintic
Dedekind - cuts
Banneker - 1918 journal article about
Hamilton - Quaternions
Dodgson - commentary on mathematics - determinant theorem - England
Tait - Scottish
Maxwell - Scotland / England
Grassman - Germany / Poland
Hill - AMS
E. H. Moore - geneology
Slaught - MAA
Zermelo - axioms for set theory
von Neumann - with computer
Space filling curves
Quotes from Menger on curves:
"We can think of curves as being represented by fine wires, surfaces as
produced from thin metal sheets, bodies as if they were made of
wood. Then we see that in order to separate a point in the
surface from points in a neighbourhood or from other surfaces, we have
to cut the surfaces along continuous lines with a scissors. In
order to extract a point in a body from its neighbourhood we have to
saw our way through whole surfaces. On the other hand in order to
excise a point in a curve from its neighbourhood irrespective of how
twisted or tangled the curve may be, it suffices to pinch at discrete
points with tweezers. This fact, that is independent of the
particular form of curves or surfaces we consider, equips us with a
strong conceptual description."
"A continuum K is called a curve if to each point in K there exist
arbitrary small neighbourhoods whose boundaries do not contain any
continua. A continuum K embedded in a space is called a curve if
to any point in K arbitrary small neighbourhoods exist whose boundaries
do not have any continua in common with K. A continuum is
describe in the usual way as a non-empty closed set which is
indecomposable (a set which, if written as a disjoint union of two
closed sets, would imply that one was empty)." Menger, 1925.PR
Rejewski - Bomb
Turing - Bombe
Goldbach - Renyi
includes some discussion of philosophy
More will be added to this page as the semester progresses.
Please ask me if there is something you would like to see
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