Mathematics 390
Bring a copy of this full syllabus
to class on Friday, January 22.
Here's my single favourite
history of
mathematics web site. Look there for more
information about
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
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
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
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.
links by section:
§1.2
Quick answers for this section.
The Rosetta
Stone (Rosetta
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
detailed version.
§1.3
Quick answers.
Here's a historical
map of the region.
Babylonian quadratic solution on copy of YBC
6967 Details of
original solution.
Bablyonian square root of 2 on YBC
7289 (schematic)
§2.1
Quick answers.
Thales, Pythagoras (tuning), Hippasus, Hippocrates lune
On-line
piano for interval demonstrations.
A monochord
(and a cuter
picture)
Euclid's proof of the Pythagorean
Theorem
Quick answers.
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
§2.2
Quick answers.
Archimedes circle formula,
volumes, and pi, Hipparchus (and
the moon). Roman
calendars.
Quick answers.
Heron's formula.
§3.1
Very
old music for Friday
Annotated Bibliography assignment
Quick answers.
An image
of nine chapters, and another
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).
Quick Answers
Yang
Hui's triangle
§3.2
Quick answers
Numerals
Trig tables
Lilavati contents
§4.1
Quick answers
Early decimal point
§4.2
Quick answers
Abu'l Wafa's finger reckoning was an influence on things
like this.
§4.3
Quick answers
Great
mosque - detail.
Friday
mosque
al-Khayyami on the cubic
§4.4
Quick answers
al-Mun'im's arithemetic triangle
§5.1
Quick answers
Translators, Rabbits, Pisa,
and more
§5.2
Quick answers
Letters and Sestina
Quick answers
Jordanus
Levi ben Gerson justifies theory.
§5.3
Quick answers
Nicole
Oresme, graphs
and infinite
series
Chuquet
§6,1
Quick answers
Room
of Masks (first century BC? - Rome)
Abraham
with Angels (early christian)
Annunciation
- Simone Martini (14th century) attractive but not perspective
Madonna
in Majesty - Duccio (14th century), progress is being made Last
Supper
Paolo
Uccello - Pawning
of the Host more progress
Filippo
Brunelleschi - Peepshow
Leon
Battista Alberti
Piero
della Francesca - Flagellation
School
of Athens
Luca
Pacioli - excerpts
from his Summa
diagams by da Vinci Last
Supper
Albrecht
Dürer - St.
Jerome, Designer of the sitting man, Designer
of the lute. Melancholia
Persepctive Example
Tartaglia notes on the controversy
Cardano - Ars Magna (both his work and Ferrari's)
§6.2
Quick answers
Quick answers
Regiomontanus - on triangles
Riese
Copernicus
§7.1
Quick answers
Viete
Fermat - Last & Little, Coordinates
Mersenne
Pascal - Triangle, Conics (applet to visualise for circles - works for any conic section)
§-7.2.3
Quick Answers
Simon Stevin - decimals
Rene Descartes - coordinates, normals/tangents
§7.2.4-
Quick Answers
Rembrandt's painting
Hudde & van Heuraet - works
Leibniz - derivatives, FTC
§-7.3.5
Quick Answers
Recorde - English arithmetic
Gerardus Mercator - schematic map (straight cylindrical - not Mercator) - map projection
Harriot - equations with curious notation
Napier - logarithms
Burgi
§7.3.6-
Quick Answers
Wallis
Barrow - FTC
Newton - calculus
Berkeley - analyst
§8.1
Quick Answers
DeMoivre
Stirling
Johann Bernoulli - integrating rational functions
l'Hospital
Simpson
Maclaurin - calculus
Brook Taylor
§8.2
Quick Answers
Bernoulli family tree
Jakob Bernoulli - large numbers
Nikolas Bernoulli
Daniel Bernoulli
Gabriel Cramer
Euler - trig & FLT
Agnesi
Lambert - irrational π
Saccheri
-§8.3.3
Quick Answers
d'Alembert - limits
Laplace
Lagrange
Borda
Condorcet
§8.3.4-
Quick Answers
Monge
Gauß
Germain
Brianchon - theorem
Poncelet
§9.1
Quick Answers
Cauchy - derivatives, FTC
Dirichlet
Galois - and Berlioz
DeMorgan
Babbage
Lamé
Kummer
Liouville
§9.2-3
Quick Answers
Sylvester
Cayley
Boole
Jevons
Betti
Abel - quintic
§9.4
Quick Answers
Jacobi
Eisenstein
Riemann
Dedekind - cuts
Weierstraß
Kronecker
Klein
Lie
§10.1
Quick Answers
Banneker - 1918 journal article about
Bowditch
Adrian
Hamilton - Quaternions
Quick Answers
Peirce
Dodgson - commentary on mathematics - determinant theorem - England
Gibbs
Tait - Scottish
Maxwell - Scotland / England
Grassman - Germany / Poland
§10.2
Quick Answers
Garfield
Hill - AMS
Glaisher
Steinmetz
E. H. Moore - geneology
Bolza
Slaught - MAA
§11.1
Quck Answers
Lecture notes
§11.2
Quick Answers
Wiener
Borel
Zermelo - axioms for set theory
Noether
Courant
von Neumann - with computer
LS Hill
§11.3
Quick Answers
Cantor set
Sierpinski triangle/gasket
Tarski
Banach
Hahn
Menger sponge
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
Lebesgue
Frechet
Fraenkel
Hausdorff
Gödel
Brouwer
§11.4
Quick Answers
Bieberbach
Pasch
Weyl
Lefschetz
RL Moore
Alexander
Bell
Quick Answers
Dehn
Enigma, again
Rejewski - Bomb
Turing - Bombe
Goldbach - Renyi
Nash
Arrow
**Tuesday
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
included.
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