New Information
New InformationLectures will summarize themes and present the relevant
mathematics.
Facts are of course the basis for discussion, and will be used as such,
but not all historical details from the reading will be covered in the
lecture; students are responsible for reading this material in the
text,
on the schedule shown below. This is your principal source
of facts. Read the assigned material for historical background,
people
involved, and general overview of the mathematics BEFORE the lecture.
You
do NOT need to worry about the details of the mathematics until after
the
lecture covering that material. The lecture will highlight the
mathematical
details for which you are responsible. After the lecture you
should
reread text material specific to the mathematics covered in the
lecture. The shedule below is tentative.
Project 1: Explore a Math Problem
Due Feb 12 Scoring
Rubric
You may pick your topic from the list provided or propose your
own.
The list of available projects appears below (once someone takes a
topic
it will be colored red). More
information
about each project is in the Description
of Projects.
All Project 1 choices must be approved by me by January 29. No
duplication
is allowed, so pick early for more choice of projects (email me your
choice
of one of mine or a proposal for your own idea).
Your paper should include both a brief (~ 1 page) historical setting of
the
problem,
and a mathematical solution. The paper should be typed (2-4
double
spaced pages, 12 point font, exclusive of figures, no penalty for
exceeding
limit if justified by mathematical content). It may include
hand drawn diagrams, formulas and symbols (although typeset
formulas/symbols
are preferred). Any diagram you did not personally make
must
give the source (it is preferred you make your own diagrams). Any
entire sentence that is quoted must be in quotation marks and give the
source. Although the paper will contain formulas, the written
part
should be well written, using correct grammar, spelling, and
punctuation.
It should include a list of sources consulted (if any- for project 1
the
text is an acceptable source for the histoical background and for most
projects you can do the mathematics by yourself).
Number Base and
Regularity
Thales and the
Pyramid
Trisection of the
Angle
Prime Numbers
Perfect numbers
Abundant and
Deficient Numbers
Figurate Numbers
Euclidean and
Modern Compasses
Construction with
Straightedge and Compass I
Construction with
Straightedge and Compass II
Construction with
Straightedge and Compass III
Regular Solids I
Regular Solids II
Regular Solids III
Archimedes'
quadrature of the parabola
Archimedes
approximation of pi
"Heron's" Formula
for the area of a triangle
in terms of its sides
Plane and Solid
Geometry I
Plane and Solid
Geometry II
Spherical Zones
and Sections
Arithmetic,
Geometric and Harmonic Means
Project 2: Biography of a Mathematician
Due March 25 scoring
rubric
This project is a biography of a mathematician,
including a brief discussion of that mathematician's life and cultural
setting, and more extensive discussion of his/her mathematics and
intellectual
life. It should include a list of references. In general, the
text
should not be your major source for this project. You may pick
your
subject from the list below or propose your own, but you may not select
a mathematician you have done a project on for another class. To
select your subject e-mail me your request. All projects must be
approved by me by March 8. No duplication is allowed. (Red
means already taken.)
The paper must be typed. The length must not exceed 8 double
spaced pages, 12
point
font, exclusive of illustrations, diagrams, and references.
It may include hand drawn diagrams, formulas and symbols (although
typeset
formulas/symbols are preferred). Any diagram you did not
personally
make must give the source with the diagram Any entire sentence
that
is quoted must be in quotation marks and give the source.
Although
the paper may contain formulas, the written part should be well
written,
using correct grammar, spelling, and punctuation. It should
include
a list of sources consulted (at least 3 reputable ones beyond the
text).
| Eudoxus Menaechmus Apollonius Diophantus Hypatia Liu Hui Al Khowarizmi Brahmagupta Umar al Khayyami Bhaskara Qin Jiushao Nicole Oresme Scipione del Ferro Niccolo Tartaglia Gerolamo Cardano |
Lodovico Ferrari Rafael Bombelli François Viète Simon Stevin John Napier Marin Mersenne René Descartes Pierre de Fermat Bonaventura Cavilieri Evangelista Toricelli Blaise Pascal Isaac Barrow Maria Agnesi Joseph Fourier |
Sophie Germain Leonhart Euler Karl Freidich Gauss Niels Henrik Abel Evariste Galois Augustin Cauchy Richard Dedekind Sofia Kovalevskaya Emmy Noether Srinivasa Ramanujan Kurt Gödel Alan Turing Nathan Jacobson Paul Erdos Andrew Wiles |
Project 3: Panel Discussion Tracing a Topic through History
Presented in class as scheduled
Scoring rubric
Project 3 is a panel discussion tracing a single mathematical concept
through history and/or across cultures, or a debate related to a
priority
dispute. Each participant will be responsible for a particular
part,
and the entire panel will be responsible for making a coherent whole
from
the pieces. Some possible topics to trace through history include
the concept of real numbers, the development of algebraic symbolism,
the
concept of function, the number pi, the Pascal triangle, the
development
of mathematical rigor, the concept of infinity, the influence of
paradoxes
on mathematics, etc. Suggested panel size is 4 people. No
panel
may have more than 5 people on it. Panels will be organized
during
class Tuesday April 1. Topics should be selected at that time;
no topic requests will be taken prior to that time. The
presentation
date may also be scheduled at that time; it should be scheduled by
4/19.
Your grade will be based primarily on your individual presentation but
may be enhanced by your panel's whole presentation.
Project 3 scoring rubric
On line:
MacTutor
Euclid's
Elements
Wilkins' Math History
site
All test questions will be on topics specifically covered in the
lecture
or homework, but required additional matrial on such a topic may be
available
only in the reading.
Additional topics list for final
Test 2 topics
Old Test 2
Old Test 2 solutions (sort of)
Chitchen Itza (Mayan)
Collegium Maius (where Copernicus studied),
Cracow
Xi'an (Chinese capital during the time of Liu Hui)
"In precisely the same way that a novelist invents characters,
dialogs
and situations of which he is both the author and master, the
mathematician
devises at will the postulates upon which he bases his mathematical
systems.
Both the novelist and the mathematician may be conditioned by their
environments
in the choice and treatment of their material, but neither is compelled
by any extrahuman, external necessity to create certain characters or
invent
certain systems."
- E. T. Bell
"Intellectual civilization was born only once, in Greece. It
flickered
out after several hundred years and was reborn in Western Europe in the
17th century. This greatest creation of Greek genius has been the
powerhouse of Western civilization for more than two thousand years; it
has set this civilization apart from all others and has spread over the
whole earth from China to Peru; and it started with Thales and his
discovery
of skepticism."
-George F. Simmons
"We do not know whether the northern savages who overran the
north-eastern
portion of the Mediterranean really were blue-eyed or really had fair
hair.
We know that there is not a particle of justification for the belief
that
the scientific achievements of Greek civilization were the fruit of
their
racial equipment. Two men who are reputed to be the founders of
Greek
geometry, Thales and Pythagoras, were both of Phoenician parentage."
-Lancelot Hogben
Euclid’s proof of I.5 was nicknamed “pons asinorum” or ass’s bridge.
In the days all schoolboys studied Euclid, it “made so many boys
conclude
they have no capacity for geometry because this proof, the first of any
difficulty in Euclid, leaves the proposition to their minds less
evident
than they found it.”
-Logician and philosopher Charles S. Pierce (1834-1914)
Source: Saul Stahl, Geometry from Euclid to Knots.
“Euclid’s Elements is one of the greatest books ever written.”
-Bertrand Russell
“It is also one of the dullest….The Elements begin with a
definitions-
‘A point is that which has no part’- and marches with inhuman,
undeviating
monotony through 13 Books and 465 Propositions, none of which are
discussed
or motivated in any way.”
-George F. Simmons
“All in all, for more than 2000 years, the intellectual architecture
of the Elements has rivaled the Parthenon as a symbol of greek
genius.
Both have deteriorated somewhat in recent centuries, but perhaps the
book
has sustained less damage than the building.”
-George F. Simmons
“Archimedes, who was certainly the greatest mathematician,
physicist,
and inventor of the ancient world, was one of the supreme intellects of
Western civilization.”
-George F. Simmons
"No Roman ever died in contemplation of a geometrical diagram."
Alfred North Whitehead
"It is absolutely clear that the Greeks studied geometry for the
sheer
pleasure of it, as a form of play, without any thought of application
to
science or practical life. For them, geometry- and perhaps also
philosophy
and drama- were serious games, in much the same way chariot races and
gladiatorial
contests were for the Romans. If we consider the Greeks, and the
Romans, and perhaps ourselves as well from this point of view, it
begins
to appear that nothing reveals the quality of a culture so clearly as
the
games it plays."
-George F. Simmons
"In the conflict between the thinkers and the thugs, the thugs
always
win, but the thinkers always outlive them."
-Petr Beckmann
"Who would not rather have the fame of Archimedes than that of his
conqueror
Marcellus?"
-Sir William Rowan Hamilton
"The mathematical life of the ancient world came to a sudden and
violent
end one March day in the year 415. On that day Hypatia, the first
woman mathematician in history- beautiful, eloquent, and brilliant- was
dragged from her carriage on a street in Alexandria and brutally
slaughtered
by a howling Christian mob."
-George F. Simmons
“Out of this [colonial] domination rose the ideology of European
superiority,…with
traces to be found in histories of science that emphasized the unique
role
of Europe.…This comforting rationale for European dominance has become
increasingly untenable.”
-George
Gheverghese Joseph
"Nothing that we would recognize as analytic geometry can be found
in
Descartes' essay, except perhaps the idea of using algebra as a
language
for discussing geometric problems. Fermat had the same idea, but
he did something important with it....[Descartes] did introduce several
notational conventions that are still with us...The result is that
superficially
Descartes' essay looks as if it might be analytic geometry, but isn't;
while Fermat's doesn't look it, but is."
-George F. Simmons
Disability Accommodations
Iowa State University complies with the American with Disabilities
Act and Section 504 of the Rehabilitation Act. If a student has a
disability that qualifies and requires accommodations, he/she should
contact
the Disability Resources (DR) office for information on appropriate
policies
and procedures. DR is located on the main floor of the Student Services
Building, Room 1076; their phone is 515-294-6624. Any student who
requires
an accommodation under such provisions should contact Prof. Hogben
privately
as soon as possible and no later than the end of the first week of
class
or as soon as documentation of the need for accommodation is obtained.
Contact may be made by e-mail (LHogben@iastate.edu), telephone
(4-8168),
or in person (office 488 Carver). It may take up to a week to
implement
an accommodation. No retroactive accommodations will be provided in
this
class.
| Leslie Hogben's Homepage | updated after each class period |   |