Lecture 12
Friday, September 30, 2016
11:16 AM
Apollonius (~200BC)
You learned an ellipse has equation x2/a2 + y2/b2 = 1
a2+b2=c2
If e = 1 you get a parabola
If e > 1 you get a hyperbola
The smaller e gets the closer the ellipse gets to a circle.
This un

Lecture 26
Friday, November 4, 2016
10:36 AM
Up to ~1800 calculus was done without limits, convergence,
differentiability,
THE SHIT HIT THE FAN when weird functions popped up. Like
continuous functions with no derivative anywhere.
Cauchy (1789-1857)

Lecture 13
Monday, October 3, 2016
10:30 AM
Know for test!
(2) is not a number
There's no biggest prime
Pythagorean theorem
(PROOF)
Today's lecture not on test.
Back to the Greeks
The Greek saints:
- Thales
- Pythagoras *
- Eudoxus (similar triangles

Lecture 10
Monday, September 26, 2016
10:37 AM
The importance of Euclid's "elements" (besides the beautiful
proofs) is this program: The five axioms are obviously true, all
other mathematics can be deduced from the five axioms, so all
of math is forev

Lecture 18
Monday, October 17, 2016
10:37 AM
Uman ibn Ibrahim al Khayammi
~1000 AD: Gave a geometric solution to cubic equations " + =
Omar Khayamm: astronomer, mathematician, poet.
Main contributions of Muslim mathematics involved switching from
geome

Lecture 24
Monday, October 31, 2016
10:38 AM
17th - 18th century calculus
Invented by Newton & Leibniz
They found the general formula for derivatives and linked derivatives to
integrals.
In the Following years, they and others solved differential equati

Lecture 3
Friday, September 9, 2016
10:46 AM
*Read the stuff online
Big event ~600 B.C. - Thales brought math to Greece and asked how do yo
this shit is true?
Eg. Triangle ( ) = 180o
The Egyptians and Babylonians used experiments and observation to find

Lecture 21
Monday, October 24, 2016
10:35 AM
1580 Francois Viete (Viet): introduced + * = , random
coefficients axx (ax2)+, the "unknown" x (actually used c)
1620 Pierre Fermat had a copy of "Arithmetica" (Diophantus)
Fermat:
"ap-a (p prime) is divisib

22
Mathematics in Islamic Countries
When we speak cf Arabic mathematicians, we must remember that Arabic
was the ccmmcn language cf intellectuals in the Isiamic wcrld, just as Latin
was in medieval Eurcpe. In fact, the mathematicians mayr have been Turks

MW
21
Mathematics in China and India
Nut much is knuwn abcut the develcpment of mathematics in China befc-re
ccntact with the West was established. The Arithmetic in Nine Sectiensi
(Chin Chang Suan Shu) was written hefere 20s AD. Like the Rhind Pa-
pyrus.

30 e
The Eighteenth Century
We shall only mention some of the most important mathematicians of the
eighteenth century:
0 Brook Taylor (1685-1731),
0 Colin Maclaurin (16894746),
0 Abraham de Moivre (1667~1754),
o Leonhard Euler (17074783),
0 Joseph Lou

Lecture 14
Wednesday, October 5, 2016
10:36 AM
Euclid's proof of the Pythagorean theorem - test!
*
P
*
PD
Find Conic with excentricity 2:
If P is a point on conic
PF/PD = 2
PF = 2(PD)
PF
Sun is at the focus of the
solar system, not the center.
Earth go

Lecture 17
Friday, October 14, 2016
10:34 AM
History
~550 AD Emperor Justinian closed Plato's and all other schools in the
empire
~650 AD Muslims captured Alexandria and burned the library
~750 AD built Bagdad and opened the "House of Wisdom" and
colle

Lecture 5
Wednesday, September 14, 2016
10:32 AM
Read notes on Pythagorean theorem!
The first debate of math philosophy
Thales: "all is water"
- Can't count water, you can measure water.
- Everything can be measured.
Pythagoras: "all is number"
(if y

Lecture 9
Friday, September 23, 2016
9:45 AM
Euclid's Five Axioms
1. Two points determine a segment
2. Any segment may be extended indefinitely
3. Any segment is the radius of a circle
4. All right angles are equal
=
5. "The parallel postulate"
If two li

Lecture 7
Monday, September 19, 2016
10:32 AM
&
= 2% + 1
Fermat thought these were all prime, oops.
F5 is not prime.
F6 is not prime.
Is there any n > 4 so that Fn is prime? - Nobody knows (yet)!
There is another way to try to build primes,
+ = 2+ 1 (

Lecture 22
Wednesday, October 26, 2016
10:35 AM
~1620 The new physics required a new mathematics of
motion to explain velocity and acceleration.
Greek philosopher Zeno came up with "Zeno's paradoxes":
"The flying arrow never moves". At any given time

qual to
r 2 sides.
mbers
B
b
A
We will show A = C1 & B = C2
So, A + B = C1 + C2 = C
C1
C2
A
a
a
T1
b
*
T2
Claim:
A = 2 x T1
C1 = 2 x T2
b
C1
Claim: T1 = T2
= 90 + *
= 90 + *
By s-a-s T1 = T2.
Do same thing with B and prove that B =
C2
B

Lecture 11
Wednesday, September 28, 2016
10:30 AM
Circle
PF
P
*F
PF is a constant (the
radius), doesnt depend
on P.
In 200 BC, Apollonius wrote a book called "Conics" in which
he showed an ellipse has two "foci", two focal points
P
F1
F2
And if P is

Lecture 20
Friday, October 21, 2016
10:39 AM
1440: Printing Press was invented.
1545: Cardano solved the general cubic (cosa cubis sum 7 cosa quad sum 3
cosa aequs 9)
All written in
words,
algebraic
notation
wasnt
invented yet.
Shortly after, "they"

Lecture 19
Wednesday, October 19, 2016
10:34 AM
Chinese Mathematics: Han Dynasty (~300BC - 200AD)
They used base 10 with place values (like the Hindus).
The three birds problem:
Suppose chickens cost $2 each, ducks cost $3 each, and geese
cost $7 each.

Lecture 23
Friday, October 28, 2016
10:32 AM
The area problem: Find area "under" a curve y=f(x) between
x=a and x=b
(x,y)
/
= +
y
0
x
Cut the area into little strips and then add them up.
Strip at x has area ydx.
That "integral" is an infinite sum o

Lecture 8
Wednesday, September 21, 2016
10:38 AM
Philosophy (of math)
Epistemology: Thales said "deductive reasoning" (proof)
Ontology: Debate between Thales (magnitude, measure) and
Pythagoras (numbers, count)
- Thales wins because you can't use numbe

Lecture 16
Wednesday, October 12, 2016
10:29 AM
Greek Math: Thales (600 BC) - Hypatia (415 AD)
Roman Math:
European Math: (415- 1415)
India: used a base ten number system
4
5
6
Big ideas (by 600 AD):
- Places values 26
- The number 0
- Negative number

MATH 338 History and Philosophy of Mathematics
Course Outline (2016)
Instructor: Tom Fox, Burnside Hall 1243, [email protected]
Office Hours: Wednesday 12:30-14:00 (provisional) or by appointment
Textbook: None. Notes and readings will be posted on line.