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
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 b
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 th
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 func
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
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
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 contributio
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 Foll
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 an
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 "Arithme
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 Eu
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 Sh
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 (nu
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
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 cos
COMMENTARX ON
G. H. HARDY
H. HARDY was a pure mathematician. The boundaries of this
' subject cannot be precisely dened but for Hardy the word pure
as applied to mathematics had a clear, though negati
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
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.
- Everythi
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 a
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)!
T
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 paradoxe
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.