Great Ideas in Science
Mathematics
Fall 2012
References:
Marvin Jay Greenberg, Euclidean and NonEuclidean Geometries: Development and History,
4th ed., New York: W. H. Freeman, 2007.
H.L. Resnikoff & R.O. Wells, JR., Mathematics in
Civilization, Dover Edi
LIFE SCIENCE MODULE
5-6
What is life?
?
Week 1
How is life described?
Technology advancement drives the details of description.
Describing life with its primitive codes.
Week 2
Mechanisms behind the codes.
How should the codes be read (How were they
SCIE1110: Great Ideas in Science
Fall 2012 Chemistry Module:
Prof. Ian D. Williams Rm 4540 chwill@ust.hk
Lecture 6. Chemical Fingerprints
Chemical Analysis
In this final lecture we see how we can look at Chemistry in the
world around us and analyse it
A
SCIE1110
Great Ideas in Science
Fall 2012
Solution: Assignment 5
Exercise 17:On the set cfw_0,1,2,3, define S(0)=1, S(1)=2, S(2)=3,
S(3)=0. Which, if any, Peanos axioms are valid here?
Solution: We have the u
SCIE1110
Great Ideas in Science
Fall 2012
Solution: Assignment 4
Exercise 13: Given two rulers, A and B. Both rulers have only two
markings. The two markings on ruler A can mark off a segment of n
units an
SCIE 1110
Great Ideas in Science
Fall 2012
Solution to Assignment 2
Exercise 4: Prove Proposition I.2.
Solution: D is a point in the line segment AB.
(ADC)+ (BDC)=[180o DAC ACD CDA] + [180o DBC
BCD CDB]
SCIE1110
Great Ideas in Science
Fall 2012
Solution: Assignment 3
Exercise 10: Use the Gauss-Bonnet Formula to show that in Hyperbolic
Geometry (curvature =-1) similar triangles have the same area.
Solution: (Sketch)This is a straightforward consequence of
SCIE1110
Great Ideas in Science
Fall 2012
Solution to Assignment1
Exercise 1: Problem 2 of Euclids Elements is to draw a segment of given
length at a given point. The proof seems to be more complicated than
necessary. Can you explain why Eucli
LIFE SCIENCE MODULE
3-4
What is life?
?
Week 1
How is life described?
Technology advancement drives the details of description.
Describing life with its primitive codes.
Week 2
Mechanisms behind the codes.
How should the codes be read (How were they
5. Attempts to prove the 5th Postulate in history
Since antiquity mathematicians were not
comfortable with the 5th Postulate as it
involves extending the straight lines
indefinitely. In fact, we could argue that Euclid
himself did not quite trust this pos
4. Diffie-Hellman Key Exchange Scheme
In this section we show that a profound
understanding of the algebraic operations on
integers can have important applications.
Example:
3x3=9
3 x 3 x 3 = 27
3 x 3 x 3 x 3 = 81
3 x 3 x 3 x 3 x 3 = 243
= 32
= 33
= 34
=
:
How to find common divisor of two numbers?
Given two positive integers m, n, find the
largest positive integer that divides m and n, It
is called the Greatest Common Divisor of m,
n, and is denoted by GCD(m, n)
Method 1: Factorize m, n and then take all
II.Number:
0. Introduction
Numbers are human inventions to represent
physical quantities. It is as old as written
language. In fact, there are archaeological
findings that human used symbols to keep
tallies 30,000 years ago.
Kronecker: God made the number
SCIE1110: Great Ideas in Science
Fall 2012 Chemistry Module:
Prof. Ian D. Williams Rm 4540 chwill@ust.hk
Lecture 4. Chemical Structures
Chemical Structures
1.
Structures based on Logic and Inference
Organic structures: Chains and Rings: Benzene
Isomers, R
SCIE1110: Great Ideas in Science
Fall 2012 Chemistry Module:
Prof. Ian D. Williams Rm 4540 chwill@ust.hk
Lecture 5. Chemical Reactions
What are Chemical Reactions ?
We have shown several simple reactions so far in the course. A chemical reaction
involves
SCIE 1110: Great Ideas in Science
Fall 2012 Chemistry Module:
Prof. Ian D. Williams Rm 4540 chwill@ust.hk
Lecture 1. Atoms and Elements
SCIE1110 Fall 2012
C1.1
SCIE 1110: Great Ideas in Science
Fall 2012 Chemistry Module:
Prof. Ian D. Williams Rm 4540 chw
Climate
Change
How do we know that Earth has warmed? How do we know
that humans are causing greenhouse gas concentrations
to increase? How do we know the current warming trend
isnt caused by the Sun? How do we know that the warming
trend is not caused by
SCIE1110: Great Ideas in Science
Fall 2012 Chemistry Module:
Prof. Ian D. Williams Rm 4540 chwill@ust.hk
Lecture 2. The Periodic Table
Humphrey Davy: Metals by Electrolysis
Real progress on element isolation followed the work of Davy
in 1807. Lavoisier wa
Global Climate Change?
Global Warming?
The Science
And the Rest.
Three Questions
1. Is there evidence for global warming?
a. If not, case closed. Nothing to worry about
b. If yes, then
2. Is this global warming caused by human activities
(anthropogenic)
The Quantum Revolution
Invention of
Transistor (1947)
Laser (1959)
and the Information Revolution (1990 - ?)
M.Loy
1
Some Inventions around 1900s
Steam Locomotive (1814)
Telegraph (1840)
Typewriter (1867)
Telephone (1876)
Moving Pictures (1877)
Automobile
Relativity
Time dilation
E=MC2
SCIE 1110
1
Relativity
Relativity: How two people reconcile
their views of the world when moving
with respect to each other
Do you know how fast you are moving
now?
Galileo and Newton
Short video http:/www.youtube.com/wa
We have been using a lot of useful energy :
that is why we need to conserve.
All forms of useful energy, with the exception of nuclear energy,
can ultimately be traced to the energy provided to us (free!) by
the sun.
Fossil fuel (coal, natural gas, oil
SCIE1110
Great Ideas in Science
Fall 2012
Assignment 2
Exercise 4: Prove Proposition I.2.
Exercise 5: Show that in Neutral Geometry that the hypotenuse is the longest
side in a right triangle.
Exercise 6: Use Theorem I.1 (Sum of interior angles of a trian
SCIE 1110
Great Ideas in Science
Fall 2012
Assignment 3
Exercise 10: Use the Gauss-Bonnet Formula to show that in
Hyperbolic Geometry (curvature=-1) similar triangles have equal
area.
Exercise 11: Show that t
SCIE1110
Great Ideas in Science
Fall 2012
Assignment 5
Exercise 17:On the set cfw_0,1,2,3, define S(0)=1, S(1)=2, S(2)=3,
S(3)=0. Which, if any, Peanos axioms are valid here?
Exercise 18: On Z, the set of i
SCIE1110
Great Ideas in Science
Fall 2012
Assignment 4
Exercise 13: Given two rulers, A and B. Both rulers have only two
markings. The two markings on ruler A can mark off a segment of n
units and the two