GDST1013 The Power of Science and Technology

An Introduction

Content

Course Introduction

What is Science

A Brief Introduction to the Scientific Revolution

The Power and Limits of Science

Course Introduction

Course Code: GDST1013 Title: The Power of Science and

Technology

Textbook: none

Website: ISpace

Teachers

Instructor: Prof. Ken Tsang Office: E409 Phone: 3620606 Email: kentsang@uic.edu.hk

Teaching Assistant (TA) Ms. Garbo Hu Email: garbohu@uic.edu.hk

Time & Venue (3) 8:00-9:50am, Tuesday C208

13:00-13:50pm, Thursday E301

Course Content & schedule

(subject to adjustment) Week 1: Introduction Week 2~4: Statistics Module Week 5: Quiz Week 6-7: Group presentation Week 8-10: Computer Module week 11: Guest Lecture or other activity? Week 12-13: Group presentation Week 14: Review for Final Exam

Assessment (from syllabus)

Class Participation 10% Written assignment/Project 40%

Quiz/test (week ~5) 10% Final Examination 40%

Part I: What is Science

What is Science

Can we describe what science is using your own language?

Can you give a few examples of what you consider to be science?

Can you name a few scientists? And a few examples of what is NOT

science?

Science in Chinese-- 科学 据说文解字，科，会意字：“从禾从斗，斗者

量也”；故“科学”一词乃取“测量之学问”之义为名。

从唐朝到近代以前，“科学”作为“科举之学”的略语，“科学”一词虽在汉语典籍中偶有出现，但大多指“科举之学”。

“ 科学”一词由近代日本学界初用于对译英文中的“ Science” 及其它欧洲语言中的相应词汇。

Science -- 科学 中国传统上将所有的知识统称“学问”，关于自

然物道理的学问称为“物理” 。因此古代的物理即是自然科学， “数学”则独立于“物理”。

自明代以后中国称研究自然物道理的学问为格致学 ( 王阳明 ) ，即格物致知之学。

中国近代最早使用“科学”一词的学者大概是康有为。他出版的《日本书目志》中就列举了《科学入门》、《科学之原理》等书目。“科学”一词才逐渐取代“格致学”。

Definition: Science

(knowledge from) the careful study of the structure and behavior of the physical world, especially by watching, measuring and doing experiments, and the development of theories to describe the results of these activities. – from the Cambridge Dictionary

Science: (From Wikipedia)

Science (from Latin scientia, meaning "knowledge") is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe.

In an older and closely related meaning, "science" also refers to a body of knowledge itself, of the type that can be rationally explained and reliably applied.

Definition: Measure & Experiment

Measure: to discover the exact size or amount of something, or to be of a particular size. (quantification)

Experiment: a test done in order to learn something or to discover is something works or is true (verification)

Can you give a few important scientific experiments in the history?

Definition: Theory

Theory: a formal statement of the rules on which a subject of study is based or of ideas that are suggested a fact of event or, more generally, an opinion or explanation

Theories are powerful explanations for a wide range of phenomena.

Definition: Technology

Technology: (the study and knowledge of) the practical, especially industrial, use of scientific discoveries

Can you give a few examples of technology?

Discussion & Sharing

Is mathematics science? Why?

Is Chinese medicine science? Why?

Is Feng shui ( 风水 ) science? Why?

Is Astrology science? Why?

Example of Scientific Study: Free Falling Objects

Given two balls, one is ten-pound and the other one-pound. If dropping both balls off at the same time, which ball will hit the ground first? The heavier one, or the lighter one?

What Aristotle Said Aristotle (384BC-322BC)

A Greek philosopher, student of Plato and teacher of Alexander the Great

He studied many subjects encompassing physics, logic, politics, ethics, aesthetics and metaphysics

He had taught: that heavy objects fall faster than lighter ones, in direct proportion to weight.

Is this theory true or false? How to prove?

What Galileo Did

Galileo (1564-1642) An Italian physicist, mathematician, astronomer

and philosopher who played a major role in the Scientific Revolution. He is considered as the “father of modern science”

A biography by Galileo's pupil Vincenzo Viviani stated that Galileo had dropped balls of the same material, but different masses, from the Leaning Tower of Pisa to demonstrate that their time of descent was independent of their mass.

Discovering the Laws of Nature

Galileo was willing to change his views in accordance with observation.

Galileo was one of the first modern thinkers to clearly state that the laws of nature are mathematical

Galileo: physics should be mathematicalPhilosophy [i.e. physics] is written in this grand book — I mean the universe …but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures

Galileo’s On Motion (1590) “Some superficial observations have been

made as, for instance, that the free motion of a heavy falling body is continuously accelerated. But to just what extent this acceleration occurs has not yet been announced. For so far as I know, no one has yet pointed out the distances traversed during equal intervals of time by a body falling from rest stand to one another in the same ratio as the odd numbers beginning with unity.”

Galileo's Inclined Plane Experiments

Start the ball rolling at time t-zero and count equal intervals of time as it rolls down the plane.

Take the distance covered in the first time interval as a unit of measure

Experiment Results

Galileo’s Result on Free Fall Objects

In the absence of air resistance, all objects experience the same acceleration due to gravity

g is the acceleration due to gravity (9.81 m/s2 near the surface of the earth)

What Can We Predict

Using Galileo’s theory, if we drop a feather and a stone at the same time from the Pisa’s Tower, which will hit the ground first? Why?

What else can we predict? What experiment condition do we

need to verify Galileo’s theory?

Hammer and Feather Drop In 1971, Apollo 15 astronaut David Scott on the

Moon recreating Galileo's famous experiment. A 1.32-kg aluminum geological hammer) and a

light object (a 0.03-kg falcon feather) were released simultaneously from approximately the same height (1.6 m)

the objects were observed to undergo the same acceleration and strike the lunar surface simultaneously

Practical Application of the Theory

To estimate how deep the well is Count the number of seconds (n) taken for

the stone to hit the water at the bottom of the well.

Add up the first n odd numbers starting at 1. Multiply the result by 5 metres. For example, the stone takes three seconds

to fall. That means the water is 1+3+5=9*5m or 45 metres down the shaft.

Summary: the Scientific Method

Testing ideas with evidence gathered from the natural world Ask a question Formulate a hypothesis Perform experiments Collect and analyze data Draw conclusion (Induction) Make predictions (deduction) Further Verification to confirm

The Scientific Community

The progress of science depends on interactions within the scientific community – that is,

the community of people and organizations that generate scientific ideas, test those ideas, publish scientific journals, organize conferences, train scientists, distribute research funds, etc.

The Scientific Community

This scientific community provides the cumulative knowledge base that allows science to build on itself.

It is also responsible for the further testing and scrutiny of ideas and for performing checks and balances on the work of community members.

Think Science

Question what you observe Why does an apple fall onto the

ground? Investigate further

Find out what is already known about your observations (literature review)

Be skeptical Challenge existing ideas

Think Science Try to refute your own ideas

Look at things from the other side of the argument

Seek out more evidence Be open-minded

Change your mind if the evidence warrants Think creatively

Try to come up with alternate explanations

What Science Does Not Do

make moral judgments, make aesthetic judgments, tell you how to use scientific knowledge, draw conclusions about supernatural

explanations.

Science is an important part of human knowledge, but it isn’t everything.

Part II: A Brief History ofScience

A Brief History of Science

The Origin of Classical Science

The Scientific Revolution

Human History & technology

Human history has always been shaped by science & technology. In the pre-history, there were: The Stone Age The Neolithic Era (New Stone age, the

Agricultural Revolution) The Bronze Age The Iron Age

?? Beginning of history

The Origin of Science Ancient Greeks are seen as the intellectual

forefathers of the western civilization Greek philosophers made great discoveries

of theorems by deductive reasoning (logic) Pythagoras (570-495BC毕达哥拉斯 ): “number is the

ultimate nature of reality” Euclid’s (欧几里德 ) Elements of Geometry Plato: “let no one ignorant of Geometry enter”

The Origin of Science Greek scholars were in general mostly

theoretical thinkers in philosophy & logic …

With some exceptions: Aristotle （亚理斯多德 , 384BC ~ 322 BC） Archimedes （阿基米德 , 287 BC ~ 212 BC） Euclid （ 欧几里得 , "Father of Geometry" ~300BC）

They sowed the seed of modern science.

Greek

Roman Empire

First Roman Emperor: Augustus 63 BC-14 AD

A brief history of ancient Western Civilization

Byzantine Empire 330-1453 AD

476 AD End of the western Roman Empire Germanic Roman general Odoacer deposed Emperor Romulus Augustulus

Constantine I legalized Christianity in Roman Empire,330 AD moved the capital to Constantinople

395 AD Christianity became official state religion

800 BC (Greek epic poem) Iliad & OdysseySocrates 470? ~ 399 BC; Plato 424? ~ 348 BCAristotle 384? ~ 322 BC

Homer's Iliad and the Odyssey: Trojan WarThe Trojan War was waged against the city of Troy by the Achaeans (Greeks) after Paris of Troy took Helen from her husband Menelaus, king of Sparta. The ancient Greeks thought that the Trojan War was a historical event that had taken place in the 13th or 12th century BC, and believed that Troy was located in modern-day Turkey.

Alexander the Great (356 –323 BC)

The last pharaoh of Ancient Egypt, Cleopatra, consummated a liaison with Julius Caesar that solidified her power.

Shakespearean tragedy: Antony and Cleopatra

After Caesar's assassination in 44 BC, she aligned with Mark Antony (Roman general and important supporter of Julius Caesar) in opposition to Caesar's legal heir, Gaius Julius Caesar Octavianus (Augustus). After losing the Battle of Actium to Octavian's forces, Antony & Cleopatra committed suicide.

Greek: Fate and Order of Nature

The Greek view of nature was dramatic Their vision of fate, remorseless and

indifferent, urging a tragic incident to its inevitable end, is the vision possessed by science

Fate in Greek Tragedy becomes the order of nature in modern thought

The laws of physics are the decrees of fate

Medieval Europe After centuries of civil war and corruption the western Roman

Empire disappeared when Odoacer deposed the last Roman Emperor in 476AD. Barbarian hordes swept over the west and razed the last vestiges of this once mighty empire. Europe entered what is commonly called "The Dark Ages". Most major city centers lay in ruins, however, monasteries, because they were remote and hard to access, remained and within them were retained the culture and book knowledge lost everywhere else.

In medieval Europe only the monks and nobility could read and write and study knowledge. Monasteries became the keeper of knowledge and center of education, until Johann Gutenberg invented the first printing press in the 1450's and changed the situation so that knowledge was made available to everyone.

Medieval Europe: Rationality & God

In the Middle Ages, there was a belief in the rationality of God (Christianity)

There is a secret in the nature that can be unveiled: every detailed occurrence can be correlated with its antecedents in a perfectly definite manner, exemplifying general principles

The search of natural laws could result in the vindication of the faith in rationality

Precursors to the Scientific Revolution

Fall of Constantinople 1453: the migration of Greek scholars and texts to Italy

Renaissance Leonardo da Vinci 1452–1519, Michelangelo

1475–1564 The Printing Press: Gutenberg Bible ~1450 Discovery of America: Christopher

Columbus 1492

Renaissance: rediscovery of the Greek spirit

Venus de MiloCreated ~130 - 100 BC

Statue of DavidMichelangelo 1504

The Printing Press

The world's first movable type printing technology was invented and developed in China by Bi Sheng (毕升 ？ -1051) between the years 1041 and 1048. [沈括《梦溪笔谈》 ]

Re-invented and improved by a goldsmith from Mainz, Germany, Johannes Gutenberg, ~1450.

Moveable typePaper

Wine Press Screw

Carolingian Script

The Printing Press First book ever

printed on a printing press using moveable type:

The Gutenberg Bible ~1450

Why Printing Press is so important to the Scientific Revolution

Books became more affordable to ordinary people (cost producing a book becomes 300 times cheaper).

No more transcription errors, making knowledge accumulation much easier. “nothing new under the sun”, ancient

discoveries soon became forgotten.

Books produced per Year

Economic Impact of the Printing Press

1687-Newton published Principia Mathematica

1905-Special Relativity

1945-Atomic bomb1776 “The Wealth of Nations” published

The Historical Revolt

Consequence of the invention of movable type printing press In 1517, Martin Luther started the

Protestant Reformation (宗教改革 ) In science, the spread of Heliocentric

cosmology and the inductive method of reasoning with experimental data

The Scientific Revolution

The "Scientific Revolution" refers to historical changes in thought & belief that unfolded in Europe between roughly 1550-1700;

Beginning with Nicholas Copernicus (1473-1543), who asserted a heliocentric (sun-centered) cosmos, it ended with Isaac Newton (1642-1727), who proposed universal laws and a Mechanical Universe.

Before Copernicus

The accepted geocentric Aristotelian system, which placed the earth at the center of the solar system, with the sun and planets in orbit.

Copernicus’ Revolution

Why Did Copernicus put the Sun at the center?

As improvements were made in the skills of observation, more and more circles and epicycles were called for to explain the movement of heavenly bodies.

A simple, regular, ordered and hierarchical system had, over time, become very complicated.

Copernicus wanted a simpler model

On the Revolutions of the Heavenly Bodies (1543) He began to believe that the earth went

round the sun about 1507. Realizing his theory would offend, he

decided to publish his findings in 1543, the year of his death.

The knowledge of the time was not sufficient to prove his theory; his great argument for it was from its simplicity as compared to the epicycle hypothesis

Giordano Bruno (1548-1600)

Italian philosopher mathematician, poet and astronomer

executed by the Roman Catholic Church because of his Copernican view and belief the Sun was just another star moving in space.

Remembered as the martyr of free thought and modern scientific ideas.

Johannes Kepler （ 1571－ 1630 ）

A German mathematician and astronomer

Kepler was forced to the realization that the orbits of the planets were not the circles demanded by Aristotle and assumed implicitly by Copernicus, but were instead the "flattened circles" that geometers call ellipses

The Laws of Planetary Motion

Later, Sir Isaac Newton utilized Kepler's theories and observations in formulating his theory of gravitational force.

Galileo Galilei (1564-1642)

The key to all of Galileo's discoveries was the accurate measurement of time.

Galileo used the uniform motion of the pendulum to measure time

Galileo experimented with various sorts of motions and falling bodies.

He formulated the basic law of falling bodies, which he verified by careful measurement.

Galilei’s Confession

In 1610 Galileo pointed his telescope at Jupiter and observed the orbits of four of its moons.

On the basis of his scientific observations Galileo became a heliocentrist.

On 22 June 1633 Galileo was forced to make a 'confession' to the Cardinals of the Holy Office of the Church.

After Galileo’s Death The weight of papal authority which had

succeeded in halting the growth of the new science in Italy.

Following Galileo's death in 1642 that the greatest advances in science would come from outside Italy in Protestant countries (with a tradition of protest and toleration) like England, Holland and Germany.

1642 as a Significant Year Isaac Newton (1642-1727雍正五年 ), the man

most responsible for producing modern science was born.

1620. Francis Bacon published Novum Organum Scientiarum

1644. René Descartes: (Principles of Philosophy) “I think, therefore I am”

1644. The Manchu conquer China ending the Ming Dynasty.

~1760: beginning of Industrial Revolution

The Scientific Methodology By the 17th century, science,

scientific thinking had spread to the rest of Europe Occam's razor (~ 1300) The Baconian method: empiricism René_Descartes’ rationalism: "That we

cannot doubt of our existence while we doubt, and that this is the first knowledge we acquire when we philosophize in order."

Occam’s Razor (奥卡姆剃刀 )

a principle first developed by the Franciscan friar and philosopher, William of Ockham (1287 – 1347)

The simplest answer is most often correct. If you have more than one hypotheses that

could explain an observation, the hypothesis with the fewest and simplest assumptions should be selected.

Sir Francis Bacon (1561-1626)

Bacon has been called the creator of empiricism.

He established and popularized inductive methodologies for scientific inquiry.

Bacon's empirical approach helped to clearly separate science from philosophy.

Bacon’s Bee Metaphor“Those who have handled sciences have been either men of experiment or men of dogmas. The men of experiment are like the ant, they only collect and use; the reasoners resemble spiders, who make cobwebs out of their own substance. But the bee takes a middle course: it gathers its material from the flowers of the garden and of the field, but transforms and digests it by a power of its own.”Francis Bacon: The New Organon [Book One]. 1620.

Bacon’s Bee Metaphor

Good scientists are not like ants (mindlessly gathering data) or spiders (spinning empty theories). Instead, they are like bees, transforming nature into a useful product. “Not unlike this is the true business of philosophy; for it neither relies solely or chiefly on the powers of the mind, nor does it take the matter which it gathers from natural history and mechanical experiments and lay it up in the memory whole, as it finds it, but lays it up in the understanding altered and digested. Therefore from a closer and purer league between these two faculties, the experimental and the rational (such as has never yet been made), much may be hoped.”

Knowledge(Science) is Power

Bacon was one of the first to fully understand that knowledge is power.

He believed science would serve to improve the human condition and create a better world

Bacon noted in his Novum Organum Scientiarum (1620): "printing, gunpowder, and the nautical compass . . . have altered the face and state of the world: first, in literary matters; second, in warfare; third, in navigation,"

Rene Descartes (1596-1650)

A French philosopher and mathematician

He invented the Cartesian Coordinate System, credited as the “father of analytical geometry”

A major figure in the 17th-century Continental rationalism (deduction)

Rene Descartes (1596-1650)

He is considered as the “father of modern philosophy”

Best known for his philosophical statement "Cogito ergo sum" (I think, therefore I am)

Dualism: he suggested that the body works like a machine and the mind was a nonmaterial and does not follow the laws of nature

English Reformation Henry VIII (1531): “sole protector and

Supreme Head of the Church of England” Edward VI (1547-1553): more Reformation Mary I (1553-1558): Catholic Restoration Elizabeth I (1558-1603): “Supreme

Governor of the Church of England” James I: King James Bible, most widely printed

book in history

Henry VIII & his children: The family that changed the History of England

Under Queen Elizabeth I’s leadership, England defeated the Spanish Armada in 1588 and enjoyed prosperity.

The irony of history

Queen Elizabeth I’s contribution

Isaac Newton (1642-1727)

Born when the Church of England was totally independent from Rome

In 1687, Newton finished his greatest work, The Mathematical Principles of Natural Philosophy

The most influential book in the history of science

Newton’s Contribution’s to Science & mathematics

Three laws of motion Theory of universal gravitation The first practical reflecting telescope A theory of color Shares the credit for the development

of the differential and integral calculus The generalized binomial theorem, the

study of power series

Newton’s Quote

If I have seen further it is by standing on the shoulders of giants

I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me

The Newtonian Worldview

Reductionism to understand any complex phenomenon,

you need to take it apart; properties of a system are explainable by explaining the individual behavior of its smallest parts.

Materialism all phenomena, whether physical,

biological are ultimately constituted of matter

The Newtonian Worldview

Determinism/mechanism If you know the initial positions and

velocities of the particles constituting a system together with the forces acting on those particles (which are themselves determined by the positions of these and other particles), then you can in principle predict the further evolution of the system with complete certainty and accuracy.

The Newtonian Worldview

Dualism The Newtonian worldview considers

the physical and spiritual realms to be entirely separate.

while material objects obey mechanical laws, the mind does not

This way physics can avoid conflicting with religion.

The Clockwork Universe

The Universes is like a giant clock that was assembled and wound up by “God”, but no longer needs anything else to keep functioning according to its rule of operation.

…if we conceive of an intelligence that at a given instant comprehends all the relations of the entities of this universe, it could state the respective position, motions, and general affects of all these entities at any time in the past or future. Pierre-Simon Laplace (1749 –1827)

Influence of NewtonianWorldview

Newtonian thinking has had a profoundinfluence on society: the concept ofnatural law inspired democracy The mechanistic and deterministic view

of nature also inspired communism. Dualism has had a profound impact on

the way we see ourselves in relation to nature.

The Expectation of the Newtonian Worldview

PHYSICS would eventually explain CHEMISTRY; CHEMISTRY would explain BIOLOGY; and BIOLOGY would explain PSYCHOLOGY.

Love, joy and courage had been reduced to chemical reactions within the brain and the body

Do you agree, yes or not? Why?

Discussion & Sharing

Do you agree that love can be eventually reduced to some physical movements of the chemicals within your body? Why?

Do you agree that the universe is a huge machine, or an organism? Why?

Scientists Were Very Optimistic

In the late 1800s, most physicists believed that physics was complete, described by classical mechanics, thermodynamics, and the Maxwell theory.

All that remains to do in physics is to fill in the sixth decimal place (Albert Michelson, 1894)

Nothing New to be Discovered

There is nothing new to be discovered in physics now. All that remains is more and more precise measurement. (Lord Kelvin, an influential British physicist, 1900)

The Two Clouds of Physics

But Lord Kelvin also mentioned two ‘clouds’ on the horizon of physics: The beauty and clearness of the dynamical theory, which asserts heat and light to be modes of motion, is at present obscured by two clouds. 1) Blackbody radiation 2) Michelson-Morley experiment

Modern Physics

Kelvin's two "clouds" instead represented fundamental limits to a classical approach to understanding the universe.

Their resolution introduced whole new (and clearly unanticipated) realms of physics, known collectively as "modern physics.” The first cloud: Quantum Physics The second cloud: Relativity

Fortunately

“No matter how we may single out a complex from nature...its theoretical treatment will never prove to be ultimately conclusive... I believe that this process of deepening of theory has no limits.” (Albert Einstein, 1917)

Part III The Power and Limits of

Science:Advances of science in the

20th Century

The Discovery of DNA

1953, James Watson and Francis Crick deduced the double helix structure of DNA; Nobel Prize for Physiology or Medicine (1962)

One of the most important scientific discovery of the 20th century

Atom Bomb

First Atomic Bomb, codenamed Trinity, tested near Alamogordo, New Mexico, on July 16, 1945

Atomic bomb mushroom clouds over Hiroshima (left: August 6, 1945) and Nagasaki (right: August 9)

Manned Moon Landing

The Apollo 11 mission: astronauts Neil Armstrong and Buzz Aldrin landed their Lunar Module (LM) on the Moon on July 20, 1969, and walked on its surface while Michael Collins remained in lunar orbit in the command spacecraft, and all three landed safely on Earth on July 24.

The Invention of the Computer

The ENIAC, 1946: the first general-purpose electronic computer.

Transistor & Integrated Circuit John Bardeen, Walter Brattain & William

Shockley: Nobel Prize in Physics (1956) "for their researches on semiconductors and their discovery of the transistor effect (1947)”

Jack Kilby (& Robert Noyce): Nobel Prize in Physics (2000) "for his part in the invention of the integrated circuit (1958)"

The Internet Packet switched networks in US, such as ARPANET, Tymnet, and Telenet, were developed in the late 1960s and early 1970s using a

variety of protocols. In 1982, the Internet Protocol Suite (TCP/IP) was standardized and the concept of a world-wide network of fully interconnected TCP/IP

networks called the Internet was introduced.

Discovery of Quantum Mechanics

In 1929, theoretical physicist Paul Dirac announced: "The general theory of quantum mechanics is now complete. . . . The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known." The discipline at the point was four years old. Dirac himself was just 27.

The Limits of Science

The limit of measurement

The limit of mathematics

The limit of prediction

The limit of computation

The Limit of Measurement The Uncertainty (Heisenberg) Principle

the more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa.

The Observer Effect: measurements of certain systems cannot be

made without affecting the systems the uncertainty principle is inherent in the

properties of all wave-like systems

The Limit of Mathematics

Gödel's incompleteness theorems1. Any effectively generated theory capable of

expressing elementary arithmetic cannot be both consistent and complete. There is an arithmetical statement that is true, but not provable in the theory

2. such a system cannot demonstrate its own consistency

The Limit of Prediction

Chaos Theory When the present determines the future,

but the approximate present does not approximately determine the future.

Tiny difference of the input will produce totally different output

Therefore the future is unpredictable http://en.wikipedia.org/wiki/Chaos_theor

y

Discussion and Sharing

Is the stock market predictable? Why?

Is your own behavior predictable? Why?

The Limit of Computation

Most real world problems are not computable, i.e., there does not exist a step-by-step procedure to solve it For example, the halting problem to decide

whether a computer program will halt or not For most computable problems, there is no

known efficient way to solve them NP-complete problems, for example, the

travelling salesman problem

The travelling salesman problem

Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?

The problem was first formulated in 1930 and is one of the most intensively studied problems in optimization. It is used as a benchmark for many optimization methods.

Summary

What is Science

A Brief Introduction to the Scientific Revolution

The Power and Limits of Science

The Rest of the Course

Science has many fields We will not cover all of them

The Rest of the Course

We will focus on the following two very useful areas: Statistics & Financial Mathematics Computer science

You will learn to appreciate the power of beauty of science and technology