Summary for the course

My thoughts 2008

Sir Isaac Newton

I frame no hypotheses; for whatever is not deduced from the phenomena is to be called a hypothesis, and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy.

Truth is ever to be found in the simplicity, and not in the multiplicity and confusion of things.

On Calculus

Newton and Leibniz's approach to the calculus fell well short of later standards of rigor. We now see their "proof" as being in truth mostly a heuristic hodgepodge mainly grounded in geometric intuition. Wikipedia

dxx

dt

fdx F

On Calculus• George Berkeley, in a tract called The

Analyst and elsewhere, ridiculed this and other aspects of the early calculus, pointing out that natural science grounded in the calculus required just as big of a leap of faith as theology grounded in Christian revelation.

• Modern, rigorous calculus emerged in the 19th century, thanks to the efforts of Augustin Louis Cauchy, Bernhard Riemann, Karl Weierstrass, and others, who based their work on the definition of a limit and on a precise understanding of real numbers.

Jean-Baptiste-Joseph Fourier

1807 “On the Propagation of Heat in Solid Bodies”

1812 Grand Prize of Paris Institute

“Théorie analytique de la chaleur”

‘... the manner in which the author arrives at these equations is not exempt of difficulties and that his analysis to integrate them still leaves something to be desired on the score of generality and even rigor.’

1817 Elected to Académie des Sciences

1822 Appointed as Secretary of Académie

paper published

Fourier’s work is a great mathematical poem. Lord Kelvin

Oliver Heaviside1850 - 1925

Why should I refuse a good dinner simply because I don't understand the digestive processes involved.

學而不思則妄思而不學則殆

Learning without thinking

will be in vain.

Thinking without learning

Will be tiring and risky.

The Battle Hymn for HHTBy Ingrid Daubechies

You can use wavelets or Fourier And find something that is useful,But if you want something new to say, You cannot be any old fool.

You then find a new kind of algorithm And let it loose on the world.Before they even know what hit’em, They’re up to their necks on work.

Rushing in to met your frustrating challenge, They filter and stretch and squeeze.

But always some signal throws a monkey wrench, And make them huff and sneeze.

Your name is, of course, Norden Huang, Long may you live and smile!We’re here to learn and get the hang And will not quit for a very long while.

Hilbert-Huang transform, you will triumph!

Composed on 17 December 2008 in Guangzhou, to be sung to the tune of ‘The Internationale’.

At The Second International Conference on the Advances of Hilbert-Huang Transform and its Applications.

Better lucky than smart.

I am lucky to have found this simple method.

You are smart to take this course.

Good luck!!