The Role of Mathematics

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The Role of Mathematics In Information Technology
Lance Wu Vista Incubation
Technology Corp.
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Agenda
1.The Era of Digital Convergence 2. Application
of Mathematics in the digital World 3.
Looking for new Mathematics in the Non-Linear
applications 4. Conclusions
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The Era of Digital Convergence
All Digital
00s
Audio/Video
90s
80s
Computer
Communications
70s
60s
Digital
Analog
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Analog Engineering and Mathematics
Engineering Components
Mathematical Tools
Field
Filters, Modulators Amplifiers
Fourier Transform, ODE/PDE,
Audio Video
Fourier Transform, ODE/PDE,statistics Continuous
time random processes
Filters, Modulators Amplifiersreceivers Transmitt
ers
Communications
CPU, Memories ( All Digital)
Queing Theory, Discrete Mathematics
Computers
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Application of Mathematics in the Digital World
Communication Technology
Engineering field
Mathematics
Discrete Fourier Transform Discrete Time Series
Analysis Recursive Regression..
Digital Signal Processing Image
Processing Digital Compression
Adaptive Algorithms Machine Learning, Neural
Networks
Statistical Analysis Data Analysis Random
Processes,
Encryption Network Security Traffic
Analysis Switching Theory Information Theory
Number Theory Algebra Graph Theory
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Application of Mathematics in the Digital World
Computer and Software Technologies
Engineering field
Mathematics
Discrete Mathematics Probability Queing
Theory Statistical Analysis Numerical
solutions Differential Geometry Group
Theory Number theory
celluler Automata Search Engine Data Mining 3D
Graphic Virtual Reality Parallel
Architecture Intelligent Agent
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Application of Mathematics in the Digital World
Audio/ Video Technologies
Engineering Field
Mathematics
Recursive Regression Fourier Analysis Time
Series Statistical Estimation Wavelet
Analysis Cluster Analysis
Signal Compression ( MPEG, JPEG, Wavelet) Color
Technologies Audio/ Video Synthesis Video Pre-
processing
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Looking for new Mathematics in the Non-Linear
applications
Engineering Problems
Non Linear Mathematics (? )
Internet Traffic Management Speech
Recognition Virtual Reality Artificial
Intelligence
Fractal Analysis Non Linear Dynamic
Systems Wavelet Analysis
Internet Mapping
Topology and ???
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The Non Linear World and Complex Systems..
Is the emerging hot topics in IT research..
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A Mandelbrot Set
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A Snap Shot of Internet Has Self-Similar
Structure
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Traffic Bursts over 1000,100,10 and 1 Sec.
100 Sec.
1000 Sec.
10 Sec.
1 Sec.
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Mapping the Internet
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A Map of Renaissance Period
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A Primitive CyberMap
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Lumeta are developing network measurement and
mapping tools for analysing large corporate
intranets. This graph part of this graph show the
portion of a corporate intranet that are
'leaking' with the Internet
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les cartes du web. An interesting network
metaphor as a visual interface to search engine
results.
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The Starlight visual information analysis
environment developed by John Risch and
researchers at the Pacific Northwest National
Laboratory. The system provide an immersive,
fully 3D environment to display and analyse
complex multimedia information collections and it
was originally developed for US intelligence.
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An Info Space Map of YAHOO!
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Searching by reorganized Layers
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The Historical Linkage of Art and Science
Aural
Visual
Number/Picture
Veda
Pythagoras
Plato/Euclid
Renaissance Music
Renaissance arts Architecture
Da Vinci
Gregorian Chant
Kepler
Bach/Fugue
Newton
Music of the Sphere
God is The Geometer
Klee
Kandinsky
Schoenberg
Einstein
Superstring Theory
Fractal /Chaos
Fractal Music DNA Music
Digital Renaissance
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Conclusions

• In the Digital Era, the fundamental Sciences
• ( Mathematics, Physics ) become more
• important and closer to applications than
  ever !!

2. Now is the beginning of Digital Renaissance,
the fundamental sciences is becoming the
driving force again after 500 years
3. Mathematics is in the center of all new
technologies !! Know Mathematics well and the
rest are SIMPLE!!