Employment%20in%20Mathematical%20Sciences

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Employment in Mathematical Sciences

• Education Secondary and Elementary Schools,
  Colleges and Universities
• Research Labs Government, Industry
• Development in Business and Industry (computer,
  communications, finance, defense, environmental,
  aerospace, engineering, film, biomedical, . . .)

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Resources

• Canadian Math Society(www.cms.math.ca)
• -- Education www.cms.math.ca/Education
• American Math Society(www.ams.org)
• -- Employment www.ams.org/employment
• Society for Industrial and Applied Mathematics
• American Statistical Association
• Association for Computing Machinery
• UBC (www.math.ubc.ca)
• ---Math Workshops www.math.ubc.ca/Schools/Worksho
  p/index.shtml
• PIMS (www.pims.math.ca)

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Data Transmission


   
Noise
Input Message



Noisy Output
CHANNEL
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Designing Antennas

• Goldstone tracking station tracks deep space
  missions.
• Design required simulation of wind and heat loads.

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Disk Drive Technology

• computers
• music (CD, iPod)
• video (DVD, PSP)
• digital camera
• pda (palm)

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This IBM Disk Drive was made in 1956.
Capacity 5MB Size 50 24inch disks Weight 500
lbs
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In 1998, IBM introduced the Microdrive. Size
1.1 inch diameter disk Capacity 170MB
(1998)
6 GB (2005)
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Mathematics used in data recording

• Sampling Theory How to represent a continuous
  wave as a sequence of 0 and 1 bits
• Trigonometry and Calculus How to focus the laser
  on circular tracks and adjust the speed of the
  rotating disk
• Algebra How to correct errors dust, scratches,
  imperfections in disk surface, electronics noise

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Data storage in the future
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Public key cryptography

• Each agent has two keys
• Private key which he/she keeps secret.
• Public key which everyone knows.
• Agent A encrypts a message by using Agent Bs
  public key.
• Agent B decrypts the message using his private
  key.

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What makes this work?

• There is a mathematical relation between the
  public and private keys, which involves two large
  prime factors of a large number.
• It is nearly impossible to derive the private key
  from the public key.
• In order to break the code, you must factor a
  large number.