Transcript Careers in the Mathematical Sciences

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, . . .)
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/Workshop/index.shtml
 PIMS (www.pims.math.ca):
Data Transmission
Noise
Input
Message
Noisy
Output
CHANNEL
Designing Antennas
• Goldstone tracking station – tracks deep space missions.
• Design required simulation of wind and heat loads.
Disk Drive Technology
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computers
music (CD, iPod)
video (DVD, PSP)
digital camera
pda (palm)
This IBM Disk Drive
was made in 1956.
Capacity: 5MB
Size: 50 24inch disks
Weight: 500 lbs
In 1998, IBM introduced the Microdrive.
Size: 1.1 inch diameter disk
Capacity: 170MB (1998)
6 GB (2005)
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
Data storage in the future
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 B’s public
key.
 Agent B decrypts the message using his private key.
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.