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Employment in Mathematical Sciences

Explore the intersection of mathematics and data recording technology, from IBM's historic disk drives to public key cryptography. Discover how trigonometry, calculus, and algebra play critical roles in error correction and encryption methods.

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Employment in Mathematical Sciences

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  1. 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, . . .)

  2. 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): Resources

  3. Data Transmission Noise Input Message Noisy Output CHANNEL

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

  5. Disk Drive Technology • computers • music (CD, iPod) • video (DVD, PSP) • digital camera • pda (palm)

  6. This IBM Disk Drive was made in 1956. Capacity: 5MB Size: 50 24inch disks Weight: 500 lbs

  7. In 1998, IBM introduced the Microdrive. Size: 1.1 inch diameter disk Capacity: 170MB (1998) 6 GB (2005)

  8. 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

  9. Data storage in the future

  10. 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.

  11. 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.

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