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 • • • • • 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.