09-240/Classnotes for Thursday September 17
NSERC - CMS Math in Moscow Scholarships
The Natural Sciences and Engineering Research Council (NSERC) and the Canadian Mathematical Society (CMS) support scholarships at $9,000 each. Canadian students registered in a mathematics or computer science program are eligible.
The scholarships are to attend a semester at the small elite Moscow Independent University.
Math in Moscow Program http://www.mccme.ru/mathinmoscow/
Application details http://www.cms.math.ca/Scholarships/Moscow
For additional information please see your department or call the CMS at 613-733-2662.
Deadline September 30, 2009 to attend the Winter 2010 semester.
- Dori Eldar's work on "mechanical computations": and .
- The "Dimensions" video on "Nombres complexes", is at http://dimensions-math.org/Dim_reg_AM.htm (and then go to "Dimensions_5".
Class notes for today
• Convention for today: will be real numbers; will be complex numbers
Dream: Find a field that contains and also contains an element such that
• must be in
• Find another element of , such that
- are given
• (Note: We can divide since we assumed that
Def: Let be the set of all pairs of real numbers
...you know what
• 0 = you know what
• 1 = you know what
- is a field
• Show that
• NEXT WEEK: Complex numbers have geometric meaning, geometric interpretation (waves)