09-240/Classnotes for Thursday September 17

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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.

Some links

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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


  1. is a field
  1. by


Example: (distributivity)

• Show that



• NEXT WEEK: Complex numbers have geometric meaning, geometric interpretation (waves)