University of Manitoba Mathletics
Miscellaneous problems with solutions, 24 November 2009
Many Putnam exams have at least one or two fairly straightforward questions. Here are
a few that might bring t
University of Manitoba, Mathletics 2009
Session 8: Geometry
1
Facts and denitions
Things to remember:
Proper drawing helps.
Vector geometry and dot product.
Similar triangles.
Complex numbers for
University of Manitoba, Mathletics 2009
Session 5: Inequalities
1
Facts and denitions
AM-GM inequality: For a1 , a2 , . . . , an 0,
a1 + a2 + + an
(a1 a2 an )1/n ,
n
with equality i all ai s are equa
MATH 3740 Methods of Advanced Calculus Winter 2008 Midterm 5 Solutions
Remarks: This examination is 3 hours. It consists of 10 questions, for a total of 140 marks. Notes, texts, calculators and cellph
MATH 3740 Methods of Advanced Calculus Fall 2007 Midterm 1
Solutions
Remarks: The marks are low in general. They range from 12 to 38.5 (the maximum possible mark was 40), with an average of 21.91 and
Analysis
University of Manitoba, Mathletics 2009
1
Some Facts and Examples
Need to know denitions and properties of continuous/dierentiable functions, sequences,
innite series, etc. (everything that