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2005 UMOMC

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Practise Problem Set #1 Yes, this was the 2005 CMO (a high-level Canadian High School contest)
Practise Problem Set #2
Practise Problem Set #3
Practise Problem Set #4
Practise Problem Set #5

2005 NCS All-Day practise problems (with solutions)

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What little I (R. Craigen) know about the prehistory of mathletics at U of M:

-  Barry Wolk was a Putnam Fellow while  enrolled here in 1961 (unofficially we know his score was highest, although this information is not publicly released with the rankings -- Putnam Fellows are listed in no particular order).  That year U of M ranked fourth -- our highest ranking to date.  Barry still drops in on our sessions and shares his expertise with the latest crop of aspiring Putnam Fellows.
-  In some other year, unknown to me, but prior to 1963, U of M achieved a team Honourable Mention. 
-  Sometime in the 1970's Dr. Tom Kucera (an undergraduate student at the University of Manitoba at the time), received an individual Honourable Mention.
-   Dr. Nathan Mendelsohn, a longtime member of our department who recently passed away, was part of the (U. Toronto) team which won the very first Putnam competition many years ago and for decades served on the problems selection committee for the Putnam exam. 

When I arrived in 1999 U of M students had not participated in Mathletics competitions for a few years (nobody has ever clarified how many). 

Those with a history here:  Please add to my meagre knowledge here ...

Since then, here's how we've done:

1999:
Putnam team rank: 80th
Top ranking UM student: Mark Wiebe (203rd)
UM teams with top 10 NCS/MAA rankings:
    UM1:  Matthew Greenberg, Mark Wiebe, Kurt Thompson (2nd)
 
2000:
Putnam team rank: 121st
Top ranking UM student: Craig Kasper (245th)
UM teams with top 10 NCS/MAA rankings:
    UM 2Geeks&aNerd:  Mark Wiebe, Kurt Thompson, Dan Nielson (4th)
    UM Crablegs:  Tim Nikkel, Delene Matula, Evan Janzen Roth (10th)

2001:
Putnam team rank:  69th
Top ranking UM student:  Matthew Hasselfield (494th)
UM teams with top 10 NCS/MAA rankings:
    UM TBA:  Xi Wang, Matthew Hasselfield, Tim Nikkel (tie for 2nd/3rd)
    UM MetricallySpaced:  Roger Woodford, Nick Harland, Dan Potter (4th)

2002:
Putnam team rank: 23rd
Top ranking UM student:  Matthew Hasselfield (111th)
UM teams with top 10 NCS/MAA rankings:
    UM DuckDuckGauss:  Tim Nikkel, Matthew Hasselfield, Xi Wang (tie for 2nd/3rd)
    UM Metrically Spaced:  Nick Harland, Roger Woodford, Stephanie Richards (tie for 2nd/3rd)

2003:
Putnam team rank:  N/A
Top ranking UM student: Karen Johannson (641st)
UM teams with top 10 NCS/MAA rankings:
    UM InsertNameHere:  Mike deDenus, Gabriel Faucher, Anh Le (5th)
    UM BarsbyBunch:  Mike Lipnowski, Will Guest, David Liu (tie for 6th/7th)
    UM CompactTorus:  Karen Johannson, Tim Nikkel, Mercedes Scott (10th)

2004:
Putnam team rank:  66th
Top ranking UM student:  Trevor Wares (778th)
UM teams with top 10 NCS/MAA rankings:
    UM Shire:  Trevor Wares, Will Guest, Anh Le (3rd)

2005:
Putnam team rank: N/A
Top ranking UM student:   Will Guest (483rd)
UM teams with top 10 NCS/MAA rankings:
    UM Pi Ladies:  Trevor Wares, Anh Le, Ed Knapp (4th)
    UM BecauseWeSaidSo:  Will Guest, Jonathan Lee, Michael Himbeault (6th)

2006:
Putnam team rank: 51st
Top ranking UM student:   Will Guest & Trevor Wares (tie, 747th)
UM teams with top 10 NCS/MAA rankings:  none ("Team X" ranked 12th)

2007: 
Putnam team rank:  150th
Top ranking UM student:   Ruiqiong Liu (503rd)
UM teams with top 10 NCS/MAA rankings: 
    UM CJ:  Ruiqiong Liu, Garrett Klus (8th)

2008:
COMC Winner:  Ruiqiong (Richard) Liu
Putnam team rank:  71st
Top ranking UM student:   Garrett Klus (619th)
UM teams with top 10 NCS/MAA rankings:  none  ("UManitobaTeamA" ranked 17th)

2009:
COMC Winner:  Todd Sierens
Putnam team rank: 85th (out of 546)
Top ranking UM student:  Liji Huang & Yuchen Mu (tied at 892nd)
UM teams with top 10 NCS/MAA rankings:
    UManA: Liji Huang, Yuchen Mu and Duy Nguyen (9th)

2010:
COMC Winner:  Mak Ka Tsun
Putnam team rank:  (N/A)
Top ranking UM student:  (N/A)
UM teams with top 10 NCS/MAA rankings:  none (top team:  26th)

2011:
COMC Winner:  Kevin Mather
Putnam team rank:  (N/A)
Top ranking UM student:  Suraj Srinivasan
UM teams with top 10 NCS/MAA rankings:  none (two teams in top 20)

2012-2015:  To be updated

CONTEXT OF RANKINGS: 
-    Generally there are about 500 institutions competing in the Putnam, so top 100 ranking ≈ top 20%. 
-    "N/A" generally means one or more of the 3 students preselected for our Putnam team obtained a score of 0. 
       Other team members and students we hadn't selected for the team may still have done quite well.
-    There are about 4000 individual participants in the Putnam exam, so a rank in the 1000 means top 25% (out of an already select group!). 
-    About 70 teams participate each year in the NCS/MAA contest.

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SOME THINGS YOU SHOULD KNOW

First, never memorize a mathematical tool without:

• being prepared to prove it on demand or else knowing for sure that it is well-known but difficult to prove in an elementary fashion
• learning how it can be exploited and how to recognize places where it might apply (i.e., by solving hard problems with it)

Second, practice!  A "natural" problem solver will do moderately well without much preparation, but nobody will distinguish themselves without preparing and working on problems for months in advance to become familiar with problem types and tools, and to keep one's brain "in the groove".  At our practice sessions we provide tools and experiences that have proven to be most effective in preparation.  A musician may be good but cannot play the sonata without many hours of scales and arpeggios; an athlete may be a backyard jock but won't shine in varsity athletics without running drills all season with their teammates.  In the same way a mathlete may be naturally "good" but will not distinguish themselves without deliberately laying a foundation of basics and honing their skills.

Third, your brain is not separate from your body.  Eat well; get plenty of sleep -- especially before competitions -- and exercise; manage the stress in your life; maintain a positive attitude, approach each question with confidence, and enjoy your mathletics activities.

Some outside links to fundamental tools (come to the weekly practise for help with these and much more!)

Jensen's Inequality  (NOTE:  Possibly the most powerful and versatile inequality. Learn to master all the ideas in it:  convexity, means, etc.)
Pick's Theorem   (A crazy fact about polygons with vertices on the integer lattice.  It is subtlely behind many contest problems -- learn to recognize it even when it is masked)
Cauchy-Schwartz Inequality  (Absolutely fundamental)
AM-GM inequality (You can't get along in contests without at least this.)
Fermat's Little Theorem (and Gauss' Generalization)
Modular arithmetic and various standard tricks with it
Viete's relations (between the roots of a polynomial and its coefficients) -- and how they are exploited
The pigeonhole principle  (Simple yet versatile.  More profound than it sounds at first)
Power of an inside/outside point  (Makes light work of many geometry problems!)
Heron's formula for the area of a triangle  (An old formula for the area of a triangle; a good thing to know for triangle problems)
Properties of matrix determinants  (Knowing some of these solves nasty-looking problems with a light touch).

...email me some additions/links for this list...