CAP High School Prize Exam
April 14th, 2015
9:00 - 12:00
Competitors Information Sheet
The following information will be used to inform competitors and schools of the exam results, to determine
eligibility for some subsequent competitions, and for statist
Bijections
Yufei Zhao
[email protected]
In this lecture, we will look at using bijections to solve combinatorics problems.
Given two sets A and B, a bijection (also called bijective correspondence) is a map
f : A B that is both injective and surjective, mean
UMA Putnam Talk
LINEAR ALGEBRA TRICKS FOR THE PUTNAM
YUFEI ZHAO
In this talk, I want give some examples to show you some linear algebra tricks for the
Putnam. Many of you probably did math contests in high school, but you might not have
had much experienc
Canadian Association of Physicists
2001 Prize Exam
Question 2
The diagram below shows various positions of a child in
motion on a swing. Somewhere in front of the child a stationary whistle is blowing. At which position will the child hear
the highest fre
Canadian Association of Physicists
1994 Prize Exam
This is a three hour exam. National ranking and prizes
will be largely based on a students performance on the
three questions in part B of the exam for which written so-
lutions are required. However, per
MOP 2007 Blue Group
Tiling
Yufei Zhao
Tiling: Coloring and Weights
June 15, 2007
Yufei Zhao
[email protected]
Main discussion: Packing boxes with bricks
Probably the most basic problem about tiling is to show that an 8 8 chessboard with two opposite
corners
Trinity Training 2011
Power of a Point
Yufei Zhao
Power of a Point
Yufei Zhao
Trinity College, Cambridge
[email protected]
April 2011
Power of a point is a frequently used tool in Olympiad geometry.
Theorem 1 (Power of a point). Let be a circle, and P
Canadian Association of Physicists
2000 Prize Exam
Part A: Multiple Choice
Question 1
This is a three hour exam. National ranking and prizes
will be based on a students performance on both sections A
and B of the exam. However, performance on the multiple
Canadian Association of Physicists
1996 Prize Exam
This is a three hour exam. National ranking and prizes
will be based on a students performance on both sections A
and B of the exam. However, performance on the multiple
choice questions in part A will be
MOP 2007 Black Group
Counting in Two Ways
Yufei Zhao
Counting in Two Ways
Incidence Matrices
June 26, 2007
Yufei Zhao
[email protected]
Problems to be discussed in lecture
Problem 1. In a certain committee, each member belongs to exactly three subcommittees,
UMA Putnam Talk Lecture Notes
Determinants: Evaluation and Manipulation
Yufei Zhao
September 22, 2009
Appetizer problem
(This problem doesnt actually use determinants.)
Problem 1. Do there exist square matrices A and B such that AB BA = I?
Solution. No. T
AwesomeMath 2007
Track 1 Combinatorics
Week 3
Lecture 10 : A Contest of Contests
Yufei Zhao
July 31, 2007
1. (IMC 2002) Two hundred students participated in a mathematical contest. They had six
problems to solve. It is known that each problem was correctl
Canadian Association of Physicists
1995 Prize Exam
This is a three hour exam. National ranking and prizes
will be based on a students performance on both sections A
and B of the exam. However, performance on the multiple
choice questions in part A will be
Canadian Association of Physicists
1997 Prize Exam
This is a three hour exam. National ranking and prizes
will be based on a students performance on both sections A
and B of the exam. However, performance on the multiple
choice questions in part A will be
Winter Camp 2009
Cyclic Quadrilaterals
Yufei Zhao
Cyclic Quadrilaterals The Big Picture
Yufei Zhao
[email protected]
An important skill of an olympiad geometer is being able to recognize known configurations.
Indeed, many geometry problems are built on a few
Winter Camp 2010
Three Lemmas in Geometry
Yufei Zhao
Three Lemmas in Geometry
Yufei Zhao
Massachusetts Institute of Technology
[email protected]
1
Diameter of incircle
A
T
B
X
C
D
Lemma 1. Let the incircle of triangle ABC touch side BC at D, and let DT
Canadian Association of Physicists
1998 Prize Exam
This is a three hour exam. National ranking and prizes
will be based on a students performance on both sections A
and B of the exam. However, performance on the multiple
choice questions in part A will be
an 1
Trinity Training 2011
Yufei Zhao
an 1
Yufei Zhao
Trinity College, Cambridge
[email protected]
April 2011
In this lecture we look at some problems involving expressions of the form an 1. Lets
start with a couple of warm up problems.
Problem. Let a,
Canadian Association of Physicists
1999 Prize Exam
This is a three hour exam. National ranking and prizes
will be based on a students performance on both sections A
and B of the exam. However, performance on the multiple
choice questions in part A will be
IMO Training 2007
Similarity
Yufei Zhao
Similarity
Yufei Zhao
July 12, 2007
[email protected]
1. Let ABCD be a convex quadrilateral. Show that
AC 2 BD2 = AB 2 CD2 + AD2 BC 2 2AB BC CD DA cos(A + C).
2. (IMO Shortlist 1998) Let ABCDEF be a convex hexagon such
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Chapter 6
Communicating and Interpreting
Accounting Information
Chapter Overview
Role
The
of Players in the Accounting Communication Process
Disclosure Process
LO1
Players in the Accounting
Communication Process
LO1
Regulators
Regulator
Primary Purpose
Ca
English 109
October 25, 2016
What your Critical Essay Will Look Like
An Opening paragraph
Opening paragraph should describe and briefly contextualize the
work
What kind of story/game/film is it? Name the genre.
What is it about? What story does it tell
1
Z is a funny Z used for the set cfw_.,3, 2, 1, 0, 1, 2, 3,..
Z+ or N is the set of positive integers cfw_1, 2, 3, 4,..
COS1501 symbols
is the same as N0 which is the set cfw_0, 1, 2, 3, 4, . .
Q is a funny Q used for the set of all rational numbers, i.e
The C+ Programming
Language
Dynamic Memory Management
Techniques
Outline
Dynamic Memory Management
Interaction with Malloc and Free
Interaction with Arrays
Interaction with Constructors and Destructors
Object Placement Syntax
Overloading Global Operator N
Engineering and Information Technology
C+ Memory management
Storage types
Allocation and deallocation
malloc()/free() vs. new/delete
Memory management internals
Engineering and Information Technology
Advanced C+ for Java
Programmers
Memory Management
2
C+
Generic Programming with C+
Generic Programming
Generic programming a style of programming
supported by C+
Similar to OOP trying to make it simple to reuse code,
and abstracting general concepts
Different from OOP in OOP, the emphasis is on data
aspect, i
Introduction to C+
Operator Overloading
Topic #6
CS202 6- 1
CS202 6- 2
Intro to Operator Overloading
Copy Constructors, Issues of Memberwise Copy
Constant Objects and Constant Member Functions
Friend Functions
When to define operators as Members vs. N
C+ OVERLOADING OPERATORANDFUNCTION
http:/www.tutorialspoint.com/cplusplus/cpp_overloading.htm
Copyright tutorialspoint.com
C+ allows you to specify more than one definition for a function name or an operator in the
same scope, which is called function ove