Computer Science 1032 Class
Notes
September 10, 2013
A computer is simply an box-shaped object with
lights it requires software to function to its full
capacity
Computers are only aware of electronic pulses (whether they are on or off in
computer science,
MOP 2007 Black Group
Counting in Two Ways
Yufei Zhao
Counting in Two Ways
Incidence Matrices
June 26, 2007
Yufei Zhao
yufeiz@mit.edu
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
yufeiz@mit.edu
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
yufei.zhao@gmail.com
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
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
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
Trinity Training 2011
Power of a Point
Yufei Zhao
Power of a Point
Yufei Zhao
Trinity College, Cambridge
yufei.zhao@gmail.com
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
Final Exam
A
p
r
i
l
1
8
1
4
6
:
4
1
P
M
Chapter 5
A
p
r
i
l
1
8
1
4
7
:
0
8
P
M
Chapter 5
What Is Content?
In the broadest sense content is property, and is often
closely related to intellectual property
Intellectual Property = A form of creating endeavo
Lesson 1 - HTML
Protocols
Mail: Simple Mail Transport Protocol (SMTP)
Files: File Transfer Protocol (FTP)
E-Commerce and Web Applications: Hypertext Transfer Protocol (HTTP)
E.C
User Tier: Computers with browsers, request and process Web Pages
o
ommerce T
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
yufeiz@mit.edu
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
yufeiz@mit.edu
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
an 1
Trinity Training 2011
Yufei Zhao
an 1
Yufei Zhao
Trinity College, Cambridge
yufei.zhao@gmail.com
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
COS1501/Hints & Activities
HINTS AND ACTIVITIES
Theoretical Computer Science 1
COS1501
Dear Student,
This document provides hints and activities that will help you to avoid making common errors
when solving questions. More hints are provided in your assig
C+ PRELIMINARIES
TOKENS : As we know the smallest individual units in a program are known as
tokens. C+ has the following tokens Keywords
Identifiers
Constants
Strings
Operators
A C+ program is written using tokens, white spaces and the syntax of the
Pointers
C and C+
3. Pointers Structures
Stephen Clark
University of Cambridge
(heavily based on last years notes (Andrew Moore) with thanks to Alastair R. Beresford
and Bjarne Stroustrup)
Michaelmas Term 2011
Computer memory is often abstracted as a sequ
CS32 Homework 02
NAME:
_
1. Declare a pointer variable named ptr to an integer.
ANSWER: int *ptr;
2. Write the code that assigns to p1 (an integer pointer variable) the pointer
to a dynamically created integer.
ANSWER: p1 = new int;
3. Write the code to r
Unit 6
Loop statements
Summary
6.1
Repetition of statements
The while statement
Input loop
Loop schemes
The for statement
The do statement
Nested loops
Flow control statements
Statements in Java
Till now we have seen different types of statements (without
Pointers and Dynamic Arrays
A pointer is the memory address of a variable.
Memory is divided into adjacent locations (bytes).
If a variable uses a number of adjacent locations, the address of the location with the smallest
address is the address of the va
IMO Training 2007
Similarity
Yufei Zhao
Similarity
Yufei Zhao
July 12, 2007
yufeiz@mit.edu
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