Summer 2008
www.cs.cmu.edu/~leap
Andrew’s Leap is a summer enrichment program
run by the Carnegie Mellon University School of Computer Science. All
local area high school students are encouraged to apply (and occasional middle
school students).
Through special classes and guest faculty seminars, students will be exposed to the frontiers of computer science. They will “leap” ahead approximately ten years. Students will have an opportunity to interact with some of the country’s leading scientists, and will emerge from the program with a vivid overview of Computer Science at Carnegie Mellon. Andrew’s Leap has been run every summer since 1991.
What isn't it?
Leap is not for academic credit. We do not evaluate or grade the participants. We want students who want to do it for the fun of it.
We are not a residential program. Students must live close enough to commute each day.
When is it?
The program runs for seven weeks, weekdays
from June 23 -- Aug 8, 2008. Each day
starts at
What is each day like?
Each day is scheduled approximately as follows:
10-12 Theoretical Aspects of Computer Science
12-1:30 Lunch
The morning class concentrates on the great theoretical ideas in computer science. Topics include mathematics, economics, game theory, cryptography, decision theory, algorithms, complex theory, graph theory, computer security, and the theory of infinities.
Our most popular afternoon class is the design and programming of robots. For those students wishing to have a more hands-on experience in mathematical discovery, Professor Rudich will supervise deeper expansions into the morning material.
Many of the Computer Science faculty will give presentations on their current projects and research. By the end of the program, students will have a broad view of the frontiers of computer science research.
Some students stay late to work on their own projects. Students are given keys so that they can come and go when convenient. Past projects have included a new video compression algorithm (patent pending) and a robot that could play a real violin.
Is it easy to be admitted?
Unfortunately, no. We only have the resources to admit 35 students each year. To pick a group we administer a special exam called “The Interesting Test”. From your answers on this test we will be able to tell how ready you are for the curriculum. We do not take into consideration your performance in school. This is a deliberate choice on our part. Most of our students seem to be at the top of their high school class, but we are open minded enough to select a brilliant “drop-out”.
What is The Interesting Test?
The Interesting Test is a collection of mathematical problems to be solved. The material is designed to be unfamiliar to almost all high school students; this is our way of putting everyone on an equal footing. Despite initial appearances, each problem has a simple, short, correct answer. At the end of this document, we include some questions and answers from past exams.
What if I don't get in?
If you had fun trying, please try again. Many of our students were not admitted on the first try.
What does it cost?
Leap tuition is $3,180. It is possible to request financial aid as well. We provide books and materials. The exam is free of charge.
Who runs the Leap?
Professor Steven Rudich is the program
director and teaches the morning session. George Kantor runs the robotics
portion.
How do I apply?
To arrange to take The Interesting Test, please contact:
Phone: (412) 268-5099
Email: kmm@cs.cmu.edu
We are currently scheduling the following exam dates. If you are unable to take the test at any of these times, Kathy will arrange an alternative time for you. You must take the exam by March 7, 2008. The exam will be given in Wean Hall 5409 except for Wednesday, February 20.
SATURDAY,
Feb. 2 10:00 AM TO 1:00 PM
SUNDAY,
Feb. 10 11:00 AM TO 2:00 PM
WEDNESDAY,
Feb. 20 4:00 PM TO 7:00 PM – Wean 7220
SATURDAY,
Feb. 23 9:00 AM-Noon
Each exam session is three hours long. This
gives plenty of time to complete it. In fact, most applicants do not stay the
full three hours. The student is
permitted to use a calculator during the exam.
When can I find out if I was admitted?
We will send out notification letters by March 21. If you call
A SAMPLE FROM THE INTERESTING TEST
1. Name a body part that almost everyone on earth has an above average number of! Justify your answer.
2. A woman and her husband attended a party with four other couples. As is normal at parties, handshaking took place. Of course, no one shook their own hand or the hand of the person they came with. And not everyone shook everyone else's hand. But when the woman asked the other (9) people present how many different people's hands they had shaken they all gave a different answer. Question (this is NOT a trick!): How many different people's hands did the woman's husband shake?
3. A man starts walking up a narrow mountain
path at
True or false? There is some point on the path that the man occupied at exactly the same time on the two different days. Explain your answer.
ANSWERS
1. Fingers. Most people have all their fingers (10). Of the remaining people, it is far more common to have fewer than 10 fingers than to have more than ten fingers. Thus the average number of fingers is nine point something. Thus, almost all people have an above average number of fingers.
2. The maximum number of hands that any person might have shaken is eight. Therefore, the nine people asked by the woman must have given the answers 0, 1, 2, 3, 4, 5, 6, 7, 8. Let's refer to the person who answered i as person i. Person 8 must have shaken everybody's hand but their own and their spouse's. Thus, everyone except their spouse has shaken at least one hand. Therefore, 8 and 0 are married. Similarly, 7 must have shaken everybody's hand except for 0 and 1 (who used up his/her shake with 8). So 1 must be 7's spouse (0 is spoken for). Continuing in this way we see that (6 and 2) and (5 and 3) are married to each other. This leaves 4 as the only unmatched person. 4 must therefore be matched to the woman.
3. Imagine that on the first day a clone of the man starts down the mountain
at