Young Scholars Program in Discrete Mathematics

Sample Schedule and Courses

This is a sample schedule, based on past years' programs. It is presented here as an example of the kinds of activities you can expect to participate in if you attend the program. This summer's schedule may not necessarily be the same. This is the typical schedule for most days except Fridays, when you will be leaving at 4:30. The schedule is modified for certain activities that may require more time, or for special activities.

Schedule

7:30 - 8:15   Breakfast
(except Monday)
8:30 - 11:00   Morning Instructional Session
11:00 - 12:00   Homework Session
12:00 - 12:30   Lunch
12:30 - 1:15   Recreation
1:15 - 3:45   Afternoon Instructional Session
3:45 - 4:45   Homework Session
4:45 - 5:45   Variety Sessions
(except Friday)
5:45 - 6:30   Dinner
6:30 - 8:00   Scheduled Open Recreation
8:00 - 10:00   Residential Evening Program
10:00 - 11:00   Free Time

Each instructional session (except Monday) begins with a homework review session at which you will be presenting your solutions to homework assigned the previous day, and it concludes with a homework session based on material introduced in the instructional session.

Each week there is a five-session morning course and a five-session afternoon course, each taught by a college professor. Following is a sample sequence of the eight courses; some may be replaced by other courses (for example, Codes and Cryptography).

Courses

Week 1   AM:   General Mathematics Background
  PM:   Graphs and Applications
Week 2   AM:   Combinatorics
  PM:   Robotics Challenge
Week 3   AM:   Algorithms in Graph Theory
  PM:   Number Theory
Week 4   AM:   Problem Solving
  PM:   Fractals

During the instructional sessions, you will be sitting around a table with about 5 students and a teaching assistant, who is a Rutgers undergraduate or graduate student in mathematics, computer science, or a related area. During the instructional session, there will be several repetitions of the following cycle: the instructor will present some material, you will discuss the material with your group and do some problems, and the material will be discussed by everyone. At the conclusion of the homework session, the teaching assistants will announce who will present each of the homework problems the following day. There won't be homework sessions in the evening, but you will need to prepare your homework presentation with the members of your group, and you will be given additional optional challenging problems that you can work on.

Variety Sessions

The final program of the afternoon will be the variety session, held on Monday-Thursday. It is called the "variety session" because we schedule a variety of activities during this period. During the first week of the program, for example, there will be tour of the campus, a discussion of mathematical careers, and a challenge presented by the director of the program.

Scheduled Open Recreation

On most evenings after dinner there will be a one and a half-hour open recreation period, so that those of you who wish can work out, play basketball, racquetball, tennis or volleyball, go swimming, work on the YSP newsletter, monthbook or T-shirt committees, or engage in other social activities. If you like to rollerblade, skateboard, or bike there are some great places on campus for these activities, so please bring your equipment along. The Open Rec period is under the supervision of the three residence life counselors, so that each evening there will be three choices of activities.

Residential Evening Program

During the residential evening program (generally from 8pm to 10pm), you will be involved in fun activities conducted by the residence hall staff. Some of these activities might include a participant talent show, dance, roommate games, international food exchange night, beach party, and much more. Some may want to work on our weekly newsletter; others may want to work on publishing the YSP Monthbook. Between 10pm and 11pm each evening, you have free time, during which some of you might continue to work on homework, but others may want to relax or watch movies. During this time, participants will be expected to remain inside the residence hall.

Content of Courses

Assuming that the eight courses will be the courses listed above in the indicated sequence ... following are how some instructors have described their courses:

In the first week, the morning course will focus on strengthening your general mathematics background; topics include mathematical induction, basic logic and types of proof, the use of mathematical abstraction in practical problems, and basic counting arguments. The afternoon course will focus on graphs and applications, including basic concepts of graph theory, directed graphs, Euler tours, and Hamilton cycles.

In the second week, the morning course on combinatorics focuses on techniques for systematic listing and counting - for example, how many different pizzas can you make using three of eight available toppings? The afternoon will involve a robotics challenge; you will learn a Robotics System and, in teams, use it to solve an open-ended design problem.

In the third week, the morning course will be on algorithms and graphs. (An algorithm is a systematic procedure for solving a complex problem.) Some of the topics to be covered will be greedy algorithms, polynomial algorithms, divide and conquer techniques, and searching and sorting. The afternoon course on number theory focuses on interesting properties of numbers, such as how to tell that 22000 -1 is a multiple of 11, that 2000!-1 cannot be expressed as a sum of two perfect squares, although 2000!+1 can be so expressed (if it's prime).

In the fourth week, the morning course on problem solving discusses general problem-solving techniques, but focuses, in particular, on problems involving puzzles and games, and revisits the problems that accompanied the Application Kit, and other such problems. The week concludes with a Tour D'Euler, a problem-solving competition for teams of participants. The afternoon course discusses the fascination of fractals, starting with the Sierpinski triangle and the Koch snowflake, and moving to computer simulations and Julia and Mandelbrot sets.


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