This workshop will lead up to combinations and permutations, incorporating discussion of Pascal's triangle and the use of counting arguments to determine the number of different ways, for example, of ordering a pizza with three out of eight possible toppings or the number of RNA sequences with a given number of bases.
Graphs and Applications of Graph Coloring
This workshop will introduce the basic terminology needed for mathematical modeling using graphs, focusing on graph coloring, and discuss applications of graph coloring to scheduling, communications, and situations involving conflict resolution.
Patterns in Numbers
Building on the Systematic Counting workshop, this workshop will focus on problems which are really sequences of problems (e.g., handshake problem, number of regions created by lines on a page), will use iterative methods such as difference equations to analyze these problems, and will analyze and discuss applications of polynomial and exponential growth.
Building on the graph notions introduced in the Systematic Counting workshop, this session will introduce the notion of paths in graphs, and discuss applications of Euler paths and circuits, for instance to computerized graph drawing, algorithms for street cleaning, and problems involving genetic codes.
Finding the Best Solutions Using Algorithms
Building on the Euler Circuits workshop, this workshop will discuss a variety of graph-related problems - spanning tree problems, shortest path problems, and traveling salesperson problems - and the algorithms used to solve them. Connections to current work at DIMACS will be given, for instance to the solution to the "world's largest traveling salesperson problem".
Critical Path Analysis
This workshop will apply algorithms to directed graphs in order to find the best way of scheduling the individual tasks that compose a major project so that the total time taken to complete the project is a minimum.
Patterns in Geometry
Building on the iteration ideas introduced in the Patterns in Numbers workshop, this session will develop how the idea of recursion is used in geometry, with particular focus on the development of fractals.
Continuing the topic of the Patterns in Geometry workshop, this session will focus on generating several particular kinds of fractals.
This session will focus on how individual preferences can be combined into a group preference, as when selections have to be made or elections conducted. Applications will be made to the computational difficulty of computing different ways to determine the winner in an election.
Codes and Modular Arithmetic
This session will focus on how bar codes are used in a variety of situations (ISBN numbers, zip codes, UPC codes) and the mathematics underlying these codes.
This session will focus on the various algorithms, central to computer science, that can be used to take a set of scattered items and sort them, alphabetically or numerically, into order.