and Theoretical Computer Science

to the Mathematical Sciences Enterprise

Workshop Descriptions

Systematic Counting

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.

Euler Circuits

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.

Infinite Snowflakes

Continuing the topic of the Patterns in Geometry workshop, this session will
focus on generating several particular kinds of fractals.

Elections

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.

Sorting

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.

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