Many topics of interest to coding theory, cryptography, and number theory require a broad base of knowledge in other areas of mathematics. The challenge of graduate students beginning research in these areas is to get “up to speed” quickly on the background material they need in order for to get a feel for research problems and to get started doing research themselves. To meet this challenge, will we teach a four-week summer “bridge” program. We will choose topics to help new students understand basic objects, and we will pitch these topics at a level which requires minimal background. In this way, we will acquaint students with fundamental coding theory, cryptography, and number theory subjects which they would ordinarily wait at least one or two years to see in course work. A secondary goal of the program is to give students a primer on basic and essential general mathematics topics such as finite fields, linear algebra, and complex analysis, which will also assist them in preparing for qualifying examinations.
We will implement our bridge program as follows. We will offer one course each summer with a primary instructor
and one teaching assistant (senior graduate student). The instructor will lecture for 1.5 hours in the morning;
in the afternoon, the teaching assistant will meet with students for one hour to answer questions and work examples.
The instructor will assign homework and students will present solutions in a relaxed and friendly environment. In-class presentations will give students valuable classroom speaking practice. We plan to introduce SAGE via homework requiring computation.