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The Summer Mathematics Program for High School Students consists of four parts: (1) a three-week long class, "Explorations in Number Theory," (2) lunch, where participants get to know each other and the program staff, and where they have the opportunity to discuss mathematics in an informal setting, (3) an afternoon colloquium series with talks on a variety of topics, (4) a computer lab, where students will explore number-theoretic questions using the flexible and powerful Python language (no background in Python needed).
The morning class is a rapid three-week introduction to Number Theory, one of the deepest and most exciting branches of modern mathematics. We start with properties of prime numbers and methods for finding integer solutions to equations, then quickly develop enough background to state and discuss unsolved problems and applications to modern technology. One of the major applications is cryptography, the science of sending secret messages. Cryptography and the number theory it depends on is an active area of research which is also vital to our national security. Students will learn to encode and decode messages which they send to each other.
Problem sessions are integrated into the morning class. Participants work both individually and in groups and are assisted by program staff, including faculty and graduate students. These sessions give all participants direct experience in problem-solving and in communicating the results of their work.
The afternoon talks cover topics such as knot theory, fractals, probability, and mathematical biology. They give students an idea of the great range of ideas, problems, and applications in mathematics.
The lunch break provides students with an opportunity to get to know each other and the program staff outside the classroom.