Program Description

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The Summer Mathematics Program for High School Students is an intensive four-week program in number theory for motivated high school students. Because the integers are such a fundamental mathematical object, for thousands of years mathematicians from all over the world have studied number-theoretic questions; nevertheless, the subject is rich enough that it is studied today more actively than ever. It moreover has essential contemporary applications to cryptography, the science of sending and deciphering secret messages.

Participants will work closely throughout the day with one another and with the program staff (the director and three graduate students), exploring a series of challenging problem sets. Students will be asked to experiment with the subject, formulating conjectures about what they believe to be true, and then to justify their claims rigorously. Each student will, with the assistance of the counselors, substantially develop her or his ability to communicate mathematical ideas and arguments precisely.

Each day the students and the staff will share a lunch break in which they get to know one another better and continue more informally their mathematical discussions. In addition to the core number theory course, once each week a member of the Utah mathematics department will run an afternoon program devoted to other areas of mathematics, both theoretical and applied, so that students can catch a glimpse of the staggering range of the contemporary mathematical landscape.