Stanford University Mathematics Camp (SUMaC) Program 1: Abstract Algebra & Number Theory

The Stanford University Mathematics Camp (SUMaC) welcomes an elite group of talented rising high school juniors and seniors from around the world for intensive study in advanced mathematics. SUMaC's four-week residential program is held on Stanford University’s campus. Two courses – Program I and Program II – are taught during this time, with participants taking one or the other, but not both. This allows students who are math enthusiasts the opportunity to participate in SUMaC over two succeeding summers. Research Topics: Cryptography, Constructibility, Coding Theory, and Symmetry Program I topics are introduced through five motivating problems: constructibility in geometry, classification of patterns in two dimensions, error-correcting codes, cryptography, and the analysis of symmetry in structures. The mathematics central to solving these problems comes from the areas of abstract algebra and number theory. Abstract algebra originated in the early part of the 19th century through the study of polynomial equations. This branch of mathematics lies at the core of many areas of modern mathematical research. Number Theory concerns properties of the integers, and has its origins in ancient mathematics. Number Theory remains a very active field of study with interesting open problems and important applications in computer science. Financial aid is available in the form of partial and full scholarships. Aid is granted based upon need, as well as other factors including merit. Members of underrepresented groups are encouraged to apply. Once you have started the application process you will have access to our Financial Aid application. The application should be submitted within one week of the main SUMaC application. Admission is competitive. SUMaC students are selected based on their grades in math courses, their performance on standardized math exams and math contests, their teacher recommendations, their reasons for wanting to come to SUMaC as expressed on the SUMaC application, and their performance on the SUMaC admission exam. Particular emphasis is placed on the admission exam, which is a collection of challenging math problems for applicants to work on at home over an extended period. SUMaC is for students who are sophomores and juniors at the time of application, and who have an exceptional interest and ability in mathematics.