Stanford University Mathematics Camp (SUMaC) Program 2: Algebraic Topology

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. Program II centers on algebraic topology, a major area of current mathematics research. Topology is the study of the properties of shapes that remain unaffected by deformations. For example, a sphere made out of rubber can be deformed into the shape of a cube. While it may appear that a sphere and a cube don't have that much in common, it turns out that they are topologically equivalent and in a way that can be made precise mathematically. This course will explore different ways of analyzing topological properties of shapes using algebraic concepts, such as the notion of group. 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.