SUMaC 2013

Stanford University Mathematics Camp
July 14-August 10, 2013

Who is SUMaC designed for?

SUMaC is designed for current high school tenth and eleventh graders (students who will be in eleventh or twelfth grade in Fall 2013) who have exceptional interest and ability in mathematics. SUMaC is for those who seek to be challenged in mathematics and those who would enjoy four weeks of intensive, in-depth, mathematical pursuits. SUMaC provides an environment that fosters social and intellectual development centered on the study and enjoyment of mathematics.

What are the requirements for attending SUMaC?
SUMaC participants must be current high school tenth or eleventh graders, and they must be between 15 and 17 years of age on the first day of the program (July 14, 2013). For complete application information go to the Application Materials page.

What is the application process?
For a detailed description of the application requirements, and all application materials, go to the Application Materials page.

Who gets into SUMaC?
SUMaC students are selected based on their grades in math courses, their performance on standardized math exams, their teacher recommendations, their reasons for wanting to come to SUMaC as expressed on the personal information form of 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. However, success in high school certainly increases one's chances of admission. Special attention is paid to students who are in academic environments that do not offer the framework to excel in mathematics beyond the usual school curriculum. In recent years, about four times as many applications are received as there are spaces in the program.

What does SUMaC cost?
Tuition for SUMaC 2013 is $6150. This includes campus housing and dining, all course materials, expenses for organized activities, plus transportation to and from the San Francisco airport, if required. Financial aid is available. To apply for financial aid please submit the financial aid form included in the application packet.

What topics does SUMaC cover?
 SUMaC uses topics that are central to the field of mathematics through their historical significance and their relevance to current lines of mathematical research. The SUMaC courses focus on pure mathematics - that is, mathematics that is motivated independently of ties to other sciences - nonetheless, important applications are introduced and pursued.

SUMaC is divided into two programs:

  • Program I topics are introduced through five motivating problems: non-constructibility in geometry, classification of patterns in two dimensions, error-correcting codes, cryptography, and the analysis of the Rubik's cube. The mathematics that is 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 is concerned with properties of the integers. Although number theory has its origins in ancient mathematics, it remains a very active field of study with interesting open problems and important applications in computer science.

  • Program II contains an introduction to selected topics in combinatorial, differential and algebraic topology. The emphasis will be on developing ideas from, and problems in, geometric topology where methods from algebra and calculus have proved to be effective tools. These include the Euler characteristic as a way of distinguishing between various surfaces, the famous Koenigsberg bridge problem, and degree theory. Applicants to Program II need to be conversant with high school algebra, and must have taken a single-variable calculus course.

How do the SUMaC courses compare to advanced high school and college-level courses?
The usual mathematics sequence at the advanced high school, and beginning college level, takes students through courses designed for the pursuit of science and engineering, leading to topics that are motivated almost entirely by the subject's applicability to "real-world" problems. While SUMaC recognizes applicability as an added bonus in most areas of pure mathematics, our topics are selected independently of concern for these applications. SUMaC leaps ahead in the sequence to give a glimpse of advanced material appropriate for those with a genuine interest in mathematics. Topics covered at SUMaC are included in various college math courses at about the junior level, but the topics are not presented in the format of the usual college courses where they would ordinarily be introduced. In order to reasonably give talented high school students a glimpse of such advanced topics, in only four weeks, the material is streamlined, and not developed to the extent it would be in a university course.

Should you apply for Program I or Program II?
Program II is designed for students who either have a special interest in the topics, or who have seen the Program I material before. Program II is thus especially suited for students who want to return to SUMaC having attended in the past, or who have participated in a similar program somewhere else. Program II is more advanced, but advanced students will be challenged in Program I as well. Applicants are welcome to apply to both programs.

What is the SUMaC daily routine?
Monday through Thursday students spend the morning in class learning the central program topics and working on problems as a class, in small groups, and individually. After lunch students begin work on the daily problem sets. During that time the teaching assistants meet individually with students in 20-60 minute sessions to go over the problem set from the previous day (turned in that morning). Also, throughout the afternoon and evening, members of the SUMaC staff are available to help on that day's problem sets. On Fridays students meet in groups of four or five to work on research topics. This activity allows students to pursue a more in depth study of a focused aspect of the course material; in doing so they research books and articles that go beyond what is presented in class. This culminates in an in-class presentation in the final week of the program. Throughout the four weeks, there will be frequent guest lectures given by internationally renowned mathematicians. These talks provide an introduction to areas of current mathematical research. And, of course, there will be a variety of non-math activities including organized sports activities during the week and on the weekends, and field trips every Saturday. Although the SUMaC staff will be available for tutoring and other needs, there will be no mandatory organized activities on Sundays.

What is the SUMaC residence like?
SUMaC students are housed in a residence on campus that is occupied by Stanford students during the academic year. SUMaC is the only group occupying the residence during the camp. Each student will have a roommate. Rooms for boys and girls are on separate floors. Dining takes place at a separate dining hall shared by other summer youth programs. Special dietary needs are accommodated.

What is the SUMaC teaching philosophy?
 The SUMaC program engages students by introducing the course material through problems that are of historical significance, that are important to the development of mathematics, that have applications to current lines of research in mathematics and the sciences, and that will be found interesting by students who enjoy mathematics. Additionally, the view is that one learns mathematics by doing mathematics-- by working on, tackling, and solving interesting and challenging problems. The SUMaC program gives participants a variety of problems at different levels of abstraction, starting with problems that are relatively concrete and to some extent familiar. These initial problems are used to develop basic intuitions about a particular topic, as well as to strengthen general mathematics skills. Often these problems are followed by a series of more probing ones which dig successively deeper into the abstract, attempting to both fine-tune and generalize one's intuitions and knowledge about the underlying mathematical objects. The research project that students partake in as part of the program allows for the in-depth study of a focused portion of the course material. This is done with the assistance of a teaching assistant, and students use articles and books as sources of additional material. Students share what they have learned in the research project by giving a short presentation at the end of the program. Constant emphasis is placed on developing the ability to reason both formally and informally, and to express one's ideas in mathematically coherent and precise language.

What do SUMaC participants get out of SUMaC?
Many participants find the math-friendly social environment the best part of the program; students comment that it's great to be at a place where it's considered fun to discuss a math problem during dinner or over a game of pool. Every student leaves with a deeper understanding of mathematics and an appreciation for parts of mathematics that they never knew existed. Some students leave with the plan to pursue mathematics further. Everyone makes new friends and contacts based in their common interests and abilities-- friendships that will remain strong for years to follow. Students return home with good memories and much to share with family, friends, and teachers. Although we do not give course credit or grades, we do keep records of each student's performance, and we readily provide that information for use in college applications.

Who are the people behind SUMaC?
SUMaC was founded in 1995 by Professors Rafe Mazzeo and Ralph Cohen of the Stanford Mathematics Department, and is currently directed by Prof. Mazzeo and Dr. Rick Sommer. Rick was an Assistant Professor in the Stanford Mathematics Department and is currently Managing Director of the Education Program for Gifted Youth (EPGY), at Stanford; he designed the Program I course and has been teaching versions of it since the first SUMaC in 1995. The Program II course is designed by Prof. Rafe Mazzeo. The Program II instructor will be announced at a later date. Most of the SUMaC residential counselors and teaching assistants are Stanford mathematics graduate students and undergraduate math majors. SUMaC provides at least a 1-to-4 ratio of staff to students, with most of the teaching assistants serving in the role of live-in counselors. Many of the SUMaC teaching assistants and counselors will be returning from previous years, and some attended SUMaC in high school. The counselors and teaching assistants play a key role in creating the social and academic atmosphere enjoyed by the students.

Does SUMaC receive outside funding?
SUMaC is funded, in part, by a grant from the American Mathematical Society Epsilon Fund and also receives financial support from the Stanford Department of Mathematics.

How do I contact SUMaC?

Email: sumacinfo@stanford.edu
Phone: (888) 423-6040 or (650) 721-2947