Top Summer Programs: Stanford University Mathematics Camp

Stanford University Mathematics Camp (SUMaC) was started in the fall of 1994 by Professors Rafe Mazzeo and Ralph Cohen. Initially, the camp was a small program for high school students in the San Francisco Bay Area. Gradually, over the years the mathematics camp has become one of the most competitive math summer programs for high school students in the world. The students don’t earn any credit or grades for this program. SUMaC is for students who want to attend this exceptional program for the gain of pure mathematical knowledge.

For the summer of 2023, SUMaC is offering options of 2 online sessions and 1 residential session for 3 weeks. The residential program will serve 40 participants and the online program will serve 64 participants with an average class size of 16 students. It provides two distinct courses named Program I and Program II, each with its own set of topics. Both courses delve into the historical significance and current relevance of mathematical research. Students are required to choose one of the two courses while applying and express their preference. The Admissions Committee then assigns the students to their preferred course for the duration of the program.

Program I – Abstract Algebra & Number Theory

The study of polynomial equations in the early 1800s marked the origin of abstract algebra. Abstract algebra has now become a fundamental aspect of various modern mathematical research fields. On the other hand, number theory deals with the properties of integers and dates back to ancient mathematics. Number theory remains a vibrant area of exploration. It presents intriguing unresolved problems and holds significant applications in computer science.

Program I topics are introduced through five motivating problems such as limitations of straight-edge and compass constructions, classification of patterns in two dimensions, error-correcting codes, cryptography, and the analysis of symmetry in structures.

As a student, who is applying for Program I you should have studied number theory, and be comfortable with modular arithmetic and some basic theoretical results involving modular arithmetic. You should also be proficient in high school algebra and geometry with a focus on reading and writing mathematical proofs.

Program II – Algebraic Topology

Program II centers on algebraic topology, a major area of current mathematics research.

Topology is a branch of mathematics that investigates the characteristics of shapes that remain unaltered by deformations. To illustrate, consider a rubber sphere that can be altered to take on the shape of a cube. Although a sphere and a cube may seem quite distinct, they are topologically identical, and this can be rigorously demonstrated through mathematical means. In this class, various methods for examining the topological qualities of shapes utilizing algebraic principles, such as the concept of group, will be explored.

If you are applying for Program II, you should have immense experience in proof, and group theory, and a deep interest in higher-level mathematics.

SUMaC participants get the opportunity to experience college-level mathematics. The students are expected to tackle a heavy workload of assignments outside the classroom. During the program, the students are engaged in group problem-solving, guided research, and enriching lectures.

Admission and Cost

Students in grades 10 and 11 who have attained mathematical expertise beyond their school curriculum are highly encouraged to apply for SUMaC. Every year SUMaC receives thousands of applications and it is a very competitive program.

The 3-week online program costs $3,550. It does not include the cost of the required textbook. The 3-week residential program costs $8,250. It includes housing and meals, instruction and course materials, field trips, and transportation between Stanford and SFO at select times.

To finalize the application, you must satisfy the following conditions:

Create a SUMaC application account and complete the form.
Submit your high school transcripts for the last two years.
Standardized test scores are optional for domestic and international applicants.
An online recommendation form from a math teacher.
Essays: The application also includes 3 essays. First is to describe what kind of student you are. The second one is to describe a memorable experience when you engaged meaningfully in mathematics outside of class. Finally, the third one is to talk about your personal goals for the next 5 to 10 years.
Optional video essay: Even though the video is optional, we highly encourage you to include the video as a part of your application.
Admission exam: This is the most unique aspect of the SUMaC application. It is a collection of challenging proof-based math problems. The applicants get a chance to work on the problems at home for an extended period of time.

If you need help to understand what you should include in your essays and the video, you can contact us and we can help you find your niche!

SUMaC (Stanford University Mathematics Camp) is an exceptional program that offers high school students the opportunity to deepen their understanding of mathematics and engage in research projects. Students develop their problem-solving skills, critical thinking abilities, and gain exposure to various mathematical concepts through a rigorous and challenging curriculum. The program also provides a supportive community that fosters academic growth and personal development. SUMaC is one of the best competitive math summer programs which has helped many students pursue their passion for mathematics. Overall, SUMaC is an excellent option for students who want to advance their mathematical skills and gain valuable research experience.

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