Mathematics Opportunities for Undergraduates
Research Experiences for Undergraduates:
See what it's like to do research, just like in graduate school. It is possible to do research under a math faculty member. There are also nation-wide undergraduate research centers. For more information, see REU website, or a helpful list of research opportunities at Math Forum for students. Also, George Washington University and Carleton College host summer programs for undergraduate women in mathematics.
The AMS-MAA-SIAM Frank and Brennie Morgan Prize for outstanding undergraduate research is offered every year. The Alice T. Schafer Prize goes to an outstanding woman undergraduate each year.
Cryptology programs and internships:
The National Security Agency offers a popular internship for those interested in cryptography, signals, and number theory. http://www.nsa.gov/programs/employ/college.html
Go to scenic Budapest for the Budapest Semesters in Mathematics for a semester or a year. Take classes from famous Hungarian mathematicians. Focus is on problem solving. Classes are in English.
The Putnam exam each December is a nation-wide collegiate competition in mathematics. Each school gives out the exam simultaneously.
Each summer the Institute for Advanced Study holds a joint workshop called the Park City Mathematics Institute in Park City, Utah, where there are separate programs for undergraduates, graduate students, researchers, and high school teachers. Generally a lot of opportunities for undergraduates to learn math and meet lots of people.