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A Diophantine equation is an equation with integer (or rational) coefficients that is to be solved in integers (or rational numbers). A focus of study for hundreds of years, Diophantine analysis remains a vibrant area of research. It has yielded a multitude of beautiful results and has wide ranging applications in other areas of mathematics, in cryptography, and in the natural sciences. In this project-based tutorial, we will focus on studying and implementing various methods for solving previously unsolved infinite families of Diophantine equations. Depending on their interests, students may choose one or several methods to apply to open problems in the field.
Grading: no pass/fail option,
no fifth course option
Weekly homework and oral presentations, and a final written project manuscript that will be continually edited all semester (the length of which will depend on the mathematical content and choice of topic)
MATH 250 or permission of the instructor
Sophomores, Juniors, and Seniors based on a short questionnaire of interests.
This course requires working with various number systems, performing explicit computations, and proving mathematical results using logical reasoning practices.