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Number Theory Pre-Collegiate
Feb 10, 2025

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Stanford University's Number Theory Pre-Collegiate is an introduction to number theory and its applications. The course covers topics such as Euclid's algorithm, divisibility, prime numbers, congruence of numbers, theorems of Fermat, Euler, Wilson, Lagrange's theorem, residues of power, quadratic residues, magic squares, continued fractions, Diophantine equations, quadratic fields, and quadratic integers. This course is delivered online. The curriculum is designed to be rigorous and advanced, originally created to match the Stanford Mathematics Department's curriculum. The required text for the course is 'An Introduction to Number Theory' by Stark, serving as a vital resource to understand the concepts and apply them practically. The prerequisites for this course include Precalculus or an equivalent course. It is desirable, although not necessary, for students to have proof-writing experience and participation in math competitions. This ensures that students have a solid mathematical foundation to understand and engage with the complex topics covered in this pre-collegiate course. The instructor for the course is Dr. Margarita Kanarsky, who has extensive experience in math instruction, including the Online High School under Stanford Pre-Collegiate Studies. Her expertise and experience contribute to the high-quality learning experience offered by the course. The primary outcome of this course is to provide students with a comprehensive understanding of number theory and its applications. Upon completion, students will have a solid grounding in various aspects of number theory, such as prime numbers, quadratic residues, and Diophantine equations. This knowledge and the skills acquired in the course would serve as a strong foundation for further studies in mathematics.

written by
Rishab Jain