MATH 3240: Introduction to Number Theory
Description: Number theory is the study of the integers, but this description hardly conveys the beauty of this part of mathematics. One of the main goals of this course is pedagogical: to see that mathematics is a vibrant intellectual activity and not a set of fixed rules developed by some higher authority. This viewpoint is especially useful for future teachers. Students will carry out many numerical experiments, generate conjectures based on patterns observed, and then prove or disprove these conjectures.
The content focuses on those parts of classical number theory which still have modern relevance in the subject: the Euclidean algorithm, modular arithmetic, distribution of primes, diophantine equations, applications to cryptography, arithmetic in quadratic rings and polynomial rings, and quadratic reciprocity. The examples in this course will provide a lot of food for thought for anyone who later takes abstract algebra.
Prerequisites: A grade of C or better in MATH 2142 or 2710.
Offered: Fall Spring
Sections: Fall 2017 on Storrs Campus
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