Theory of Numbers

Plot of points on x-y axis with both straight and curved lines connecting plotted points.

Some rational points on the hyperbola x^2 - 2y^2 = 1. The projection from away from (1,0) gives a bijection with the rational points on the y-axis, with the point (0,-m) going to x = (2m^2 + 1)/(2m^2 - 1), y = 2m/(2m^2 - 1). (Image by Abhinav Kumar.)


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As Taught In

Spring 2012



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Course Description

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Course Description

This course is an elementary introduction to number theory with no algebraic prerequisites. Topics covered include primes, congruences, quadratic reciprocity, diophantine equations, irrational numbers, continued fractions, and partitions. 


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Abhinav Kumar. 18.781 Theory of Numbers. Spring 2012. Massachusetts Institute of Technology: MIT OpenCourseWare, License: Creative Commons BY-NC-SA.

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