Math 453: Elementary Theory of Numbers


This course is a basic introduction to the theory of numbers. Core topics include divisibility, primes and factorization, congruences, arithmetic functions, quadratic residues and quadratic reciprocity, primitive roots and orders. Additional topics covered include sums of squares, Diophantine equations, and continued fractions.

This course satisfies the General Education Criteria for Quantitative Reasoning II.


NetMath 453 Syllabus.pdf


MATH 241 or equivalent.

Credit Hours



Undergraduate Students  
Graduate Students  
Courseware Cost None

Students must be able to print out assignments, write out solutions, then scan their written work and upload it to Moodle. 


Exams: This course has three 90-minute midterm tests and a 3-hour final exam.

Proctorship Information: This course requires that you obtain a proctor. Please see our Proctor Information for further instructions.

Course Options

Please Note:

Students currently registered in a University of Illinois Graduate Degree program will be restricted from registering in 16-week Academic Year-term NetMath courses. Matriculating UIUC Grad students will be allowed to register in Summer Session II NetMath courses. 

This page has information regarding the self-paced, rolling enrollment course. If you are a UIUC student interested in taking a course during the summer, you may be interested in a Summer Session II course.


Individual students enrolled in this course are assigned to a course instructor. 

Course Timeline

Your time in the course begins on the date your registration is processed. This course is 16 weeks long with the possibility of purchasing an extension. Eligible students may purchase up to two 1-month extensions for $300 each. Click here for information about extensions for this course. Click here to apply for an extension.