This course has a limited number of seats. To find out about availability or to be put on a waitlist, please contact our office at


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 was created by UIUC Mathematics Professor Bruce Berndt, who was recently named one of the world’s ten most influential mathematicians by Academic Influence. Math 453 features recorded lectures from Professor Berndt's course that was taught at the University of Illinois in Spring 2018. For more on Professor Brent, see Analytic and Combinatorial Number Theory: The Legacy of Ramanujan, LAS Faculty Honors, November 2020, Department of Mathematics Faculty Honors page, An Overview of Ramanujan’s Notebooks and Ramanujan, the Ultimate Superhero.

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


NetMath 453 Syllabus.pdf


MATH 241 or equivalent.


Credit Hours



Undergraduate Students $1272
Graduate Students $1530
Courseware Cost None

Students must be able to view assignments online, write out solutions, then scan or take photos of their written work and upload it to Moodle. 

Students with a Bachelor's degree will be assessed graduate level tuition rate for this course. However, one cannot receive graduate level credit for courses numbered below 400 at the University of Illinois.


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

Proctorship Information: All exams in this course may be taken online.

Please refer to our Proctor Information page for further exam taking information.

Once registered, students can also find relevant exam taking information and all other course requirements within their Nexus student dashboard.

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

Time in the course begins on the date your registration is processed. This course is 16 weeks long with the possibility of purchasing up to two 1-month extensions.

Extension information is posted here. Extension applications must be made via the student Nexus Dashboard. Nexus access will be granted upon course registration.