Math 447: Real Variables


Careful development of elementary real analysis for those who intend to take graduate courses in Mathematics. Topics include completeness property of the real number system; basic topological properties of n-dimensional space; convergence of numerical sequences and series of functions; properties of continuous functions; and basic theorems concerning differentiation and Riemann integration. Credit is not given for both MATH 447 and either MATH 424 or MATH 444.


Math 447 Syllabus.pdf


Prerequisite: MATH 241 or equivalent; MATH 347 or MATH 348

Credit Hours:



Undergraduate Students  
Graduate Students  
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: Exams in this course may be taken online.

Students with a course start date prior to January 1st, 2023 should use proctor information on this page to take their exams.

Students with a course start date on or after January 1st, 2023 should refer to this page for exam taking information.

Once registered, students will 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.

Students with course start dates on or after 1/1/2023:

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