And yet, there are a few such distance learning courses. (I'm talking about for-credit courses, from non-profit universities.) Aside from the Harvard Extension courses (which have pretty specific syllabi posted online), it's very unclear how "proof-y" some of these courses are, or whether they are "advanced calculus"/"advanced engineering math"-type courses.
- Use of texts like Ross and Abbott indicate that instructors are trying to make the course "friendly" for students who aren't trying for math Ph.D.s (e.g., prospective HS/CC math teachers). For example, at Stanford, non-honors (Math 115) uses Ross while honors (Math 171) uses Johnsonbaugh & Pfaffenberger; at Berkeley, non-honors (Math 104) uses Ross while honors (Math H104) uses Pugh or baby Rudin. You see frank comments from instructors about the perception of books/courses for the "average" vs. the "elite"... (See also this thread about H104.)
- Use of full-on "transition" texts like Lay are even more likely aimed at prospective math teachers.
- Some of the texts, like Brown/Churchill, are aimed at engineering students and not very rigorous (proof-y) compared to texts aimed at math students.
Anyway, digressions aside, here are some of the courses I've found (in no meaningful order).Textbooks are in [brackets].
- Harvard Extension School (math courses)
- MATH E-23A Linear Algebra and Real Analysis I [Ross]
- MATH E-216 Real Analysis, Convexity, and Optimization [Luenberger]
- SUNY Empire State
- REAL ANALYSIS: THE THEORY OF CALCULUS (SMT-274344) [Abbott]
- COMPLEX VARIABLES (SMT-273314) [Brown/Churchill]
- University of West Florida (M.S. program; non-degree option)
- MAA 6306 Real Analysis
- MAA 6426 Complex Analysis
- Emporia State, Kansas (M.S. program; non-degree option)
- MA 734 Complex Variables
- MA 735 Advanced Calculus I [Bressoud]
- MA 736 Advanced Calculus II [Wade]
- UMUC
- University of Idaho (historical course listing)
- Math 420 Complex Variables [Brown/Churchill]
- Math 471 Introduction to Analysis I [Fitzpatrick]
- Math 472 Introduction to Analysis II [Fitzpatrick]
- Texas Tech (certificate program; non-degree option)
- MATH 5366 - Introduction to Analysis I
- MATH 5367 - Introduction to Analysis II
- Chadron State College, Nebraska
- Indiana University East (certificate program; non-degree option)
- MATH-M 413 Intro to Real Analysis I [Lay]
- MATH-M 414 Intro to Real Analysis II [Lay]
- MATH-M 511 Real Variables I [Lay]
- MATH-M 512 Real Variables II
- University of Houston (M.A. program)
- MATH 5333: ANALYSIS [Lay]
- MATH 5334: COMPLEX ANALYSIS
- Texas A&M (teaching M.S.)
- Math 615 - Intro to Classical Analysis
- Ottawa University, Kansas
- Southern New Hampshire University
- MAT 470 Real Analysis