Online analysis courses

Does it make sense to teach mathematical ({real,complex,functional}) analysis in a distance learning format? In the transition from "math as a bunch of mechanical procedures" (where problem sets can be graded fairly mechanically) to "math as idiomatic communication between mathematicians" (aka reading and writing proofs), somebody who is already a competent mathematician has to actually critique the proofs being written by the novice students.  From the outside, I somehow imagine it would be like trying to teach a writing or design discipline by distance learning.  

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. 

(From the outside, it's interesting to me that distance learning courses don't try to teach using proof systems like Mizar and then auto-grade. Since half of the exercise of "fill in the gaps in Rudin's proofs" is to spot the gaps in an idiomatically-written proof and learn to fill them in for oneself, then assigning the task of mechanically filling gaps in proof templates misses the mark.)

Anyway, digressions aside, here are some of the courses I've found (in no meaningful order).Textbooks are in [brackets].

1. Harvard Extension School (math courses)
1. MATH E-23A Linear Algebra and Real Analysis I [Ross]
2. MATH E-216 Real Analysis, Convexity, and Optimization [Luenberger]
2. SUNY Empire State
1. REAL ANALYSIS: THE THEORY OF CALCULUS (SMT-274344) [Abbott]
2. COMPLEX VARIABLES (SMT-273314) [Brown/Churchill] 
3. University of West Florida (M.S. program; non-degree option) 
1. MAA 6306 Real Analysis
2. MAA 6426 Complex Analysis
4. Emporia State, Kansas (M.S. program; non-degree option)
1. MA 734 Complex Variables
2. MA 735 Advanced Calculus I [Bressoud]
3. MA 736 Advanced Calculus II [Wade]
5. UMUC 
   
1. Concepts of Real Analysis I (MATH 301) [Lebl]
6. University of Idaho (historical course listing)
1. Math 420 Complex Variables [Brown/Churchill] 
2. Math 471 Introduction to Analysis I [Fitzpatrick]
3. Math 472 Introduction to Analysis II [Fitzpatrick]
7. Texas Tech (certificate program; non-degree option)
1. MATH 5366 - Introduction to Analysis I 
2. MATH 5367 - Introduction to Analysis II
8. Chadron State College, Nebraska
1. MATH 434 INTRODUCTORY ANALYSIS [Lay]
9. Indiana University East (certificate program; non-degree option)
1. MATH-M 413 Intro to Real Analysis I [Lay]
2. MATH-M 414 Intro to Real Analysis II [Lay]
3. MATH-M 511 Real Variables I [Lay]
4. MATH-M 512 Real Variables II  

There are a number of other courses that probably have more restricted enrollment. Stanford's Online High School program lists courses in real analysis [Ross] and complex analysis [Brown/Churchill]. Wow!  But I doubt many people reading this are high-schoolers trying to take analysis. Other programs may or may not allow enrollment a la carte, as the courses are part of undergraduate math programs or graduate programs for math teachers - presumably, any mathematics department offering an online math degree must offer an analysis course. But if analysis isn't a core requirement, it may not be offered regularly.

1. University of Houston (M.A. program)
1. MATH 5333: ANALYSIS [Lay]
2. MATH 5334: COMPLEX ANALYSIS
2.  Texas A&M (teaching M.S.) 
1. Math 615 - Intro to Classical Analysis

There are a few other courses at private schools. I only list these separately because, unlike Harvard/Stanford and state schools, I have no idea about what these schools are about. They do at least appear to be not-for-profit schools.

1. Ottawa University, Kansas
1. MAT 45143 Introduction to Real Analysis 
2. Southern New Hampshire University
1. MAT 470 Real Analysis

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