It seems there are two groups of people- one group goes the python /less math way and you , and the developers I see in my team at work, are in that category.
The other approach is to view it as applied math. In that regard, the Coursera course is excellent. It focuses on the concept, and Matlab ( which you can download for free for the course) lets you code up complex algorithms rapidly . Note how you mention neural nets was hard. Its hard enough on Matlab , so I can imagine how it would be in python.
In 8 weeks , the coursera course can take you to what took you 6 months in Python. What I would suggest is to a) Watch the Udacity Georgia tech course like you did ( 1 month) b) preview the coursera course a few weeks before c) officially taking it.
However coursera does not talk about stochastic gradient detail in depth, making a passing reference. You can look at the original Standford course. CS 229. I also looked at Udemy , there are a few courses on convolutional neural nets and deep learning out there for $10 each. But the mode of instruction is rather dull and I have not benefitted much. Google has a talk on Tensorflow, which is very nice and on youtube. They also have a website with examples.