I would like to learn about bicycle design and manufacturing, so I started a search for those places and universities where it is possible to do it.

The University of Oregon in Portland has a Master of Science in Sports product design. Here is the link:

https://pd.uoregon.edu/sports-product-design

The University of Iowa has a hand build bicycle program. They have also a facebook page:

http://bicycledesign.net/2014/10/the-university-of-iowa-hand-built-bicycle-program/

https://www.facebook.com/IowaDBR

The University of the Fraser Valley offers courses in bicycle maintenance and bike frame building. The course in bike frame building is a two-week course and has a cost of 2950 Cdn (I think it is canadian dollars):

http://www.ufv.ca/bicycle-technology/bike-frame-building-101/

 The University of Toronto and its Human powered vehicle design team:

http://hpvdt.skule.ca/

The University of Stanford ME204 Bicycle Design and Frame Building course

http://www.pureirishstout.com/index.html