http://www.amazon.com/Connections-James-Burke/dp/0316116726
Our university offered an engineering class that used this as the textbook.
http://www.amazon.com/Connections-James-Burke/dp/0743299558
I loved this series as a kid. It was my favorite TV show. Now that I know more about the history of technology, the connections sometimes seem a bit strained, but even so I know of no better introduction to the topic.
The one that amazed me was how the technology of the auto loom lead to the computer (via punch cards). Again, this won't give you insight into the math of things, but it will show you how one innovation lead to another.
http://www.amazon.com/Connections-James-Burke/dp/0743299558