Muhammed Al-Khwarizmi is the guy and Al Jabr literally means the reconstructer..
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The history of algebra can be traced all the way back to the Ancient Babylonians. The term algebra is first found in a book written by Mohammed ibn Musa al-Khwarizmi.
Algebra, as the Arabic origin of its name suggests, originated with the work of the Persian mathematician al-KhwÄrizmÄ« (780 – 850).
Not sure how to answer your question, however i know that the name Algebra came fom an Arabic name which was the person who started Algebra as we call it today......smart guy...
foundations algebra is probably pre algebra, which is before algebra, so no.
algebra 1a is the first part of algebra 1 and algebra 1b is the second part. :)