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**1 - 1**of**1**### §1. Problem of Algebra Lecture 0 Page 1 Lecture 0

"... This lecture is an orientation on the central problems that concern us. Specifically, we identify three families of “Fundamental Problems ” in algorithmic algebra (§1 –§3). In the rest of the lecture (§4– §9), we briefly discuss the complexity-theoretic background. §10 collects some common mathemati ..."

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This lecture is an orientation on the central problems that concern us. Specifically, we identify three families of “Fundamental Problems ” in algorithmic algebra (§1 –§3). In the rest of the lecture (§4– §9), we briefly discuss the complexity-theoretic background. §10 collects some common mathematical terminology while §11 introduces computer algebra systems. The reader may prefer to skip §4-11