Today I decided to binge on discrete mathematics after a three year hiatus. I tackled three proofs, and all of them required the introduction of assumptions that seemed to not be found in the givens as well as caffeine. Out of those three proofs, I got two incorrect after contemplating for 30 minutes to an hour. This early work led to the introduction of some of the main structures of modern abstract algebra, groups, rings and ﬁelds. These structures have been intensively studied over the past two hundred years. For an interesting historical account of the origins of algebra the reader may consult the book by van der Waerden [15].

(An introduction to complex numbers can be found next, if needed) The Fundamental Theorem of Algebra states that every such polynomial over the complex numbers has at least one root. The Corbettmaths Practice Questions on Algebraic Proof. Videos, worksheets, 5-a-day and much more

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