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Lecture Notes for MATH 3230 - Abstract Algebra I with Gross at Connecticut (UConn)

Notes Information

Material Type:Class Note
Professor:Gross
Class:MATH 3230 - Abstract Algebra I
Subject:Mathematics
University:University of Connecticut
Term:Fall 2009
Keywords:
  • Immediately
  • Assumptions
  • Definitions
  • Contradiction
  • Rational Number
  • Contrapositive
  • Consequences
  • Interesting
  • Real Number
  • Formal Statement
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Sample Document Text

The Process of Mathematical Proof Introduction. Mathematical proofs use the rules of logical deduction that grew out of the work of Aristotle around 350 BC. In Math 213 and other courses that involve writing proofs, there may have been an unspoken assumption that you and everyone else would instinctively follow those rules. Along the way you have likely acquired an understanding of what is - and is not - acceptable mathe- matical argument. To make sure that everyone starts this course from the same logical point of view, this document discusses explicitly the ground rules of math- ematical proof. You may find it a handy reference, especially at the start, to check your reasoning. A fundamental precept of deductive reasoning is the law of the excluded mid- dle: every statement is either true or false, never both. Mathematics classifies statements about mathematical ideas and sets as true or false. The most basic true statements are the axioms of the particular branch of mathematics under study. T...

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