From the course: Programming Foundations: Discrete Mathematics
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Abstract discrete math
From the course: Programming Foundations: Discrete Mathematics
Abstract discrete math
- [Voiceover] Abstract Math Problems. Abstract math provides the conceptual background and theory that justifies the way math is used in applications. Abstract math requires conceptual reasoning about abstract ideas, as well as manipulating symbols, particularly, understanding and constructing proofs. In doing abstract math, you state theorems and prove them mostly in the context of mathematical ideas. The level of abstraction allows for solving complex problems by breaking them down into smaller problems. When completing proofs, we often start with a statement similar to this one. One supposes that a particular but arbitrarily chosen element x in D, where D is the domain, for which P(x), the proposition, is true, and proves that Q(x) must also be true. As you can see, this is an abstract version of the proof which allows us to determine the validity of the proof, and therefore we can use this to generalize to more specific solutions. In discrete mathematics, there are relatively few…
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