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Discrete Structures Lecture Notes

Discrete StructuresLecture NotesVladlen Koltun1 Winter 20081 Computer Science Department, 353 Serra Mall, Gates 374, Stanford University, Stanford, CA94305, Sets and Defining sets .. Set operations .. More sets ..42 Introducing induction .. Strong induction .. Why is the induction principle true? ..83 More Proof Proofs by contradiction .. Direct proofs ..124 The division algorithm .. Remainders .. Greatest common divisors .. Greatest common divisors and linear combinations ..185 Prime The fundamental theorem of arithmetic .. The infinity of primes ..226 Modular Congruences.

addition to being reasonably formal and unambiguous, your mathematical writing should be as clear and understandable to your intended readership as possible. Here are the rational numbers: Q = na b: a ∈ Z,b ∈ Z,b 6= 0 o. Instead of a ∈ Z,b ∈ Z, you can write a,b ∈ Z, which is more concise and generally more readable.

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