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Logic - where is it used all over the place. Also used all over the place incorrectly. ‘Yield Priority Seats to riders with disabilities and seniors’ Logic = circuit design. The NAND and NOR stuff that we had you do is to convince you that every boolean function can be realized with just these NAND and NOR gates

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Counting/combinatorics usages Counting arguments Probability = counting for the numerator/ counting for the denominator Where is probability used? – Las Vegas, Atlantic City, Monte Carlo, Macau – Wall street – Machine learning – Randomized algorithms – what is the ‘expected’ running time

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Where is induction used? ANY result about patterns in numbers can potentially be proven using induction Sum of the first n numbers Theorems about n-sided polygons Theorems about binary trees of size n Dynamic programming (proving it works) Recursion Make a guess about the computational complexity and prove it using induction And oh yeah ….CIT596

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Where is graph theory used Graph theory + probability + 2 PhD students + the internet = …. Google maps Linkedin (3 rd connection etc) And oh yeah http://www.cis.upenn.edu/grad/documents/bhu snurm.pdf http://www.cis.upenn.edu/grad/documents/bhu snurm.pdf

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