Introduction Why Study Algorithms? Design and Analysis of Algorithms I.

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Presentation transcript:

Introduction Why Study Algorithms? Design and Analysis of Algorithms I

Tim Roughgarden Why Study Algorithms? important for all other branches of computer science

Tim Roughgarden Why Study Algorithms? important for all other branches of computer science plays a key role in modern technological innovation

Tim Roughgarden Why Study Algorithms? important for all other branches of computer science plays a key role in modern technological innovation – “Everyone knows Moore’s Law – a prediction made in 1965 by Intel co- founder Gordon Moore that the density of transistors in integrated circuits would continue to double every 1 to 2 years….in many areas, performance gains due to improvements in algorithms have vastly exceeded even the dramatic performance gains due to increased processor speed.” Excerpt from Report to the President and Congress: Designing a Digital Future, December 2010 (page 71).

Tim Roughgarden Why Study Algorithms? important for all other branches of computer science plays a key role in modern technological innovation provides novel “lens” on processes outside of computer science and technology – quantum mechanics, economic markets, evolution

Tim Roughgarden Why Study Algorithms? important for all other branches of computer science plays a key role in modern technological innovation provides novel “lens” on processes outside of computer science and technology challenging (i.e., good for the brain!)

Tim Roughgarden Why Study Algorithms? important for all other branches of computer science plays a key role in modern technological innovation provides novel “lens” on processes outside of computer science and technology challenging (i.e., good for the brain!) fun

Tim Roughgarden Integer Multiplication

Tim Roughgarden The Grade-School Algorithm

Tim Roughgarden The Algorithm Designer’s Mantra “Perhaps the most important principle for the good algorithm designer is to refuse to be content.” -Aho, Hopcroft, and Ullman, The Design and Analysis of Computer Algorithms, 1974

Tim Roughgarden A Recursive Algorithm

Tim Roughgarden Karatsuba Multiplication