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Mathematics for Computer Science: By Google Inc. And Massachusets Institute of Technology
Mathematics for Computer Science by Eric Lehman
Google Inc.
F Thomson Leighton
Department of Mathematics and CSAIL, MIT
Akamai Technologies
Albert R Meyer
Massachusets Institute of Technology
This text explains how to use mathematical models and methods to analyze problems that arise in computer science. Proofs play a central role in this work because
the authors share a belief with most mathematicians that proofs are essential for
genuine understanding. Proofs also play a growing role in computer science; they
are used to certify that software and hardware will always behave correctly, something that no amount of testing can do.
Simply put, a proof is a method of establishing truth. Like beauty, “truth” sometimes depends on the eye of the beholder, and it should not be surprising that what
constitutes a proof differs among fields. For example, in the judicial system, legal
truth is decided by a jury based on the allowable evidence presented at trial. In the
business world, authoritative truth is specified by a trusted person or organization,
or maybe just your boss. In fields such as physics or biology, scientific truth1
is
confirmed by experiment. In statistics, probable truth is established by statistical
analysis of sample data.
Philosophical proof involves careful exposition and persuasion typically based
on a series of small, plausible arguments. The best example begins with “Cogito
ergo sum,” a Latin sentence that translates as “I think, therefore I am.” It comes
from the beginning of a 17th century essay by the mathematician/philosopher, Rene´
Descartes, and it is one of the most famous quotes in the do a web search
on the phrase and you will be flooded with hits.
Deducing your existence from the fact that you’re thinking about your existence
is a pretty cool and persuasive-sounding idea. However, with just a few more lines
Google Inc.
F Thomson Leighton
Department of Mathematics and CSAIL, MIT
Akamai Technologies
Albert R Meyer
Massachusets Institute of Technology
This text explains how to use mathematical models and methods to analyze problems that arise in computer science. Proofs play a central role in this work because
the authors share a belief with most mathematicians that proofs are essential for
genuine understanding. Proofs also play a growing role in computer science; they
are used to certify that software and hardware will always behave correctly, something that no amount of testing can do.
Simply put, a proof is a method of establishing truth. Like beauty, “truth” sometimes depends on the eye of the beholder, and it should not be surprising that what
constitutes a proof differs among fields. For example, in the judicial system, legal
truth is decided by a jury based on the allowable evidence presented at trial. In the
business world, authoritative truth is specified by a trusted person or organization,
or maybe just your boss. In fields such as physics or biology, scientific truth1
is
confirmed by experiment. In statistics, probable truth is established by statistical
analysis of sample data.
Philosophical proof involves careful exposition and persuasion typically based
on a series of small, plausible arguments. The best example begins with “Cogito
ergo sum,” a Latin sentence that translates as “I think, therefore I am.” It comes
from the beginning of a 17th century essay by the mathematician/philosopher, Rene´
Descartes, and it is one of the most famous quotes in the do a web search
on the phrase and you will be flooded with hits.
Deducing your existence from the fact that you’re thinking about your existence
is a pretty cool and persuasive-sounding idea. However, with just a few more lines
717 pages, Kindle Edition
Published October 14, 2020
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