What do you think?
Rate this book
Mathematics for Computer Science
Mathematics for Computer Science by Eric Lehman ,F Thomson Leighton , Albert R Meyer
This text explains how to use mathematical models and methods to analyze prob-
lems 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, some-
thing that no amount of testing can do.
Simply put, a proof is a method of establishing truth. Like beauty, “truth” some-
times 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 of argument in this vein, Descartes goes on to conclude that there is an infinitely
beneficent God. Whether or not you believe in an infinitely beneficent God, you’ll
probably agree that any very short “proof” of God’s infinite beneficence is bound
to be far-fetched. So even in masterful hands, this approach is not reliable.
Mathematics has its own specific notion of “proof.”
This text explains how to use mathematical models and methods to analyze prob-
lems 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, some-
thing that no amount of testing can do.
Simply put, a proof is a method of establishing truth. Like beauty, “truth” some-
times 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 of argument in this vein, Descartes goes on to conclude that there is an infinitely
beneficent God. Whether or not you believe in an infinitely beneficent God, you’ll
probably agree that any very short “proof” of God’s infinite beneficence is bound
to be far-fetched. So even in masterful hands, this approach is not reliable.
Mathematics has its own specific notion of “proof.”
Kindle Edition
Published December 4, 2020
5 people are currently reading
6 people want to read
Ratings & Reviews
Friends & Following
Create a free account to discover what your friends think of this book!
Community Reviews
No one has reviewed this book yet.