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Understanding mathematical proofs is essential for grasping mathematical arguments and theorems. Proofs are crucial not only in mathematics but also in computer science for verifying program outputs, algorithm correctness, and system security. This chapter will cover the components of correct mathematical arguments, various proof methods, and the development of mathematics through conjectures.

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14 views1 page

That

Understanding mathematical proofs is essential for grasping mathematical arguments and theorems. Proofs are crucial not only in mathematics but also in computer science for verifying program outputs, algorithm correctness, and system security. This chapter will cover the components of correct mathematical arguments, various proof methods, and the development of mathematics through conjectures.

Uploaded by

jastrime
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© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as TXT, PDF, TXT or read online on Scribd
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To understand mathematics, we must understand what makes up a correct mathematical

argument, that is, a proof. Once we prove a mathematical statement is true, we call
it a theorem.A
collection of theorems on a topic organize what we know about this topic. To learn
a mathematical
topic, a person needs to actively construct mathematical arguments on this topic,
and not just
read exposition. Moreover, knowing the proof of a theorem often makes it possible
to modify
the result to fit new situations.
Everyone knows that proofs are important throughout mathematics, but many people
find
it surprising how important proofs are in computer science. In fact, proofs are
used to verify
that computer programs produce the correct output for all possible input values, to
show that
algorithms always produce the correct result, to establish the security of a
system, and to create
artificial intelligence. Furthermore, automated reasoning systems have been created
to allow
computers to construct their own proofs.
In this chapter, we will explain what makes up a correct mathematical argument and
introduce tools to construct these arguments. We will develop an arsenal of
different proof methods
that will enable us to prove many different types of results. After introducing
many different
methods of proof, we will introduce several strategies for constructing proofs. We
will introduce the notion of a conjecture and explain the process of developing
mathematics by studying
conjectures.

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