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Explain the major subdisciplines of modern mathematics as mentioned in the text.
The major subdisciplines of modern mathematics mentioned in the text are number theory, algebra, geometry, and analysis.
What does a proof in mathematics consist of, according to the text?
A proof consists of a succession of applications of deductive rules to already established results, including previously proved theorems, axioms, and some basic properties that are considered true starting points of the theory under consideration.
Explain the relationship between fundamental truths of mathematics and scientific experimentation as mentioned in the text.
The fundamental truths of mathematics are independent from any scientific experimentation, although mathematics is extensively used for modeling phenomena.
How is mathematics essential in various fields mentioned in the text?
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Give an example of areas of mathematics developed in close correlation with their applications as mentioned in the text.
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What percentage of the cellular volume is occupied by molecules on average?
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Where do proteins primarily operate within the cell?
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What is the primary focus of recent research in molecular and cell biology?
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What is the main factor that considerably modifies the behavior of proteins in their natural milieu?
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Where are proteins accustomed to be thought of as highly purified entities that act in isolation?
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