Mathematics: Major Subdisciplines and Concepts

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What are the major subdisciplines of modern mathematics mentioned in the text?

Geometry, algebra, and number theory

What is the main activity involved in mathematics according to the text?

Using pure reason to prove properties of abstract objects

In modern mathematics, what are entities stipulated to have?

Certain properties called axioms

Why is mathematics essential in various fields like natural sciences, engineering, and finance?

To model phenomena without any scientific experimentation

Which areas of mathematics are developed in close correlation with their applications according to the text?

Statistics and game theory

Explore the fundamental topics in modern mathematics, including number theory, algebra, geometry, and analysis. Delve into the diverse areas of mathematical knowledge and their applications in various fields.

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