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What is Mathematics?

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Questions and Answers

What are the major subdisciplines of modern mathematics?

Number theory, algebra, geometry, and analysis (correct)

Calculus, trigonometry, statistics, and logic

Algebra, geometry, logic, and calculus

Arithmetic, calculus, topology, and probability

How is mathematical activity described in the text?

Primarily based on experimentation and observation

Involves the discovery of properties of abstract objects and the use of pure reason to prove them (correct)

Focused on modeling natural phenomena through scientific experiments

Dependent on the applications in natural sciences

What are the fundamental truths of mathematics independent from?

Applied mathematics

Natural phenomena

Engineering and medicine

Any scientific experimentation (correct)

Which areas extensively use mathematics for modeling phenomena?

Natural sciences, engineering, medicine, finance, computer science, and social sciences Signup and view all the answers

3

How are mathematical proofs constructed? Signup and view all the answers

What did Galois theory allow to be reduced to group theory?

Certain problems in field theory Signup and view all the answers

In Galois theory, what type of equations are solvable by radicals?

Equations expressible using integers, nth roots, and basic arithmetic operations Signup and view all the answers

What problem does the Abel–Ruffini theorem address?

Solvability of polynomial equations by radicals Signup and view all the answers

What classic problems have been solved using Galois theory?

Doubling the cube and trisecting the angle Signup and view all the answers

Who published Galois' work fourteen years after his death?

Joseph Liouville Signup and view all the answers