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?

<p>Natural sciences, engineering, medicine, finance, computer science, and social sciences (D)</p> Signup and view all the answers

3

<p>How are mathematical proofs constructed? (D)</p> Signup and view all the answers

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

<p>Certain problems in field theory (A)</p> Signup and view all the answers

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

<p>Equations expressible using integers, nth roots, and basic arithmetic operations (C)</p> Signup and view all the answers

What problem does the Abel–Ruffini theorem address?

<p>Solvability of polynomial equations by radicals (A)</p> Signup and view all the answers

What classic problems have been solved using Galois theory?

<p>Doubling the cube and trisecting the angle (A)</p> Signup and view all the answers

Who published Galois' work fourteen years after his death?

<p>Joseph Liouville (A)</p> Signup and view all the answers

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