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Questions and Answers
What are the major subdisciplines of modern mathematics?
What are the major subdisciplines of modern mathematics?
- Calculus, statistics, trigonometry, and topology
- Logic, probability, differential equations, and topology
- Arithmetic, calculus, algebra, and geometry
- Number theory, algebra, geometry, and analysis (correct)
What does most mathematical activity involve?
What does most mathematical activity involve?
- Intuition and guesswork to derive mathematical principles
- Discovery of properties of abstract objects and use of pure reason to prove them (correct)
- Observation of natural phenomena and formulation of empirical laws
- Memorization of formulas and application of algorithms
What do mathematical objects consist of in modern mathematics?
What do mathematical objects consist of in modern mathematics?
- Intangible concepts and theoretical constructs
- Abstractions from nature or entities stipulated to have certain properties (correct)
- Physical representations and tangible manifestations
- Empirical observations and experimental data
What does a proof in mathematics consist of?
What does a proof in mathematics consist of?
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What are the starting points of a theory in modern mathematics?
What are the starting points of a theory in modern mathematics?
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