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What are the major subdisciplines of modern mathematics mentioned in the text?
What are the major subdisciplines of modern mathematics mentioned in the text?
- Logic, probability, differential equations, and topology
- Arithmetic, calculus, algebra, and geometry
- Calculus, statistics, trigonometry, and topology
- Number theory, algebra, geometry, and analysis (correct)
What does most mathematical activity involve?
What does most mathematical activity involve?
- Discovery of properties of abstract objects and the use of pure reason to prove them (correct)
- Relying on intuition rather than reasoning
- Trial and error methods to solve problems
- Memorization of formulas and their applications
What are the entities in modern mathematics stipulated to have?
What are the entities in modern mathematics stipulated to have?
- Random properties based on observations
- Certain properties called axioms (correct)
- Properties derived from natural phenomena
- Properties that are not relevant to the theory
What does a proof in mathematics consist of?
What does a proof in mathematics consist of?
What are the topics included in the area of mathematics according to the text?
What are the topics included in the area of mathematics according to the text?
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