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Questions and Answers
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 combinatorics
- Calculus, statistics, trigonometry, and topology
- Number theory, algebra, geometry, and analysis (correct)
- Arithmetic, calculus, algebra, and geometry
What is the primary method used in mathematical activity according to the text?
What is the primary method used in mathematical activity according to the text?
- Experimental testing and observation
- Intuition and guesswork
- Reliance on historical mathematical principles
- Discovery of properties of abstract objects and use of pure reason to prove them (correct)
What do proofs in mathematics consist of according to the text?
What do proofs in mathematics consist of according to the text?
- Appeal to authority and tradition
- Reliance on empirical evidence
- Trial and error approach
- Succession of applications of deductive rules to already established results (correct)
What are the entities in modern mathematics stipulated to have certain properties called?
What are the entities in modern mathematics stipulated to have certain properties called?
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What does most mathematical activity involve according to the text?
What does most mathematical activity involve according to the text?
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