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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?
- Algebra, calculus, topology, and probability
- Arithmetic, calculus, statistics, and trigonometry
- Number theory, algebra, geometry, and analysis (correct)
- Number theory, geometry, calculus, and statistics
What is the primary method of mathematical activity mentioned in the text?
What is the primary method of mathematical activity mentioned in the text?
- Collection and analysis of empirical data
- Discovery of properties of abstract objects and use of pure reason to prove them (correct)
- Intuitive guessing and approximation
- Experimental testing and observation
What are the objects of mathematical study in modern mathematics?
What are the objects of mathematical study in modern mathematics?
- Physical objects and observable phenomena
- Social constructs and human behaviors
- Historical artifacts and cultural symbols
- Abstractions from nature or entities stipulated to have certain properties (correct)
What does a proof in mathematics consist of, according to the text?
What does a proof in mathematics consist of, according to the text?
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What is the role of axioms in modern mathematics, as mentioned in the text?
What is the role of axioms in modern mathematics, as mentioned in the text?
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