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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, statistics, and logic
- Arithmetic, calculus, topology, and probability
- Calculus, statistics, trigonometry, and logic
- Number theory, algebra, geometry, and analysis (correct)
What does most mathematical activity involve?
What does most mathematical activity involve?
- Application of statistical methods to real-world problems
- Memorization of formulas and algorithms
- Collection of data and experimental testing
- Discovery of properties of abstract objects and the use of pure reason to prove them (correct)
What do mathematical objects consist of in modern mathematics?
What do mathematical objects consist of in modern mathematics?
- Only abstractions from nature
- Entities derived from practical applications
- Either abstractions from nature or entities stipulated to have certain properties (correct)
- Only entities stipulated to have certain properties
What does a proof in mathematics consist of?
What does a proof in mathematics consist of?
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What are considered the starting points of a mathematical theory in the case of abstraction from nature?
What are considered the starting points of a mathematical theory in the case of abstraction from nature?
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