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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?
- Calculus, trigonometry, statistics, and probability
- Logic, set theory, combinatorics, and differential equations
- Arithmetic, calculus, topology, and algebra
- Number theory, algebra, geometry, and analysis (correct)
What does most mathematical activity involve, according to the text?
What does most mathematical activity involve, according to the text?
- Discovery of properties of abstract objects and the use of pure reason to prove them (correct)
- Application of statistical methods to solve problems
- Experimental observation of natural phenomena
- Memorization of formulas and algorithms
What do mathematical objects consist of in modern mathematics?
What do mathematical objects consist of in modern mathematics?
- Physical representations of mathematical concepts
- Random collections of numbers and symbols
- Abstractions from nature or entities stipulated to have certain properties (correct)
- 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 considered as starting points of a mathematical theory in modern mathematics?
What are considered as starting points of a mathematical theory in modern mathematics?
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