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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, differential equations, combinatorics, and topology
- Calculus, statistics, trigonometry, and topology
- Arithmetic, calculus, algebra, and probability
- 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)
- Memorization of formulas and the application of algorithms
- Application of statistical methods to analyze data
- Experimentation with physical objects and observation of their behavior
What do mathematical proofs consist of?
What do mathematical proofs consist of?
- A series of experiments to validate hypotheses
- A collection of empirical observations
- A succession of applications of deductive rules to already established results (correct)
- An iterative process of trial and error
What are the topics included in the area of knowledge of mathematics?
What are the topics included in the area of knowledge of mathematics?
What are mathematical objects stipulated to have in modern mathematics?
What are mathematical objects stipulated to have in modern mathematics?
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