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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?
- Calculus, statistics, trigonometry, and topology
- Probability, differential equations, set theory, and logic
- Number theory, algebra, geometry, and analysis (correct)
- Arithmetic, calculus, algebra, and geometry
What do mathematical proofs consist of, based on the text?
What do mathematical proofs consist of, based on the text?
- A series of experimental trials and observations
- An accumulation of anecdotal evidence
- A succession of applications of deductive rules to already established results (correct)
- An iterative process of refining hypotheses
What does most mathematical activity involve, according to the text?
What does most mathematical activity involve, according to the text?
- Empirical observation and experimental verification
- Intuitive guessing and trial-and-error methods
- Application of statistical methods to real-world problems
- Discovery of properties of abstract objects and the use of pure reason to prove them (correct)
What are the objects of mathematical proofs in modern mathematics?
What are the objects of mathematical proofs in modern mathematics?
What is the nature of the properties considered true starting points of the theory in modern mathematics?
What is the nature of the properties considered true starting points of the theory in modern mathematics?
What are the major subdisciplines of modern mathematics mentioned in the text?
What are the major subdisciplines of modern mathematics mentioned in the text?
What is the nature of the properties considered true starting points of the theory in modern mathematics?
What is the nature of the properties considered true starting points of the theory in modern mathematics?
What do mathematical proofs consist of, based on the text?
What do mathematical proofs consist of, based on the text?
What is the primary activity in most mathematical endeavors, as per the text?
What is the primary activity in most mathematical endeavors, as per the text?
What do mathematicians use to prove properties of abstract objects?
What do mathematicians use to prove properties of abstract objects?
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