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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?
- Number theory, algebra, geometry, and analysis (correct)
- Arithmetic, calculus, statistics, and trigonometry
- Logic, topology, calculus, and probability
- Algebra, arithmetic, calculus, and geometry
What is the primary method used in mathematical activity, as per the text?
What is the primary method used in mathematical activity, as per the text?
- Discovery of properties of abstract objects and use of pure reason to prove them (correct)
- Observation of natural phenomena and inductive reasoning
- Application of statistical analysis and data interpretation
- Experimentation and empirical evidence
What do mathematical proofs consist of, according to the text?
What do mathematical proofs consist of, according to the text?
- An iterative process of refining hypotheses
- A succession of applications of deductive rules to already established results (correct)
- A series of experimental trials and observations
- A collection of anecdotal evidence and case studies
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 most mathematical activity, according to the text?
What is the nature of most mathematical activity, according to the text?
Which major subdiscipline of modern mathematics is concerned with quantities and their changes?
Which major subdiscipline of modern mathematics is concerned with quantities and their changes?
What do mathematicians use to prove properties of abstract objects?
What do mathematicians use to prove properties of abstract objects?
What are the entities in modern mathematics stipulated to have certain properties called?
What are the entities in modern mathematics stipulated to have certain properties called?
What does a proof in mathematics consist of?
What does a proof in mathematics consist of?
What does most mathematical activity involve?
What does most mathematical activity involve?
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