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What are the major subdisciplines of modern mathematics?
What are the major subdisciplines of modern mathematics?
- Logic, differential equations, combinatorics, and set theory
- Arithmetic, calculus, topology, and algebra
- Number theory, algebra, geometry, and analysis (correct)
- Calculus, trigonometry, statistics, and probability
What does most mathematical activity involve?
What does most mathematical activity involve?
- Experimental testing of mathematical concepts in real-world scenarios
- Application of mathematical concepts in engineering and technology
- Discovery of properties of abstract objects and the use of pure reason to prove them (correct)
- Memorization of mathematical formulas and theorems
What do mathematical objects consist of in modern mathematics?
What do mathematical objects consist of in modern mathematics?
- Entities that are stipulated to have certain properties, called axioms (correct)
- Randomly selected elements from the real number line
- Empirical data collected from mathematical experiments
- Physical representations of natural phenomena
What does a proof in mathematics consist of?
What does a proof in mathematics consist of?
What is the nature of mathematical activity according to the text?
What is the nature of mathematical activity according to the text?
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