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What are the major subdisciplines of modern mathematics as represented in the text?
What are the major subdisciplines of modern mathematics as represented in the text?
- Logic, differential equations, combinatorics, and set theory
- Calculus, trigonometry, algebra, and statistics
- Number theory, algebra, geometry, and analysis (correct)
- Arithmetic, calculus, topology, and probability
What does most mathematical activity involve?
What does most mathematical activity involve?
- Memorization of formulas and algorithms
- Experimental testing of mathematical conjectures
- 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 do proofs in mathematics consist of?
What do proofs in mathematics consist of?
- A series of experimental demonstrations
- A succession of applications of deductive rules to already established results (correct)
- Logical guesses based on observed patterns
- A collection of statistical data supporting a hypothesis
What are the entities in modern mathematics stipulated to have?
What are the entities in modern mathematics stipulated to have?
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What do the results in mathematical proofs include?
What do the results in mathematical proofs include?
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