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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, trigonometry, statistics, and probability
- Logic, set theory, combinatorics, and differential equations
- Arithmetic, calculus, topology, and algebra
- Number theory, algebra, geometry, and analysis (correct)
What does most mathematical activity involve according to the text?
What does most mathematical activity involve according to the text?
- Discovery of properties of abstract objects and the use of pure reason to prove them (correct)
- Experimental testing and application of mathematical concepts
- Memorization of mathematical formulas and algorithms
- Intuitive guessing and approximation of mathematical solutions
What do proofs in mathematics consist of according to the text?
What do proofs in mathematics consist of according to the text?
- A succession of applications of deductive rules to already established results (correct)
- An accumulation of experimental evidence supporting a mathematical statement
- A demonstration of practical applications of mathematical concepts
- A series of logical guesses leading to a probable conclusion
What are the entities in modern mathematics stipulated to have according to the text?
What are the entities in modern mathematics stipulated to have according to the text?
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What do abstract objects in mathematics consist of according to the text?
What do abstract objects in mathematics consist of according to the text?
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