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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?
- Arithmetic, calculus, topology, and logic
- Number theory, algebra, geometry, and analysis (correct)
- Algebra, calculus, statistics, and geometry
- Calculus, trigonometry, statistics, and probability
What is the primary method used in mathematical activity, as described in the text?
What is the primary method used in mathematical activity, as described in the text?
- Intuitive guessing and trial-and-error methods
- Discovery of properties of abstract objects and use of pure reason to prove them (correct)
- Collection of empirical data and statistical analysis
- Experimentation with physical objects and observation of patterns
What do proofs in mathematics consist of, according to the text?
What do proofs in mathematics consist of, according to the text?
- A series of experimental trials leading to a conclusion
- A succession of applications of deductive rules to already established results (correct)
- A set of assumptions based on personal beliefs
- A collection of anecdotal evidence supporting a hypothesis
What are the objects involved in modern mathematics, as mentioned in the text?
What are the objects involved in modern mathematics, as mentioned in the text?
What is the nature of the general consensus among mathematicians regarding a common definition for their academic discipline, according to the text?
What is the nature of the general consensus among mathematicians regarding a common definition for their academic discipline, according to the text?
What is the formula for calculating the perimeter of a shape?
What is the formula for calculating the perimeter of a shape?
What is the perimeter of a circle or an ellipse called?
What is the perimeter of a circle or an ellipse called?
What practical application does the calculated perimeter have?
What practical application does the calculated perimeter have?
How can the perimeter of a wheel/circle be described?
How can the perimeter of a wheel/circle be described?
What is the mathematical representation for the distance around a shape?
What is the mathematical representation for the distance around a shape?
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