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What are the major subdisciplines of modern mathematics?
What are the major subdisciplines of modern mathematics?
- Calculus, trigonometry, statistics, and probability
- Logic, set theory, combinatorics, and abstract algebra
- Number theory, algebra, geometry, and analysis (correct)
- Arithmetic, calculus, topology, and differential equations
What does most mathematical activity involve?
What does most mathematical activity involve?
- The approximation of real-world phenomena using mathematical models
- The collection of empirical data and the use of statistical analysis to draw conclusions
- The discovery of properties of abstract objects and the use of pure reason to prove them (correct)
- The development of new numerical methods and computational algorithms
What do proofs in mathematics consist of?
What do proofs in mathematics consist of?
- Experimental evidence obtained through scientific observation
- Numerical simulations and computational analyses
- A succession of applications of deductive rules to already established results (correct)
- The formulation of conjectures based on patterns observed in data
In which academic disciplines is mathematics essential?
In which academic disciplines is mathematics essential?
What are the fundamental truths of mathematics independent from?
What are the fundamental truths of mathematics independent from?
What do mathematicians use to prove properties of abstract objects?
What do mathematicians use to prove properties of abstract objects?
What is the narrower and more technical meaning of the word 'mathematics' in Classical times?
What is the narrower and more technical meaning of the word 'mathematics' in Classical times?
Which mathematical problem had no practical application before its use in the RSA cryptosystem?
Which mathematical problem had no practical application before its use in the RSA cryptosystem?
What did the word 'mathēmatikḗ tékhnē' mean in Latin?
What did the word 'mathēmatikḗ tékhnē' mean in Latin?
Who were likely the first to constrain the use of the word 'mathematics' to just the study of arithmetic and geometry?
Who were likely the first to constrain the use of the word 'mathematics' to just the study of arithmetic and geometry?
What led to a correlated increase in the development of both mathematical innovations and scientific discoveries?
What led to a correlated increase in the development of both mathematical innovations and scientific discoveries?
What did Saint Augustine's warning about 'mathematici' mean?
What did Saint Augustine's warning about 'mathematici' mean?
What were areas of mathematics such as statistics and game theory often grouped under?
What were areas of mathematics such as statistics and game theory often grouped under?
In which centuries were algebra and infinitesimal calculus introduced as new fields?
In which centuries were algebra and infinitesimal calculus introduced as new fields?
What does the word 'máthēma' mean in Ancient Greek?
What does the word 'máthēma' mean in Ancient Greek?
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