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Mathematics: Understanding the Fundamentals

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Mathematics: Understanding the Fundamentals

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Questions and Answers

What are the major subdisciplines of modern mathematics as mentioned in the text?

Set theory, combinatorics, calculus, and logic

Differential equations, linear algebra, probability, and discrete mathematics

Number theory, algebra, geometry, and analysis (correct)

Calculus, statistics, trigonometry, and topology

What is the primary activity in mathematics according to the text?

Experimental testing of mathematical theories

Development of mathematical software and tools

Application of mathematical models to natural phenomena

Discovery of properties of abstract objects and use of pure reason to prove them (correct)

What do proofs in mathematics consist of?

Visual demonstrations and experiments

A succession of applications of deductive rules to already established results (correct)

Statistical analysis and probability calculations

Empirical evidence and experimental data

What are the fundamental truths of mathematics independent from according to the text?

Any scientific experimentation Signup and view all the answers

In which fields is mathematics essential according to the text?

Natural sciences, engineering, medicine, finance, computer science, and social sciences Signup and view all the answers

What do mathematicians not have a general consensus about according to the text?

A common definition for their academic discipline Signup and view all the answers

Which of the following best describes the relationship between applied mathematics and pure mathematics?

Applied mathematics is developed independently from any application, while pure mathematics is developed in close correlation with applications. Signup and view all the answers

What did the problem of integer factorization, dating back to Euclid in 300 BC, have no practical application before?

Its use in the RSA cryptosystem Signup and view all the answers

When did algebra and infinitesimal calculus become introduced as new fields of mathematics?

16th and 17th centuries Signup and view all the answers

What does the word 'mathematics' come from?

Ancient Greek máthēma (μάθημα) Signup and view all the answers

What did the term 'mathematics' more commonly mean in Latin and English until around 1700?

Astrology Signup and view all the answers

What does the word mathēmatikḗ tékhnē (μαθηματικὴ τέχνη) refer to?

'The mathematical art' Signup and view all the answers

What did one of the two main schools of thought in Pythagoreanism, known as the mathēmatikoi (μαθηματικοί), mean at the time?

'Learners' rather than 'mathematicians' in the modern sense Signup and view all the answers

What did Saint Augustine's warning about mathematici mean?

'Astrologers' Signup and view all the answers

'Mathematical study' had what meaning even in Classical times?

'That which is learnt', 'what one gets to know', hence also 'study' and 'science' Signup and view all the answers