Mathematics: Numbers, Formulas, and Structures Quiz

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What are the major subdisciplines of modern mathematics?

Probability, linear algebra, differential equations, and discrete mathematics

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

Abstract algebra, combinatorics, set theory, and logic

Calculus, trigonometry, statistics, and topology

What is the main activity involved in mathematics?

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

Experimental testing of hypotheses and empirical validation

Modeling real-world phenomena using mathematical equations

Data collection and statistical analysis

What do mathematical proofs consist of?

Statistical analysis and hypothesis testing

Empirical evidence and experimental data

Conjectures and inductive reasoning

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

How are fundamental truths of mathematics related to scientific experimentation?

Independent from any scientific experimentation Signup and view all the answers

In which areas is mathematics essential?

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

What are mathematical objects stipulated to have?

Certain properties called axioms Signup and view all the answers

What is the etymological meaning of the word 'mathematics'?

That which is learnt or what one gets to know Signup and view all the answers

Which areas of mathematics are often grouped under applied mathematics?

Statistics and game theory Signup and view all the answers

What problem had no practical application before its use in the RSA cryptosystem?

The problem of integer factorization Signup and view all the answers

What was primarily divided into geometry and arithmetic until the 16th and 17th centuries?

Manipulation of natural numbers and fractions Signup and view all the answers

What does the adjective 'mathēmatikós' mean?

Related to learning or studious Signup and view all the answers

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

Astrology Signup and view all the answers

What did Saint Augustine's warning about 'mathematici' actually refer to?

'Astrologers' or 'astronomers' Signup and view all the answers

Who likely constrained the use of the word 'mathematics' to just the study of arithmetic and geometry?

Pythagoras Signup and view all the answers

What did the foundational crisis of mathematics lead to at the end of the 19th century?

'Systematization of the axiomatic method' Signup and view all the answers