Overview of Mathematics
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Questions and Answers

What are the major subdisciplines of modern mathematics?

  • Calculus, statistics, trigonometry, and logic
  • Differential equations, topology, probability, and combinatorics
  • Linear algebra, discrete mathematics, set theory, and logic
  • Number theory, algebra, geometry, and analysis (correct)
  • What is the most common activity in mathematics?

  • Discovery of properties of abstract objects and use of pure reason to prove them (correct)
  • Application of statistical methods to analyze data
  • Experimentation and testing of mathematical theories
  • Measurement and quantification of natural phenomena
  • What do mathematical proofs consist of?

  • A series of experiments and observations leading to a conclusion
  • A succession of applications of deductive rules to already established results (correct)
  • A collection of mathematical formulas and equations
  • An analysis of statistical data to support a hypothesis
  • What are the fundamental truths of mathematics independent from?

    <p>Any scientific experimentation</p> Signup and view all the answers

    In which fields is mathematics essential?

    <p>Natural sciences, engineering, medicine, finance, computer science, and social sciences</p> Signup and view all the answers

    What are the entities in modern mathematics stipulated to have?

    <p>Certain properties called axioms</p> Signup and view all the answers

    What was the problem of integer factorization used for before its application in the RSA cryptosystem?

    <p>It had no practical application.</p> Signup and view all the answers

    In Ancient Greek, what does the word 'mathematics' (máthēma) mean?

    <p>That which is learned, study, and science.</p> Signup and view all the answers

    During which centuries were algebra and infinitesimal calculus introduced as new fields in mathematics?

    <p>16th and 17th centuries</p> Signup and view all the answers

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

    <p>Astrology</p> Signup and view all the answers

    What did mathēmatikḗ tékhnē (μαθηματικὴ τέχνη) mean in Ancient Greek?

    <p>The mathematical art</p> Signup and view all the answers

    What did mathēmatikós (μαθηματικός) mean in Ancient Greek?

    <p>'Related to learning' or 'studious'</p> Signup and view all the answers

    What did mathēmatikoi (μαθηματικοί) mean in Ancient Greek?

    <p>'Learners'</p> Signup and view all the answers

    When was the foundational crisis of mathematics that led to the systematization of the axiomatic method?

    <p>19th century</p> Signup and view all the answers

    'Mathematics' in Latin gradually changed to its present meaning from about which century to which century?

    <p>1400 to 1600</p> Signup and view all the answers

    'Mathematics' in English gradually changed to its present meaning from about which century to which century?

    <p>-1500 to -1300</p> Signup and view all the answers

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