History of Mathematics: Renaissance Europe
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Questions and Answers

Who independently found the relation between derivative and integral?

  • Isaac Newton and Gottfried Leibniz (correct)
  • F. de Viete and S. al-Tusi
  • Tartaglia and Cardano
  • Pierre de Fermat and René Descartes

    • What was introduced by René Descartes?

  • Algebra problems with letters
  • The Fundamental Theorem of Calculus
  • Analytical Geometry and cartesian coordinate system (correct)
  • The concept of derivative

    • In which century did the golden era of Mathematics begin in Europe?

  • 17th century (correct)
  • 18th century
  • 19th century
  • 16th century

    • What was the primary resource for research in Europe after 1450?

    <p>Greek materials</p> Signup and view all the answers

    Who used letters such as a, b, c for constants and x, y for unknowns for the first time?

    <p>F. de Viete</p> Signup and view all the answers

    Who introduced the Hindu-Arabic numeral system to Europe?

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

    What made it difficult to develop science in Europe before the 16th century?

    <p>Roman numerals were difficult to write</p> Signup and view all the answers

    What was the significance of Pierre de Fermat's invention in 1636?

    <p>The invention of the derivative</p> Signup and view all the answers

    What was the significance of the relation between derivative and integral?

    <p>It is the Fundamental Theorem of Calculus</p> Signup and view all the answers

    When did original research in Mathematics start in Europe?

    <p>After 1500</p> Signup and view all the answers

    Who found the roots of 3rd degree polynomials algebraically?

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

    When did the Hindu-Arabic numeral system become widely used in public?

    <p>After French Revolution</p> Signup and view all the answers

    How did mathematics enter into Europe?

    <p>Through three different means including Christians, students, and Andalusia</p> Signup and view all the answers

    What was unique about Cordoba in the 11th century?

    <p>It had a central library with a collection of 400 thousand books</p> Signup and view all the answers

    What happened in the middle of the 12th century in Italy?

    <p>Students came together in communities called 'universita'</p> Signup and view all the answers

    What was the significance of Andalusia in the history of mathematics?

    <p>It was the biggest factor in the spread of mathematics to Europe</p> Signup and view all the answers

    What was the outcome of the Bishop of Toledo's translation group?

    <p>Many scientific resources were translated into Latin</p> Signup and view all the answers

    Which of the following universities was established as a result of these developments?

    <p>University of Cologne in Germany</p> Signup and view all the answers

    What is the name of the scientist described as the most productive in human history?

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

    What was the impact of the invention of the derivative on Physics and Mathematics?

    <p>It entered a new era</p> Signup and view all the answers

    What was the outcome of Euler's work in Mathematical Analysis?

    <p>It became a universal scientific method</p> Signup and view all the answers

    What was the scope of Euler's application of Calculus?

    <p>In numerous areas from Number Theory to Differential Equations and applications in Engineering</p> Signup and view all the answers

    How many pages of scientific research did Euler prepare?

    <p>Over 30,000 pages</p> Signup and view all the answers

    Where did Euler spend his life?

    <p>Petersburg and Berlin</p> Signup and view all the answers

    What was the main reason behind the crisis in Mathematics at the beginning of the 1800s?

    <p>Inconsistent use of the term 'infinitely small'</p> Signup and view all the answers

    What was not properly defined in the 1800s, leading to its use in different contexts?

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

    What was Cauchy's contribution to Mathematics?

    <p>Defining the concept of limit</p> Signup and view all the answers

    What was the status of the theory of complex functions in the 1800s?

    <p>It was not born yet</p> Signup and view all the answers

    Why was integration not studied independently from derivative in the 1800s?

    <p>Because it was considered the inverse of derivative</p> Signup and view all the answers

    What was the status of the understanding of function continuity in the 1800s?

    <p>It was not understood</p> Signup and view all the answers

    Who, along with Riemann and Weierstrass, contributed to the creation of the Theory of Complex Functions?

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

    Who defined the notion of functions, which ended a factor in the crisis in Mathematics?

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

    What was the area of Mathematics to which Gauss made significant contributions?

    <p>Number Theory, Differential Geometry, Mathematical Physics, and Astronomy</p> Signup and view all the answers

    What did Cauchy's work save the society of Mathematics from?

    <p>The crisis due to 'infinitesimally small'</p> Signup and view all the answers

    What is the name of the theorem proved by Gauss, which was a great advancement in the century?

    <p>The Fundamental Theorem of Algebra</p> Signup and view all the answers

    What was the area of Mathematics to which Riemann made significant contributions?

    <p>Riemann Integral, Riemann Surfaces, Riemann Geometry, and Topology</p> Signup and view all the answers

    Who is considered one of the greatest scientists of all time?

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

    What was the significance of Cauchy's work in Mathematics?

    <p>He saved the society of Mathematics from the crisis due to 'infinitesimally small'</p> Signup and view all the answers

    What was the area of Mathematics to which Dirichlet made a significant contribution?

    <p>The notion of functions</p> Signup and view all the answers

    Who were the three mathematicians who worked together to create the Theory of Complex Functions?

    <p>Cauchy, Riemann, and Weierstrass</p> Signup and view all the answers

    What was the primary crisis in Mathematics that Cauchy's work solved?

    <p>The use of infinitesimally small quantities</p> Signup and view all the answers

    Who among the following mathematicians did not contribute to the creation of the Theory of Complex Functions?

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

    What was the significance of Dirichlet's contribution to Mathematics?

    <p>He defined the concept of functions</p> Signup and view all the answers

    What was the area of Mathematics that Riemann primarily contributed to?

    <p>All of the above</p> Signup and view all the answers

    What was the significance of Gauss's contribution to Mathematics?

    <p>He proved the Fundamental Theorem of Algebra</p> Signup and view all the answers

    What was the outcome of the crisis in Mathematics in the 1800s?

    <p>The resolution of the crisis due to Cauchy's work</p> Signup and view all the answers

    Who is considered one of the greatest scientists of all time, according to the text?

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

    What was the primary area of contribution of Riemann to Mathematics?

    <p>Differential Geometry</p> Signup and view all the answers

    What was the significance of Cauchy's work in saving the society of Mathematics?

    <p>It resolved the crisis due to infinitesimally small quantities</p> Signup and view all the answers

    What was the area of Mathematics that Cauchy, Riemann, and Weierstrass contributed to together?

    <p>Theory of Complex Functions</p> Signup and view all the answers

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