History of Mathematics: Renaissance Europe

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

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 (D)</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 (B)</p> Signup and view all the answers

Who introduced the Hindu-Arabic numeral system to Europe?

<p>Fibonacci (A)</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 (C)</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 (D)</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 (A)</p> Signup and view all the answers

When did original research in Mathematics start in Europe?

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

Who found the roots of 3rd degree polynomials algebraically?

<p>Tartaglia (D)</p> Signup and view all the answers

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

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

How did mathematics enter into Europe?

<p>Through three different means including Christians, students, and Andalusia (D)</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 (B)</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' (A)</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 (D)</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 (D)</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 (D)</p> Signup and view all the answers

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

<p>Euler (C)</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 (D)</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 (D)</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 (C)</p> Signup and view all the answers

How many pages of scientific research did Euler prepare?

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

Where did Euler spend his life?

<p>Petersburg and Berlin (D)</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' (C)</p> Signup and view all the answers

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

<p>Function (D)</p> Signup and view all the answers

What was Cauchy's contribution to Mathematics?

<p>Defining the concept of limit (C)</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 (C)</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 (C)</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 (B)</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 (B)</p> Signup and view all the answers

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

<p>Dirichlet (B)</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 (C)</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' (A)</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 (D)</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 (D)</p> Signup and view all the answers

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

<p>Gauss (D)</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' (A)</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 (B)</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 (D)</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 (A)</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 (A)</p> Signup and view all the answers

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

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

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

<p>All of the above (D)</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 (A)</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 (C)</p> Signup and view all the answers

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

<p>Gauss (A)</p> Signup and view all the answers

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

<p>Differential Geometry (B)</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 (A)</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 (C)</p> Signup and view all the answers

Flashcards are hidden until you start studying

Related Documents

More Like This

Use Quizgecko on...
Browser
Browser