History of Mathematics: Renaissance Europe

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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?

Greek materials 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?

F. de Viete Signup and view all the answers

Who introduced the Hindu-Arabic numeral system to Europe?

Fibonacci Signup and view all the answers

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

Roman numerals were difficult to write Signup and view all the answers

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

The invention of the derivative Signup and view all the answers

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

It is the Fundamental Theorem of Calculus Signup and view all the answers

When did original research in Mathematics start in Europe?

After 1500 Signup and view all the answers

Who found the roots of 3rd degree polynomials algebraically?

Tartaglia Signup and view all the answers

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

After French Revolution Signup and view all the answers

How did mathematics enter into Europe?

Through three different means including Christians, students, and Andalusia Signup and view all the answers

What was unique about Cordoba in the 11th century?

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

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

Students came together in communities called 'universita' Signup and view all the answers

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

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

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

Many scientific resources were translated into Latin Signup and view all the answers

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

University of Cologne in Germany Signup and view all the answers

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

Euler Signup and view all the answers

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

It entered a new era Signup and view all the answers

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

It became a universal scientific method Signup and view all the answers

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

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

How many pages of scientific research did Euler prepare?

Over 30,000 pages Signup and view all the answers

Where did Euler spend his life?

Petersburg and Berlin Signup and view all the answers

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

Inconsistent use of the term 'infinitely small' Signup and view all the answers

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

Function Signup and view all the answers

What was Cauchy's contribution to Mathematics?

Defining the concept of limit Signup and view all the answers

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

It was not born yet Signup and view all the answers

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

Because it was considered the inverse of derivative Signup and view all the answers

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

It was not understood Signup and view all the answers

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

Cauchy Signup and view all the answers

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

Dirichlet Signup and view all the answers

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

Number Theory, Differential Geometry, Mathematical Physics, and Astronomy Signup and view all the answers

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

The crisis due to 'infinitesimally small' Signup and view all the answers

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

The Fundamental Theorem of Algebra Signup and view all the answers

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

Riemann Integral, Riemann Surfaces, Riemann Geometry, and Topology Signup and view all the answers

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

Gauss Signup and view all the answers

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

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

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

The notion of functions Signup and view all the answers

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

Cauchy, Riemann, and Weierstrass Signup and view all the answers

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

The use of infinitesimally small quantities Signup and view all the answers

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

Gauss Signup and view all the answers

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

He defined the concept of functions Signup and view all the answers

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

All of the above Signup and view all the answers

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

He proved the Fundamental Theorem of Algebra Signup and view all the answers

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

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

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

Gauss Signup and view all the answers

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

Differential Geometry Signup and view all the answers

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

It resolved the crisis due to infinitesimally small quantities Signup and view all the answers

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

Theory of Complex Functions Signup and view all the answers

History of Mathematics: Renaissance Europe

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Questions and Answers

Who independently found the relation between derivative and integral?

What was introduced by René Descartes?

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

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

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

Who introduced the Hindu-Arabic numeral system to Europe?

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

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

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

When did original research in Mathematics start in Europe?

Who found the roots of 3rd degree polynomials algebraically?

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

How did mathematics enter into Europe?

What was unique about Cordoba in the 11th century?

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

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

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

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

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

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

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

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

How many pages of scientific research did Euler prepare?

Where did Euler spend his life?

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

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

What was Cauchy's contribution to Mathematics?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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