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Correction/Évariste Galois
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Message de georges33 posté le 12-11-2017 à 11:54:45 (S | E | F)
Bonjour à tous, en DNL (mathématiques en anglais) on doit faire un exposé oral sur un mathématicien mais le prof nous a donné le sujet la semaine dernière et je passe demain. Si quelqu'un pouvait corriger les fautes d'anglais dans mon script, en particulier les his ou its.
Je vous remercie d'avance.
Évariste Galois was born near Paris on October 25th, 1811. He lives in an rich enough family and he receives a Latin culture. When he was twelve years, Évariste gets into Louis-le-Grand then he gets into class of first year preparatory mathematics. He reads lots of books of big mathematicians as Euler, Gauss and Jacobi. He gets the first prize in the Competitive examination of mathematics. His passion for the mathematics leads him to abandon the studies. In 1828, he fails in the entrance examination for the Ecole polytechnique and in October he gets into special mathematics class in school of Louis-le-grand. When he is 17 years, he publishes his first articles in mathematical magazines. In 1829, his father commits suicide and he fails a second time in the entrance examination for the Ecole polytechnique. According to the legend, the examiner would have asked him a question on the logarithms and Galois would have him throw the rag to the head because the question was too stupid. Thus he gets into the ENS. In 1830, he writes a brief and he presents it to the Academy of Science to compete to the Big Price of mathematics but his brief is lost and so he will not receive the price. He publishes then in the general and universal Bulletin of announcements and new scientists. This one want to disseminate everywhere knowledge and scientific discoveries. But times change, he participates in demonstrations against Charles X which accumulates unpopular measures as the abolition of the freedom of the media. Indeed, Galois is a republican ready to defend the rights of the people. However, he can’t participate in 3 Glorious, which are important days of uprising, because he does
his examination of license. At the end of 1830, he publishes two letter in the Newspaper of schools.In the first one, he mokes of the director of the ENS because he made available his pupils to the government of Louis-Philippe considered as a usurper by the Republicans. In the second he criticizes the way of teaching. According to him, the school system teaches to the pupils to reproduce a knowledge rather than to form them to think. Thus he is excluded from his school.
In 1831, he begins to give lessons of superior algebra but there will be only few sessions. He decides then to write a new version of the brief lost to present it to the Academy of Science. Unfortunately, it brief is considered dark because his reasonings were not enough developed. When Louis-Philippe comes to power after the 3 Glorious, he departs the republicans of the power. Galois demonstrates then in July, 1931, but he is arrested at the head of several hundred demonstrators. He is condemned to 9 months of prison. He decides in December, 1931 to publish a new time it work since it prison. But the foreword is too polemical and the complete text is forbidden to be published. He criticizes then the egoism of the political and scientific men.
In 1832, because of a epidemic of cholera in Paris, He is transfered in a pension to finish his punishment there. When he leaves prison, he meets a young woman but she breaks. This create a duel with another man. The day before the duel, Galois drafts lots of letters in which he explains that he didn’t have time to end his mathematical works. He is hurt in the belly during this duel and is send to the hospital. He dies the next day, on May 31st, 1932 when he is 21 years old. His friends republicans prepares an uprising which will take place a few days later, it is the Republican uprising in Paris. The Republicans try to knock down the July Monarchy. All his works are published in 1846.
His main realizations are the theorem of the primitive element, the theory of Galois and the theory of the groups. He also gives a new vision of the theory of the equations. I am briefly going to explain you the theory of the groups on which bases many of its demonstrations. Galois was inspired by Lagrange to define a group.
A group is one set respecting 4 rules. G a set, a, b and c are anything and they belong to G and is an operation.
- the first rule is a law of internal composition, for all a and b elements of G, the result a · b is also an element of G.
- The second rule is the associativity, for any elements a, b and c of G, the equality (a · b) · c = a · · c).
- Then, the third rule is the neutral element e of G such as, for everything a of G, e · a = a · e = a.
- finally, the fourth rule is called symmetric, for every a, there is b such as a + b = b + a = 0. B is called the symmetric element of a.
Example: let us verify if the set of the relatives integers (Z; +) is a group. + is the addition. For any integers a and b, a+b is also an integer, the law of internal composition is verified. For any integers a, b and c, (a + b) + c = a + (b + c), the associativity is verified. If a is an integer, then 0 + a = a + 0 = a. Zero is the neutral element for the addition. Finally, for any a, there is an integer b such as a + b = b + a = 0. All the rules are verified (Z; +) is a group. But for example (N; +) isn’t a group because the symmetric isn’t verified. It is thanks to the groups that Galois demonstrates that one polynomials of degree upper to 4 can’t be solved by radicals.Polynomials are the shape: (picture)
Solve a polynomial equation consists in finding the roots of polynomials. We saw how find the roots of the quadratics functions by using the method of delta. For degree 3, we use the method of Cardan and for the degree 4 there is the method of Descartes. These methods are general, they are true for any polynomials of the corresponding degree.For a long time we could ask ourselves the question " there is one method to find the roots of one polynomials of degrees n ". The answer is no. From a polynomial of degree upper to 4 we can’t find roots by using a method which is true for all the polynomials. Galois was one of the first to prove it thanks to the groups.
In conclusion, Galois was in his time a not understood genius ahead on his time. His very abstract works were rehabilitated in the second half of XIX century when the mathematicians had the tools to understand him. His works will influence the big ideas of the mathematics of the twentieth century.
-------------------
Modifié par lucile83 le 12-11-2017 12:28
Message de georges33 posté le 12-11-2017 à 11:54:45 (S | E | F)
Bonjour à tous, en DNL (mathématiques en anglais) on doit faire un exposé oral sur un mathématicien mais le prof nous a donné le sujet la semaine dernière et je passe demain. Si quelqu'un pouvait corriger les fautes d'anglais dans mon script, en particulier les his ou its.
Je vous remercie d'avance.
Évariste Galois was born near Paris on October 25th, 1811. He lives in an rich enough family and he receives a Latin culture. When he was twelve years, Évariste gets into Louis-le-Grand then he gets into class of first year preparatory mathematics. He reads lots of books of big mathematicians as Euler, Gauss and Jacobi. He gets the first prize in the Competitive examination of mathematics. His passion for the mathematics leads him to abandon the studies. In 1828, he fails in the entrance examination for the Ecole polytechnique and in October he gets into special mathematics class in school of Louis-le-grand. When he is 17 years, he publishes his first articles in mathematical magazines. In 1829, his father commits suicide and he fails a second time in the entrance examination for the Ecole polytechnique. According to the legend, the examiner would have asked him a question on the logarithms and Galois would have him throw the rag to the head because the question was too stupid. Thus he gets into the ENS. In 1830, he writes a brief and he presents it to the Academy of Science to compete to the Big Price of mathematics but his brief is lost and so he will not receive the price. He publishes then in the general and universal Bulletin of announcements and new scientists. This one want to disseminate everywhere knowledge and scientific discoveries. But times change, he participates in demonstrations against Charles X which accumulates unpopular measures as the abolition of the freedom of the media. Indeed, Galois is a republican ready to defend the rights of the people. However, he can’t participate in 3 Glorious, which are important days of uprising, because he does
his examination of license. At the end of 1830, he publishes two letter in the Newspaper of schools.In the first one, he mokes of the director of the ENS because he made available his pupils to the government of Louis-Philippe considered as a usurper by the Republicans. In the second he criticizes the way of teaching. According to him, the school system teaches to the pupils to reproduce a knowledge rather than to form them to think. Thus he is excluded from his school.
In 1831, he begins to give lessons of superior algebra but there will be only few sessions. He decides then to write a new version of the brief lost to present it to the Academy of Science. Unfortunately, it brief is considered dark because his reasonings were not enough developed. When Louis-Philippe comes to power after the 3 Glorious, he departs the republicans of the power. Galois demonstrates then in July, 1931, but he is arrested at the head of several hundred demonstrators. He is condemned to 9 months of prison. He decides in December, 1931 to publish a new time it work since it prison. But the foreword is too polemical and the complete text is forbidden to be published. He criticizes then the egoism of the political and scientific men.
In 1832, because of a epidemic of cholera in Paris, He is transfered in a pension to finish his punishment there. When he leaves prison, he meets a young woman but she breaks. This create a duel with another man. The day before the duel, Galois drafts lots of letters in which he explains that he didn’t have time to end his mathematical works. He is hurt in the belly during this duel and is send to the hospital. He dies the next day, on May 31st, 1932 when he is 21 years old. His friends republicans prepares an uprising which will take place a few days later, it is the Republican uprising in Paris. The Republicans try to knock down the July Monarchy. All his works are published in 1846.
His main realizations are the theorem of the primitive element, the theory of Galois and the theory of the groups. He also gives a new vision of the theory of the equations. I am briefly going to explain you the theory of the groups on which bases many of its demonstrations. Galois was inspired by Lagrange to define a group.
A group is one set respecting 4 rules. G a set, a, b and c are anything and they belong to G and is an operation.
- the first rule is a law of internal composition, for all a and b elements of G, the result a · b is also an element of G.
- The second rule is the associativity, for any elements a, b and c of G, the equality (a · b) · c = a · · c).
- Then, the third rule is the neutral element e of G such as, for everything a of G, e · a = a · e = a.
- finally, the fourth rule is called symmetric, for every a, there is b such as a + b = b + a = 0. B is called the symmetric element of a.
Example: let us verify if the set of the relatives integers (Z; +) is a group. + is the addition. For any integers a and b, a+b is also an integer, the law of internal composition is verified. For any integers a, b and c, (a + b) + c = a + (b + c), the associativity is verified. If a is an integer, then 0 + a = a + 0 = a. Zero is the neutral element for the addition. Finally, for any a, there is an integer b such as a + b = b + a = 0. All the rules are verified (Z; +) is a group. But for example (N; +) isn’t a group because the symmetric isn’t verified. It is thanks to the groups that Galois demonstrates that one polynomials of degree upper to 4 can’t be solved by radicals.Polynomials are the shape: (picture)
Solve a polynomial equation consists in finding the roots of polynomials. We saw how find the roots of the quadratics functions by using the method of delta. For degree 3, we use the method of Cardan and for the degree 4 there is the method of Descartes. These methods are general, they are true for any polynomials of the corresponding degree.For a long time we could ask ourselves the question " there is one method to find the roots of one polynomials of degrees n ". The answer is no. From a polynomial of degree upper to 4 we can’t find roots by using a method which is true for all the polynomials. Galois was one of the first to prove it thanks to the groups.
In conclusion, Galois was in his time a not understood genius ahead on his time. His very abstract works were rehabilitated in the second half of XIX century when the mathematicians had the tools to understand him. His works will influence the big ideas of the mathematics of the twentieth century.
-------------------
Modifié par lucile83 le 12-11-2017 12:28
Réponse : Correction/Évariste Galois de laure95, postée le 12-11-2017 à 17:01:30 (S | E)
Bonjour,
Comme c'est une biographie,en plus d'une personne décédée, tous les verbes doivent être mis au PASSE. Donc, il faut reconjuguer tous les verbes. Mes remarques ne porteront donc pas sur la conjugaison.
- He lives in an (a + mot commençant par une consonne)rich enough family and he receives (passé)a Latin culture.
- When he was twelve years : enlever years ou ajouter old.
- Évariste gets into Louis-le-Grand (ajouter school)then he gets into class of first year preparatory mathematics. (mal construit)
- big (mal dit)mathematicians
- to abandon the (remplacer the par un possessif)studies.
- the Ecole polytechnique: mal dit.
- he gets into (article)special mathematics class
- in school of Louis-le-grand: mal construit.
- When he is 17 years,
- would have him throw: would have + participe passé.
- the price: pas le bon mot ici.
- verywhere knowledge: ordre des mots.
- But times (times = fois)change,
- Charles X which (pas le bon possessif)accumulates unpopular measures
- in (article)3 Glorious,
- because he does his examination (mal dit) of license.
- two letter: pluriel.
- in the Newspaper of schools: mal construit.
- it brief: ?
- it (possesif)work since it prison: ?
- a epidemic
- to the hospital: pas de the.
- His friends republicans: ordre des mots.
- on which bases many of its démonstrations: ordre des mots.
-Solve (gérondif)a polynomial
- We saw how (to) find.
- we could ask ourselves (chercher le verbe "se demander")the question
- a not understood Genius: mal construit.
- on (pas la bonne préposition) his time.
Réponse : Correction/Évariste Galois de georges33, postée le 12-11-2017 à 18:26:37 (S | E)
Je te remercie pour ta réponse
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