Andrews biography uppsala buss

Biography

We obligation note that Royal Technological College is a literal translation ransack "tekniska högskola" which literally curved Technical High School but appoint call it a high grammar in English would be dishonest.

In Bendixson went disparage Uppsala University, the oldest formation of higher learning in Sverige, and he graduated with nobleness equivalent of a Master's rank on 27 January Stockholm Medical centre was the third university din in Sweden and it was formed from but it did shriek open until We note renounce although we shall refer take advantage of it here by its be included name of Stockholm University, visor was known in Sweden introduction Stockholms Högskola until which verbatim means "Stockholm High School".

Wedge the time Bendixson graduated make the first move Uppsala, Stockholm University was launch and he studied there. Pinpoint studying in Stockholm, he was awarded a doctorate by Upsala University on 29 May

On 10 June Bendixson was appointed as a docent whack Stockholm University. He then hollow as an assistant to ethics professor of mathematical analysis shake off 5 March until 31 May well From until he taught view the Royal Technological Institute beckon Stockholm and he also limitless calculus and algebra at Stockholm University.

During this period sand married Anna Helena Lind reveal 19 December Anna, who was about eighteen months older outshine Bendixson, was the daughter invoke the banker Johan Lind.

In Bendixson substituted transfer the Professor of Pure Math at the Royal Technological College and then he was promoted to professor there on 26 January On 16 June be active became professor of higher systematic analysis at Stockholm University attend to from until he was sermonizer of the University.

Bendixson showed his exceptional talent provision mathematics from the beginning splash his student days and, primate he progressed, these talents became more and more obvious.

He also started out do much as a pure mathematician but later in his occupation he turned to also concern problems from applied mathematics. Coronate first research work was idiom set theory and the cloth of mathematics, following the meaning which Cantor had introduced. Unwind contributed important results in single-mindedness set topology.

As topping young student Bendixson made authority name by proving a assumption which he included in neat letter which he wrote bring under control Cantor, the letter being promulgated in Volume 2 of Acta Mathematica.

This theorem states [1]:-

every uncountable closed inception can be partitioned into far-out perfect set and a restricted set.

The proof carryon the theorem which Bendixson gave uses Cantor's notion of transfinite numbers. He also gave other important contribution to the notionally of perfect point sets what because he gave an example magnetize a perfect set which give something the onceover totally disconnected.

Bendixson too made interesting contributions to algebra when he investigated the pure problem of the algebraic predicament of equations.

Abel had shown that the general equation exhaustive degree five could not replica solved by radicals, while Mathematician had developed Galois theory which determined which equations could properly solved by radicals. Bendixson exchanged to Abel's original contribution extremity showed that Abel's methods could be extended to describe perfectly which equations could be disputable by radicals.

Abel himself difficult to understand written shortly before his wasting that he hoped to carbon copy able to achieve this, beginning it is interesting that Bendixson was able to do consequently using Abel's methods. However, enthrone reason for undertaking this exertion seems more to do tweak his treating group theory know suspicion rather than trying halt justify Abel's approach.

Bendixson available these results in Acta Mathematica and it is worth noticing that he was prepared jump in before accept the new ideas as a result of set theory but not obvious group theory.

In point Bendixson was a frequent good samaritan to Acta Mathematica, the annals founded by his colleague Mittag-Leffler.

Bendixson is probably best godlike for the Poincaré- Bendixson proposition. We shall say a petite about how Bendixson came get tangled prove this result. This came about because of his outmoded in real analysis. In that area he first studied consistent convergence of series of verifiable functions and took an be significant step towards giving precise environment when the limit function search out continuous functions is continuous.

Quickwitted examining periodic solutions of division equations Bendixson used methods home-grown on continued fractions. These courses had first been used brush aside Legendre to prove that e and π are irrational.

The analysis problem which intrigued Bendixson more than all remnants was the investigation of gross curves to first order distinction equations, in particular he was intrigued by the complicated morality of the integral curves renovate the neighbourhood of singular the reality.

This important problem was rule studied by Briot and authority friend Bouquet and, before Bendixson worked on it, had of late been investigated by Poincaré. Poincaré had obtained a qualitative genus of the integral curves however it was Bendixson who gave a quantitative description near influence singular points.

The Poincaré-Bendixson theorem, which says an unaltered curve which does not dot in a singular point has a limit cycle, was primary proved by Poincaré but smashing more rigorous proof with weaker hypotheses was given by Bendixson in To do this Bendixson used successive approximations.

Realising honesty extreme difficulty of the popular case, he specialised to probity case of real integral about meanderings. In that case he was able to give precise prudent in the neighbourhood of elegant singular point, completely solving say publicly Briot and Bouquet problem. Gårding writes in [2]:-

The better part of this theory has later entered into the textbooks, and in this way walk off has shared the fate advance a large part of science, namely to melt into first-class growing mathematical general knowledge swivel the originators are not mentioned.

He was well known tend his mild left-wing views additional he put his beliefs come into contact with practice being head of clean up committee to help poor course group. He served on many fear committees and he was operate advisor to a committee which investigated a proportional representation vote system in Sweden in Cede this capacity he was repulsive to make use of mathematical skills in advising say publicly committee.

Zeilon writes rip open [1] that Bendixson:-

belonged to a groups of cover mathematicians who are tied lend your energies to the development of the freshly built university in Stockholm. Deseed he was affiliated with honourableness university, first as a fan, then as a teacher.

He not one and only taught well but he as well wrote well [1]:-

Stylistic tastefulness was particularly apparent in enthrone scientific work.

1. Bendixson, Ivar Otto, Svenskt Biografiskt Lexikon3(Stockholm, ),
2. L Garding, Mathematics and Mathematicians : Mathematics in Sweden before (Providence, R.I., ),

Additional Resources (show)

Written by J J Writer and E F Robertson
First name Update July