Logic

While at Cambridge he taught a course on the foundations of mathematics.

While at Cambridge he taught a course on the foundations of mathematics.     

Maxwell Herman Alexander Newman

Newman also wrote an important paper on theoretical computer science, produced a topological counter-example of major significance in collaboration with Henry Whitehead, and wrote an outstanding paper on periodic transformations in abelian topological groups. He only wrote one book Elements of the topology of plane sets of points (1939). Writing in [4], Peter Hilton claims that:- ... this is the only text in general topology which can be wholeheartedly recommended without qualification. It is beautifully written in the limpid style one would expect of one who combined clarity of thought, breadth of view, depth of understanding and mastery of language. Newman saw, and presented, topology as part of the whole of mathematics, not as an isolated discipline: and many must wish he had written more. In 1962 Newman was presented with the De Morgan Medal from the London Mathematical Society. The President of the Society, Mary Cartwright, gave a tribute to Newman's work which is reported in [3]:- His early work on Combinatory Topology has exercised a decisive influence on the development of that subject. At a time when the study of manifolds was based on a number of different combinatory concepts, he established a simple combinatory system of simplicial complexes with an equivalence relation based on elementary moves. ... He has proved two important results about fixed points. The first was an early inroad on Hilbert's Fifth Problem, in which he proved that abelian continuous groups do not have arbitrarily small subgroups, the second was a simplified proof of a difficult fixed point theorem of Cartwright and Littlewood arising in the study of differential equations. ... In 1964 Newman retired from his Manchester chair but he most certainly did not give up mathematics. He taught a course at the University of Warwick and at this time I [EFR] was a research student there and met him and attended lectures he gave. He was an outstanding teacher, clearly giving much attention to the organisation of his material. Retirement was also an opportunity for Newman to relaunch his research career which he did with the vigour of a young academic. He published a highly significant paper in 1966 which proved the Poincaré Conjecture for topological manifolds of dimension greater than 4. Lynn Newman died in 1973, and later in the same year he married Margaret Penrose, the daughter of a professor of physiology, who was the widow of the physician Professor Lionel Sharples Penrose. Mostrar detalle

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IMO

International Mathematical Olympiad Foundation

International Mathematical Olympiad Foundation     The IMO is an international competition for high school students which has been running annually since 1959 and now has over 100 countries competing, including all members of the G20. The IMO is a self-governing autonomous organization, though it is affiliated to UNESCO. Its Council is elected by participating countries, and is called the IMO Advisory Board. The IMOF is a charitable organization which accepts donations from organizations which wish to support the IMO. The volunteers who administer the IMOF pass on donations to support the IMO, principally in the form of grants to host countries to defray the costs of hosting the event (which involves over 1000 people for 10 days). Mostrar detalle

ID: 145 C: 1 I: 10775 F: 7.416
    

Algorithmic

Research Shows Students Learn Better When They Figure Things Out On Their Own

Research Shows Students Learn Better When They Figure Things Out On Their Own     In some instances, research illuminates a topic and changes our existing beliefs. For example, here’s a post that challenges the myth of preferred learning styles. Other times, you might hear about a study and say, “Well, of course that’s true!” This might be one of those moments. Last year, Dr. Karlsson Wirebring and fellow researchers published a study that supports what many educators and parents have already suspected: students learn better when they figure things out on their own, as compared to being told what to do. Mostrar detalle

ID: 144 C: 1 I: 11047 F: 7.309
    

Education-system

Facts About Finland's Unorthodox Education System

Facts About Finland's Unorthodox Education System     Since it implemented huge education reforms 40 years ago, Finland's school system has consistently come at the top for the international rankings for education systems. So how do they do it? It's simple — by going against the evaluation-driven, centralized model that much of the Western world uses.

  • Finnish children don't start school until they are 7.
  • 66 percent of students go to college.
  • Compared with other systems, they rarely take exams or do homework until they are well into their teens.
  • The children are not measured at all for the first six years of their education.
  • 30 percent of children receive extra help during their first nine years of school.
  • Finland spends around 30 percent less per student than the United States.
  • All children, clever or not, are taught in the same classrooms.
  • There is only one mandatory standardized test in Finland, taken when children are 16.
  • The school system is 100% state funded.
  • All teachers in Finland must have a masters degree, which is fully subsidized.
  • The national curriculum is only broad guidelines.
  • Teachers are selected from the top 10% of graduates.
  • In 2010, 6,600 applicants vied for 660 primary school training slots
  • Finland has the same amount of teachers as New York City, but far fewer students.
  • Science classes are capped at 16 students so that they may perform practical experiments every class.
  • The average starting salary for a Finnish teacher was $29,000 in 2008
  • However, high school teachers with 15 years of experience make 102 percent of what other college graduates make.
  • Teachers only spend 4 hours a day in the classroom, and take 2 hours a week for "professional development".
  • Elementary school students get 75 minutes of recess a day in Finnish versus an average of 27 minutes in the US.
  • The difference between weakest and strongest students is the smallest in the World.
  • 43 percent of Finnish high-school students go to vocational schools.
  • 93 percent of Finns graduate from high school.
  • There is no merit pay for teachers
  • Teachers are effectively given the same status as doctors and lawyers
  • In an international standardized measurement in 2001, Finnish children came top or very close to the top for science, reading and mathematics.
  • In an international standardized measurement in 2001, Finnish children came top or very close to the top for science, reading and mathematics.
  • And despite the differences between Finland and the US, it easily beats countries with a similar demographic
Mostrar detalle

ID: 480 C: 1 I: 12248 F: 6.363
    

Education

Polynomials evaluated at integers by John D. Cook

Polynomials evaluated at integers by  John D.  Cook     Let p(x) = a0 + a1x + a2x2 + … + anxn and suppose at least one of the coefficients ai is irrational for some i ≥ 1. Then a theorem by Weyl says that the fractional parts of p(n) are equidistributed as n varies over the integers. That is, the proportion of values that land in some interval is equal to the length of that interval. Clearly it’s necessary that one of the coefficients be irrational. What may be surprising is that it is sufficient. If the coefficients are all rational with common denominator N, then the sequence would only contain multiples of 1/N. The interval [1/3N, 2/3N], for example, would never get a sample. If a0 were irrational but the rest of the coefficients were rational, we’d have the same situation, simply shifted by a0. This is a theorem about what happens in the limit, but we can look at what happens for some large but finite set of terms. And we can use a χ2 test to see how evenly our sequence is compared to what one would expect from a random sequence. Mostrar detalle

ID: 908 C: 1 I: 2598 F: -0.421
    

Health

¿Qué es la malaria?

¿Qué es la malaria?     La Malaria es una enfermedad parasitaria que involucra fiebres altas, escalofríos, síntomas seudogripales y anemia. Causas La malaria o paludismo es causada por un parásito que se transmite a los humanos a través de la picadura de mosquitos anofeles infectados. Después de la infección, los parásitos (llamados esporozoítos) viajan a través del torrente sanguíneo hasta el hígado, donde maduran y producen otra forma, llamada merozoítos. Los parásitos ingresan en el torrente sanguíneo e infectan a los glóbulos rojos. Los parásitos se multiplican dentro de los glóbulos rojos, los cuales se rompen al cabo de 48 a 72 horas, infectando más glóbulos rojos. Los primeros síntomas se presentan por lo general de 10 días a 4 semanas después de la infección, aunque pueden aparecer incluso a los 8 días o hasta 1 año después de esta. Los síntomas ocurren en ciclos de 48 a 72 horas. La mayoría de los síntomas son causados por: La liberación de merozoítos en el torrente sanguíneo Anemia resultante de la destrucción de glóbulos rojos Grandes cantidades de hemoglobina libre liberada en la circulación luego de la ruptura de los glóbulos rojos Mostrar detalle

ID: 901 C: 1 I: 2132 F: -0.631
    

Education

José Andalón explica las leyes de las desigualdades por medio de un video. @mistertwingo

José Andalón explica las leyes de las desigualdades por medio de un video. @mistertwingo      Mostrar detalle

ID: 442 C: 2 I: 6818 F: 34.151
    

Math

Implicit differentiation, a revealing video.

Implicit differentiation, a revealing video.     Implicit differentiation can feel weird, but what's going on makes much more sense once you view each side of the equation. Mostrar detalle

ID: 993 C: 2 I: 987 F: 30.761
    

MATH

THE UNREASONABLE EFFECTIVENESS OF MATHEMATICS

THE UNREASONABLE EFFECTIVENESS OF MATHEMATICS     By R. W. Hamming
Prologue. It is evident from the title that this is a philosophical discussion. I shall not apologize for the philosophy, though I am well aware that most scientists, engineers, and mathematicians have little regard for it; instead, I shall give this short prologue to justify the approach. Man, so far as we know, has always wondered about himself, the world around him, and what life is all about. We have many myths from the past that tell how and why God, or the gods, made man and the universe. These I shall call theological explanations. They have one principal characteristic in common - there is little point in asking why things are the way they are, since we are given mainly a description of the creation as the gods chose to do it. Philosophy started when man began to wonder about the world outside of this theological framework. An early example is the description by the philosophers that the world is made of earth, fire, water, and air. No doubt they were told at the time that the gods made things that way and to stop worrying about it. From these early attempts to explain things slowly came philosophy as well as our present science. Not that science explains "why" things are as they are - gravitation does not explain why things fall - but science gives so many details of "how" that we have the feeling we understand "why." Let us be clear about this point; it is by the sea of interrelated details that science seems to say "why" the universe is as it is. Our main tool for carrying out the long chains of tight reasoning required by science is mathematics. Indeed, mathematics might be defined as being the mental tool designed for this purpose. Many people through the ages have asked the question I am effectively asking in the title, "Why is mathematics so unreasonably effective?" In asking this we are merely looking more at the logical side and less at the material side of what the universe is and how it works. Mathematicians working in the foundations of mathematics are concerned mainly with the self- consistency and limitations of the system. They seem not to concern themselves with why the world apparently admits of a logical explanation. In a sense I am in the position of the early Greek philosophers who wondered about the material side, and my answers on the logical side are probably not much better than theirs were in their time. But we must begin somewhere and sometime to explain the phenomenon that the world seems to be organized in a logical pattern that parallels much of mathematics, that mathematics is the language of science and engineering. Once I had organized the main outline, I had then to consider how best to communicate my ideas and opinions to others. Experience shows that I am not always successful in this matter. It finally occurred to me that the following preliminary remarks would help. In some respects this discussion is highly theoretical. I have to mention, at least slightly, various theories of the general activity called mathematics, as well as touch on selected parts of it. Furthermore, there are various theories of applications. Thus, to some extent, this leads to a theory of theories. What may surprise you is that I shall take the experimentalist's approach in discussing things. Never mind what the theories are supposed to be, or what you think they should be, or even what the experts in the field assert they are; let us take the scientific attitude and look at what they are. I am well aware that much of what I say, especially about the nature of mathematics, will annoy many mathematicians. My experimental approach is quite foreign to their mentality and preconceived beliefs. So be it! The inspiration for this article came from the similarly entitled article, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" [1], by E. P. Wigner. It will be noticed that I have left out part of the title, and by those who have already read it that I do not duplicate much of his material (I do not feel I can improve on his presentation). On the other hand, I shall spend relatively more time trying to explain the implied question of the title. But when all my explanations are over, the residue is still so large as to leave the question essentially unanswered. Mostrar detalle

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Education

World University Rankings 2018 UCV, USB and ULA Ranked 801 - 1001+.

World University Rankings 2018 UCV, USB and ULA Ranked 801 - 1001+.     The Times Higher Education World University Rankings 2018 list the top 1,000 universities in the world, making it our biggest international league table to date. It is the only global university performance table to judge research-intensive universities across all of their core missions: teaching, research, knowledge transfer and international outlook. We use 13 carefully calibrated performance indicators to provide the most comprehensive and balanced comparisons, trusted by students, academics, university leaders, industry and governments. Central University of Venezuela (UCV), Simón Bolivar University USB and University of Los Andes (ULA). Ranked 801 - 1001+. Mostrar detalle

ID: 916 C: 2 I: 1550 F: 10.480
    

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