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Bertram Kostant, 88 Dies in Massachusetts

Bertram Kostant was one of the world’s foremost mathematicians.  The Professor emeritus at MIT died last month aged 88 years old in the Hebrew Senior rehabilitation Center in Roslindale.

Kostant held the post of Professor of Mathematics at MIT from 1962 until 1993 when he officially retired however he continued to lead an active life engaging in research, travel and he even continued to lecture at Universities across the world.

Over 60 years, Lostant published well over a hundred papers and he was responsible for some diverse and inspiring ideas within his core subject mathematics and theoretical physics.   he was born in 1928 in Brooklyn, New York and graduated from Peter Stuyvesant HIgh School in 1945 at the end of the war.  He first started studying chemical engineering at Purdue University but later switched to mathematics.  He was mainly inspired to this which by the lectures of Arthur Rosenthal and Michael Golomb who had emigrated from Germany.  He graduated with a bachelor’s degree in mathematics with distinction.

Later in his career he was awarded the Atomic Energy Commission Fellowship for graduate studies at the University of Chicago.  It was here that  he began working with some of the premier American mathematicians like Marshall Stone and Paul Malmos plus many others.   It was only in 1951 that Kostant received his MS and three years later his PhD with a thesis entitled -” Representations of a Lie Algebra and its enveloping algebra on a Hilbert Space “.

Kostant spent many more years in Chicago until he joined the faculty at MIT in 1962 which was to be the last move of his academic career.  His earliest lectures were focussed around his Lie Theory and over the years he mentored many influential mathematicians like James Symons the differential geometer.

Over the years, he has received many awards and was often cited by colleagues in other research areas.  His theories were often discussed and indeed you could often hear his theories discussed on TV particularly on the Open University broadcasts on the BBC.  There is rumour that some of these will be made available from the archive although you will need a VPN to access BBC iPlayer abroad like this  from outside the UK.

In May 2008, the Pacific Institute for Mathematical Sciences hosted a conference: “Lie Theory and Geometry: the Mathematical Legacy of Bertram Kostant,” at the University of British Columbia, which covered his work and celebrated this life when he was 80 years old.  In the second half of 2012, he was finally elected to the inaugural class of fellows of the American Mathematical Society. When in las June, Kostant traveled to Rio de Janeiro for the Colloquium on Group Theoretical Methods in Physics, he was also to receive the prestigious Wigner Medal, “for his fundamental contributions to representation theory that led to new branches of mathematics and physics.”

James Hawkins

Author of BBC in Ireland, history of the broadcaster, 2016.

 

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The Wonderful World of Calculus

Welcome to the word of calculus. This really is probably the most difficult part of calculus. As stated in an earlier Calculus article, the two major branches of the subject are differential and integral. Students have various difficulties with pre-calculus.

Limits aren’t easy to explain in plain terms. The initial one is L’Hopitals rule, a favorite topic of calculus haters. Here are a number of examples worked out. The rule may even be extended for functions which are products of over two functions.

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Isaac Newton invented calculus so as to solve selected issues in physics, including computing the gravitational force on an apple close to the surface of the planet. Sooner or later, the idea of inverse functions is introduced. The result could be the inverse function. There are only two main kinds of calculus, generally known as Infinitesimal Calculus and that part of the total that’s called Differential Calculus.

You won’t ever learn calculus. How can calculus do this. Make certain you know what will be dealt with on the exam. Nevertheless, you can acquire exceptional individualized mathematics education less the stress, anxiety or cumbersome troubles that come up with traditional methods.   There are some useful maths study resources on the BBC website, and if you get a good VPN you can also watch BBC World news streaming too.

There isn’t any denying that calculus is among the most troublesome classes a serious math student will come up against. It is significant for the student to master precalculus as a way to succeed in succeeding courses. Just much like many math concepts, it’s very important for learners to take a seat and practice using their new calculator. Pre-calculus can indicate a couple of different things, contingent on where it’s studied.

You won’t have enough time to imbibe how to utilize your calculator during the exam. See whether you can receive the exact same outcome. If you practice, remember to write down your answers in a great deal of detail. That’s a superb sign that the topic will really be on the exam.

Your math department may have a list of individuals who tutor. You also need to be clear about your own goals and expectations before going trying to find a calculus tutor. Knowing what sort of problems will really be on the exam is vital to the way you’ll spend your own time studying. Although you certainly must know calculus to do well, that is not enough!

Function is among the most crucial ideas in all of mathematics. The limit is among the crucial features of calculus that permits us to do these extraordinary things. With the suggestions provided above, together with some superior study time together with the above calculus formulas, you ought to be on your own way to success at calculus, and all these differentiation tasks will get second nature to you personally. So as to define the slope of the function at a point, it’s first required to study infinitely-small quantities referred to as infinitesimal quantities.

A paradox of mathematics when applied to the actual world which has baffled lots of people through the years. Yet there are times, the moment the result isn’t obvious in any respect. Before calculus, there would never have been really a strategy to solve this type of problem, and when this were a true world impending disaster, no method to avert this type of tragedy. Math anxiety is to some extent prevalent in a whole lot of people.

John Heather

Author: Finding Best VPNs for Netflix, Arbour Press, 2015

 

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Students Enjoy Vedic Mathematics

It takes 11-year old Aditya Ray only seconds to multiply a five-digit number using a four-digit one, thanks to Vedic mathematics, which he claims makes it quicker and accurate. By traditional method, he would have significantly more than a minute to get the answer.

“It takes me around one plus a half minutes to multiply such large numbers utilizing the conventional technique. However, if I take the Vedic maths course, I could solve it in 30 seconds,” the Class 6 student explained.

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The Kolkata-based Ray added that while his school anticipates him to solve problems using the traditional manner, he at times uses Vedic maths.

Discovered by Hindu seer Swami Bharati Krishna Tirthaji in the early 20th century, additionally it is said to not be difficult to consider, creates inquisitiveness, offers multiple ways of doing precisely the same computation and improves analytic thinking.

According to the School of Vedic Maths (SOVM), Tirthaji was born in Tirunelveli in Tamil Nadu in 1884. After finishing his Master of Arts he was a faculty principal. The college principal quit that to embrace a religious path. It was during deep meditation that he got inner revelations on the 16 sutras from the appendix of Atharva Veda, one of the four vedas, the primeval Indian scholastic and religious texts.

Tirthaji declared that any mathematical problem can be solved using them.
Gaurav Tekriwal, president of the Vedic Math Forum India, said Vedic maths was a collection of techniques to calculate faster when compared to the traditional systems.
“With just a little practice in Vedic maths one can make routine computations easier, simpler and quicker so much so that you can call it ‘World’s Fastest Mental Maths System’. It’s applications mainly in arithmetic and algebra and therefore is a favorite of competitive exam aspirants who wish to handle maximum problems in less time,” Tekriwal told IANS.

On-line courses spread over 30 hours for pupils and 40 hours for teachers are held by the Forum. The classes are one on one.

Pradeep Kumar, founder director of Magical Methods, which supplies training shared that using such calculations, choosing the square of any number ending with five becomes incredibly simple.

“Say you are looking for square of 85. You multiply 5 by 5 and set 25 as your right part of the solution. Then, multiply 8 and set 72 as your left element of the solution. Your answer is 7,225,” he said, including the same formula can be used to locate square of any number ending with five.

The division is slowly gaining popularity among students “because it’s quite useful, especially for anyone planning to consider competitive examinations”, Kumar said.

“Nowadays, there is a large number of competitive exams. Speed is really one of the factors that are key to crack any assessment which tests numeric ability. Vedic maths is an excellent instrument.

Nair added that from a teacher’s perspective, it gives “tremendous possibilities to research learning mathematics from many positions as well as in innovative ways”.

“It has little importance. We might as well forget it. Though it may have a few useful bits, the aura around it makes it very damaging on the whole,” Dani told IANS over email.

Retired 85-year-old teacher and educationist Dinanath Batra, who got American scholar is batting for the debut of Vedic maths in universities and schools.

Those people who have profited from Vedic Maths and want it introduced in the schooling system favour it. Teachers of conventional mathematics and school principals we  spoke to agreed that it should be formally introduced.  It was interesting to see that there were examples on the internet, including in Japan and accessible using a Russian proxy – in schools in Moscow.

“There is no damage in introducing it in the primary level in schools, at least some parts of it. It’ll only make the pupils’ base stronger. It has been seen that pupils take interest when new techniques are taught,” Rekha Dwivedi, a mathematics teacher at a government school in Dwarka in Delhi.

She added that teachers ought to be first trained.

Agreed Nair, who said that introducing Vedic maths will be good notably in Courses 6 to 9, “but with no suitable pedagogy in teaching and appropriate training to teachers, it mightn’t be quite powerful.”
In fact, vedic maths got the attention of Japan over a decade ago and it could establish an international occurrence like the Chinese abacus if channelized properly.

Additional Information

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Listing of Top 10 IT Courses and also Courses

Information technology is the strategy to handle as well as treat information. IT is composed of acquisitioning, keeping, as well as propagating the info by using a combo of telecommunication and also computing based upon microelectronics. It covers several different varieties of locations successfully. These spots consist of computer hardware, home computer software application, setting language, data system, processes, information constructs, etc. Right here are the Top 10 it training courses
and Programs:

Information Technology in the Health Care System of the Future at MIT

This program focuses on how the speciality of infotech has impacted the medical markets. Pupils study about network included decision support tools, patient care distribution, medical and also e-commerce.

Information Technology and the Labor Market at MIT

Pupils participating in this program find out regarding how the labor market has actually been influenced by computer systems and infotech. A chance is likewise offered to discover precisely how the labor market has actually been constructed by information technology and caused changes in economy-wide labor output.

Practical Information Technology Management at MIT

The important factors of information technology administration, such as corporate strategy, refines, IT facilities and also IT composition, are explained in this course.

Information Technology Essentials at MIT

Students in this infotech essentials program find out pertaining to safety and also cryptography, electronic commerce, operating as well as equipment systems and networks. The class is for students who have restricted information technology encounter.

Information Technology I at MIT

This introductory infotech class is composed of 24 lectures and also features subject matters such as relational database design, working systems, comprehensive region networks, user interface structure and computer architecture.

Networked Computing: Storage, Communication and Processing

The aim of this class is to inform students regarding what factors comprise modern information systems.

Networks: Theory and Application

A graduate-level course in networks deals with metrics and also models, network idea, network data investigation and social as well as data networks.

Digital Government 2: Information Technology and Democratic Administration

This class explores democratic governance of infotech as well as the resulting difficulties as well as options that emerge as a result of this convergence. Additional topics dealt with in the lecture notes incorporate digital federal government research and practice, IT and organizational change, worldwide e-government and also exam, preparation and also resident engagement.

Management of Libraries and Information Services

Pupils find out the many features of details and also collection services administration in this program. Subjects dealt with feature monetary management, marketing, employees administration, organizing and also planning. Assignments are composed of case studies that cover regions such as preparation, budgeting, human sources as well as organizational design.

Seminar on Information Policy

This graduate seminar on info policy permits pupils to develop a research paper on a region of interest in the field. The program contains a single lecture on data policy and can be downloaded from the program website.

There are lots of additional courses like online MBA in IT, ms in Information-technology that gives a magnificent career in the field of IT but thisTop 10 IT Courses are all excellent and also useful to every pupil that wishes to come to be an IT. Information technology can assist attain success in numerous parts of life as it is and innovation as well as receiving trained in IT will supply the person with an impressive idea to execute any sort of activity in a much better means.

 

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Mathematics In Business

BBC ProxyIt is an understatement to say that maths is important in business, but growing up some of us forget, especially when it comes to doing your homework to make sure that you passed your maths exams at school!

Whether you dreamt of running your own business, becoming a pilot or perhaps an engineer – mathematics is one of the most important skills that you can garner through your education.  A lot of the businesses over at the Birmingham business directory can attest to that to.

For example, if you are a solicitor in Birmingham, or anywhere else for that matter, you will need a firm grasp of maths, as not only will you have to calculate fees for your clients, you will also have all the other elements of running a business.  If you are one of our local mechanics then a good grasp of number is vital too.  You don’t want to undercharge your time and skills.  Maybe our driving instructors felt they wouldn’t need too much maths in their profession but not only do they have to charge customers by the lesson, they have to make sure they budget enough for fuel, car maintenance and insurance.

Among the most vital and earliest sciences is math. Mathematicians’ work is broken up into two big groups. They may be pure or theoretical mathematics and applied mathematics. These categories may frequently overlap and aren’t clearly identified.

Mathematical knowledge increases by detecting unknown correlations or relationships between principles in mathematics which are in use and creating new principles. Without considering the practicality of its own use, such additional knowledge is discovered; yet, these abstract notions have been powerful in furthering or creating numerous engineering and scientific achievements.

Applied mathematicians use theories and processes, like computational techniques and mathematical modeling, to find formulas and remedies to authorities company; engineering; and physical, life, and social science issues. A number of the following are examples of their work: reviewing the efficacy of other methods to produce products, assessing security and the effects of the most recent drugs, assessing the aerodynamic features of an experimental automobile, or finding the most expert airline flight program.

Used mathematicians get inside their heads the identifying components in the solving procedure start with a realistic issue, and eventually reduce the components to mathematical variants. To examine organizations among the variables and solve issues that are complex, computers are often used by them and make models with other options.
Others perform a bulk of the job in applied mathematics with differing names than mathematician.  Computer programmers who designed this software which allows you to watch the BBC Player Canada using a complicated encryption network.  Professions that use mathematics at length comprise computer scientists, engineers, physicists, and economists. A number of professionals, including statisticians, actuaries, and operations research analysts, are actually mathematicians using a focus that is given. Frequently applied mathematicians could be asked to team up with other associated workers to find solutions to specific issues.

As you can see, no matter what your chosen career path, mathematics and the ability to manipulate numbers and budgets is a vital life skill.  Makes you wish you paid more attention back at school doesn’t it!

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How Math and Wine Fit Together

When people talk about math and wine fitting together, they’re usually talking about wine in terms of the programming language and not the drink.

I’m talking about the drink.

It’s more interesting and certainly more fun!

So how can the Mathematics Survey and math in general go together with wine and winemaking, or even a wine of the month club?

Most people aren’t aware, but the average winemaker gets into the professional with a math and science background.  Attention to detail is one of the most important parts of the job in fact.  Additionally, even organic wines often have sulfur or another ingredient or two added at some point of the production process.  Getting the wrong amount of sulfur would certainly ruin the wine, as would picking the wrong amount of grapes from a certain clone of fruit.

It’s funny, but math tends to find its way into much more of our daily lives then we initially think it does.

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Maths in popular culture

 

It seems as if maths is becoming a major part of popular culture, perhaps we have an innate desire to find the answers to problems, or maybe we just like the feeling of self-satisfaction when we find the right answer.

I often see mathematical problems posted on Facebook, and you are prompted to either ‘like’ or ‘comment’ on the post, this is dependent on which answer you get. Similarly, a popular radio show in the UK gives its listeners a question to solve every week, you are then encouraged to text your answer to the host. The host then appeals to our desire for self-satisfaction as he then proceeds to read out the names of people who have given the right answer, as well as a list of people who were not correct.

Some people even see mathematical problems as a good way to relax and take them away with them on their travels. If you walk along beaches and pool sides whether at home or abroad, it is probable that you will see at least one person testing themselves with a Sudoku puzzle, or some other maths based puzzle.

Even when the confines of a cramped maths classroom seem like a distant memory, we still like to test ourselves now and again. Maths, then, can be seen as a pleasurable activity, and not one that we should shy away from. It can be a great way to keep your brain active and stay sharp, provided that the questions aren’t too hard!

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Recreational Mathematics In Use

Recreational mathematics might seem as a term related to financial or tourism industry, however it is one of so called umbrella terms, referred to mathematical games such as puzzles, mathematical logic games, juggling, origami and others. This part of mathematics is often required deductive reasoning, aesthetics of higher maths and even amusing stories from the history of mathematics or mathematicians themselves.

Basics of SSL

First publications about recreational mathematics dates back to 1939 from a group of scientists in Cambridge University. Since than, the theory has developed drastically and many famous scientists such as Stephen Hawking, Martin Gardner and Roger Penrose, have been studying and developing the theory. More than 60 scientific articles has been published regarding recreational maths and nowadays it involves such things as magical numbers, numerology, folding, sports, dissection and even mathematical humor.

Mathematical games are most likely played by several players and involves an extensive knowledge of mathematics applied for real life situations, mathematical logic and common sense. Mathematical game rules goes strictly together with mathematical theory and is a great way to check your high-school knowledge as well as more in-depth problems resolved by higher maths. Such simple games can be played with friends or family and are truly educational and fun. It is perfect for a family holiday as well as break out of the city. Mathematical games can develop your logic and the way of thinking as well as taking your mind of work and every day troubles.

Recreational mathematics can be truly beneficial for you, your family and friends, especially as an nice escape from city to a quiet rented luxury lodge near lake for example. You can discover some really great luxury holiday deals in Ireland from anywhere in the world, just route your connection through an Irish proxy and you’ll be able to book online:  Remember to revise your mathematical skills and even show off with your recreational mathematics knowledge while resolving mathematical game problems in style!

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The Concept of Mathematical Proof

Proof is a funny word it can mean different things to different people. For example there is a difference in the concept proof between scientists and mathematicians.  The difference is actually quite subtle but without understanding it then you have little chance of understanding the work of any mathematician.

Classical mathematical proof is to start with a set of statements and axioms  which are true, or at least are self evidently true.  Then by using logic and deduction, you can move step by step to a conclusion.  As long as the underlying axioms are correct, and the logic is flawless then the conclusion should be undeniable.  The conclusion is termed the ’theorem’ by the mathematician.

A mathematical theorem is dependent on the process of logic and so should be true forever.  To the mathematician, their proofs are absolute there is no scale or level to this proof.  When you compare this to the scientists proof you see the underlying difference.  The scientist will put forward a hypothesis to explain a phenomenon  or occurence.  Then it is observed and compared with this hypothesis – the scientist will then gather evidence in favour of the hypothesis or against it.  Eventually evidence will way up either overwhelmingly in favour or against the hypothesis which will decide if it becomes part of scientific law.

The level of proof is not absolute in science, it is never approaching the level of mathematical absolute proof.  The scientists rely on perception and observation both of which can be subjective and are certainly fallible.

To quote Arthur C Clarke

“if an eminent scientist states that something is undoubtedly true, then it is likely to be proved false the next day.” 

Mathematical proof is absolute and devoid of any doubts, whereas scientific proof is frequently rewritten or proved to be false.  Take for instance the wonderful BBC program on Fermat’s Last Theorem and you’ll see some of the difficulties involved in attaining the level of mathematical proof.  It is often available on the BBC Iplayer if you check – if you live outside the UK – try this technique to watch Iplayer abroad.  It works by masking your true IP address and allowing you to use a false one in order to bypass the geotargeting restrictions.   You can even do this by simply using something called Smart DNS where you don’t even change your address – http://www.theninjaproxy.org/ninja/change-ip-address-region-free-smart-dns/

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Playing The Numbers Game

Mathematics in business is usually left to the financial team but numbers are getting ever increasingly important in tracking the development and popularity of a business be it with a new starter company or an established company that is seeking information on its customer base.

One specific way we are seeing this in practice is through social media with most companies having Facebook pages or Twitter accounts. This allows them to stay in contact with their customers as well as gauge responses to certain things. For example following a tesco facebook marketing campaign you would be able to see how liked the specific campaign is as well as read comments to really see what is being said about it.

The number of followers or ‘likes’ on a Facebook page can obviously show how popular a company or brand is but can also be of use by putting information direct to the consumer allowing them to take advantage of deals.

This can work well for companies, although, as was experienced by Tesco in the Scottish town of Greenock it can also mean information about mistakes can spread like wildfire. On discovery that a deal regarding beer was put through wrong offering the customer a ridiculously low price word spread across social media sites leading to crowds of people attempting to take advantage of the mistake before it was rectified.

Here we can see the power of Social media and that is why more and more companies are trying to harness that power and use it to benefit both themselves and their customers. Keeping a good open communication has proved to be very beneficial to the companies that are already taking advantage of this simple way of getting into peoples homes.

I believe in the future we will see a greater dependence on this sort of interaction.

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