2017 MINDS Scholarship Program for Leadership Development

 

MINDS offers scholarships to Africans who wish to pursue post-graduate studies within Africa, outside of their own countries. Through tailored leadership development activities, the MINDS Scholarship Program aims to nurture leaders who have a continental development mindset; leaders who will facilitate greater cohesion and cooperation between African countries.  

MINDS scholarships are applicable to full-time studies of a one or two year Honors or Master's degree at one of the MINDS preferred institutions (listed below). MINDS does not prescribe the course to be studied.  

The scholarship will cover some or all of the expenses below, depending on whether a partial or full scholarship is awarded:

• Tuition,
•  Accommodation and meals,
• One return ticket per duration of studies,
• A fixed stipend.

Individuals with a Pan-African outlook, demonstrated leadership ability and an excellent academic record who wish to study on the African continent, outside their home country are invited to apply for the scholarships. 

Eligibility Criteria

MINDS scholarships are awarded to meritorious applicants following a rigorous selection process.  To be considered for a MINDS scholarship, you must:

• Be a national of an African country, residing in any African country;  
• Have been formally accepted by one or more MINDS preferred institution/s to pursue postgraduate studies within the following year;
• Have obtained at least 70% in each subject/ course in the last two completed years of study;
• Produce evidence of demonstrated leadership abilities or potential guided by the questions/ requirements set out in the application form;
• Submit a complete online application form (see below) with the required supporting documentation. 

Applying for a MINDS Scholarship

MINDS is currently receiving applications from students who commence their studies in 2017. Interested individuals are invited to submit applications as soon as they receive official acceptance from a MINDS preferred university at which they wish to study. Applications will be processed in the order they are received.

If you meet the eligibility criteria above, you can submit your application by clicking on the link below. Please have the following documents scanned, saved and ready for uploading. All documents uploaded must be in PDF format. Each attachment  should not exceed 2MB  in size.

• A copy of the data/ bio page of your passport.
• A certified academic transcript/ results slip of the last two years of study.
• A copy of the official acceptance letter from the university. The letter must:
• Be addressed to the applicant.
• State the degree which the applicant has been accepted to study.
• State the academic year at which the degree will commence.
• State the duration of the course (e.g. one year).
• A copy of a valid study permit or visa OR proof of application.
• A detailed CV/ Resume of not more than four (4) single sided pages.
• Two reference letters (of not more than 3 pages each) addressing the applicant's demonstration of integrity, their competency and/or potential as a leader and their commitment to the development of the African continent.        

For more information please visit:

http://minds-africa.org/ScholarshipProgram.html

2017 AIMS Structured Master's Applications August intake

 

source: opportunitiesforafricans.com

The AIMS Master’s degree in the mathematical sciences is a unique, innovative program providing problem-solving and computational skills as well as exposure to cutting edge fields.

Key features:

• Courses taught by outstanding African and international lecturers and supported by a team of resident tutors
• Students and lecturers sharing a 24-hour learning environment
• A climate of highly interactive teaching where students are encouraged to learn together through questioning and discovery
• Emphasis on computational methods and scientific computing with 24/7 access to computer labs and the internet
• A pan-African student body including a minimum of 30% women
• AIMS graduates progressing to top advanced degree programs and careers in Africa and all over the world.

Requirements:

• Applicants should hold, or anticipate completing by the start date of the AIMS course, a 4-year university degree in mathematics, or any science or engineering subject with a significant mathematics component.
• An applicant’s record should demonstrate strong aptitude in mathematics, leadership and community service
• Women applicants are strongly encouraged to apply.

Selection Process
Each applicant’s dossier will be evaluated in light of prior educational opportunities available to them. Potential applicants must demonstrate both a high degree of motivation and the ability to complete the course successfully. Applications open on 1 December, and Master’s degree applicants are strongly advised to apply before 19 March for courses beginning in August. Accepted applicants will be notified by May. Late applications will be considered on a case-by-case basis. Master’s degrees are awarded in partnership with leading local academic institutions affiliated with AIMS centres.

Financial Assistance
There are no course fees for successful Master’s degree applicants. Full bursaries covering tuition, accommodation, meals and travel costs are also awarded to successful applicants.

Deadline: March, 2017.

To apply, visit:
http://applications.nexteinstein.org

HOW TO PROVE THAT 2 = 1

source: youtube.com

A student was given an assignment to show that 2 = 1. He successfully showed this using the argument below.

PROOF

Let a, b be real numbers, such that

a = b = 1  

Then,

a^2 = ab

a^2 - b^2 = ab - b^2

(a-b) (a+b) = b(a-b)

This imply,

(a+b) = b

Since a=b=1

Hence,

2 = 1   QED.

 

An alternative proof is;

For any x real number,

x^2 = x^2

x^2 - x^2 = x^2 -x^2

x(x - x) = (x -x)(x + x)

This imply

x = x + x

x = 2x

Hence, 1 = 2  QED.

 

REMARK 

There is something wrong with these proofs. kindly spot out the line where the argument has a flaw.



Math Jokes that Cracks the Rib

Source: dailystormer.com

Applying For A Job There are three people applying for the same job. One is a mathematician, one a statistician, and one an accountant.

The interviewing committee first calls in the mathematician. They say "we have only one question. What is 500 plus 500?" The mathematician, without hesitation, says "1000." The committee sends him out and calls in the statistician.

When the statistician comes in, they ask the same question. The statistician ponders the question for a moment, and then answers "1000... I'm 95% confident." He is then also thanked for his time and sent on his way.

When the accountant enters the room, he is asked the same question: "what is 500 plus 500?" The accountant replies, "what would you like it to be?"

They hire the accountant.

Airport Security A stats professor plans to travel to a conference by plane. When he passes the security check, they discover a bomb in his carry-on-baggage. Of course, he is hauled off immediately for interrogation.
"I don't understand it!" the interrogating officer exclaims. "You're an accomplished professional, a caring family man, a pillar of your parish - and now you want to destroy that all by blowing up an airplane!"
"Sorry", the professor interrupts him. "I had never intended to blow up the plane."
"So, for what reason else did you try to bring a bomb on board?!"
"Let me explain. Statistics shows that the probability of a bomb being on an airplane is 1/1000. That's quite high if you think about it - so high that I wouldn't have any peace of mind on a flight."
"And what does this have to do with you bringing a bomb on board of a plane?"
"You see, since the probability of one bomb being on my plane is 1/1000, the chance that there are two bombs is 1/1000000. If I already bring one, the chance of another bomb being around is actually 1/1000000, and I am much safer..."

Catholic School A father who is very much concerned about his son's bad grades in math decides to register him at a catholic school. After his first term there, the son brings home his report card: He's getting "A"s in math.
The father is, of course, pleased, but wants to know: "Why are your math grades suddenly so good?"
"You know", the son explains, "when I walked into the classroom the first day, and I saw that guy on the wall nailed to a plus sign, I knew one thing: This place means business!"

...LOL "The fear of the cross is the beginning of knowing maths"

Little Boy Son: "My math teacher is crazy".
Mother: "Why?"
Son: "Yesterday she told us that five is 4+1; today she is telling us that five is 3 + 2."

Half Bread or Heaven
At a church service, a mathematician was asked to choose between Half bread and Heaven. HE CHOSE HALF BREAD claiming that he can prove that a half bread is better than heaven. This was his proof; We know that Half bread is better than Nothing, we also know that Nothing is better than Heaven. Hence, by transitivity Half bread is better than Heaven. QED

Top ten excuses for not doing homework:

I accidentally divided by zero and my paper burst into flames.

Isaac Newton's birthday.

I could only get arbitrarily close to my textbook. I couldn't actually reach it.

I have the proof, but there isn't room to write it in this margin.

I was watching the World Series and got tied up trying to prove that it converged.

I have a solar powered calculator and it was cloudy.

I locked the paper in my trunk but a four-dimensional dog got in and ate it.

I couldn't figure out whether i am the square of negative one or i is the square root of negative one.

I took time out to snack on a doughnut and a cup of coffee.

I spent the rest of the night trying to figure which one to dunk.

I could have sworn I put the homework inside a Klein bottle, but this morning I couldn't find it.

Salary Theorem
The less you know, the more you make.
Proof:

Postulate 1: Knowledge is Power.
Postulate 2: Time is Money.

As every engineer knows: Power = Work / Time
And since Knowledge = Power and Time = Money
It is therefore true that Knowledge = Work / Money .
Solving for Money, we get:
Money = Work / Knowledge
Thus, as Knowledge approaches zero, Money approaches infinity, regardless of the amount of Work done.

The encounter between e^x and  d/dy
A constant function and e^x are walking on Broadway. Then suddenly the constant function sees a differential operator approaching and runs away. So e^x follows him and asks why the hurry. "Well, you see, there's this differential operator coming this way, and when we meet, he'll differentiate me and nothing will be left of me...!" "Ah," says e^x, "he won't bother ME, I'm e to the x!" and he walks on. Of course he meets the differential operator after a short distance.
e^x: "Hi, I'm e^x"
differential operator: "Hi, I'm d/dy" 

LOL...your CALCULUS should tell you e^x is in trouble.

Finally, let us consider how Mathematicians do their things
HOW WE DO IT...

Aerodynamicists do it in drag.
Algebraists do it in a ring, in fields, in groups. Analysts do it continuously and smoothly. Applied mathematicians do it by computer simulation. Banach spacers do it completely. Bayesians do it with improper priors. Catastrophe theorists do it falling off part of a sheet. Combinatorists do it as many ways as they can. Complex analysts do it between the sheets Computer scientists do it depth-first. Cosmologists do it in the first three minutes. Decision theorists do it optimally. Functional analysts do it with compact support. Galois theorists do it in a field. Game theorists do it by dominance or saddle points. Geometers do it with involutions. Graph theorists do it in four colors. Hilbert spacers do it orthogonally. Large cardinals do it inaccessibly. Linear programmers do it with nearest neighbors. Logicians do it by choice, consistently and completely. Number theorists do it perfectly and rationally. Mathematical physicists understand the theory of how to do it, but have difficulty obtaining practical results. Pure mathematicians do it rigorously. Quantum physicists can either know how fast they do it, or where they do it, but not both. Real analysts do it almost everywhere Ring theorists do it non-commutatively. Set theorists do it with cardinals. Statisticians probably do it. Topologists do it openly, in multiply connected domains Variationists do it locally and globally. 

---

Cantor did it diagonally. Fermat tried to do it in the margin, but couldn't fit it in. Galois did it the night before. Mðbius always does it on the same side. Markov does it in chains. Newton did it standing on the shoulders of giants. Turing did it but couldn't decide if he'd finished.

AND I DID IT AND I KNOW I HAVE FINISHED!!

For more jokes, you can check
http://jokes4us.com/miscellaneousjokes/mathjokes/

http://www.math.utah.edu/~cherk/mathjokes.html

40-year math mystery and four generations of figuring

Source: dreamstime.com

 

 

 

This may sound like a familiar kind of riddle: How many brilliant mathematicians does it take to prove the Kelmans-Seymour Conjecture?

 

 

But the answer is no joke, because arriving at it took mental toil that spanned four decades until this year, when mathematicians at the Georgia Institute of Technology finally announced a proof of that conjecture in Graph Theory.
Their research was funded by the National Science Foundation.
Graph Theory is a field of mathematics that's instrumental in complex tangles. It helps you make more connecting flights, helps get your GPS unstuck in traffic, and helps manage your Facebook posts.
Back to the question. How many? Six (at least).
One made the conjecture. One tried for years to prove it and failed but passed on his insights. One advanced the mathematical basis for 10 more years. One helped that person solve part of the proof. And two more finally helped him complete the rest of the proof.
Elapsed time: 39 years.
So, what is the Kelmans-Seymour Conjecture, anyway? Its name comes from Paul Seymour from Princeton University, who came up with the notion in 1977. Then another mathematician named Alexander Kelmans, arrived at the same conjecture in 1979.
And though the Georgia Tech proof fills some 120 pages of math reasoning, the conjecture itself is only one short sentence:
If a graph G is 5-connected and non-planar, then G has a TK5.
The devil called 'TK5'
You could call a TK5 the devil in the details. TK5s are larger relatives of K5, a very simple formation that looks like a 5-point star fenced in by a pentagon. It resembles an occult or Anarchy symbol, and that's fitting. A TK5 in a "graph" is guaranteed to thwart any nice, neat "planar" status.
Graph Theory. Planar. Non-planar. TK5. Let's go to the real world to understand them better.
"Graph Theory is used, for example, in designing microprocessors and the logic behind computer programs," said Georgia Tech mathematician Xingxing Yu, who has shepherded the Kelmans-Seymour Conjecture's proof to completion. "It's helpful in detailed networks to get quick solutions that are reasonable and require low computational complexity."
To picture a graph, draw some cities as points on a whiteboard and lines representing interstate highways connecting them.
But the resulting drawings are not geometrical figures like squares and trapezoids. Instead, the lines, called "edges," are like wires connecting points called "vertices." For a planar graph, there is always some way to draw it so that the lines from point to point do not cross.
In the real world, a microprocessor is sending electrons from point to point down myriad conductive paths. Get them crossed, and the processor shorts out.
In such intricate scenarios, optimizing connections is key. Graphs and graph algorithms play a role in modeling them. "You want to get as close to planar as you can in these situations," Yu said.
In Graph Theory, wherever K5 or its sprawling relatives TK5s show up, you can forget planar. That's why it's important to know where one may be hiding in a very large graph.
The human connections
The human connections that led to the proof of the Kelmans-Seymour Conjecture are equally interesting, if less complicated.
Seymour had a collaborator, Robin Thomas, a Regent's Professor at Georgia Tech who heads a program that includes a concentration on Graph Theory. His team has a track record of cracking decades-old math problems. One was even more than a century old.
"I tried moderately hard to prove the Kelmans-Seymour conjecture in the 1990s, but failed," Thomas said. "Yu is a rare mathematician, and this shows it. I'm delighted that he pushed the proof to completion."
Yu, once Thomas' postdoc and now a professor at the School of Mathematics, picked up on the conjecture many years later.
"Around 2000, I was working on related concepts and around 2007, I became convinced that I was ready to work on that conjecture," Yu said. He planned to involve graduate students but waited a year. "I needed to have a clearer plan of how to proceed. Otherwise, it would have been too risky," Yu said.
Then he brought in graduate student Jie Ma in 2008, and together they proved the conjecture part of the way.
Two years later, Yu brought graduate students Yan Wang and Dawei He into the picture. "Wang worked very hard and efficiently full time on the problem," Yu said. The team delivered the rest of the proof quicker than anticipated and currently have two submitted papers and two more in the works.
In addition to the six mathematicians who made and proved the conjecture, others tried but didn't complete the proof but left behind useful cues.
Nearly four decades after Seymour had his idea, the fight for its proof is still not over. Other researchers are now called to tear at it for about two years like an invading mob. Not until they've thoroughly failed to destroy it, will the proof officially stand.
Seymour's first reaction to news of the proof reflected that reality. "Congratulations! (If it's true…)," he wrote.
Graduate student Wang is not terribly worried. "We spent lots and lots of our time trying to wreck it ourselves and couldn't, so I hope things will be fine," he said.
If so, the conjecture will get a new name: Kelmans-Seymour Conjecture Proved by He, Wang and Yu.
And it will trigger a mathematical chain reaction, automatically confirming a past conjecture, Dirac's Conjecture Proved by Mader, and also putting within reach proof of another conjecture, Hajos' Conjecture.
For Princeton mathematician Seymour, it's nice to see an intuition he held so strongly is now likely to enter into the realm of proven mathematics.
"Sometimes you conjecture some pretty thing, and it's just wrong, and the truth is just a mess," he wrote in an email message. "But sometimes, the pretty thing is also the truth; that that does happen sometimes is basically what keeps math going I suppose. There's a profound thought."
For more information, see http://arxiv.org/abs/1511.05020 and http://arxiv.org/abs/1602.07557

Story Source
https://www.sciencedaily.com/releases/2016/05/160525132837.htm?utm_source=feedburner&utm_medium=email&utm_campaign=Feed%3A+sciencedaily%2Fcomputers_math%2Fmathematics+%28Mathematics+News+--+ScienceDaily%29

Georgia Institute of Technology. "40-year math mystery and four generations of figuring." ScienceDaily. ScienceDaily, 25 May 2016. <www.sciencedaily.com/releases/2016/05/160525132837.htm>.

CIMPA-NIGERIA research school at the University of Ibadan

CIMPA-Research School on Combinatorial and Computational Algebraic Geometry
Ibadan, June 11-24, 2017

This research school will introduce the participants to some basics of algebraic geometry with an emphasis on computational aspects, such as Groebner bases and combinatorial aspects, such as toric varieties and tropical geometry. We will also learn how to use the freely available software Macaulay2 for studying algebraic varieties. The lecturers for this school are all active in these areas and collectively have deep experience both as researchers and educators through the supervision of students; Ph.D. and postdoctoral, as well as the organization of and lecturing in short courses.

Administrative and scientific coordinators

Praise Adeyemo, (University of Ibadan, Ibadan, Nigeria), praise.adeyemo13@gmail.com
Erwan Brugallé, (École polytechnique), Erwan.Brugalle@math.cnrs.fr

Scientific Committee

Dr. H. Praise Adeyemo, (University of Ibadan, Ibadan, Nigeria), Co-chair.
Erwan Brugallé, (École polytechnique), Co-chair.
Victoria Powers, Emory University, Atlanta, Georgia, USA.
Frank Sottile, Texas A&M University, College Station, Texas, USA.

Local Organizing Committee

Prof. G.O.S Ekhaguere, University of Ibadan .
Prof. Ezekiel Ayoola, University of Ibadan .
Prof. Grace Ugbebor, University of Ibadan .
Dr. V.F Payne, HOD Mathematics, University of Ibadan .
Dr. Deborah Ajayi, University of Ibadan .
Dr. H. Praise Adeyemo, University of Ibadan .

Scientific Program

This CIMPA Research School will last two weeks, and will have seven short courses of four or five lectures each, as described below. These will range from foundational to provide background through more advanced topics. We plan to have lectures in the morning and just after lunch (approximately four hours each day) with afternoon exercise sessions, including computer labs to gain experience using open-source software such as Macaulay2. Each day of the research school will conclude with a more advanced research talk given by participants and by some distinguished Nigerian Mathematicians. This model of lectures, exercise sessions, and research talks has been used successfully at past summer schools.
Dr. H. Praise Adeyemo, University Ibadan, Ibadan, Oyo, Nigeria. Ideals and Varieties.
Dr. Erwan Brugallé, École polytechnique, Paris, France. Introduction to enumerative geometry of plane curves.
Dr. Damian Maingi, University Nairobi, Kenya. Gröbner Bases.
Prof. Victoria Powers Emory University, Atlanta, Georgia, USA. Positive polynomials and sums of squares
Dr. Kristin Shaw, Technische Universität Berlin. Applications of tropical geometry to discrete and classical algebraic geometries.
Prof. Frank Sottle, Texas A&M University, College Station, Texas, USA. Toric Ideals and Combinatorics.
Prof. Bernd Sturmfels University of California, Berkeley, California, USA. Eigenvectors of Tensors

Deadline for registration: February 5, 2017

Application procedure only for applicants not from Nigeria.
Applicants from Nigeria must contact local organizer: Praise Adeyemo, (University of Ibadan, Ibadan, Nigeria), praise.adeyemo13@gmail.com

View online : Local website

2016/2017 CIMPA Rsearch Schools

The following schools will be organized by International Center for Pure and Applied

Mathematics;

Lattices and applications to cryptography and coding theory

CIMPA-ICTP-VIETNAM, Ho Chi Minh, August 1-12

Research School co-sponsored with ICTP

Mathematical Models for Security Applications

CIMPA-CUBA, Havana, August 29 - September 9

Mathematical and Computer Models in Epidemiology, Ecology and Agronomy

CIMPA-CAMEROON, Yaoundé, September 19-30

Mathématiques pour la Biologie

CIMPA-TUNISIA, Tunis, October 4-14

Théorie Spectrale des Graphes et des Variétés

CIMPA-TUNISIA, Kairouan, November 7-19

On Geometric Flows

CIMPA-INDIA, Kolkata, December 1-12

Mathematical models in biology and medicine

CIMPA-MAURITIUS, Quatre Bornes, December 5-16

For more information http://www.cimpa-icpam.org/ecoles-de-recherche/ecoles-de-recherche-2016/liste-chronologique-des-ecoles-de/

Check the link below for the list of research schools for 2017

http://www.cimpa-icpam.org/ecoles-de-recherche/ecoles-de-recherche-2017/liste-chronologique-des-ecoles-de/

Wish you good luck in your application
 

African Mathematical School you must take Advantage of before the end of 2016

CIMPA is supporting African Mathematical Schools (EMA) of the African Mathematical Union (AMU). The duration of an EMA is between 2 and 4 weeks. Their main objectives are :

 To provide Master students or early PhD students with the mathematical foundations and essential tools of selected active areas of mathematics.

 To contribute to the development of mathematics in all regions of the African continent by promoting the exchange of knowledge between young African mathematicians and the international mathematical community.

 To break the isolation of African mathematicians by providing a platform for meeting fellow mathematicians from around the world, for exchanging knowledge and for sharing experience.

List of EMA Schools 

August 22 - September 2, Luanda, Angola.
Harmonic analysis, PDEs and applications. Contact.

September 4 - 17, Natitingou, Bénin.
Algèbre, Géométrie et Applications. Contact.

September 5 - 16, N’Djamena, Tchad.
Géométrie, Analyse numérique et Applications. Contact.

November 28 - December 10, Ouagadougou, Burkina Faso.
Interactions entre Cryptographie et Géométrie Algébrique. Contact.

December 12 - 23, Maradi, Niger.
Algèbre et Géométrie, Ondelettes et EDPs. Contact.

Application into these Schools is still open.

Best of Luck

2016 Les Erudits Gifted Camp

About 2016 Gifted Camp

The Gifted camp is a 2-week academic, residential and fun-filled camp for Junior and Senior Secondary School students. It promises to emphasize on increasing students’ Mathematics, Sciences and ICT knowledge and skills while introducing them to Mathematics & Science Olympiad topics, Coding (Computer Programming) and as well as brain tasking games.

Each day, Campers will attend classes and participate in challenges. Chess and Rubik’s cubing are also involved, all these to be taught and coordinated by experienced coaches with relevant instructional materials.

Who Can Attend?

• Junior Category: Grade 7-9/JS 1-3 students.
• Senior Category: Grade 10-12/SS 1-3 students.
• Teachers: Who will like to learn more about Olympiad syllabus are also invited to oversee and attend classes.

Venue

Thames Valley College, Km 10, Sagamu-Ikoroodu Expressway, Sagamu, Ogun State.

 

Date

Arrival     = Sunday July 31st, 2016

Departure = Saturday 13th August, 2016

For more details click the link below

http://erudits.com.ng/Gifted-Camp

The Mathematical Equation that Caused the Banks to Crash in 2012

 

 

It was the holy grail of investors. The Black-Scholes equation, brainchild of economists Fischer Black and Myron Scholes, provided a rational way to price a financial contract when it still had time to run. It was like buying or selling a bet on a horse, halfway through the race. It opened up a new world of ever more complex investments, blossoming into a gigantic global industry. But when the sub-prime mortgage market turned sour, the darling of the financial markets became the Black Hole equation, sucking money out of the universe in an unending stream. Anyone who has followed the crisis will understand that the real economy of businesses and commodities is being upstaged by complicated financial instruments known as derivatives. These are not money or goods. They are investments in investments, bets about bets. Derivatives created a booming global economy, but they also led to turbulent markets, the credit crunch, the near collapse of the banking system and the economic slump. And it was the Black-Scholes equation that opened up the world of derivatives.

The equation itself wasn't the real problem. It was useful, it was precise, and its limitations were clearly stated. It provided an industry-standard method to assess the likely value of a financial derivative. So derivatives could be traded before they matured. The formula was fine if you used it sensibly and abandoned it when market conditions weren't appropriate. The trouble was its potential for abuse. It allowed derivatives to become commodities that could be traded in their own right. The financial sector called it the Midas Formula and saw it as a recipe for making everything turn to gold. But the markets forgot how the story of King Midas ended.

 

Black-Scholes underpinned massive economic growth. By 2007, the international financial system was trading derivatives valued at one quadrillion dollars per year. This is 10 times the total worth, adjusted for inflation, of all products made by the world's manufacturing industries over the last century. The downside was the invention of ever-more complex financial instruments whose value and risk were increasingly opaque. So companies hired mathematically talented analysts to develop similar formulas, telling them how much those new instruments were worth and how risky they were. Then, disastrously, they forgot to ask how reliable the answers would be if market conditions changed.  Black and Scholes invented their equation in 1973; Robert Merton supplied extra justification soon after. It applies to the simplest and oldest derivatives: options. There are two main kinds. A put option gives its buyer the right to sell a commodity at a specified time for an agreed price. A call option is similar, but it confers the right to buy instead of sell. The equation provides a systematic way to calculate the value of an option before it matures. Then the option can be sold at any time. The equation was so effective that it won Merton and Scholes the 1997 Nobel prize in economics. (Black had died by then, so he was ineligible.)

 

If everyone knows the correct value of a derivative and they all agree, how can anyone make money? The formula requires the user to estimate several numerical quantities. But the main way to make money on derivatives is to win your bet – to buy a derivative that can later be sold at a higher price, or matures with a higher value than predicted. The winners get their profit from the losers. In any given year, between 75% and 90% of all options traders lose money. The world's banks lost hundreds of billions when the sub-prime mortgage bubble burst. In the ensuing panic, taxpayers were forced to pick up the bill, but that was politics, not mathematical economics.

The Black-Scholes equation relates the recommended price of the option to four other quantities. Three can be measured directly: time, the price of the asset upon which the option is secured and the risk-free interest rate. This is the theoretical interest that could be earned by an investment with zero risk, such as government bonds. The fourth quantity is the volatility of the asset. This is a measure of how erratically its market value changes. The equation assumes that the asset's volatility remains the same for the lifetime of the option, which need not be correct. Volatility can be estimated by statistical analysis of price movements but it can't be measured in a precise, foolproof way, and estimates may not match reality. The idea behind many financial models goes back to Louis Bachelier in 1900, who suggested that fluctuations of the stock market can be modelled by a random process known as Brownian motion. At each instant, the price of a stock either increases or decreases, and the model assumes fixed probabilities for these events. They may be equally likely, or one may be more probable than the other. It's like someone standing on a street and repeatedly tossing a coin to decide whether to move a small step forwards or backwards, so they zigzag back and forth erratically. Their position corresponds to the price of the stock, moving up or down at random. The most important statistical features of Brownian motion are its mean and its standard deviation. The mean is the short-term average price, which typically drifts in a specific direction, up or down depending on where the market thinks the stock is going. The standard deviation can be thought of as the average amount by which the price differs from the mean, calculated using a standard statistical formula. For stock prices this is called volatility, and it measures how erratically the price fluctuates. On a graph of price against time, volatility corresponds to how jagged the zigzag movements look.

Black-Scholes implements Bachelier's vision. It does not give the value of the option (the price at which it should be sold or bought) directly. It is what mathematicians call a partial differential equation, expressing the rate of change of the price in terms of the rates at which various other quantities are changing. Fortunately, the equation can be solved to provide a specific formula for the value of a put option, with a similar formula for call options.

 

The early success of Black-Scholes encouraged the financial sector to develop a host of related equations aimed at different financial instruments. Conventional banks could use these equations to justify loans and trades and assess the likely profits, always keeping an eye open for potential trouble. But less conventional businesses weren't so cautious. Soon, the banks followed them into increasingly speculative ventures.

Any mathematical model of reality relies on simplifications and assumptions. The Black-Scholes equation was based on arbitrage pricing theory, in which both drift and volatility are constant. This assumption is common in financial theory, but it is often false for real markets. The equation also assumes that there are no transaction costs, no limits on short-selling and that money can always be lent and borrowed at a known, fixed, risk-free interest rate. Again, reality is often very different.

When these assumptions are valid, risk is usually low, because large stock market fluctuations should be extremely rare. But on 19 October 1987, Black Monday, the world's stock markets lost more than 20% of their value within a few hours. An event this extreme is virtually impossible under the model's assumptions. In his bestseller The Black Swan, Nassim Nicholas Taleb, an expert in mathematical finance, calls extreme events of this kind black swans. In ancient times, all known swans were white and "black swan" was widely used in the same way we now refer to a flying pig. But in 1697, the Dutch explorer Willem de Vlamingh found masses of black swans on what became known as the Swan River in Australia. So the phrase now refers to an assumption that appears to be grounded in fact, but might at any moment turn out to be wildly mistaken. Large fluctuations in the stock market are far more common than Brownian motion predicts. The reason is unrealistic assumptions – ignoring potential black swans. But usually the model performed very well, so as time passed and confidence grew, many bankers and traders forgot the model had limitations. They used the equation as a kind of talisman, a bit of mathematical magic to protect them against criticism if anything went wrong.

 

Banks, hedge funds, and other speculators were soon trading complicated derivatives such as credit default swaps – likened to insuring your neighbour's house against fire – in eye-watering quantities. They were priced and considered to be assets in their own right. That meant they could be used as security for other purchases. As everything got more complicated, the models used to assess value and risk deviated ever further from reality. Somewhere  underneath it all was real property, and the markets assumed that property values would keep rising for ever, making these investments risk-free.

 

The Black-Scholes equation has its roots in mathematical physics, where quantities are infinitely divisible, time flows continuously and variables change smoothly. Such models may not be appropriate to the world of finance. Traditional mathematical economics doesn't always match reality, either, and when it fails, it fails badly. Physicists, mathematicians and economists are therefore looking for better models.

At the forefront of these efforts is complexity science, a new branch of mathematics that models the market as a collection of individuals interacting according to specified rules. These models reveal the damaging effects of the herd instinct: market traders copy other market traders. Virtually every financial crisis in the last century has been pushed over the edge by the herd instinct. It makes everything go belly-up at the same time. If engineers took that attitude, and one bridge in the world fell down, so would all the others.

 

By studying ecological systems, it can be shown that instability is common in economic models, mainly because of the poor design of the financial system. The facility to transfer billions at the click of a mouse may allow ever-quicker profits, but it also makes shocks propagate faster.

Was an equation to blame for the financial crash, then? Yes and no. Black-Scholes may have contributed to the crash, but only because it was abused. In any case, the equation was just one ingredient in a rich stew of financial irresponsibility, political ineptitude, perverse incentives and lax regulation.

 

Despite its supposed expertise, the financial sector performs no better than random guesswork. The stock market has spent 20 years going nowhere. The system is too complex to be run on error-strewn hunches and gut feelings, but current mathematical models don't represent reality adequately. The entire system is poorly understood and dangerously unstable. The world economy desperately needs a radical overhaul and that requires more mathematics, not less. It may be rocket science, but magic it's not.

 

Ian Stewart is emeritus professor of mathematics at the University of Warwick. His new book 17 Equations That Changed the World is published by Profile (£15.99)

 

Source: https://www.theguardian.com/science/2012/feb/12/black-scholes-equation-credit-crunch

Distinguishing Profile of G.O.S Ekhaguere

Prof Godwin Osakpemwoya Samuel Ekhaguere
Born: 23 May, 1947

Birthplace: Benin City, Edo State, Nigeria

B.S. (1971) Physics University of Ibadan, Nigeri; D.I.C. (1974) in Mathematical Physics Imperial College of Science & Technology
he earned a Ph.D. (1976) Mathematical Physics University of London.

Image: Otedo.com

Professor Ekhaguere's high academic ability was evident at an early age, when he won the competitive five-year scholarship of the Western Region of Nigeria tenable in the prestigious Immaculate Conception College (ICC), Benin City in 1961. He completed his secondary school education with a First Division Certificate in 1965. He was awarded a scholarship in 1966 by the ICC for his Higher School Certificate (HSC) education (1966-67). Best known among his friends and colleagues simply as Gos, he gained admission into the University of Ibadan, Nigeria (West Africa) for his undergraduate studies in 1968. In 1971, he earned a Bachelor of Science degree with Honors in Physics. He then proceeded to the Imperial College of Science & Technology (now Imperial College of Science, Technology & Medicine) London where he earned the Diploma of Imperial College (D.I.C.) in Mathematical Physics in 1974. In 1976, he earned a Ph.D. in Mathematical Physics from the University of London (Bedford College).

Dr Godwin Osakpemwoya Samuel EKHAGUERE is a Professor of Mathematics at the University of Ibadan, Ibadan, Nigeria. His research activities are in the core areas of mathematical physics; algebras and partial algebras; and classical and noncommutative stochastic analysis including financial mathematics.  He has made landmark contributions to these branches of mathematics, especially his:

• C*-algebraic characterization of the super selection sectors of the free electromagnetic field;

• proof, for the first time, of a central limit theorem in probability gage spaces over semi-finite W*-algebras of operators, including a noncommutative Levy-Khinchine representation for the Fourier transforms of limit probability gage spaces;
• pioneering and opening up of an entirely new field of mathematical research when he introduced quantum stochastic differential inclusions, and then studied the classes of Lipschitzian quantum stochastic differential inclusions, hypermaximal monotone quantum stochastic differential inclusions and quantum stochastic evolutions;
• introducing, for the first time, of a wide class of noncommutative semimartingale-driven stochastic integral/differential equations in seven different locally convex operator topologies and studying the existence and uniqueness of their solutions; and
• characterization of the completely positive maps on certain partial *-algebras; introduction and study of unbounded partial Hilbert algebras; his formulation and characterization of Dirichlet forms on partial *-algebras, and his study of the structure and representations of partial algebras.

In global recognition of his seminal publications, Professor Ekhaguere has held several visiting scientist/professor positions in reputable research institutions around the world and won many highly competitive and prestigious scholarships/fellowships/sponsorships from diverse academic foundations/institutions, including the Associateship and Senior Associateship of the Abdus Salam International Centre for Theoretical Physics, Trieste, Italy, Fellowship of the Alexander von Humboldt Foundation, Bonn, Germany, as  well as Sponsorship of the Volkswagen-Stiftung, Sponsorship of the Deutsche Forschungstemeinschaft, Sponsorship of the Japanese Society for the Promotion of Science, Sponsorship of the Commemorative Association for the Japan World Exposition (1970), Sponsorship of the Swedish Agency for Research Cooperation with Developing Countries, Sponsorship of the Forschungsinstitut für Mathematik, Eidgenossische Technische Hochschule (ETH), Zürich, Switzerland, Staff Exchange Fellowship of the Association of African Universities, and Sponsorship of the London Mathematical Society. He has given many invited lectures in Nigeria and abroad. For example, he has already been invited this year 2013 to give one of the distinguished plenary lectures at the continental Pan-African Congress of Mathematicians, which brings together all mathematicians in Africa every four year, which is scheduled to hold in Abuja, Nigeria, in July 2013.   Professor Ekhaguere serves on the Editorial Boards of the following journals: Journal of the Nigerian Mathematical Society, Journal of the Nigerian Association of Mathematical Physics, Journal of the Mathematical Association of Nigeria, Journal of Science Research (Faculty of Science University of Ibadan)),  Afrika Matematika (Springer Verlag), and the South Pacific Journal of Pure & Applied Mathematics (University of Papua New Guinea). He also acts as a reviewer for several international journals of mathematics/mathematical physics, including: Abacus: Journal of the Mathematical Association of Nigeria, Journal of Science Research (Faculty of Science, University of Ibadan), Journal of the Nigerian Mathematical Society, Journal of the Nigerian Association of Mathematical Physics, Journal of Mathematical Analysis & Applications, Elsevier Publishers, USA, Journal of Mathematics & Mathematical Sciences, Hindawi Publishers, USA, Mediterranean Journal of Mathematics, Springer Publishers, Germany, Stochastic Analysis & Applications, Taylor & Francis Publishers, USA, Afrika Matematika, Springer Verlag, Acta Mathematica Sinica, Elsevier Publishers, USA. Professor Ekhaguere has served as an assessor of candidates for appointment/promotion to the grade of Associate Professor/Professor of Mathematics and as an external examiner at several universities in Nigeria and on the continent.  In addition to his Professorship at the University of Ibadan, Professor Ekhaguere is the Founder and President of the International Centre for Mathematical & Computer Sciences (ICMCS), Lagos (www.icmcs.org). An inspiring lecturer and mentor, he upholds the highest standard of mathematical research and training, as evidenced by the high quality of the MSc, MPhil and PhD graduates supervised by him. 

Indeed this man is a distinguishing scholar. At age 69 he remains vibrant, calm and very inspiring.

 

Culled from http://www.aasciences.org/index.php/nigeria/286-ekhaguere-dr-godwin-osakpemwoya-samuel-prof

 

 

8th International Tournament of Young Mathematicians

The ITYM is a team competition for high school students from all over the world. Its purpose is to stimulate interest in mathematics and its applications, to develop scientific thinking, communication skills and teamwork.
In contrast to Olympiads, the problems for the ITYM are published several months in advance and contain parts with no known solution. During the tournament the participating students present their results in a kind of research debate involving Reporter, Opponent, Reviewer and Observer.The ITYM developed out of national tournaments in some countries, especially from Eastern Europe. The need for an international tournament became increasingly clear over the last few years. The ITYM was motivated, in particular, by the growing popularity of the International Young Physicists' Tournament (IYPT).
The 8th ITYM is being co-organised by the Laboratory of Continuous Mathematical Education and Animath and will take place in Saint Petersburg,  the cultural capital of Russia,

Date: from 4^th to 11^th of July 2016.

The problems of the ITYM 2016 have been published.

For more details, click here http://www.itym.org/ 

1ST PASTOR E. A. ADEBOYE ENDOWED CHAIR ENRICHMENT TRAINING WORKSHOP IN APPLIED MATHEMATICS

University of Lagos in Collaboration with National Mathematical Centre, Abuja is organizing the 1st Pastor E. A. Adeboye Endowed Chair Enrichment Training Workshop in Applied Mathematics.

This is scheduled to hold from 5th to 11th June, 2016 with the theme ‘Complex Fluid flows and it's Environmental Applications’.

 

Workshop Highlights
Provide adequate foundational principles of mathematics and statistics
Highlight examples after examples on each principle
Bridge the gap between theory and practice
Expound the knowledge base of participants
Enrich expertise in modelling, analysis and numerics
Build manpower through mentoring
Assess the educational development and performance of participants

 

Click here for details;

http://www.aecunilag.org/workshop2016/

Academic Research and Project Writing Training

To stem the rising tide in research ineptitude among undergraduate students in the country, COLLOQ in partnership with Irawo University Center will be organizing a one day training on how to write excellent academic project. This training will focus on Undergraduate project writing in Pure and Applied Science, Engineering, Social Science and Art. This training is fully funded and for students in University of Ibadan.

Date: Saturday, April 16th, 2016.

Venue: Irawo University Center, Agbowo, UI, Ibadan.

Benefits:
Project writing training
Access to research materials
Mentoring opportunity and support for  participants writing projects
Access to academic information for participants
Free Registration

Eligibility:
University of Ibadan undergraduate students in Semi final or Final year of their programme.
Academic standing of at least a second class upper.

Application Procedure:
Send an email with your; Name, Course, Faculty, Gender and a sentence on why you should be selected for the training  to thecolloq@gmail.com.
Please the subject of the email should be ACADEMIC RESEARCH AND PROJECT WRITING TRAINING.

Registration: FREE

Application deadline: Saturday, 9th April, 2016.

Note: Only shortlisted candidates will receive an invitation email on Wednesday, 13th April, 2016. Please you do not have to contact the organizer on the status of your application.

Second Round Olympiad Result is Out

You can check the result for the Olympiad second round competition by clicking http://nmcabuja.org/olympiads/second_round_olympiad_results_2016.htm

Good luck

 

2016 AAS/ AMU Symposium and School

To solve the enormous problems confronting STEM and in particular Mathematical Sciences higher Education and Research in Africa, the African Academy of Science in collaboration with African Mathematical Union will be organizing a symposium tagged "Current Research Trends in Mathematical Sciences and Application"

Venue: National Mathematical Center, Abuja
Date: May 17-20, 2016.

There will be a pre- symposium school in the following areas;
Algebra (Prof. Aderemi Kuku, Nigeria)
Analysis on Manifolds (Prof. Leonard Todjihounde, Benin Republic)
Theoretical Physics (Prof. Samuel Howusu, Ghana and J. Tossa, Benin Republic)
Financial Mathematics (Prof. Matte Marsili, Italy).

Details of the Pre-symposium school;

Venue: National Mathematical Center, Abuja
Date: May 3-16, 2016.

To apply for the Symposium/School, send an email to;

1. Distinguished Professor Aderemi Kuku (Chairman, International Committee)
National Mathematical Center, Kaduna-Lokoja Road, Sheda
PMB 118, Garki Post office, Abuja
Email: aderemikuku@yahoo.com; president@aasciences.org

2. Professor A.R.T Solarin (Vice-Chairman, International Committee)
National Mathematical Center, Kaduna-Lokoja Road, Sheda
PMB 118, Garki Post office, Abuja
E-mail: asolarin2002@yahoo.com; director@nmcabuja.org

Your email should indicate the following;
1. If you will present a paper (attach the title and abstract of the paper)
2. If you need a travel support (partial or full)
3. Attach your CV

Note: Please state if you are applying for the Symposium or Pre-Symposium School

Deadline: March 10, 2016.  

How funny is this word? The 'snunkoople' effect

Credit: © flytoskyft11 / Fotolia

 

How do you quantify something as complex and personal as humour? University of Alberta researchers have developed a mathematical method of doing just that -- and it might not be quite as personal as we think.

 

"This really is the first paper that's ever had a quantifiable theory of humour," says U of A psychology professor Chris Westbury, lead author of the recent study. "There's quite a small amount of experimental work that's been done on humour."
"We think that humour is personal, but evolutionary psychologists have talked about humour as being a message-sending device."
The idea for the study was born from earlier research in which test subjects with aphasia were asked to review letter strings and determine whether they were real words or not. Westbury began to notice a trend: participants would laugh when they heard some of the made-up non-words, like snunkoople.
It raised the question -- how can a made-up word be inherently funny?
The snunkoople effect
Westbury hypothesized that the answer lay in the word's entropy -- a mathematical measure of how ordered or predictable it is. Non-words like finglam, with uncommon letter combinations, are lower in entropy than other non-words like clester, which have more probable combinations of letters and therefore higher entropy.
"We did show, for example, that Dr. Seuss -- who makes funny non-words -- made non-words that were predictably lower in entropy. He was intuitively making lower-entropy words when he was making his non-words," says Westbury. "It essentially comes down to the probability of the individual letters. So if you look at a Seuss word like yuzz-a-ma-tuzz and calculate its entropy, you would find it is a low-entropy word because it has improbable letters like Z."
Inspired by the reactions to snunkoople, Westbury set out to determine whether it was possible to predict what words people would find funny, using entropy as a yardstick.
"Humour is not one thing. Once you start thinking about it in terms of probability, then you start to understand how we find so many different things funny."
For the first part of the study, test subjects were asked to compare two non-words and select the option they considered to be more humorous. In the second part, they were shown a single non-word and rated how humorous they found it on a scale from 1 to 100.
"The results show that the bigger the difference in the entropy between the two words, the more likely the subjects were to choose the way we expected them to," says Westbury, noting that the most accurate subject chose correctly 92 per cent of the time. "To be able to predict with that level of accuracy is amazing. You hardly ever get that in psychology, where you get to predict what someone will choose 92 per cent of the time."
People are funny that way
This nearly universal response says a lot about the nature of humour and its role in human evolution. Westbury refers to a well-known 1929 linguistics study by Wolfgang Köhler in which test subjects were presented with two shapes, one spiky and one round, and were asked to identify which was a baluba and which was a takete. Almost all the respondents intuited that takete was the spiky object, suggesting a common mapping between speech sounds and the visual shape of objects.
The reasons for this may be evolutionary. "We think that humour is personal, but evolutionary psychologists have talked about humour as being a message-sending device. So if you laugh, you let someone else know that something is not dangerous," says Westbury.
He uses the example of a person at home believing they see an intruder in their backyard. This person might then laugh when they discover the intruder is simply a cat instead of a cat burglar. "If you laugh, you're sending a message to whomever's around that you thought you saw something dangerous, but it turns out it wasn't dangerous after all. It's adaptive."
Just as expected (or not)
The idea of entropy as a predictor of humour aligns with a 19th-century theory from the German philosopher Arthur Schopenhauer, who proposed that humour is a result of an expectation violation, as opposed to a previously held theory that humour is based simply on improbability. When it comes to humour, expectations can be violated in various ways.
In non-words, expectations are phonological (we expect them to be pronounced a certain way), whereas in puns, the expectations are semantic. "One reason puns are funny is that they violate our expectation that a word has one meaning," says Westbury. Consider the following joke: Why did the golfer wear two sets of pants? Because he got a hole in one. "When you hear the golfer joke, you laugh because you've done something unexpected -- you expect the phrase 'hole in one' to mean something different, and that expectation has been violated."
The study may not be about to change the game for stand-up comedians -- after all, a silly word is hardly the pinnacle of comedy -- but the findings may be useful in commercial applications such as in product naming.
"I would be interested in looking at the relationship between product names and the seriousness of the product," notes Westbury. "For example, people might be averse to buying a funny-named medication for a serious illness -- or it could go the other way around."
Finding a measurable way to predict humour is just the tip of the proverbial iceberg. "One of the things the paper says about humour is that humour is not one thing. Once you start thinking about it in terms of probability, then you start to understand how we find so many different things funny. And the many ways in which things can be funny."

Source:
University of Alberta. "How funny is this word? The 'snunkoople' effect." ScienceDaily. ScienceDaily, 30 November 2015. <www.sciencedaily.com/releases/2015/11/151130131847.htm>.

Quantum physics problem proved unsolvable (Gödel and Turing enter quantum physics)

Source: Planet-science.com

 

A mathematical problem underlying fundamental questions in particle and quantum physics is provably unsolvable, according to scientists at UCL, Universidad Complutense de Madrid -- ICMAT and Technical University of Munich.

 

It is the first major problem in physics for which such a fundamental limitation could be proven. The findings are important because they show that even a perfect and complete description of the microscopic properties of a material is not enough to predict its macroscopic behaviour.
A small spectral gap -- the energy needed to transfer an electron from a low-energy state to an excited state -- is the central property of semiconductors. In a similar way, the spectral gap plays an important role for many other materials. When this energy becomes very small, i.e. the spectral gap closes, it becomes possible for the material to transition to a completely different state. An example of this is when a material becomes superconducting.
Mathematically extrapolating from a microscopic description of a material to the bulk solid is considered one of the key tools in the search for materials exhibiting superconductivity at ambient temperatures or other desirable properties. A study, published today in Nature, however, shows crucial limits to this approach. Using sophisticated mathematics, the authors proved that, even with a complete microscopic description of a quantum material, determining whether it has a spectral gap is, in fact, an undecidable question.
"Alan Turing is famous for his role in cracking the Enigma code," said Co-author, Dr Toby Cubitt from UCL Computer Science. "But amongst mathematicians and computer scientists, he is even more famous for proving that certain mathematical questions are `undecidable' -- they are neither true nor false, but are beyond the reach of mathematics. What we've shown is that the spectral gap is one of these undecidable problems. This means a general method to determine whether matter described by quantum mechanics has a spectral gap, or not, cannot exist. Which limits the extent to which we can predict the behaviour of quantum materials, and potentially even fundamental particle physics."
One million dollars to win!
The most famous problem concerning spectral gaps is whether the theory governing the fundamental particles of matter itself -- the standard model of particle physics -- has a spectral gap (the `Yang-Mills mass gap' conjecture). Particle physics experiments such as CERN and numerical calculations on supercomputers suggest that there is a spectral gap. Although there is a $1m prize at stake from the Clay Mathematics Institute for whoever can, no one has yet succeeded in proving this mathematically from the equations of the standard model.
Dr Cubitt added, "It's possible for particular cases of a problem to be solvable even when the general problem is undecidable, so someone may yet win the coveted $1m prize. But our results do raise the prospect that some of these big open problems in theoretical physics could be provably unsolvable."
"We knew about the possibility of problems that are undecidable in principle since the works of Turing and Gödel in the 1930s," added Co-author Professor Michael Wolf from Technical University of Munich. "So far, however, this only concerned the very abstract corners of theoretical computer science and mathematical logic. No one had seriously contemplated this as a possibility right in the heart of theoretical physics before. But our results change this picture. From a more philosophical perspective, they also challenge the reductionists' point of view, as the insurmountable difficulty lies precisely in the derivation of macroscopic properties from a microscopic description."
Not all bad news
Co-author, Professor David Pérez-García from Universidad Complutense de Madrid and ICMAT, said: "It's not all bad news, though. The reason this problem is impossible to solve in general is because models at this level exhibit extremely bizarre behaviour that essentially defeats any attempt to analyse them. But this bizarre behaviour also predicts some new and very weird physics that hasn't been seen before. For example, our results show that adding even a single particle to a lump of matter, however large, could in principle dramatically change its properties. New physics like this is often later exploited in technology."
The researchers are now seeing whether their findings extend beyond the artificial mathematical models produced by their calculations to more realistic quantum materials that could be realised in the laboratory.

Source:
University College London. "Quantum physics problem proved unsolvable: Gödel and Turing enter quantum physics." ScienceDaily. ScienceDaily, 9 December 2015. <www.sciencedaily.com/releases/2015/12/151209142727.htm>.

 

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