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Main article: Von Neumann introduced the study of rings of operators, through the von Neumann algebras. A von Neumann algebra is a of on a that is closed in the weak operator topology and contains the. The shows that the analytic definition is equivalent to a purely algebraic definition as being equal to the bicommutant. Von Neumann embarked in 1936, with the partial collaboration of F.J. Murray, on the general study of classification of von Neumann algebras.

The six major papers in which he developed that theory between 1936 and 1940 'rank among the masterpieces of analysis in the twentieth century'. The was later introduced in 1949 by John von Neumann. Bahar E Shariat Pdf Free Download. Measure theory [ ].

See also: In, the 'problem of measure' for an n-dimensional Euclidean space R n may be stated as: 'does there exist a positive, normalized, invariant, and additive set function on the class of all subsets of R n?' The work of and had implied that the problem of measure has a positive solution if n = 1 or n = 2 and a negative solution (because of the ) in all other cases. Von Neumann's work argued that the 'problem is essentially group-theoretic in character': the existence of a measure could be determined by looking at the properties of the of the given space.

The positive solution for spaces of dimension at most two, and the negative solution for higher dimensions, comes from the fact that the is a for dimension at most two, and is not solvable for higher dimensions. 'Thus, according to von Neumann, it is the change of group that makes a difference, not the change of space.' In a number of von Neumann's papers, the methods of argument he employed are considered even more significant than the results. In anticipation of his later study of dimension theory in algebras of operators, von Neumann used results on equivalence by finite decomposition, and reformulated the problem of measure in terms of functions. In his 1936 paper on analytic measure theory, he used the in the solution of in the case of compact groups. In 1938, he was awarded the for his work in analysis. Geometry [ ] Von Neumann founded the field of.

It followed his path-breaking work on rings of operators. In mathematics, continuous geometry is a substitute of complex, where instead of the dimension of a subspace being in a discrete set 0, 1., n, it can be an element of the unit interval [0,1]. Von Neumann was motivated by his discovery of with a dimension function taking a continuous range of dimensions, and the first example of a continuous geometry other than projective space was the projections of the. Lattice theory [ ] Between 1937 and 1939, Von Neumann worked on, the theory of in which every two elements have a greatest lower bound and a least upper bound. Von Neumann provided an abstract exploration of dimension in completed topological lattices (properties that arise in the of ): 'Dimension is determined, up to a positive linear transformation, by the following two properties.

It is conserved by perspective mappings ('perspectivities') and ordered by inclusion. The deepest part of the proof concerns the equivalence of perspectivity with 'projectivity by decomposition'—of which a corollary is the transitivity of perspectivity.' Writes: 'John von Neumann's brilliant mind blazed over lattice theory like a meteor'. Von Neumann founded the field of based on lattice theoretic principles. Earlier, Menger and Birkhoff had axiomatized complex in terms of the properties of its lattice of linear subspaces. Von Neumann, following his work on rings of operators, weakened those axioms to describe a broader class of lattices, the continuous geometries. While the dimensions of the subspaces of projective geometries are a discrete set (the non-negative integers), the dimensions of the elements of a continuous geometry can range continuously across the unit interval [0,1].

Von Neumann was motivated by his discovery of with a dimension function taking a continuous range of dimensions, and the first example of a continuous geometry other than projective space was the projections of the. Additionally, '[I]n the general case, von Neumann proved the following basic representation theorem. Any complemented modular lattice L having a 'basis' of n ≥ 4 pairwise perspective elements, is isomorphic with the lattice ℛ( R) of all principal of a suitable R. This conclusion is the culmination of 140 pages of brilliant and incisive algebra involving entirely novel axioms. Anyone wishing to get an unforgettable impression of the razor edge of von Neumann's mind, need merely try to pursue this chain of exact reasoning for himself—realizing that often five pages of it were written down before breakfast, seated at a living room writing-table in a bathrobe.' Mathematical formulation of quantum mechanics [ ].

Von Neumann's wartime ID badge photo Manhattan Project [ ] Beginning in the late 1930s, von Neumann developed an expertise in —phenomena that are difficult to model mathematically. During this period von Neumann was the leading authority of the mathematics of. This led him to a large number of military consultancies, primarily for the Navy, which in turn led to his involvement in the.

The involvement included frequent trips by train to the project's secret research facilities at the. Von Neumann's principal contribution to the was in the concept and design of the needed to compress the core of the weapon that was later dropped on.

While von Neumann did not originate the ' concept, he was one of its most persistent proponents, encouraging its continued development against the instincts of many of his colleagues, who felt such a design to be unworkable. He also eventually came up with the idea of using more powerful shaped charges and less fissionable material to greatly increase the speed of 'assembly'. When it turned out that there would not be enough to make more than one bomb, the implosive lens project was greatly expanded and von Neumann's idea was implemented. Implosion was the only method that could be used with the that was available from the. He established the design of the required, but there remained concerns about 'edge effects' and imperfections in the explosives. His calculations showed that implosion would work if it did not depart by more than 5% from spherical symmetry. After a series of failed attempts with models, this was achieved by, and the construction of the Trinity bomb was completed in July 1945.

In a visit to Los Alamos in September 1944, von Neumann showed that the pressure increase from explosion shock wave reflection from solid objects was greater than previously believed if the angle of incidence of the shock wave was between 90° and some limiting angle. As a result, it was determined that the effectiveness of an atomic bomb would be enhanced with detonation some kilometers above the target, rather than at ground level. Implosion mechanism Along with four other scientists and various military personnel, von Neumann was included in the target selection committee responsible for choosing the Japanese cities of and Nagasaki as the. Von Neumann oversaw computations related to the expected size of the bomb blasts, estimated death tolls, and the distance above the ground at which the bombs should be detonated for optimum shock wave propagation and thus maximum effect. The cultural capital, which had been spared the, was von Neumann's first choice, a selection seconded by Manhattan Project leader General.

However, this target was dismissed. On July 16, 1945, with numerous other Manhattan Project personnel, von Neumann was an eyewitness to the first atomic bomb blast, code named Trinity, conducted as a test of the implosion method device, at the near, 35 miles (56 km) southeast of. Based on his observation alone, von Neumann estimated the test had resulted in a blast equivalent to 5 (21 ) but produced a more accurate estimate of 10 kilotons by dropping scraps of torn-up paper as the shock wave passed his location and watching how far they scattered.

The actual power of the explosion had been between 20 and 22 kilotons. It was in von Neumann's 1944 papers that the expression 'kilotons' appeared for the first time. After the war, remarked that the physicists involved in the Manhattan project had 'known sin'.

Von Neumann's response was that 'sometimes someone confesses a sin in order to take credit for it.' Von Neumann continued unperturbed in his work and became, along with Edward Teller, one of those who sustained the. He collaborated with on further development of the bomb, and in 1946 the two filed a secret patent on 'Improvement in Methods and Means for Utilizing Nuclear Energy', which outlined a scheme for using a fission bomb to compress fusion fuel to initiate. The Fuchs–von Neumann patent used, but not in the same way as is used in what became the final hydrogen bomb design, the. Their work was, however, incorporated into the 'George' shot of, which was instructive in testing out concepts that went into the final design.

The Fuchs–von Neumann work was passed on to the Soviet Union by Fuchs as part of his, but it was not used in the Soviets' own, independent development of the Teller–Ulam design. The historian has pointed out that ironically, 'John von Neumann and Klaus Fuchs, produced a brilliant invention in 1946 that could have changed the whole course of the development of the hydrogen bomb, but was not fully understood until after the bomb had been successfully made.'

For his wartime services, von Neumann was awarded the in July 1946, and the in October 1946. Atomic Energy Commission [ ] In 1950, von Neumann became a consultant to the (WSEG), whose function was to advise the and the on the development and use of new technologies. He also became an adviser to the (AFSWP), which was responsible for the military aspects on nuclear weapons. Over the following two years, he became a consultant to the (CIA), a member of the influential of the, a consultant to the newly established, and a member of the of the.

In 1955, von Neumann became a commissioner of the AEC. He accepted this position and used it to further the production of compact suitable for delivery.

He involved himself in correcting the severe shortage of and needed for these compact weapons, and he argued against settling for the intermediate range missiles that the Army wanted. He was adamant that H-bombs delivered into the heart of enemy territory by an ICBM would be the most effective weapon possible, and that the relative inaccuracy of the missile wouldn't be a problem with an H-bomb. He said the Russians would probably be building a similar weapon system, which turned out to be the case. Despite his disagreement with Oppenheimer over the need for a crash program to develop the hydrogen bomb, he testified on the latter's behalf at the 1954, at which he asserted that Oppenheimer was loyal, and praised him for his helpfulness once the program went ahead.

Shortly before his death, when he was already quite ill, von Neumann headed the United States government's top secret ICBM committee, and it would sometimes meet in his home. Its purpose was to decide on the feasibility of building an ICBM large enough to carry a thermonuclear weapon.

Von Neumann had long argued that while the technical obstacles were sizable, they could be overcome in time. The passed its first fully functional test in 1959, two years after his death. The feasibility of an ICBM owed as much to improved, smaller warheads as it did to developments in rocketry, and his understanding of the former made his advice invaluable. Mutual assured destruction [ ]. Nuclear test in July 1956 Von Neumann is credited with developing the equilibrium strategy of (MAD). He also 'moved heaven and earth' to bring MAD about.

His goal was to quickly develop ICBMs and the compact hydrogen bombs that they could deliver to the USSR, and he knew the Soviets were doing similar work because the interviewed German rocket scientists who were allowed to return to Germany, and von Neumann had planted a dozen technical people in the CIA. The Russians considered that bombers would soon be vulnerable, and they shared von Neumann's view that an H-bomb in an ICBM was the of weapons; they believed that whoever had superiority in these weapons would take over the world, without necessarily using them.

He was afraid of a 'missile gap' and took several more steps to achieve his goal of keeping up with the Soviets: • He modified the ENIAC by making it programmable and then wrote programs for it to do the H-bomb calculations verifying that the Teller-Ulam design was feasible and to develop it further. • Through the Atomic Energy Commission, he promoted the development of a compact H-bomb that would fit in an ICBM. • He personally interceded to speed up the production of lithium-6 and tritium needed for the compact bombs. • He caused several separate missile projects to be started, because he felt that competition combined with collaboration got the best results.

Von Neumann's assessment that the Soviets had a lead in missile technology, considered pessimistic at the time, was soon proven correct in the. Von Neumann entered government service primarily because he felt that, if freedom and civilization were to survive, it would have to be because the United States would triumph over totalitarianism from, and. During a committee hearing he described his political ideology as 'violently, and much more militaristic than the norm'.

He was quoted in 1950 remarking, 'If you say why not bomb [the Soviets] tomorrow, I say, why not today? If you say today at five o'clock, I say why not one o'clock?' On February 15, 1956, von Neumann was presented with the by President. His citation read: Dr. Von Neumann, in a series of scientific study projects of major national significance, has materially increased the scientific progress of this country in the armaments field. Through his work on various highly classified missions performed outside the continental limits of the United States in conjunction with critically important international programs, Dr.

Von Neumann has resolved some of the most difficult technical problems of national defense. Computing [ ].

Merge sort animation. The sorted elements are represented by dots. Von Neumann was a founding figure in. Cites von Neumann as the inventor, in 1945, of the algorithm, in which the first and second halves of an array are each sorted recursively and then merged. Von Neumann wrote the 23 pages long sorting program for the in ink. On the first page, traces of the phrase 'TOP SECRET', which was written in pencil and later erased, can still be seen. He also worked on the philosophy of with when the latter visited Princeton in the 1930s.

Von Neumann's hydrogen bomb work was played out in the realm of computing, where he and Stanislaw Ulam developed simulations on von Neumann's digital computers for the hydrodynamic computations. During this time he contributed to the development of the, which allowed solutions to complicated problems to be approximated using. His algorithm for simulating a with a biased coin is used in the 'software whitening' stage of some.

Because using lists of 'truly' random numbers was extremely slow, von Neumann developed a form of making, using the. Though this method has been criticized as crude, von Neumann was aware of this: he justified it as being faster than any other method at his disposal, writing that 'Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin.'

Von Neumann also noted that when this method went awry it did so obviously, unlike other methods which could be subtly incorrect. While consulting for the at the on the EDVAC project, von Neumann wrote an incomplete. The paper, whose premature distribution nullified the patent claims of EDVAC designers and, described a in which the data and the program are both stored in the computer's memory in the same address space. This architecture is the basis of most modern computer designs, unlike the earliest computers that were 'programmed' using a separate memory device such as a. Although the single-memory, stored program architecture is commonly called as a result of von Neumann's paper, the architecture was based on the work of Eckert and Mauchly, inventors of the computer at the University of Pennsylvania.

John von Neumann consulted for the Army's, most notably on the ENIAC project, as a member of its Scientific Advisory Committee. The electronics of the new ENIAC ran at one-sixth the speed, but this in no way degraded the ENIAC's performance, since it was still entirely. Complicated programs could be developed and in days rather than the weeks required for plugboarding the old ENIAC. Some of von Neumann's early computer programs have been preserved. The next computer that von Neumann designed was the at the Institute for Advanced Study in Princeton, New Jersey.

He arranged its financing, and the components were designed and built at the nearby. John von Neumann recommended that the, nicknamed the defense computer include a magnetic drum. It was a faster version of the IAS machine and formed the basis for the commercially successful IBM 704. Was first introduced in a pioneering paper by von Neumann in 1953.

However, the theory could not be implemented until advances in computing of the 1960s. Cellular automata, DNA and the universal constructor [ ].

Von Neumann's gravestone In 1955, von Neumann was diagnosed with what was either. He was not able to well accept the proximity of his own demise, and the shadow of impending death instilled great fear in him.

He invited a Roman Catholic priest, Father Anselm Strittmatter,, to visit him for consultation. Von Neumann reportedly said, 'So long as there is the possibility of eternal damnation for nonbelievers it is more logical to be a believer at the end,' essentially saying that had a point, referring to. He had earlier confided to his mother, 'There probably has to be a God. Many things are easier to explain if there is than if there isn't.' Father Strittmatter administered the to him.

Some of von Neumann's friends (such as and Oskar Morgenstern) said they had always believed him to be 'completely agnostic.' Of this deathbed conversion, Morgenstern told Heims, 'He was of course completely agnostic all his life, and then he suddenly turned Catholic—it doesn't agree with anything whatsoever in his attitude, outlook and thinking when he was healthy.' Father Strittmatter recalled that even after his conversion, von Neumann did not receive much peace or comfort from it, as he still remained terrified of death. On his deathbed, Von Neumann entertained his brother by reciting, by heart and word-for-word, the first few lines of each page of. He died at age 53 on February 8, 1957, at the in, under military security lest he reveal military secrets while heavily medicated. He was buried at in Princeton,. Honors [ ] • The of the (INFORMS, previously TIMS-ORSA) is awarded annually to an individual (or group) who have made fundamental and sustained contributions to theory in and the management sciences.

• The is awarded annually by the (IEEE) 'for outstanding achievements in computer-related science and technology.' • The John von Neumann Lecture is given annually at the (SIAM) by a researcher who has contributed to applied mathematics, and the chosen lecturer is also awarded a monetary prize.

• The crater on the is named after him. • The in, was named in his honor. • The professional society of Hungarian computer scientists,, is named after John von Neumann. It was closed in April 1989.

• On May 4, 2005 the issued the American Scientists commemorative postage stamp series, a set of four 37-cent self-adhesive stamps in several configurations designed by artist. The scientists depicted were von Neumann,,, and.

• The of the was named in his honor, and has been given every year since 1995 to professors who have made an outstanding contribution to the exact social sciences and through their work have strongly influenced the professional development and thinking of the members of the college. Selected works [ ] • 1923. On the introduction of transfinite numbers, 346–54. An axiomatization of set theory, 393–413. • 1932., Beyer, R.

T., trans., Princeton Univ. 1996 edition:. Von Neumann, John (1981). Halperin, Israel, ed.. Memoirs of the American Mathematical Society.

• 1944., with Morgenstern, O., Princeton Univ. 2007 edition:. 'The general and logical theory of automata,' in Cerebral Mechanisms in Behavior: The Hixon Symposium, ed., John Wiley & Sons, New York, N. Y, 1951, pp. 1–31,. Von Neumann, John (1998).. Princeton Landmarks in Mathematics.... Collected Works of John von Neumann, Taub, A.

H., ed., Pergamon Press. Theory of Self-Reproducing Automata,, ed. Pro Tools Edirol Ua 25 Driver. , University of Illinois Press. See also [ ].

• • • • • • • • • •;,,,. • — International Social Science Review • at •,,, Minneapolis. And describe,, and computers, and John von Neumann's contribution to the development of computers. •,, University of Minnesota, Minneapolis. •,, University of Minnesota.

• — from •, audio talk by •, article by on von Neumann's 100th birthday. • from the • •, December 2, 1954 (audio recording) •, The American Presidency Project •.. • from the Institute for Operations Research and the Management Sciences.

Seven at night on the Friday before Christmas and I was rushing to meet a deadline. With less than an hour to finish a documentary I was working on, my fingers were flying over my keyboard as I wrestled with the script, phone calls and emails with a researcher abroad while watching multiple TV screens in the cutting room and talking simultaneously to people around me. Suddenly an alarming email popped into my Yahoo mailbox from Yahoo itself, saying my account was about to be shut down unless I confirmed all my details with them.

Many people fall victim to 'phising' when they receive hoax emails appearing to have been sent from a legitimate source It looked authentic - the graphics, the text, the disclaimer at the bottom were identical to the ones used by Yahoo - even some of the details about my account were accurate. I panicked, distracted by all the activity around me, worried I would lose all the precious material in my emails. So I did what I never should have done.

I filled in all the boxes, including my password, and pressed the enter key. Within a minute my screen went blank, my electronic lifeline was severed and the nightmare began. I had become one of thousands of victims of 'phishing' - the word is a combination of 'fishing' and ' phreaking', which means breaking into a phone system.

Phishing refers to electronic bait put out by criminals to catch financial information and carry out fraud by using your computer passwords. Within seconds of pressing that enter key, a message written by the hackers but under my name went out to everyone in the computerised address book attached to my email account.

I had become one of thousands of victims of 'phishing' - the word is a combination of 'fishing' and ' phreaking', which means breaking into a phone system Within a minute, phone calls started flooding in from alarmed contacts who had received the message. I did not know at first what they were talking about - the hackers had changed my password to shut me out of my computer. The first call came from an MP whose name begins with 'A' and was top of my address list. He was in his car and had received an email on his BlackBerry supposedly sent by me, saying I was in trouble in Spain and urgently needed money wired to me. The same email and text was sent out in my name to nearly 1,000 people all over the world. 'I am in a critical situation in Madrid' the emails said, 'all my money got stolen in the hotel where I lodged due to a robbery incident - I want you to help me with a loan of 1,500 pounds'. It went on to say that the hotel phone lines had been cut and I did not have my mobile with me - this was to stop people trying to check if the story was true.

Being the victim of phishing can be very distressing and stressful The message was unconvincing of course - the grammar was wrong, the English stilted - but as I discovered later many people thought it really did come from me and some emailed back asking where to send the money. My life was in chaos as calls continued round the clock from Afghanistan and India, from Africa and Washington, from anxious friends and people I knew as a journalist working internationally.

Several Army and security people joked that they might have believed the email if it said the Taleban had kidnapped me in Kandahar. But defeated by a spot of bother in Spain? Highly unlikely!

I could not raise anyone at Yahoo - there were no phone numbers listed and my electronic pleas for help on their website disappeared into the black hole of cyberspace. Just before midnight I unearthed a 'corporate public relations' phone number somewhere in California where it was still office hours.

An automaton answered saying the 'media hotline' was on answerphone and it remained that way for the whole weekend. Who was doing what inside my email and, more to the point, did Yahoo even care?

Finally on Monday, three days later, smooth-sounding Jessica from 'the Yahoo concierge service' called to help me get back into my account and reassure me that Yahoo took such violations very seriously. She would not be drawn on who might be responsible at Yahoo for stopping hackers.

I wanted to know why Yahoo's own filter system hadn't spotted a bogus email sent in their name and taken it out before I opened it. I quickly realised my bank account and cash and credit cards were vulnerable, as those details were in my emails and I knew that scammers run special programmes to harvest financial numbers from the accounts they break into. My bank was more efficient - their help line was operating on a Friday night and they stopped my cards.

However, it took five working days to get new ones, which meant I had no cash and could not use plastic to buy my Christmas presents. It's amazing what comes to light when electronic fraud hits you.

Barclays asked me if I knew my bank account had already been put on a 'watch list' at the request of the Ministry of Defence. Phishing can lead to suicide, kidnap and murder as desperate victims fight to get their money back Apparently a computer disc full of data had gone missing from the MoD and my name was one of many it contained - presumably because I am a journalist who has reported on defence. I had no idea about any of this, but surely under data protection laws I should have? In case you think phishing and other web scams and frauds are not really serious but just a nuisance, then a browse (courtesy of Google) of past cases makes chilling reading. There are many variations - and for some reason a huge number of them originate in Nigeria, where they are dubbed the '419 scam', named after the article of the Nigerian criminal code dealing with fraud.

Lots of us have received those begging emails supposedly from a deposed Nigerian politician or businessman who knows of a large amount of unclaimed money or gold and invites you to share in the windfall by sending funds. Incredibly, people do respond to these emails asking for money, and lose thousands of pounds. Phishing can even lead to suicide, kidnap and murder as desperate victims fight to get their money back. Jane Corbin was told by Yahoo that they took any internet hacking very seriously Leslie Fountain, a senior technician at Anglia Polytechnic University, set fire to himself and died after falling victim to a lottery scam on the internet. The hackers, from Amsterdam, emailed people to tell them they had won the lottery - Mr Fountain believed he had won nearly $1.2 million and was asked for bank account details so the money could be transferred. In Prague, pensioner Jiri Pasovsky shot and killed an innocent official at the Nigerian embassy who tried to tell him the embassy could not return $600,000 he'd lost to Nigerian scammer, while both a Japanese and a Swedish businessman who travelled to Africa to try to retrieve money were kidnapped and millions demanded in ransoms before the criminals were caught.

Figures for financial losses from these frauds are hard to quantify, but experts say that most experienced scammers get two interested replies for every thousand messages they send out and can make several thousand pounds per scam. In 2006 a research group concluded such internet fraud cost the UK economy £150million a year, with the average victim losing £31,000. In 2006 a research group concluded internet fraud cost the UK economy £150million a year, with the average victim losing £31,000 The third biggest banking scam in history - after Nick Leeson's spree at Barings Bank and the looting of the Iraqi Central Bank following the invasion in 2003 - was carried out by Chief Emmanuel Nwude, one of Nigeria's most successful fraudsters who, posing as the Governor of the Central Bank of Nigeria, convinced a Brazilian businessmen to send him vast sums. He made hundreds of millions of dollars, and the fraud led to at least two murders. At last the Nigerian authorities seem to be getting serious about the crime which stains their country's reputation.

Last October they announced 'Operation Eagle's Claw' a joint effort with Microsoft to apprehend the Nigerian scammers. There are even individuals who set themselves up as white knights and engage in their own version of phishing or 'scam baiting' to catch the fraudsters or upset their plans. In one case, an American who had been approached by a Nigerian scammer replied under the name of 'James T Kirk'. The scammer had evidently never heard of Star Trek, and when after a correspondence of several emails, he asked for his victim's passport details, the American sent him a copy of a fake passport with a photo of Star Trek's Captain Kirk. 'Ha, Ha,' said the American on his blog, 'Hopefully he will try to use it and get arrested.' Once I was able to get back online, I was overwhelmed by emails which friends and colleagues had sent back to the fraudsters.

Some were na've, if touching - saying how alarmed they were and how could they get the money to me. Many were clever and witty, weaving in security questions only I would know the answer to. One, from a former SAS soldier, tried to get a street address where he could find me - 'to draw them out' as he explained and mount a rescue attempt if it was really necessary and I'd been kidnapped. Old habits die hard. Many victims of electronic conmen speak of the betrayal as the psychological equivalent of rape or at the least a nasty burglary. I felt my Yahoo account had been defiled, someone rifling through its private contents just like rooting through your drawers at home.

Justice Secretary Jack Straw also fell victim to a phishing scam I could at least comfort myself that I was in excellent company - Jack Straw, the Justice Secretary, had his Hotmail account phished last year. The crooks claimed Mr Straw was stranded in Nigeria and needed $3,000 to get home. Most of us now depend on the web for email and a host of other chores like electronic banking and internet shopping, but it is increasingly compromised by criminals. Graham Cluley of Sophos, one of the UK's leading computer security firms, says they receive notification of 40,000 new pieces of 'malware' (malignant software) every day, and they are all about trying to make money out of gullible people. My 20-year-old son was also targeted recently, locked out of his Facebook account by pranksters who changed his profile and sent bogus personal information.

It took two months and the threat of bringing in the data commissioner to get Facebook to deal with his problem. People are increasingly susceptible to attacks through social networking sites apparently, as they tend to respond more readily to someone they think is a 'friend'. With 350 million active users of Facebook, there is plenty of scope for criminals. According to Graham Cluley, there are three ways of protecting yourself from internet fraud. First choose a good strong password - a random mix of letters and characters and not a recognisable name.

Second, use different passwords for different websites - 40 per cent of us apparently use the same one everywhere. That means if a phisher gets your password he can use it to raid your bank account, your email, your various shopping accounts and goodness knows what else. Third, run good anti-virus software. And don't break the golden rule, as I did, and reply to any email you are not 100 per cent sure of.