Friday, February 12, 2010

How to Study Mathamatics for College Students and Higher Secondary School students

Mathematics and war have been directly linked since the Babylonian times around 1800 B.C. and will continue to develop together well into the distant future.In 1939, the British crystallographer and science historian John Desmond Bernal wrote: "Science and warfare have always been most closely linked; in fact, except for a certain portion of the nineteenth century, it may be fairly claimed that the majority of significant technical and scientific advances owe their origin directly to military or naval requirements."

This project intends to look at the role of maths and mathematicians throughout the history of warfare, looking specifically at Archimedes and the siege of Syracuse, fortifications and gunnery.

The siege of Syracuse was fought from 214 B.C. to 212 B.C. between the rebellious city of Syracuse, and a Roman army under command of Marcus Claudius Marcellus, sent to put down the city's rebellion. Marcellus attacked the coastal walls of Syracuse with sixty quinqueremes (battleships with five man oar banks) while his co-commander, Appius Claudius Pulcher, attacked the inland walls with ground troops.

"The Romans' wicker screens, missiles and other siege apparatus had been made ready beforehand, and they felt confident that with the number of men at their disposal they could within five days bring their preparations to a point which would give them the advantage over the enemy. But here they failed to reckon with the talents of Archimedes or to foresee that in some cases the genius of one man is far more effective than superiority in numbers."

Archimedes, the Greek mathematician had been King Hiero's military advisor for many years and had well prepared Syracuse for any attack. Archimedes had built ingenious defences including advanced catapults, scorpions and trebuchets, Polybius describes some of these defences

"Archimedes had constructed artillery which could cover a whole variety of ranges, so that while the attacking ships were still at a distance he scored so many hits with his catapults and stone-throwers that he was able to cause them severe damage and harass their approach. Then, as the distance decreased and these weapons began to carry over the enemy's heads, he resorted to smaller and smaller machines, and so demoralized the Romans that their advance was brought to a standstill."

Archimedes also devised the 'Archimedes Claw' and the 'Archimedes' Death Ray'.
The 'Archimedes claw' was in essence a large crane, at the outer walls of the city, equipped with a grappling hook that could lift attacking ships partly out of the water, and then either cause the ship to capsize or suddenly drop it. Plutarch depicts the devastating effects of the 'claw'

"Other were seized at the bows by iron claws or by beaks like those of cranes, hauled into the air by means of counterweights until they stood upright upon their sterns, and then allowed to plunge to the bottom, or else they were spun round by means of windlasses situated inside the city and dashed against the steep cliffs and rocks which jutted out under the walls, with great loss of life to the crews. Often there would be seen the terrifying spectacle of a ship being lifted clean out of the water into the air and whirled about as it hung there, until every man had been shaken out of the hull and thrown in different direction, after which it would be dashed down empty upon the walls."

Lucian wrote that during the Siege of Syracuse, Archimedes repelled an attack by Roman forces with a burning glass. Archimedes "constructed a kind of hexagonal mirror, and at an interval proportionate to the size of the mirror, he set similar small mirrors with four edges, moving by links and by a kind of hinge, and made the glass the centre of the suns beams...So after that, when the beams were reflected into this, a terrible kindling of flame arose upon the ships, and he reduced them to ashes. Thus by his contrivances did [Archimedes] vanquish Marcellus."

Archimedes magnificent inventions were so effective that "at a council of war the decision was reached to abandon the assault, as all attempts were baffled, and to confine operations to a blockade by sea and land."

However in 212 B.C. while the inhabitants were participating in a festival to their goddess Artemis, the Romans managed to get over the walls and the onslaught began.
The city of Syracuse fell and "was turned over to the troops to pillage as they pleased."
It was at this time that Archimedes was killed while "carrying to Marcellus mathematical instruments, dials, spheres, and angles, by which the magnitude of the sun might be measured to the sight, some soldiers seeing him, and thinking that he carried gold in a vessel, slew him," much to the distress of Marcellus who "pleased with the man's exceptional skill, he gave out that his life was to be spared, putting almost as much glory in saving Archimedes as in crushing Syracuse."

The fact that the besieging army's commander is distraught at the death of the man who masterminded the destruction of his forces shows the incredible impact that this great mathematician and his ingenious inventions had.

Fortifications are military constructions and buildings designed for defence in warfare. The Renaissance period was the golden age of fortification. During these 400 years, fortification achieved the stature of art and science. Fortification's most striking achievement was the construction of many impressive fortresses found all over the world.

During the 15th century, a revolution in the development of arms, in the form of the canon made it necessary for fortifications and fortresses to be made stronger and harder to be breached. The original medieval castle walls were high and constructed to prevent the scaling of the castle wall, by means of ladders.

However with the new developments in artillery, the high walls were easy targets and simply shattered under the accuracy and strength of the cannon. This necessitated a change in the design of fortifications. In the early 1500's, a simple square with bastions was the first, most basic design. However, the small flanks and sharp angle characteristics of this design produced cramped interiors and hence limited the troops and cannon that could be garrisoned there. The square bastion design was quickly replaced by polygonal shaped fortifications. These polygonal walls offered more sides and were clearly easier to defend. It also allowed for expansion to achieve even greater interior space - this was carried out by increasing the number of bastions and the length of the enclosing walls. Although most theories for a bastioned fortress were based on geometrical designs, nature often called for readjustments in the original design.

Many fortifications had to accommodate terrain with mountains, swamps and rivers and were hence constructed as irregular polygons.By the end of the 16th Century, the system of fortification was quite well developed and new elements were added to the bastion design. Defences located the near the castle walls, but behind the enclosing ditch were developed, known as Outworks. A ravelling, a free-standing triangular outwork equidistant between the bastions, was situated almost as an island in the moat in front of the castle wall. The ravelling was designed to produce crossfire over the ground in front of the neighbouring bastions. If an attacker captured the ravelling, he would find himself isolated in the middle of the ditch, and in the midst of vicious flanking fire. The defensive fortification structured in this way facilitated transportation of cannon and ammunitions from one defensive point to another during period of siege. The final shape of the new defensive structures resembled a star, and for this reason they were known as star forts.
Gunnery became a subject for practical mathematics in the 16th century. Printed books and new mathematical instruments dealt with the measurement of shot, the elevation of guns and mortars, and the calculation of the range of fire. The prediction of range in relation to the elevation of a gun was considered the pinnacle of artillery as a mathematical science.
Tartaglia, who had experimented with almost every type of cannon in existence in Europe, had a great deal of data on cannons and so was able to develop the first ballistic firing tables; these tables were instrumental in educating gunners and developing artillery as a precise military tool.
The next major contribution to ballistics came from Galileo who showed that the acceleration due to gravity is the same for all objects and air drag was the factor that changed their descent velocities. He was able to determine that ballistic trajectories are parabolic.

He theorized that the velocity of a projectile was related to the drag acting upon the projectile.
Sir Isaac Newton made the most important contributions to ballistics and the study of aerodynamic drag. In Principia, he derived formulas and explained the mechanics of ballistics. He concluded that the retarding force (drag) that acts on a projectile through air is proportional to the density of air, the cross sectional area of the projectile and approximately the square of its velocity.

In conclusion it can be seen that maths and mathematicians play a key role in the art of warfare, and the two disciplines directly affect the development and style of one another. Also maths and war have continued to work together to advance civilisation and provide protection for the free world, seen through the developments of the computer and other types of machinery constructed for military application by mathematicians. Truly the power, influence and wealth of the armed forces offered and continues to offer fantastic opportunities for mathematical advancements.

Very Intresting News about WATER(H2o)

Water boils quicker when on top of a mountain than at the beach.
AT the beach- water boils at 212 degrees F. But on top of a mountain, say 5,000 feet- water boils at 202 degrees F. As the altitude gets higher, the air pressure becomes less. Since there is less pressure pushing on a pot of water at a higher altitude, it is easier for the water molecules to break their bonds and attraction to each other, thus it boils more easily.

Raindrops are actually shape like a hamburger bun.

DROPS of water coming out of a faucet are shaped like tear drops as we see them by the naked eye. The reason is the back end of the water drop sticks to the water which is still in the faucet until it can't hold on anymore. But- using high-speed camera- scientists have found that falling raindrops look more like a small hamburger bun. As the rain falls- the air below the drop pushes up from the bottom, causing the drop to flatten.Seawater is slightly more acidic than most natural fresh water.

NEUTRAL water such as distilled water has a pH of 7 which is in the middle point of being acidic and alkaline. Seawater happens to be slightly alkaline with a pH of about 8. Most natural water has a pH of between 6 - 8, although acid rain can have a pH as low as 4.

It takes about 7 times as much energy to turn boiling water into steam as it does to heat water at room temperature to the boiling point.

Distilled water is more pure than rainwater. Rainwater contains small amount of dissolved minerals that have been blown into the air by the winds. It contains tiny particles of dust and dissolved gases such as carbon dioxide and sulfur dioxide. Rain is produced by water vapor evaporating from the earth and condensing in the sky while distilled water comes from water vapor condensing in a closed container such as glass jar.

More things can be dissolved in water than sulfuric acid.

WATER can dissolve more substances than any other liquid. This is beneficial for mankind. Imagine what will happen if water will not dissolve the sugar at the bottom of your soft drinks and coffee. The water we see in the river, lakes, seas and oceans may look clear but it actually contains many dissolved minerals and elements. And because these things are dissolved- they can easily moved with water to all surfaces of the earth.

Condensation is water coming out of the air.

WATER that forms outside of a cold glass is liquid water condensing from water vapor in the air. Air contains water vapor. In cold air- water vapor condenses faster than it evaporates. So- when the warm air touches the outside of your cold glass- the air next to the glass gets chilled and some of the water in that air turns from water vapor to tiny liquid water droplets. Clouds in the sky on a cold day are condensed water-vapor particles.

Water has a high surface tension.

AMONG common liquids- water has the highest water tension. Mercury is higher. Surface tension is the ability of a substance to stick to itself- cohere. That's why water forms drops. Plants are happy that water has a high surface tension because they use capillary action to draw water from the ground up through their roots and stems.

Water expands when it frees

ACTUALLY, water expands when it freezes. This is unusual for liquids. Consider ice- it is one of the few things that floats as a solid. If it didn't then lakes would freeze from the bottom up and some lakes would be permanent blocks of ice.

Incrediable science for childrens and kids

In these technology days, it is one of the easiest tasks for children to learn science quickly. Most of the children would like to do their science experiments with some incredible science toys and kits. Science is one of the easiest subjects to learn with these science kits. And here one thing to remember that science is different from scientific.

Obviously, the science experiments involve with great project group discussion, which often lead to toy science fun. There are so many stores situated at the country are selling these incredible science experiment kits, which are made by some esteemed manufacturers are presented in an easy way. And also with the design of these kits, your children will learn some incredible facts about the different scientific disciplines. For example, with a single experiment with these kits, so many children would be able to understand the atmosphere conditions around our planet.

After the completing the experiment, your children will amaze about these kits. And also it will help them to learn science quickly, and also it is very much useful in their future research and education. There are various types of kits available like chemistry, biology, ecology, astronomy and some other various fields of experiment kits. It has been observed in various American schools that so many children are easy to learn that why sky is the blue, cause of rains, bending lights and some other experiments that also reveals the mysteries of earth.

Instead of giving some old regular toy, you can give these experimental kits to your beloved children as a gift. When they are doing experiments with these kits, they are using their imagination, as well as they have some interest to learn real science that will help them both in the school and real world. If they are really understandable with these experiments, they are starting to think differently. During these experiments, they are asking some questions and reasons. At the time, as teacher or parent, you need to be patient about give some proper answer to your children.

And also there is an important point that parents are the first teacher for any children. Instead of saying the short answer to the children questions, you need to give some elaborated answers. With these answers, they are able to keep this information as a memory, and they know the importance of the science. In earlier stage of learning will help them to be easier in school, and as they grow older. And also is the absolute best way for kids to learn science.

Psychology

Counseling psychology is the largest specialty area within psychology. The Society of Counseling Psychology describes this field as "...a psychological specialty that facilitates personal and interpersonal functioning across the lifespan with a focus on emotional, social, vocational, educational, health-related, developmental and organizational concerns." Those pursuing or wanting to pursue counseling psychology as a career will find a large vista of optional career paths also opening up to them. These can be related to research, teaching, vocational counseling, and of course, psychotherapy.

There is a gamut of options when it comes to studying counseling psychology courses online or through distance education, but before enrolling into one, make sure that the course has international accreditation. While most online courses offer all or most of the above qualifications, it is still better to do a thorough background check on the colleges one has shortlisted before paying the course fees. However, one also has to decide before enrolling into a counseling psychology course which area of specialization one is looking for as there is virtually no limit to career options available after graduating from such courses. Even large corporate houses these days employ counselors, therapists and psychologists as workplaces are becoming sources of great emotional and psychological stress.

Counseling psychologists can even work independently. Many schools and colleges look for counseling psychologists and therapists for guiding their students. One's job could be guiding students to the right career path by way of career counseling or counseling hyperactive or troubled students to ease their problems. Other fields where services of counseling psychologists are required are crisis counseling centers, hospitals, individual self-help groups, as well as rehabilitation centers. Even though to become a practicing counseling psychologist requires a education and training, what is perhaps most important is patience. Without patience one cannot hope to become a good counselor or a therapist in the field. One has to deal with different kinds of people and with a wide spectrum of mental problems. Sometimes things might get a little nasty too. But with patience, perseverance, and above all dedication one can chalk out a successful career path in counseling psychology. Counseling psychologists do a great service to society by helping people in need of guidance. They are directly responsible for fostering good mental health and preventing mental, physical, and social disorders.

Best Universities in the world

With the widespread use of internet, human lives have undergone a radical transformation. Education and training have also been facilitated a lot because of the various online modes being devised. Conventional courses as well as industry-oriented courses are both being taught through the online mode. Distance education has really come as a boon for those who have paucity of time or are busy with other chores. To further ones existing qualifications by availing the online courses being offered by the top online universities is really a wise decision. A person has the facility to choose his suitable time and schedule his activities conveniently in this mode of learning.

In the present era many advanced courses are being taught with the aid of distant-learning. Many working people are talking up courses which augment their current work profile. Different online tools are being implemented for teaching like teleconferencing, video-conferencing, podcasting, chatting, emailing, etc. However in this apparently upbeat scenario, certain false/dubious universities and institutes are trying to dupe the students. Hence students are advised to always check the authenticity of the courses and the degrees being offered or their money, energy and time would go in waste. Given below are some top online universities which deliver quality education programs online and meet the requisite industry standards satisfactorily.

1. University of Phoenix - This is among the top online universities offering on-campus, online as well as hybrid programs for getting degrees at associate, bachelor, master and doctoral levels. Both theoretical and practical training is provided in this university in a balanced fashion. All the education programs which are being taught online are accredited and are designed by taking inputs from experienced and competent industry and academic professionals. Quality is of prime importance in this university which happens to be among the biggest North American universities. There are 200 locations where training is imparted conveniently and internet delivery is provided in most of the countries worldwide. The strength of this university is in providing a perfect synthesis of conventional education and practical requirements of the dynamic market scenario.

2. Argosy University - This private university is popular for imparting online programs in the fields of business, psychology, and education in a flexible manner. A large percentage of student community in the U.S. is supported by this university. The Higher Learning Commission has also given regional accreditation to this university. All the online lectures that are provided have been designed to enhance the student's knowledge in practical applications. The greatest advantage of taking online classes from Argosy University, one of the top online universities, is that students can take accelerated classes according to their convenience. One can take classes during the day or at night to suit one's work schedule.

3. Capella University - This University also comes in the list of top online universities with its online degrees in the domains of business, psychology, information technology, human services, and public health. Any online course that is offered by this university is taught by highly experienced and competent industry - professionals.

About London Universites

If you're thinking about studying abroad, then why not consider London? As well as being an important centre for business and finance, sports, culture, fashion and music, it's also well known for its universities.

Here's why it will appeal to you.

1. London is the capital city of England, and for many international students this city is their first taste of the UK. Like many capital cities there are many languages and cultures in London, so no matter where you're from, you're bound to be able to bond with people from a similar background to you whilst you study.

2. London is well known for the variety of industries on offer. These include business and financial, to IT, hospitality, culture and sports. Many students from abroad will be able to use their qualifications to enhance their career in their chosen industry.

3. Your university in London is likely to have links with local businesses, and you might be able to call on them for help with your course, or work experience. London companies might also think of students when they are looking for temporary staff, or people to help carry out with research.

4. London offers more job opportunities than many other university towns, so if you're going to be studying a competitive subject, you'll want to give yourself the best chance of getting a job after you've finished your degree at your London university.

5. Many international students choose to study and live in London, and with influences from around the globe, you'll be exposed to a wide range of cultures and experiences, so it's not hard to see why London is so popular with students. If you want to broaden your horizons, or see more of the world you can't go wrong with studying at a London University.

6. Modern universities are seeing more and more students from all over the world, and London universities are no different. If you want to help improve your English, to learn more about a different culture or way of life, then you won't go wrong by moving to London.

7. London offers a myriad of things to see and do, so you'll always be busy. Whether you're going to football matches, shopping, West End shows or museums, there's always something going on, and somewhere new to explore.

8. There are lots of universities to choose from in London, so you're sure to be able to find the course you're looking for. No matter whether you're looking for an English Literature Masters course, or an MBA, you'll be able to study in this truly amazing city.

9. London is an excellent place to be when you've finished studying, and you're bound to want to stay here, or explore more of the UK. Perhaps you'll decide to make the UK your new permanent home if you're not originally from here.

10. Because there are so many students in London, there are many things targeted towards students. No matter whether you're looking for a night out, discounts on your shopping, or somebody to play football with, you're bound to be able to make the most of your time here.

Learning Human cloning

A child who is a clone may be a very different child from all her peers. She looks like a normal child, having been born with the standard set of components - two eyes, two ears, ten fingers, ten toes, all standard issue from top to bottom. But in one crucial characteristic she is radically distinct from all other children. She is the product of one parent's entire genome, rather than being the product of the combination of randomly assorted genes from two parents.

When she becomes sufficiently self-aware she notices she is a nearly identical copy of her genetic mother, if she in fact lives with that person. Same hair color and consistency, same eye color, same skin tones, same overall features. The remarkable resemblance may be commented upon frequently by strangers. Or, if her parents purchased her genetic material from a service, she may encounter a photo of her genetic mother by accident in a magazine or on television.

For example, with commercialization of human cloning technology, celebrity genomes will be much sought after. Parents may want to have a child with the genetic attributes of their favorite professional athlete, music icon, or film star. Any celebrity on the downside of his career, who previously enjoyed a sufficiently high Q rating, could generate a substantial, never-ending income stream by selling access to his genome.

Many untoward scenarios will unfold. In one possible sequence years after a cloning event, the cloned child is sitting in a barbershop, waiting his turn, flipping through sports magazines. He turns a page which reveals an action close-up of a famous NFL quarterback. Unbeknownst to the child, this particular football player's genome is a popular cloning source. The shock of recognition is paralyzing, not electrifying.

The boy has the very possibly unwelcome experience of seeing a picture of himself as someone else. His sense of himself as a unique individual is immediately and profoundly disrupted.Depending on the quality of his upbringing and the degree of his experience of unconditional love, the child who is a clone may successfully move past this deep challenge to his sense of self. In contrasting circumstances, the ramifications of this discovery may affect his welfare and well-being throughout his lifetime. In either situation, many questions will arise that may ongoing impact his sense of being-in-the-world.

He may question his value as a human being. "Why am I a clone?" he may wonder. "Would I not have been good enough if my birth hadn't been planned in this way?" "Do my parents expect me to behave in a certain way?" "Do they expect me to turn out exactly like the person from whom I was cloned?" "Do I have any choice in the matter of who I become?".In different circumstances these existential questions may be relevant to all of us. They have immediate and critical impact on the day-to-day living of the cloned child.