Award-winning boston schools

Attending an excellent public school is one of any parents highest priorities. For those living in or considering a move to Boston, the award-winning Boston Schools are an excellent choice. Boston Schools and their governing board have the following plan in place to continue the excellence that is the most appealing feature for parents and the community.

A national commendation to the district of Boston Schools was recently awarded by the National School Public Relations Association (NSPRA). The award considers a variety of print and on-line publications in its annual awards competition. Publications of two Boston Schools have earned Awards of Excellence: the Boston Public Schools Career and College Guide, and The Boston Educator.

“Effective communication is critical to engaging students, families, staff, and the community in the success of Boston Schools,” said Superintendent Michael G. Contompasis. “I am pleased that our improved communications efforts have been recognized, and I congratulate the Boston Schools staff and external partners who worked to create these award-winning products.”

On September 19, 2006, Boston Mayor Thomas M. Menino, School Committee Chair Elizabeth Reilinger, and Interim Superintendent Michael Contompasis traveled to New York City to accept the Broad Prize for Urban Education from Eli Broad and the Broad Foundation as the most improved urban school district in the country. The Broad Prize includes $500,000 in scholarship money for the students of Boston Schools. This was Boston's fifth year as a finalist. Boston has earned a total of $1 million in scholarship money, having earned $500,000 total for being selected as a finalist in the previous four years.

"… the School Committee, Superintendent Contompasis and his staff have been working hard to accelerate the improvement in all of the city's schools," Mayor Menino said. "This award today could not have been accomplished without the hard work of the staff in Boston Schools and of the students and their families who make Boston Schools an exciting place to be and a great place to learn."

There are 146 schools in the district of Boston Schools. The enrollment in Boston Schools is 57,000 students.

Boston Schools have a unique history; it is the first district in the United States to open a school; the Boston Latin School was founded in 1635, and Mather, the oldest public elementary school opened it doors in 1639. The public school system in Boston Schools is the oldest public school system, started in 1647, and opened the nation’s first public high school in 1821.

Truly, a public school system that serves, that has a rich history, and continues to be recognized nationally, is one that all Boston Schools parents (or parents considering a move to a new city) should consider enrolling their children in.

A technology degree offers endless opportunities

Every minute of every day some new form of technology is being invented. Technology is popping up all over the place and it does not seem to be slowing down anytime soon. Every year companies try to out do each other by coming up with the biggest and best product and knock their competitors out of the water. Now, if you buy a computer, IPod or any other electronic device, it is practically out of date before you even walk out the door of the store because a new company came up with a better idea. This is why the career field of computers and technology continues to grow making room for individuals with a technology degree.

When the IPod was first marketed, people all over the world rushed out to the nearest electronic store to purchase the latest technological craze. As soon as they took that product home and got used to the features, Apple was pushing out a new product, the IPod Nano. This IPod was smaller than the first and had more memory, making it more portable and easier to use. Similar to Apple, video game companies are coming out with new game systems and games before customers are used to the one they already have. With the high turn around of computer games and electronic devices, the need for experts with a technology degree continues to grow. That makes the technology career field one of the fastest growing career fields today.

With a technology degree, individuals can work in many different places and hold various jobs. These jobs include computer programming, network engineering, information technology, database technologies, network security and management information systems. All of these fields offer numerous jobs and opportunities for students. Because of the diverse curriculum and the wealth of knowledge available in these technology programs, students are not stuck in one dead end job for their whole life. Receiving a degree in a technology field allows students flexibility and the ability to adapt to any computer or electronic related career.

There are numerous institutions in the United States that offer a technology degree, but not all of them offer certification in certain programs as well. Not only do employers look for employee candidates who have a degree, they also look for candidates who are knowledgeable, have real world experience and are certified in certain programs. Gaining a certification will set students apart from other candidates who do not have these certifications or real world experience. By obtaining a technology degree, students can become a Cisco Certified Network Associate, a Microsoft Certified Systems Engineer, a Microsoft Certified Systems Administrator or a Microsoft Certified Application Developer among other certifications.

While obtaining a technology degree, there are also many opportunities for students to gain hands-on experience in the field of computers and electronics. Since there is a large job market in this particular career field, there leaves open the opportunity for a large internship market. Internships are important to students because employers look for individuals with real world experience. This career field is so fast paced that one minute an individual can be programming a computer game and the next minute they can be coming up with a new database. This makes it important to gain as much real world experience as possible before attempting to break into the work force. It is also important for individuals to stay on top of the current technology that is out there. New products come out every day leaving room for new improvements and advancements in technology.

Salt lake city schools see first utah scholarship grads

Salt Lake City Schools recognized the academic success of both a federally funded program, and of its individual students in May. The first group of 150 Utah Scholars has graduated from the rigorous academic high school program.

Utah Scholars is a federally funded program that was with the goal of encouraging academic rigor at the high school level. Several Salt Lake City Schools including the Granite, Jordan, Park City and Prove districts had participating students. Utah was one of 22 states to benefit with a grant of $300,000 to fund the program for two years.

Salt Lake City Schools require students to meet state guidelines of 4 years of English, and 3 of math and science to graduate. Those Salt Lake City Schools students in the Utah Scholars program are required to complete 4 years of English, 3 Ѕ of social studies, 3 of science, 3 of math, and 2 of a foreign language. One main incentive is the possibility of grants and scholarships for successful graduates of the program.

The program was launched for two reasons. Educators in Salt Lake City Schools and around the nation have noticed a direct correlation between a demanding high school course load and success in both college and college entrance exams - like the SATs. There has also been national concern over the decreasing number of students enrolling in college programs and completing degrees on time.

Declining numbers of advanced degrees have been an ongoing concern for Salt Lake City Schools. In 2004 the Utah Foundation reported that the number of bachelor degrees among residents was steadily declining. Less young people were pursuing the degree and Utah schools were 31st in the nation with the 25-34 year old crowd. A 2006 report issued by the US Census Bureau confirmed concerns when it released figures that said only 27% of Utah residents hold bachelors degrees.

One reason that this may be a problem in the Salt Lake City Schools is it’s large Mormon population. The famous founders of Brigham Young University encourage their members to marry young and to do missionary work for the (Mormon) Church of Latter Day Saints before beginning their education.

Salt Lake City Schools are trying to educate its students on the vast discrepancies in income between those with bachelor’s degrees and those without. The Utah Scholars program is helping them to do that. This past school year the Salt Lake City Schools targeted eighth graders who will enroll in the program next year. These selected students at Salt Lake City Schools will work with mentors from local colleges and counselors in their own schools. Salt Lake City Schools are hopeful that they can graduate another crop of Utah Scholars and turn the trend around.

The 2500-year-old pythagorean theorem

Pythagoras of Samos was a Greek philosopher responsible for important developments in mathematics, astronomy and the theory of music. He left Samos because of the tyrant who ruled there and went to southern Italy about 532 BC. He founded a philosophical and religious school in Croton that had many followers.

PYTHAGOREAN THEOREM

Although the theorem now known as Pythagoras's theorem was known to the Babylonians 1000 years earlier he may have been the first to prove it.

It's the fact that

“THE SQUARE OF THE HYPOTENUSE OF A RIGHT TRIANGLE IS EQUAL TO THE SUM OF THE SQUARES OF THE TWO ADJACENT SIDES”.

According to one legend, Pythagoras (c.580 B. C.-c.500 B. C.) discovered the theorem while waiting to see Polycrates, the tyrannical ruler of the city of Samos. Cooling his heels in a palace hall, Pythagoras spent the time pondering the floor's square tiling. He imagined how a diagonal line cutting across a square would divide the square into two right triangles. He noted that the area of a square erected over the diagonal is double the area of the square erected on an adjacent side. In other words, the square on the hypotenuse is equal to the sum of the squares on the triangle's two legs. Pythagoras came to believe that the same relationship would hold when the legs have unequal lengths.

The theorem's history, however, is more complex than this legend would suggest. The use of the 3-4-5 triangle for constructing a right angle, for instance, goes back to much earlier times in Egypt, Babylon, and China. In his textbook The History of Mathematics, Roger Cooke of the University of Vermont describes how the Babylonians might have discovered the Pythagorean theorem more than 1,000 years before Pythagoras.

Basing his account on a passage in Plato's dialogue Meno, Cooke suggests that the discovery arose when someone, either for a practical purpose or perhaps just for fun, found it necessary to construct a square twice as large as a given square. Simply doubling a square's side actually quadruples the square's area. If you contemplate the quadrupled square for a while, you might think to join the midpoints of adjacent sides--in effect, drawing the diagonals of the four copies of the original square.

"Doing so creates a square in the center of the larger square surrounded by four copies of a right triangle whose hypotenuse equals the side of the center square; it also creates the two squares on the legs of that right triangle and two rectangles that together are equal in area to four copies of the triangle," Cooke writes. This construction adds up to the Pythagorean theorem.

"The Pythagorean theorem was an early example of an important fact rediscovered independently and often," Veljan remarks. Moreover, more than 400 different proofs of the theorem are known today

PYTHAGOREAN TRIPLES

The famous Babylonian clay tablet known as Plimpton 322 goes a step further. Dating from the period between 1900 B. C. and 1600 B. C., the tablet has columns of numbers that apparently represent what are now called PYTHAGOREAN TRIPLES.

The whole numbers a, b, and c are a Pythagorean triple if a and b are the lengths of two sides of a right triangle with hypotenuse c, so a2 + b2 = c2.

In general, for any number k, the corresponding Pythagorean triple is a = 2k + 1, b = 2k(k + 1), and c = b + 1. For example, when k = 1, a = 3, b = 4, and c = 5. When k = 2, a = 5, b = 12, and c = 13.

The Babylonians used a sexagesimal, or base 60, number system. The Plimpton tablet has several columns of numbers, written in cuneiform script. The following table shows the numbers in two of the columns written in decimal notation. One apparent error is corrected (4825 replaces 11521 in the second row).

119 169

3367 4825

4601 6649

12709 18541

65 97

319 481

2291 3541

799 1249

Mathematics historian Howard Eves has conjectured that each pair of numbers represents two of the three members of a Pythagorean triple, corresponding to one side and the hypotenuse of a right triangle.

The numbers also fit the following formula for finding Pythagorean triples: a = 2uv, b = u2 - v2, and c = u2 + v2, where u and v are relatively prime, one number is odd while the other is even, and u is greater than v. For example, when u = 12 and v = 5, b = 119 and c = 169 (as given in the first row of the table) and a must be 120.

It's straightforward to extend the Pythagorean formula to right triangles in three and higher dimensions. For example, for a rectangular box that is a units long, b units wide, and c units high, the diagonal d obeys the following relationship: d2 = a2 + b2 + c2. Moreover, you can look for analogous relationships for triangles on the surface of a sphere, on the hyperbolic plane, and in other spaces.

Generalizing the Pythagorean equation for triangles with integer sides to powers greater than 2 leads to Fermat's last theorem and the so-called ABC conjecture.

THE AMAZING ABC CONJECTURE

In number theory, straightforward, reasonable questions are remarkably easy to ask; yet many of these questions are surprisingly difficult or even impossible to answer.

Fermat's last theorem, for instance, involves an equation of the form x^n + y^n = z^n. More than 300 years ago, Pierre de Fermat (1601-1665) conjectured that the equation has no solution if x, y, and z are all positive integers and n is a whole number greater than 2. Andrew J. Wiles of Princeton University finally proved Fermat's conjecture in 1994.

In order to prove the theorem, Wiles had to draw on and extend several ideas at the core of modern mathematics. In particular, he tackled the Shimura-Taniyama-Weil conjecture, which provides links between the branches of mathematics known as algebraic geometry and complex analysis.

That conjecture dates back to 1955, when the late Yutaka Taniyama published it in Japanese as a research problem. Goro Shimura of Princeton and Andre Weil of the Institute for Advanced Study provided key insights in formulating the conjecture, which proposes a special kind of equivalence between the mathematics of objects called elliptic curves and the mathematics of certain motions in space.

The equation of Fermat's last theorem is one example of a type known as a Diophantine equation -- an algebraic expression of several variables whose solutions are required to be rational numbers (either whole numbers or fractions, which are ratios of whole numbers). These equations are named for the mathematician Diophantus of Alexandria, who discussed such problems in his book Arithmetica.

In fact, it was in the margin of a page of a Latin translation of Arithmetica that Fermat first set down the proposition that came to be known as Fermat's last theorem. He had studied the book closely, making marginal notes in his copy. After Fermat's death, his son published a new edition of Arithmetica that included the notes in an appendix.

Interestingly, the Wiles proof of Fermat's last theorem was a by-product of his deep inroads into proving the Shimura-Taniyama-Weil conjecture. Now, the Wiles effort could help point the way to a general theory of three-variable Diophantine equations. Historically, mathematicians have always had to state and solve such problems on a case-by-case basis. An overarching theory would represent a tremendous advance.

The key element appears to be a problem termed the ABC conjecture, which was formulated in the mid-1980s by Joseph Oesterle of the University of Paris VI and David W. Maser of the Mathematics Institute of the University of Basel in Switzerland. That conjecture offers a new way of expressing Diophantine problems, in effect translating an infinite number of Diophantine equations (including the equation of Fermat's last theorem) into a single mathematical statement.

Like many problems in number theory, the ABC conjecture can be stated in relatively simple, understandable terms. It incorporates the concept of a square-free number: an integer that is not divisible by the square of any number. For instance, 15 and 17 are square free, but 16 and 18 are not.

The square-free part of an integer n is defined to be the largest square-free number that can be formed by multiplying the prime factors of n. That quantity is denoted sqp(n). Thus, for n = 15, the prime factors are 5 and 3, and 3 x 5 = 15, a square-free number. So sqp(15) = 15. On the other hand, for n = 16, the prime factors are all 2, which means that sqp(16) = 2. Similarly, sqp(17) = 17 and sqp(18) = 6.

In general, if n is square free, the square-free part of n is just n. Otherwise, sqp(n) represents what's left over after all the factors that create a square have been eliminated. In other words, sqp(n) is the product of the distinct prime numbers that divide n. So sqp(9) = sqp(3 x 3) = 3; sqp(1400) = sqp(2 x 2 x 2 x 5 x 5 x 7) = 2 x 5 x 7 = 70.

With these preliminaries out of the way, mathematician Dorian Goldfeld of Columbia University describes the ABC conjecture in the following terms: The problem deals with pairs of numbers that have no factors in common. Suppose A and B are two such numbers and that C is their sum. For example, if A = 3 and B = 7, then C = 3 + 7 = 10. Now, consider the square-free part of the product A x B x C: sqp(ABC) = sqp(3 x 7 x 10) = 210.

For most choices of A and B, sqp(ABC) is greater than C, as in the example above. In other words, sqp(ABC)/C is larger than 1. Once in a while, however, that isn't true. For instance, if A is 1 and B is 8, then C = 1 + 8 = 9, sqp(ABC) = sqp(1 x 8 x 9) = sqp(1 x 2 x 2 x 2 x 3 x 3) = 1 x 2 x 3 = 6, and sqp(ABC)/C = 6/9 = 2/3. Similarly, if A is 3 and B is 125, the ratio is 15/64, and if A is 1 and B is 512, the ratio is 2/9.

Masser proved that the ratio sqp(ABC)/C can get arbitrarily small. In other words, if you name any number greater than zero, no matter how small, you can find integers A and B for which sqp(ABC)/C is smaller than that number.

In contrast, the ABC conjecture states that [sqp(ABC)]^n/C does reach a minimum value if n is any number greater than 1 -- even a number such as 1.0000000000001, which is just barely larger than 1. The tiny change in the expression makes a vast difference in its mathematical behavior.

Astonishingly, a proof of the ABC conjecture would provide a way of establishing Fermat's last theorem in less than a page of mathematical reasoning. Indeed, many famous conjectures and theorems in number theory would follow immediately from the ABC conjecture, sometimes in just a few lines.

"The ABC conjecture is amazingly simple compared to the deep questions in number theory," says Andrew J. Granville of the University of Georgia in Athens. "This strange conjecture turns out to be equivalent to all the main problems. It's at the center of everything that's been going on."

"Nowadays, if you're working on a problem in number theory, you often think about whether the problem follows from the ABC conjecture," he adds.

"The ABC conjecture is the most important unsolved problem in Diophantine analysis," Goldfeld writes in Math Horizons. "It is more than utilitarian; to mathematicians it is also a thing of beauty. Seeing so many Diophantine problems unexpectedly encapsulated into a single equation drives home the feeling that all the sub disciplines of mathematics are aspects of a single underlying unity, and that at its heart lie pure language and simple expressibility."

“Though more than 2,500 years old, Veljan concludes, "this 'folklore' theorem remains eternally youthful, as many people continue to find new interpretations, generalizations, analogues, proofs, and applications.”

BIBLIOGRAPHY

October issue of Mathematics Magazine.2000

The History of Mathematics, Roger Cooke of the University of Vermont

Ahmed, A. 1999. Extension of Pythagorean triples. Mathematics Enrichment

Beardon, A. 1997. Pythagorean triples. Mathematics Enrichment.

Beardon, T., and B. Hardy. 1998. Picturing Pythagorean triples. Mathematics Enrichment

Veljan, D. 2000. The 2500-year-old Pythagorean theorem. Mathematics Magazine 73(October):260.

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Foreign student studying in the us getting a social security number

If you are a foreign student studying in the US, chances are that there are a lot of things that are unfamiliar to you. International students pay more than American students for tuition (sometimes almost double!) and so often have to get a job. If you are going to get a job, here are a few tips about getting a Social Security Number (SSN).

1. Try to work on-campus.

Working on campus is good for a number of reasons. Firstly, it helps you get a better feel for the campus, which will make you more comfortable in a foreign place. Secondly, the campus often have a lot of support resources that can help you. But most importantly, if you work on campus (in a library, as a research assistant, or in whatever capacity you can find) the international students office of you school will write you a letter to take with you to get your social security number.

2. Why do I need a Social Security Number?

You need a Social Security Number (SSN) if you are getting paid in any way in the United States. This means that you will need a social security number even if you are receiving a scholarship. (Even that money is taxable, and trust me, they will be taxed). Don’t delay in your SSN application because sometimes employers won’t be able to give you your pay check until you have your number.

3. How long does it take?

It takes about four weeks to get a social security number, once you have gone to the government office. This means that you need to make sure that you begin your paperwork right away.

4. Where do I start?

The first step is to apply for jobs on campus (or off-campus). Once you have a printed job offer in your hand, then you can go to the office of international students. They will probably photocopy your job offer, your passport, and your visa. If you are not getting a job on campus, you will still need a written version of your job offer to take with you.

5. What should I bring?

Find out where the nearest SSN office is to you. When you go there, you will need quite a few things: a) Your Letter of Offer (from your job or scholarship), b) A letter from the office of international students (if you are applying for an on-campus job; this letter will say that you are currently enrolled and attending classes; you don’t need it for an off-campus job), c) your passport, d) your visa (F-1, J-1, etc), e) all other immigration papers that you have (this means bring in any forms that you can think of, such as your I-94 form; you can even consider brining your SEVIS fee form…it never hurts to bring too much).

When I went to get my SSN, they also asked to see my birth certificate, which is not on the list of mandatory items to bring. For a friend of mine, they asked to see her driver’s license. It is better to bring these just in case. You don’t want to be turned away or have to come back with more information.

There aren’t any forms to fill out for the SSN before you get there. A person at the office will help you fill out all of the forms that you need to.

Good luck!

I’m sure that you won’t have any problems finding a job, or getting your SSN. It’s a lot of paperwork, but in the end it’s worth it.

Educational toy ideas for your preschooler

If you are searching for the right educational toys for your preschooler, you may be overwhelmed with all the options available. Toy manufacturers are now busier than ever, working hard to keep up with the latest trends and styles, and competing to make their toys the best and most popular among small children. Though the decision of what to buy your child can be difficult, here are several suggestions that may help you.

When choosing an educational toy, you want to be sure it will serve its educational purpose. You want your child to learn something while playing with a particular toy, and for that to remain a popular one with your preschooler for a reasonable amount of time. This is why you should choose carefully.

When selecting educational toys, it is also important to keep your child's interests in mind. Remember, it isn't the educational factor that will interest your child, rather the fun the toy will bring. Encourage your child to play with different toys and learn new things, but always try to give preference to the more educational preschool-level toys, whether they teach basic math or reading skills, color recognition, or just stimulate different parts of a child's developing brain. After all, these simple, educational games can often be the most entertaining.

Chalkboards are among the most popular toys for preschoolers. They are also among the oldest. And since many modern chalkboards are double-sided-- with a chalkboard on one side and a magnetic board for plastic letters on the other, this toy can also serve a dual purpose. By playing with it, your child will be able to learn the letters of the alphabet with the magnetic letters, and then be able to practice those letters on the chalkboard once this is accomplished. It also allows for free-hand drawing and hours of creative fun.

Toy pianos are also among the most popular and most beneficial toys. As shown in recent studies, children who learn music, even on the most basic level, tend to perform better in math and science-oriented subjects, and also tend to score higher on scholastic exams. Aside from that, this kind of toy is a great way for your child to be creative while making his or her very own music.

Blocks have long been among the most basic, yet most fun toys a child can own. There are many types from which to choose, from blocks that interlock, to those that simply balance on one another. Your child will have hours of fun building towers, houses, or just simply learning to stack and count.

No matter which educational toys you choose, be sure they are age-appropriate for your child. Check to be sure they don't have loose parts that could be harmful to your child, and that they aren't too complicated for his or her age and education level. You do not want your child to become discouraged by playing with a toy he or she does not understand. Also, play with your children. If you show an interest in the toys you buy, they are more likely to do the same.