Sunday 11 December 2011

Year 3 mental arithmetic: Sets 5 and 6

This week I have the following two sets of mental arithmetic questions published for 3 years. They concentrate on one-step problems, recalling addition and subtraction facts up to 20, adding and subtracting multiples of ten and know 5 and 4 times tables.

There are several ways that these questions can be used and how children to answer them. It is sometimes a good idea to use a numeral cards, so that children can keep up the answer. Number of fans a similar goal. Sometimes you might want to be called the answers, or to be written. The sheets of the question can be used for this purpose.

Y3 mental arithmetic set 5 and 6

Wednesday 7 December 2011

Bad boys of physics

In the July issue, about Lenny Susskind Scientific American runs a bad boy or Physics story (see also here). Here is the "nut graph":

Physicists want to understand the deepest levels of reality now largely working within a framework of Susskind. But a funny thing happened along the way. Susskind wonder or physicists reality can understand.

In the interview, Susskind explains that he was a bad boy as a youth, but "just so much better than anyone else, including the professor." In recent years he is the most prominent promoter of the string theory multiverse, and now claims that this pseudo-science convincing the area dominates (SciAm seems agree ...), with the situation like in the early days of QCD:

A large part of the physics community has left trying to explain our world so unique, as the only mathematically possible world. Right now the multiverse is the only game in town. Not everyone is working, but there is no coherent, sharp discussion against it.

In 1974 I had an interesting experience on how scientific consensus forms. People worked on the as yet untested theory of hadrons [subatomic particles such as protons and neutrons], that Quantum Chromodynamics or QCD is called. At a Conference of physics I asked, "you people, I would like to know your belief about the likelihood of QCD the correct theory of hadrons." I took a poll. Nobody gave it more than 5 percent. Then I asked: "what are you working on?" QCD, QCD, QCD. They worked all on QCD. The consensus was formed, but for some strange reason, people wanted their skeptical side. They wanted to be hard-nosed. There is an element of the same thing around the multiverse idea. A lot of physicists don't want to just fess up and say, "look, we do not know another alternative."

Susskind had a DISTINGUISHED career as a theorist for many years, and has managed to do very well with his multiverse campaign for quite a while now. There's a lot of coverage of this story on this blog, for some high points, see here, here, here and here.

In other news, the media full of stories about another physicist who has been a bad boy, David Flory. He began his career as a HEP theorist back in the late 1960s, as a student at the Yeshiva University, and collaborator with Susskind. Just as a large number of other people, he got his permanent academic job in 1969, and has since then at Fairleigh Dickinson University.


Saturday 3 December 2011

Year 5 Division problems: calculation of mentally

Here is the second page that year 5 Division problems who looks using mental skills can be answered. The questions deal with a number of concepts relating to Department, including:

scrap

divisibility rule for 9

and factors.

Watch out for errors that in issues such as number 9 occur, where the number of whole lengths of wire is calculated and the rest is irrelevant.

This page, and other similar worksheets can be found in the year 5 category.

Division problems (2)

Tuesday 29 November 2011

Year 4 mathematics worksheet: tenths of rectangles

A good way of working with decimals is the use of shapes that are divided into ten equal parts. The form is a single whole and each part is a tenth, which can be written as 0.1.

This page has a selection of shapes and asks the child to write down the amount that is gray. When all parts of a shape are shady this counts as ten tenths, or entire one.

While the printed pages almost always display the decimal point located on the line most schools show like half way up the line: the main thing is that it appears clear.

This page can be found in our year 4 mathematics worksheets in Counting the number and category.

Tenths of rectangles (1)

Friday 25 November 2011

Year 1 mathematics vocabulary

If a child does not respond on a mathematical question can it be because they don't understand the words or instructions used. Another problem can occur when a mathematical term has a different meaning in everyday English, for example, ' table '.

In the category of mathematics year 1 there is an excellent list of the vocabulary children needed to understand and use in year 1. For example, the following list has the new words that they are in school in year 1 encounter have to do with the compute and solve problems.

Words to do with the compute and solve problems:

plus near double

How much more is. ..?     how much less is. ..?

subtract min

half                                     halve

equals sign

number sense

operation

There are similar lists for the calculation, measures, and position. These words may greater be printed so that they can be used as ' flashcards ' or displayed on the wall.

Go to the year 1 vocabulary lists.

Monday 21 November 2011

Local Blogs

There are now several excellent blogs somehow to mathematics is carried out by the local population, including a few new ones, so I thought that would be a good idea to mention here these related:

Andrew Gelman of Columbia Statistics Department runs the very active Statistical Modeling, causal inference and Social Science blog, which boasts a wealth of all kinds of different subjects, from technical ones about statistics, to social sciences applications.Emanuel Derman, who began his career as a HEP theorist, was one of the early migrants to the financial industry and now has here teaches at Columbia in the Financial Engineering program, a new blog at Reuters. His last book was the very interesting my life as a Quant, this autumn, he has a new coming out right models worn Badly. Cathy O'Neil, a mathematician who learned here for a while before you change career path, starting with a job at the hedge fund D.E. Shaw, has recently started with the beautiful Mathbabe blog. I think I mentioned this already, but one of my colleagues, Johan de Jong (Cathy's husband) also has a blog, the stacks Project Blog. If your metrics to evaluate blogs like "quality of information is" x "degree of abstraction and technical", are the best blog in the world.

If you have comments on these blogs, I encourage you to post them there rather than here. I would be interested in hearing about any other local mathematics/physics related blogs that I am not aware of.

Update: another local mathematics, physics-related blog has made its debut today, Davide Castelvecchi degrees of freedom. It is part of a network of new blogs today being launched by Scientific American, who is based in New York.


Thursday 17 November 2011

Toddlers and Math

Learning mathematical concepts actually beginning with toddlers. After all, think about how excited a toddler is when they tell you they are going to be 2 years or 3 years old. They are so quick to parrot those numbers, although they are still not sure about conservation of number or number correspondence. However, it is a great time to promote number concepts and develop a joy of math in concrete methods. discover what these early number concepts are and how to use them to promote and develop the significance of those years toddler and beyond.

See also: math concepts learned in kindergarten.


Sunday 13 November 2011

Source of the Week: reflective symmetry

There is quite a lot of work in the year 6 on symmetry and the subject often comes in the key stage 2 SATs.

This number includes important vocabulary and by the end of the year 6 children must know and be able to read, write and use the following quite tricky words:

Mirror, line of symmetry, line symmetry, symmetrical, reflect, reflection, translation, axis of symmetry, reflective symmetry.

They must also be able for symmetry with the help of a mirror and by folding testing.

Children are expected to outline the reflection of a simple form in a line of the mirror where no or only a part of the shape's edges parallel or perpendicular to the line of the mirror.

This might seem simple, but actually prove problematic to many children. A small mirror or tracing paper can be a great help with this.

Year 6 maths worksheet: reflective symmetry

Wednesday 9 November 2011

Year 6 equivalent fractions

Here is another page of equivalent fractions. A part of each pair of fractions is missing and the missing numerator or denominator should be entered. Remember, equivalent fractions are fractions that have the same total value.

One interesting way to check whether two groups equivalent is to perform a couple of multiplications; What is known as cross multiplication. To verify that a/b is equal to c/d just multiply a by d, and then (b) multiplying c. If the two answers are equal then the fractions equivalent. This is a really good way to check to see if the answers are correct.

Equivalent fractions (pg 2)

Friday 4 November 2011

Year 5 mathematics: written multiplication

Here we have a second page questions that an intermediate step in the progress in the development of an efficient, standard written method of multiplication. It assumes a good knowledge of tables before you start.

This method breaks the task in four parts. For example, when multiplying 538 by 4, the four parts are:

1. the multiplication of 500 by 4

2. the multiplication of 30 at 4

3. multiplying 8 by 4.

4. Add the four answers to reach the final answer.

While this is a good method I prefer to work in the reverse order of starting with the units, then the trans-European networks and finally the hundreds, although if the child understand what happens it makes little real difference.

Multiply a number by a 3 digit number 1 digit (2)

Monday 31 October 2011

Year 1 mathematics resources

All worksheets mathematics for year 1 must be found by clicking on the link for free math worksheets at the top of the page. The worksheets are organized into categories according to the directives of the primary framework for mathematics, although this is now revised.

The categories are:

Counting and number: watching small numbers in steps of one count and write numbers.

Some facts to know: count on and back in two and knowing addition facts to 5.

Calculation: including small numbers, and an introduction to add money

Understanding form: in this stage recognition of triangles, rectangles and squares, as well as the introduction of some 3D shapes

Measuring: using non-default measures and compare

Treatment data: mainly creating lists

Using and applying mathematics: number of stories and investigations.

While there is a significant amount of here is that it is next to nothing compared to the URBrainy site the best that I found online, with more than 1,700 colorful pages of mathematics for the year 1 is have, including full answers.

Go to our year 1 mathematics resources

Thursday 27 October 2011

Mathematics resources: Written addition

One of the most popular parts of the site for parents is our free math worksheets: four rules pages on written addition.

Many parents think that the methods they learned at school (and for many this would in the 1990s) different from today. This is only partially true. Since the beginning of the numeracy strategy and later that the primary framework for mathematics has been the emphasis on the preparation of children so they understand the written methods that they use. There's a lot of preparatory work and methods, often called "the pursuit of the standard written method ' so that cannot be known to parents, but the end result is pretty much the same. It is this intermediate stages which some parents find puzzling.

The default method is written the layout the sum vertically, with numbers will be added under each other. The units are added first, then the trans-European networks and so on. We have several worksheets to illuminate this method completely.

Go to written methods of addition

Sunday 23 October 2011

Fast printing: chart, grids, and Dot paper

Can't make it to your stationary shop? Some isometric paper needed? graph paper? grid paper? No worries, it's okay here. Four grids per page or per a grid page, you will find some quick PDF is printed here. dotted grids with or without numbers, everything to your homework needs is here, only thing needed is your printer and paper.


Thursday 20 October 2011

Building better Math teachers

Many educational jurisdictions have school improvement programmes in place to improve the overall performance in mathematics., however, what does this look like?

A change in curriculum? A change in the developmental sequence of concepts learned? Hiring more qualified teachers? Larger blocks of time spent on teaching mathematics?Providing professional development to existing mathematics teacher?

A professor and Chairman of mathematics education in the Faculty of education, Dr. Brent Davis has a few answers, I am inclined to support. Davis claims "We can build a better math teacher." "But it's more about the fascinating Deconstructing concepts than about learning more advanced math or involved in solving problems with each other." Science daily.

Teachers who work with teachers in support of the evidence and research-based strategies takes time and money, but it seems that the benefits are there, but all too often that a teacher wants to learn in the way they were taught, however with the support, mentoring and ongoing professional development, it seems we may ' build better teachers. "


Monday 17 October 2011

Maximize summer holiday

Teachers often complain about the lag in learning when students come back from summer vacation. There really doesn't need to be a delay as learning during the summer in a fun and engaging way. Especially so with mathematics.

The Math Playground is interactive and offers practice in fractions, decimals, percent, angles, early algebra, trig, multiplication and much more. If children just spent 15 or so minutes 4 or 5 times per week, the results will surprise you and will most definitely keep happy teachers. Although worksheets fine for practice, they are not a lot of fun and holidays are taking a break and some fun! ?


Friday 14 October 2011

Year 6 maths worksheet: Equivalent fractions

equivalent fractions pg 1

Insight into equivalent fractions is the core of understand how fractions work. Much work needs to be done in previous years to show that fractions such as 1/2 and 2/4 have the same value. This is usually done by colors or shading parts of rectangles, circles.

Two fractions that are equal in value that we say are are equivalent.

2/5 is equal to 4/10 which is equivalent to 40/100.

If we start with a group and both the numerator (top number) as the denominator (bottom number) multiplied by the same number remains the break with the same value. The same goes with Division, but not add or subtract.

This makes multiplying fractions much easier than adding or subtracting from them.

Equivalent fractions (pg 1)

Sunday 9 October 2011

Strings 2011

Strings 2011 began today in Uppsala, with presence quite a bit lower than in the past (259 registered participants, versus 500 or so on some of the past such conferences). One reason for this may be the cost of the Conference on high (discussed here), another possible that excellent video of the talks is available, so why bother travel to Uppsala?

The opening talk was by David Gross, who tried to address the question "where do we stand?" for string theory. He claimed that the field is "very healthy", "lively and exciting", "enormous progress in a variety of areas", with "huge progress" in N = 4 flat nr. At the same time, he acknowledged that it was "very disappointing" that string theory was 43 years old.

Strings XXXX conferences featured in the past, often a call for progress towards making predictions which could be tested on the LHC. With LHC data now, gross acknowledged that this has been a failure: there are no string theory LHC predictions. He put a positive spin on this by noting that the absence of any BSM signal on the LHC so far not a concern for string theory, since string theory cannot be tested on the LHC. As for the absence of any supersymmetry signal so far, he says that "I personally am not still concerned", while acknowledging that some people are becoming increasingly pessimistic. While no SUSY not a concern for string theory is, he feels that "it would be very nice for string theory as SUSY appeared". Presumably, he bets on SUSY at the LHC, but he gave no indication of when he would begin to worry (or the bets pay) as SUSY remains there are not.

The main area of progress he sees is the usual gauge-gravity duality that has dominated the field for years, along with progress in N = 4 SYM amplitudes. He sees the Verlinde "entropic Gravity" as an "exciting development I find immensely interesting". Apparently later this week to discuss Verlinde his latest ideas which supposedly an explanation of dark energy and dark matter.

Gross went on quickly the questions about string theory he first raised in a similar talk 26 years ago, which usually are unanswered, including the basic "what is string theory?". The supplementary questions raised by attempts to understand the emergence of space time in the background of a deSitter were a factor that inspired him to end up with the quote that:

The main product of the knowledge is ignorance.

To which he added "after 43 years of string theory, it would be nice to have some answers."

Surprisingly, not a word of gross on great ape or the multiverse. I assume that he is still an opponent, but perhaps feels that there is no point in beating a dying horse. Susskind is not there and oddly enough, the only multiverse-related conversations are from the two speakers brought to do public lectures (Brian Greene and Andrei Linde, hawking's health has kept him from a scheduled appearance of). So is the multiverse with a large proportion of the public profile of the Conference, but pretty well suppressed on the scientific sections. It is also pretty well suppressed "string phenomenology", or any attempt to use string theory to do integration. From 35 or so conversations I see only a few related to this, which is still the advertised primary objective of string theory.

I'm curious about the discussions of Witten, Gaiotto and Gukov, which I hope provides a gentle introduction to their intriguing recent long papers on the arXiv. As far as I find time to watch discussions this week and have comments about them, I will try and add updates to this post.

Update: after most of the discussions online look, is the most notable thing about Strings 2011 how little there is about string theory. One of the speakers, Chris Hull, began his speech with the comment:

During the lunch today was one of the organizers observe that my talk was unusual in one of the few actually talks about string theory. It would be interesting to speculate about what that could mean about the condition of the field, but it would be shameful to do here.

One of the main themes of the Conference so far has been the study of mathematically interesting supersymmetric QFTs in 3, 4, 5 and 6 dimensions, often obtained from a specific class of 6 d theories, which itself remain poorly understood (what is known about them was reviewed by Greg Moore). Witten gave an overview of his work relating Khovanov Homology and QFT, where a chain of different 6 d, 5 d, 4 d, 3D and 2d QFTs. Nati Seiberg reviewed the technology used for the construction of these theories over different backgrounds, noting that this was all about "rigid" SUSY theories and Supergravity, string theory create no appearance.

Update: the videos of the talks are all now. I took a look at the Verlinde spoken, and the ideas he sets still seems to me pretty much empty of all important content. In Jeff Harvey's summary of the Conference he notes that many people have noted that the Conference has not been a lot of string theory. About the landscape is his comment that "personally, I think it's probably not possible to do science in this way." He describes the situation of string theory unification as the Monty Python parrot "no, he is not dead, he rest." while some hope that a miracle will take place on the LHC or in the study of string vacua, revival of the Parrot to speak out.

That the summary main speaker at the Conference for a field the State of the main public motivation for the field as similar to that of the parrot in the Monty Python sketch would compare is pretty remarkable. In the sketch, the whole joke is the Parrot's seller reluctance, no matter what, admit that what he sold was a dead parrot. It is a good analogy, but surprisingly that Harvey would use.


Tuesday 4 October 2011

Year 3 mental arithmetic Sets 3 and 4

Two sets of mental arithmetic questions suitable for 2 years. These sets of 10 questions relate to the count and back in dozens, addition, subtraction, and place value.

I have been asked for more in the way of mental arithmetic questions on many occasions and as the weeks go by this must be in a really useful resource. I'm also trying to match the questions to the primary framework for mathematics Planning, so this could be particularly relevant for the first few weeks of the autumn term.

Year 3_Mental arithmetic (3 and 4)

Friday 30 September 2011

Source of the Week: magic square with negative numbers

magic square negative numbers

With the year 6 SATs and another half term in mathematics to get by there never been a better time to some studies and puzzles. One of my favorite topics is the magic square, as it can be incredibly simple or extremely complex. This special magic square is quite challenging when it comes to adding positive and negative numbers, so it is a good check to see if children trust dealing with negative numbers

To convert the numbers in the squares is given on all three magic squares and on the first puzzle there is an indication that each row, column and diagonal adds up to-3.

One of the best strategies to use with this is to work out what the number should be and what the total for each row etc should be. It is also a good idea to cut out small squares with the numbers on around the Board so that they can be moved with ease.

Please note that there are several ways of solving this magical squares and only one way it appears on the page response.

Magic square negative numbers

Monday 26 September 2011

Short Division of decimals (2)

Here is another page of practice on the use of the short method of Division of decimals. All unnecessary write numbers with the short method is avoided. The numbers are distributed are just units and tenths that helps with getting the method correctly.

One of the best ways to smooth with this method is to talk through out loud. Eventually this leads to talk by, ' in your head '.

If we look at question 1 divided by 3 7.2, the verbal stages:

a. how many 3s in 7?

b. 2 times 3 is 6 so there 2 with a remainder of 1.

c. Insert the 2 on the line response, directly above the 7.

(d). Insert the decimal answer just above the line, so that it can be clearly seen.

e. the rest 1 is placed just before the 2 (usually smaller written).

f. how many 3s in 12?

g. 3 x 4 is 12 so the answer is 4.

h. place the 4 on the line response, directly above the 2 (tithes).

i. reply 2.4

This page can be found in our four lines, Division category.

Division of decimals (2)

Thursday 22 September 2011

$ 6.5 million for entropic gravity

One of this year the Spinoza prize goes to Erik Verlinde. It comes with 2.5 million euros to the winner of research fund. Last autumn Verlinde received a 2 million euro ERC Advanced Grant for the funding of its research programme, so that's a total of 4.5 million euros, or about $ 6.5 million this past year.

Verlinde's current research focuses on the ideas about "emergent gravity" (see here and here). According to Wikipedia explains his work the observed value of the cosmological constant.

I have no idea how Verlinde will spend the money, but it seems that emerging Ernst research particularly well will be financed. 6.5 million dollars that I would estimate corresponds to approximately 100 post-doctoral years. In a few weeks will Verlinde reveal his latest work on strings 2011. Because that is one of the most expensive conferences around (see here), maybe he could chip in to fund. He must be able to finance one strings 20XX via at least 2,050 I would estimate.


Sunday 18 September 2011

Know Division facts: year 5 maths worksheet

There is no doubt that most children find Division harder than multiplication, but there is little real reason for this to be so. Most Division questions can be turned on their head be made to look like multiplication. For Example:

30 ÷ 5 =??  can be considered as 5 times what number makes 30?

?? ÷ 6 = 7 can be considered as 6 times 7.

60 ÷?? = 10 can be considered as 10 60 times what number makes?

The key to success with Division is a really good knowledge of times tables.

This worksheet looks on this species Division question, all with simple numbers and no waste and is a good assessment sheet to see if Division is understood and tables known.

This can be found in our category year 5 know number facts.

Know Division facts (1)

Tuesday 13 September 2011

How the Hippies stored physics

An outline that I wrote of how David Kaiser of the Hippies stored physics is now available from the American scientist. A short summary is that I think it's a wonderful book, tell in well researched and entertaining a story that I've always wanted to know more about fashion. I am not convinced by the main argument of the title, that this group of people "Physics saved", rescuing a suffocating ideology "shut up and calculate" by the road to the importance of the theorem of Bell's tones and help start the field of quantum information theory. Maybe emulates the author just his subjects, known for their playful outlandishness.

There are quite a few interesting things I learned from the book that didn't make it in the review. An example is the story of the (of EST fame) Werner Erhard theoretical physics conferences in the late 1970s and early 1980s, organised in collaboration with Sydney Coleman and Roman Jackiw. One of the factors that these events put an end to was the advent of string theory: it was felt that no string theory Conference without attending the whites would be taken seriously, and then nothing wanted to Whiten with EST and its founder (although he had attended, with the likes of Feynman and Weinberg, the earliest Conference in the series back in 1977).

If you do find interesting this topic, I highly recommend the book.

For a different take on the same subject, one of the main participants, is Jack Sarfatti memoirs Stargate free available these days in a pre-publication version here.

I'm afraid that my own description of where the physicists described in the Kaiser would not book ended the field of quantum information theory, but the much larger quagmire of dubious claims about quantum physics which is still very influential. For example, this week at the AAAS meeting in San Diego there is a session on Quantum Retrocausation is, see this listing from the world of parapsychology.

Update: I must also mention that Chad Orzel the book discusses here and here.


Friday 9 September 2011

Singapore Math the answer? Look again ... ...

More than 2000 schools throughout the US have adopted the Singapore math method. Singapore is doing well with its methods, then again, Singapore is Singapore. And, although Singapore on the 2nd in fourth grade math and, researchers tend to support their strategies, working in the same way here? Perhaps not. Unfortunately, when tried, the scores have dipped lower than normal. In fact, the scores were very disappointing. One would think that a heavy focus on the ' back to basics ' approach to transitional period type students. If not Singapore, what works? In my opinion-balance! And I will stop there. However, it's worth checking out the challenges that faced a school while trying of Singapore.


Monday 5 September 2011

6 times table space challenge

Children need so many opportunities as possible to practice their knowledge of tables and teachers are always looking for something else to maintain interest. Hopefully this page will be useful, since there is a bright and fun way to show how well the 6 times table is known and it can also be used as a timed challenge.

Beginning at the start moving to the first box, and write the number 6 time shown on the left side, then on to the next box, and so on. There are 20 questions at all; Some children can be ' stuck ' on a question, encourage them to go and then return to the end. If they are stuck remind them, for example, that if they forget 6 x 6 is the only six more than 5 x 6 which they must be able to remember.

This page can be found in our section math worksheets, multiplication four lines, and hopefully I will be adding similar pages for other tables times did not last long.

6 x tables space challenge

Thursday 1 September 2011

Quick Links

"I felt that he had destroyed my life," says Morris. It left him for the next few years reeling: he remembers in a coffee shop in Berkeley with Daniel Friedan, a fellow Princeton exile and the son of the feminist icon Betty and commiserating about the frustrating time they had from East.

"I'm talking about all these problems I had with Kuhn, which is a constant refrain was, and he tells me about all the problems he had in the Department of applied physics," recalls Morris. "He said, you know, ' she just could not appreciate me. I had discovered a new kind of Physics! " And I thought, ' Oh, no. This looks bad. This looks very, very, very bad. This is not going to turn out good. We go both to the nuthouse. " ”

Of course, they're not. Friedan would go on to win a Macarthur Fellowship, and be recognized for his pioneering work on string theory. Morris, meanwhile, left academia once and for all to make a movie about a pet cemetery, called "Gates of heaven," which became a cult classic, and Roger Ebert described as one of the 10 greatest films ever made.


Saturday 27 August 2011

Algebra Word problems

Are you one of those students who freeze when it comes to solving algebra word? lose the math anxiety, attitude and develop a can use these steps to help you more confidence about solving algebra word problems. do not freeze, put that big brain of yours to use, determine what the problem is, figure out what you know, formulate a plan, decide what is necessary to the implementation of the plan and you're almost there!


Tuesday 23 August 2011

Dyscaculia is Math dyslexia is language

Dyscalculia refers the problems that often with individuals be seen when performing mathematical calculations. Likewise, where refer to language problems, the term dyslexia is used. However, for the term Discalculia math is used. Math discalculia is essentially a learning disability for arithmetic or mathematical concepts. Science Daily reports that there are just so many people with dyscalculia if there with dyslexia. Make sure you understand all the facts before jumping to conclusions.


Thursday 18 August 2011

This week's Hype

Last month, the Quark matter 2011 Conference was a place for discussion of the new results of the first heavy-ion run at LHC energies last autumn. I looked a bit on the slides of the talks, but this is an environment far from my expertise. One thing I wonder about is whether the highly promoted application of AdS/CFT on heavy-ion physics might be tested on the LHC. Create AdS/CFT each distinctive predictions about how things will change as one of RHIC energies to LHC energies, and these are checked? Looking at the slides, there seem to be all sorts of interesting things to be learned about heavy-ion physics, but little mention of AdS/CFT modelling of such phenomena. Maybe an expert can help by pre-LHC predictions to point out and explain already have tested, or they can be in the future.

Symmetry breaking magazine today covers Quark matter 11, with String theory may hold answers about quark-gluon plasma, which seems to contain mostly the same hype about string theory and heavy ion physics that current for the last half-dozen years now has been:

Now, scientists have begun to see striking similarities between the properties of the early universe and a theory that would unify gravity with quantum mechanics, a long-standing goal for physicists.

Unfortunately, there is nothing in the article about some LHC test of these ideas. This Is the closest we get to that of Krishna Rajogopal (his talk is here):

"String theory is like a gift to us," said Rajagopal. "We are challenged with understanding the quark-gluon plasma as a liquid, and while string theory does not give us precision, we get a feel for the shape of the topic help."

So, I understand that AdS/CFT no precise, testable predictions, the best thing is to be made that "the us get a feel for the shape of the subject can help", whatever that means. A question for experts: as "String theory answers about quark-gluon plasma can", what are the questions for that string theory is giving answers, and what the LHC data have to say about these questions?

Update: David Mateos has posted a write-up of his Quark matter 2011 talk here. In it, he explains what the problems are with the use of AdS/CFT to say something about QCD. In terms of the issue of the LHC predictions, he gives an example: the relationship of the dispersion of heavy quarkonium Mesons moving through the quark-gluon plasma. Unfortunately, this seems to be much of a prediction:

I would like to stress that whether one obtains a visible peak, just a statistical enhancement or imperceptible effect sensitive many parameters related to the in-medium J/Psi physics hangs. The latter is not sufficiently well understood a precise prediction to make, so we should all take away from Figure 3 (right) is that there is an observable effect for some values of the parameters are within acceptable range might be.


Sunday 14 August 2011

Impossible question in mathematics under paper

Well, it's not unusual for me an error with the articles and worksheets published here, but I don't have a team of proof readers to help me. Much more serious is the error in mathematics as the paper this year.

More than 6,000 students took the paper and the question with the highest number of brands was impossible to answer! The question that 8 brands of 72 is granted for the entire document. This meant that many students would have agonised about, wasting a lot of minutes in unsuccessfully trying to reach a correct answer.

A spokesman for the exam board said,

"We regret that there was a mistake ... and that our quality assurance procedures failed to identify this error.

"Because we have been alerted to this so early, we are able to take into account this error when the paper marker. We will also use this in the boundary rank. We have sent a letter to all schools and universities explain in more detail what we'll do.

"We once again apologize that this has happened."

Obviously some of the students think that this is a less than satisfactory result is as some would have spent a lot more than others on the question, leaving less time for the rest of the exam.

Read more

Thursday 11 August 2011

Math worksheets: distribution of money

There are not many questions on this worksheet mathematics, but they are very tricky and a good knowledge of tables and how to do long Division is needed.

Each question has an amount of money to be shared by a 1 or 2-digit number. In all cases have the answer to a zero in the column to the pound.

If the process is long division there are several important things to remember when doing this, including:

1. turn the hash in the answer

2. set the zero in the column pound

3. the introduction of the decimal point.

Money division (1)

Monday 8 August 2011

Geometry intuitive?

When I came across this article in the New York Times, I must admit, I was somewhat amused by what the findings revealed. The study sees that geometry may be innate. Comparing the results using children and adults who received some formal training and a group of isolated indigenous natives have showed that the lack of formal education in geometry does not have the ability to understand the concepts. hinder shows that nature provides many examples and chance simple geometry concepts such as apply the rule, the point and positional relationships such as parallel and congruency. interesting to note that American children who are a little younger were not fare as well, so it could be deduced that experience is still the teacher is, albeit the ' best ' label is for the full article discussion. See.


Thursday 4 August 2011

Year 1 addition and subtraction

In year 1, there are several important addition and subtraction and skills that must be learned. Addition is related to what children have plenty of practice with should count. It is also important to realize that addition can be done in any order.

Subtraction is seen as ' take away ' or ' find a difference '.

We have a number of simple addition and subtraction worksheets in our calculators section of our resources year 1. One of my favorites is the dice: 3 in a row – game that a simple two-player game where add the totals when two dice. A mix of strategy and luck will help win this game.

Go to our year 1 addition and subtraction worksheets

Sunday 31 July 2011

Year 3 mental arithmetic: Sets 1 and 2

I'm embarking on something new this week which will hopefully to a really useful source will grow as time goes by. It is the first in a series of mental arithmetic questions aimed at 3 years.

It consists of two sets of ten questions, followed by an answer sheet. Each set is a full A4 page so they can be used in different ways. If given orally, the teacher/parent page-only the answer print, like all questions are included on this and the kids can just write the answers or call them out. If the teacher/parent wants the child to read the questions can then they print the question sheets as well. This can also be displayed on a whiteboard.

The first series of questions focus on writing integers, count on and back in the trans-European networks, addition, subtraction, and place value.

Year 3 mental arithmetic (set to 1 and 2)

Wednesday 27 July 2011

Summer Vacation

Summer holiays are great! We've been anticipating them for weeks now. summer provides us with a time to relax, a time to leave the stress behind and enjoy the great weather. However, the major concern for educators about summer vacation is that the potential gap in learning. Summer Vacation offers a great opportunity to learn without the gap to give summer! How is this done? Well, take the a subject that causes grief. For many students, this is all it takes to close the gap, or to ensure the gap no wider math., is 20 or so minutes 3 o 4 times per week do a little exercise and reviewed. The benefits are considerable.

Check out the following worksheets to ensure that you stay on top of these mathematical concepts this summer:


Friday 22 July 2011

Year 5 line charts

With a nice hot summer for us, what better way to spend a mathematics lesson then watch line graphs of temperatures?

In year 5 children should build and interpret line graphs. The important aspect of a line chart is that each point on the line will have a value. The chart in this worksheet indicates the minimum and maximum temperatures every month for London. It would be very worthwhile to find other temperature charts for cities around the world and compare them.

Another great idea is to find data for countries in the southern hemisphere and compare the shape of the line graph to London.

Why not go to our page Handling data and probability for year 5?

Tuesday 19 July 2011

Mathematics and physics, in the summer 2011

This week in Philadelphia the String-Math 2011 Conference is underway, scheduled as the first of a series, with String-Math 2012 next summer in Bonn. Slides of the talks are listed here. There was also supposed to video, but the saved video seems to be a kind of UPenn login required, and I haven't been able to get the streaming video to work. Public talk by Cumrun Vafa crosses the classic message that strings have come to the rescue of physics, unifying QM and gravity, and which:

Flexible geometry of strings seems to explain all known interactions (at least in principle)

The techinical talks relate to a lot of ground, much of it having little to with string theory. Michael Douglas's talk surveys that related to find non-Perturbative formulations of quantum field theory hold that one could hope to have something to say about it exactly, but it contains many more questions than answers. I am most curious about David Ben-Zvi talk tomorrow, so hope that slides or video of that will be available.

The circle of ideas on gauge theory, geometric Langlands, TQFTs and representation theory gets even more attention than the mathematics of string theory this summer. In a few weeks will start with a two-part program on Luminy and then Cargese on double affine Hecke Algebras, the Langlands program, affine varieties of the flag, Conformal Field Theory, Super Yang-Mills theory. I do not know who the author is, but some person or group has written for the occasion a wonderful summary of the current activity in these and related areas of mathematics, see here. Next month, will be hosting a program KITP on non securities and dualities in QFT and Integrable systems that relate to some of the same topics will have.

In some other non-related news, if you understand French, you can listen to an interesting series of interviews with Pierre Cartier here. Finally, it was recently announced that $ 1 million this year is to share my colleague Richard Hamilton Shaw Prize for Mathematics with Demetrios Christodoulou. Richard Congratulations!


Saturday 16 July 2011

The Quantum story

Jim Baggott of The Quantum Story: A History in 40 moments is now here and I have already starting to see it in the bookstore. I read most of it a year or two ago, when he sent me a draft of the manuscript questions if I had a look at it, and very much enjoyed getting the chance to see it than would take. If you are looking for an excellent popular level physics book to read, I recommend that you consider this one, that is accessible for just about everyone, no matter what their background.

The subject of the book is in General, the story of quantum physics told historical with a structure of 40 vignettes. The first three chapters deal with mainly dramatic events of the period of the mid-1980s to the early 1930s during which physicists the basic structures of the quantum theory discovered struggled to get some sense of them. The following two takes the late 40s to mid-70s during which a long sequence of discoveries about elementary particle physics reed theoretical progress in quantum field theory and measure theory, culminating in the standard model fall into place in 1973. The material that Baggott works here is the subject of many other books, but he did a wonderful job of bringing together in a quick but very clear and entertaining story. Along the way, the individual stories he often tells contain fascinating details I never heard before, although I thought this was a subject I already knew too well.

The next last chapter starts with the 1950s and David Bohm, picking up the thread of subsequent debates and discoveries in connection with the general problem of interpretation of quantum mechanics. It brings this story on the pitch, explain some of the current questions that are still being discussed. The last chapter gives an appropriate short discussion of speculative ideas in quantum gravity and string theory which theoretical research have dominated the last few decades, make clear that they still have a long ways from the solid science which is the main subject of the book.

The LHC and the search for the Higgs makeup a final epilogue or 41st vignette, accurately describing the high expectations and the drama surrounding the last period of the long wait for new data that finally put an end this year. The story of quantum theory is not ready, and we all hope that very soon we will have some clues about where the next will go.


Monday 11 July 2011

This week's Hype

The latest New Scientist has a much larger dose of M-theory/multiverse hype than I in one place have seen in a while. There is a four-part series on M-theory (here, here, here and here) by Mike Duff. It tells the story of the progress of modern physics in the last century, according to the dominant ideology: general relativity Kaluza-Klein extra dimensions, super-symmetry, Superstrings, branes, ends in the apotheosis of M-theory more than fifteen years ago. For the current state of affairs, Duff describes his "M-theory" predictions about the real world (that 4 qubits 31 different ways can be entangled, something discussed here). He ends with the M-theory multiverse and the following comments on whether this can ever be tested:

So is M-theory the final theory of everything? With rival attempts falsifiable predictions are hard to come by. Some generic functions such as supersymmetry or extra dimensions can be displayed on the collider experiments or in astrophysical observations, but the diversity of the possibilities offered by the multiverse allows precise predictions difficult.

Are all the laws of nature that we set theory of fundamental theory perceive? Or are some mere accidents? The jury is still out.

In my opinion, many of the important issues remain unresolved for quite some time. Finding a theory of everything is perhaps the most ambitious scientific undertaking in history. No one said that it would be easy.

Here he makes clear that, at least while he is still around and enjoy academic notoriety because of M-theory, there is no danger that it will be faced with a kind of test can not. He answered the critics of M-theory by claiming that the failures not important. It is the dominant paradigm, and as such will reign until someone comes up with a different theory of everything that is not a failure.

Elsewhere in the magazine there is a fawning article on the recent Bousso-Susskind paper (see here):

TWO of the strangest ideas in modern physics – that the Cosmos continually in parallel universes in which every conceivable outcome of each event happens splits, and understanding that our universe is part of a larger multiverse is-have are grouped in a single theory. This has lost a bizarre but fundamental problem in Cosmology and physics circles buzzing with excitement, as well as some bewilderment.

No critics of the idea were by the writer, with the discussion about blogs described as:

The paper has caused a flurry of excitement on Physics blogs and in the wider physics community. "It's a very interesting document that a lot of new ideas," says Don page, a theoretical physicist at the University of Alberta in Edmonton, Canada. Sean Carroll, a cosmologist at the California Institute of Technology in Pasadena and author of the blog Cosmic Variance, thinks that the idea has some merit. "I have a confused skeptic a believer for the time being," he wrote on his blog. "I realized that these ideas fit very well with other ideas that I've been thinking about myself!"

One way or the other of Lubos "them on crack" to take on the subject was missed.

Finally, the meaning of it all summarized in an editorial that States that Bousso-Susskind finally pulls the plug on religion and replaces it with the Science:

Cosmologists can now begin to take God seriously, precisely because they him (or her) can explain away.


Thursday 7 July 2011

Year 3 Mathematics worksheet: time and calendars

An aspect to learn over time that is often neglected is the use of a calendar. They don't need any explanation for children who do not come across them before and they come in different formats. The month appears in this spreadsheet starts the week on Monday, although many start on Sunday. It may seem puzzling to children as to why there are some ' empty ' days at the beginning of the first week so it's a good idea to have a calendar with available all year.

This can lead to much discussion, such as the number of days in each month, why birthdays on any other day of the week every year etc.

Using a calendar (1)

Sunday 3 July 2011

Carroll diagrams: 2 year treatment of data

Carroll diagrams are named after the famous writer, Lewis Carroll and are a way of grouping things in a ' yes or no ' way. They can be as simple as just two boxes but usually they are seen as four boxes with two attributes. In this case the two characteristics are swimming and cycling and the children may or may not each.

Carroll diagrams were introduced in year 2 as a means of sorting, but it is not until at the end of the year or 3 years where she would meet these types of diagram. The second page has a number of questions about the diagram and suggesting that children go about trying to collect their own data and their own Carroll diagram of this data.

Thanks to urbrainy.com for this specific set of pages and they have a large selection of the treatment of data resources on their site.

Carroll diagrams 1

Wednesday 29 June 2011

Rumor of the Week

A few months ago, CDF, the New York Times by releasing results claiming to see a resonance in the invariant mass spectrum of two rays produced together with a w. last week, they released a new analysis with twice as much data, alleging that the signal was still there, now at a statistical significance of almost 5 sigma.

I recently wrote about this here, the reasons for his skeptical, despite the high statistical significance. A very good reason for being a skeptic is that the CDF Tommaso Dorigo is not that this is really believe, go so far as to put his money where his mouth is, offering a $ 100 bet to back up his arguments. The crucial question in everyone's mind is been or D0, CDF of competition and sister detector at Fermilab, would the same thing in the data. If there really is something there, D0.

This Friday, there will be a wine and cheese talk on Fermilab D0, where the results will be revealed, and you can use this as a live video stream here. But, as one would expect, now that the D0 result is ready to be revealed, people do things like print jobs late on printers, etc., allowing editors to spread rumors. Blogs like this seem to be a place where such information tend to end up, so I can report a rumor (based on excellent sources) that Tommaso's right. D0 will on Friday report that nothing is there, that they have no evidence for a dijet resonance in the region of 110-170 GeV. They reject the CDF hypothesis of a resonance with a diameter of 4 OJ on a significance level of more than 4 sigma.

In other news, the LHC performed very well, with the official purpose of this week to achieve an integrated luminosity of fb-1, something that has been the official goal for the entire year (though, unofficially, 2-3 fb-1 if the more). Right now, they are around 8 fb-1. This kind of clarity should finally start to results that a Higgs in the region that are expected to exclude or see first indications if, in the next few months.

The KITP this week marks the beginning of a program on the first year of the LHC. Unfortunately, theorists, the only result data from the first year of the LHC had to shoot some of their favorite models, ruling from, for example, a large amount of parameter space where supersymmetry was expected to be found, which is the most popular theoretical idea of the last 30 years are considerably less popular. The first interview held at the KITP Program was this afternoon, and not with the LHC data, but with the alleged CDF resonance (it appears that news of the D0 result had not yet made it to Santa Barbara).

Update: the KITP talk is now available here.


Sunday 26 June 2011

Quick Links

The big news from the past few days is the release of more data by CDF which is still a bump in the invariant mass of two beams produced with a w. Resonaances gives an excellent description of this and the possible meaning. Tommaso Dorigo remains a skeptic.

I can't do better than the two of them on this story, but here's my summary to take on the situation:

With the new data, this may no longer be written off as a statistical fluke. 3 sigma you can claim off as such a fluke, but not 5 sigma.

The main reason to be skeptical but it is not the statistical significance, but the possibility that this is due to poor modeling of background. The signal is extracted from a huge background, so a small misunderstanding of the background would be the cause. If this is the case, expect that the new data does not change anything, you have to continue to see the effect as more data is analysed.

The fact that Tommaso a skeptic is carries much weight, as he is on the CDF experiment works and understand the problems. In general, the experimentalists to experiments that they are working on to make great discoveries, so tend to have their own results optimists. When someone skeptical about the outcome of their own experiment, that gives a break.

What would really be the case for the new physics here would be more compelling if the result is confirmed by one of the other experiments (DO at Fermilab, CMS or on the LHC ATLAS) that able to see the same effect as it's there. These groups have a certain motivation to confirm not only their competition from the discovery (raise the question why they don't find it first), but in a convincing way to shoot it down. This post by Pauline Gagnon of ATLAS says that they have nothing in their data 2010. It is expected that D0 is hard at work and should quickly free what they have found. ATLAS and CMS must also hard at work looking for the much larger 2011 examples. We will soon know the results, but the public comments from Dorigo and Gagnon not sounds to me like they would if they knew their experiments provisional confidential results confirm the CDF anomaly.

Finally, while there are numerous paper theory models out already with alleged explanation for this, are not really convincing. This is not an experimental result with theoretical explanation a naturally attractive.


Tuesday 21 June 2011

Year 3 Mathematics: couples who make 100

shape imageWhen working out how much more to make a number of up to 100 it important not to mix up two different ways to do it. Let's ask the question:

' How much more there is of 45 to 100? "

One way to do this is to add 5 to 45, 50 and then count on 50 to 100. That is a total of 55.

Another way is to count on in dozens of 45 to 95, that is 50, and then add it to the extra 5, again making 55.

Watch out for children who get something confised, adding at from 40 to 100, 60, and then on another 5. This method will always lead to ten more than the correct answer.

The ultimate goal of questions such as these is to make the answers second nature or even know them off by heart. "

This page can be found in our annual 3, calculation of the section.

Full number of sentences (pg 2)

Saturday 18 June 2011

Source of the Week: 6 year convert metric units

Children in year 6 still have plenty of practice using the metric system, in particular larger convert metric units to smaller. Here we are a page that looks meters into centimeters, pounds to grams and liters to ml mark.

One of the trickier aspects of this is to put a weight as 6.09 kg in grams, which of course is 6090 g. watch out for common mistake children write only 609 g.

This is one of several similar pages found in our year 6 measuring section of the site.

Year 6 larger units for smaller units (1)

Tuesday 14 June 2011

Stern equipment from MathsExtra

Learn the best by far the best equipment of mathematics that I am over the years come the Stern structural arithmetic program, which encourages children to reason than just rote. This approach was designed to follow a child's natural stages of learning and development in the early years, up for the development of a number of number sense, concepts, knowledge and number of relationships, as well as to ensure that the required skills in place prior to any formal work. It is also ideal for SEN children where little or no progress has been made in the past and for children who are ' on ' move to the next phase, a clear insight in the earlier phases.

Stimulate a child's cognitive processing functions is the core of the programme; the range of equipment offers beautiful ' pictures ' which Visual and auditory perceptual processing to develop.


An example is the ' trap ' in the 10-Box, where a more cube add makes it the same size as the next number. The concept is explicit-adding a to any number always will result in the next issue.

The Board of Directors position and counting introduces order. The simple task, when you are prompted for a block to fit in an empty groove indicated, develops, of course, judging, scan and discrimination ability of a child. Children discover that each block has its own special place in the series of blocks to 10. This means that there is not only to work with numbers up to 5.  Number of relationships are an essential building block. Instead, children see the small numbers of all ' live ' at the beginning, and larger ' live ' at the end, (later to be on the left and right).

As an example of the approach of the structural arithmetic, look 3 + 7 = 10. Children discover all combinations that will create 10 by fitting combinations of blocks in the 10-box. They reason that if 9 1 should make 10, 8, 2, 3 and 7, 10. By switching of the blocks around, they discover that the order of the addends can be altered without the sum. So, they understand that addition can be done in random order and put it to use, reasoning that if 7 + 3 = 10, then 3 + 7 = 10. This fact is not taught in isolation, but has been examined in a context where the relatioship to the other facts can be seen.

When children see an example like 5 + 4 = and don't know the answer, they often respond by counting ' 6, 7, 8, 9. Teachers can assume that encouraging children to count, will one day result in their stop counting and say, ' 9 '. Stern argues that, in fact, every time they see + 4 (as in 6 + 4 or 9 + 4), they are practicing automatic counting. The numbers themselves have no sense. Counting child equal 5 plus 4 not 9; It makes 9 by counting. No picture in the mind of the child makes it number fact 5 + 4 = 9 unforgettable. In addition, if children the total incorrect if 10 count, they have no certain way to check that result except by another uncertain counting procedure. On the other hand, in the structural arithmetic measuring the two addends actually 9 5 and 4 in the Track number.

The stern kits are not cheap, but I would advise having a further read on

http://www.mathsextra.com/

Thursday 9 June 2011

The path of a football ....

Sharpen your pencils, and on your thinking cap for this quadratic problem. The projected path of a kicked football is represented by a function, and your task is to know how much time the ball in the air, what the height of the ball of path is, what the the line of symmetry, axis of symmetry, quadratic zeros and corner point of the function.

Of course, when you're ready, you can have your answers here.
See also: quadratic equations


Wednesday 1 June 2011

More year 4 mental arithmetic: subtraction

This is the second page of ' very difficult ' subtraction questions for year 4, that needs to be answered by using mental arithmetic methods, although many adults would struggle to achieve the correct answers: they are really very difficult!

Once again shows that there are different ways to set up each question; the key is to choose a method that efficiently and quickly. For example, they can be performed by counting, but this is also possible the quickest way and it's speed and accuracy that we are looking for.

It is also always a really good idea to check answers by performing the inverse operation; in this case would complement the answer and smallest number the largest number.

This, and other similar pages can be found in our year 4 calculations category even if the section four lines.

Very difficult mental arithmetic: subtraction_ (2)

Free group worksheets

Fractions, fractions, fractions, they just don't get fractions! as I've heard this comment once, I've heard it 1000 times. Unfortunately, without enough practical experience, students struggling with fractions when you begin with fractions, have students find the half in sets and repeat using a quarter of the entire (half of a circle, chocolate bar and half of 10 flowers or 4 sweets). Many concrete examples use before going to the developmentally appropriate worksheets here.


Tuesday 31 May 2011

What increases the performance of the school?

We all know that smaller classes, uniforms and primary homework ways of stimulating schools performance. Or are they? Not according to a recent report from the Sutton Trust. In fact, include reduction of classes, homework during elementary school, and the introduction of school uniforms to the least effective ways to improve school results.

Look at class sizes they found that the benefits, "are not particularly large or clear, until class size is reduced to under 20 or even under 15".

Another myth seems to be that more classroom assistants rental is effective. This is contrary to what most teachers think like 44% said that hiring more assistants one of their three top priorities. The report says that hiring more assistants associated with being "very little or no impact on the achievement".

Significant gains in achievement meanwhile come from proven classroom approaches-efficient feedback on student performance, to think about their own strategies for students to encourage learning, and getting students to learn from each other. Properly implemented, these approaches students performance by an additional eight or nine months in a year of school for a very low cost, according to the Guide.

Key findings include:

On effective feedback-"even a study estimates that the consequences of the rapid feedback on learning is 124 times more cost effective that reducing class sizes."

On peer tutoring – "benefits are obvious for both tutor and tutee, although the approach should be used for filling or normal education improve, rather than replaced."

On meta cognitive approaches – "Studies report significant gains equal to a class of 50th place in a ranking of 100 schools to around 25."

On homework-is "worth more on the high school level and much less effective for children in the primary school age."

On assistants-"most studies have consistently found very little or no impact on the achievement."

On school uniforms-will "no robust evidence that the introduction of a school uniform improve academic performance."

On the reduction of class sizes-"on the whole, the benefits are not particularly large or clear, until class size reduced to under 20 or even among 15."

On one-to-one tuition – "pupils can improve by about 4 or 5 months during the program, but costs are high, because the support intensive."

About ability grouping "there may be some benefits to higher achieving students, but these are largely offset by the negative effects on attitudes of Middle and lower performing students."

The full report can be found at:

The Sutton Trust

Monday 30 May 2011

Cycles of time

Today's Wall Street Journal has a review I wrote of Sir Roger Penrose of new book cycles of time. The revision focuses on a much wider audience than this blog, and is the product of substantial edit to edit the length to get started and make it as readable as possible for as many people possible, so here are a few additional comments.

I must make it clear that I'm not convinced by what Penrose proposes. He must be the distant future of the universe to be conformally invariant, and all particles are massless. As far as we the electron is completely stable, with unchanging mass, and this will always ruin Conformal invariance. Penrose itself takes note of the problem. For this to be overcome, what is our ultimate understanding of how particles get mass change so that these masses to zero in the future. It is also seems to me that the Conformal anomaly of QCD will always be a problem, with quantization and renormalization group always Conformal invariance break and give a mass scale, indefinitely far in the future.

The other main problem is shared by most of the "pre-big-bang" ideas: how you ever test them? Penrose and a co-worker last year created a stir by claiming to see in the CMB patterns of the species he argues can be expected from black hole lapses late in an era before the Big Bang, but it's not clear there is a real prediction here, and others who have redone this analysis say they see nothing.

Attempts to create a Big Bang in our past and our future in General seems to me to be motivated by a very human desire to see in the global structure of the universe the same cyclical pattern of death and rebirth which human existence. For me, however, deeper understanding of the universe unexpected structures, fascinating precisely because of how strange to human concerns and experience. Just because we may have a cold, empty universe means an unattractive future not that that is not where things are headed.

The book is in many ways an unusual document. It includes a comprehensive annex from some of the details of the mathematics of his proposal to work. He has managed to make a trade publisher to get out of a highly technical discussion of a speculative idea within the covers of a popular book, instead of the usual route of publishing this in a refereed journal, in a sense. The only references I can find to other places where he some of this up are chapters in this book and this, if this contribution to a Conference procedure has written. The technical idea behind this, that the hypothesis of the disappearance of the Weyl curvature in the early universe which leads to possible cosmological models can be extended along the big bang singularity that he this paper of K.P. Tod attributes. There is a nice recent exposition of this by Tod here.

So, I'm not convinced by the speculation about the distant future, and for an evaluation of the ideas about extending back through the big bang singularity you need someone more expert on Cosmology than I do. These topics are very clearly marked in the book as speculative, without the support of other physicists or experimental evidence. The largest part of the book is all other material to provide a background and context the speculation, and that's what I think makes the most valuable as a popular book. Penrose is a beautiful, elegant and clear writer, and he handles a lot of ground about physics beautifully here. Most notable are the illustrations, by far the best visual representations of a series of important ideas that I know of. Physicists and mathematicians working with many internal pictures in their minds that important aspects of the concepts that they investigate, but very rarely do they have the technical skill to understand some of the essence of these photos and them down on paper. Even more rarely they make it in wide distribution in print, so I'm glad to see you here.

This entry was posted on Friday, may 27, 2011 at 11: 52 am and is filed under book reviews. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

Friday 27 May 2011

Source of the Week: 6 year mathematics challenge

Here is a bit tricky puzzle that is 6 years or upper juniors (9/11). Ideal for wet breaks!

Use only the digits 1 through 9 complete correct the number of sentences, both horizontally and vertically, so they all are.

A good knowledge of tables is needed, along with the ability to add and subtract mentally.

The hardest part of this puzzle is getting started and the best approach is to use process and improvement by picking one row or column that can have only a limited number of opportunities. This wouldn't be the first row or column down.

This particular puzzle to look at the first row is a x b – c = 34. Start by watching combinations of numbers that when multiplied, more than 34 (but no more than 43 if the maximum subtraction is 9) and then see what number can be subtracted to leave 34.

An important note about this: all calculations are done in the following order: Bodmas is not applicable.

1-9 (1A)

Thursday 26 May 2011

Read, write, and ordering numbers on level 1

Mathematics level 1 to reach children must be able to recognize the number up to 20 names, they say clear and they write. They will be counting forward and backward to 20, beginning with an integer.

To make this happen that the figures should be clearly displayed on a wall which they can often be referenced. Every opportunity must be given to the count on and back in practical situations, around the House, in the kitchen, in the supermarket, in the car, etc. There are many games where counting and dice. Number of lines and number of tracks are really useful; pointing at each number before it is said while counting up and down. Eventually the song track can be visualized in a the main child, help with quick mental arithmetic.

Herlp with all this I have a good selection of worksheets for counting:

Front Desk

Year 1

and year 2, who will help with this process.