Year 2 home guide
Summer Term 2013
Year 2 Home Guide
Summer Term 2013
Welcome back from the Easter break. We hope you all have had a super rest and are ready for the Summer term. Here is our last Home Guide for the year. This guide contains information about topics that we shall be covering the entire term and suggestions for things you can do at home with your child to extend their learning.
Sun cream and Water!
If by some chance we get a Summer this term, could we ask all parents to ensure that all children have sun cream on during any potential hot weather, have a hat to wear while outside and bring in a water bottle to quench their thirst.
Please keep reading with your child every day and make sure that they complete any Guided Reading homework.
The guide also includes ideas for activities to reinforce learning with your child in other subjects across the curriculum.
These are the topics we will be covering this term in class and suggested activities for parents and children.
The first half term we are doing the End of Key Stage 1 assessment tasks and activities. These include: reading comprehensions, 1-1 reading assessments and a short and long writing activity. Please note that these are not tests. Rather, they are independent activities that will give us extra information when we assess your child to give an academic level for the end of Key Stage 1.
The children will write a diary about travelling to Scutari, the hospital in the Crimea where Florence Nightingale worked. There will also be more opportunities for extended story-writing.
The children will write poems about Night-time and another topic linked to our geography work.
Non-fiction: Non-Chronological Reports.
The children are going to write non-chronological reports on topics such as batteries and electric circuits (linked to Science work) and Night-time (a SATs activity). They will also write a character profile on a fictional character.
Guided Reading: (April-July)
Please ensure your child brings back their Guided Reading books on their allotted homework day.
Please keep practising multiplication tables with your children – 2, 5 and 10 times tables to start with and then move onto 3s and 4s. They are a very valuable tool for quick mental calculation.
• Get your child to write and mentally recall number bond sentences to 10 and 20 and 100 using addition and subtraction. For example: 8+2 = 10, 18+2 = 20, 20 – 8 = 12. 10 - 7 = 3.
• Be able to order whole numbers to at least 100. Give your child a sequence of numbers and get them to continue it.
• Be able to place a series of numbers on a blank number line, making sure the numbers are in the right numerical order.
• Quick mental doubling of one and two digit numbers and halving of even two digit numbers.
• A correct use of a number line to solve addition, subtraction, multiplication and division problems.
• Practical division activities; i.e., dividing up pizza, sharing out sweets, etc.
• Exploring the link between division and basic fractions: halves and quarters.
• To continue practising telling the time and knowing how many minutes there are in an hour; how many hours in a day; how many weeks in a month, etc.
• Continue talking about money, encouraging the correct units of measure (pounds and pence) and how money is used in a real-life sense.
• This half term we will be introducing weight (g, kg) and capacity (ml, l) for the first time.
• Get your child to partition two-digit numbers into multiples of 10 and 1, and then recombine them.
• We will be increasing an emphasis on missing number calculations (which is basic algebra). For example: 5 + ? = 19. You can use any number operation (+, -, x, ÷) and the missing number can be in any place in the calculation. The important factor here is that the children have to use a range of mathematical skills to answer the questions. The numbers do not need to be big.
• Discuss how addition is related to subtraction (they are opposites or inverse) and how multiplication (x) is related to division (÷) (they are opposites or inverse). For example: 7 + 7 = 14 AND 14 – 7 = 7.
5 X 5 = 25 AND 25 ÷ 5 = 5
Our two topics this term are Variation and Electricity. Variation will explore the differences between plants and animals and look more closely at plants. More details will follow… Electricity will introduce children to electricity and electric circuits and electrical safety. At the same time, there will be a week’s worth of cross-curricular non-fiction literacy teaching on the subject. We will also be looking at Living and Growing as part of Science and how we are born, the differences between boys and girls, growing up and how we are made.
The topic this term is Florence Nightingale and Mary Seacole. The children will learn in detail about the events before, during and after the Crimean War (1860s). Then, they will write about it in a week’s worth of cross-curricular Literacy lessons. We have already booked a visit to the Florence Nightingale museum.
Y2 MP Wednesday 1st May 2013
Y2 NR Thursday 2nd May 2013
For this subject we will be looking at Going to the Seaside, exploring the human and physical aspects. We recommend Google Earth as a research tool and any non-fiction fact books.
We have also booked a Seaside trip for Wednesday 3rd July. Details will follow so watch this space.
We will follow the scheme of work dictated by the Social and Emotional Aspects of children’s Learning (SEAL). The topics this term are ‘Relationship’ and ‘Changes’.
The topics for this term are ‘Belonging’ and ‘Beliefs’. Both topics look at a range of religions and how religious people demonstrate their faith.
Where possible, we will use the ICT suite working in pairs to learn the basics of word-processing, internet use and painting programs as well as using the new iPads.
Art and Design and Technology:
In the last half term the children will design and make wind-up toys.
A weekly Music lesson with Mr Morris, a weekly PE lesson with Morris, and a weekly Dance lesson with Ms Robbins.
Please make sure your child has a PE kit that consists of: trainers, sensible trousers and a t-shirt. Morris will not allow children to do PE if they don’t have a kit.


Following the construction of a Bézier curve, the next important task is to find the point C(u) on the curve for a particular u. A simple way is to plug uinto every basis function, compute the product of each basis function and its corresponding control point, and finally add them together. While this works fine, it is not numerically stable (i.e., could introduce numerical errors during the course of evaluating the Bernstein polynomials).
In what follows, we shall only write down the control point numbers. That is, the control points are 00 for P0, 01 for P1, …, 0i for Pi, …, 0n for Pn. The 0s in these numbers indicate the initial or the 0-th iteration. Later on, it will be replaced with 1, 2, 3 and so on.
The fundamental concept of de Casteljau’s algorithm is to choose a point C in line segment AB such that C divides the line segment AB in a ratio of u:1-u(i.e., the ratio of the distance between A and C and the distance between A and B is u). Let us find a way to determine the point C.
The idea of de Casteljau’s algorithm goes as follows. Suppose we want to find C(u), where u is in [0,1]. Starting with the first polyline, 00-01-02-03…-0n, use the above formula to find a point 1i on the leg (i.e. line segment) from 0i to 0(i+1) that divides the line segment 0i and 0(i+1) in a ratio of u:1-u. In this way, we will obtain n points 10, 11, 12, …., 1(n-1). They define a new polyline of n – 1 legs.
The new points are numbered as 1i‘s. Apply the procedure to this new polyline and we shall get a second polyline of n – 1 points 20, 21, …, 2(n-2) and n– 2 legs. Starting with this polyline, we can construct a third one of n – 2 points 30, 31, …, 3(n-3) and n – 3 legs. Repeating this process n times yields a single point n0. De Casteljau proved that this is the point C(u) on the curve that corresponds to u.
Let us continue with the above figure. Let 20 be the point in the leg of 10 and 11 that divides the line segment 10 and 11 in a ratio of u:1-u. Similarly, choose 21 on the leg of 11 and 12, 22 on the leg of 12 and 13, and 23 on the leg of 13 and 14. This gives a third polyline defined by 20, 21, 22 and 23. This third polyline has 4 points and 3 legs. Keep doing this and we shall obtain a new polyline of three points 30, 31 and 32. From this fourth polyline, we have the fifth one of two points 40 and 41. Do it once more, and we have 50, the point C(0.4) on the curve.
This is the geometric interpretation of de Casteljau’s algorithm, one of the most elegant result in curve design.
Given the above geometric interpretation of de Casteljau’s algorithm, we shall present a computation method, which is shown in the following figure.
Thus, from the initial column, column 0, we compute column 1; from column 1 we obtain column 2 and so on. Eventually, after n applications we shall arrive at a single point n0 and this is the point on the curve. The following algorithm summarizes what we have discussed. It takes an array P of n+1 points and au in the range of 0 and 1, and returns a point on the Bézier curve C(u).
Input: array P[0:n] of n+1 points and real number u in [0,1]
Output: point on curve, C(u)
Working: point array Q[0:n]
for i := 0 to n do
Q[i] := P[i]; // save input
for k := 1 to n do
for i := 0 to n – k do
Q[i] := (1 – u)Q[i] + u Q[i + 1];
A Recurrence Relation
The above computation can be expressed recursively. Initially, let P0,j be Pj for j = 0, 1, …, n. That is, P0,j is the j-th entry on column 0. The computation of entry j on column i is the following:
if i = 0 then
return (1-u)* deCasteljau(i-1,j) + u* deCasteljau(i-1,j+1)
This procedure looks simple and short; however, it is extremely inefficient. Here is why. We start with a call to deCasteljau(n,0) for computing Pn,0. Theelse part splits this call into two more calls, deCasteljau(n-1,0) for computing Pn-1,0 and deCasteljau(n-1,1) for computing Pn-1,1.
if n = 0 or n = 1 then
return Fibonacci (n-1) + Fibonacci (n-2)
This program takes an exponential number of function calls (an exercise) to compute Fibonacci(n). Therefore, the above recursive version of de Casteljau’s algorithm is not suitable for direct implementation, although it looks simple and elegant!
An Interesting Observation
The triangular computation scheme of de Casteljau’s algorithm offers an interesting observation. Take a look at the following computation on a Bézier curve of degree 7 defined by 8 control points 00, 01, …, 07. Let us consider a set of consecutive points on the same column as the control points of a Bézier curve. Then, given a u in [0,1], how do we compute the corresponding point on this Bézier curve? If de Casteljau’s algorithm is applied to these control points, the point on the curve is the opposite vertex of the equilateral’s base formed by the selected points!
By the same reason, 70 is the point on the Bézier curve defined by control points 60 and 61. It is also the point on the curve defined by 50, 51 and 52, and on the curve defined by 40, 41, 42 and 43. In general, if we select a point and draw an equilateral as shown above, the base of this equilateral consists of the control points from which the selected point is computed.


The numbers on p.5 are wrong. A Purity Squad of four characters gets (4x2)+2=10 equipment rolls. A purity squad of 8 characters gets (8x2)+4= 20 equipment rolls. The numbers on p. 5 are from a previous version of the rules. Heck, I have a math disability and I don't see numbers when I re-read a document... sorry.
A band of 3 humans and two humanoids would get (2x3)+ (1x2)= 8 equipment rolls.


Computers are excellent calculators.. Not.
Now I'm pretty much used to dealing with floating point precision errors, but this one is just silly..
A fun example trying to calculate a ResMed pressure from a stored integer value, converted normally.
470.0 * 2.0 / 100.0 = 9.39999962
470.0 * 0.02 = 9.39999962
470.0 / 50.0 = 9.39999962
An even simpler example:
float var=9.4; // ie, the real answer, which even my foggy brain can work out..
the result that actually gets stored? 9.39999962!
Gah!! A standard floating point variable can not hold the number 9.4. It must be a dastardly evil unholy number.
Using 64bit double precision gives the answer for all of the above as 9.4000000000000004, also wrong.
Rounding to two decimal places is enough to get it to display right, and of course it won't really effect calculations (except the particular one I was working on that exposed it), but there is a heck of a lot to be said for using integer maths..
Did I mention I'm starting to hate computers.. ;)
Some more info as to why this happens for anyone who's interested:


(Note: Ordinary level Maths being discussed here)
Yes, pure gammy. I have done every single exam paper from 2009 back over and over again, yet somehow they manage to pull the most obscure weird little summies out of nowhere. Let me see:
Q1: I have completely forgotton how to do scientific notation or whatever. I punched in the numbers and pressed the EXP button over and over again, yet each time got a different answer. I gave up. The part (c) had me thinking for a bit, but on reviewing the question I figured it out and I’m pretty sure I got it right. Yay! At this point in the exam I liked Maths.
Q2: Oh algebra. We’ve never been friends. At least I can rest happy in the knowledge that I will never have to do it again! Question (b) bothered me a bit as it said “Solve for x and for y” and to me that implies one answer, and I got two. Who knows. Part (c) of that question I completely ignored, as the method for alegbraic division has entirely left my mind. I started to dislike Maths.
Q3: I did the (a) part, then decided I would leave it out completely and only do the required 6 questions. Still disliking Maths.
Q4: Complex numbers = not complex! Except for the (c). I can normally do those sort of questions, but the reals and the imaginaries would not sort themselves out no matter how many times I tried. At this stage I reasoned with myself: Maths isn’t so bad, right?
Q6 (we don’t do Q5, for undisclosed reasons): Again, the part (c) got me. How the hell do you get f ‘(x) of that thing? No idea. The little table thing was a cute idea. Thanks SEC. Hate you.
Q7: The first principles and product rule were ridiculously easy, but they had to make up for it in that weird-ass part (c). I answered (ii), acceleration question, and left it at that. Well and truly despising Maths at this point.
Q8: Part (v)! What was that? Three real roots? Guh?
At half 4, I laboriously treasury-tagged my graph sheets to my exam booklet (how gammy were they? About as gammy as the paper, in my opinion) and handed it up. I just have to pass Maths, as I’m not counting it, but I was kinda hoping I’d be confident enough that I had passed it. Oh well.
Irish next (yes, I just deliberately ignored Maths Paper 2.) I’m slightly worried about the essay, because the only way I’ll be able to produce a good one is if I learn it off. I’ve got Polaitaiocht, An gCulu Eacnamaiochta, Drugai agus Difhostaiocht prepared, but who knows what’ll turn up on the day. Any tips? My teacher doesn’t “do” predictions, but she’s been going pretty heavy on Politics all year, so I’m going to focus on that. Though if we’ve learned anything from English Paper 2: Predictions mean absolutely NOTHING.
Good luck good luck good luck!


Visual Lottery Analyser 2.1.6
OS: Win98,WinME,Windows2000,WinXP,Windows2003,Windows Vista Starter,Windows Vista Home Basic,Windows Vista Home Premium,Windows Vista Business,Windows Vista Enterprise,Windows Vista Ultimate
Publisher: Sprintbit Corporation
Visual Lottery Analyser 2.1.6
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favoriteshareware.com Editor: Visual Lottery Analyser - Visual Lottery Analyser is state-of-the-art lottery analysis software with many unique features. Work with almost all lottery games in the world. Program use new innovative analysis methods like visual drawings analysis, use geometry with special Ticket View for showing lottery game view at hand, use also colors to differentiate between special numbers groups. Everything is for better and faster understanding how you games and their number s goes in the real. Whether you are professional player or beginner here you will find everything that you need to play, analyze, calculate and keep statistics of your lottery games. To help you to increase your chances of winning software introduces new lottery theories and analysis methods: Geometrical Ticket View, Contact and Outside numbers, traditional Hot and Cold numbers and more. You can analyze single numbers, groups / blocks of numbers, our special numbers, numbers that are located in vertical or horizontal lines, by the date etc. Instead of looking on columns with numbers that really do not tell too much, you can now know how the numbers may go with just taking one look. Some of major features are Create My Tickets, Tickets Advanced Generator for creating smart lottery tickets that are created according to the software rules or rules defined by you. Create My System is a powerful feature dedicated to work with mathematical systems. Program comes with over 100 mathematical systems included. You may use them to create lottery tickets by replacing system numbers with yours. Apply our filters to the system and reduce the combinations to those that match your analysis criteria. Other major features are: Games & Drawings Database, My Tickets Manager, Lottery Notepad, Financial & Hits Statistics, and Mathematical Systems Editor, Check Game Results. In addition to all new visual analyzing techniques program includes Numbers Report feature that analyzing games using old-fashion mathematical methods.
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An Introduction to Roulette
Roulette has been called the overall game of luck, and for many players it is true, nonetheless it is also a game of strategy that can deliver great rewards in the event that you play it right. Roulette is played with a set of cards which are face through to a table before you. A participant will pick one of the cards and place the bet. At the end of the count, there will be a winner and a loser. Roulette isn’t based on luck, but on skill and strategy. Which means that a player can win a lot more than she loses, but moreover, she can lose less than she gains.
One great strategy for betting on roulette, or any other type of gambling, is the Fibonacci system. The Fibonacci system is a system of studying and predicting the results of a number by its appearance in the Fibonacci sequence. If you look at any book about gambling, you will find that the Fibonacci numbers come up quite often. They are even used to help cops to determine in case a suspect is guilty.
In roulette, the initial stake is low, as in slot machines, which means that your success depends not on how much you bet, but on what often you bet. Each time you place a bet, it counts as an “operation”. Betting may take place at exactly the same place and at the same time every time, but the odds are often stacked contrary to the home player. That is why it is easier to walk away with a small win than it is to walk away with a large win. If you’re looking for a simple way to increase your chances of winning, then your Fibonacci numbers can be a valuable aid.
The Fibonacci numbers don’t possess anything to do with the actual numbers in roulette, though they can help you determine the probability of a winning bet. Once you view a wheel of cards, the numbers which are on the wheel are arranged in a Fibonacci pattern. Small the number, the more likely that the winning bet will undoubtedly be large. You can determine the chances of that happening by calculating the Fibonacci ratio, that is the square of the ratio between the high and low bets. For example, if the high bet is 50 cents, and the low bet is two dollars, you then will want to bet on the low side of the wheel so that you can maximize your likelihood of winning.
In the event that you look carefully at many casino games, you will observe that the odds vary greatly. It may look like 더나인카지노 they all focus on the same premise, but each game includes a different outcome dependent on where you place your bets. For example, when playing roulette at a land-based casino, you are only dealing with a small amount of cards. The casinos offering virtual roulette, such as for example internet casinos, have much larger decks of cards. Therefore, the chances of winning are much greater once you play on a virtual table than in a genuine casino.
In roulette, the wheel is used to provide randomness to the game. As the wheel spins around the tiles, it randomly chooses numbers for every spin. While this may not appear to be too random, the amount of times that these numbers come up will eventually add up. That is why, many gamblers believe that the roulette wheel is useful in determining the odds of winning. By placing bets on the correct number combinations, you ensure that you will be among those people that gets lucky.
Another way to increase the odds would be to place inside bets and outside bets. The word inside bet identifies bets that are made using inside information about the existing situation of the ball. For instance, you may bet a five dollar bet on a machine that’s off by three points. This might indicate that the ball is on the edge, so it is best to bet a small amount. Outside bets are bets that are placed based on rumors along with other random situations.
While creating a wager is very easy, winning is more challenging. There are a variety of roulette systems that have been developed to help gamblers determine how to place their bets and win. Many of these systems include the American roulette system, which analyzes each bet individually to determine whether or not it is worth the volume of the bet. After that it uses these factors to calculate the expected payout of the bet. Other systems involve analyzing the chip count and applying a statistical analysis to provide an idea of the chances of the specific bet, in addition to the direction of the chip.


Thursday, September 12, 2013
Saturday, February 02, 2013
New Paper in Psychological Science...
Tuesday, August 28, 2012
Sunday, September 23, 2007
Book Signing @ Kepler's in Menlo Park
Meanwhile the book is selling well and getting a lot of good press. Here's the amazon link:
Thursday, May 24, 2007
The book is available for pre-order
You may go to Princeton University Press or to Amazon to pre-order it.
Thankfully, the reviews have been very good:
Martin Gardner : A Certain Ambiguity is an amazing narrative that glows with a vivid sense of the beauty and wonder of mathematics. The narrator is deeply troubled by the ancient question of whether the objects and theorems of mathematics have a reality independent of human minds. Mixing fiction with nonfiction, A Certain Ambiguity is a veritable history of mathematics disguised as a novel. Starting with the Pythagorean theorem, it moves through number theory and geometry to Cantor's alephs, non-Euclidean geometry, Gödel, and even relativity.
Eli Maor, author of "e: the Story of a Number" and "The Pythagorean Theorem: A 4,000-Year History" : This is a truly captivating thriller that will take you on a whirlwind tour to infinity--and beyond. But be warned: once you start reading, you won't be able to put it aside until finished! A masterly-told story that weaves together criminal law, ancient and modern history, a young man's quest to know his deceased grandfather-and some highly intriguing mathematics.
Keith Devlin, Stanford University, author of "The Math Gene" : This rich and engaging novel follows the path that leads one young person to become a professional mathematician. By deftly blending the young man's story with mathematical ideas and historical developments in the subject, the authors succeed brilliantly in taking the reader on a tour of some of the major highlights in the philosophy of mathematics. If that were not enough, the book also examines, through the minds of its characters, the natures of faith (religious and other) and truth. I am strongly thinking of building a university non-majors math course around this novel.
Joan Richards, Brown University : A Certain Ambiguity is a remarkably good effort to work through some fundamental issues in the philosophy of mathematics in the context of a novel. Crucial to the success of such a venture is creating characters and a plot that are strong enough to hold a reader's interest. Suri and Bal succeed particularly well in the story of Vijay Sahni and Judge Taylor. This well-written book will, I believe, find readers not only among mathematicians, but in a wider audience that is intrigued by mathematical meaning.
Alexander Paseau, University of Oxford : Suri and Bal convey the beauty and elegance--as well as the fascination--of basic mathematical concepts.
Sunday, August 28, 2005
The human heart yearns for absolute truth and certainty. But can we be truly certain about anything—or is everything we believe accidental and meaningless, shaped by the happenstance of genetic and social inheritance? Perhaps mathematics alone, with its uncompromising rigor, can lead us to certainty. In our 90,000 word novel, we examine where mathematics can and cannot take us in the quest for certainty.
Our book will show the reader the following: First, that mathematics can be deeply beautiful—in this regard it is not unlike music or painting; second, that mathematics has profound things to say about whether absolute truth is obtainable; and lastly, that a novel is the best medium through which to convey the excitement and meaning of doing mathematics
Our protagonist, Vijay Sahni, an Indian mathematician, has glimpsed the certainty that mathematics can provide and does not see why its methods cannot be extended to all branches of human knowledge, including religion. Arriving to pursue his academic career in a small New Jersey town in 1919, his outspoken views land him in jail, charged under a little-known Blasphemy law (on the state statute books to this day). His beliefs are challenged by Judge John Taylor, who does not believe that mathematical deduction can be applied to matters of faith. In their discussions the two men discover the power—and the fallibility—of Euclid's axiomatic treatment of geometry, long considered the gold standard in human certainty. In the end both Vijay and Judge Taylor come to understand that doubt must always accompany knowledge.


Monday, August 31, 2009
Here's some statistics ... although some of the numbers had to be assumed. Benjamin wears an average of 8 diapers a day (not counting the times he had the runs). Which means we have changed approximately 5840 dirty diapers. and at an average of 30 cents a piece, we have spent over $1,800 just in diapers ... that's not counting the wipes. ...... Baby's are VERY expensive .... but we love him and he's worth every diaper.


Math classes are highly beneficial for kids at a young age. It can develop their problem-solving skills easily and will benefit in their further academic life. At Time Master, we train students to learn calculations enhancing their IQ power. This Maths Course will nurture and stimulate children's passion and build their confidence! Our qualified teachers aim to spend quality time with every child.
At the Time Master, your child will be involved in various easy-to-learn, fun activities that help in the complete development of their mind and body.
Our Maths classes can build a strong foundation for kids that will help them in higher classes. We promote their skills and build interest to learn and solve maths. Through various curricular and co-curricular activities, we help them understand concepts better. We focus on blending learning and playing, to make kids learn new things easily and meticulously. We ensure appropriate mentoring towards your Child’s holistic growth.
Our training in maths classes in Abu Dhabi is very unique and methodical. Our Maths training by well-trained tutors is an opportunity that shouldn’t be missed.
With our coaching, the children will be developing skills that would benefit them in the future. Children will also learn to work as part of a team that will better build their confidence.
Our course programs are a secure option for working parents to leave their children in, while they are at work. We take care of your little ones and keep them engaged while you can pursue your careers. Parents can always contact us for any concerns and support. With us, we guarantee that your kids will fly out in colors.
|Medium of instruction||English|
Help your kids to make math fun to learn with Maths Classes at Abu Dhabi. Mathematics involves big ideas that can be learnt quickly. See how your child’s calculation skills become sharp in no time. Learn calculations with Maths Classes at Abu Dhabi to enhance your kid’s memory and improve their problem-solving skills. Make learning more engaging and productive with Maths Classes at Abu Dhabi!
Maths Classes at Mussafah trains children to discover maths concepts. Help your child learn Math without anxiety and build a strong foundation for higher classes. With well-equipped trainers and activities, children will learn to do mental calculations easily by the end of the classes at Mussafah. If you wish to remove the fear of mathematics in your kids, Maths Classes at Mussafah is your choice!


At St Norbert’s Catholic Voluntary Academy, we inspire our children through the Inspire Mathematics Curriculum. As a foundation for our Mathematics curriculum, we use White Rose Maths, which offers a framework to teach the Mathematics Programme of Study as laid out by the National Curriculum and the Statutory Framework for the Early Years Foundation Stage, alongside other high-quality resources, including National Centre of Excellence in the Teaching of Mathematics (NCETM), NRICH. White Rose has been influenced, inspired and informed by the work of leading maths researchers and practitioners across the world and is based on the latest pedagogical research.
At St Norbert’s, we strive to have children develop a positive attitude and interest towards mathematics. From the earliest years, we encourage children to ‘have a go,’ to have children notice numbers, patterns, shapes, and connections and to be able to discuss their findings with others. It is important to instil a love of learning from an early age and to teach children that we learn from making mistakes.
Inspire Knowledge and Skills
Proficiency in mathematical concepts and skills is vital for engaging successfully with the real world. We want to open children’s eyes to this and help them to see the importance of how what they learn in the classroom applies to the real world, both every day for everyone and more broadly across disciplines and careers. We provide a maths curriculum that balances acquiring rapid fluency alongside opportunities to apply reasoning skills in various problem-solving contexts. Each classroom environment is set up to enable children to build independence in learning maths, from up-to-date working walls, carefully chosen scaffolds and accessible resources. Beyond teaching maths discretely, we give children the opportunity to apply and develop what they have learnt across wider learning within the curriculum, such as in science, design and technology lessons, to support our intention that children see mathematical skills as something that is essential for their daily life.
Inspire Creativity & Adventure
We believe all children can achieve highly in maths. For some children, this demands a great deal of perseverance and resilience, and we talk explicitly about this in lessons and link it to other areas of curriculum learning, such as PSHCE. We encourage children to support one another to build a classroom climate of endeavour. In every lesson, children have the opportunity to apply mathematical reasoning to solve problems, which deepens their understanding and supports making connections across the curriculum. We take every opportunity to promote creativity in maths. This is particularly evident in the continuous provision on offer in our Lower School, through role play, small world and other exploration-based activities. In older years, creativity is embedded within our CPA approach, where children represent their understanding in a range of ways, such as using models to represent fractions or finding numbers, shapes and patterns in the real world.


- About Linwood
- Learning Areas
Mathematics is an excellent vehicle for the development and improvement of a person’s intellectual competence in logical reasoning, spatial awareness, analysis and abstract thought. Students develop numeracy, reasoning, thinking skills, and problem solving skills through the learning and application of mathematics. These are valued not only in science and technology, but also in everyday living and in the workplace. When ideas are discovered and insights gained, students are spurred to pursue mathematics beyond the classroom wall.
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Do you want to program an application that uses a timer that uses a relatively high resolution timer (milliseconds) and that can be at the same time compiled on other OS's? Then is this the right code snippet for you ;-). I will show you a function that returns the elapsed processor time in ms. Here it is:
The standard function clock() returns the clock ticks of elapsed processor time. The constant CLOCKS_PER_SECS holds the number of clocks the processor does in one second. Under Windows, this constant equals 1000 so you could simply return clock() without the other mathematics.
But this value may vary on other platforms. So what we do, is to divide CLOCKS_PER_SEC first by 1000. As clock() divided by CLOCKS_PER_SEC would return seconds, CLOCKS_PER_SEC/1000 will return ms (1000 ms = 1 second).
Mail me if you have problems, suggestions or whatever. Happy Coding!


Times Table Rock Stars (TTRS) & Numbots
Times Table Rock Stars (TTRS) and Numbots
All children from Reception to Year 6 have access to Numbots (EYFS and Year 1) and Times Table Rock Stars (Year 1 -6). It is a fun, rock and roll way to learn times tables. The children can practice at home, at school and via the app. It will help children to secure their times table knowledge. It encourages children to practice their times tables little and often. Through games, the children will learn their times tables. A clever algorithm adapts question specific to the child in order to target an area they may need to improve. All children have their login details in the back of their reading records/ homework diaries. Please speak to your child’s class teacher if you do not have yours.
Numbots is platform for learning to add and subtract!
NumBots is all about every child achieving the “triple win” of understanding, recall and fluency in mental addition and subtraction so that they move from counting to calculating.
Please see the video below to explain our NumBots work!
TTRS Parent guide:
Times Tables chant videos:


Lesson 9: Clustering¶
Note that in Python syntax, you will have to use a dot to specify where you want to get a function from. For example, there is a package called numpy, with a module called random, with a function called seed. The seed function is called by typing out
np.random.seed(), telling python where exactly it needs to look.
WE ARE USING PYTHON3, NOT PYTHON
Clustering: The process of partitioning a dataset into groups based on shared unkown characteristics. In other words, we are looking for patterns in data where we do not necessarily know the patterns to look for ahead of time.
In: N points, usually in the form of a matrix(each row is a point).
In: A distance function to tell us how similar two points are. The most intuitive distance function is euclidean distance. The type of distance measure you use can vary depending on the type of data you are using. One specific example of how fine tuned distance metrics can be is a distance metric that weights substitutions in DNA strings heavier than indels because indels are more common sequencing errors. This means that such a metric would not separate two DNA strands due to sequencing error.
Out: K groups, each containing points which are similar to each other in some way. Some algorithms cluster for a preset number K, others figure it out as they go along.
How is DNA a point? One common way we translate DNA strings to points is by making a string of DNA into a kmer vector. A kmer is a string of length k, and there are 4^k possible kmers in any DNA strand. Usually we think of kmers as ordered lexicographically like this: AAA, AAC, AAG, AAT, ACA, ACC, ACG, ACT, AGA and so on. One way to represent a DNA strand is to create an array of zeros of length 4^k and increment by one for each time that kmer appears in the DNA strand.
Problem: Find the kmer vector of “AG” (k=2).
Bioinformatics Applications of Clustering:¶
- Finding what genes are up and down regulated under certain conditions. Imagine you have a matrix, where each point is a set of gene expression recorded for a variety of conditions. If two points are close to each other, that means they had similar expression levels throughout those conditions.
- Discerning different species present in a sample of unkown contents. This can be done with an algorithm that does not have a predetermined amount of clusters. An example application is taking HIV sequences from a patient, clustering them, and filtering clusters under a certain size to find the sequences of prevalent strains within the patient.
- Finding evolutionary relationships between samples using hierarchical clustering. The earlier on two centers were combined, the closer their corresponding points are from an evolutionary perspective.
In order to demonstrate the differences between different clustering methods, we need datasets that cluster differently depending on technique.
Copy the starter file into your directory:
clust.py contains a plotting function - don’t touch it! We will be creating stuff for that plotting function to plot in a minute, so write your code below that function.
Start by creating some blobs using numpy’s random normal generator. First, create a seed for the random number generator with
Make a few blobs of points (probably two) with centers between 0 and 20 and varied stdevs (keeping the array dimensions the same). Example syntax:
clust1 = np.random.normal(5, 2, (1000,2))
Put the point blobs into one structure so that we can cluster them all at once with
dataset1 = np.concatenate()
We will be comparing how our point blobs cluster to the way that circles of datapoints cluster. Create two concentric circles as the second dataset.
dataset2 = datasets.make_circles(n_samples=1000, factor=.5, noise=.05)
If you want to see what your datasets look like, use the
cluster_plots will save your plots to a pdf file in your current directory, the name of which can be changed.
scp email@example.com:/home/username/path /localpath/
(We present the Lloyd Algorithm here, but there are other algorithms for k-means clustering) I. Select K centers. This can be done a variety of ways, the easiest of which is to select k random points; maybe find a random point, find the farthest point from that and select it, find the furthest point from the previous and so on; this is called farthest first traversal
II. Assign each point to the center nearest to it. (Centers to Clusters step)
III. For each center, take all the points attached to it and take their average to create a new center for that cluster.
IV. Reassign all points to their nearest center (Clusters to Centers step) and continue reassigning + averaging until the iteration when nothing changes.
We will be using the KMeans algorithm from sklearn’s cluster package to dataset1 and dataset2. Remember that k is the number of clusters the KMeans algorithm will assign points to, so give Kmeans the appropriate k. The points returned from the KMeans function will be separated into clusters, making them easy for the cluster_plots function to distinguish and color accordingly.
kmeans_dataset1 = cluster.KMeans(n_clusters=k).fit_predict(dataset1) cluster_plots(dataset1, dataset2, kmeans_dataset1, kmeans_dataset2)
(While using the sklearn implementation as a black box is the general practice as we’ve seen so far, it is a good learning practice and a nice coding challenge to implement the Lloyd Algortihm yourself. Check out this Rosalind problem “Implement the Lloyd Algorithm for k-Means Clustering” (You could solve the previous problem on Rosalind for distance calculation)
2. Agglomerative Hierarchical¶
I. Start with every point being its very own cluster center.
II. Find the two centers which are closest to each other and combine them into one cluster. The new center is the average of the two previous ones.
III. Continue combining the closest centers until all points are under a single cluster.
Let’s look at the blobs and circles we made again. Look at the documentation page for agglomerative clustering and figure out the proper calls for the two datasets (syntax is very similar to what you did for k-means).
cluster_plots() to graph and
scp to view the results. Do you notice a difference in quality of the clustering of the left and right graphs?
Unfortunately, this still does not solve our circlular cluster issue. For that, we can ask the sklearn package to build a graph out of our circles which restricts the amount of nearest neighbors a point can cluster with.
#this line limits the number of nearest neighbors to 6 connect = kneighbors_graph(dataset2, include_self=False, n_neighbors = 6) #in this line, you need to set linkage to complete, number of clusters to 2, and set connectivity equal to the graph #on the previous line hc_dataset2_connectivity = cluster.AgglomerativeClustering().fit_predict(dataset2)
cluster_plots() to graph the plot resulting from the regular AgglomerativeClustering beside the graph that plots the connected AgglomerativeClustering. As you may have guessed, this fixes the circle problem.
3. Soft Clustering¶
This is essentially the same thing as k-means, but points cannot be hard assigned to a cluster. Instead, each point has a probability of being in each cluster, and points with higher probabilities influence the center of that cluster more.
I. Select K centers randomly (or slightly less randomly, like farthest first traversal.
II. Expectation step: Assign a responsibility (a likelihood) for each point in respect to each cluster. Basically, the closer a point is to a center the higher the likelyhood of that point. This can be calculated in a variety of ways, but the main idea is that it is some function relating the distance from a point to a center to the distances between all points and that center to see if it is much closer or further than other points
III. Maximization step: compute new cluster centers by using a weighted average of the points based on the likelihoods calculated in step II.
Let’s go ahead and see what will happen with our blobs and circles under this clustering algorithm:
Use these new clusters in our
Also feel freee to check out Rosalind problem “Implement the Soft k-Means Clustering Algorithm”](http://rosalind.info/problems/ba8d/).
Head over here to complete our clustering challenge!
Lloyd Algorithm k-means clustering and Soft Clustering explanation and challenge are adapted from Rosalind, particularly Rosalind problem “Implement the Lloyd Algorithm for k-Means Clustering” and Rosalind problem “Implement the Soft k-Means Clustering Algorithm”


Together Everyone Achieves More
Power Maths at Fleetdown
What is Power Maths?
New to this academic year, at Fleetdown Primary Academy we are adopting a maths scheme called Power Maths to support our teaching of maths from Reception to Year 6. Fully aligned with the new National Curriculum and recommended by the Department of Education, Power Maths is a whole-class, textbook-based mastery resource that empowers every child to understand and succeed.
Children are encouraged to solve problems each day through the use of concrete, pictorial, abstract approach. Pupils are first introduced to an idea or skill by acting it out with real objects/equipment. They then relate the ‘hands on’ representations to a picture or diagram of the problem. Finally, pupils represent problems using mathematical notations.
What does a lesson look like?
Every lesson is divided into sections that involve plenty of discovery, sharing, collaboration, practice and reflection.
There are different elements, informed by research into best practice in maths teaching, that bring the lessons to life:
· Discover – each lesson begins with a problem to solve, often a real-life example, sometimes a puzzle or a game. These are engaging and fun, and designed to get all children thinking.
· Share – the class shares their ideas and compares different ways to solve the problem, explaining their reasoning with hands-on resources and drawings to make their ideas clear. Children are able to develop their understanding of the concept with input from the teacher.
· Think together – the next part of the lesson is a journey through the concept, digging deeper and deeper so that each child builds on secure foundations while being challenged to apply their understanding in different ways and with increasing independence.
· Practice – now children practice individually or in small groups, rehearsing and developing their skills to build fluency, understanding of the concept and confidence.
· Reflect – finally, children are prompted to reflect on and record their learning from each session and show how they have grasped the concept explored in the lesson.
What if my child needs a confidence boost, or wants to be challenged further?
Power Maths Power enables children to build number fluency, confidence and understanding, step by step. This means that the concepts are broken down so that your child can master one idea without feeling over-whelmed. There are a range of fluency, reasoning and problem solving questions in each lesson that are designed to support the different needs and confidence levels within a class, while at the same time fostering a spirit of working and learning together. Each lesson includes challenge questions for those children who can delve deeper into a concept.
At the core of this programme is the notion that all children can achieve and become successful mathematicians with the right growth mindset. Power Maths promotes five child friendly characters (Ash, Flo, Dexter, Astrid and Sparks), each with their own positive skillset, to inspire and motivate children in every lesson. These characters are:


Published November 1996 by McGraw-Hill/Contemporary .
Written inRead online
|The Physical Object|
|Number of Pages||194|
Download Teach Your Child Math
As the book suggests, the book is geared for parents who want to teach their children math. It might be a good system for a home-school parent, but I find that since my 6 year old daughter is in 1st grade the lessons are going to be a tad different from what she's learning in school/5(4).
So if you don't find math all that interesting, and if the kids you're trying to teach are having a hard time with math, then this book probably won't be very helpful.
Read more. 8 people found this helpful. Helpful. Comment Report abuse. absent_minded_prof. out of 5 /5(4). Teach Your Child Math book Your Child the Multiplication Tables, Fast, Fun & Easy with Dazzling Patterns, Grids and Tricks.
is an innovative workbook, designed for parents wishing to reinforce classroom teaching or home school their children.
Designed for Grades 2 and 3, this workbook is also suitable for children with special needs. Unlike conventional methods, this workbook teaches the child to. 2 Helping Your Child Learn Mathematics Helping Your Child Learn Mathematics 3 Some Important Teach Your Child Math book Your Child Needs to Know About Mathematics You can help your child learn math by offering her insights into how to approach math.
She will develop more confidence in her math ability if she understands the following points: 1. Buy a cheap copy of Teach Your Child Math: Making Math Fun book by Michael Shermer.
Suggests a variety of games that help teach math and problem-solving skills, and includes activities for preschoolers up to fifth-graders. Free shipping over $/5(1).
Although we left it till the end, this is actually the most important reason of all for teaching your young child math. Kids – at a very young age – love learning about quantity, and they love seeing equations as long as both of these concepts are presented in a fun, happy way.
Corduroy Math: Learning with Buttons Since I was a little girl, Corduroy by Don Freeman has been one of my absolute favorite books.
I was so excited that it is this month’s pick for our Virtual Book Club for Kids. Teach your child math the fun way with LIFEPAC Kindergarten Math Student Book 1. This bright, full-color workbook teaches beginning math skills like direction, comparisons, colors, cardinal and ordinal numbers, shapes, and number order.
Eighty step-by-step lessons, perforated pages, and helpful guide bars are included in this Alpha Omega. Wondering how to teach math to your child with dyslexia.
Use multi-sensory techniques and help your dyslexic child learn math. I’m sharing exactly how we teach math in our homeschool. Thank you for joining me for day 2 of a 5-day series on Homeschooling With Dyslexia by the Subject.
To start at the beginning, click here. Peter Usborne is the founder and Managing Director of Usborne Publishing, one of the world’s leading children’s book publishing companies and Children’s Publisher of the Year He was previously one of the founders of the magazine Private Eye, and was recently awarded an MBE for services to publishing.
While some families find it a bit dry, most parents and educators prefer the simple, straightforward, but timeless “Teach Your Child to Read in Easy Lessons,” by Siegfried Engelmann and Phyllis Haddox. Originally published inthe book includes a teacher’s guide and scripted lessons that parents can deliver in 20 minutes a day.
Wow, parents like that make my blood boil. We should never tell a child they a “math person” or a “non-math person”. What a stigma to saddle a child with. It seems this student is good at math (chess. strategy games. my goodness!!!) I think the parent is transferring their own fear of math to the a shame.
The kids absolutely love this game - and they're learning. The game has been funded by the Usborne Foundation, a charity set up to support initiatives to develop early literacy. Our mission is to help as many children learn to read as possible. The computer version is % free and we put profits from the app back into the Usborne Foundation.
A great summer (or any season) project is to bring this concept to reality for your child. Below are a few fun, creative ways to help your kids total costs using dollars and change, as well as calculate and make change.
Create a family coin jar. Use it to collect all loose change on daily basis. As a family, create a list of activities and. Teach Your Child to Read in Easy Lessons is a fantastic book for teaching children to read.
I've created this sticker chart to help track the student's progress through the book. I usually print it on colored cardstock for added fun.
I highly recommend offering some time of. If you are at home with your children during temporary school closings, these workbooks offer: Many practice pages, instructions, record-keeping pages, answers, and more.
FREE Shipping on any size order. See free tips to teach math facts. Children need to learn and memorize math facts. Five Times Five Is Not Ten. Select *Scuffed: $ Save. Teach Your Child to Read in Easy Lessons is a complete, step-by-step program that shows parents simply and clearly how to teach their children to read.
Twenty minutes a day is all you need, and within teaching days your child will be reading on a solid second-grade reading s: The How To Teach Your Baby Math Deluxe Program This program provides parents with a simple and clear daily program for teaching small children mathematics.
The authors show clearly just how easy it is to teach a young child the reality of quantity and the simple truth behind the symbols we use in mathematics.
Teach Your Child Math: Making Math Fun for the Both of You Arthur Benjamin, Michael Brant Shermer By transforming math "problems" into games, this easy-to-follow book gives parents a fun way to help their children learn math.
Addition Facts That Stick is an open-and-go, all-in-one book for teaching your child the addition facts. It provides detailed lesson plans, fun games, and simple worksheets for every step of the process, so that you can teach your child addition facts that truly stick. 6 Books to Help Young Kids Build Math Skills By Ginny Osewalt Save.
Save. Save. Email. Print. Sms. Share To find more books for your child, explore the Book Finder tool from Understood founding partner This beach-themed book uses groups of feet to teach kids about counting.
For example, the number 1 is a snail (yes, snails have one foot Author: Ginny Osewalt. In only twenty-to-thirty minutes a day, you can have your preschoolers and non-reading elementary-aged children at a second-grade reading level within days.
A complete, step-by-step program, Teach Your Child to Read in Easy Lessons includes everything parents need; using the DISTAR method, lessons follow a sensible, simple plan that doesn't require /5(43). Our book is filled with easy to follow explanations of all the subjects you will need to understand so you can teach your child.
Worksheet Sample Page We have also included worksheets that you can copy from the printed book or download from our website to use with your children. Help your child recognize and identify real-world examples of right angles (the corner of a book) and parallel lines (railroad tracks) While driving together, direct your child to look for objects with the same size and shape; Measurement: Teach your child how to set the kitchen timer when you’re cooking.
Your home is a great place for you to begin to explore and "talk" mathematics with your child. Incorporating math activities and language into familiar daily routines will show your child how math works in his everyday life and provide him with a safe environment in which to take risks by trying new things.
Teach a few new facts each day, and make a 3″ by 5″ card for each one. Add these new facts to the stack of known facts, and continue to practice daily. Remember to teach a way to remember the fact. Repeat the process so that over time, the child masters all of the facts, and will not have to count out answers when working on math.
10 Top Math Apps for Elementary School Children Is your child struggling with math in elementary school. You may be able to get him or her excited about learning math by using an educational app on your iPad, iPhone, Android or other mobile device. Here are ten apps for elementary school children that may hold the key to math success.
After your child reads a chapter the first time, he should identify the major points, and decide what was a key idea, and what was simply a detail.
Once he knows that the chapter focuses on two main ideas, for example, he can read the chapter again, keeping in mind how these topics interplayed with one another/5(24). Did you know that math talk — which is as easy as using numbers while talking with your child &mdash can set your kindergartner up for a lifetime of success in math class.
Children who develop emotional intelligence skills are kinder, happier, healthier, and more successful. A 7-year-old girl is humiliated by her teacher after failing a math. Talk math with your child as a matter of routine. For example, diapering, meal and bath times, neighborhood walks, and shopping trips are ideal times to count, point out shapes and sizes, talk about patterns, and describe how things are the same and different.
Make a list of math talk words and phrases. Post it on the refrigerator or somewhere. Teach Your Children Well offers lots of free teaching resources.
It includes over free maths worksheets. Lots of free resources for English and science. It includes free big book teaching programs. You can decide which worksheets are the most suitable for your child/student. Reading math is much harder than reading fiction.
5 skills to teach your kids so they can learn from their math books and be more independent in math. Why is reading math so difficult. When your kids read a novel, there’s a lot of context to help them understand the author’s point.
As a parent or a teacher, there are a number of techniques which can be put to use in order to make a child learn to read. Among such techniques, the synthetic phonics and phonemic awareness. Get this from a library. Teach your child math: making math fun for the both of you.
[Arthur Benjamin; Michael Shermer] -- By transforming math "problems" into games, this easy-to-follow book gives parents a fun way to help their children learn math.
With an expanded section on problem solving, fun word problems, and. Parents and older siblings can count somewhat as "The Count" does on Sesame example, you can help a child to count coins in order to spend them for a small treat, as part of family can also teach toddlers and young children almost anything that is simple enough by just being clear and having fun with it.
Then they will love to learn maths, because 75%(8). Ruth Beechick, You Can Teach Your Child Successfully Dr. Beechick left behind a series of books written specifically to homeschoolers which help parents become familiar with the “language” of teaching, build self-confidence, learn to rely less heavily on “the book,” and teach their children in a more natural way.
Get this from a library. Teach your child math: making math fun for the both of you. [Arthur Benjamin; Michael Shermer] -- Introduces your preschooler to math by using visuals and then progresses to games and concepts that can be enjoyed by a fourth or fifth grader.
As I read through Teach a Child to Read with Children’s Books, I felt like I was reading a description of my own experience. One of the most important recommendations in this book is that we read lots and lots of books to our children from the time they are little.
Teach Your Kids Math is a useful tool for those who are applying the method for early learning, created by Glenn Doman.
You'll let your child see some virtual /5(). not only is it possible to teach your baby to read, it’s also easy to do (easier than if you wait until your child is five or six years old). More importantly, your baby will love it. If you’ve never encountered babies reading before, you probably have some questions or doubts about whether this is something you’d like to do with your baby.


Do know how to determine chances of succeeding the lottery, like the Florida Lottery? You can estimate each set of odds for each different lottery activity you play. Along with the assistance of any small hand held calculator or together with the free online car loan calculator on your computer, you just multiply the numbers together plus add one split process when “the order” of your respective picked numbers is just not expected for a particular lottery game.
Precisely what you “need to know” will be the number of total projectiles that the succeeding numbers are driven from….. could it be fifty nine, 56, 42, forty nine, or 39? When there is a secondary drawing with regard to the single more ball, such as the “red ball” with Powerball or perhaps the Mega Millions’ “gold ball” you should know how many tennis balls are in this group as well. Are there 49 or 39?
It doesn’t subject if it’s the Sarasota, Ohio, Texas, PENNSYLVANIA or NJ Lottery. This strategy or even formula gives a person the actual odds. Fl Lottery is 6/53. Ny Lottery is usually 6/59. The Kansas Lottery, Massachusetts Lottery, Wisconsin Lottery, in addition to the State regarding Washington Lottery carry a 6/49 lotto numbers ratio. Illinois Lottery includes a 6/52.
Once you have this information vsmb.vn correctly in front of an individual along with your calculator throughout hand, you can begin doing work the formulas. An individual need to choose five regular balls then one extra golf ball correctly matched in order to the winning drawn numbers to get the multi-million dollar jackpot that a lot of involving us dream about winning someday.
Throughout the first illustration there are 56 balls in the first group plus 46 balls within the secondary team. In order in order to win the Jackpot feature you should match most these balls (5 + 1) accurately, but not actually to be able. The Florida Lottery’s Super Gruppo Plus is 47/27. The top drum will be spinning with the initial part of the getting. You have the 1/56 chance to be able to match your number to this 1st ball.
With a single ball removed after the first number has been drawn, you nowadays have a 1/55 probability of matching one more one of your current numbers to typically the second ball sketched. With each driven number a ball is removed reducing the number of remaining balls simply by a total of one.
The chances of you appropriately matching the quantity on the 3 rd ball to end up being drawn is now 1/54 from the entire number of balls remaining in the drum. With the third ball taken out from the drum and sitting together with the other two succeeding numbers, your likelihood of correctly matching your fourth ball is decreased to 1/53.
Unsurprisingly each time a ball is introduced from the carol the odds are usually reduced by 1. You started together with a 1/56 opportunity, then with each and every new winning amount it is decreased to 1/55, 1/54, 1/53, and along with the fifth golf ball you have the odds of 1/52 appropriately matching this sixth winning number. This can be the first part regarding the mixture of just how to calculate your current odds of winning the lottery, like the Florida Lottery.
Now take these kinds of five odds representing the five earning numbers (1/56, 1/55, 1/54, 1/53, and even 1/52). The “1” on top regarding the fraction symbolizes your one in addition to only chance in order to correctly match the particular drawn number.
Now you in order to finance calculator and multiply most top numbers (1x1x1x1x1) equal one (1). Next you increase in numbers all the underside numbers (56x55x54x53x52). Correctly entered and increased you find the complete is 458, 377, 920. The brand new fraction becomes 1/458, 377, 920. This can be a 458 million to just one chance to win. If you were required to pick the numbers throughout order just just like they can be drawn, after that these would become the odds towards you to succeed this Pick 5/56 ball lottery video game.
Fortunately or regrettably, you’re not required in order to pick the numbers in the precise order they happen to be drawn. The 2nd step of the formulation will reduce the odds, which enables you to match up these five winning numbers in virtually any order. In this particular step you may increase the number involving balls drawn — five (1x2x3x4x5). With calculator in hands you see how the total equals a hundred and twenty.
To give a person the right to be able to choose your 5 matching numbers within any order, an individual create these possibilities by dividing 120/417, 451, 320. An individual definitely need some sort of calculator for this specific one. 120/458, 377, 920 drops your chances of winning this particular lottery to one-half, 819, 816. They are over 3. a few million to a single odds against an individual of winning this Pick 5/56 soccer ball lottery game.
When this were typically the Mega Millions Lotto, you need to be able to add the “gold ball” to these five winning attracted balls to be able to win the Multi-Million Dollar Jackpot. The only platinum ball is determined as a 1/46 chance of complementing it correctly, in addition to since you might be pulling just one quantity it has in order to be an precise match. Again, a person only have that will “1” possiblity to do it right. Today you must increase 3, 819, 816 by 46.
Grab your calculator and even do the propagation. Your final chances against you winning the Mega Thousands Jackpot are worked out to be a hundred seventy five, 711, 536 or perhaps clearly stated a hundred seventy five million, 711 thousand, 5 hundred 36 thirty-six to just one (175, 711, 536 to 1). You now know precisely how to calculate the odds of winning typically the Mega Millions Lottery.
The Powerball Lottery calculations are established on a 1/59 for the initial five white balls and 1/39 for that “red” power ball. The first set in place of multipliers is usually 59x58x57x56x55. This group totals 600, 766, 320. Now separate 600, 766, 360 by 120 (1x2x3x4x5). Your new overall is 5, 006, 386. There is usually a 1/39 chance to catch the particular “red” ball. 39 x 5, 006, 386 gives you the actual odds of winning the Powerball Jackpot, namely 195, 249, 054 in order to 1.
Another your five +1 Lottery of which seems to get everywhere in typically the Usa is the “Hot Lotto” which offers a 39/19 matter. It is played out in 15 various States. DC Lotto, Delaware Lottery, Florida Lottery, Iowa Lottery, Kansas Lottery, Maine Lottery, Minnesota Lottery, Montana Lottery, New Hampshire Lottery, New Mexico Lottery, North Dakota Lottery, Ok Lottery, South Dakota Lottery, Vermont Lotto, as well as the West Virginia Lottery. The ultimate odds of winning the minimum $1 Million Jackpot is 12, 939, 383 to 1.
A Pick 6/52 ball Lottery video game formula looks just like this: (1/52, 1/51, 1/50, 1/49, 1/48, 1/47) for the total of fourteen, 658, 134, 4 hundred divided by 720 (1x2x3x4x5x6) for the possibilities of 1/20, 358, 520. Your chance to win the 6/52 Lottery is more than 14. 5 , 000, 000 to a single to get, like the Illinois Parte.
The Hoosier Lottery that uses Indiana State’s nickname, carries a 6/48. The state of michigan Lottery is 6/47, Arizona Lottery plus Missouri Lottery happen to be 6/44, Maryland Lottery is 6/43, and Colorado Lottery is definitely 6/42. Compare this kind of to the Sarasota Lottery.
A Pick 5/39 ball Lotto game formula seems like this: (1/39, 1/38, 1/37, 1/36, 1/35) for a total of 69, 090, 840 divided simply by 120 (1x2x3x4x5) with regard to the odds of 1/575, 757 of succeeding the Jackpot many of these as the The state of illinois Little Lotto. Other States with the identical 5/39 lottery figures include the NORTH CAROLINA Lottery, Georgia and Florida Lottery Fantasy 5, and Tennessee Lottery’s Pick five. Virginia Lottery’s Money 5 posesses 5/34 range.


Abstract：The singularity problem is inherent in controlling articulated robot manipulators. In this paper, we determine the required joint motion of the end effectors by evaluating their accuracy and feasibility. The robust inversion of singularity of the Jacobian matrix provides a motion approaching to the desired cartesian trajectory at or in the neighborhood of singular points for the end effector, even when the inverse kinematic solution represented by Jacobian matric inversion or pscudo inversion is infeasible.
 KJcma V C, L,sub A J. The singular value decomposition, its computation and some application. IEEE Trans on Automatic Control, 1980;AC-25:164-177
 Iri M, Kodama S, Suda N, Singular value decomposition and its application to system control. J of SICE, t982;2I:763-772
 李可弼.矩阵分析.东北工学院,1983 谢绪恺.现代控制理论.东北工学院.1984


It’s estimated that around 10,000 people a week choose 1,2,3,4,5 and 6 as their lottery numbers.
This despite the odds that any 6 numbers being drawn are exactly the same as any other combination. If they ever come up (there are 13,983,816 possible combinations of six numbers from 49 numbers so the lottery odds of winning the jackpot are 1 in 13,983,816), chances are you’ll be disappointed with having to share your loot with so many others.
Oxford professor of mathematics, Marcus Du Sautoy, says: ‘My advice is to pick consecutive numbers, like 31, 32, 33. Not many people do, but it is just as likely as any other combination.’
The logic behind this was also used by Apple to redesign its iTunes ‘shuffle’ software. After some customers complained Apple made the randomiser software ‘less random’, preventing iPods from playing a track more than once.
But when it comes to such large odds, does logic really matter? In 1998, unemployed Scot John Roberts was planning to spend his last pound on a meat pie. Instead, he spent it on a lucky dip lottery ticket – and a £3m win was more than adequate compensation for missing out on the pie!


See those harsh grey lines? That’s called quantizing or color banding.
Would more sampling remove this artifact? Is it an error in the renderer or the light sampling?
While rendering, we’re generating a floating point result for each color (red, green, blue) that gets converted, losing some accuracy, to 8 bit integer red, 8 bit integer green and 8 bit integer blue. 8 bits per channel in 3 channels.
So we have 24 bits per pixel, but in a grey image like this, the red, green and blue are all the same, so we really only have 8 bits total for pure grey colors. 8 bits gives us 256 shades of grey.
Even though those colors are really close to each other, our eyes and brains are good at noticing the change between them when it’s a sharp line like these are. With only 256 steps between pure deep black and bright clamped white, our eyes can pick out the line between each step. Click on this 256 step grey ramp image to see for yourself:
The more accurate the render, the more accurate and clean these bands will become. So more light samples would actually make the lines sharper, not softer.
Counter-intuitively, the answer is just a teeny bit of error added on purpose. If the steps are in 1/256 increments, then we can randomize the transition a bit by adding a random number between half an increment down and half an increment up to the float before converting to an int. In other words, add a random number between -1/512 and +1/512 to the float before converting to an int. All this error does is affect the rounding, making the transition between levels actually represent the real transition the floating point numbers had a lot better when perceived by a human.


How Is Logical Math Intelligence Applied In Everyday Life?
Understand Logical/Mathematical Intelligence
Keywords searched by users: How is logical math intelligence used Intrapersonal intelligence, Bodily kinesthetic intelligence, Linguistic intelligence, Interpersonal intelligence, Multiple intelligences, Mathematical intelligence, Verbal linguistic intelligence characteristics, Multiple intelligences in the classroom
How To Use Logical-Mathematical Intelligence In The Classroom?
Utilizing Logical-Mathematical Intelligence in the Classroom
To effectively harness logical-mathematical intelligence within the classroom, educators should implement a range of strategies that cater to this specific cognitive domain. Here are some key approaches to consider:
Promote Problem-Solving: Encourage students to engage in problem-solving activities. Present them with real-world challenges that require analytical thinking and logical reasoning.
Incorporate Calculations: Incorporate mathematical concepts and calculations into your teaching materials. Use relevant examples and exercises to help students strengthen their mathematical skills.
Cipher Challenges: Create opportunities for students to decipher codes or cryptograms. These exercises not only enhance logical thinking but also add an element of fun and intrigue to the learning process.
Pattern and Logic Games: Integrate pattern recognition and logic games into your lessons. These can range from Sudoku puzzles to more complex logical puzzles, all of which stimulate the logical-mathematical intelligence of students.
Structured Information: When presenting new information, consider organizing it in an outline format. This visual structuring can aid students in grasping and categorizing knowledge in a logical and systematic way.
By incorporating these strategies into your teaching approach, you can effectively tap into and nurture logical-mathematical intelligence among your students, ultimately enhancing their overall cognitive development and problem-solving abilities.
What Are Some Examples Of Logical-Mathematical Intelligence?
What are some examples of logical-mathematical intelligence? Logical-mathematical intelligence refers to a cognitive ability characterized by proficiency in various analytical and problem-solving skills. Individuals with a strong logical-mathematical intelligence are adept at a range of activities, including:
Mental Calculation: They can effortlessly perform complex mathematical calculations mentally, showcasing their numerical aptitude.
Problem Solving: These individuals excel in tackling intricate problems by breaking them down into manageable components and devising effective solutions.
Pattern Recognition: They possess an exceptional talent for identifying and discerning patterns, which aids them in making connections among seemingly unrelated information.
Drawing Inferences: Logical thinkers are skilled at drawing meaningful conclusions based on factual data and evidence, enabling them to make informed decisions.
Logical Argumentation: They have the ability to construct and present logical arguments coherently and persuasively, making them effective communicators and debaters.
Chess Mastery: Many individuals with strong logical intelligence excel in strategic games like chess, where planning, prediction, and logical thinking are paramount.
Information Integration: They are proficient at synthesizing and connecting disparate pieces of information to form a comprehensive understanding of complex topics or situations.
In essence, logical-mathematical intelligence encompasses a diverse range of cognitive abilities that contribute to effective problem-solving, critical thinking, and analytical reasoning.
What Are 3 Characteristics Of Logical And Mathematical Intelligences?
Certainly, here’s a revised and more comprehensive version of the paragraph:
Logical-mathematical intelligence is a cognitive ability characterized by several key traits. Individuals with this intelligence exhibit exemplary problem-solving skills, enabling them to analyze and tackle complex challenges effectively. They have a natural inclination towards pondering abstract concepts and ideas, demonstrating a keen interest in exploring theoretical and mathematical principles. Moreover, those with logical-mathematical intelligence often find joy in conducting scientific experiments, using their analytical prowess to explore and understand the physical world. They are also adept at solving intricate mathematical computations, applying their logical reasoning to solve numerical problems. This unique intelligence type empowers individuals to excel in fields such as mathematics, science, engineering, and analytical professions. (Note: The date “11 thg 3, 2023” in the original passage seems to be a date stamp and may not be relevant to the content, so it has been omitted in the revision.)
Summary 37 How is logical math intelligence used
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Helps understand and use abstract relationships. The processes used in logical-mathematical intelligence include categorization, classification, inference, generalization, calculation, and hypothesis testing. It is attributed to people looking for patterns, performing mental math, and classifying objects.Kids with increased logical-mathematical intelligence are typically methodical and think in logical or linear order. A child with this learning style strength may be adept at solving math problems in their head and drawn to logic puzzles and games.
- Provide opportunities for problem-solving.
- Involve calculations.
- Create activities that involve deciphering a code.
- Use pattern or logic games.
- Organize new information in an outline format.
- Easily calculate mathematical sums in their heads.
- Be terrific problem-solvers.
- Identify and recognize patterns.
- Draw conclusions from facts.
- Pose logical arguments.
- Be good at playing chess.
- Connect different pieces of information.
- Have excellent problem-solving skills.
- Enjoy thinking about abstract ideas.
- Like conducting scientific experiments.
- Can solve complex computations.
Learn more about the topic How is logical math intelligence used.
- Logical-Mathematical Intelligence: Definition, Characteristics …
- Multiple Intelligences in the Classroom for Teaching and Learning
- Logical Intelligence – Multiple Natures
- Gardner’s Theory of Multiple Intelligences – Verywell Mind
- Logical-Mathematical Learning Style – Verywell Family
- Teaching Logic to Elementary Students – The Why and How


Blackjack – The House Edge
There are several types of casino game, however the most popular among them are blackjack, baccarat, and training video poker. While most people have their very own favorite casino game, the best way to learn and enjoy it really is to obtain tips from experts. Playing a new game is always a little confusing, so learning the basics of a casino game is essential.
In a normal casino game, there is a set amount of rounds played, called a dealer’s rounds. After every dealer circular, the dealer will apply a standard deviation which is a kind of random number generators. This means that instead of obtaining a single number from each circular of randomness, the ball player will get a group of numbers, and this can be used to determine the outcome of a hand. There are several other uses for typical deviation in the casino activity world, including calculating the probability of an exact payoff and the worthiness of a dollar to cash out.
Just about the most popular casino games 더킹 바카라 is slots. Slots are played with a deck of cards, and the target is to get the “low” card – the jackpot – while staying on the correct side (i.e., your group if you are playing in a progressive casino). There are two forms of slots, progressive and non-progressive. In progressive casinos, all earning cards go to the same owner; non-progressive casinos work with a random number generator to decide who gets the jackpot. Slot machines are accessible in online and offline casinos as well, rendering it easy for players to change from one casino to some other.
Blackjack, alternatively, is a game of chance. Although there is a house edge, or i.e., the expected benefit of a single investment, since jackpots are non-confirmed, the expected value of an individual bet is figured utilizing a mathematical algorithm. While every bet on a casino video game is section of a mathematical equation, some casino games have much larger sums of money at stake than others. Blackjack participants can benefit when the house edge is small; the smaller the house edge, the more likely that a player will undoubtedly be lucky enough to hit the jackpot. The disadvantage to the approach is that in a modern casino game with a little house edge, the home always wins, so any player not playing aggressively will in the long run drop.
Poker players will encounter frustrating moments within their gaming careers. Most often, inexperienced poker players don’t understand that the odds to getting a specific card (the “jack”) upon any granted round of betting are not consistent. So as to increase their chances of hitting the jackpot, they need to bet larger quantities during each hand, hoping that the amount of times they hit that jackpot will equal the likely frequency of drawing that one card. Although the house constantly wins, inexperienced poker players may find themselves in the losing conclusion of an extended and drawn-out game, because they were not able to capitalize on an opportunity to acquire.
It is critical to remember that the house edge only identifies the difference between the initial casino investment and the final payout. The actual casino investment is much higher than the initial price of the gaming machine, and this figure does not include any additional profits made through house advertising and marketing. This number represents the casino’s profit percentage and is what models a casino apart from other gambling venues. The modern casino may offset the losses from residence edge in various ways, but the two most typical ways are by reducing house edge through technological advancements in video and sound techniques and through slightly higher ticket prices.
Despite the differences in casino design, a very important factor that all casinos have as a common factor is that slots and roulette are enjoyed on a fixed slate. No matter how a particular game is set up, whether the casino chooses to add a four-suit or seven-go well with or blackjack or perhaps a variety of other options, every time the game begins, it is the same slate that will be used for the gambler to try to beat the odds and make money. If no initial luck comes along, or if the gambler loses on multiple occasion, the internet casino can adjust the odds and the result of the game in order to make the gamble a little more favorable. This can be the basic idea behind internet casino gambling, and it is the basis for all of the various kinds of gambling available to the public.
As a way to fully appreciate just how important the house edge would be to the long-term good results of a casino, it’s essential for us to have a closer understand this concept in its most essential form. Essentially, the casino really wants to make as much money as you possibly can off of each and every bet that is positioned on the table. The house edge essentially means that a new player who throws a few dollars up for grabs and gets away a similar amount has basically lost the equivalent of two or three times that amount by enough time the game ends and the ball player has to walk away along with his money. It generally does not help matters if that participant is using their own money or someone else’s; what really matters can be how badly he really wants to win the game. If you know that you are likely to place big money on the line and you are emotionally involved with the results, then chances are good that you will place plenty of bets and make some fast cash.


Are you worried about the solution of Exponential expressions? It is really not so difficult as you think. It may confuse you or irritate you when you experience solving them for the first time. But I assure you, It is going to be very interesting to learn how to get rid of exponents. Just stay with me.
I think it is very necessary to introduce you to the exponents to make a clear and lucid concept about exponents. Exponents/Indices are the repeated multiplication of a number. For example,
2^2 = 2.2, it is repeated multiplication of 2.
3^2 = 3.3, it is repeated multiplication of 3.
X^3 = X.X.X, it is repeated multiplication of X.
Y^4 = Y.Y.Y.Y, it is repeated multiplication of Y.
If 2 is the index of a number 3, it means number 3 will be multiplied with itself two times. Same as, if 4 is the index of a variable Y, it means Y will be multiplied with itself four times.
One more noticeable thing is, Commutative property does not exist in exponential expressions eg, 2^5 ≠ 5^2
How To Get Rid Of Exponents?
To learn, how to get rid of exponents, I shall introduce you to the Laws of Exponents.
How To Get Rid Of Zero Property Exponents?
Zero property is the funniest property in learning, how to get rid of exponents. If the index/exponent of a number is zero, it results in 1.
e.g. 2^0 = 1
3^0 = 1
X^0 = 1 (0^0 = 1)
Let us see another example
It does not matter what is the Base, when it gets ‘o’ index it becomes equal to 1.
How To Get Rid Of Negative Exponents?
Negative exponents mean that the Index of a Non zero number is negative. Usually, when students face a negative exponent they get worried and think about how to get rid of negative exponents. I am going to show you from a simple negative exponent to a complex negative exponent solution.
(1) For example; 2^-2 here, the base is 2, and the exponent is -2. We shall solve it according to the Negative property of Exponents. As we know that expression(2^-2) is in the numerator, We’ll simply move it to the Denominator to make the Exponent positive.
e.g. 1/2^2 which is equal to 1/4.
It means you get rid of negative exponents by changing its position in a fraction. Let us see some other examples to make the concept clear.
(3) Look at some other examples,
(4) Example: In the case of a complex expression, you’ll solve it in this way.
I hope these examples would have made your concept clear. Now you will find it easy, ‘how to get rid of negative exponents’.
How to Solve the Product Property of Exponents?
It is also very easy to solve such non zero numbers that have exponents and are multiplied with each other. According to the Lw of Product Property Exponents, when two bases are multiplied then their exponents are added. Let us look at some simple as well as complex examples to make a proper sense.
(1) Example: (Note; It is valid when bases are the same.)
If exponents are the same but bases are different then bases are multiplied and exponent remains the same. The complex form will be solved like this,
This is how to get rid of exponents in product property.
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How to Solve Quotient Property of Exponent?
When you multiply two exponents with the same base, you add the exponents and when you divide two exponents with the same base you subtract the exponents,
Simply, this is how to get rid of exponents in quotient in quotient form.
How to Solve Power of a Power Property Exponent?
When an exponential expression has power, then both the powers are multiplied to simplify the statement. Let us take a glimp of some examples.
This is how to get rid of exponents in the property power of the power.
How to Solve Power of a Product Property of Exponent?
If there is more than one term in parenthesis, with an exponent outside the parenthesis, then the exponent is multiplied to every term in the parenthesis. Here, are some examples to make sense clear.
the power is distributed to every term in the parenthesis.
I hope you are enjoying learning, how to get rid of exponents with respect to the different properties of exponents.
How to Solve the power of Quotient Property of Exponents?
To solve the Power of quotient property, Power is distributed to every term in the parenthesis. See some examples for clarification.
That’s the simplest way to learn how to get rid of exponents when the expression is the power of a quotient.
Now I am going to introduce you to some worrying form of exponential expressions. I recommend you, students, just go through the deep guidance and try once before you quit.
How to Get Rid of Exponents in Algebra?
When you move from the solution of simple exponential expressions towards the solutions of Algebric exponential expressions, you may get confused. But don’t worry students, the main purpose of this article is to root out this confusion and make the exponent’s solution easy to you. YOu will cover here the different type of Algebraic equations which confuse the most.
Negative Exponents Algebraic Equation
It is easier to learn than you think, how to get rid of exponents with a negative sign in the equation.
Another example is
Look at another type
Another type is
A fractional case is solved in this way
This is how to get rid of exponents in fractions.
Getting an expert in mathematics is all about practice. The more you practice the more you will find it easy and interesting. However, if you think you need more practice you should watch this video.
Final words :
I hope you will find this article much helpful for you even if you are totally unfamiliar with the exponents. After reading this explanation you will know how to get rid of exponents. You will feel much confident to solve the simple as well as complex exponential expressions. Make learning math joyous


The letters – prefaces of Hellenistic mathematical texts were in relation with the circulation and transmission of these treatises. We have no information of the origin of this practice of mathematical prefaces. We have in Ancient Greek and Hellenistic mathematical tradition texts with and without prefaces. These precious prefaces give us informations on the correspondent personalities – mathematicians of the original authors (Archimedes, Apollonios...) and also on the different intellectual and research centers of the Antiquity. The letters-prefaces could give place to heuristic and historical considerations. In one part of the Hellenistic period (3rd-2nd century BC) authors of these treatises cultivate the challenge. These prefaces show that the goal was to pose the problems to their colleagues, resolve the problems posed by them and give critiques on imperfect solutions given by others. But they show also the need to publish very quickly and give more perfect demonstrations or solutions subsequently.
The main questions in the frame of this symposium will be : which was the status, the role and the content of the letters – prefaces in Ancient – Greek and Hellenistic mathematical treatises? Which was their status, role and content in the context of Arabic and Latin mathematical traditions? Was in everyone of these above mentioned cases the intentions expressed in these letters – prefaces in absolute correspondence with their real practice in the texts.
Konstantinos Nikolantonakis, University of Western Macedonia - Greece
Marouane ben miled, Univeristy of Tunis and IMeRA


HLS, HSL, HSB and HSV are used to specify numerical Hue, Lightness (or Brightness) and
Saturation in place or as a complement of the standard RGB values.
There are two major problems related to these color spaces:
1. There is no standard defining the way to compute these value. Specially the
Lightness (or Brightness) is usually calculated as L = (R + G + B) / 3, versus a more
realistic implementation (L = xr * R + xg * G + xb * B) that involves hue-dependent
2. The mentioned simple Lightness calculation conflict badly with the properties of
color vision. Also Hue linearity is a problem in this space definition
For the above reasons this site does not directly support these color spaces.
a reference, the standard Windows conversion algorithm is anyway posted on our


-- Detect if the year is a LEAP year
DECLARE @dt datetime
DECLARE @yr int
DECLARE @y char(4)
SET @dt = GETDATE()
SET @yr = YEAR(@dt)
SET @y = CAST(@yr as char(4))
-- Years like 2000, 2400 are always leap years
WHEN @yr % 400=0 then @y + ' is a Leap Year'
-- Years like 1700, 1900 divisible by 100
-- but not divisible by 400, are not leap years
WHEN @yr % 100=0 then @y + ' is not a Leap Yr'
-- Years like 2004 that are not divisible by
-- 400 and 100 but are divisible by 4, are leap years
WHEN @yr % 4=0 then @y + ' is a Leap Year'
ELSE @y + ' is not a Leap Yr'


At Westfield CP School we teach Maths in discrete daily lessons and are firm believers that it can also be used in all areas of the curriculum. We feel that fluency in Mental Maths and the skill of being able to use number facts quickly and accurately is extremely important. Therefore we place it at the heart of our teaching of the subject.
We ensure children receive lots of opportunities to apply their Maths skills through problem solving and reasoning lessons. These are taught throughout the week in each class. We also take part in STEM activities which combine the subjects of Science, Technology and Maths together. The children show great enthusiasm during these lessons and particularly enjoy problem solving in other areas of the curriculum.
Please click on the following link to view what this looks like at Westfield.
Please click the links below to view what Maths learning looks like in each year group.
At Westfield we have identified the need to strengthen the children’s fluency skills in Maths. As a result of this we have introduced the Ninja Maths programme.
What is Ninja Maths?
- Rapid recall of times table facts and number bonds.
- Each ‘Ninja Rank’ has a coloured wristband that children can earn the right to wear.
- Nine different coloured bands available that represent a Ninja.
- Once a child has earnt all of the bands, they begin again with division and subtraction.
Why Ninja Maths?
A secure knowledge of times tables is going to benefit your child throughout primary school and into secondary school as well. In fact, most of today’s jobs require some element of maths. Learning multiplication is an important foundation for learning different aspects of mathematics such as division, algebra, long multiplication, and even fractions. For students that do not have a solid grasp of the times tables, they may find these other areas hard to understand as well.


Matheus C Fernandes
PhD Candidate at Harvard University
Matheus is currently a graduate student at the Harvard John A. Paulson School for Engineering and Applied Sciences and the Harvard Institute for Applied Computational Science pursuing a PhD in Applied Mathematics with a secondary field of study in Computational Science and Engineering. He is currently working in Prof. Katia Bertoldi's group on modeling bio-inspired optimized materials and applying generative parametric machine learning algorithms to control soft robotic actuators and classify objects based on embedded sensor data. In 2015, he earned a M.Eng. in Engineering Sciences at Harvard University and worked with Prof. James R. Rice on modeling the physics of subglacial hydrology. In 2013, he graduated with a BSE in Mechanical Engineering from Case Western Reserve University with thesis titled "Design and Implementation of Wind Turbine Torque Measurement Device."


On 17 December of 2009, Friday on 3:00 pm, room 407 there will be held a seminar on the topic: “Globalization and New Media”. Speaker: Associate Professor Elisabeth Asabashvili.
The following topics will be discussed at the Seminar:
- Modern Communication Media
- New Voices via RSS
- Communication with Visualization
On 10 December 2009, Thursday, 4:00 pm in room 407 of the UG, there will be held a seminar “Numerical Analysis of Election Systems and Arrow Theorem”; Speaker: Associate Professor Merab Uridia. Election systems of various types will be discussed on the seminar and their elementary comparative analysis will be done; the Arrow Theorem will be formed. There will be presented the proof of its classical and immovable point’s existence.
On 3 December 2009, Thursday, 3:00 pm in room 407 auditorium of University of Georgia will be held the seminar on the topic “Centrosymmetric matrices of one type in eigenvalue problems” Speaker: Associated professor Liana Karalashvili. There is considered general form of the third order matrices, which are at the same time symmetric too and have such a property, that sum of elements in each row is the same number. The characteristic equation of such matrices is constructed in factorized form. All eigenvalues and eigenvectors are given in explicit form. Besides, such type of matrices has the same eigenvectors. There is constructed a matrix of spectral decomposition (its columns represent orthonormal eigenvectors of the initial matrix) and its inverse, which reduce the initial matrix to the diagonal matrix. It gives a possibility to evaluate any degree of the given matrix.
On 26 November 2009, Thursday, 3:00 pm, room 407 of the UG, there will be held a seminar on the topic “Land and Other Real Estate Information Systems”; Speaker: Professor Sergo Tsiramua.
There will be presented information about one of the first successful projects implemented by “World Bank”, the main aim of which was the development of the real estate market in Georgia. The project was carried out by using modern information technologies, in particular by using database management and Geo Information systems. Therefore, participation at the seminar will be interesting for the students of Computer Technologies.