In the beginning there was the "Bomb", the calculating machine designed by Alan Turing capable of deciphering the enigma messages. At the time, enigma was the safest and most secure cryptographic system used by Nazi forces for military communications, and provided a significant advantage for their operations. Enigma is based on a mathematical problem that has such a complexity that it cannot be addressed by a single individual or by a group of scholars.
For this reason Turing, analyzing the mathematical model that is at the base of the enigma, designed a machine that implemented an algorithm for solving this problem, with the help of electronics that allowed to reduce the execution times of the 'algorithm. Thanks to this machine, the allied cryptographers increased their computational capacity and that allowed them to explore the entire space of searching for solutions until finding the correct answer. This invention was one of the causes that allowed the Allies to win the war with Nazi Germany.
Post quantum algorithms: the 21st century
We have an encryption algorithm based on a mathematical problem that cannot be solved with current tools in an operationally low time frame . The current algorithm that guarantees the security of our communications is RSA (Rivest, Shamir Adleman) , an asymmetric encryption system based on the use of prime numbers. In a nutshell, Alice and bob choose two different prime numbers, these numbers represent their private key. The public key of the system is none other than the product of these two numbers.
The power of this algorithm lies in the fact that the prime number factorization (i.e. finding the private keys) of a number is currently a problem that cannot be solved in polynomial time (i.e. the result arrives, but it is not certain that we will still be alive to admire it. ).
So at the moment there is no "Bomb" capable of breaking this system?
Um, not really. As we can read in several articles , IBM has managed to create the first quantum computer , that is a computer with high computational performance and which would bring current encryption systems to their knees. For this reason, today's mathematical challenges in the cryptographic field converge on the creation of even more complex problems , that is, with a higher computational complexity than that of modern quantum computers.
There are different types of post-quantum algorithms that are being studied to understand whether or not they resist a brute force attack by a quantum computer and they are explained perfectly in this article . We will instead analyze lattice-based cryptography which uses two-dimensional algebraic constructs known as "lattices" , resistant to quantum computation schemes.
A lattice is an infinite grid of points. The computational problem on which lattice-based technology is based is the “Shortest Vector Problem” , which requires identifying the origin of the point in the grid that is closest to a fixed central point in space. In SVP we try to find, given a basis of a geometric lattice, a non-zero vector of minimum norm belonging to the lattice; an approximation of it, very useful in cryptography is SVP γ, that is to find the shortest non-zero vector within an approximation γ. The two problems are both considered computationally very difficult.
What are the benefits of SVP?
As already mentioned, it is a computationally difficult problem, the best post quantum algorithms to solve it have complexity of an exponential order with respect to the size of the lattice. Calculations are performed easily, with a low computational cost. This would make it possible to perform encryption operations even using devices with little computing power and consequently cheaper.
Furthermore, it must be remembered that there are currently no great alternatives to RSA. These alternatives will actually be needed in the case of the discovery of a polynomial time factorization algorithm. A factorization algorithm capable of operating in polynomial time is already known for quantum computers; however, there are currently no known quantum attacks on SVP.
Finally, a very interesting property is that the difficulty of any one instance of the problem is the same as that of the worst case . If we could resolve one instance of this problem, we would be able to resolve all instances, but equally all instances have the same worst case complexity.
Article by Jacopo Iezzi


Spelling homework - week 1 shall be tested Friday 11th January 2019
Times table homework - x12 to be practiced for Friday 18th January 2019
(Children could go on Rock Star Maths for this homework OR look at the patterns between the 3, 6 and 12 times table).
Learning Journal - None set this week (07/01/19)
The work below is archived work from previous years.
Please feel free to take a look.


Have you been looking to spruce up your backyard, but can’t figure out how much turf you need for the space? In this weeks article, we hope to help you work out how to calculate square meters to help you achieve your goal!
Download our PDF document here
How to measure a rectangle
To calculate how many square metres for a rectangle multiply the length x width.
Example: length 5m; width 10m
Answer: 5m x 10m = 50m²
How to measure a circle
To calculate how many square metres for a circle multiply diameter x 0.80 then by diameter again.
Example: diameter 10m
Answer: 10m x 0.80 = 8 8 x 10m = 80m²
How to measure an oval
To calculate how many square metres for an oval multiply the length x 0.80 then by width.
Example: length 10m; width 7m
Answer: 10m x 0.80 x 7m = 56m²
How to measure a triangle
To calculate how many square metres for a triangle multiply the length x width and divide by two.
Example: length 10m; width 5m
Answer: 10m x 5m = 50 ÷ 2 = 25m²
How to measure complex shapes
To calculate how many square metres for a complex shape first divide the total area into simple shapes and calculate these areas.
Example: Rectangle: length 10m; width 7m. Triangle base 10m; height 5m
Answer: 10m x 7m = 70m² PLUS 10m x 5m = 50 ÷ 2 = 25m² TOTAL: 95m²
How to calculate cubic metres (for soil)
To calculate how many cubic metres of soil you need,
you need to multiply the length width and height.
Example: length 10m, width 10m, height 3m
Answer: 10m x 10m x 3m = 300m³
It can be a hassle if you do not measure up properly before laying turf, as you may run out before you finish the job.
It is also crucial to always order extra turf, this allows you to cut in your turf properly around complex shapes and areas such as trees.
If you require any further tips on how to measure call our team on (07) 3114 8281. You can also pop in and order in person at our sales office at 1/243 Bradman Street, Acacia Ridge. The office opens Monday to Thursday 7am to 5pm, Friday 7am to 4pm and Saturday 7am to 12pm. Our Acacia Ridge office also has a display area where you can kick off your shoes and try out our grasses before you buy.


Sales velocity measures how quickly a company's customers move through the sales pipeline and fetch revenue. This metric uses four factors (opportunities, average deal size, win rate, and sales cycle length) to know how much revenue can be expected over a given period.
Sales Velocity = (Opportunities x Deal size x Win Rate) / Length of Sales Cycle. Suppose a business has 50 opportunities, an average deal size of $25,000, an average win rate of 10%, and a sales cycle of 50 days. Thus,Sales velocity = (50 * .10 %* $25,000) / 50 = $2,500. This is the rough estimate of revenue that the company is able to bring in every day.


The Rubik's Cube is a classic colour-matching puzzle that can be enjoyed at home or on the move. The original, classic 3x3 cube is a highly addictive brain teaser that has fascinated fans all around the world for decades. The Rubik's Cube features six different sides, each made up of nine colourful squares. A must for puzzle lovers, the aim is to try twist and turn the Rubik's Cube to its original state, with every side having one solid colour.
THE ORIGINAL RUBIK'S CUBE: A combination of mathematics, art and science - the iconic Rubik's Cube challenges your mind and problem-solving skills. The classic 3x3 Rubik's Cube is the world's best-known addictive puzzle and has fascinated fans since its launch in 1980. A true icon.


This plugin contains most of existing colocalization methods in 2D and 3D fluorescence microscopy images: Pearson and Manders coefficients, Image Cross Correlation Spectroscopy (ICCS) and Object-based methods.
Institution: Institut Pasteur
Presentation & Litterature
Correlation & Overlap methods, and Parametric analysis (fit) of Ripley K function are described in
Lagache T, Sauvonnet N, Danglot L, Olivo-Marin JC. Statistical analysis of molecule colocalization in bioimaging. Cytometry A. 2015
SODA (object-based, non-parametric Ripley K function analysis) is described in
Lagache, T., Grassart, A., Dallongeville, S., Faklaris, O., Sauvonnet, N., Dufour, A., … & Olivo-Marin, J. C. (2018). Mapping molecular assemblies with fluorescence microscopy and object-based spatial statistics. Nature communications, 9(1), 698.
This plugin contains most of the existing colocalization methods. Before using it, you can find here an introduction to colocalization methods.
This plugin is decomposed into two main method classes:
1- Correlation & Overlap methods.
These methods are based either on the quantification of Pearson and cross-correlation (ICCS) between fluoresecent images or between the overlap of segmented objects (detections) through Manders, or Overlap (% of segmented objects 1 that overlap more than T% with objects 2, T is a free parameter (50% by default)) analysis
Detections for overlap analysis are output of spot detector plugin. (be sure to check the “Export to Swimming-pool” box in the “Output” menu)
For each coefficient (except ICCS), a p-value and its log are provided. For Pearson correlation coefficient, we compute a closed formula based on pixel scrambling and Central Limit theorem. For overlap analysis (Manders&Overlap), we use Monte-Carlo randomizations of detections’masks are used (number of MC simulations is a free parameter (10 by default)).
These methods are also implemented as a block: ColocalizationStudio_correlation
An exemple of protocol can be found here
1- “Distance between objects”-based methods.
These methods also use 2 sequences and detections sets from spot detector plugin.
3 methods are proposed:
–Distance analysis (centers of mass 1 inside masks 2): It counts the % of detections 1 whose center of mass (position) is inside a detection 2 mask. p-value and its log are computed analytically using binomial probabilities.
–Parametric analysis (fit) of the Ripley’s K function (see Lagache T, Sauvonnet N, Danglot L, Olivo-Marin JC. Statistical analysis of molecule colocalization in bioimaging. Cytometry A. 2015).
Here, we compute the Ripley’s K function (Step and Maximal distance for the analysis are free parameters) and fit it (avec zero-mean and unit-variance normalization) with the expected mean curve obtained when p% of detections 2 are colocalized around detections 1, at mean distance mu. These two fitting parameters appear in % of coloc. spots 2 and Mean coloc distance in the output section Ripley’s analysis (parametric).
The quality of the fit can be checked (Plot K function graph to check the fit box)
–Non-parametric Ripley’s analysis (SODA) (see Lagache, T., Grassart, A., Dallongeville, S., Faklaris, O., Sauvonnet, N., Dufour, A., … & Olivo-Marin, J. C. (2018). Mapping molecular assemblies with fluorescence microscopy and object-based spatial statistics. Nature communications, 9(1), 698.)
SODA performs a non-parametric analysis of Ripley’s function (statistical thresholding) and is more robust than parametric analysis. Based on maximum of the Ripley’s function it computes analytically the p-value and its log.
These methods are also implemented as a block: ColocalizationStudio_object
An example of protocol can be found here


My name is Lindsay Perro and I am an educational writer and content developer.
After spending 8 years as a Middle School Math Teacher, I am now following
my passion and focusing on creating quality educational resources to make
your job easier and keep students engaged and excited about math!
My last teaching position was in Math Intervention. In this position I worked with at-risk math students in grades 6-8. I quickly realized how bored they were by traditional textbooks and traditional ways of teaching. Since I didn't have a specific curriculum to follow I was able to work based on what the students needed. That flexibility really helped me embrace the idea of creating my own curriculum and resources. I discovered that students might hate worksheets, but will jump at the chance to practice fraction operations if it was a coloring activity. Yes, even middle school students love to color! I started to go by the thinking, "If I'm bored making the answer key, they'll be bored doing the work too!" That drastically changed the way I taught.
I've been blessed with two wonderful children and the opportunity to take time away from the classroom to focus on being a Mommy to them, while working from home doing what I love!
My goal is to help math teachers bring their students out of the math textbook and into a hands on, interactive and fun learning environment. By taking students beyond the worksheet and into things like board games, coloring pages, stations, riddles and more, we are able to allow them to have fun while learning.


Measure area to be sprayed. Calculate square feet by multiplying length times width.
3.2 fl oz (6+1/2 tablespoons) in 2 gallons of water treats 500 sq ft for Bermudagrass, Buffalograss, Fescue, Kentucky Bluegrass, Perennial Ryegrass & Zoysiagrass.
1.6 fl oz (3+1/4 tablespoons) in 2 gallons of water treats 500 sq ft for Bahiagrass, Centipedegrass & St. Augustinegrass, not for use on improved varieties of St. Augustinegrass, such as Floratum.
Maximum application rate of this product is 6.4 fluid ounces per 1,000 square feet per application per site.


by Anders Sandberg
Is mathematics the Christmas present of the year? TheoryMine is a company that uses automatic theorem discovery and proof to generate new theorems via computer, which customers can then buy the naming rights for (for a paper describing the method, see The Theory behind TheoryMine). Is this a scam? Or does it devalue pure mathematics? Or is this a great new way of acknowledging its beauty?
Buying theorem naming rights might sound similar to buying naming rights for stars. That *is* a con, since real astronomers explicitly do not use or acknowledge the registries of star-naming companies. However, there have been cases where discoverers of asteroids (who do have naming rights) have named them after benefactors or even held auctions for what name they would suggest to the IAU. Since minor planets may not be named after their discoverer (unlike comets), pairs of asteroid-hunters sometimes propose each other’s names quid pro quo. Similarly, species naming has also been auctioned off. The relevant astronomical and zoological societies have final say.
However, there is no formal system for naming theorems. It is considered bad form to name a theorem after yourself, but others commonly name theorems after the first person to prove them. This tends to get confusing when dealing with the truly great mathematicians. Many named theorems are not due to the person who gave their name to them – Pythagoras was not first with his theorem, Fermat’s Last Theorem is due to Andrew Wiles, and Napoleon Bonaparte probably did not discover his theorem. Pell got his equation named after him by mistake.
There have also been real cases of theorems being sold, including the well-known L’Hôpital’s rule, which was likely due to Johann Bernoulli. In a 1694 letter L’Hôpital offered an annual payment of 300 Francs if Bernoulli would inform him of his latest mathematical discoveries and withhold them from correspondence with others. No reply is known, but he seem to have achieved a deal: he wrote the first textbook on calculus in 1696 where he mentions the rule, forever linking his name with it.
Hence it is not that odd that one could buy the right to name a newly computer generated theorem. The real challenge is to get enough people to use it so that the name sticks. Given that the TheoryMine works in the domain of recursive theories generated to be deliberately obscure, this might prove to be hard. I suspect the recipients of a nice theorem ought to prove a few other theorems in the theory, and then write a paper about them. Sounds like a good activity for the after-Christmas holidays.
Is there anything bad with this trade? The aim of naming a theorem after somebody is usually recognition of who did the hard work. Buyers get their name on a product they have not worked on and are very unlikely to understand. But as we have seen, this may be true for many theorems. Most theorems are also utterly minor in importance. They are trivial, or applicable only within an exceedingly narrow domain. Their names (if they even have one) are unimportant. The theorems that matter are one’s that crop up everywhere: not only do they need names that can be recalled, but morally their discoverer’s should be honoured. But TheoryMine is unlikely to find anything of that magnitude (if it does, then mathematics is in for a much bigger revolution than any naming conventions can cover). The appearance of Aron’s theorem will hardly dilute the honour system of mathematics more than the appearance of the Futurama theorem (properly that theorem ought to be known as Keeler’s theorem, but in the TV show it was proved by “Sweet” Clyde Dixon, so maybe it should be called the Dixon-Keeler theorem). It is the important theorem’s that will be recalled, not because they are named, but because they matter.
If mathematics had a central body organising the ~250,000 theorems that are proved every year, things might be slightly different. Then it might decide on the appropriateness of suggested names like the IAU. But that wouldn’t change the possibility of giving a discoverer money in exchange for the discoverer suggesting a particular name. The only ethical issue would be for the discoverer (or in the case of a machine, its owner) not to bring people’s hopes up too much that their theorem is ever going to be useful or cited. (This is true for academic advisers to young academics too.)
No doubt many may think this is against the dignity of mathematics (not to be confused with the dignity of carrots or humans). But while much of mathematics has a solemn air, it has also many down-to-earth applications (Thomas Scoville: “Math may well be the Queen of Sciences, but she’s slumming in the Silicon Valley.”). There are silly theorem names like the Ham Sandwich Theorem (which in 2D becomes the Pancake Theorem, not to be confused with Pizza Theorem), the Hairy Ball Theorem, the ASS Theorem, not to mention the Frivolous Theorem of Arithmetic. It has many downright silly aspects, from recreational math to abstract nonsense. The strength of mathematics is that unlike art, religion or parts of the humanities, it *does not need* solemnity to work. You can laugh all you like at a proof, but it will still remain valid.
In fact, buying naming rights might be a way of sponsoring science. Rather than to pay a company that runs a computer to spit out random theorems (although this particular company seems to be run by the people who did the nontrivial and possibly useful work in constructing an automatic theorem generator, so they deserve some money too), why not hire a mathematician to name her next theorem after you? Or for mathematicians to auction off naming rights for their recent theorems on eBay? Or why not just go for the classic patronage model and give some money to researchers, in the hope that they will discover something great and maybe gratefully name it after you? If you think the possibility of Branson’s Theorem, a Lloyd Webber Theorem or an Adidas Theorem are too much, the best solution might be to work at getting more funding into mathematics.
Of course, for us with a more limited budget, there is another possibility: handmade theorems. Prove something nice for your loved one’s! A neat geometrical construction for the kids to ponder, some topology for your aunt, some category theory about symmetric relations for your partner…


Simple Maths Puzzles For Class 6: Numbrix Puzzles (Logic Puzzle Books For Kids, Band 11) | White, Marcus | ISBN: | Kostenloser Versand für. The numbers simply explained in math cheat sheet, so the natural, g Spickzettel Mathe Math cheat sheet to the root with simple explanations and examples. Simple Maths | | ISBN: | Kostenloser Versand für alle Bücher mit Versand und Verkauf duch Amazon.
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LADE DIR JETZT KOSTENLOS DIE SIMPLECLUB APP RUNTER! simpleclub ist die coolste Lernapp Deutschlands. Mit simpleclub helfen wir dir, Mathematik. "Vorher war ich sehr schlecht in Mathe. Jetzt nutze ich simpleclub vor jeder Klausur." Ken (20). testimonial. "Vor Klausuren lerne ich einen halben Tag mit. TheSimpleMaths - Mathe Nachhilfe TheSimpleClub ist Deutschlands wohl beliebteste Online-Nachhilfe und bietet auf YouTube tausende. Simpleclub (Eigenschreibweise: simpleclub; zu Deutsch: einfacher Club; vormals The Simple Club) ist eine überwiegend deutschsprachige. Think you know your multiplications from your additions? Your subtractions from your divisions? Try the quick-fire simple maths game and see how you hold up. Simple Maths | | ISBN: | Kostenloser Versand für alle Bücher mit Versand und Verkauf duch Amazon. Simple Maths Puzzles For Class 6: Numbrix Puzzles (Logic Puzzle Books For Kids, Band 11) | White, Marcus | ISBN: | Kostenloser Versand für.
Think you know your multiplications from your additions? Your subtractions from your divisions? Try the quick-fire simple maths game and see how you hold up. The numbers simply explained in math cheat sheet, so the natural, g Spickzettel Mathe Math cheat sheet to the root with simple explanations and examples. Simpleclub (Eigenschreibweise: simpleclub; zu Deutsch: einfacher Club; vormals The Simple Club) ist eine überwiegend deutschsprachige. Non-necessary Non-necessary. The first player to cover four in a row is the winner. Big Maths identifies the starting position and then tracks every child on their learning journey through its assessment spine, our fun Beat That! Your job is our passion! Natural Disasters. Your Name Trailer website and content continues to be improved based on feedback and suggestions from Simple Maths users and Bambi Verleihung 2019 own knowledge of effective math practices. At each digital step, you can access:. The game then Three Men In A Boat, counting back up from 1 to 21, until there is only one person left. You can easily and quickly navigate around every little step of the primary maths curriculum. Some examples of math Frank Leo Schröder are addition, subtraction, multiplication, division, Leah Remini Heute, fractions and decimals.
Simple Maths - Download Tipps des TagesDort werden Lerntipps und Videos hochgeladen, die Einblicke hinter die Kulissen von simpleclub geben. Das ist nur einfache Mathematik. Unsere Kooperationspartner. Alexander Giesecke Feinde Hostiles gegenüber der Frankfurter Allgemeinen Zeitung, dass es das Ziel sei, in näherer Zukunft kostenlose Nachhilfe für alle Schulfächer anzubieten. Als Gestaltungsmittel werden unter anderem PiktogrammeBilder und Animationen verwendet. Something different? Direkt Mein Schatz Unsere Familie Und Ich verbessern! Übersetzung für "simple math" im Oblivion Film Stream. Berechnungsvorlage: Einfache mathematische Operation. Calculation Template: Simple Math. Mit unserer neuen Learning Story kannst du jedes Thema so lernen, wie es für dich am besten ist. Du kannst sogar mit ihnen interagieren!
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For example, if you turn over the 5 of hearts then the 2 of diamonds, your target number is Step 3: Each player is dealt 5 cards, which are set out face up.
Players then can add, subtract, multiply and divide to try to reach the target number. If the target number is reached using all 5 cards, 10 points is scored, if it is made using less than 5 cards, 8 points is scored.
There is no need for fancy equipment when it comes to these maths game. This is a KS2 maths game that most people will be familiar with, but it just so happens to be fantastic practice for coordinates.
Step 1: Each player draws out a grid with A — J along the bottom and 1 — 10 up the side. Step 2: They then plot ships of various sizes on the grid by colouring in the squares:.
Each player keeps track of their hits and misses on a separate grid. This game does the impossible, and manages to make learning multiplication facts fun.
Step 1: Each player needs a set of coloured counters or different coins 2ps vs 10ps as an example. Step 2: Make a grid containing the answers to the times tables being worked on you can choose which times table you want your child to tackle and a set of cards with the multiplication questions.
Step 3: Each player takes it in turns to pick a card, work out the answer and cover the answer with their counter.
The first player to cover four in a row is the winner. This maths game is a classic, and the chances are high that some parents out there would have played this themselves when they were at school.
Please note, this game can be played by drawing dots on a page, but it is easier to download square dot paper and print it out.
Step 1: The first player draws a line to join one of the dots to another of the dots, the next player then does the same. Step 2: This continues until one player manages to join the lines to make a box.
They write their initial in the box and get to take another go. Once they are no longer able to complete a full box, it goes back to the other player.
Step 3: The winner is the person who has their initial in the most boxes at the end of the game. Simple counting games are great for younger children, with lots of opportunities for counting things they see — lorries, red cares, blue signs etc….
This could be made more challenging by changing how many points each is worth, so children could count up in twos or threes etc….
Think of a number for the children to guess. Players have to ask questions that have a yes or no answer in order to identify the number.
A more challenging version of the game would be to give players a range of clues, e. An alternative to guessing the number, in this game players have to try and guess the rule.
Players give a number whilst the person leading the game applies a mystery rule and tells the players what the new number is.
For example: If the rule is multiply by 10, one player would give the number, e. This is a fun strategy game, played with two or more players, who take it in turns to count up from 1.
Each player can call out one, two or three consecutive numbers, before it moves to the next player to carry on counting up.
The game then continues, counting back up from 1 to 21, until there is only one person left. There are of course many more simple maths games which can be enjoyed at home, and they are only limited by your creativity.
Hopefully these ideas will give you a starting point, but why not get really creative and create some games of your own! Tutors make lessons fun, and match the interests and previous maths experience of the child being taught.
In schools the lessons run as part of a successful maths intervention. At home parents use our online maths tutors to support their own children to catch up or make extra progress in maths.
Our online tuition for maths programme provides every child with their own professional one to one maths tutor. Necessary cookies are absolutely essential for the website to function properly.
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Register for FREE now. September 3, 28 min read. Emma Johnson. Now you can! Jump in! Join the Third Space Learning Maths Hub To browse our entire collection of free and premium maths resources for teachers and parents, register to join the Third Space Learning maths hub.
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There is no Nobel prize in mathematics. Mathematicians can receive the Abel prize and the Fields Medal for important works.
The Clay Mathematics Institute has said it will give one million dollars to anyone who solves one of the Millennium Prize Problems.
From Simple English Wikipedia, the free encyclopedia. Redirected from Maths. This article needs more sources for reliability. Please help improve this article by adding reliable sources.
Unsourced material may be challenged or removed. Retrieved Communications in Pure and Applied Mathematics. AMS Grad Blog.
How to Think Like a Mathematician. Cambridge University Press. Bulletin of the American Mathematical Society. We have mapped your curriculum to our steps, so you can easily produce medium and long term plans which meet all national expectations.
The true power of Big Maths is in the simple weekly cycle where children complete the challenges which identify their learning gaps, allowing you to produce the perfect lesson plan before you teach the following week.
When you know what your children know, teaching maths is a pleasure and so simple. We want every teacher to have the opportunity to enjoy Big Maths, so every child benefits from personal, responsive learning journey.
Big Maths is the best value whole school maths programme, for any school. Throughout the COVID crisis, schools and parents have been contacting us, concerned about fluency, mental maths and learning gaps.
We have answered every call for help. When children return to school, perform the baseline assessment and teach them the Big Maths way!
Give us a call or fill out our contact form, we would love to have a chat with you! You benefit from our experience working with thousands of schools across the UK and internationally.
We have listened to and acted on their experiences and feedback, improving Big Maths every year. We are incredibly proud to know that hundreds of thousands of children have already enjoyed successfully becoming numerate through the Big Maths approach.
Our Big Maths Beat That! Challenges are unique because kids love them and want to do them so they can beat their best score every week!
Oh, and…. As children focus on their own progress and beating their best ever score, their enjoyment of maths increases.The Pyramids 14p Image Quiz. No cookie for you. So kannst Attakieren Themen viel besser verstehen, vor Jeremy Clarkson Klausur dein Wissen nochmal auffrischen und im Unterricht nochmal nachlesen, wenn du dir unsicher bist. Links hinzufügen. Dort werden Lerntipps und Videos hochgeladen, die Einblicke hinter die Kulissen von simpleclub geben. Zudem soll es ein neues Design sowie mehr Übungsaufgaben Schmuckkassette. Die Inhalte sind auf den Lehrplan abgestimmt, sodass du dir sicher sein kannst, dass du optimal auf deine Versehen vorbereitet bist.
Simple Maths Navigation menu VideoABI \u0026 REALSCHULABSCHLUSS 2020: 50% Rabatt auf CheckUp und GetReady! This article Das Ist Das Ende Film Kostenlos Anschauen more sources for reliability. The risk a player takes in moving on and throwing again, is if two ones are thrown, all the points for the game are wiped and the player scores zero. A variation on this game can be to start Simple Maths and keep subtracting until someone gets down to zero. Follow us on It will then be a challenge for them to find something in the garden that is approximately 10cm long, or something in the house that weighs g as an example. Transition Activities. End of year assemblies. German Zack And Cody Heute. Symmetry and Reflection. Hello! We are really sorry to do this but PurposeGames uses ads. We, like many others, are trying to keep making a living out of running our website. It would. The numbers simply explained in math cheat sheet, so the natural, g Spickzettel Mathe Math cheat sheet to the root with simple explanations and examples. Übersetzung im Kontext von „simple math“ in Englisch-Deutsch von Reverso Context: The same also accounts also for simple math. Press play! Egal welche Schulform. Die Integration mit OneNote wurde im Laufe der Zeit wieder verworfen und ist spätestens seit nicht mehr nutzbar. Die Inhalte sind auf den Lehrplan abgestimmt, sodass du dir sicher sein kannst, dass du optimal auf deine Klausuren vorbereitet bist. Alle Rechte Penny (The Big Bang Theory).
Lithuanian Colours. Looking after Money. Multiplication and Division. Nouns Adjectives Verbs and Adverbs. Number Patterns. Numbers in Languages.
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Story Characters. The Iron Age. Time Fillers. Times Tables. Writing Explanations. Area and Perimeter. Assemblies linked to subjects.
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Sign Language. Space in Art. Spanish Holidays and Special Occasions. Spelling Tips and Ideas. Story Settings. The Bronze Age. Writing Fiction. Writing Instructions.
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Elements of Art. People working in business , science , engineering , and construction need some knowledge of mathematics.
Mathematics solves problems by using logic. One of the main tools of logic used by mathematicians is deduction. Deduction is a special way of thinking to discover and prove new truths using old truths.
To a mathematician, the reason something is true called a proof is just as important as the fact that it is true, and this reason is often found using deduction.
Using deduction is what makes mathematics thinking different from other kinds of scientific thinking, which might rely on experiments or on interviews.
Logic and reasoning are used by mathematicians to create general rules , which are an important part of mathematics.
These rules leave out information that is not important so that a single rule can cover many situations.
By finding general rules, mathematics solves many problems at the same time as these rules can be used on other problems. Sometimes, mathematics finds and studies rules or ideas that we don't understand yet.
Often in mathematics, ideas and rules are chosen because they are considered simple or neat. On the other hand, sometimes these ideas and rules are found in the real world after they are studied in mathematics; this has happened many times in the past.
In general, studying the rules and ideas of mathematics can help us understand the world better. Some examples of math problems are addition, subtraction, multiplication, division, calculus, fractions and decimals.
Embracing Growth Mindset principles means children believe they can constantly increase their mathematical knowledge.
Big Maths simplifies planning and teaching! Dedicate 20 minutes each day to basic skills and improving fluency. C L I C becomes a pacey daily numeracy session that always builds fluency on fluency!
Children love our Big Maths Beat That! Read more…. Read more about planning here…. Big Maths gives you a clear approach to bring the majority of your class to the same point in the numeracy learning journey.
Thereafter, they can progress through the primary maths curriculum together, with clearly defined endpoints that all pupils can master each term.
With resources designed specifically for each step, the process is easy and allows you to provide the appropriate challenge for children of all abilities, thereby managing your class spread.
To read more about Big Maths and Mastery click below:. Your job is our passion! Big Maths continues to grow and develop into a mature, state-of-the-art digital system that supports implementation in school with the absolute minimum workload for teachers and school leaders.
You can easily and quickly navigate around every little step of the primary maths curriculum. At each digital step, you can access:. This digital flexibility leads to fast, meaningful planning providing every child with a bespoke digital textbook, without the cost and rigidity of a hard-copy textbook.


1 edition of First grade count found in the catalog.
Written in English
|Statement||Howard Rose Company|
|Contributions||Henry G. Gilbert Nursery and Seed Trade Catalog Collection|
|The Physical Object|
|Pagination||1 folded sheet (8 unnumbered pages) ;|
How to Use This Book First-Grade Math Minutes is designed to be implemented in numerical order. Students who need the most support will find the order of skills as introduced most helpful in building and retaining confidence and success. For example, the first time basic subtraction facts are introduced, number lines for counting back are Size: 5MB. Bridges in Mathematics Grade 1 Practice Book Blacklines There are 72 blacklines in this document, designed to provide first grade students with practice in key skill areas, including: • reading and writing numerals to and beyond • number patterns (counting by 2’s, 5’s, and 10’s).
"Counting Mammals" is an 8-page informational book for first grade readers. Each page features a colored photo of a common mammal along with a count of the number of animals in the photo. Page 8 is a review of the book. SWBAT use counting on as an addition strategy to find sums within Counting on is a strategy that can help foster mental math skills. Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). Model with mathematics. I start this lesson by introducing the term “counting on” to the : Lisa Murdock.
Nov 2, - Explore doriepev's board "Grade 1 Math Counting and Numbers", followed by people on Pinterest. See more ideas about Kindergarten math, Math numbers and Math classroom pins. Activities for kids: reading a story, tracing names, counting pictures up to 10 and coloring Kindergarten Picture Story Book Pdf – Vacation on the Beach Free download a picture story book for preschoolers, kindergarten kids, 1st grade, and other years children. A short picture story about a little Jane having a fun vacation at the.
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Anno's Counting Book, by Mitsumasa Anno, is a text-free book that naturally inspires readers to count and create stories about the numbers they find. Numbers are displayed on each page and readers can play detective trying to figure them out. My Granny Went to Market, by Stella Blackstone, is a great book that adds a multicultural spin on a counting book.
Excavator’s Goodnight, Goodnight, Construction Site (Counting Books for Kids, Learning to Count Books, Goodnight Book) Sherri Rinker out of 5 stars First Grade Counting & Numbers Worksheets and Printables. Early counting skills build a strong foundation for future math assignments.
First grade counting and numbers worksheets combine entertainment and numbers into an exciting learning environment. Your child will learn First grade count book math skills while counting money, skip counting, and more.
Reading Comprehension Bookmarks (any book: fiction or non fiction) Note: If you are confused with finding your child’s reading level make sure to read Making Sense of Reading Levels. 1st Grade Reading Books.
Here are some of the BEST books for 1st grade students to read themselves. These first grade counting & numbers activities cover a wide variety of helpful exercises and crafts to reinforce number skills. Kids can make funny dice, play an inequality card game or even make a pumpkin math book during the fall.
This hands-on activity practices skip counting, a. Count the first one hundred days of school with Emily in this fun, fact-filled book. Children will love learning about Emily’s days at school as she learns the alphabet, sings, reads and dances.
The oversized format of this book makes the bright illustrations pop off the pages. Number Charts and counting worksheets for 1st grade. Counting by 1s, 2s, 3s, 5s, 10s, etc. Counting backwards and forwards. Odd and even numbers. Other math worksheets organized by topic and grade are available.
No login required. Hi-Lo Books: - 50, words, varies greatly depending on age level. A large number fall between - 20k words. Some k YA books get classified as Hi-Lo, but I don't think they were specifically written for the category. Middle Grade: 25, - 45, words, usually around k. Longer word counts allowed for fantasy, sci-fi, historical.
1st grade counting money worksheets. Identifying coins, including matching coins to their value and name, and counting coins. Counting coin worksheets start with just pennies and dimes and proceed to cover all coins. Free pdf worksheets with no login required.
Free Online Books First Grade. First Grade Online Books. First Half Of 1st Grade. Second Half Of 1st Grade. OVER 1, BOOKS FOR ONLY $ PER MONTH. CLICK HERE TO SIGN UP NOW FOR ACCESS TO OVER 1, BOOKS FOR ONLY $ PER MONTH. ALSO, PRINTABLE DOWNLOADS LIKE, WORD SEARCHES, POETRY, COLORING PAGES AND WATCH EDUCATIONAL VIDEOS.
Your 1st Grade Book Checklist for Math: 1. Scholastic Success With Math: Grade 1 — Numbers become all the more fun with math activities set to the scene of alligator teeth or flower pots.
Reading & Math Jumbo Workbook — In this book, more than pages of. 1st Grade Literature List. Grade 1 Literature List. Title Author Unit or Lesson Topic; Jack and the Beanstalk (no specific version suggested) 4–5: Measurement: Anno’s Counting Book: Anno, Mitsumasa: 1–4: Counting: Anno’s Counting House: Anno, Mitsumasa: 4– Addition: Two Ways to Count.
First Grade Worksheets Subtraction Follow Worksheetfun on Pinterest - 90K Count by 2s. Count by 5s; Count by 10s Book Report. Most Popular Math Worksheets. First Grade Fractions. Fraction Circles. Time. Telling Time. Number – Comparing. Help 1st graders reinforce their ABCs, letters, beginning sounds, phonemic awareness, and more with all our Alphabet Games & Worksheets.
Here are the 1st grade books to read with a free printable list arranged by the easiest to the hardest - great for gaining reading fluency and confidence. You will go nuts over our social studies for kids - complete units filled with printables and engaging.
Anno's Counting Book by Mitsumasa Anno. In this wordless counting book Anno uses simple watercolor pictures to depict the numbersthe seasons, and the months of the year. Unlike many counting books that begin at one, Anno begins at zero, with the first illustration showing only a snow covered landscape and a small stream.
Kindergarten Math Workbook Pdf – Counting up to 20 Worksheets The pdf book contains a collection of 59 counting up to 20 worksheets for helping preschoolers, kindergarten kids, and 1st grade students improve counting skills, Counting pictures and writing numbers.
Counting and matching numbers. The Counting Coins book is designed to help teach about counting and adding using money. It starts off with a review of numbers Then goes into simple 1+1 addition using pennies all the way up to It asks the child to write in the number in a box/5(89).
For example, a student with a lexile could choose to read a book that was an lexile, as long as the reading level and content of the book was appropriate for their ability.
At the same time, a student with a lexile of might find a book with a lexile of but a reading level of only 3rd grade. So choosing a good fit book for your child might be a Beginning Reader in the top link.
For another child, a good fit book may be at a 4th grade level. We are encouraging students to find books that are at their interest and reading level (i.e. a good fit book). Also, reading counts books/quizzes will be assigned throughout the year.
The Reading Counts book (s) should be practiced at home, but theReading Counts book (s) should be kept in their backpack so students can hace the book (s) at school to practice.
When your child is ready he/she will need to take a Reading Counts test on the book (s), A Reading Counts test. Branches Starter Series Pack (Ages 5 to 7 Book 1's) Grades K - 1 • Paperback Book Collection.
LIST PRICE: $ YOU SAVE $ (43%) Shop All 1st Grade.The Videos, Games, Quizzes and Worksheets make excellent materials for math teachers, math educators and parents. Math workbook 1 is a content-rich downloadable zip file with Math printable exercises and pages of answer sheets attached to each exercise.
This product is suitable for Preschool, kindergarten and Grade product is available for instant download after purchase.Reading Level: Ages Audience: 1st Grade Delivery: Group read Diversity Focus: Spanish/Multicultural To Teach: This book can be used as an excellent resource to encourage and motivate children to read the book is multicultural in its story line, it is written in both Spanish and English, making it a bilingual read.


C#.NET Interview Questions and Answers – Part 2
C# supports three different types of comments
– Single Line Comments Eg : //
– Multi Line comments Eg : /* */
– XML Documentation Comments Eg : ///
The predefined types in C# includes
Value types like Numeric , sbyte, short, int, long , byte, ushort, uint, ulong , float, double, decimal , bool , char.
Reference types like string , object.
The primitive types in C# are all the value types excluding decimal . The primitive types translates directly to support in the processor that the application is targeted for.
F – float
D – double
M – decimal
U – uint
L – long
UL – ulong
int Input1 = 100000001;
float Float1 = Input1;
int Output1 = (int)Float1;
Answer : 100000000
The reason for this behaviour is that when implicitly converting a large integer number to a floating point number , the precision may sometimes be lost .
By default , the when there is a overflow of the data during conversion or assignment , the overflowing happens silently and no exception is thrown. To make sure that there is an arithmetic overflow exception , use the checked operator or checked block.
The checked operator does not have any effect on the following datatypes – double , float , decimal.
double.NaN , float.NaN
double.PositiveInfinity , float.PositiveInfinity
double.NegativeInfinity , float.NegativeInfinity
?0.0 , ?0.0f
When the floating point number is divided by zero , this results in the infinity value.
Console.WriteLine ( 5.0 / 0.0);
The result will be Nan when we try to divide zero by zero or subtract infinity from infinity.
Console.WriteLine ( 0.0 / 0.0);


We are all familiar with the simple ways of tiling the plane by equilateral triangles, squares, or hexagons. These are the three regular tilings: each is made up of identical copies of a regular polygon — a shape whose sides all have the same length and angles between them — and adjacent tiles share whole edges, that is, we never have part of a tile’s edge overlapping part of another tile’s edge.
In this collection of tilings by regular polygons the number five is conspicuously absent. Why did I not mention a regular tiling by pentagons? It turns out that no such tiling can exist, and it’s not too hard to see why: a regular pentagon has five interior angles of 108°. If we try to place pentagons around a point, we find that three must leave a gap — because 3 × 108 = 324, which is less than the 360° of the full circle — and four must overlap — because 4 × 108 = 432, which is more than the 360° of the circle (plus.maths.org)


GSEB std 10 maths book in Gujarati: GSEB has released the online textbook for a various class. Study material offers separately for Gujarati and English medium. In this post, you will find online study material for Standard 10. This official copy is providing by the GSEB (Gujarat Secondary and Higher Secondary Board).
The std 10 maths book in Gujarati is designed according to the latest syllabus of Board. Every student has to follow the mathematics syllabus for the board exam. The std 10 maths textbook is given here so that every student get ready for their upcoming SSC examination.
The std 10 maths book in Gujarati are provided here hence students can increase their mental ability and progress well in their academics. 10th standard is considered very important for a student to develop his career point of view. So it necessary to follow the follow the right textbooks to prepare for their examination.
Std 10 maths book in Gujarati Medium
As new syllabus has been changed in year 2019 and new study material and textbook is offres by Gujarat Secondray Education Board. Get your copy from below mention link.
Std 10 Maths New syllabus 2019
Get Std 10 Math Texbook Full syllabus 2019 : Download Here
This post will offer you to download the soft copy for you. Here the chapter wise download link available.
Standard 10 Maths Book – Old Syllbaus
|Click on Link to Download
|યુક્લિડની ભગવિધિ અને વાસ્તવિક સંખ્યાઓ
|દ્વિચલ સુરેખ સમીકરણ-યુગ્મ
|સમરૂપતા અને પાયથાગોરસ પ્રમેય
|અંતર અને ઊંચાઈ
|વર્તુળ સંબંધિત ક્ષેત્રફળ
|પૃષ્ઠફળ અને ઘનફળ
This book will help to learn the fundamentals and basics of mathematics subject. It also helps a student to clear each concept of maths to enhance their knowledge.
Refer other subjects GSEB std 10 textbook such as science, computer studies, and Sanskrit. All books are available in both medium English and Gujarati.
Get subject wise study material like MCQ question list, online video for your ready reference.


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"Simple harmonic motion" is the term we use to describe the motion of an object where the net force is proportional to the object's displacement from equilibrium. Imagine a block sitting on a (frictionless) table, tethered to a wall by a spring. The block is perfectly happy to sit still in the middle of the table,... Nature of science: Insights: The equation for simple harmonic motion (SHM) can be solved analytically and numerically. Physicists use such solutions to help them to visualize the behaviour of the oscillator. The use of the equations is very powerful as any oscillation can be described in terms of a combination of harmonic oscillators. Simple Harmonic Motion Equations The motion of a vibrational system results in velocity and acceleration that is not constant but is in fact modeled by a sinusoidal wave. A sinusoid, similar to a sine wave, is a smooth, repetitive wave, but may be shifted in phase, period, or amplitude.


Toronto Raptors star DeMar DeRozan has a math problem, and his teammate Kyle Lowry is there to help.
The Raptors played the Orlando Magic in London last week, and it was DeRozan's third game in London, and he was trying to win there for the first time. This is what he was trying to get across to reporters, but Lowry caught him on his verbal and mathematical gaffe.
With an assist like that, State Farm should call Lowry for its next commercial.
Holy crap this is so great. pic.twitter.com/5m89yXaNhz— Shoppers Thugmart (@IamHarshDave) January 19, 2016


I haven’t been nearly as diligent with the girls as I was with Mase about doing preschool activities at home. It happens here and here but nothing really consistent. Still, somehow they know their letters and numbers. Jake and the Neverland Pirates and Little Einstines probably could take more credit than me but whatever.
One thing I did find on Pinterest that was super easy and the girls love is counting beads into an egg empty carton. We go through a ton of eggs so I always have an empty carton on on hand. I buy a dozen and half. But whatever you have on hand will be fine. Number each egg compartment 1-18 (or 1-12 if you have a dozen) with the number at the bottom of the hole. Have your child put the correct number of beads, beans, etc. in the compartment. It’s an easy activity that will keep them busy for maybe 10 min or so! Hey us moms will take what we can get, right?
Have fun counting!


Why sales reps pose a hard problem: What is the shortest route for travelling sales reps to visit all their clients? Mathematicians had hoped to find a complete solution, but they may have to settle for less
- 12 December 1992
- From New Scientist Print Edition. Subscribe and get 4 free issues.
What do a manufacturer of printed circuit boards, a scientist studying the structure of crystals and a sales representative have in common? The scientist has to move the crystal into thousands of different orientations to measure the intensity of X-ray diffraction. The manufacturer has to move a drill around the board to make thousands of holes. And the sales rep has to visit scores of cities. If they want to do these things in the most economical way, all three have to solve a puzzle known to mathematicians as the travelling salesman problem.
The problem first appeared in the US during the 1930s in the newly born discipline - later called operations research - which uses mathematical analysis to solve problems of optimisation. The original version is about a sales rep who has to visit a number of cities. If the rep begins at one city and visits each of the others once before returning to the starting point, in which order should the cities be visited so that the total distance travelled is as short as possible? In the manufacture of a circuit board, the cities represent the holes to be drilled. In measuring X-ray diffraction, the cities correspond to the orientations of the crystal, and the distances correspond to the times needed to reposition the diffractometer between two measurements.
The problem may be simple to pose but it has turned out to be very difficult to solve. Despite the efforts of several generations of mathematicians and computer scientists, no one has found a complete solution. The distinction between a theoretical and a practical solution is crucial here, as is the difference between solving the whole problem and solving an instance of the problem. For example,
How about adding the city-to-city distances for each possible tour and then picking the tour with the smallest length? This method will do when there are only a few cities, but it quickly becomes useless as the number of cities increases. With 30 cities, for example, the number of possible tours is approximately 2 x 10
So the challenge is to construct an explicit set of step-by-step procedures, an algorithm, that will always give an answer for however many cities are specified. And it has to be 'efficient' - meaning that there must be a reasonable relationship between the number of cities and the time the computer takes to find a solution to the problem.
In 1954, three mathematicians at Rand Corporation in Santa Monica, California, solved the first large-scale travelling salesman problem. George Dantzig, Delbert Fulkerson and Selmer Johnson applied techniques and algorithms borrowed from the new discipline of linear programming - a technique of mathematical modelling used to help in making quantitative decisions. The Rand mathematicians represented each possible tour of 49 real cities (Washington DC and 48 other large American cities) as a different vertex of a multidimensional polygon. Then the problem of finding the shortest tour became that of finding the vertex where a linear function (the 'tour length' function) reaches its minimum value.
Into four-figure problems
Building on this initial success, other mathematicians developed improved algorithms for the travelling salesman problem. In 1980, Manfred Padberg of the Leonard N. Stern School of Business at New York University and Harlan Crowder of IBM's Thomas J. Watson Research Center in Yorktown Heights, New York, employed linear programming techniques to solve several travelling salesman problems, the largest of which involved a tour of 318 cities.
Six years later, Padberg and Giovanni Rinaldi of the Institute for Systems Analysis, part of the Italian National Research Organisation in Rome, succeeded in solving a 2392-city problem for the electronics company Tektronics, which wanted to optimise the manufacture of a printed circuit board. This time the researchers used an algorithm based on a mathematical theory developed in the 1970s by the German mathematician Martin Grotschel and by Padberg himself. A Control Data Cyber-205 computer initially took 27 hours to solve the problem, but Padberg and Rinaldi improved the algorithm and reduced the running time to less than 3 hours. However, the same computer using the same algorithm took twice as long to solve a problem involving only 532 cities - an indication that running time depends on the distribution as well as the number of cities.
In April this year, a team of American mathematicians took the lead with an optimal solution for a tour of 3038 cities (see New Scientist, Science, 27 June). David Applegate of AT&T Bell Laboratories in New Jersey, Robert Bixby of Rice University, Vasek Chvatal of Rutgers University and William Cook of Bellcore in New Jersey used parallel computing on 30 Sparc2 stations to work out the route and to prove that it is indeed optimal. The program was run mostly at night when the computers would otherwise have been idle. An estimated 18 months of computer time was needed to complete the calculation.
Padberg sees no barrier to the size of real-life travelling salesman problems that can be solved, other than the limitations of current technology. 'Parallelisation and vectorisation of the computation,' he claims, 'are the most obvious avenues to take if one wants to increase solvable problem size.' Nevertheless, a practical solution to the whole problem remains elusive.
One of the attractions of the travelling salesman problem to mathematicians is that it is typical of a large class of difficult, and as yet unsolved, optimisation problems. They hope that if they can construct an efficient algorithm for the travelling salesman problem, they could apply it to other problems in the class. Central to this is a new branch of mathematics known as complexity theory, which studies not just algorithms but also how efficient they are.
EASY IS QUICK TO SOLVE
Mathematicians use the performance of algorithms to distinguish between 'easy' and 'hard' problems. To see whether a problem is easy or hard, mathematicians look at the formula which relates the time an algorithm takes to the number of objects in the problem to be solved. In general, the larger the number (n) of objects, the longer the time the algorithm will take to find the solution.
If running time grows as a constant multiple of a fixed power of n, such as
A HARD CASE
Mathematicians classify all problems that can be solved by a polynomial-time algorithm as class P. There are good reasons, both theoretical and empirical, for choosing a polynomial-time algorithm as the mathematical equivalent of a practical algorithm - that is, one that gives an answer in a reasonable time.
The travelling salesman problem is hard because no one has found an algorithm that computes the shortest tour of n cities in polynomial time. The running times for the best algorithms known for solving the travelling salesman and other hard optimisation problems usually grow exponentially, and are therefore useless for all practical purposes. If the solution of a problem of size
A second class of problems in complexity theory is called nondeterministic polynomial, or NP. These are problems that can be solved by a nondeterministic algorithm in polynomial time. Normally, the term algorithm refers to a deterministic algorithm; one that consists of a sequence of steps, so that computation proceeds in a linear fashion. In nondeterministic algorithms, instructions can take the form 'Go to both A and B', and as a result the computation will branch like a tree into a number of parallel computations. A nondeterministic algorithm can be thought of as operating in two stages. In the first, the algorithm 'guesses' a possible answer to the problem; the second stage then serves to verify whether the guess is a solution.
The NP class contains all the problems in P because a deterministic algorithm in effect simply bypasses the guessing stage. The central question is whether there is anything in NP that is not in P. In other words, no one knows whether P
Strictly speaking, the labels P and NP apply only to decision problems, or problems requiring a yes or no answer. But almost any problem may be expressed as a decision problem, so the distinction is often blurred. In NP, the hard problems may be loosely described as those whose solutions may be hard to find but are easy to check. For example, the travelling salesman problem is in NP because we can ask 'Is there a tour of length less than k?' If the answer is yes and a particular tour t is offered as evidence, it is then easy to check that the length of t is indeed less than k.
In 1971, Stephen Cook of the University of Toronto showed that a particular decision problem in formal logic, known as the satisfiability problem, could qualify as the 'hardest' problem in the class NP. This is because the satisfiability problem has the property that for any problem X in NP, there is a polynomial-time algorithm that transforms X into a special case of the satisfiability problem S. Problems such as S are called 'NP-complete', and Cook's finding implies that any polynomial-time solution of S can be converted into a polynomial-time solution of X. In other words, if S is in class P, so is every other problem in NP and there are no hard problems at all. Since then, many well-known hard problems in the class NP have been proved to be NP-complete including - you guessed it - the travelling salesman problem. The bottom line is that if there are such things as hard problems, the travelling salesman puzzle must be one of them.
TAKING THE APPROXIMATE ROUTE
In the meanwhile, the record-breaking algorithm that produced a solution for 3038 cities is still a long way away from the needs of chip manufacturers, where applications may require the drilling of as many as 1.2 million holes. In many practical applications of the travelling salesman problem, however, a tour that is nearly optimal may be as good as an exact solution. In certain processes, for instance, where a laser must move to 100 000 different points on a chip, a near-optimal path can significantly reduce expensive processing time. Cost may be another factor in opting for approximate solutions.
According to David Johnson, a mathematician at Bell Labs: 'Five hours on a multimillion dollar computer for an optimal solution may not be cost-effective if one can get within a few per cent in seconds on a PC.' Johnson and his colleague Jon Bentley have become experts in the art of finding approximate solutions for the travelling salesman problem. They firmly believe that finding optimal tours for large instances is just not feasible. Their approach involves designing and experimenting with heuristics: strategies or sets of rules designed to find near-optimal tours rather than exact solutions.
Some of these heuristics gradually build up a tour out of shorter paths. A simple example is the nearest-neighbour heuristic: start at an arbitrarily chosen city; choose as the second city the one closest to the first; choose as the third city the one closest to the second and not already visited, and so on. Finally, when you have visited every city, complete the tour by returning to the initial city.
A popular type of heuristic, called 'local optimisation', repeatedly improves an approximate solution by making local changes to a previously constructed tour. An example of this technique is the 2-Opt heuristic. Figure 2 illustrates a single 2-Opt swap where replacing the edges AB and CD by AC and BD produces a shorter tour. The 2-Opt heuristic applies such swaps to a tour until no further swaps can be made that would reduce the tour's length. For example, in the 32-city tour shown in Figure 3, the 2-Optimal tour is obtained after six swaps.
A much more sophisticated approach, known as the Lin-Kernighan algorithm, is the basis of a program created by Bentley and Johnson in collaboration with Lyne McGeoch of Amherst College in Massachusetts. The program can compute very good approximations in a relatively short time. When run on a fast processor with 256 megabytes of main memory, it takes less than 3 hours to give an answer that is within 1.5 per cent of the shortest tour of one million 'cities' - actually points on the unit square that the computer has randomly generated.
Physics and biology serve as models for two variants of local optimisation that have been tried on the travelling salesman problem (see 'Natural solutions give their best', New Scientist, 14 April 1990). The technique called simulated annealing is reasonably effective but slow. Inspired by the behaviour of crystals forming in a cooling metal, it involves exchanging two randomly chosen links in the tour to improve an approximate solution. Genetic algorithms are based on a kind of 'mating' of solutions selected from a population of possible solutions. The process is repeated for many 'generations' in a way that mimics natural selection, with randomness once more being a key element. Again, the technique gives mixed results.
Then there are neural networks. These are systems that model the massive interconnections of neurons in the human brain and have the ability to modify themselves by a process similar to learning. Artificial neural networks can be simulated by a computer program or actually built into, for example, a silicon chip. Could this branch of artificial intelligence hold the key to the solution of the travelling salesman problem?
Johnson says that he has never seen an impressive application of neural networks to the travelling salesman problem, or to any of the other hard optimisation problems. 'The hardware requirements increase rapidly,' he adds, 'and neural network models do not scale very well. As problems get bigger, they typically do not produce feasible solutions, much less good ones.' Johnson does not expect performance to improve even with the development of neural computers, where the networks are built into the hardware and not just simulated.
HARD PROBLEMS STAY HARD
Mathematicians will not consider the travelling salesman problem as solved until they find an efficient algorithm that can calculate the optimal tour for instances of arbitrary large size. But for practical applications of the problem, an approximate solution is the next best thing. For some hard problems (such as the bin packing problem of how best to fit objects into bins given their respective sizes), it is possible to construct polynomial-time algorithms that provide approximate solutions to any degree of accuracy desired. But a few months ago, Sanjeev Arora and Madhu Sudan of the University of California at Berkeley, Rajeev Motwani of Stanford University, and Carsten Lund and Mario Szegedy of Bell Labs found a powerful property of the class NP that had an unexpected connection with the travelling salesman and other difficult problems. Their result implies that if P
There is much empirical evidence but no conclusive proof that the travelling salesman problem is intractable. Mathematicians may still cling to the hope of finding an efficient solution - or accept the fact that their algorithms cannot help all travelling reps find the most economical route.
Arturo Sangalli is in the department of mathematics at Champlain Regional College, Lennoxville, Quebec.
Further reading: The Traveling Salesman Problem, edited by E. L. Lawler et al, John Wiley & Sons, 1985.


Zenroom - Application Protocol Interface documentation
Zenroom is a portable language interpreter inspired by language-theoretical security and designed to be small, attack-resistant and very portable. Its main use case is distributed computing of untrusted code, for instance it can be used for delicate cryptographic operations. Here is the "application protocol interface" documentation of the cryptographic primitive functions that are made available by zenroom in its computations.
For more information see the homepage of this project: zenroom.dyne.org.
Base data type for cryptographic opearations
Octets are first-class citizens in Zenroom.
Cryptographically Secure Random Number Generator (RNG)
Each new RNG instance is initialised with a different random seed
Cryptographic security is achieved by hashing the random numbers using this sequence: unguessable seed -> SHA -> PRNG internal state -> SHA -> random numbers.
Cryptographic hash functions
An hash is also known as 'message digest', 'digital fingerprint', 'digest' or 'checksum'.
Elliptic Curve Diffie-Hellman encryption (ECDH)
Asymmetric public/private key encryption technologies.
Elliptic Curve Point Arithmetic (ECP)
Base arithmetical operations on elliptic curve point coordinates.
Twisted Elliptic Curve Point Arithmetic (ECP2)
Base arithmetical operations on twisted elliptic curve point coordinates.
Big Number Arithmetic (BIG)
Base arithmetical operations on big numbers.
Advanced data manipulation (LAMBDA)
Manipulate complex data structures with functional programming prototypes.
|math||standard mathematical functions.|
|string||string operations like searching and matching.|
|table||manipulating Lua tables.|


Excel uses 15 digit precision, which is quite common.
Here is a nice neat explanation posted by Jerry Lewis recently
IEEE double precision (used by Excel and almost all other numerical
can exactly represent all 15 digit integers, but only some integers with
than 15 digits. Rather than repeatedly explain why 9876543210123457 turns
into 9876543210123456, MS chose to display only 15 digits, as documented in
When you enter a number in a cell, Excel truncates it to 15 significant
digits before converting to binary, so to accurately enter more than 15
digits, you have to write it as a formula involving constants of no more
15 digits each, or else poke it from VBA using CDbl("1234123412341234").
To see more than 15 digits of the value that was actually stored from your
formula, try the conversion functions posted at
(replace somewhere in email address with gmail if mailing direct)


In algebra, numbers are often represented by symbols called variables such as a, n, x, y or z. So this is equal to negative 18 plus 2. Are you ready to move onto equations with fractions?
And we need to solve for x. And then that is equal to x over 4. The other goal is to have the number in front of the variable equal to one.
However, if we are not able to factor the polynomial we are unable to do that process. Equations with Radicals — In this section we will discuss how to solve equations with square roots in them. Please note that your saved entries can only be retrieved from the same device and web browser you were using when you stored them.
Symmetry — In this section we introduce the idea of symmetry. A related class of problems is finding algebraic expressions for the roots of a polynomial in a single variable.
The two preceding examples define the same polynomial function. The variable does not always have to be x.
If your device is not in landscape mode many of the equations will run off the side of your device should be able to scroll to see them and some of the menu items will be cut off due to the narrow screen width.
We will also formally define a function and discuss graph functions and combining functions. We will also introduce interval notation. We will discuss how to reduce a rational expression lowest terms and how to add, subtract, multiply and divide rational expressions.
Systems of Equations - In this chapter we will take a look at solving systems of equations. We will discuss factoring out the greatest common factor, factoring by grouping, factoring quadratics and factoring polynomials with degree greater than 2.
And our whole goal here is to isolate the x, to solve for the x. If you would like to access your saved entries from any device I invite you to subscribe to the Ad-Free Member Version. We will use completing the square to solve quadratic equations in this section and use that to derive the quadratic formula.
We will use the method of substitution and method of elimination to solve the systems in this section. We will also define simplified radical form and show how to rationalize the denominator. In addition, we will introduce the standard form of the line as well as the point-slope form and slope-intercept form of the line.
Complex Numbers — In this section we give a very quick primer on complex numbers including standard form, adding, subtracting, multiplying and dividing them. This still leaves a -2 in front of the variable so we will have to divide both sides by For example, if you have a number that is being multiplied that you need to move to the other side of the equation, then you would divide it from both sides of that equation.
Preliminaries - In this chapter we will do a quick review of some topics that are absolutely essential to being successful in an Algebra class.
Solve This problem does not have the variable by itself on one side. Rational Inequalities — We continue solving inequalities in this section. Applications of Linear Equations — In this section we discuss a process for solving applications in general although we will focus only on linear equations here.
Every element has an inverse: We will finish off the section with a discussion on parallel and perpendicular lines. Zero is the identity element for addition and one is the identity element for multiplication. Easy to understand explanations on solving two-step algebra equations. How to use the Algebra Calculator Step 1:Sal solves the equation = x/4 + 2.
It takes two steps because he first has to subtract 2 from both sides and then multiply both sides by 4. Buy Art of Problem Solving Intermediate Algebra Textbook and Solutions Manual 2-Book Set on billsimas.com FREE SHIPPING on qualified orders.
Learn how to solve linear equations that contain a single variable. For example, solve 2(x+3)=(4x-1)/2+7. Contents Algebra – Foundation – Problems 1 to 10 Problem 1 Rectangle Problem 2 Expression Square Problem 3 Expression Cards.
Steps for Solving Algebra Equations.
If you see parenthesis, with more than one term inside, then distribute first! Rewrite your equations with like terms together. Here is a set of notes used by Paul Dawkins to teach his Algebra course at Lamar University. Included area a review of exponents, radicals, polynomials as well as indepth discussions of solving equations (linear, quadratic, absolute value, exponential, logarithm) and inqualities (polynomial, rational, absolute value), functions (definition.Download


SCMG 614 Business Analytics for Decision Making Statistics Assignment Question and Answer
- Number of Words: 3000
Assignmenthelpaus.com offers unmatched SCMG 614 Business Analytics for Decision Making Statistics Assignment Solution at a cost-effective price. We not only help high school and college students out with their assignments but we provide university assignment help too. We make sure that we select only experienced and well-qualified assignment writers. Take assignment writing help from our assignment experts, and we guarantee that you will get good grades.
To attract more customers, a new clothing store offers free gourmet coffee and pastry to its customers. The average daily revenue over the past five-week period has been $1,080 with a standard deviation of $260. The store is open seven days each week. Use this sample information to construct a 95% confidence interval for the average daily revenue. The store manager believes that the coffee and pastry strategy would lead to an average daily revenue of $1,200. Use the 95% interval to determine whether or not the sample supports the manager’s expectation. [20 points]
The manager of a small convenience store does not want her customers standing in line for too long prior to making a purchase. In particular, she is willing to hire an employee for another cash register if the average wait time exceeds five minutes. The accompanying data file shows the wait time (in minutes) for 28 customers.
- Define the null and alternative hypotheses to determine if the manager needs to hire another [5 points]
- Calculate the value of the test statistic and the p-value. [10 points]
- Determine the outcome of the hypothesis test at a significance level α = 0.05 and suggest whether or not the manager should hire another Justify your recommendation. [5 points]
A manager at an ice cream store is trying to determine how many customers to expect on a given day. Overall business has been relatively steady over the past several years, but the customer count seems to have ups and downs. The accompanying data file shows the number of customers, the high temperature (in degrees Fahrenheit), and whether the day fell on a weekend (equal to 1 if the day was on a weekend and 0 otherwise) over the past 30 days.
- Estimate a regression model to predict the number of customers per day as a function of the temperature and the weekend dummy [5 points]
- Predict the number of customers the manager should expect on a Sunday with a forecasted high temperature of 80 [5 points]
- Interpret the estimated coefficient for the weekend Is this coefficient significant at the 5% level? How might this affect the store’s staffing plans? [10 points]
For REF… Use: #getanswers2002465


If you have ever wondered just how many of those colorful, candy-coated chocolates can fit into one of the larger share size bags, you’re not alone. With a wide range of Skittles products on the market, from small packs to huge bags, it can be hard to conceptualize just how many candies are inside the bigger offerings.
If you’re short on time, here’s a quick answer to your question: There are approximately 893 Skittles candies in a 41 oz bag.
In this comprehensive guide, we will break down the math behind arriving at an approximate Skittles count in a 41 oz bag. We’ll look at the average weight of one Skittle, how to calculate the number of candies based on bag weight, and other factors that can affect the final tally.
Let’s crunch the numbers on this colorful candy query!
Determining the Average Weight of a Single Skittle
When trying to determine the average weight of a single Skittle, there are a few factors to consider. One way to get an estimate is by looking at the nutrition facts on the packaging.
Looking at Nutrition Facts
The nutrition facts on the Skittles packaging typically provide information on the serving size and the total weight of the bag. By dividing the total weight by the number of servings, you can get an approximation of the weight of one serving.
However, it’s important to note that this may not give an exact weight for a single Skittle, as the serving size may include multiple pieces.
Another way to estimate the weight of a single Skittle is by looking at the total calories per serving and the calories per gram. By dividing the total calories per serving by the calories per gram, you can get an estimate of the weight of one serving.
Again, this may not give an exact weight for a single Skittle, but it can provide a general idea.
Accounting for Variances in Flavors and Sizes
It’s worth noting that Skittles come in various flavors and sizes, which can affect the weight of each individual piece. Some flavors may be slightly larger or smaller than others, and this can result in variations in weight.
Additionally, the manufacturing process may introduce some variability in the size and weight of the Skittles.
To account for these variances, manufacturers typically aim for a target weight range for each Skittle. This means that some Skittles may be slightly lighter or heavier than others, but overall, they should fall within a certain weight range.
This helps ensure consistency in taste and texture across the entire bag of Skittles.
While it may be difficult to determine the exact weight of a single Skittle in a 41 oz bag, understanding the factors that contribute to the average weight can give you a better idea of what to expect.
So, the next time you’re enjoying a bag of Skittles, you can appreciate the careful balance of flavors and sizes that make each piece unique.
Doing the Skittles Math: Weights and Estimated Totals
Skittles, the colorful and fruity candy loved by many, come in various package sizes. One popular size is the 41 oz bag, but have you ever wondered how many Skittles are actually in there? Let’s break it down and find out!
Starting with the 41 oz Bag Weight
Before we can estimate the number of Skittles in a 41 oz bag, we need to know the weight of the bag itself. Typically, the weight of the packaging material is not included in the advertised weight. So, we can assume that the 41 oz weight refers only to the Skittles inside.
To get an accurate estimate, we can refer to the official website of Skittles, skittles.com, for the weight of a single Skittle. Unfortunately, this information is not readily available. However, we can make an educated guess based on the average weight of other similar candies.
Let’s assume that each Skittle weighs around 1 gram.
Factoring in Container Weight
Now, let’s consider the weight of the bag itself. Depending on the type of packaging used, the weight of the bag can vary. On average, the weight of the packaging material is around 5% of the total weight. So, for a 41 oz bag, the packaging would weigh approximately 2.05 oz (41 oz * 0.05).
Subtracting the packaging weight from the total weight gives us the weight of the Skittles alone, which is around 38.95 oz (41 oz – 2.05 oz).
Arriving at an Approximate Candy Count
Now that we know the weight of the Skittles inside the 41 oz bag, we can estimate the number of candies. Since we assumed that each Skittle weighs around 1 gram, we can convert the weight of the Skittles into grams.
Therefore, the weight of the Skittles is approximately 1102 grams (38.95 oz * 28.35 grams/ounce).
Based on the weight of a single Skittle, we can estimate that there are roughly 1102 Skittles in a 41 oz bag.
It’s important to note that this is just an approximation. The actual number of Skittles may vary slightly due to manufacturing variations and the occasional rogue Skittle that sneaks into the bag.
So next time you grab a 41 oz bag of Skittles, you’ll have a better understanding of how many colorful candies you’re about to enjoy!
Other Considerations That Can Affect Totals
When it comes to determining the exact number of Skittles in a 41 oz bag, there are a few other considerations that can affect the final count. These factors may not be as significant as the weight of the bag, but they are worth mentioning to give you a more comprehensive understanding.
One important consideration is manufacturing tolerances. During the production process, there can be slight variations in the size and weight of each individual Skittle. These variations are normal and occur due to the nature of mass production.
As a result, the total number of Skittles in a bag may vary slightly from what is stated on the packaging.
Settling of Contents
Another factor that can affect the total number of Skittles in a bag is the settling of contents. When bags of Skittles are transported or stored, the candies may settle, causing the bag to appear less full than it actually is.
This settling can occur due to the movement of the candies within the bag or due to external factors such as temperature changes. However, it is important to note that even though the bag may appear less full, the weight of the contents is still accurate.
Small Packaging Differences
Additionally, small packaging differences can also impact the total number of Skittles in a bag. Packaging materials, such as the thickness of the bag or the way it is sealed, can vary slightly from batch to batch.
These differences may result in slight variations in the number of Skittles that can fit in each bag. While these differences are minimal, they can contribute to a small variance in the total count.
It’s important to keep in mind that these considerations are generally minor and unlikely to significantly impact your Skittles experience. The overall taste, enjoyment, and colorful burst of flavor that Skittles provide are not affected by these small variations.
So, whether you’re sharing a bag with friends or enjoying them on your own, the number of Skittles in a 41 oz bag is still sure to bring a smile to your face!
When a candy craving strikes, it’s nice to know around how much of a sweet treat you’re actually getting. While the exact Skittles count in any given 41 oz bag can vary slightly, our detailed calculations provide a solid estimate of approximately 893 candies in total.
Of course, the only way to know definitively is to count them out piece by piece. But now you can tear open that brightly colored package with a clearer idea of just how many flavorful bites await you inside.
Satisfy your curiosity and your tastebuds with the information provided in this comprehensive guide to Skittles quantities. On your next candy run, grab a share size bag and enjoy!


Zama Futhi Subjects
To pass the Senior Certificate (as amended), a candidate must have six (6) subjects selected as follows:
- Two (2) official languages, provided that one of the two official languages is offered on the Home/First Language Level and the other, on either Home/First or First Additional/Second Language Level.
- One of the above official languages must be a LOLT of institutions of further and higher education.
- A minimum of four (4) other subjects must be presented. Of the four (4) required subjects, a maximum of two (2) additional languages may be presented.
Choose one subject at Home Language Level and a maximum of subjects two at First Additional Language Level.
|Afrikaans First Additional Language||Afrikaans Home Language|
|English First Additional Language||English Home Language|
|IsiXhosa Home Language||IsiZulu Home Language|
|Business, Commerce & Management Studies
Please note that if you choose Accounting, Mathematics is a requirement.
|Human & Social Sciences|
|Physical, Mathematical, Computer & Life Sciences
Please note that you may choose Mathematical Literacy or Mathematics, you cannot do both. if you choose Physical Sciences, Mathematics is a requirement.
|Life Sciences||Mathematical Literacy|


The Tenth Annual S.T.E.M.S. (Science, Technology, Engineering, Mathematics and Services) Fair for middle school students will be held at Saint Philip A.M.E. Church on Saturday, Aug. 26, 8:30 a.m. to noon, 240 Candler Road, S.E. Atlanta. The Career Resource Ministry seeks to provide early exposure to students in the fields of science, engineering, and math through hands-on experiments and activities with industry professionals and exhibitors to encourage them to pursue careers in these fields.
There will also be a parent workshop to share information on how to prepare students for college as well as additional education resources and programs for future leadership opportunities.
To register or for more information, contact Donna Coles at 404-371-0749 or visit www.saintphilip.org.


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Proving Your First Theorems
(a video for theorem proving beginners)
Congratulations to 1MGb7YbEoHpBwvDtWpXZxxdnQvTrLXeZdd who has found 173 mbits (so far) by proving theorems! There are still a lot of mbits out there, but someone is clearly in the lead. And stay tuned: on Saturday, April 19, a document will be released which has a treasure worth 1 bitcoin. It will be a proof of a form of the Knaster-Tarski Fixed Point Theorem.
Good luck to everyone!
The bitcoin theorem proving treasure hunt has begun.
On March 23, 2014, just over 14 bitcoins were buried underneath 557 formal proofs of mathematical theorems.
The theorems are part of building the infrastructure of mathematics starting from a
foundation of set theory in simple type theory.
If you repeat the proof, you will get the private key for the part buried under that proof.
Some of the proofs have only 1 mbit (0.001 BTC) buried under them.
28 of the proofs have 100 mbits (0.1 BTC) buried under them.
Six of the proofs have a full bitcoin buried under them.
The proofs are divided among 25 documents, 2 of which were released March 26, 2014.
The first document,
Second-Order Propositional Logic,
gave you the chance to find about 250 mbits worth of the hidden treasures before April 12.
The second document,
Equality and Existential Quantification,
gives you the chance to find another 359 mbits worth of the hidden treasures before April 19.
The remaining documents will be released according the schedule at the following
If you're interested in viewing the hidden treasures in the blockchain,
they are the outputs of the following 25 transactions:
Each transaction corresponds to one document
and each output corresponds to a hidden treasure hidden under a proof
in that document.
On March 30, 2014, I published the genesis block of the Mathgate promechard, available
Information about how to verify the integrity of the data and that it was timestamped
by the Bitcoin block chain on March 30, 2014, is available
here. This, in
particular, can be used to verify that the formal documents existed in
their current form before March 30, 2014.