Multi-Sensory Math Manipulatives
Thank you to the Goddard Education Foundation and generous donors. Innovative Teacher Grants are engaging Goddard Public Schools Students in new and exciting ways each day. In Kristina Scott’s Elementary Math classes, her Innovative Teacher Grant is putting math in the palm of her student’s hands (literally!).
Mrs. Scott’s Innovative Teacher Grant provided TouchMath into her small group instruction classes. TouchMath is a research-based method of instruction with the ability to bridge the gap between concrete and representational mathematics. These manipulatives provide students with another unique learning experience that helps them achieve learning goals. “This is that One More Thing as a teacher I needed to help some of my students ‘get it’, says Mrs. Scott.” She goes on to say, “It helps bridge the gap visually using these manipulatives and adds to a variety of different tools we have to offer concepts based on the needs of each student.”
In the short time utilizing these new manipulatives, Mrs. Scott has seen a positive impact in students, not only by improving their math skills but also by increasing their self-esteem and confidence that comes with understanding math concepts. First Grade student, Vada Moore said “Making the numbers felt good. It made me feel like I was doing it on my own. I know how to draw these numbers now.” The excitement of Mrs. Scott's rising mathematicians was evident in her math class as her students’ smiles lit up the classroom, smiles that captured the moment they “got it”.
Without our generous donors, resources like TouchMath would not be possible for our Goddard USD Students. The Goddard Education Foundation is dedicated to creating opportunities and expanding possibilities for Goddard students to be successful learners, like Vada Moore a rising first-grade Mathmetician.


Mathematics is a subject that requires strong analytical skills and critical thinking. Traditionally, teaching and learning mathematics involved textbooks, paper and pencil, and a chalkboard. But technology has dramatically transformed how we teach and learn mathematics in recent years. Gone are the days when math was about memorizing formulas and crunching numbers. Today, with technology, students can learn mathematics in a much more interactive and personalized way. As we explore how technology is changing the teaching and learning of mathematics, browse this website for some insights.
Technology can show learners the real-world applications of mathematical concepts. With the help of simulations and modeling tools, students can see how mathematical concepts are used in real-world situations. For example, they can use mathematical modeling tools to predict the spread of a disease or simulate the behavior of a financial market. This makes math more engaging and helps students understand how mathematical concepts are used in the real world.
Gamification is well-known in entertainment, but due to technological advancement in education, gamification plays a significant role in teaching and learning. Gamification can make learning math more engaging and interactive, as students are motivated to solve problems to progress in the game. Besides, it can help students develop critical thinking skills as they need to think about how to solve the challenging levels of games with different demands at each level. Also, this technique has improved student engagement and retention of knowledge and skills.
Virtual and augmented reality
Imagine learning math as if you’re living it. With virtual reality, students can immerse themselves in mathematical concepts and explore them in a three-dimensional space. For example, they can visualize geometric shapes in 3D or explore complex equations in a virtual environment. Augmented reality, on the other hand, can bring mathematical concepts to life in the real world. Learners can use their smartphones or tablets to scan real-world objects and see mathematical concepts overlaid on top of them. For example, they can scan a soda can and see the surface area and volume calculations displayed on the screen. These technologies are making teaching and learning simplified and interactive, motivating scholars to want to learn more.
The internet has modernized information access, which is no different for mathematics. There are now countless online resources available for learners to learn math. From online courses and tutorials to interactive videos and games, scholars can access a wealth of information and resources 24/7 to help them learn math. This has democratized education, enabling anyone with an internet connection to learn mathematics.
With the help of online platforms, students can learn at their own pace and level, thanks to adaptive learning systems. The systems use data analytics to personalize the learning experience for each student. Adaptive learning systems assess each student’s strengths and weaknesses and provide them with personalized feedback and learning activities. Besides, adaptive learning algorithms can adjust the difficulty of questions and exercises based on the student’s performance, ensuring they are neither bored nor overwhelmed. This personalized approach to learning makes math more engaging and fun and helps students build confidence and a deeper understanding of the subject.
As much as some argue that technology has no room for collaboration, you can ask yourself how learners work on group assignments. Or rather, how buyers and sellers come to a common ground about product/service and their prices. Technology has made it easier for students from different social settings to collaborate and work together. Online platforms like Homeworkdoer.org and tools allow scholars to work on math problems together. This makes learning math more interactive and fun and helps students develop essential teamwork and problem-solving skills, thus creating a supportive learning community.
Mathematics is essential to our life and education as it provides a foundation for various fields, from science and engineering to finance and computer science. But, the traditional methods of teaching and learning mathematics have often been criticized for being dry, uninspiring, and challenging to understand. Fortunately, with the advent of technology, how we teach and learn mathematics has changed significantly, leading to new, more engaging, interactive, and practical approaches.


ALL students registering for a first math course at Oregon Tech must take the mathematics Placement Test. Further guidelines regarding the mathematics Placement Test can be found by contacting Oregon Tech Testing Services at 541.885.1791 or by going to the website listed under Additional Resources.
Practice problems, organized be mathematical level, are available under the Math Practice Problems section below. You may use these to get an idea of the mathematical abilities needed for the respective mathematical level listed. If you have further questions, please contact a faculty member in the Mathematics Department.


It's been a busy week with all sorts of mathematical challenges. Many children dressed up as rock stars as part of the Times Table Rock Stars competition, with a final in-school battle on Friday where our junior winners were Harry, Dovydas, Reggie and Peter.
Some children in the 6/5 classes took part in the Primary Mathematics Challenge and were presented with gold, silver and bronze certificates.
Each day, an online problem was posted as a video from a mathematician somewhere in the country. Our children were eager to solve the puzzles and upload the answers to the website. Even the staff struggled with some of the problems!
Another activity was the maths quiz, with answers being entered for the national competition. We wait and see whether we were winners!


inch to cm
Welcome to inch to cm, our category with posts explaining the conversion from a certain length in inches to centimeters. For such a conversion we use the symbols and write x″ in cm, and in every post we explain you the math for your height, length or width in the unit inch. Every article also contains an inch to cm converter, and what makes our calculator particularly useful is that it can be used in conjunction with feet. That means you can change feet + inch to centimeters. For a specific conversion of inch to cm, we additionally give you the equivalent of your result in cm in millimeter, decimeter, meter, as well as kilometer. Of course, all our posts also include useful information about inch in cm, and a comment form to leave a feedback or to raise a question. Note that using our Google Custom Search in the sidebar, you can locate a particular conversion most efficiently.


IEK-10 focuses on the optimal design and operation of integrated, decentralized energy systems with a high share of renewable energy. Computer simulation and numerical optimization are our essential tools to arrive at efficient, reliable, and cost-effective solutions. We contribute both to the development of mathematical models and to the development of improved simulation methods and optimization algorithms. Our methods and software-tools are validated against operating data of real systems. Furthermore, we conduct comprehensive case studies in order to test and further improve the scalability and the performance of our models and algorithms. Specially adapted methods and codes enable us to exploit the potential of high-performance computing with the aim of solving particularly large and complex problems.
Scope of the Master Thesis:
Due to the large size of modern power networks, the computational burden of their real-time simulations is increasing, leading to always more challenging simulations. In order to be able to maintain the simulation timestep below a certain limit, dedicated parallelization solutions are needed. The real-time simulator OPAL-RT provides a parallelization method, called SSN block, to decouple sections of the network that will be simulated separately. The optimal placement of these blocks, and thus the parallelization, must be carried out by considering graph theory aspects and clustering techniques such as centrality measures. As part of a collaboration with OPAL-RT, your goal will be the development of a technique aimed at the parallelization of the simulation through the automatic placement of SSN-blocks.
- You are a student with very good background in Mathematics, Physics, Mechanical Engineering, Electrical Engineering, or a comparable subject
- Interests in numerical methods and analysis, and energy system modelling and simulation
- Basic understanding of energy system modelling and real-time simulation is preferable
- Good knowledge of and some experience in a programming language, preferably MATLAB, Simulink, and RT-LAB.
- Fluent in English (spoken and written)
- Highly motivated scientists of different subject areas working together
- Interdisciplinary work combining physics, mathematics, computer science, and engineering
- Intensive supervision by one or more experienced and helpful colleague(s)
- Friendly and welcoming work environment
Forschungszentrum Jülich GmbH
Institut für Energie- und Klimaforschung - Modellierung von Energiesystemen (IEK-10)
E-Mail: [email protected]
More Information about our institute: https://www.fz-juelich.de/iek/iek-10/EN


Line Edslev Andersen publishes "The Social Epistemology of Mathematical Proof"
In: Handbook of the History and Philosophy of Mathematical Practice, edited by Bharath Sriraman (Springer, 2021).
If we want to understand why mathematical knowledge is extraordinarily reliable, we need to consider both the nature of mathematical arguments and mathematical practice as a social practice. Mathematical knowledge is extraordinarily reliable because arguments in mathematics take the form of deductive mathematical proofs. Deductive mathematical proofs are surveyable in the sense that they can be checked step by step by different experts, and a purported proof is only accepted as a proof by the mathematical community once a number of experts have checked the proof. Hence, the reliability of the body of mathematical knowledge is in part obtained through the surveyability of proofs and the social process of proof validation. This chapter reviews work relating to (1) the norm in the mathematical community of only counting as argument deductive mathematical proof, and (2) the norm of only counting as deductive mathematical proof an argument that has been confirmed to be a deductive mathematical proof by a number of experts. The chapter also presents cases of unusual mathematical proofs or arguments that challenge these norms.
Keywords: Social epistemology of mathematical proof, Norms in mathematics, Surveyability of proofs, Proof validation, Ghost theorems, Complex proofs


In the name of Allah, most gracious and most merciful,
Table of Contents
1. Engineering and Mathematics
Machine learning has transformed many industries, and we observe these in our daily lives. That is because of the way machine learning works to solve problems. Before machine learning, we had to figure out the physical laws governing the complex phenomena which are usually difficult to describe and to get into its nitty-gritty details. Therefore, we simplify things by making assumptions so that we can at least come up with something close to reality describing the phenomenon we are seeing. At the end of the day, we want to solve our problems.
Let me elaborate more on this before delving into what I want to say about machine learning because I see that understanding this point is crucial. What is engineering? It is solving problems. But how can I solve problems? Well, by describing it in a precise way so that we understand it on a deeper level then we could use the tools we have to fix that problem. Yes, I understand but what do you exactly mean by describing a problem in a precise way? I mean describing it mathematically so that we could use our pools of mathematical tools to solve that problem. In other words, mathematics is the tool we use to describe our problems, represent them in very great ways that may reveal even more great insights, and then using mathematics again we can find solutions to our problems and also optimize them.
But how on earth could we describe things mathematically? Well, usually a lot of things in life could be looked at as entities, and relationships between entities. For example, a car is an entity that is composed of many components entities like the gear system, the braking system, the lighting system, and so on. These entities are interconnected through input-output relationships so the output(s) of one or more entities could be fed as input(s) to one or more systems. In the world of mathematics, each of these entities could be described as a mathematical model (i.e. mathematical equation). This mathematical model could have more than one input and outputs more than one output. Therefore now we converted a lot of things in life as mathematical models which usually have some assumptions to make the model complexity acceptable. Why assumptions? Again because the reality is too much difficult to describe so we make reasonable assumptions to simplify the mathematical model to be able to use it in our engineering applications.
2. Put on Your Engineering Eyes
Now that I explained these ideas, let’s put on our engineering eyes and see the physical world differently. Now under the hood, the physical world consists of some simplified mathematical models “Entities”, and there are input-output relationships between these mathematical models. To accommodate some mathematical model’s nature we could do some acceptable transformations to the inputs and outputs so the mathematical model gets what it expects as input, and therefore produces reasonable outputs.
3. The Machine Learning Revolution
But what is the usefulness of what you just said? Why mention these too many details and complexities? Because I want you to understand how machine learning works and the beauty of it. Now the machine learning is about using data to generate these models instead of purely understanding the governing physical laws and equations. For example in supervised (one type of machine learning), give me too many inputs and outputs of your model and guess it! I will try to figure out the approximate mathematical model for you! Do you see? it is another transformative great way of solving problems that needed three very important things to have:
- Data (Since we are living in the age of big data, so data is everywhere)
- High computational power to process these huge amounts of data (Computers are becoming more powerful and cheaper. You could look up at something called Moore’s law.)
- Mathematical tools that will help us fit the data on adjustable mathematical algorithms, optimization tools to ensure that the algorithms are learning from data properly, and analytical tools that will tell us how far we are from the correct more accurate mathematical models
In other words, part of the complexity of discovering the entities’ mathematical governing equations is reduced by relying on high-quality data.
But beware that that doesn’t mean that we don’t want to discover the entities’ mathematical governing equations from physical laws. There are often inaccuracies in machine learning and even the deep learning models that could be mitigated by complementing these models with some rules and heuristics that are from the domain knowledge or the mathematical governing equations. Therefore, domain experts still have their place but their jobs are somehow changed from having to do everything alone to feeding their domain knowledge into the machine so that the machine could do great work with the help of the data and the domain experts. In addition to this, machine learning and deep learning have their own difficulties, and they are not necessarily the solution for every problem. There are tradeoffs that one should evaluate to finally have the most effective and efficient model. Sometimes doing 95% accuracy in a short time could be better than doing 99% in a long time.
In summary, machine learning has revolutionized the way we solve problems especially super difficult problems that need many details that are hard to solve using rules or deriving the exact governing equations. For example, we have observed great recent advancements in Natural Language Processing and Computer Vision applications thanks to machine learning and deep learning unique and smart ways of solving problems.
4. What to Learn from Data
Machine learning could be divided into two approaches:
- Instance-based learning: It is when the system learns by using a similarity measure to measure how similar is a new data point it didn’t see before to a data point it learned on. So it would for example classify a new data point with the same class as the old data point if the similarity distance is within a certain threshold.
- Model-based learning: When the system learns specific parameters using the training data to make prediction on new unseen test data. So it learns parameters and not just sees how much something is similar to another thing as in instance-based learning.
5. How to Learn from Data
5.1 How to Split Data
Split it into training, and testing sets. You learn from the training data, and then evaluate the “generalization error” or the “out-of-sample” error using the test data. But wait, that’s not the whole story. There is another thing called validation set which is part of the training set. Therefore the training set is further reduced to (Reduced Training Set + Validation Set). The validation set is used to tweak the model’s hyperparameters which don’t depend on the data so they are manually set. However, the model’s parameters are the parameters that are learned by fitting the data on the model. Therefore there is a difference between the model’s automatically fitted parameters using the data and the model’s manually set hyperparameters.
It is super important to know that the testing and validation sets must be as representative as possible to the real-life data or the data in production since they are the sets that you evaluate the model’s performance on. So what if your evaluation method is flawed, well you are collapsing the whole model since how would you know if your model is good or bad without proper evaluation.
5.2 Further Split
Again this is not the whole story of splitting. Let me elaborate more. Let us assume that we have too much data that is non-representative of the production data, but we have another small representative data what could we do then? Given that the testing and validation sets must be as close as possible to production data we could divide the small representative data by half 50% – 50% on the testing and validation sets. Then we could train our data on the training set and then evaluate and see.
If the validation set results are disappointing, the problem could be either that you are overfitting the training data or the data mismatch “i.e. non-representativeness” is the problem. How could you know then what is the exact problem?
We want to isolate the mismatch problem so let us look only at the non-representative data we have to know the exact problem. So, as Dr. Andrw Ng. suggests, we could further split the reduced training set into another further reduced training set and a train-dev set. Then train on the further reduced training set, and see the train-dev set performance. If it is poor, then that means that you have overfitted the non-representative training data so you should try to simplify the model or regularize it or get more training data. Otherwise, if the train-dev set performance is good then that means that your model isn’t overfitting but is generalizing well on unseen train-dev set. Therefore the original validation set poor results could be due to data mismatch “i.e. non-representativeness” so you could see how to get more representative data for instance.
5.3 How Much Data to Use
- Batch Learning (Offline Learning): The system learns on all the data at once which will generally take much time and computational resources so it is usually done offline. The system is trained, deployed to production, and runs without anymore learning but it just applies what it learned.
- Online Learning: You could learn on batches of data incrementally batch by batch. On fitting each batch, you update the model’s parameters for instance. You are taking small steps to fit the model bit by bit. Each learning step is fast and cheap so the system can learn from new data as it arrives on the fly.
You could do something similar to this online learning when you have too much data that couldn’t be fit on one machine’s main memory (hence out-of-core learning), but this is usually done offline so online learning here could be confusing. Therefore, you could think of it as incremental learning.
5.4 How Fast to Learn (Learning Rate) – Adapting to Changing Data
- On using a small learning rate, the system learns more slowly, it is stable and less sensitive to noisy data and outliers.
- On using a high learning rate, the system will fastly adapt to new data, but it will also tend to forget the old data.
6. Machine Learning Challenges
Since machine learning relies on both data and machine learning algorithms, challenges exist in both of these things:
- Poor Quality Data: If the data you have has irrelevant features, whatever machine learning model you have you won’t do much good. It is like teaching a baby to learn the correct answer from the wrong answer. He will learn the wrong answer and won’t be able to get the correct answer.
- Not Enough Data: When data is abundant and is in high quality you could observe that different machine learning models yield very close results. Therefore having enough data could make a big difference. However, it may not necessarily be always the case. There could be exceptions and other details, but I am just giving you the big picture.
- Data not representative of the real-world scenario “Data Mismatch”: It is very important that your data specifically “your test and validation set” is representative of the real-world data it will encounter. If the data is too small, you may fall into the “Sampling Noise” problem (i.e. data is nonrepresentative as a result of chance). This representativity problem could also occur because of the way you sampled which could be flawed and biased like asking biased questions or whatever biased data collection method even If you have a large amount of data it is still not representative and this is called the “Sampling Bias”.
- Overfitting: The algorithm is memorizing the patterns in your data very well that it didn’t distinguish between the signal and the noise. Therefore your model has learned the noise as well which made it perform very well on training data but can’t generalize well on unseen new data.
- Underfitting: The algorithm is so simple that it couldn’t detect enough patterns in the data. So its performance is bad on both the training data and the testing (unseen new) data. It is like trying to fit non-linearly separable data using a linear model.
Thank you. I hope this post has been beneficial to you. I would appreciate any comments if anyone needed more clarifications or if anyone has seen something wrong in what I have written in order to modify it, and I would also appreciate any possible enhancements or suggestions. We are humans, and errors are expected from us, but we could also minimize those errors by learning from our mistakes and by seeking to improve what we do.
Allah bless our master Muhammad and his family.


FURTHER MATHS AT KGV
For the keenest students there is the opportunity to study Further Maths A-Level at KGV. On this programme you will take an entire A-Level in Maths in one year and in the second year you will study Further Pure Maths. This includes the study of a while new number system involving the square roots of negative numbers, a new system of coordinates for plotting graphs and how to describe transformations using matrices. You will also have opportunities to learn more Statistics, Mechanics and Decision Maths, which involves solving problems using algorithms in much the same way that computer programs work. You will leave KGV with a broad, transferable skill set including problem-solving, critical thinking and the ability to work independently.
WHAT WILL I STUDY?
In our Further Maths A-Level Course you will learn how to calculate the the probability of an event in Statistics, discover how to aim a projectile to hit its target in Mechanics, and find out how a SatNav calculates the shortest route in Decision. You’ll learn real life application of Mathematics and develop the skills that are needed to understand the relationship between growing or decaying substances and time in Core Maths.
You will have the opportunity to take part in local and national Maths competitions, such as UKMT Senior Challenge and the LMS Pop Quiz. Trips to relevant, interesting talks including the Maths Inspiration lectures are also planned. Each week every Maths class has an intervention session where extra help is available to everyone.
BUILD YOUR FUTURE
With 100% pass rates, over 60% of students achieving high grade passes, Further Maths at KGV gives students the opportunities to go far and explore all different types of career paths. Students who take Further Maths are likely to progress onto Maths related degrees at University, studying courses such as Engineering, Computing, Science, and Medicine. We currently have ex-students studying related courses at Oxford University after achieving A* Grades in Further Mathematics.


Quantum Mechanics - A branch of physics providing a mathematical description of the dual particle-like and wave-like behavior and interaction of matter and energy. QM describes the time evolution of physical systems via a mathematical structure called the wave function. The wave function encapsulates the probability that the system is to be found in a given state at a given time. QM also allows one to calculate the effect of making measurements of properties by defining the effect of those measurements on the wave function. Cunnilingus - Eating pussy.


A crane alone can lift a load as high as his main wheel permits. This maximum wheel load depends on several factors. The rated capacity of course is important, but the impact reduction factor determines its importance. The other factors are the overall weight of the crane and the weight of the trolley and mounting hoist, In addition to the load of the crane, using the maximum load of the wheel to select other crane components, such as beam size.
- Divide the weight of the crane, measured in pounds, in 2. If the weight of the crane is 6,000 pounds (2700 kg): 6000/2 = 3000.
- Add the weight of the crane and truck, also measured in pounds. If they are weighing 2500 pounds (1100 kg) combined: 3000 + 2500 = 5500.
- Multiply the weight of the nominal load capacity by reducing the impact factor. If the first is 10,000 pounds (4500 kg) and the second is 1.2: 1.2 x 10,000 = 12,000.
- Add the answers from steps 2 and 3: 5,500 + 12,000 = 17,500.
- Divide the result by 2: 17.500 / 2 = 8750 pounds (4000 kg). This response is the maximum load of the crane.


In previous articles in this series, we have addressed how to assess the validity of a diagnostic test. We have also reviewed how to assess its accuracy or reliability. To date, we have discussed the methods used to measure the accuracy of discrete data, nominal (kappa statistic) and ordinal (weighted kappa statistic). In this article, we will broach the methods that apply to continuous data: the within-subject standard deviation, the intraclass correlation coefficient and the Bland and Altman method.
Within-subject standard deviation
When the result of a test is measured on a continuous scale, we can estimate the measurement error by calculating the variability that exists between repeated measurements in the same subjects. The parameter that best reflects such variability is the within-subject standard deviation (excluding the variability observed between subjects). To calculate it, we need a set of subjects to undergo at least two measurements each. Table 1 presents the results of performing two repeated transcutaneous bilirubin measurements in newborns with jaundice.1 The within-subject standard deviation can be calculated easily using software that performs analysis of variance (ANOVA). ANOVA breaks down the variation present in the set of measurements (estimated based on the squared differences of each value and the mean of all subjects) into several components: the variation in measurements taken in different subjects (between rows in Table 1) and the variation in the residuals, which in one-way ANOVA corresponds to the variation in the measurements taken in each subject (between columns in Table 1).
Table 1. Results of two repeated transcutaneous bilirubin measurements (Jaundice-Meter 101, Minolta Air Shields) in the anterior surface of the thorax in 20 newborns with jaundice. Data retrieved from a larger study.3 Show/hide
Table 2 shows the ANOVA for the data in Table 1. The parameter called mean square of the residuals (MSr) is the residual or within-subject variance (which depends on the differences between repeated measures in each subject). If we take the square root of the MSr, we obtain the within-subject standard deviation (sw). The sw can also be calculated using the results of ANOVA in designs with more than two measurements per subject.
Table 2. One-way analysis of variance for the data in Table 1. Show/hide
We can use the sw to quantify the margin of error in our measurements. Thus, we can estimate that the difference between a specific measurement and the true value will not be greater than 1.96 times the sw in 95% of observations (assuming that the data follow a normal distribution, 95% of the measurements will be contained in the interval formed by the actual value plus and minus 1.96 times the standard deviation). It also allows us to estimate that the difference between two measurements for the same subject will not exceed 2.77 times the sw in 95% of observations.2,3 In our example, the sw is 0.54 (square root of 0.3), so the estimated difference from the true value would be of less than 1.05 (1.96 × 0.54) and the difference between two measurements would be of less than 1.49 (2.77 × 0.54).
Intraclass correlation coefficient
If only two measurements are taken per subject, the most intuitive way to compare them is to plot measurement pairs in a scatter diagram, assess whether there is a linear association between them, and calculate the corresponding correlation coefficient. Figure 1 shows the scatter diagram for the data in Table 1. The Pearson correlation coefficient (r) for these data is 0.97 (the closer r is to 1, the stronger the correlation).
Figure 1. Scatter plot and linear correlation for the data in Table 1. Show/hide
However, the presence of a strong linear association with a high correlation coefficient does not prove a strong agreement between the measurements, but only that the points in the plot fit a straight line well. The correlation coefficient is largely dependent on inter-subject variability and thus changes substantially based on the characteristics of the sample for which it is calculated, and is especially sensitive to the presence of extreme values. If one of the measurements is systematically greater than the other, the correlation coefficient will be very high, despite the fact that the measurements never agree. These pitfalls can be avoiding by using the intraclass correlation coefficient.
The intraclass correlation coefficient (ICC) estimates the agreement between two or more repeated measurements. The calculation of the ICC is based on a repeated measures ANOVA model, applying different formulas based on the design and objectives of the study.4 In the simplest scenario, we would estimate the variability of the measurements without taking into account the variability contributed by different raters (one-way random effects model). Choosing this model, and using the results of ANOVA, we can calculate the ICC with the following formula:
where k stands for the number of observations per subject, MSp for the mean square between patients (which depends on the differences in measurements between subjects) and MSr for the mean square of the residuals (which depends on the differences between repeated measurements in each subject).
Using the data of the ANOVA in Table 2, the ICC will be:
In our example, there is hardly any difference between the ICC and the Pearson correlation coefficient (r). If the ICC were much smaller than r, one would assume that there is a systematic change between one measurement and the other, which may result from a learning effect. In this case, the measurements would not have been made under the same circumstances, so the conditions required for performing a reliability analysis would not be met.5
Bland and Altman method
An alternative approach to analysing the agreement between two repeated observations measured on a continuous scale is the graphical method described by Bland and Altman.6 It consists of plotting the difference of each pair of measurements against the mean of the two measurements (Figure 2). The points tend to cluster around zero in the axis representing the difference between paired measurements, and the greater the dispersion around zero, the lesser the agreement between the two measurement methods. One possible way to assess agreement is to draw horizontal lines at the level of the maximum difference that would be acceptable from a clinical standpoint, and check whether the points, or most of the points, are grouped between these two horizontal lines. An alternative approach is to estimate the standard deviation of the differences and the interval in which we would expect to find 95% of them.
Figure 2. Bland and Altman method applied to the data in Table 1. Show/hide
This method can also be used to assess the magnitude of the differences and their association with the magnitude of the measurement. When the variability in the measurements is not constant, but changes as the magnitude of the measurement increases or decreases, the calculation becomes complicated.7 If there is a significant correlation between the differences and the means, the variability will not be constant (there may be an acceptable agreement in a specific value interval, but not in others). In this case, a logarithmic transformation of the data can be attempted, or else the variability can be analysed separately for various data intervals, although we should always hold reservations about the validity of measurements in these intervals.
Ochoa Sangrador C, Marugán Isabel VM, Tesoro González R, García Rivera MT, Hernández Calvo MT. Evaluación de un instrumento de medición de la bilirrubina transcutánea. An Esp Pediatr. 2000;52:561-8.
Bland JM, Altman DG. Measurement error. BMJ. 1996;312:1654.
Altman DG, Bland JM. Comparing several groups using analysis of variance. BMJ. 1996;312:1472.
Fleiss JL. The design and analysis of clinical experiments. New York: John Wiley & Sons 1986. p. 1-32.
Bland JM, Altman DG. Measurement error and correlation coefficients. BMJ. 1996;313:41-2.
Bland JM, Altman DG. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet. 1986;1:307-10.
Bland JM, Altman DG. Measurement error proportional to the mean. BMJ. 1996;313:106.


|The Revised Maclisp Manual||Page A-9|
There are three numeric datatypes in Maclisp: FIXNUM, FLONUM, and BIGNUM. Some functions which manipulate numbers may handle only one or two of these types. Check the documentation to be sure which kinds of numbers are acceptable.
Integers are broken into two classes in Maclisp: fixnums and bignums. The FIXP predicate returns true if its argument is either a fixnum or a bignum, and returns false otherwise.
Small integers are represented as fixed point binary numbers. Which integers are fixnums is a machine-dependent feature since word size varies between Maclisp implementations. The FIXNUMP predicate returns true iff its argument is a fixnum; it returns false for other kinds objects including flonums and bignums.
Integers whose magnitude is too large to be represented in a single machine word are called bignums. A bignum is an infinite-precision integer. It is impossible to get “overflow” in bignum arithmetic, since any integer can be represented by a bignum. However, fixnum and flonum arithmetic is faster than bignum arithmetic and requires less memory. The BIGP predicate returns true iff its argument is a bignum.
Non-integers (what some languages refer to as “real” numbers) are called flonums. They are also sometimes referred to as floating point numbers. They are represented internally as a base and an exponent according to the floating point storage strategy native to the hardware in any given implementation. Their precision and range of values is therefore machine dependent.
Integers (fixnums and flonums) are printed as a series of digits in the current output radix (controlled by the variable BASE). If the BASE is decimal and the value of the variable *NOPOINT is NIL, a decimal point is displayed as well to make it obvious that the output is decimal. If *NOPOINT is NIL and you don't see a period after an integer, then decimal output is not selected. For example, the number nine would be displayed as 11 in octal (Maclisp's default input and output radix); it would be displayed as 9 or 9. in decimal, depending on the setting of *NOPOINT; and it would be displayed as 21 in base four. A minus sign precedes negative integers; negative four is -4, for example.
Flonums are always displayed in decimal radix in spite of the setting of BASE. Flonums are displayed as at least one digit (frequently more than one), followed by a decimal point, followed by at least one digit. So the sequence 4.75 means four and three quarters. A minus sign, of course, will precede a negative number. Some flonums may be displayed in an alternate notation called “exponential form.” In this notation, the letter E follows the flonum and then an integer (with no decimal point) denoting the power of ten by which the flonum is to be multiplied. For example, 3.0E+5 and 300000.0 denote the same number.
To enter a number as input, you can basically just invert the printing technique described above. Note, however, that IBASE controls the default input radix and typing a decimal point after an integer forces decimal input regardless of the input radix. So, in base eight, the list (12 10.) contains two tens.
The EQ predicate is not guaranteed to return true for two numbers with the same sign and magnitude. It sometimes will, but frequently does not. When comparing two fixnums or two flonums, use the = predicate. When comparing two bignums, use EQUAL. When comparing numbers of differing datatypes for numerical equality, you must first coerce the numbers to be of the same datatype before calling EQUAL; otherwise, EQUAL will return NIL.
By the way, when dealing with very large flonums, it's worth noting that some flonums are too large to be able to accurately represent all their integral digits. On the PDP-10, to take an example, 1.0e+20 does not have 20 digits of accuracy. Hence, an operation like (ADD1 1.0e+20) will return 1.0e+20, which may confuse some algorithms if they are not expecting it.
Returns the largest integer less than or equal to its argument n. The argument, n, may be any type of number. The result will be a fixnum or bignum, depending on n's magnitude.
(fix 7.3) => 7
(fix -1.2) => -2
Returns the largest fixnum less than or equal to its argument, k, which must be a fixnum or flonum. For use when k is known to be small enough to be represented as a fixnum. When in doubt, use FIX.
(ifix 3.0E5) => 300000.
(ifix -250.3) => -251.
(ifix 5) => 5.
Returns the flonum equivalent of n. n may be any kind of number.
(float 4) => 4.0
Numerical Type Predicates
Predicate returns true if q is a number (fixnum, bignum, or flonum); otherwise returns false. q may be any kind of object.
Predicate returns true iff q is a fixnum; otherwise returns false. q may be any kind of object.
Predicate returns true if q is a bignum; otherwise returns false. q may be any kind of object.
Predicate returns true iff q is a flonum; otherwise returns false. q may be any kind of object.
|PLUS||Function||(PLUS n1 n2 ...)|
Plus returns the sum of its arguments, which may be any kind of numbers.
(PLUS) => 0 ;Identity Element
(PLUS 3) => 3 ;Trivial Case
(PLUS 1.0E+20 1)=> 1.0E+20 ;not always precise
|+||Function||(+ i1 i2 ...)|
Returns the sum of its arguments. The arguments must be fixnums and the result is always a fixnum. Overflow is ignored.
(+) => 0 ;identity element
(+ 3) => 3 ;trivial case
(+ 2 6 -1) => 7
|+$||Function||(+$ x1 x2 ...)|
Returns the sum of its arguments. The arguments must be flonums and the result is always a flonum.
(+$ 4.1 3.14) => 7.24
(+$ 2.0 1.5 -3.6) => -0.1
(+$ 2.6) => 2.6 ;trivial case
(+$) => 0.0 ;identity element
Exactly equivalent to (PLUS n 1).
Exactly equivalent to (+ i 1).
Exactly equivalent to (+$ x 1.0).
|DIFFERENCE||Function||(DIFFERENCE n1 n2 ...)|
Returns its n1 minus the rest of its arguments. It works for any kind of numbers.
(difference) => 0 ; identity element
(difference 5.3) => 5.3 ; identity operation
(difference 5.3 2) => 3.3 ; flonum arithmetic
(difference 9 2 3) => 4 ; fixnum arithmetic
Returns the negation of its argument, which can be any kind of number.
(minus 1) => -1
(minus -3.6) => 3.6
|-||Function||(- i1 i2 ...)|
This is the fixnum-only subtraction/negation function. Accepts and returns only fixnums.
(-) => 0 ;identity element
(- 5) => -5 ;argument negation
(- 5 3) => 2 ;subtraction
(- 8 4 3) => 1 ;repeated subtraction
|-$||Function||(-$ x1 x2 ...)|
This is the flonum-only subtraction/negation function. Accepts and returns only flonums.
(-$) => 0.0 ;identity element
(-$ 5.0) => -5.0 ;argument negation
(-$ 5.0 3.0) => 2.0 ;subtraction
(-$ 8.0 4.0 3.0) => 1.0 ;repeated subtraction
Exactly equivalent to (DIFFERENCE n 1).
Exactly equivalent to (- i 1).
Exactly equivalent to (-$ x 1).
|TIMES||Function||(TIMES n1 n2 ...)|
|*||Function||(* i1 i2 ...)|
Returns the product of its arguments. The arguments must be fixnums and the result is always a fixnum.
(*) => 1 ;identity element
(* 3) => 3 ;trivial case
(* 4 5 -6) => -120.
|*$||Function||(*$ x1 x2 ...)|
Returns the product of its arguments. The arguments must be flonums and the result is always a flonum.
(*$) => 1.0 ;identity element
(*$ 6.1) => 6.1 ;trivial case
(*$ 3.0 2.0 4.0) => 24.0
|EXPT||Function||(EXPT n j)|
n to the j power. The exponent j may be a bignum if the base n is 0, 1, or -1; otherwise j must be a fixnum. n may be any kind of number.
If j is a flonum, n is converted to floating point and the exponentiation is done using logarithms.
|^||Function||(^ i1 i2)|
Fast fixed point exponentiation; like EXPT but for the case where n1 and n2 are both known to be fixnums.
|^$||Function||(^$ x i)|
|QUOTIENT||Function||(QUOTIENT n1 n2 n3 ...)|
(quotient) => 1. ;identity element
(quotient 5) => 5. ;identity operation
(quotient 6.0 1.5 2.0) => 2.0
|REMAINDER||Function||(REMAINDER k1 k2)|
Returns k1 mod k2, the remainder of the division of k1 by k2. The sign of the remainder is the same as the sign of the dividend. The arguments must be fixnums or bignums.
Same as ln n, the natural log of n. The input may be any type of positive number (including a bignum) as long as it can be represented as a flonum. If (FLOAT n) would err, then so will (LOG n). The value returned will be a flonum.
(log 33.7) => 3.51749784
(log 5.0) => 1.60943791
(exp (log 5)) => 5.0
(log 2.71828184) => 1.0
(log 123456789123456789.) => 39.3546677
|DIVOV||Status Option||(STATUS DIVOV)|
If NIL, the default, create an error when either a division by zero occurs or a floating point overflow occurs in a bignum/flonum conversion. If T, no error occurs but an undefined result may be generated. This switch affects only closed coded calls to generic arithmetic functions (e.g., QUOTIENT). Calls to type specific operations (e.g., //) and calls to generic arithmetic functions which have been open coded due to compiler declarations are also unaffected; they never generate errors, so behave as if this switch were always set to T.
|DIVOV||SStatus Option||(SSTATUS DIVOV flag)|
With respect to the type-specific division functions, here are some points to remember:
* The name of these functions must be typed in as //, since Maclisp uses / as an escape character.
* The results of one-argument division and of division by zero are undefined. That case will not err and its results may frequently appear predictable, but meaningfulness of the results are not guaranteed. Those results are primarily determined by (though not defined by) the behavior of hardware in any given implementation.
|//||Function||(// i1 i2 ...)|
This is the fixnum-only division function.
(//) => 1 ;the identity element
|//$||Function||(//$ x1 x2 ...)|
This is the flonum-only division function.
(//$) => 1.0 ;the identity element
(//$ 2.0) => 0.5 ;the one-arg case is
(//$ 0.0) => 0.0 ; not well-defined.
(//$ 3.3 2.0) => 1.65 ;x/y
(//$ 3.3 2.0 2.0) => 0.825 ;(x/y)/z
|\||Function||(\ i1 i2)|
Returns the remainder of the division of i1 by i2, with the sign of i1. Both arguments are supposed to be fixnums. The interpreter currently allows bignum arguments to \ but this should not be relied upon, nor should it be expected to compile correctly with other than fixnum arguments.
Warning: There is a bug in the relation between interpreted and compiled versions of this function such that the pathological case (\ i 0) returns different results interpreted and compiled. This should probably be fixed sometime.
|EQUAL||Function||(EQUAL n1 n2)|
There is no function which will compare just two bignums specifically. However, EQUAL, among its other uses, can compare two bignums for numeric equality. In fact, EQUAL will return true for any two numbers as long as they are of the same datatype and have the same sign and magnitude. See the full description of EQUAL elsewhere in this manual.
|=||Function||(= k1 k2)|
Compares k1 and k2, returning true if k1 is numerically equal, or false otherwise. k1 and k2 may be either both fixnums or both flonums.
|GREATERP||Function||(GREATERP n1 n2 ...)|
Compares its arguments, which must be numbers, from left to right. If any argument is not greater than the next, returns NIL. But if the arguments are strictly decreasing, the result is T. Arguments may be any kind of number. The arguments need not all be of the same type.
|>||Function||(> k1 k2)|
|LESSP||Function||(LESSP n1 n2 ...)|
Compares its arguments, which must be numbers, from left to right. If any argument is not less than the next, returns NIL. But if the arguments are strictly increasing, the result is T. Arguments may be any kind of number. The arguments need not all be of the same type.
|<||Function||(< k1 k2)|
(GREATERP n 0)
(LESSP n 0)
Returns |n|, the absolute value of the number n.
|SIGNP||Special Form||(SIGNP c n)|
The SIGNP predicate can be used to test the sign of a number. Returns T if n's sign satisfies the test c, NIL if it does not. n is evaluated but c is not. n may be any kind of number; NIL will be returned if n is not a number. c can be one of the following:
|GCD||Function||(GCD k1 k2)|
Returns the greatest common divisor of k1 and k2. The arguments must be fixnums or bignums. If either k1 or k2 is 0, the other argument will be returned. The result will be a positive number except when both args are 0, in which case 0 is returned.
(GCD 5 3) => 1.
(GCD 15. 36.) => 3.
(GCD -13424. 80.) => 16.
(GCD 0 5) => 5.
(GCD -3 0) => 3.
(GCD 0 0) => 0.
|\\||Function||(\\ i1 i2)|
|MAX||Function||(MAX n1 n2 ...)|
Returns the largest of its arguments, which must be numbers. If any argument is floating point, the result will be floating point; else the result will be of the type of the largest argument.
|MIN||Function||(MIN n1 n2 ...)|
Returns the smallest of its arguments, which must be numbers. If any argument is floating point, the result will be floating point; else the result will be of the type of the largest argument.
|ATAN||Function||(ATAN k1 k2)|
Returns the trigonometric arctangent of k1/k2, in radians. k2 may be 0 as long as k1 is not also 0. k1 and k2 may be any kind of numbers. The answer is returned in the range 0 to 2 pi.
(ATAN 1.0 3.0) => 0.321750563
(ATAN 1.0 -3.0) => 2.8198421
(ATAN -1.0 3.0) => 5.9614348
(ATAN -1.0 -3.0) => 3.46334323
(ATAN 3.0 0.0) => 1.57079633
(ATAN 8.0 5.0) => 1.01219705
Returns the trigonometric cosine of k. k is a fixnum or flonum specification of radians.
(COS 1.0) => 0.540302314
(COS 3.0) => -0.98999251
(COS -3.0) => -0.98999251
(COS 5.0) => -0.95892429
(COS 8) => -0.145500086
Random Number Generator
If no argument is given, returns a random fixnum. If i is NIL, restarts the random sequence at its beginning. (RANDOM i), where i is a fixnum, returns a random fixnum between 0 and i-1 inclusive. For info on how to read and set the internal state of the generator, see documentation on (STATUS RANDOM ...) and (SSTATUS RANDOM ...).
|RANDOM||SStatus Option||(SSTATUS RANDOM seed)|
Controlling Math Operations
Notes about Declarations
Some functions, such as ABS, have no fixnum-only or flonum-only versions but still do not compile well in the absence of declarations. You can silence compiler warnings about inefficient compilations with
or, if efficiency matters, you can do appropriate declarations as in:
(DEFUN F1 (X Y) (DECLARE (FIXNUM X Y)) (> X (ABS Y))) (DEFUN F2 (X Y) (> (FIXNUM-IDENTITY X) (ABS (FIXNUM-IDENTITY Y))))
|The Revised Maclisp Manual (Sunday Morning Edition)|
Published Sunday, December 16, 2007 06:17am EST, and updated Sunday, July 6, 2008.


Trigonometry: A Practical Introduction presents an approach that involves the whole being of students so they develop clarity of thought and enthusiastic involvement in challenging, meaningful activities. The author advises that, when students work outdoors or are at at their desks measuring distances and angles, the topics being discussed are better understood.
- Right Triangle Calculations
- Oblique Triangle Calculations
- Problems in Surveying
- and many other helpful notes and suggestions.
About the Author
Harry Kretz taught high school math for many years at Hawthorn Valley Waldorf School in New York. Since retiring from full-time work, he has worked more than full time traveling to teach courses for a few weeks at a time in various Waldorf schools and in teacher training centers.


Adjusting items for sale as fractions or partial item sale is simple to do from the order screen.
To do a fraction or partial item sale, Click on the item/s in the guest check.
The edit item box will appear. Click on the Quantity field.
This function is typically used for restaurants that weigh items.
Enter the fractional or partial amount as a decimal and type 0 first. i.e. 0.5 or 0.25
Note: The price on the screen will NOT automatically adjust.
The item price will show the final updated sale price and decimal item amount on the guest check.


Pricing Analytics Manager/ Senior Manager
Reporting to the COO/CPO, the Growth Team seeks to identify and optimize growth strategies for the company through insights, analysis, experiments, and data. The projects the Pricing Analytics unit work on serve to establish, develop, and augment our core understanding of pricing in LINE MAN Wongnai, and provide an analytical framework for subsequent strategy and optimization. This role is focused on pricing optimization of our ads business and will operate under a matrix structure, reporting to the head of the Growth team, but also to the head of the Ads team.
• Build deep knowledge around LINE MAN Wongnai's merchant partners who advertise on our platform, particularly with regards to price sensitivity and elasticity
• Design an appropriate pricing strategy that maximises revenue and value for our partners using complex algorithmic and machine learning tools
• Design and develop modular automated data models/ analytic systems that integrate with existing data and analytic systems to support algorithmic price strategies
• Design and execute experiments and simulations to validate optimal pricing strategies and structures
• Consult on product development of the Ads platform to ensure compatibility with our pricing strategy
• A hacker's mindset – the ability to build simple but clever and elegant solutions to new problems within significant resource, operational and time constraints through deep understanding of the business, creative problem solving, and a wide range of expertise in data, analytics, automation, programming, and prototyping.
• A good understanding of statistics, computer science, and data, and the ability to implement this understanding in complex business situations.
• Experience with complex analytics and statistical/machine learning techniques using R/Python/Spark
• Ability to read, understand, and implement state of the art algorithms, approaches, and methods from conference papers or published research
• 4+ years of experience in data science, statistical or mathematical research, operations research, or complex data modelling/ analytics
• Master's degree in statistics, mathematics, operations research, or data science is preferred
• Familiarity with Markov-chain modelling, simulations, various forms of gradient-based optimization in Hilbert spaces and mathematical (convex) optimization is a plus
• Familiarity with price discovery methodologies and strategies is a plus
• Familiarity with bash scripting, server-side app development (Linux, CentOS), Apache Kafka, APIs, R shiny, or Python Dash is a plus


Multilevel Modeling of Hierarchical and Longitudinal Data Using SAS
This course teaches how to identify complex and dynamic patterns within multilevel data to inform a variety of decision-making needs. The course provides a conceptual understanding of multilevel linear models (MLM) and multilevel generalized linear models (MGLM) and their appropriate use in a variety of settings.
What it takes to earn this badge
The owner of this badge completed Multilevel Modeling of Hierarchical and Longitudinal Data Using SAS (BHLM42).
- View Additional Information ›


South Side Sox' Chris Getz Community Projection
|Avg + Std Dev||492||.286||.361||.418||39||20||135|
|Avg - 5%||384||.259||.324||.342||27||13||100|
|Avg - 2 Std Dev||227||.248||.301||.303||9||2||47|
Thanks to all who participated. The final projection uses 76 entries (after I removed 4-5 crazy-to-impossible entries), and came out much more realistic that I originally thought. Full spreadsheet of the data is available here.
Obviously, we have a bit of a bias when making these so I thought I'd do some PECOTA-style adjustments to our average to come up with a more well rounded picture. For an unbiased projection I simply subtracted 5% from each category (10% for SLG). Then I gave you a High and a LOW projection by adding or subtracting the standard deviation.


Calculator Plus 1.0Free
This program is a great utility for everyone, it is a better and complete version of the windows calculator.
This one has a lot of great mathematical and conversion functions which are not easy to find all in one program.
You can choose from three types of calculators:
-The standard that has the most common mathematical operations.
-The scientific that is for those who use more specific mathematical operations, such as sin, cos, log, tan, Exp. You can also choose from hexadecimal, decimal, octal or binary calculator.
-The conversion calculator. That is a calculator that converts between a large range of units and categories.
The categories supported are:
Area(square meters, square inches, square feets, cares, etc), Consumptions(liters/kilometers, liters/mile, etc.), Currencies(Euro, pound, frank, mark ), Energy(kilowatt hours, nutrition calories) Lengths(meters, inch, miles), Power(watts, horsepower), Pressure(bars, pascals), Temperature(Celsius, kelvin, fahrenheit), Velocity(knots, mach), Volume(liters, barrels), Weights(pounds, tons).
This calculator is a must have it is easy to install and to operate.
Download it and you wont regret!
- Easy ,
- Quick Launch


Pythagoras of Samos
(lived roughly 580-500 BC)
Pythagoras was born on the Greek island of Samos, which made
him a Samian.
By the way, another bright man born on this island was
Aristarchus of Samos. But we are 200 years ahead of ourselves.
Back to Pythagoras.
Pythagoras' strong suit was mathematics and philosophy. He went to
Crotone in southern Italy and started his own learning center.
And here you can find Crotone, Italy, on
the Google map (see red marker).
What is the Theorem of Pythagoras?
The Pythagorean theorem goes as follows
a2 + b2 = c2
In other words, the sum of the squares
on the legs of a right triangle is equal to the square of the hypotenuse. Algebra is
Euclid agreed and proofed the
theorem right by means of his windmill, you know it as Euclid's
First of all, pythagoreanism is a
wonderful word. Try to weave it into your conversation today.
Secondly, it was the big P's spiritual
inheritance; so much more than algebraic formulae, but rather a form
of religion. Transmigration of the soul, astronomy, mathematics in
music, numbers in everything, vegetarianism, and much more were covered in
the teacher's outline.
And of course there were disciples, the
There was another Pythagoras, a
sculptor, who was born roughly around the time of the death of the
philosopher Pythagoras of Samos.
About the Ancient


Disclaimer: This is the world of the trauma specialist. They know what they’re doing. This is only for general education purposes.
How To Calculate Burn Percentage
Here’s the general equation for calculating the percentage of body that has been burned.
Rule of 9s: 18 on back, 18 on front, 9 head, 9 arm, 9 leg; 18 child head
Once the percentage of body burned is calculated, another formula allows the clinician to calculate how much fluids will need to be replaced.
4 x SA x kg = ml NS, First 1/2 in 8H
Four times the surface area calculated by the rule of nines above
times the patient’s weight in kilograms…
Will yield the amount of cc of normal saline that needs to be replaced by IV.
The first half of that must be replaced in eight hours.


I was developing a website where people would place horse bets and the system should be able to calculate all the possible permutations based on the user selection. That means: finding all the possible combinations in a two dimensional array. I found a couple of functions but none of them would keep the array keys […]
Google started rolling the +1 button as an experimental version of Google Search. Today, the +1 button is available to everyone and this means that “you” as a webmaster can add the +1 button to your website and let people share on Google your content.


Poisson equations appear in many graphics settings including, but not limited to, physics-based fluid simulation. Numerical solvers for such problems strike context-specific memory, performance, stability and accuracy trade-offs. We propose a new Poisson filter-based solver that balances between the strengths of spectral and iterative methods. We derive universal Poisson kernels for forward and inverse Poisson problems, leveraging careful adaptive filter truncation to localize their extent, all while maintaining stability and accuracy. Iterative composition of our compact filters improves solver iteration time by orders-of-magnitude compared to optimized linear methods. While motivated by spectral formulations, we overcome important limitations of spectral methods while retaining many of their desirable properties. We focus on the application of our method to high-performance and high-fidelity fluid simulation, but we also demonstrate its broader applicability.


There is a common mistake for math students confusing and thinking that mathematical skills is overly the same as the mathematical concepts. Basically, skills and concepts are two different things are always working together. The only way to embrace math education and challenges is having an indispensable understanding of how basic math concepts and skills work together. First and foremost, you need to discover more on what math skills are and what math concepts are. Math skills are mastered actions. The only way to progress your math skills is through regular and gradual practicing. Math concepts are the mathematical ideas. It is fundamental for a mathematician to understand these concepts or rather theories articulately. These mathematical theories are learned. Throughout this article, you will come across reliable info about the relationship between math theories and math skills.
It is through focusing on skills that mathematical training becomes effective. Therefore, a teacher will always test your skills through examinations as they ask you to handle a particular mathematical question through using certain concepts. Your skills help determine whether you are capable of applying the learned math concepts. Basically, it necessitates a high level of competence and skills to help the teacher understand and acknowledge that you comprehend these math concepts.
Generally, you can reserve and acknowledge all mathematical theories or concepts but this can never be said about the skills as you can lose them at any time. Well, it requires a high level of competence to keep skills. You get to sharpen your abilities through regular practicing. The time you practice your skills, you will always elevate and enhance your math theories understanding. This skill will weaken and disappear where you fail to practice them regularly. Concepts are a little bit different as where you understand one, you will understand it forever.
Mathematical abilities and actions are gradual or progressive and so are the mathematical theories. The very moment you learn new mathematical perceptions is the very moment you will advance and elevate your skills. Your brain is always bready tom embrace and accommodate any new info that you have been enrolled to. Therefore, your understanding for these concepts tends to sharpen and so will your skills.
the last but not the least, basic math skills and concepts are helpful in excelling through your education. It is essential and chief how mathematical skills and concepts help you excel mathematically. It is through skills that you manage to understand how to handle certain mathematical challenges. It is possible to be aware of BODMAS theory but where you lack skills of multiplying and division, you might miss the whole point.
It necessitates that you fathom all the math concepts and skills alluringly. You can never upgrade or enhance your math skills without first learning the math concepts. It is alluringly imperative that you acquire more info about the relationship between math skills and concepts.


In the world of transport, a weight is not just a weight, or a pallet just a pallet. Here is a small overview of what Freight calculation weight or rather payweight is, and how you can recalculate the weight of your shipment. The payweight is the weight that is used, among others, to find the correct price for the shipment.
Firstly you need to find out if the goods measure more than they weigh
Firstly you must find out if the goods measurements exceeds the weight. Voluminous cargo is either cubic meters/m3 or loading meters/LDM. Loading meter goods (LDM) equals goods that cannot be combined and is non stackable. E.g. goods can be damaged if we load other goods on top, cannot double stack the pallets or dangerous goods. 1 EUR pallet = 0.4 LM.
Cubic meter (m3) is calculated when the goods can be placed on top of other shipments when the weight is low. Calculating CBM can be done by measuring: length x width x height. 1 m3 = 333 kg.
|Scandinavia||1 ldm = 2000 kgs||1 pallet = 800 kgs||1,20 m length * 0,8 m width|
|Europe||1 ldm = 1850 kgs||1 pallet = 740 kg||1,20 m length * 0,8 m width|
|Seapallet||1 pallet = 1000 kgs||1,20 m length * 1,00 m width|
|Seapallet||1 pallet = 1200 kgs||1,20 m length * 1,20 m width|


Cultural Aff. Sec.
This page is temporarily avalable in persian.
To visit the page in persian click
Dr. Ali Foroush Bastani , bastani[at]iasbs.ac.ir
Room: 118 Mathematics Building
Farzaneh Zamanlou , zamanlou[at]iasbs.ac.ir
Room: 119 Mathematics Building
(Head of Section)
To study in a high quality center with a
scientific, friendly atmosphere and wide international connections? Apply to the IASBS.
Developed by the IASBS Computer Center


Greetings Year 3 from Mr Hussain and Mrs Robinson
You can find a selection of work set on Purple Mash under the 2DO icon at the top of the Purple Mash homepage. Some of the activities have an option for me to feedback so be sure to check back.
We have also allocated a variety of maths tasks to extend your leaning on Active Learn.
Log on to the TT Rockstars you will find set timetables.
If you need to contact me please email firstname.lastname@example.org.


Regent Admission Index
The Regent Admission Index (RAI) combines four factors that strongly predict success at Iowa's regent universities: ACT score (or SAT equivalent), high school percentile rank, high school grade-point average (GPA), and the number of high school courses completed in core subject areas.
How is the RAI Used?
A student's RAI score is used for admission to the College of Liberal Arts and Sciences and is one of the criteria used for admission to the College of Engineering. It also is used in awarding some University of Iowa scholarships.
How to Calculate Your RAI:
2 x ACT Composite Score (or the SAT Equivalent)
1 x High School Percentile Rank
20 x High School GPA
5 x Number of Core Courses Completed
by High School Graduation
Online RAI Calculator
Let us do the math to Compute Your Unofficial RAI Score.
Which Core Courses Count in the RAI?
Any college-prep course in English, mathematics, science, social studies, and world language can be used in calculating a student’s RAI score. To be considered for admission, students must have taken (or plan to take) at least 15 college-prep courses (full-year) including the following:
- 4 years of English
- 3 years of mathematics, including Algebra I, Algebra II, and geometry (Engineering requires a 4th year of mathematics)
- 3 years of social studies (Engineering requires only 2 years)
- 2 years of the same world language
- 3 years of science, including one year from two of these areas: biology, chemistry, and physics; and a third year from any science area.
All other courses in these areas (above and beyond those required for admission), can be used in calculating the RAI. High school counselors can help students and parents determine which courses qualify as “college-prep” or students can call the Office of Admissions.
How to Calculate Your Percentile Rank
To calculate your percentile rank, subtract your position in your high school class from the number of students in that class, divide the resulting number by the number of students in your class, and multiply by 100. The Online RAI Calculator can compute this for you.
If Your High School Does Not Rank
If your high school does not rank, you will not be able to calculate an RAI score. We will base our admission decision on your GPA, ACT and/or SAT test scores, and high school courses.


The 2:1 Ratio is a geometric relationship which describes the allowable working space of plain bearings. It is the “Binding Ratio”, which is officially defined as the maximum ratio of moment arm distance to bearing length that will not bind (prevent motion). Since the 2:1 Ratio was first introduced to the marketplace by PBC Linear (originally Pacific Bearing Company) in the 1990’s, it has been quickly adapted by most self-lubricating, linear plain bearing manufacturers as one of the guiding principles regarding their use.
When a force is applied to a bearing at some distance away from the center of the bearing, a moment force is created. In order to resist the moment, two resulting forces are created at each end of the bearing. When these resulting forces are multiplied by the Coefficient of Friction, a drag force is created. At some point the drag force will surpass the drive force and motion will cease.
Within the Demystifying the 2:1 Ratio and the Stick-Slip Phenomenon white paper, we explain the importance of the 2:1 ratio as well as practical complications, limitations & troubleshooting. After reading this white paper, you should have a clearer understanding of the mathematics behind the 2:1 rule and a better comprehension of how to implement it.
Additional related content and downloads:


Rayquander Posted June 5, 2019 Share Posted June 5, 2019 Cactus farm is a very good starting farms for starters in skyblock, and then followed by IronGolem farm (which is not recommended to make atm because of low spawn rate) The randomtickspeed is different than your normal singleplayer's randomtickSpeed, therefore cactus grows faster in this server. But to get 10k cactus, you will need a certain amount of cactus in your farm. According to minecraft gamepedia, a cactus grow with an average of 18minutes. Therefore, to get 1 cactus per minute, you will need 18 cactus in your farm: and 1 stack of cactus for 64 minutes. 1 cactus per second need 18*60 = 1080 cactus in your farm. At one cactus per second , you fill one slot of a dub every 64 seconds, to fill an entire dub it would take 54(slot of dub chest) *64= 3456 seconds or 57.6 minutes, roughly 10k per hour. How much cactus would be needed to make 10k per minute? Per second? To get 10k/minute, if we round 57.6 up to 60 , then we can multiply 1080*60 =64,800 cactus Then just multiply 64,800*60= 3,888,000 cactus to get 10k per second. Afking one chunk with every alternate block as cactus then divided by 2 for the blanks rows needed for cactus to fall. A chunk is 16*16*256=65,536 blocks dividing it by 2 for alternate blocks and 2 again for the rows gets 65,536/4 =16384 , enough to get roughly 10k cactus every 4 minutes for a whole chunk cactus farm, 4 chunks needed for around 10k a minute and 240 chunk cactus farm (60*4) for 10k per second This calculation is not originally from me but i would like to share this to everybody, hope it will help in your island. Source: https://desteria.com/community/threads/cactus-farm-math.86084/ Link to comment Share on other sites
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MATH in the News
The next time you take a walk through the garden or the park, take a closer look at the plants and rocks around you. You might find a spider hiding in plain sight! A spider that looks remarkably like a leaf has been discovered in the forests of Yunnan province in southwestern China...
Each issue has a wealth of online resources. Here’s a FREE sample of some of the additional activities you get with your subscription:
Trying to find the value of an angle in a polygon? This month’s instructional video shows how to find the interior angle sums of different shapes.
In these printable PDFs, students will calculate the interior angles of various shapes and learn how to use the triangulation method to find the sum of any regular polygon’s interior angles.


What a fantastic first week we have had in Saplings. The children have settled in so well and we are extremely proud of each child and their eagerness to learn.
The children have all been showing us how well they know their numbers and whether they are able to write their own name! If you have a chance this weekend perhaps you could have a practice of these skills at home.
We are all looking forward to getting stuck in next week and hope that everyone gets a really good rest this weekend ready for another busy week ahead.


We’re tipping the scales, not from the extra candy that’s begun showing up but with DATA! Numerical Scales allow you to get great quantitative feedback for those on your team who are more… by the numbers.
Here’s how to get feedback from your numerical scales that’ll have your team on cloud nine:
Find the major key! The first thing to do when asking a numerical scale question is ensuring your participants know exactly how they are scoring an experience. They’ll definitely need to know what metric is being tested, whether it be Difficulty, Interest, or Usefulness, as well as which side of the scale represent the ends of the spectrum.
Establish a Net Promoter Score. A popular use of 0 to 10 numerical scales is through an NPS test. This tells you how likely a consumer is to recommend your product or service to a friend. Helio provides the specific Net Promoter Score on all our numerical scales so you don’t have to do the math yourself!
Mix match for greater value. Single survey questions can be useful, though they’re not all that powerful on their own. Compare your numerical scale feedback with other survey data to understand the difference between what someone says and what they do. For instance, we might bring someone through an experience using click tests to understand where they would take action, and then follow up with a numerical scale to determine how interested they were in certain features.
Using numerical scales isn’t all 6’s and 7’s, they’re a fantastic way to get quick feedback from your users! They’re super useful for gathering quantitative feedback, and become even more powerful when you use Helio followup questions to get coinciding qualitative data. The next time you need some quantitative feedback, fast, give Numeric Scales a go!
Check out our survey below to see how we set up our Numerical Scales!


Press Brake Operator
Corry, PA 16407
We have a great job opportunity for a Local Manufacturing company for an entry level Press Brake Operator 1st and 2nd shift. Press Brake Operators work per the project design using the press brake to make precise bends or punches along with being able to properly set-up the machine according to the correct program. Our Press Brake Operators also possess good math skills, problem solving skills, technical & mechanical acumen, and have a strong understanding of how schematics work. Ability to read micrometers, dial calipers, squares, etc.


Sudbury iAchieve Tuition Centre – Maths & English (Tudor Primary)
Welcome to the Sudbury iAchieve Centre – Maths and English! Tudor Primary.
iAchieve has a proven track record of delivering high quality, private tutoring in maths and English, raising attainment and building confidence. We plan individually for each child and our group sizes never exceed 6. Students join iAchieve for a variety of reasons. Some may have fallen behind in maths and/or English and just need that extra bit of help to ‘close the gap’ and build confidence. Others are high achievers who want to be extended in their chosen area of study, perhaps with a view to moving on to our specific iAchieve 11+ Programme. Whatever your child’s reason for joining, you can be assured of a warm welcome from our exceptional tutors!
The iAchieve Maths & English Tuition Centre, Sudbury is located within Tudor Primary School and is open to children and young people from Sudbury and the surrounding areas. The centre is adjacent to The Ormiston Academy and is easily accessed via the A131.
We are able to offer the Sudbury iAchieve Maths & English Programme on both a Term Time or Full Year basis. However, students should note that holiday sessions are currently delivered at Essex University in Colchester. Double Sessions are available at a discounted price, with students attending the nearby St. Gregory’s Tuition Centre for their second weekly session.
Term Time Single Session 1 hour a week x 37 weeks (£53.95 per month)
Term Time Double Session 2 hours a week x 37 weeks (£97.10 per month — 10% discount applied to both sessions)
Full Year Single Session 1 hour a week x 50 weeks (£72.95 per month)
Full Year Double Session 2 hours a week x 50 weeks (£131.25 per month – 10% discount applied to both sessions)
(School holiday sessions are delivered at Essex University)
Click below to secure your child’s place, or add their name to the iAchieve Waiting List if your preferred session is sold out. If you wish to find a centre that operates on a different day of the week why not visit the iAchieve Maths and English map (HERE) where you can click on each pin to see opening days?
If you would like to talk to a member of our team, before booking, please call Learning Academies on 0845 463 1342 or email firstname.lastname@example.org.
We look forward to working alongside your child and maximising their chance of success.
Where we areSudbury iAchieve Tuition Centre – Maths & English (Tudor Primary)
- Tudor Primary School,
7 Mount View,
- Download Calendar
Thursdays 3.15 - 4.15pm at the Sudbury iAchieve Tuition Centre – Maths & English (Tudor Primary)
Fill in the form below to register for the Sudbury iAchieve Tuition Centre – Maths & English (Tudor Primary) Maths & English Course (£30.00 registration fee).


You could just fill up your jars but you want to make sure that you have enough for each person to share! This will mean filling up your jars part way through your event sometimes, the extra lollies that you have can usually be easily stored under the table.
Don't forget it is very important that you work out roughly how many lollies will fit in the containers that you give your guests so that you order enough. Usually, the guests will fill them all the way up to the top so it is best to know how much this will be.
An easy guide is to work out the volume of water that your containers will hold. For each 100ml of water they hold you will need just under 100g of
candy depending on the type. For example if your container holds 2.4 litres of water then you will need about 2 kg of lollies. (Obviously, the candy weight and size will change this. eg: Marshmallows are much bigger than mini jelly beans but weigh a lot less.)
Depending on your guests we recommend you plan on 150 to 300gm of lollies per person.
The easiest way to estimate how much you will need to fill your containers is to buy a small quantity of the product (many of our products can be bought from us in small 250 Gm bags) or buy a similar sized product from a supermarket and measure how much you would need from this small bag.
Or you could try the following:
This is very difficult to estimate without actually filling a jar with the lollies of your choice however, you could use the following information to make an educated guess. Remember that ml is a liquid measurement & Gm is a weight.
1. Fill your jar or container with water from a measuring jug to work how much water it will hold in Millilitres. (ml)
2. Use the following approximate figures to help you:
Choc Buttons 95 - 100 pieces per 100 Gm (approx 95 - 100 Gm per 100 ml)
Bon Petite 120 pieces per 100 Gm (approx 73 Gm per 100 ml)
Mini Jelly Beans 73 pieces per 100 Gm (approx 103 Gm per 100 ml)
Choc Buds & Freckles 30 Pieces per 100 Gm (approx 61 Gm per 100 ml)
Gummi Bears 42 pieces per 100 Gm (approx 75 Gm per 100 ml)
Mini Musk Sticks 33 pieces per 100 Gm (approx 50 Gm per 100 ml)
Please note that these estimates are approximate only but they should be pretty close.


Hit the button games math
Hit the button games math
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Dr. Deepa Bevinagidad
- Department: Mathematics
- Designation: Associate Professor
- Phone: 9481682555
- Teaching Experience: 12 Years
- Industry Experience: NIL
- Research Experience: 6.0 Years
No Research Details Found.
No Awards Details Found.
Grants Received Research/Projects Guided (Beyond Academic)
No Grants Details Found.
No. of International Journals Publications:1
Some properties of Cycle graphs in " The Annals pf pure and applied Mathematics"
No. of National Journals Publications:1
Cycle complete Graphs "Journal of Computer & Mathematical Sciences"
No International Conferences Found.
No. of National Conferences :4
1. Skill Development and Entrepreneurship
2. Annual Conference of Ramanujan Mathematical Society
3. Algorithms, Computing, Graph Theory and Combinatorics
4. Make in India - An Opportunity for Emerging Engineering Technologies
Workshop / Seminars
1. Mathematics for Science, Engineering & Polytechnic Lectures.
2. School on Graph Algorithm.
3. PDE And its applications.
4. Faculty Development Programme on "Innovative Teaching Methodologies".
5. Symposium on "Advances in Graph Theory"
6. Faculty Development Programming
7. National Seminar on Analysis and Applications.
8. Recent Trends in Mathematics and its Applications.
9. Faculty Development Programming
10. Effective Teaching
11. Workshop on Research Methodology
12. Mathematical and Computational Applications in Engineering
13. Lean Manufacturing and Process Improvement
14. Workshop on Engineering Mathematics- IV
15. Two-day Workshop on Graph Theory and its Applications for Scientists, Engineers, and Mathematicians
16. Three days Workshop on "Image Processing and its Applications".
17. Recent Trends in Mathematics
18. Workshop on "New Model Curriculum
19. Pedagogy for Engineering Faculty
20. Intellectual Property Rights
Projects and Exhibitions
No Projects and Exhibitions Details Found.
No Other Activities Details Found.


My maths - cool math games with cars
Learning Math Is More Fun With These Cool Math Car Games
Math is one of the most important subjects. It is the only subject that you use throughout your life. No one can escape learning math, especially in their school years. Though there are a few who love the subject, majority of the kids hate it with all their heart. Consequently, parents and teachers find different ways to increase the kids' interest in the subject. While home-made math games held appeal in the earlier days, cool math games played in the computer have taken precedence today.
Anything and everything is possible on the internet, and making math a fun subject for learning also comes under it. There are a lot of cool math games in the arcade games site. They have a separate category for themselves in most sites. The main advantage with these cool math games is that they are completely free. Another advantage is that you need not download them in order to play them.
The words “homework” and “studying” may not hold much appeal to a child, but the word “games” will definitely make their ears perk up. Is your child week at math? Maybe, he or she has problems in trigonometry alone? Whatever be the case, a cool math games site is your destination. Children will consider math games on par with their other computer games. So, they will think they are getting extra play time. Without realizing it, they'll learn their most hated subject.
These my maths games are usually flash games, and it might take some time to load them,but not too much if your internet connection is a good one. You or your child doesn't have to register at the my math game category. Click on the category, click play, and start playing; it's as simple as that. Most math car games involve levels. The levels are either in the number wise order; or in the easy, medium and tough order. This level system allows them to gradually improve.
If teachers involve these cool math games in their class activities, kids will definitely pay more attention. They can create a competition like environment. Every child likes competing on video games. So, kids will do their best to beat their classmates, and in the mean time, every kid learns the concept.
Parents are always worried when their children play computer games. It involves a high level of stress; the wastage of time is another cause for worry. With these cool math games, both the parents and children get what they want. Time counters give the excitement every child craves in a game. Parents can sit with their children and guide their children in playing these games, especially if they are in kinder-garden or elementary school. In this way, parent-child bonding can also take place.
So, how to find these cool math games? It's very simple. The internet is littered with arcade sites that offer free car math games. There are also some game sites which are built especially for math games. Search in any search engine, and pick a site that you like the best. There are also some sites that provide fun tutorials and assignments along with games. You might think that assignments would create a school environment, but they are designed in such a way that, they are not totally school-like.


If you want to get the difference between dates or time values, then you first need to get the values in the same format. The best way is to convert both dates into Unix timestamp format. In this case, the date and time information is stored as an integer so we can calculate the difference easily. You can get the Unix timestamp in various ways as you can see below:
<?php // Get current time $date1 = time(); // Get the timestamp of 2006 October 20 $date2 = mktime(0,0,0,10,20,2006); ?>
Now as you have the values getting the difference is quite easy. However the result will be an integer value, but you probably want to get it in days, hours, and minutes. To do so we need to convert back our int value into a usable date format. We know that the difference is in seconds so we can get how many full days it is. To get it we use the following code:
<?php $dateDiff = $date1 - $date2; $fullDays = floor($dateDiff/(60*60*24)); echo "Differernce is $fullDays days"; ?>
We used the floor function as we want to get only the complete days. Besides this, the 60*60*24 represents that a day has 24 hours and each hour has 60 minutes and each minute has 60 seconds.
As the next step, we need to get how many hours are still present in the remaining seconds. So from the original difference, we need to remove the complete days in seconds, and from the remaining value, we can calculate the full hours similar to as we calculated the full days. Repeating these steps for minutes as well at the end we get the difference between the original dates. The complete calculation looks like this:
<?php $dateDiff = $date1 - $date2; $fullDays = floor($dateDiff/(60*60*24)); $fullHours = floor(($dateDiff-($fullDays*60*60*24))/(60*60)); $fullMinutes = floor(($dateDiff-($fullDays*60*60*24)-($fullHours*60*60))/60); echo "Differernce is $fullDays days, $fullHours hours and $fullMinutes minutes."; ?>


I am a PhD student at Inria Rennes--Bretagne Atlantique under the supervision of Yannis Avrithis and Guillaume Gravier. I am part of the Linkmedia team which seeks to develop methodological, technological and scientific foundations to create, describe and exploit explicit links within multimedia collections on a large scale.
My research focuses on computer vision tasks; I study methods to go towards less supervision in visual learning. In particular I have worked on classification, detection and retrieval tasks. I am interested in image representation and context modeling, and machine learning in general.
I received my engineering diploma from Enseirb-Matmeca in 2015 and a MS degree in Statistics from Paul Sabatier University in 2016. I was lucky to discover several research fields in mathematics through internships during my studies; I worked on algebra and automatic differentiation with Prof. Griewank in Humboldt University (Berlin, Germany), on statistical analysis with Dr. Selvarajoo in the Institute for Advanced Biosciences Keio (Tsuruoka, Japan) and on object recognition algorithms with Dr. Herbin at Onera (Paris, France).