Overview of exam results
GCSE results 2017
66% of students gained a grade 4 or higher in both English and Maths.
In English 74% of students gained a 4 or higher.
In maths 76% of students gained a 4 or higher.
20% of all GCSE grades were awarded at A*/A.
In Chemistry 66% of grades were at A*/A. In Art 42% of grades were at A*/A.
There were some notable high achievers in this year’s results. Abbey gained the equivalent of 10 A* grades closely followed by Mahil and Robert with 8 A*s and Jenna with 7 grades at A*.
Headteacher Sam Griffin said “These are an impressive set of results for this year group. I am delighted to see so many students doing so well. I would like to congratulate all of students on their achievements and to thank their staff and parents for their ongoing support. We are looking forward to welcoming students back into our Sixth Form at the start of term.”
The latest official DfE performance tables for the school's GCSE results can be found here.
A level results 2018
We are delighted to have received another strong set of A Level results, particularly with over half of all grades at A*, A and B, and a quarter of grades at A*A! These results have enabled the vast majority of our students to progress to the university courses of their choice. Individual successes at the school include 12 students with straight A*A grades (or equivalent), with two of these students being awarded straight A* grades. Maths, Chemistry and Sport students have also performed particularly well, with over 50% of grades in these subjects at A*A or equivalent.


There are multiple functions and characteristics of logarithms and exponentials, which are highly essential to understand for the students pursuing Mathematics courses in Australia. They also need to understand all the properties of both logarithms and exponentials to solve typical problems. So, if you think writing assignment is not smooth sailing, then logarithms and exponentials assignment help from My Assignment Services will be appropriate for you.
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The concepts of logarithms and exponentials are crucial for Algebra, and the formulas are also essential for various scientific calculations and current-day applications. Invented by John Napier in 1614, logarithms primarily combine two Greek words, such as ‘logos’ and ‘arithmos.’ It is used in different mathematical calculations to represent the apparent level of variable quantities electromagnetic field strength, sound intensity, and more. If a, x and y are three real numbers, then as per the below equation X=ay,
we can represent them in logarithmic expression with base a of the logarithm of x such as
loga x = y
a logarithm is primarily the inverse function to exponentiation, and it is widely used by scientists, engineers, and navigators to conduct high-accuracy computations with precision. There are two types of logarithms used, such as common logarithm, which is also known as the base 10 logarithm, and natural logarithm and known as base e logarithm.
On the other hand, an exponential is an expression about the exponent. It involves a variable in an exponent 10x. Logarithms are the opposite of exponentials as division is the opposite of multiplications, or we can also say logarithms are the inverse of exponentials.
We can portray the relationship between exponential and logarithms with the following equation.
Y=bx is equivalent to logb(y) = x
The logarithmic function y = logax is equivalent to the exponential equation x = ay . y = logax where x = ay & a> 0 a≠1
On the other hand, if we consider the inverse of the above equation, then x = ay, and here y equals to logax. So, we can say logarithm is nothing more than an exponent, and we can also simplify an exponent as the number of times it is used in a multiplication. It is written as exp(x) or ex. we can also define a exponential function as y = ex dy/dx = ex
The exponentials functions carry essential weightage in the field of mathematics and calculation. It is also used in all the real-world applications like population growth & falloff, and more.
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Logarithms are used to calculate the magnitude of an earthquake on a logarithmic scale; the Richter Scale uses logarithmic formula such as M= log10 A + B adhere A is the amplitude and B is the distance correction which is calculated by the Seismograph. A logarithm is also used to measure sound in decibels, but in a logarithmic scale, it is calculated as dB = 10 log10 (p X 1012. In this p is the sound pressure.
Logarithms mainly minimize the time required for multiplying numbers with higher digits; it simplifies the log and complex calculations. It makes not only the scientific calculations but also real-life solutions relatively easier.
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Fibonacci Retracement Levels – Bitcoin and Altcoin Trading
A Tool For Price Target Estimations in Crypto Trading
One of the most important tools for analyzing charts are the famous Fibonacci levels. Pretty much every trader uses them, and that’s probably the reason why they are so powerful.
Fibonacci retracement levels are a tool which help in estimating possible trade entries or exits.
The Fibonacci numbers come from a mathematician named Leonardo Fibonacci, who lived in the 13th century. Within the numerical sequence of those numbers, each number is about 1.618 times greater than the one before. The calculation has to do with the famous ‘golden ratio’, which is known from mathematics as the divine proportion.
To keep it simple and not waste time, let’s skip the formula explaining how he came to that number and let’s just learn the levels and how to use them for trading.
In general terms, the Fibonacci levels are key levels for potential price reversal areas, or key levels of resistance and support. These levels are 23.6%, 38.2%, 50%, 61.8% and 100% of a move, which are measured with the Fibonacci tool. Additionally, there are extended Fib levels beyond the measured move, which can be used to estimate future levels above or below.
So, when using this tool, those levels appear as a layer over your chart. Price is automatically calculated for the levels.
How Exactly To Use Fibonacci Levels
Measuring an upward movement:
So the measurement goes from the lows at the “1” up to the highs at the “0” – using the tool from lows to highs will show us the retracements back down. First price moved down precisely to 0.382 (38.2%). You see how price also hit the 0.618 and the 0.786 levels clearly and how it had built a channel between those levels for about 2 days till it broke further down.
Measuring a downward movement:
Using the tool from highs to lows will show the retracement levels on the way back upwards.
What those retracement lines tell you, is at what price levels you should pay particular attention to. So, of course, you cannot know in advance if price will hit the 50% or 61.8% mark. However, you can use those levels for exits or to put your stop loss orders below them.
Depending on your entry price, you could already take profit at the 50% Fibonacci level, if that would already be, for example, a 15% profit area for you, depending on your entry. Skilled traders use position sizing as a hedging strategy to lock in secure partial profits earlier, then they look for possible higher gains for the rest of their position.
Chart images: © tradingview.com


How Much Math Do You Need for Computer Science?
Mathematics is an essential element in the field of computer science and plays a vital role in various areas within the discipline. Whether you are interested in coding, algorithms, data analysis, or artificial intelligence, a solid understanding of math concepts is crucial for success.
Foundational Math Skills
At the very least, computer science students should have a strong foundation in basic math skills. This includes a solid understanding of arithmetic, algebra, and geometry. These fundamental areas of math provide the building blocks for more advanced concepts, making them essential for any aspiring computer scientist.
Arithmetic (basic calculations like addition, subtraction, multiplication, and division) is essential for understanding the basics of coding and algorithms. Algebra helps students develop problem-solving skills and logical thinking, which are crucial for writing efficient and optimized code. Geometry, on the other hand, is necessary for understanding concepts related to geometric algorithms, computer graphics, and visualization.
Discrete mathematics is an area of math that focuses on countable and distinct elements, and it is highly relevant to computer science. It covers topics such as set theory, logic, graph theory, combinatorics, and probability theory. These concepts help computer scientists understand and analyze algorithms, data structures, and cryptography.
Set theory provides a foundation for understanding data structures like sets, arrays, and trees. Logic is essential for designing and analyzing the correctness of algorithms. Graph theory helps in understanding and optimizing network algorithms and data relationships. Combinatorics plays a role in analyzing the efficiency of searching and sorting algorithms. Probability theory is crucial for machine learning algorithms and artificial intelligence tasks that involve uncertainty and randomness.
Calculus and Continuous Mathematics
While not every computer science student may need to delve deeply into calculus, having a basic understanding of calculus and continuous mathematics can be beneficial, especially for certain areas within computer science.
Calculus helps computer scientists understand concepts such as optimization, approximation, and continuous change over time. It is particularly important in areas like machine learning, data analysis, and computer graphics. A solid foundation in calculus allows computer scientists to develop and optimize algorithms for complex computational problems.
Linear algebra is another important branch of math that is highly applicable to computer science. It deals with systems of linear equations, vectors, and matrices. Linear algebra is widely used in diverse areas such as computer graphics, cryptography, data compression, and machine learning.
Understanding linear algebra allows computer scientists to manipulate and analyze large data sets, apply transformations to graphical objects, optimize algorithms, and solve systems of equations efficiently.
Mathematics forms a strong foundation for computer science and is integral to many areas within the field. While the level of math required may vary depending on the specific area of focus, having a solid understanding of arithmetic, algebra, discrete mathematics, calculus, and linear algebra is crucial for success in computer science.
By mastering these math concepts, computer scientists can develop efficient algorithms, design robust systems, analyze data effectively, and explore the frontiers of artificial intelligence. So, embrace math as you embark on your computer science journey and unlock the immense possibilities it offers.
Foundational Mathematical Concepts
A solid foundation in discrete mathematics, including sets, logic, and algorithms, is essential for tackling computer science problems effectively. Discrete mathematics provides the logical framework and tools required to understand the fundamental principles of computer science and programming.
One of the key components of discrete mathematics is understanding sets. In computer science, sets are used to organize and categorize data. They are particularly useful when dealing with large amounts of information. For example, in a database, sets can be used to represent a collection of records or entities. Understanding concepts such as unions, intersections, and complements of sets is crucial for efficiently manipulating and analyzing data.
Logic is another important aspect of discrete mathematics. It provides the foundation for creating and evaluating logical statements, which are fundamental in computer science. Logic helps identify patterns, make deductions, and reason through complex problems. It allows computer scientists to construct solid and reliable arguments, which are essential for designing algorithms and creating robust software.
Algorithms form the backbone of computer science. These step-by-step procedures are used to solve problems and perform computations. To effectively design and analyze algorithms, a strong understanding of mathematical concepts is necessary. This includes grasping concepts such as efficiency and complexity, which are directly related to the mathematical representation and analysis of algorithms. By understanding these concepts, computer scientists can create efficient and optimized algorithms to solve problems in the most effective manner.
Additionally, a strong foundation in discrete mathematics helps develop critical thinking skills, which are essential in computer science. The ability to break down a problem, analyze its components, and devise a solution is crucial when working with complex algorithms and systems. Discrete mathematics provides the necessary tools and techniques to approach problems logically and systematically.
In summary, a solid understanding of the foundational mathematical concepts in discrete mathematics is crucial for computer scientists. Sets, logic, and algorithms are at the heart of computer science, and a strong foundation in these areas is necessary for tackling complex problems and creating efficient solutions. By developing a solid mathematical foundation, computer scientists can effectively navigate the ever-changing landscape of technology and contribute to advancements in the field.
Calculus and Analysis
A basic understanding of calculus, particularly differential calculus and sequences, is useful for analyzing algorithms and computational complexity. Calculus is a branch of mathematics that deals with the study of change, particularly of functions and their rates of change. It helps in understanding how quantities change over time or space.
In computer science, calculus is particularly important for analyzing algorithms and computational complexity. Algorithms are step-by-step procedures used for solving a problem, and understanding their efficiency is crucial for developing efficient programs. Computational complexity, on the other hand, deals with measuring the resources required to execute an algorithm, such as time and memory.
Differential calculus, which focuses on the concept of derivatives, is especially relevant in computer science. Derivatives measure the instantaneous rate of change of a function and have applications in optimization and approximation algorithms. For example, in machine learning, derivatives are used to optimize the parameters of a model to minimize the error between predicted and actual outcomes.
Sequences, another topic within calculus, are important for understanding the behavior of algorithms. In computer science, algorithms often deal with sequences of data, such as arrays or linked lists. Understanding the properties and behavior of these sequences helps in analyzing and designing efficient algorithms.
Overall, a basic understanding of calculus, particularly differential calculus and sequences, provides essential tools for analyzing algorithms and computational complexity in computer science. It helps in optimizing algorithms and understanding their efficiency in terms of time and memory consumption.
Linear Algebra and Matrices
In computer science, a strong foundation in linear algebra and matrices is essential. These mathematical concepts play a crucial role in various applications such as graphics, machine learning, and cryptography.
Linear algebra deals with vector spaces and linear transformations. It provides the tools and techniques to solve systems of linear equations, analyze geometric transformations, and understand the properties of vectors and matrices. Matrices are a fundamental component of linear algebra, representing linear transformations and assisting in solving complex problems efficiently.
One significant area where linear algebra is utilized in computer science is graphics. Graphics involve creating and manipulating images, animations, and visual effects using computer algorithms. Techniques such as 3D modeling, rendering, and image processing heavily rely on linear transformations and matrix operations. For instance, rotating and scaling objects in computer graphics involve applying linear transformations to vectors, and matrices are used to represent these transformations.
Another important application of linear algebra in computer science is machine learning. Machine learning algorithms train models to make predictions or decisions without being explicitly programmed. Linear algebra is used to represent and manipulate data in these models. For example, in linear regression, a popular machine learning algorithm, linear algebra is used to estimate the coefficients of a linear equation that best fits the given data.
Cryptography, the study of secure communication, also heavily relies on linear algebra. Cryptographic algorithms, like the widely used RSA algorithm, involve modular arithmetic operations that can be represented using matrices. Linear algebra techniques, such as matrix multiplication, inversion, and exponentiation, are fundamental in implementing and analyzing these cryptographic algorithms.
Having a strong understanding of linear algebra and matrices allows computer scientists to develop efficient and optimized algorithms, understand the mathematical foundations of various computer science applications, and tackle complex problems in the field.
Probability and Statistics
Probability and statistics are essential concepts in computer science, as they provide the foundation for understanding and analyzing data. Whether you’re working on data analysis, machine learning, or network modeling, a strong grasp of probability and statistics is crucial.
Probability is the study of chance and uncertainty. It allows us to quantify the likelihood of an event happening. In computer science, probability is used to analyze data and make predictions. For example, in machine learning algorithms, probability is used to determine the likelihood of a certain outcome based on patterns found in the data.
Statistics, on the other hand, involves the collection, analysis, interpretation, presentation, and organization of data. It helps us make sense of the information we gather and draw valuable insights. In computer science, statistics is used to analyze large datasets and make informed decisions.
One area of computer science where probability and statistics are extensively used is data analysis. Data analysis involves sorting, cleaning, and analyzing large sets of data to uncover meaningful patterns and insights. By applying statistical techniques, such as hypothesis testing and regression analysis, computer scientists can draw valuable conclusions from the data.
Machine learning, a subset of artificial intelligence, also heavily relies on probability and statistics. Machine learning algorithms learn from past data and use that knowledge to make predictions or decisions. Probability is used to find the most likely outcome, while statistical models help in training and evaluating machine learning algorithms.
For example, in image recognition tasks, probability and statistics are used to classify images into different categories. The algorithm compares the features of the image with the probabilities of each category to determine the most likely classification. Statistical models are then used to optimize and improve the accuracy of the algorithm.
Network modeling is another area of computer science where probability and statistics come into play. Networks, such as social networks or computer networks, are complex systems with interconnected entities. Probability is used to model the behavior of these networks and predict outcomes.
For example, in network security, probability is used to analyze the likelihood of a cyber-attack happening and the potential impact it could have. By understanding the probabilities, computer scientists can develop strategies to protect the network and mitigate the risks.
In conclusion, probability and statistics are vital for computer science. They provide the necessary tools to analyze data, make predictions, and understand complex systems. Whether you’re working on data analysis, machine learning, or network modeling, a solid understanding of probability and statistics is essential for success.


While taking a disease dynamics course, I thought it would be a good opportunity to learn how to use the
Shiny package in
R and create an interactive interface for some of my problem sets. After a few trial runs with smaller, simpler setups, I have wrapped up the side project (for now). You can see it in action here 1 and you can view the final code on my Git.
At some point, I’d like to make an analogous version of these models using network-based approaches. However, all my work in network models has been done using Python so it might take a while.
If you’re unfamiliar with compartmental models, they are deterministic models that use differential equations to describe the spread of an epidemic through a population. The Wikipedia page on them is a pretty good place to start. The parameters on the page are described below—note that certain parameters are only shown when they are applicable.
- Probability of transmission: the probability that an infectious person will infect a susceptible person at any one contact.
- Average contacts: the number of people an infected person will run into (per week).
- Disease properties:
- No recovery: when checked, if somebody becomes infected, they will be infectious forever—never recovering.
- Duration: how long an infected person remains infected
- Latent period: the time between being infected and being infectious (at which point they are neither susceptible nor infected, but are “exposed”).
- Seasonal fluctuations: a cosine function that emulates seasonal fluctuations in contact rates.
- Vital dynamics:
- Birth and death rate: Self-explanatory. In these model, kept equal to each other.
- Proportion of vaccinated a birth: assumes vaccination occurs immediately at birth (therefore, this is the proportion of new births who never enter a susceptible stage).
- Vaccine effectiveness: probability of a vaccine actually working.


By Andreas Potschka
Andreas Potschka discusses a right away a number of taking pictures process for dynamic optimization difficulties limited by means of nonlinear, in all likelihood time-periodic, parabolic partial differential equations. not like oblique tools, this process immediately computes adjoint derivatives with out requiring the person to formulate adjoint equations, that are time-consuming and error-prone. the writer describes and analyzes intimately a globalized inexact Sequential Quadratic Programming procedure that exploits the mathematical buildings of this technique and challenge classification for quick numerical functionality. The ebook positive aspects purposes, together with effects for a real-world chemical engineering separation problem.
Read Online or Download A Direct Method for Parabolic PDE Constrained Optimization Problems PDF
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Additional resources for A Direct Method for Parabolic PDE Constrained Optimization Problems
33]). The explicit algorithmic control of Jacobian approximations is usually enforced via an adaptively chosen termination criterion for an inner preconditioned Krylov solver for the solution of the linearized system. 3 Globalization of convergence 39 solve the linear system exactly (see Battermann and Heinkenschloss , Battermann and Sachs , Biros and Ghattas ). 5 is already possible. Our aim in this section is to present the theoretical tools to understand this undesirable effect and to introduce the idea of monotonicity tests.
The ﬁrst theorem which relies on ω characterizes step sizes αk which yield optimal values for a local descent estimate of generalized level functions T (z|A) in the Newton method. 16. Let D be convex, J(z) nonsingular for all z ∈ D. Let furthermore J satisfy the ω-condition in D, zk ∈ D, A ∈ GL(N), and G(zk |A) ⊂ D. Let Δzk denote the Newton direction and deﬁne the Kantorovich quantities hk := Δzk ω, hk := hk cond(AJ(zk )). Then we obtain for α ∈ [0, min(1, 2/hk (A))] that AF(zk + αΔzk ) ≤ tk (α|A) AF(zk ) , where tk (α|A) := 1 − α + (1/2)α 2 hk (A).
13) on the left hand side then delivers the assertion. 21 is the inequality ρ i ≤ ρ i (1 + ρ i ). 14) to obtain ρ i = ρ i /(1 + ρ i ), or ρ i = ρ i /(1 − ρ i ) for ρ i < 1. 15), ρ i ≤ ρ max with ρ max ≤ 13 . 14) we can only conclude ρ i ≥ ρ i /(1 + ρ i ) (and not “≤”). 18 depends on the unknown hδk = ω δ zk which must be approximated. 8) to a computable estimate of the optimal step size [α k ] = min(1, (1 − 2δk )/[hδk ]) = min(1, 1/ (1 + ρ)[hδk ] ). 20 we obtain an a-posteriori Kantorovich estimate [hδk ]i = − δ zk+1 2 δ zk+1 i 0 (1 + ρ i )α 2 δ zk = − (1 − α)δ zk 2 δ zk+1 i (1 + ρ i )α 2 δ zk ≤ hδk .
A Direct Method for Parabolic PDE Constrained Optimization Problems by Andreas Potschka


Sarycheva Ludmila Vissarionovna
Professor of the GIS Department
Professor Sarycheva L.V. teaches "GIS in the asks of monitoring", "Modeling of economic, ecological and social processes", "Discrete mathematics", "Computer support of decision-making", "Probability theory, probabilistic processes and mathematical statistics", "Decision-making under uncertainty", "Professional functions and problems of masters"
The basic area of scientific activity is modelling. Professor Sarycheva heads works in the following directions:
· Intelligent analysis of region monitoring data;
· Modeling of economic, ecological and social processes;
· Inductive methods of modeling;
· Recognition of images and clusterization;
· GIS-analysis and geoiconic modeling.
Professor Sarycheva heads the works of 2 post-graduate students
During the work in the NMU Professor Sarycheva published 119 scientific works, 4 monographies are published (two of them - on image recognition, the other two - on mathematical and geoinformation support of computer ecological and economic monitoring of regions), manuals on combination theory, field theory, the set theory, probability theory.
Born in 1957, finished the Dnepropetrovsk National University (those years - the Dnepropetrovsk State University) in 1979. After graduation from DNU three years worked in the Fund of algorithms and programs (DNU). Works in NMU since 1982, at first on Higher Mathematics Department, since 1996 - on GIS Department. The candidate of physical and mathematical sciences (1993), the senior lecturer (1995), the professor of GIS Department (2005). The experience of scientific and pedagogical work is 33 years.


We’ve sourced some of the most interesting and thought-provoking Geometry Quotes from Antony Garrett Lisi, Comte de Lautreamont, Shia LaBeouf, E. W. Howe, Jacques Lacan. Each of the following quotes is overflowing with creativity, and knowledge.
What physics tells us is that everything comes down to geometry and the interactions of elementary particles. And things can happen only if these interactions are perfectly balanced.
Arithmetic! Algebra! Geometry! Grandiose trinity! Luminous triangle! Whoever has not known you is without sense!
People were going to geometry class and I was swimming through vats of chili on ‘Even Stevens.’ It was like a dream!
It is hard to convince a high-school student that he will encounter a lot of problems more difficult than those of algebra and geometry.
A geometry implies the heterogeneity of locus, namely that there is a locus of the Other. Regarding this locus of the Other, of one sex as Other, as absolute Other, what does the most recent development in topology allow us to posit?
A multitude of bees can tell the time of day, calculate the geometry of the sun’s position, argue about the best location for the next swarm. Bees do a lot of close observing of other bees; maybe they know what follows stinging and do it anyway.
Not that the propositions of geometry are only approximately true, but that they remain absolutely true in regard to that Euclidean space which has been so long regarded as being the physical space of our experience.
I find purer philosophy in a Poem than in a Conclusion of Geometry, a chemical analysis, or a physical law.
In terms of individuals who actually inspired me, very few of the academic people that I had access to had that power over me. Maybe it’s simply because I wasn’t that committed to geometry.
One of the great challenges of modern cosmology is to discover what the geometry of the universe really is.
Golf is basically about geometry and your ability to gauge how things are, the terrain, the distances, and exerting the right amount of swing and force.
Relying on the face might be human nature – even babies prefer to look at attractive people. But, of course, judging someone based on the geometry of his features is, from a moral and legal standpoint, no better than judging him based on the color of his skin.
I was very slow in maths, geometry I actually enjoyed.
I can’t stop biting my nails. It’s a bad habit of mine. I like anything to do with math and numbers. I know a lot of people don’t like geometry, but for me it’s fun.
I’ve got a real sense of three-dimensional geometry. I can look at a flat piece of fabric and know that if I put a slit in it and make some fabric travel around a square, then when you lift it up it will drape in a certain way, and I can feel how that will happen.
There is geometry in the humming of the strings, there is music in the spacing of the spheres.
All one’s inventions are true, you can be sure of that. Poetry is as exact a science as geometry.
Human knowledge is dark and uncertain; philosophy is dark, astrology is dark, and geometry is dark.
While fractal geometry is often used in high-tech science, its patterns are surprisingly common in traditional African designs.
This is the first real evidence that we’ve seen now of high gravitational field strengths: monstrous things like stars moving at the velocity of light, smashing into each other, and making the geometry of space-time turn into some sort of washing machine.
Now being in such grace and favor by reason I learned him some points of geometry and understanding of the art of mathematics with other things, I pleased him so that what I said he would not contrary.
The citation for the 1971 Nobel Prize in Chemistry reads, ‘for contribution to the knowledge of electronic structures and geometry of molecules, especially free radicals,’ and therefore implies that the Prize has been awarded for a long series of studies extending practically over my whole scientific life.
Geometry was the first exciting course I remember.
I got good grades in math, but I never really enjoyed it. My favorite part of math was algebra, but geometry was the worst.
Plane geometry is sort of the key course where you learn about proving things and abstraction.
In things to be seen at once, much variety makes confusion, another vice of beauty. In things that are not seen at once, and have no respect one to another, great variety is commendable, provided this variety transgress not the rules of optics and geometry.
Life isn’t about algebra and geometry. Learning by making mistakes and not duplicating them is what life is about.
A pool at the edge of the ocean is the simplest geometry, yet you feel connected to the sea. In a forest with the mountains in the background, you also feel the connection to nature, yet it’s a very complex geometry. I think architecture is about controlling these feelings.
If the chemistry is right between star and photographer and the geometry of the pictures pleases the star, often the two people end up with a long-term professional friendship during which they continue to work together and to produce highly personal images.
I just toured around looking for fractals, and when I found something that had a scaling geometry, I would ask the folks what was going on – why they had made it that way.
There is no royal road to geometry.
I think the universe is pure geometry – basically, a beautiful shape twisting around and dancing over space-time.
Geometry is moribund. I want a lilt and joy to art.
Poetry is as precise a thing as geometry.
I got into animals by drawing hair follicles. I liked drawing hair, and from that I got into feathers and fur, then into images of animals. The patterning is the same, but the proportions of the body change from one animal to the next. A lot of it is just geometry and consciousness.
Projective geometry is all geometry.
Fractions, decimals, algebra, geometry, trigonometry, calculus, mechanics – these are the steps up the mountain side. How high is one going to get? For me, the pinnacle was Projective Geometry. Who today has even heard of this branch of mathematics?
One of the weird things about modern physics is that we do find there are apparently these other dimensions that we don’t directly experience that explain some aspects of the overall geometry and reality of our universe.
Fractal geometry is everywhere, even in lines drawn in the sand. It’s the cycle of life… You see fractals in plants, in flowers. Within the human lung are branches within branches.
The human heart likes a little disorder in its geometry.
You can’t criticize geometry. It’s never wrong.
Everything one invents is true, you may be perfectly sure of that. Poetry is as precise as geometry.
We learned to put discipline in the haircuts by using actual geometry, actual architectural shapes and bone structure. The cut had to be perfect and layered beautifully, so that when a woman shook it, it just fell back in.
And since geometry is the right foundation of all painting, I have decided to teach its rudiments and principles to all youngsters eager for art.
If you’re sitting across the table from someone, the geometry of the situation says ‘confrontation.’ If you’re walking with somebody, you’re heading in the same direction, and the spatial dance you’re doing is a little more cooperative.
The bones of my architecture are very much related to the structure, to the physical fact of how a building can stand up; it’s also related to geometry and a certain understanding of the architecture in which there is a balance between expression and function.
The two elements the traveler first captures in the big city are extra human architecture and furious rhythm. Geometry and anguish.
I’d been doing projects outdoors for the public. I made pigeons eat geometry by putting bread out in rhomboids and triangles. I don’t know if this activity made sense, but the work was available.
I was allergic to school. I was completely befuddled by school. I was trying so hard, but I couldn’t succeed. I took geometry for four years, the same course over and over again, and I did not graduate with my senior class. I finally passed geometry after doing summer school, and eventually, I graduated.
The geometry, the content, and the fate of the universe are all intricately linked. If you know two, you can deduce the third.


In 2011, the Trends in International Mathematics and Science Study (TIMSS) showed that South African learners have the lowest performance among all 21 middle-income countries that participated. South Africa’s development as a knowledge economy depends partly on improving the teaching of mathematics and numeracy. Furthermore, South Africa’s extremely high youth unemployment, which is currently at 50%, is closely linked to the quality of schooling; numeracy and mathematics competency in particular. We have looked at the education Stats for 2013 and 2014 as shown on department of education website, and the results show that we still have a long way to go in terms of improving the situation for the future of this country.
Nubian Smarts believes that building a solid math foundation is vital for children to succeed. Hence our interest in creating applications for primary school children. Studies have shown that students with weak basic math skills find the subject increasingly difficult and confusing thus leading them to get poor results. This often leads to math anxiety and the belief that mathematics is hard and not fun, which is how most people feel when asked about their experiences with regards to maths.
So in essence when a child develops a solid math foundation, you notice that the stress caused by poor math skills disappears, and you might notice the child even saying that maths is fun. We at Nubian Smarts believe that this is not an unattainable goal and that the key to improving these statistics is by creating mobile applications that focus on creating a lifelong love of mathematics. These mobile applications are not intended to be a unique educational method but rather to complement the other areas of the educational programme.
Studies conducted have reported that mobile apps are not only engaging, but educational, for children as young as preschool. PBS Kids, in partnership with the US Department of Education, found that the vocabulary of kids’ age’s three to seven who played its Martha Speaks mobile app improved up to 31%. Abilene Christian University conducted research around the same time that found math students who used the iOS app “Statistics 1” saw improvement in their final grades. They were also more motivated to finish lessons on mobile devices than through traditional textbooks and workbooks.
More recently, two studies that separately followed fifth and eighth graders who used tablets for learning in class and at home found that learning experiences improved across the board. 35% of the 8th graders said that they were more interested in their teachers’ lessons or activities when they used their tablet, and the students exceeded teachers’ academic expectations when using the devices.


Populations can be diverse topics such as "all persons living in a country" or "every atom composing a crystal". The famous Hawthorne study examined changes to the working environment at the Hawthorne plant of the Western Electric Company.
No, because this is a case-control study and you can not estimate risk from a case-control study design. In addition, there is more than one type of ordinal regression that can be used to analyse ordinal dependent variables.
The probability distribution of the statistic, though, may have unknown parameters.
The use of both vertical axes allows the comparison of two time series in one graphic. Consider now a function of the unknown parameter: Note that the p-values for all the coefficients with the exception of the coefficient for infant mortality are bigger than.
This is often done by using a related series known for all relevant dates. Statistics itself also provides tools for prediction and forecasting through statistical models.
Further examining the data set in secondary analyses, to suggest new hypotheses for future study. We can calculate all the entries in the Regression data analysis in Figure 5 using Excel formulas as follows: In this order, select "Tables" in the Output Types: Spline interpolation, however, yield a piecewise continuous function composed of many polynomials to model the data set.
The capital asset pricing model CAPM is an often-used regression model in finance for pricing assets and discovering costs of capital. Experiments[ edit ] The basic steps of a statistical experiment are: At this stage, the experimenters and statisticians write the experimental protocol that will guide the performance of the experiment and which specifies the primary analysis of the experimental data.
CVD was coded 1 if the participant had cardiovascular disease at the time of enrollment, and 0 if the participant did not have cardiovascular disease at the time of enrollment. In restricted circumstances, regression analysis can be used to infer causal relationships between the independent and dependent variables.
Most importantly we see that R Square is While one can not "prove" a null hypothesis, one can test how close it is to being true with a power testwhich tests for type II errors.
Most commonly, regression analysis estimates the conditional expectation of the dependent variable given the independent variables — that is, the average value of the dependent variable when the independent variables are fixed. The estimated odds ratio of cardiovascular disease for females compared to males is substantially different for smokers and non-smokers.
Forecasting on large scale data is done using Spark which has spark-ts as a third party package. The null hypothesis, H0, asserts that the defendant is innocent, whereas the alternative hypothesis, H1, asserts that the defendant is guilty.
Would this be allowable? To understand these different types, consider the definition of an ordinal variable as a categorical variable with ordered categories e. I14 The predicted values of Y, i. The only procedures that we do not cover below are those required to test assumptions 3 and 4 of the ordinal regression test, as mentioned earlier see the Assumptions section.
In restricted circumstances, regression analysis can be used to infer causal relationships between the independent and dependent variables. We can also use the Regression data analysis tool to produce the output in Figure 3.
This will add this request to the Requests: Of particular interest is whether sex was associated with the risk of cardiovascular disease CVD in the cohort participants and the population from which they were sampled.
Exploratory analysis The clearest way to examine a regular time series manually is with a line chart such as the one shown for tuberculosis in the United States, made with a spreadsheet program.
The estimated odds ratios of cardiovascular disease for females compared to males are similar across all four regression models presented A,B, C,D d. When a census is not feasible, a chosen subset of the population called a sample is studied. A different problem which is closely related to interpolation is the approximation of a complicated function by a simple function also called regression.
Again, descriptive statistics can be used to summarize the sample data. Regression analysis is widely used for prediction and forecastingwhere its use has substantial overlap with the field of machine learning.
Ratio measurements have both a meaningful zero value and the distances between different measurements defined, and permit any rescaling transformation. One particular approach to such inference is known as predictive inferencebut the prediction can be undertaken within any of the several approaches to statistical inference.Of course you can use linear regression for time series data.
It's just that there are specific tools that only work for time series data that sometimes do a better job. Regression (statistics) Statistics (academic discipline) Is regression analysis legitimate for time series data?
Which is more useful for data science: regression or. Statistics Solutions can assist with your regression analysis. Contact us to learn more or to schedule your free minute consultation. Questions the Linear Regression Answers» Read More.
Question the Logistic Regression Answers. Ordinal Regression using SPSS Statistics Introduction. Ordinal logistic regression (often just called 'ordinal regression') is used to predict an ordinal dependent variable given one. STATISTICS / PRACTICE FINAL EXAM KEY (REGRESSION ONLY) Questions 1 to 5: There is a downloadable Stata package that produces sequential sums of squares for regression.
In other words, the SS is built up as. If you were introduced to regression in an introductory statistics course and now find you need a more solid grounding in the subject, this course is for you. Time Requirement: About 15 hours per week, at times of your choosing.
You will need software that is capable of doing regression analysis, which all statistical software does. If “time” is the unit of analysis we can still regress some dependent variable, Y, on one or more independent variables.
Last time we dealt with a particularly simple variable, a “time Posc/Uapp Class 20 Regression of Time Series Page 8 6. At very first glance the model seems to fit the data and makes sense given.Download


If you are looking for a BMI Calculator , please click here. One meter is a length measurement and equals approximately 3. One foot equals 12 inches exactly. Once this is very close to 3. An answer like "6.
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Ensuring statistics best-practices. Tisane is a tool for specifying generalized linear models and generalized linear mixed-effects models (GLMMs).
Tisane is an interactive system for authoring generalized linear models (GLMs) and generalized linear mixed-effects models (GLMMs). It provides a
Tisane's study design specification language allows analysts to specify conceptual and data relationships between variables. Analysts can query Tisane for a linear model involving specific variables of interest. Tisane checks the query is well-formed based on the expressed relationships and automatically generates a space of possible linear models that respect the stated relationships. Tisane asks analysts disambiguating questions about their analysis intents through a graphical user interface (GUI). Based on the specified study design and additional responses, Tisane outputs code for fitting and visualizing a statistical model. The output model is guaranteed to be conceptually consistent with the specified relationships and optimized for generalizability.
Tisane is designed for analysts who have domain expertise, are not statistical experts, and are comfortable with minimal programming (e.g., many researchers).
The Tisane project is currently active at the University of Washington's Paul G. Allen School of Computer Science.


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Size: Approx. 220x220x33mm/ 8.66x8.66x1.30"
Fit for kids and adults, 2 to 4 players
With 2 dices and 10 numbered wooden tiles each side
The game is played with family, used in classrooms for teaching addition and probability, and is even a betting game played in pubs
Just keep on rolling until you can no longer match your roll on the remaining tiles
The lowest score wins the game
If you lay down all the tiles, then you've "shut the box"
People can define themselves if plus, minus, times, devides are applicable. And also define only 2 pieces or 3 pieces can be used
A kind of board game, several ways to play, player can also define the rules themselves
Brings hours of enjoyment to your home
Game One: Turn the wooden card according to the number of the dice thrown, which can be the sum of several cards. Finally, the flop who cannot press the number of the dice will lose.
Game two: One side continues to roll the dice and flop until no cards can be turned, and the last remaining wooden card is his score, the lower score wins.
For example: If you shake at 9 o'clock, you must turn any number and the card equal to "9". The flop can be turned one, two or three at a time, but it must be a number and equal to 9 (you can also specify the addition, subtraction, multiplication and division of various rules). If you want to turn a card, choose "9" digital card; if you want to turn two cards, you can choose "3" and "6" or "4" and "5" digital cards; if you want to turn three cards, you can choose "1" "," 2 "and" 6 "or" 2 "," 3 "and" 4 "digital cards. In addition, the game specifications can be freely determined by addition and subtraction. The children in the third grade up can set the multiplication and division rules. When our family plays stupidly, it can add, subtract, multiply and divide. , 8, and 6, why, because 3 × 8 = 24 divided by 6, which is 4, as long as you can respond quickly. There are so many ways to play, children can develop many ways to play. So there is no need to limit the single gameplay.
How To Play:
Roll the dice and lay down any numerical combination of tiles that match your roll
For example: Roll the dices and have 3 and 4 so you get number 7
You can turn on 1 and 6 at any side, because 1+6=7, you can also turn on 9 and 2 at any side, because 9-2=7
The last player who can successfully turn on as rules win the game
1 x Traditional Pub Board Dice Game
Please allow 1-3 mm error due to manual measurement.
Color might be slightly different due to the color calibration of each individual monitor.
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So, tomorrow is the great Pi day of the century. At 9:26:53 you will have the first ten digits of Pi with the day/month/year – 3.141592653.
Do you celebrate Pi day? If you don’t, you can use the following info for other days as just math lessons, but if you do there are a lot of cute ideas. One that we did was giving each number 0-9 a color and making a Pi chain. We also did Buffon’s needle (virtual and in real life) and got pretty close to 3.14.
Pi stuff, jewelry, belts, a few crafts, here.
Books – Sir Cumference and the Dragon of Pi, Why Pi?, A History of Pi, Joy of Pi.
Lots of Pi related ideas, crafts and games here.
Vi Hart shares her anti-Pi day message (she is pro-Tau) here.
And don’t forget to eat some pie (whether that it pizza or just pie) tomorrow!


This week in Sign Language & Music we explored numbers 1-10 in sign language. I mentioned that I often use number signs 1-31 in calendar time for many of my sessions. The numbers 1-10 are a great start to learning all of those number signs!
So heres the big question… Do I use signed numbers, or standard finger counting?
This really depends on what your classroom, students, or clients are using. If they have been using and gaining understanding with standard counting then that might be the most appropriate counting measure to use. Many of my classrooms use signed numbers so I use those to reiterate the method that is already being used in the classroom. At the end of the day I am always in search of the most efficient and effective means to the end. Check out this weeks video below, and have a wonderful week!


On September 16, 2016, Social Science Matrix hosted Cathy O'Neil, author of Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy. In her book (and presentation), O'Neil—a Harvard-trained mathematician and former hedge fund data analyst—discusses how many of the decisions that affect our lives—where we go to school, whether we get a car loan, how much we pay for health insurance—are being made not by humans, but by mathematical models. The problem, she explains, is that they are often WMDs—widespread, mysterious, and destructive—making them "Weapons of Math Destruction."
Curated by social science graduate students, Matrix Research Streams are themed around globally relevant, trans-disciplinary topics, with articles and videos showcasing recent social-science research findings from across the UC Berkeley campus.
Featuring your Research
Interested in having your research featured by the Matrix? Contact us and we'll have one of our reporters get in touch.


Structure of the examination:
Date of Advertisement: July 17th , 2012
Date of Examination: August 17th , 2012 (Friday) 2.30 p.m. – 4.30 p.m. at the Department of Statistics, University of Calcutta
Date of Interview: September 14th , 2012 (Friday) from 2 pm at the Department of Statistics, University of Calcutta
Publication of result: October 12th , 2012
Commencement of course work: November 20th , 2012
One Semester Course Work of 20 credits as follows
|1||Review of candidate’s research topic||:||5 credit points|
|2||Seminar presentation by the candidate||:||5 credit points|
|3||Seminar attendance||:||2 credit points|
|3||Research Methodology||:||5 credit points|
|5||Statistical Computing||:||3 credit points|
Detailed Syllabus for Entrance Examination:
Real Number System, Cluster Points of sets, Closed and open sets, Compact sets, Bolzano-Weierstrass Property, Heine-Borel Property.Sets of Real Vectors, Sequences and Series, Convergence. Real valued functions. Limit, Continuity and Uniform continuity. Differentiability of univariate and multivariate functions. Mean value theorems. Extrema of functions. Riemann integral. Improper integrals. Riemann-Stieltjes integral. Sequences and Series of functions, Uniform convergence, Power series.Term by term differentiation and integration, Differentiation and integration under the integral sign.
Classes of sets, Fields, Sigma-fields, Minimum sigma-field, Borel sigma-field in Rk, Sequence of sets, limsup and liminf of a sequence of sets. Measure, Probability Measure, Properties of a measure, Caratheodory extension theorem (statement only) Lebesgue and Lebesgue-Stieltjes measures on Rk . Measurable functions, Random variables, Expectation, Sequences of random variables, Almost sure convergence, Convergence in probability. Distribution function, Convergence in distribution. Integration of a measurable function with respect to a measure, Monotone convergence theorem, Fatou’s lemma, Dominated convergence theorem. Generating functions and Characteristic function, Inversion theorem and Continuity theorem (Statement only) ,Borel –Cantelli lemma, Independence,Weak law and Strong law of large numbers, Kolmogorov inequality. Central limit theorem for iid random variables, CLT for a sequence of independent random variables (Statement only).Radon-Nikodym theorem(Statement only) and its applications, Product measure and Fubini’s theorem (Statement only).
Linear Algebra and Linear Programming
Vectors and Matrices;Graphical Solution and Simplex Algorithm
Non-central x2, t & F distributions – definitions and properties.Distribution of quadratic forms – Cochran’s theorem. Multivariate normal distribution – independence of sample mean vector and variance-covariance matrix. Wishart distribution.Distributions of partial and multiple correlation coefficients and regression coefficients, distribution of intraclass correlation coefficient. Hotelling T2 and Mahalanobis’s D2 application in testing and confidence set construction.
Large Sample Theory
Asymptotic distributions of sample moments and functions of moments, Asymptotic distributions of Order Statistics and Quantiles. Consistency and Asymptotic Efficiency of Estimators, Large sample properties of Maximum Likelihood estimators. Asymptotic distributions and properties of Likelihood ratio tests, Rao’s test and Wald’s tests in the simple hypothesis case.
Sufficiency & completeness, Notions of minimal sufficiency,bounded completeness and ancillarity, Exponential family.Point estimation : Bhattacharya system of lower bounds to variance of estimators. Minimum variance unbiased estimators – Applications of Rao – Blackwell and Lehmann – Scheffe theorems.Testing of Hypothesis : nonrandomized and randomized tests, critical function, power function. MP tests – Neyman – Pearson Lemma. UMP tests. Monotone Likelihood Ratio families. Generalized Neyman – Pearson Lemma. UMPU tests for one parameter families. Locally best tests. Similar tests. Neyman structure. UMPU tests for composite hypotheses.
Confidence sets: relation with hypothesis testing. Optimum parametric confidence intervals. Sequential tests. Wald’s equation for ASN. SPRT and its properties – fundamental identity. O.C. and ASN. Optimality of SPRT (under usual approximation).
Pre-requisites of matrix algebra.Gauss-Markov set-up, estimable function, BLUE and Gauss-Markov Theorem, estimation and error spaces, estimation with correlated observations, least squares estimates with restriction on parameters.
Tests of linear hypotheses and associated confidence sets – related sampling distributions, Multiple comparison techniques due to Scheffe and Tukey; Applications of general linear hypothesis to regression, analysis of variance and covariance.Random and Mixed effects models (balanced case), estimation of variance components.
Residuals and their plots. Tests of fit of a model. Q-Q plots. Transformations.Detection of outliers.Departures from the usual assumptions : heteroscedasticity, autocorrelation, multicollinearity, non-normality – detection and remedies. Variable selection problems.
Design of Experiments
Block designs – concepts of connectedness, orthogonality and balance; intrablock analysis – BIB and PBIB designs; extension to row-column designs – Latin Square design and Youden Square design, Recovery of interblock information in BIB designs.Construction of complete classes of mutual orthogonal Latin squares (MOLS); construction of BIBD – through MOLS and Bose’s fundamental method of differences.Factorial experiments, confounding and balancing in symmetric factorials.Response Surface Experiments – first order designs.
Probability sampling from a finite population – Notions of sampling design, sampling scheme, inclusion probabilites, Horvitz-Thompson estimator of a population total. Basic sampling schemes – Simple random sampling with and without replacement, Unequal probability sampling with and without replacement, Systematic sampling. Related estimators of population total/mean, their variances and variance estimators – Mean per distinct unit in simple random with replacement sampling, Hansen-Hurwitz estimator in unequal probability sampling with replacement, Des Raj and Murthy’s estimator (for sample of size two) in unequal probability sampling without replacement.Stratified sampling – Allocation problem and construction of strata.Ratio, Product, Difference and Regression estimators. Unbiased Ratio estimators – Probability proportional to aggregate size sampling, Hartley – Ross estimator in simple random sampling. Sampling and sub-sampling of clusters. Two-stage sampling with equal/unequal number of second stage units and simple random sampling without replacement / unequal probability sampling with replacement at first stage, Ratio estimation in two-stage sampling.Double sampling for stratification. Double sampling ratio and regression estimators. Sampling on successive occasions.
Decision problem and two-person game. Nonrandomized and randomized rules. Risk function.
Introduction to Jackknife and Bootstrap-methods for estimating bias, standard error and distribution function based on iid random variables. Standard examples. Consistency of the Jackknife estimate of the variance in the iid set up.Jackknife and Bootstrap estimates of regression parameters and the error variance.Bootstrap confidence intervals.
Introduction to Stochastic Process, Markov Chains with finite and countable state space, Chapman-Kolmogorov equation, Classification of States, Calculation of n-step transition probability and its limit, Stationary distribution, Discrete state space continuous time Markov Chains, Poisson Process, Birth-Death Process, Renewal theory
Applied Multivariate Analysis
Hierarchical and non-hierarchical clustering methods.Classification and discrimination procedures for discrimination between two known populations – Bayes, Minimax and Likelihood Ratio procedures. Discrimination between two multivariate normal populations.Population and sample principal components and their uses. Large sample inferences.The orthogonal factor model, Estimation of factor loading, Factor rotation, Estimation of Factor scores, Interpretation of Factor Analysis.
Generalized Linear Models and Data Analytic Techniques
Types of data. Two-way classified data – Contingency Tables and associated distributions, Types of studies, Relative Risk and Odds Ratio and their properties. More-than-two-way classified data – partial associations, marginal and conditional odds. Generalized Linear Models – introduction, components of a generalized linear model, measuring the goodness of fit, deviance, residuals, maximum likelihood estimation.Applications to binary, count and polytomous data. Overdispersion. Ideas of marginal, conditional and quasi likelihoods. Longitudinal Data Analysis – introduction with motivation. Exploring longitudinal data.Linear models for longitudinal data –introduction, mean models, covariance models, mixed effects models. Predictions.Discrete longitudinal data- generalized linear marginal models, GEE for marginal models, Generalized linear subject specific models and transition models.


Non-classical logics – such as modal logics, conditional logics, intuitionistic logic, description logics, temporal logics, linear logic, dynamic logic, fuzzy logic, paraconsistent logic, relevance logic – have many applications in AI, Computer Science, Philosophy, Linguistics and Mathematics. Hence, the automation of proof search in these logics is a crucial task.
Aims and Scope
The ARQNL workshop aims at fostering the development of proof calculi, automated theorem proving systems and model finders for all sorts of quantified non-classical logics. The workshop will provide a forum for researchers to present and discuss recent developments in this area. The contributions may range from theory to system descriptions and implementations. Contributions may also outline relevant applications, describe problem formalizations, example problems, and benchmarks. We welcome contributions from computer scientists, linguists, philosophers, and mathematicians.
Topics of the ARQNL workshop will cover all aspects related to the mechanization and automation of quantified non-classical logics, including but not limited to:
- Proof theory, semantics, meta theory, and cut-elimination
- Proof search calculi, including sequent calculi, tableau calculi, connection calculi, resolution calculi, and instance-based calculi
- Modal logic, conditional logic, intuitionistic logic, description logic, temporal logic, linear logic, multivalued logic, dynamic logic, fuzzy logic, paraconsistent logic, relevance logic, free logic, and natural logic
- Techniques, strategies and heuristics to deal with first-order or higher-order quantification
- Implementation of theorem provers and experimental evaluations
- Problem libraries and benchmarking for theorem provers
- Applications, formalizations, and example problems
- User interfaces, proof representation, and syntax issues
ARQNL 2016 will be part of the International Joint Conference on Automated Reasoning IJCAR 2016 in Coimbra, Portugal.
23 July 2014, Vienna, Austria
(part of IJCAR 2014).
Proceedings: ARQNL 2014. Automated Reasoning in Quantified Non-Classical Logics. EPiC Series in Computing, Volume 33, EasyChair, 2015.


The Smooth and the Striated
Sierpensky’s sponge: more than a surface, less than a volume. The law according to which this cube was hollowed can be understood intuitively at a glance. Each square hole is surrounded by eight holes a third its size. And so on, endlessly. The illustrator could not represent the infinity of holes of decreasing size beyond the fourth degree, but it is plain to see that this cube is in the end of infinitely hollow. Its total volume approaches zero, while the total lateral surface of the hollowings infinitely grows. This space has dimension of 2.7268. It therefore lies between a surface (with a dimension of 2) and a volume (with a dimension of 3). ‘Sierpensky’s rug’ is one face of the cube; the hollowings are then squares and the dimension of the ‘surface’ is 1.2618.


Math Practices that Energize Your Classroom, Robinson, Spring 2021
||EDU 5626 C04
|Dates and Times:
||February 8 - April 26, 2021
||3 Graduate Credits
In this online course we will be exploring the 8 Standards for Mathematical Practices that will make all of our students better mathematicians and thinkers. We have all felt the frustration of teaching students the math that they are required to know and yet this doesn’t seem to translate into making them better math students. We will explore each of the math practices that are outlined in the Common Core and look at how each of the practices can change the students into becoming “math thinkers” and allow them to adapt their learning to any situation. Our focus will be on how to teach our students to think deeply and apply mathematics to any area of their life.
This course will be on a Google Site. The commenting for the course will be on a Facebook Social Learning group, which will require that you have a Facebook account.
What are the 8 Common Core Mathematical Practices?
What can we do in our classroom to foster the use of these practices by our students?
What is my role as the facilitator of a math class that has the use of rich mathematical practices?
What is the difference between the way that my math class is currently functioning and the way that a highly effective math class functions?
Articles and Websites that will be used in the course: (this is a small sample of the resources used.)
“A Guide to the 8 Mathematical Practice Standards,” Scholastic, Top Teacher Blog Meghan Everrette, March 15, 2013. http:// www.scholastic.com/teachers/top-teaching/2013/03/guide-8-mathematical- practice-standards
“How to Get Students Talking,” Math Solutions, deGarcia, Lisa Ann. http:// www.mathsolutions.com/documents/how_to_get_students_talking.pdf
“Developing a Classroom Culture that Supports a Problem Solving Approach to Mathematics,” NRICH Enriching Mathematics, University of Cambridge, Sept. 2013. http://nrich.maths.org/10341
“Common Core State Standards Initiative” Mathematics Standards. http:// www.corestandards.org/Math/Practice/, Buchheister, Kelley, Jackson, Christa and Taylor, Cynthia.
“An Inside Track: Fostering Mathematical Practices.” Teaching Children Mathematics, Aug. 2015
For additional course information
For additional registration information


EFFECT OF MATHEMATICS LABORATORY MATERIALS ON SECONDARY SCHOOL STUDENTS’ ACHIEVEMENT IN GEOMETRY
Keywords:Mathematics Laboratory Materials, Geometry, secondary school students
The study determined the effect of Mathematics Laboratory Materials on Achievement in Geometry among Junior Secondary School two (JSS2) students. Two research questions and three hypotheses guided the study. The design of the study was pretest-posttest non-equivalent control group quasi-experimental research design. The population of study was 4,027 Junior Secondary School two (JS2) students in the 31 public Secondary Schools in Nsukka Local Government Area. The sample for the study was one hundred and fifty-six (156) Junior Secondary School two (JSS 2) Students drawn from the two (2) coeducational secondary schools in Nsukka Local Government Area using simple random sampling techniques. Geometry Achievement Test (GAT) was the instrument used for data collection. The GAT was face and content validated by three experts-two in Mathematics education and one in Measurement and Evaluation. The reliability of GAT was found using Cronbach Alpha which yielded coefficient index of 0.75. GAT was administered as pretest and posttest. Data on achievement was collected using GAT. Mean () and standard deviation () were used in answering the research questions while Analysis of Covariance (ANCOVA) was used in testing the research hypotheses at 0.05 alpha level of significance. Findings revealed that using mathematics laboratory materials improved considerably students’ achievement. Furthermore, using mathematics laboratory materials was also found to have differential effect on achievement of male and female students in mathematics in favour of the male students. The study recommended that teachers should use mathematics laboratory materials in students’ achievement in geometry and teachers should involve both male and female students in mathematics laboratory materials strategy in classroom to reduce the gender inequality in mathematical achievement particularly geometry achievement.


lookout identifies outliers in data using leave-one-out kernel density estimates and extreme value theory. The bandwidth for kernel density estimates is computed using persistent homology, a technique in topological data analysis. Using peak-over-threshold method, a generalized Pareto distribution is fitted to the log of leave-one-out kde values to identify outliers.
See Kandanaarachchi and Hyndman (2021) for the underlying methodology.
You can install the released version of lookout from CRAN with:
And the development version from GitHub with:
# install.packages("devtools") devtools::install_github("sevvandi/lookout")
library(lookout) lo <- lookout(faithful) lo #> Leave-out-out KDE outliers using lookout algorithm #> #> Call: lookout(X = faithful) #> #> Outliers Probability #> 1 24 0.01371435 #> 2 149 0.00000000 #> 3 211 0.00000000 autoplot(lo) #> Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> = #> "none")` instead.
Next we look at outlier persistence. The outlier persistence plot shows the outliers that persist over a range of bandwidth values for different levels of significance. The strength is inversely proportional to the level of significance. If the level of significance is 0.01, then the strength is 10 and if it is 0.1, then the strength is 1.


How many grams in a pound? This article provides the answer and the conversion chart for the metric and imperial units. In addition, it offers a calculator to convert grams to pounds. Read on to learn more. And don’t forget to use this conversion chart to convert grams to pounds! This will give you more accurate answers! Listed below are a few examples of how to convert grams to pounds.
Gram is 1/1,000 of a kilogram
A gram is a unit of mass in the International System of Units. It was originally defined as the weight of pure water in a cubic centimeter at the temperature of ice melting. Since the definition of a kilogram is no longer based on a universal prototype, it has been renamed to reflect Planck’s constant, h. It also includes a new definition of the meter and second.
One gram equals 0.001 kilogram. The formula to convert grams to kilograms is to multiply the number of grams by 0.001 and divide it by 1000. For example, if you weigh 1500 grams, divide that number by 1,000. That way, you will get 1.5 kilograms. Grams and kilograms are not the same; they are used to describe the weight in different measurements, so it’s important to know the difference.
The gram is a common unit of mass, used in everyday life. Most grocery stores and non-liquid ingredients are measured in gram. Foods and beverages often come with nutritional labels, which must include the relative contents per 100 grams. This makes the conversion process much simpler and faster. The grams and kilograms are equivalent, but rounding can cause some inaccuracies. However, the kilogram has its advantages.
Converting between metric and imperial units
You may need to convert measurements between the metric and imperial systems to understand what you’re comparing. Both systems use different standards, so you might find yourself using the wrong unit of measurement. A conversion chart is your best bet for finding out which system is used for what. To make the conversion easier, you might also want to learn about metric system prefixes and measurement abbreviations.
Metric systems are widely used in U.S. schools. Many measurement tools are made using both USCS and SI units. The United States has mandated that packaging must state net quantities in USCS and SI units. Metric units use a meter as the base unit. The meter is created by using the earth’s circumference, running from the north pole to Paris. A kilometer is one thousand millimeters.
Despite the popularity of imperial units, metric units are easier to learn. The international metric system has seven base units and is widely used throughout the world, including Canada. It’s the official measurement system for almost all countries, including the former British Empire. Canada switched to the metric system in the 1970s. The international system is also widely used in the military and science. But changing your measuring system can be expensive.
Calculator for converting between gram and pound
If you’ve ever wondered how to convert between gram and pound, you’re not alone. Using the wrong units can result in some disastrous situations. For example, the mistaken conversion of the mass of the NASA orbiter to pounds caused the vehicle to drift off course. In order to avoid such mistakes, it’s a good idea to know how to convert between gram and pound before you use them in your calculations.
First, look for a gram to pound converter. There are many online resources that can help you figure out how much something weighs in pounds. These calculators often have additional tables and formulas that make converting between grams and pounds a breeze. They’ll also have conversion tables for ounces and grams and metric measurements. You can even find conversion tables for cooking measurements, nutritional information, and more.
Another way to convert between gram and pound is to multiply the mass of one gram by 0.002205. For example, one gram is equal to 0.002204622621848776 pounds. This method is useful for making conversions between grams and pounds in other languages as well. However, it’s not as straightforward as you may think. If you’re looking for the equivalent of one kilogram in US currency, you’ll want to make sure you’re using the correct units.


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