The intricate world of mathematics transcends beyond mere numbers and equations – Stable Diffusion Mathematical Concepts. It is an indispensable tool used for modelling and understanding various natural phenomena that occur within our world.
Our exploration focuses on one particular aspect of this mathematical influence — Stable Diffusion. In essence, stable diffusion is a robust model adopted in numerous fields such as physics, finance and data science, to make accurate predictions and drive efficient decision-making processes.
This paper peels back the layers of stable diffusion, beginning with an understanding of the fundamental concept of diffusion itself. Gradually moving through the rich tapestry of stochastic processes, stable distributions, Lévy processes, and mathematical modelling, it settles on practical, real-world applications of stable diffusion.
- 1 The Principle of Stable Diffusion Mathematical Concepts
- 2 Introduction to Stochastic Processes
- 3 Stable distributions and Lévy processes
- 4 Mathematical Modeling of Stable Diffusion
- 5 Analyzing Stable Diffusion in the Real World
The Principle of Stable Diffusion Mathematical Concepts
Understanding Diffusion in Mathematics
Diffusion in mathematical terms refers to a process that spreads the presence of particles in a gas, liquid, or a solid medium, moving from areas of higher concentration to areas of lower concentration. This occurrence can be observed in natural phenomena like smoke spreading in the air, ink droplets moving in water, or heat dispersing in a room. Mathematically, diffusion is modeled using differential equations, primarily partial differential equations (PDEs).
Fick’s Laws of Diffusion
Central to understanding diffusion mathematically are “Fick’s Laws of Diffusion,” named after the scientist Adolf Fick who formulated these principles in 1855. These laws form the basis for many diffusion models.
Fick’s First Law
The first law, often referred to as “Fick’s First Law,” states that the flux (J) of a substance is proportional to the negative gradient of its concentration. If ‘D’ is the diffusivity (a measure of the substance’s capacity to diffuse), the first law can be expressed mathematically as J = -D(grad c), where ‘grad c’ is the concentration gradient.
To elaborate, ‘grad c’ represents the rate at which the concentration changes, and the negative sign in the equation indicates that the substance moves from areas of higher concentration to lower concentration, which forms the essence of diffusion.
Fick’s Second Law
While Fick’s First Law effectively deals with steady-state diffusion, it lacks the capacity to handle changes in concentration over time, leading to what is known as Fick’s Second Law of Diffusion. This law states that the rate of change in concentration (dc/dt) is proportional to the rate of change of the concentration gradient over space. This law can be mathematically expressed as dc/dt = D(d^2c/dx^2), forming the basis of the diffusion equation.
The Math Behind Stable Diffusion
Stable diffusion refers to a state where the concentration of particles being diffused does not change with time. This scenario occurs when the system reaches equilibrium, leading to a balanced state where the rate of particles diffusing in is equal to the rate of particles diffusing out. One common attribute of stable diffusion is a uniform concentration of particles throughout the system.
Mathematically, stable diffusion can be modeled using Fick’s laws as well. In steady-state or stable diffusion, the concentration of the substance does not change over time (dc/dt = 0). Consequently, the diffusion equation simplifies to D(d^2c/dx^2) = 0. This yields a linear concentration profile (dc/dx = constant), which is a characteristic of stable diffusion.
Illustrating Stable Diffusion
Let’s look at a plain example of stable diffusion in action. Visualize a lengthy, slim metal rod. The rod is warmer at one end and cooler at the other. As time progresses, the heat will naturally flow towards the cooler side, gradually creating a uniform temperature throughout the bar. This indicates a stable diffusion state.
Moving to a biological perspective, let’s consider the diffusion of nutrients or gases across the cellular membranes. In this situation, the particles will maneuver across the membrane until an equilibrium is established between the concentrations inside and outside the cell, symbolizing a stable diffusion state.
What’s consistent in both scenarios is that the diffusion process persists until it arrives at a constant state. In this state, there are no alterations in the concentration of the diffusing substance over time or through space.
Introduction to Stochastic Processes
Grasping Stochastic Processes
To comprehend the mechanics of stable diffusion, it’s crucial to understand stochastic processes. These are mathematical models designed to chronicle phenomena wherein a certain level of randomness is introduced at every point in time.
Essentially, they are sequences of random variables, capturing the time-evolving dynamics of a system that incorporates random values. You’ll find their applications in diverse areas of study like physics, chemistry, and economics among others, basically anywhere where unpredictability plays a part.
Brownian Motion and Stable Diffusion
Another significant stochastic process that is highly relevant to stable diffusion is the concept of Brownian motion. Brownian motion describes the random movement of particles suspended in a fluid (such as a gas or liquid) resulting from their collision with the fast-moving molecules in the fluid.
These minute movements are continuous, with particles fluctuating in position due to random impacts. Albert Einstein and Marian Smoluchowski brought significant theoretical explanation to the phenomenon from a bulk fluid dynamics and detailed molecular kinetic theory aspect, resulting in a deeper understanding of the kinetic theory of gases.
This relates to stable diffusion because both Brownian motion and diffusion are processes of the random movement of particles. However, in the context of stable diffusion, specifically, it represents the movement of a substance from an area of higher concentration to one of lower concentration, until the concentration is ultimately the same everywhere. Understanding both of these stochastic processes is vital to grasp the math behind stable diffusion.
Stochastic Processes: Pivotal Elements in Stable Diffusion
In the diverse world of science and finance, stochastic processes play a major role in modeling and predicting the behavior of various uncertain systems. One prime example of this is stable diffusion, which uses these processes to calculate the motion of particles and their rate of spread and distribution.
This knowledge becomes significantly useful in domains such as environmental science. For instance, it assists in forecasting the dispersal of pollutants in air or water, or the transfer of heat in different mediums. In finance, the unpredictability of stock market prices over time can be illuminated through models built on the principles of stable diffusion.
In physics, everything from quantum mechanics to thermodynamics benefits from the theory of stochastic processes. The explanation of Brownian motion, which describes the seemingly random movement of particles in a fluid, and the foundational concepts in studying solid-state diffusion, owe much to this theory.
As recognized from these instances, achieving a comprehensive understanding of the influence of stochastic processes on stable diffusion is absolutely essential. This understanding can empower scholars and researchers in modeling and managing various phenomena influenced by randomness.
Furthermore, an in-depth grasp of these concepts becomes indispensable when it comes to fostering advancements in fields such as stochastic calculus, financial mathematics, statistical physics, and various other disciplines where these concepts are integral.
Stable distributions and Lévy processes
Deciphering Stable Distributions
Alpha-stable distributions, also renowned as Levy-Stable or simply stable distributions, are an integral part of several scientific domains encompassing physics, finance, and even image processing. These distributions owe their popularity to their remarkable statistical properties, one being the Generalized Central Limit Theorem.
While the conventional Central Limit Theorem gives rise to the normal distribution, the Generalized Central Limit Theorem goes a step further. It enables sums of a large number of independent and identically distributed heavy-tailed variables to converge into a stable distribution, distinguishing it from its more common counterpart.
Parameters and Characteristics of Stable Distributions
Essential to understanding stable distributions are the four parameters, namely, the stability parameter alpha (0 0), and the location parameter mu. Alpha defines the heavy-tailed nature: a smaller value corresponds to a heavier tail. The skewness parameter beta promotes asymmetry, with beta equals 0 implying symmetry. The scale parameter sigma determines dispersion, while mu shifts the location of the distribution.
Zolotarev’s parametrization of stable distributions is based on the notion of spectral measures. This approach uniquely determines a one-to-one mapping between the four parameters of a stable distribution and its characteristic function. This characterization is a cornerstone for further analytical exploration and application of stable distributions in various fields.
Characteristic Function of Stable Distribution
The characteristic function of a stable distribution has an integral expression derived from the inverse Fourier Transform. This function, representable as an exponential series, is essential for understanding the mathematical structure underlying stable distributions.
Although the explicit form of the Probability Density Function (PDF) is only known for certain values of alpha and beta, the characteristic function always exists and is used to compute necessary statistics such as the expectation and variance when they exist.
Understanding Lévy Processes
A Lévy process is a type of stochastic process characterized by stationary and independent increments. This means the future evolution of the process depends only on its present status and behaves independently of its past. Lévy processes have been widely used in diverse areas of science, including modeling equity prices in finance or describing anomalous diffusion in physics.
A particular facet of these processes is that they may exhibit jumps, a property resulting from their allowance for alpha-stable distributions. The name Lévy processes come from Paul Lévy, who was the first mathematician to study these processes systematically under the framework of probability theory.
Simulating Stable Random Variables
The simulation of stable random variables plays an integral role in gaining a comprehensive understanding of stable distributions and Lévy processes. A well-known and effective approach to accomplishing this is via the Chamber-Mallows-Stuck (CMS) method, an algorithm specifically designed to generate independent, one-dimensional alpha-stable random variables.
These derived stable random variables are instrumental in shaping the simulations for a Lévy process and further advancing statistical studies. In conjunction, the visualization of these simulations can provide tangible and insightful perspectives on the behavior and intrinsic qualities of these distributions, serving as a practical adjunct to the theoretical framework.
Mathematical Modeling of Stable Diffusion
Introduction to Stable Diffusion
Stable diffusion is a pivotal factor in an array of disciplines, spanning from mathematical physics and scientific computing through to various sectors of engineering. This term gives a description to a specific type of random particle motion or dispersion, which is guided and influenced by stochastic variables or a collection of random forces.
The key to comprehending stable diffusion is rooted in the fundamentals of several mathematical structures, primarily probability theory and calculus. Of particular significance are stochastic differential equations (SDEs), which provide the core framework for the modeling and understanding of this concept.
Stochastic Differential Equations and Stable Diffusion
Stochastic differential equations, widely used in mathematical finance, physics, and engineering, are differential equations in which one or more terms have a stochastic, or random, component. They are utilized to model systems that behave unpredictably. In the context of stable diffusion, a stochastic differential equation can be used to model the erratic movement of particles.
An important aspect of SDEs in the context of stable diffusion is their ability to model Lévy processes – a type of stochastic process that generalizes random walk, and characterizes stable diffusion. Lévy processes and the stable distributions associated with them allow for mathematical characteristics of random motion to be precisely described and computed.
A Solution to Stochastic Differential Equations
The solutions to stochastic differential equations, often known as stochastic processes, provide detailed behavior of the system being modeled. Unlike deterministic systems, solutions to SDEs are not single functions. Instead, they are probability distributions, denoting the likelihood of the system’s various states.
These solutions are obtained through an operation called Ito calculus, a branch of mathematical analysis that is used for manipulating stochastic integrals and solving stochastic differential equations. Despite being a complex discipline, understanding Ito calculus is considered fundamental in comprehending the math behind stable diffusion.
Relation to Stable Diffusion
Given the irregular and often unpredictable nature of particle dispersion in stable diffusion, it’s the stochastic differential equations that come handy in predicting the system’s behavior. Through these equations and their solutions, one can measure and predict the random motion of particles, evaluating their positions at different points in time.
The solutions also enable the interpretation of stochastic processes, representing the probability distribution of the diffusion system. This aspect aids in investigating vital properties of stable diffusion, including dispersion, skewness, and kurtosis.
Moreover, using the SDEs and their solutions, specific cases like anomalous diffusion, a form of diffusion that isn’t represented by normal Gaussian statistics, can be further investigated. This fact largely expands the potential applications, contributing to the field’s growing importance in many scientific and engineering disciplines.
Introduction to Stochastic Differential Equations within Stable Diffusion Mathematical Concepts
Stable diffusion, a key concept in the fields of mathematics and physics, is an instrumental model in numerous sectors, contributing to extensive research, sophisticated simulations and innovative technological progressions.
It primarily involves the application of stochastic differential equations. Understanding the mathematical intricacies of stable diffusion is thus crucial, especially for the effects that stochastic differential equations can have in diverse applications.
Analyzing Stable Diffusion in the Real World
Delving Into Stable Diffusion
From a mathematical standpoint, a random process is considered ‘stable’ if its characteristic function, a description of the process’s variance and skewness, follows a stable distribution. This scenario creates what we call a ‘stable stochastic process,’ which applies to phenomena that follow a random walk.
In such a case, the future outcomes are influenced by past results, injected with an element of randomness, resulting in an evolution of the system via a series of often random, incremental changes over time.
On the other hand, the physics behind stable diffusion (also known as ‘normal diffusion’) involves the dispersion of particles from their original position over a period. This physical attribute is a product of the microscopic, random motion of particles, affecting their macroscopic movement. More precisely, stable diffusion connects to the process where the mean square displacement of particles aligns linearly with the time elapsed.
The mathematical basis of Stable Diffusion Mathematical Concepts
Mathematically, stable diffusion gets its fundamental foundation from central limit theorem, Brownian motion, and random walks. It is modelled by the famous diffusion equation, also known as the heat equation. This equation is a vital part of many branches of physics, including statistical mechanics and quantum mechanics.
This difussion equation involves variables like the diffusion coefficient, time, and space. The diffusion coefficient quantifies the speed or intensity of diffusion. This coefficient and the other parameters allow for quantification and exact calculation of the diffusion process over given periods, offering detailed insights into how a system evolves.
Stable Diffusion in Finance
In finance, stable diffusion has been used to create models to predict and assess various financial phenomena. For instance, the Black-Scholes model, widely used in the pricing of options, applies the principles of diffusion. The idea is to gauge how the price of an option diffuses over time, thereby enabling optimal pricing strategies.
The same concept is embodied in Stochastic volatility models as well. These are used to model how financial market volatility evolves over time following a random process. The underlying security’s price variance follows a random walk, exhibiting an element of diffusion.
Stable Diffusion in Data Science
The field of data science has also borrowed these principles. Stable diffusion has proven particularly useful in areas that involve stochastic processes and time-series modelling. In theory, many forms of data, such as daily temperatures or stock market returns, could be modelled as stable processes.
For instance, predicting future data values from past ones is a common practice in time series analysis and forecasting. This process could involve predicting future stock prices based on past performance, assuming the return-to-risk ratio remains fairly stable over time.
In the field of machine learning, Markov Decision Processes represent a probabilistic model, which inherently applies principles of diffusion for modelling decision-making situations.
Understanding the mathematical basis of stable diffusion not only fortifies comprehension of several real-world phenomena but also provides a valuable tool for researchers and practitioners in diverse fields. Moreover, the application of stable diffusion improves decision-making strategies and optimizes predictive analyses.
Through the journey into the depths of Stable Diffusion Mathematical Concepts, we come to appreciate the substantial roles played by Fick’s laws, Markov chains, Brownian motion, zolotarev’s parametrization and stochastic differential equations. With this profound knowledge, it is clear that the mathematics intricately entwined with stable diffusion offers impeccable preciseness and accuracy in modeling.
The broad spectrum of its applications vary across several fields; physics, data science and the financial sector, where its contributions have proven to be of valuable support. This exploration not only enhances our comprehension of stable diffusion, but also arouses our curiosity to extend our knowledge, challenge existing models and strive to develop newer, more efficient ones.
Emad Morpheus is a tech enthusiast with a unique flair for AI and art. Backed by a Computer Science background, he dove into the captivating world of AI-driven image generation five years ago. Since then, he has been honing his skills and sharing his insights on AI art creation through his blog posts. Outside his tech-art sphere, Emad enjoys photography, hiking, and piano.


This area represents the heart of decision theory. The procedure now referred to as expected value was known from the 17th century. Blaise Pascal invoked it in his famous wager (see below), which is contained in his Pensées, published in 1670. The idea of expected value is that, when faced with a number of actions, each of which could give rise to more than one possible outcome with different probabilities, the rational procedure is to identify all possible outcomes, determine their values (positive or negative) and the probabilities that will result from each course of action, and multiply the two to give an expected value. The action to be chosen should be the one that gives rise to the highest total expected value. In 1738, Daniel Bernoulli published an influential paper entitled Exposition of a New Theory on the Measurement of Risk, in which he uses the St. Petersburg paradox to show that expected value theory must be normatively wrong. He also gives an example in which a Dutch merchant is trying to decide whether to insure a cargo being sent from Amsterdam to St Petersburg in winter, when it is known that there is a 5% chance that the ship and cargo will be lost. In his solution, he defines a utility function and computes expected utility rather than expected financial value.
In the 20th century, interest was reignited by Abraham Wald’s 1939 paper pointing out that the two central procedures of sampling–distribution–based statistical-theory, namely hypothesis testing and parameter estimation, are special cases of the general decision problem. Wald’s paper renewed and synthesized many concepts of statistical theory, including loss functions, risk functions, admissible decision rules, antecedent distributions, Bayesian procedures, and minimax procedures. The phrase “decision theory” itself was used in 1950 by E. L. Lehmann.
The revival of subjective probability theory, from the work of Frank Ramsey, Bruno de Finetti, Leonard Savage and others, extended the scope of expected utility theory to situations where subjective probabilities can be used. At this time, von Neumann’s theory of expected utility proved that expected utility maximization followed from basic postulates about rational behavior.
The work of Maurice Allais and Daniel Ellsberg showed that human behavior has systematic and sometimes important departures from expected-utility maximization. The prospect theory of Daniel Kahneman and Amos Tversky renewed the empirical study of economic behavior with less emphasis on rationality presuppositions. Kahneman and Tversky found three regularities — in actual human decision-making, “losses loom larger than gains”; persons focus more on changes in their utility–states than they focus on absolute utilities; and the estimation of subjective probabilities is severely biased by anchoring.
Castagnoli and LiCalzi (1996), Bordley and LiCalzi (2000) recently showed that maximizing expected utility is mathematically equivalent to maximizing the probability that the uncertain consequences of a decision are preferable to an uncertain benchmark (e.g., the probability that a mutual fund strategy outperforms the S&P 500 or that a firm outperforms the uncertain future performance of a major competitor.). This reinterpretation relates to psychological work suggesting that individuals have fuzzy aspiration levels (Lopes & Oden), which may vary from choice context to choice context. Hence it shifts the focus from utility to the individual’s uncertain reference point.
Pascal’s Wager is a classic example of a choice under uncertainty.


If the six comparisons can be assumed to be independent can we make a comment or reference about when this assumption cannot be made? Calculations of the means and the variance are performed as part of the hypothesis test.
Why is it not appropriate to use independent sample t-tests Introduction to one way analysis of variance test all possible pairs of treatments and to identify differences between treatments?
Tiku found that "the non-normal theory power of F is found to differ from the normal theory power by a correction term which decreases sharply with increasing sample size. For example, in a study involving four treatments, there are six possible pairwise comparisons.
Analysis of variance is used to avoid this problem. Multiple comparison procedures and orthogonal contrasts are described as methods for identifying specific differences between pairs of treatments. The number of pairwise comparisons is given by 4C2 and is equal to 4! This is the chance of incorrectly rejecting the null hypothesis i.
The case of fixed effects, fully randomized experiment, unbalanced data[ edit ] The model[ edit ] The normal linear model describes treatment groups with probability distributions which are identically bell-shaped normal curves with different means.
The commonly used normal linear models for a completely randomized experiment are: One-way analysis of variance In an independent samples t-test, the test statistic is computed by dividing the difference between the sample means by the standard error of the difference.
Hence, the chance of committing a type I error in at least one of the comparisons is 1 - 0. Assumptions[ edit ] The results of a one-way ANOVA can be considered reliable as long as the following assumptions are met: When interpreting a P value, it can be concluded that there is a significant difference between groups if the P value is small enough, and less than 0.
Response variable residuals are normally distributed or approximately normally distributed. The current view is that "Monte-Carlo studies were used extensively with normal distribution-based tests to determine how sensitive they are to violations of the assumption of normal distribution of the analyzed variables in the population.
One-way analysis of variance is the simplest form. It is an extension of the independent samples t-test see statistics review 5 [ 1 ] and can be used to compare any number of groups or treatments.
If data are ordinala non-parametric alternative to this test should be used such as Kruskal—Wallis one-way analysis of variance. Variances of populations are equal.
To answer this it is necessary to look more closely at the meaning of a P value. The general conclusion from these studies is that the consequences of such violations are less severe than previously thought. This method could be used, for example, in the analysis of the effect of three different diets on total serum cholesterol or in the investigation into the extent to which severity of illness is related to the occurrence of infection.
The variance of a set of n values x1, x Thus fitting the models requires only the means of each treatment group and a variance calculation an average variance within the treatment groups is used.
If the chance of a type I error in one such comparison is 0. If multiple t-tests are carried out, then the type I error rate will increase with the number of comparisons made. The first comprehensive investigation of the issue by Monte Carlo simulation was Donaldson However, as either the sample size or the number of cells increases, "the power curves seem to converge to that based on the normal distribution".
Abstract This review introduces one-way analysis of variance, which is a method of testing differences between more than two groups or treatments. The standard error of the difference is an estimate of the variability within each group assumed to be the same.Analysis of Variance A.
Introduction B. ANOVA Designs C. One-Factor ANOVA (Between-Subjects) An ANOVA conducted on a design in which there is only one factor is called a one-way ANOVA. If an experiment has two factors, then the ANOVA is called a The analysis of data with two scores per subject is shown in the section on within.
Analysis of Variance (ANOVA) is a statistical method used to test differences between two or more means. It may seem odd that the technique is called "Analysis of Variance" rather than "Analysis of Means.". Berger: Introduction to One-Way ANOVA 3 An equivalent test of the null hypothesis can be calculated with the F distribution, because t 2 with df = is exactly equal to F (df = 1,).
One-Way Analysis of Variance (ANOVA) Example Problem Introduction Analysis of Variance (ANOVA) is a hypothesis-testing technique used to test the equality of two. One-way ANOVA in SPSS Statistics Introduction. The one-way analysis of variance (ANOVA) is used to determine whether there are any statistically significant differences between the means of two or more independent (unrelated) groups (although you tend to only see it used when there are a minimum of three, rather than two groups).
Introduction. Analysis of Variance (ANOVA) is a hypothesis-testing technique used to test the equality of two or more population (or treatment) means by examining the variances of samples that are taken.Download


Graphs day 140, pandemic day 147, day 217 since the first cases were diagnosed. I had to look up how to write 140 in Roman numerals. Worst franchise ever.
Just a quick update of some national- and state-level data while I work on SOMETHING REALLY EXCITING!
Total cases of COVID-19 diagnosed worldwide: 18,282,208
Total deaths: 693,694
Earth is quickly headed for the new milestone of 700,000 deaths, probably later this week.
Today’s update is for some of the countries and states we have been following where cases continue at high rates. The main graph is on a slightly modified regular scale, running from zero to 250 cases per million people per day. The inset is on the infamous Qatar scale (0-700 cases per million people per day). Each region gets a unique color and is labeled close to the line with the same color. The label also gives the mortality rate (cumulative deaths per million people) in the region – cumulative because the dead stay dead. The thickness of the lines and the size of the labels depend on the cumulative case fatality rate – the number of people who died divided by the number diagnosed.
Florida is definitely doing better. California and Texas are a bit less clear, but hopefully they are moving in the right direction.
Stay tuned for SOMETHING REALLY EXCITING! Probably not tomorrow, but soon.
Want to try these graphs yourself? Go for it!!! I’ve updated my spreadsheet (still version 7) to restore the formulas. The upside is that you can now more easily make changes to make the graphs your own; the downside is that unless you are on a high-end computer, the calculations will be slooooooooooooooooow. To speed up calculations, replace formulas with values once you decide you have the right formulas. If you’re not sure how to do that, just ask – leave a comment, messenge me on social media, or send me an email at email@example.com.


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...studies Economics and Management at the University of Oxford, having achieved A* grades at A-Level in Mathematics, Further Mathematics, Economics and Music and 11 A* grades at GCSE. Quinn offers tutoring in Mathematics, Economics, Physics, Music and German for students from KS1 up to A Level, as well as instrumental tuition in violin, organ and piano up to ABRSM Grade 8. He enjoys football as well as performing, directing and listening to all kinds of music, and achieved an ARSM violin performance diploma in 2018; he is also a native German speaker, and currently attempting to teach himself Mandarin.
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...is currently on her gap year, and holds an unconditional offer from the University of Cambridge to study Asian and Middle Eastern Studies - Japanese. She achieved high grades at A Level in Mathematics, English and History, and tutors in Mathematics and English. She is a native Mongolian speaker, and has completed intensive training to teach English as a foreign language.
...is a Chemistry student at the University of Oxford. She studied Chemistry, Mathematics and French Higher Level for IB, and Physics, History and German Literature Standard Level. She achieved 765777 grades respectively, earning 41 points overall. She is a native German speaker, and has studied ABRSM Grade 5 and GCSE music theory. She offers tutoring in highlighted subjects up to a sixth form level, music theory up to Grade 5 and Latin up to Year 10, extended essays and Theory of Knowledge. She is happy to plan a series of tutorials for Oxford Chemistry interview practice and/or personal statement work in any subject. Outside academics, she enjoys playing the violin, choral singing and going for the occasional run.
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...has tutored a range of abilities in Mathematics, Biology, Chemistry and Music, and achieved A*A*A*A in these subjects at A Level. He earnt gold and silver certificates in the olympiads of the Royal Societies of Biology and Chemistry, and was one of 600 mathematicians in his year to qualify for the UK Maclaurin Olympiad. He is studying Music at the University of Oxford with a focus on classical analysis and conducting studies, and studied cello, piano, oboe and composition as a junior bursary awardee at the Royal College of Music. He has played the cello with the National Youth Orchestra GB, and as principal with local and national orchestras. He is happy to provide instrumental tuition as well as academic tuition and university application help.


At The Lancaster School we aim to make Maths meaningful, exciting and engaging. We place great emphasis upon developing the key skills in mathematics so that your child can apply a solid understanding of number, data handling, shape, space and measures, in order to solve problems in a wide range of real-life situations.
Teaching and learning focuses on the skills and knowledge required to use and apply maths, as well as giving children the opportunities to put these to use through investigation and problem solving activities.
To achieve this, teaching is rooted in the development of children’s understanding of Maths, both within a lesson and over time. Links are made between the various elements of Maths in order that children can use and apply mathematical strategies and thinking. Connections are developed via teaching through topic work, real life situations and problem solving. The ability to use and apply Mathematical thinking is an important part of problem solving and through our topic work we are able to make Maths a creative and exciting experience which is engaging and fun, whilst also establishing cross-curricular links and links to the wider world.
Our aim is to foster enthusiastic, competent mathematicians who are able to meet and exceed age related expectations. Where children find Maths challenging we initiate support strategies to ensure that their needs are met and that progress is made as speedily as possible. Accurate monitoring of progress is ensured through marking, feedback, questioning and discussion.


Manual browser: roundup(9)
|ROUNDUP(9)||Kernel Developer's Manual||ROUNDUP(9)|
NAMEroundup — macros for counting and rounding
DESCRIPTIONThe roundup() and rounddown() macros return an integer from rounding x up and down, respectively, to the next size. The howmany() macro in turn reveals how many times size fits into x, rounding the residual up.
The roundup2() macro also rounds up, but with the assumption that size is a power of two. If x is indeed a power of two, powerof2() return 1.
RETURN VALUESThe return value is an integer from the respective operation. If x is 0, all macros except powerof2() return 0. The behavior is undefined if size is 0.
EXAMPLESThe following example rounds the variable rx to a 32-bit boundary:
uint16_t rx; ... rx = roundup2(rx, sizeof(uint32_t));
CAVEATSAll described macros make no assumptions about the type of the parameters. These are implicitly assumed to be unsigned integers.
|June 1, 2011||NetBSD 7.0|


You load data from a source with an allegedly unique key.
Then you need to do some calculations on it, using data from other sources say, or perhaps do some calculations in the script (to make charts faster in the app) so you join the table back onto itself.
Imagine there's a duplicate, 2 lines with the same key in. When you join it onto itself, each line will replicate X the number of rows it matches in the table that you join it with. IE 2 rows will turn into 2 X 2 = 4 rows:
|Data||Data_2||Data - after join|
If you were to then join the table onto itself again, each row with key #4 will join back onto itself 4 times, creating 4 X 4rows = 16.
So far so obvious.


Here at OpWell Forex, we are committed to unlocking the potential of traders’ investments! In this article, we dive into the world of compound interest and introduce you to our smart compound interest calculator. If you’re looking to estimate your profit growth and maximize your returns, you’ve come to the right place. Let’s explore the fascinating concept of compound interest and how our calculator can be your trusted companion on your financial journey.
Table of Contents
What is Compound Interest?
Compound interest is a magical force that can turn even a modest investment into a substantial sum over time. Unlike simple interest, which is calculated only on the initial investment, compound interest takes into account the accumulated interest as well. This means that as your investment grows, so does the interest it earns, leading to exponential growth.
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Compound interest offers numerous benefits for long-term investors. Firstly, it accelerates wealth accumulation by continuously reinvesting the interest earned. Over time, this compounding effect can significantly boost your investment returns. Secondly, it allows you to harness the power of time. The earlier you start investing, the longer your money has to compound and grow, giving you a substantial advantage.
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To use our smart Compound Interest Calculator, simply input your initial investment amount, the interest rate, and the duration of your investment. Whether you’re saving for retirement, a down payment on a house, or your dream vacation, our calculator provides you with a clear projection of your future wealth.
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Our smart compound interest calculator goes beyond basic projections. It offers a range of features to customize your calculations and cater to your unique investment goals. You can adjust the compounding frequency, explore different interest rates, and even factor in additional monthly contributions. With these features at your disposal, you gain a deeper understanding of how small adjustments can make a significant impact on your long-term returns.
Let’s bring compound interest to life with a few real-life examples. Imagine you invest $12,000 with an annual interest rate of 25% for 5 years. Using our calculator, you’ll discover that your investment will grow to an impressive $36,621.09. That’s more than triple your initial investment! Now, consider the power of compounding over 10 or 20 years. The numbers become truly staggering, highlighting the importance of starting early and letting time work in your favor.
Maximizing Your Returns
While compound interest is a powerful tool, there are strategies to maximize its potential even further. Diversifying your investments, regularly contributing to your portfolio, and exploring higher-yield investment options can all accelerate your wealth accumulation. Our calculator allows you to test different scenarios and see the impact of these strategies firsthand.
The Power of Compound Interest in Financial Planning
Compound interest is not just a concept for the rich and experienced investors; it’s a valuable tool for everyone. Whether you’re starting with a small investment or looking to grow your existing portfolio, understanding compound interest and using our calculator can help you make informed financial decisions. It’s an essential component of long-term financial planning, allowing you to set realistic goals and track your progress along the way.
Invest with Confidence
At OpWell Forex, we believe that everyone deserves a chance to achieve financial well-being. Our smart compound interest calculator puts the power of compounding at your fingertips, giving you the confidence to invest wisely and watch your wealth grow over time. Take advantage of this valuable tool and start estimating your profit growth today.
Compound interest is a remarkable force that can significantly impact your financial future. Understanding its benefits and utilizing tools like our smart compound interest calculator can empower you to make informed investment decisions and set realistic goals. Whether you’re a beginner or an experienced financial investor, the power of compounding can work in your favor.
Each time you visit OpWell Forex, you can access the calculator link in the main menu of the website and explore our smart compound interest calculator. Unleash the potential of your investments and embark on a journey toward financial success. Start estimating your profit growth, and let the magic of compound interest guide you to a brighter financial future.
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|June 1, 2017 - Regular School Board Meeting
C7 - Eureka Math (Grades 2-8)
The Curriculum and Instruction Division is seeking permission to purchase Eureka Math manipulative kits, teacher guides and printed student materials to support our existing 2- 8 math curriculum. This open source curriculum resource, developed for New York City Schools and used by two comparable school districts in Florida (Pasco, Lee), will provide teachers with an additional tool for Tier 1, 2, and 3 instruction, assessment, and monitoring of the tested Florida Standards for Mathematics. Eureka contributes to a deeper understanding of number sense and number relationships from lesson to lesson and from grade to grade and embeds a continued emphasis on discussion, modeling, and explanation to deepen students conceptual understanding of mathematics. In addition, Eureka currently has embedded math content professional development for teachers.
Teachers are currently using a combination of GoMath, Carnegie Learning Series, standards-based linked resources, and teacher created materials to instruct their students. Teachers and administrators have expressed concern about the need for additional materials and resources to better address the rigor of our Florida Math Assessment Standards. Our INTEL professional development data reflects a significant need to deepen math content knowledge of our teachers grades K-8. Math content skills are addressed within the Eureka curriculum to help develop teachers’ mathematical content area knowledge and better prepare our students for success.
A three year trend analysis shows that Clay County Schools math proficiency has been flat and or declining in performance and the number of students scoring at Level 1 or 2 continues to be flat or increasing. This calls for a need to modify what we are doing to address individual student needs to help them meet the new rigor of FSA and higher mathematics expectations.
Grade level proficiency and students scoring Level 1 or 2 results over 3 years are included in the chart below:
Expected Outcomes: Increased student achievement in learning gains and proficiency, accompanied by a correlating decrease in the number of Level 1 and 2 students as measured by the FSA is expected. The schools and teachers implementing Eureka have volunteered to implement these new tools with fidelity. Target schools represent a range of schools from lowest performing schools in mathematics to higher performing, urban, rural and suburban schools.
|Strategic Plan Goal
Support the instructional framework problem solving by implementing standard- based instruction that enriches and improves student achievement. School based instructional coaches will provide on-site support for teachers using the Eureka resources and manipulatives kits.
We are recommending that the Board approve the purchase of the Eureka Math resources according to the purchase plan found within this agenda item.
Dr. Theresa Stahlman, Assistant Superintendent of Curriculum and Instruction
$54,990.00 - Manipulatives (one time cost) $107,921.49 Recurring cost for printing student materials annually if school numbers stay the same $5.76 Cost per student: 3,897 students will be impacted based on this implementation Funding Source: State Textbook Allocation as a supplemental resource ($177,594.80 plus shipping setup cost)


5) Probability Bridge accompanied by Maple program: ProbBridge , posted June 21, 2019. These results also appeared on wikipedia.
4) Fibonacci Identities through Matrix Method accompanied by Maple program: FiboMatrix , posted December 27, 2018.
3) Moment Calculus on Ramsey Graph accompanied by Maple program: Ramsey , posted first version April 2018, second version August 26, 2019.
2) Toads and Frogs: Three Results of Combinatorial Game Toads and Frogs , posted November 2009.
1) On the Ramsey Multiplicity of Complete Graphs , posted August 2009.


In today’s competitive world, possessing solid math skills can set you apart from the crowd and significantly enhance your chances of success in various competitive exams. Performing calculations quickly and accurately saves valuable time during tests and demonstrates a high problem solving ability. In this blog post, we will explore practical strategies and pro tips to help you improve your mental math skills, empowering you to conquer any numerical challenge that comes your way.
Develop a Strong Foundation
Before diving into advanced mental math techniques, it is crucial to establish a strong foundation in basic arithmetic operations. Familiarise yourself with addition, subtraction, multiplication, and division, ensuring you can perform calculations effortlessly. Practice mental math exercises regularly to build speed and accuracy.
Pro Tip: Start with small numbers and gradually increase the difficulty level to challenge yourself and enhance your skills progressively.
Utilise Number Patterns
Recognising and leveraging number patterns is a powerful technique to improve mental math skills. Identifying recurring patterns and relationships within numbers can simplify complex calculations.
Pro Tip: Memorise common number patterns like squares, cubes, and prime numbers to expedite calculations.
Break Down Problems
Complex math problems can appear daunting at first glance, but breaking them into simpler components can make them more manageable. Dividing problems into smaller steps allows you to focus on one task at a time, reducing mental strain and increasing accuracy.
Pro Tip: Practice the art of problem decomposition by breaking down complex equations or word problems into simpler parts and solving them step by step.
Mental Estimation Techniques
Developing the ability to make quick and accurate estimations is invaluable in competitive exams. The estimate helps approximate answers, eliminate obviously incorrect options, and save time.
Pro Tip: Improve estimation skills by practising mental calculations involving rounded numbers, simplifying fractions, and using clever approximations.
Develop Calculation Shortcuts
Specific calculation shortcuts and tricks can significantly speed up mental math. Learning these shortcuts for multiplication, division, percentages, and fractions can give you a competitive edge during exams.
Pro Tip: Memorise common multiplication tables, learn tricks for mental division and explore techniques like cross-multiplication and percentage conversion shortcuts.
Engage in Regular Practice
Mental math proficiency requires consistent practice to maintain and improve like any other skill. Dedicate regular time to solve mental math problems in a simulated exam environment and during everyday tasks.
Pro Tip: Set aside a specific time each day for mental math practice, using online resources, practice books, or mobile apps to access various problem-solving exercises.
Mastering mental math is a valuable asset for excelling in competitive exams. You can significantly enhance your mental math skills by developing a solid foundation, recognising number patterns, breaking down problems, employing estimation techniques, and utilising calculation shortcuts. Remember, regular practice is the key to maintaining and improving your abilities. So, start incorporating these pro tips into your daily routine, and watch yourself stand out from the crowd, armed with the confidence and speed to succeed in any mathematical challenge that comes your way.


ENIAC’s 60th Anniversary
Yesterday was the 60th anniversary of the creation of ENIAC, the world’s first all-electronic computer, here at U Penn. An interview with Presper Eckert, one of its co-inventor’s, was recently published on the ComputerWorld site. I was fascinated by his description of the Harvard Mark 1, ENIAC’s mechanical predecessor:
It could solve linear differential equations, but only linear equations. It had a long framework divided into sections with a couple dozen shafts buried through it. You could put different gears on the shafts using screwdrivers and hammers and it had “integrators,” that gave [the] product of two shafts coming in on a third shaft coming out. By picking the right gear ratio you should get the right constants in the equation. We used published tables to pick the gear ratios to get whatever number you wanted. The limit on accuracy of this machine was the slippage of the mechanical wheels on the integrator.
And about ENIAC itself:
The ENIAC was the first electronic digital computer and could add those two 10-digit numbers in .00002 seconds — that’s 50,000 times faster than a human, 20,000 times faster than a calculator and 1,500 times faster than the Mark 1. For specialized scientific calculations it was even faster… ENIAC could do three-dimensional, second-order differential equations. We were calculating trajectory tables for the war effort. In those days the trajectory tables were calculated by hundreds of people operating desk calculators — people who were called computers. So the machine that does that work was called a computer… ENIAC had 18,000 vacuum tubes… The radio has only five or six tubes, and television sets have up to 30.
He also mentioned that back then Philadelphia was “Vacuum Tube Valley.” My neighbor, a man in his 70s, told me he use to work on re-entry systems in an office on Walnut St. I asked if he meant programs for people re-entering the work force. “No,” he said “I worked for GE, designing re-entry systems for astronauts in spaceships.” It seems that little of this technological legacy remains here. Penn’s school of engineering isn’t what it used to be (Penn’s schools of business, architecture, communications, medicine, nursing and veterinary medicine are all top 5 schools, but engineering ranks 27th). And while there are Lockheed-Martin offices and pharmeceutical companies scattered around the tri-state area, and Drexel is a good engineering school, I don’t get any sense that the city of Philadelphia does anything to capitalize on its remaining engineering and technology assets.


Geometric Algebra 2D: Background Information
|Summary||With this applet you can develop and practice algebraic skills, like: solving equations, using parentheses and operating with negative numbers.
Equations are represented by areas with two dimensions. You can work with constants and variables (x, y, z).
This is a renewed version of the original applet.
|Age Group||middle school (gr. 7-8) | high school (gr. 9-10) | high school (gr. 11-12)|
|Author||Gerard Koolstra, Martin van Reeuwijk, Martin Kindt, Peter Boon|
|© wisweb.nl 2003 - 2012|


Looking to give your preschooler a head start on learning? Or, want to extend your older child’s learning beyond the school day? Science, Technology, Engineering, Arts and Math (STEAM) learning plays a key role in your child’s education. Plano Public Library (PPL) offers many resources to support your child’s learning and development in these key concepts. Specifically, the virtual programs available through our STEAM Connections playlist on PPL’s YouTube channel offer STEAM projects that give your child hands-on opportunities to learn.
PPL is committed to preparing the youngest of learners to be ready for a lifetime of learning through STEAM Connections. Through our STEAM programming, you can prepare your young learner(s) for school and beyond. As new activities are posted through our blog and on YouTube, we will provide you with detailed information on how the activity is connected to either Science, Technology, Engineering, Arts or Math. Oftentimes, the activities crossover to more than one area of STEAM.
Not only will your child experience learning across the different areas of STEAM, but they will gain the building blocks of critical thinking that is crucial to learning. PPL’s STEAM programming will provide you with opportunities to work with your child in developing skills that will help them achieve success in school. Not only is STEAM education essential to your child’s education, but it will also help them develop skills that will prepare them for tomorrow’s workforce. Combining STEAM concepts opens up learning opportunities that translate into future success.
Stay tuned to see more from Plano Public Library’s STEAM Connections! As STEAM programs are added, you can plan to give your child quality learning experiences that will enhance their knowledge and skills in Science, Technology, Engineering, Arts and Math while having fun!


Language problems in mathematics studies Is there a link between difficulty solving mathematical verbal problems and reading deficiency among 7th graders?
Keywords:verbal problems in Mathematics, reading deficiency, problems’ solving pressure, mathematical solving complexity
The aim of this study was to find out whether or not there is a connection between an observed difficulty in solving verbal mathematical verbal problems and reading deficiency, specifically among 7th grade students in Israeli Arab schools.
This study is a combination of a preliminary test to identify students who have difficulty in solving verbal mathematical verbal problems and a follow-up qualitative study of the students identified as having such difficulties, based on personal interviews.
The preliminary test included ninety 7th grade students from three schools in northern Israel, 30 from each school. The participants were given easy leveled verbal mathematical verbal problems. The qualitative study had been performed with 10 out of the 32 students that failed the preliminary test (scored less than 60).
The main findings indicate a connection between students’ reading ability and the ability to solve verbal mathematic problems. In the conducted preliminary test, some of those failing to solve verbal mathematical problems were found to have reading difficulties.
It was also found that compared to students with relative high academic achievements, most students with lower achievements, report low interest in learning and approach tests (in mathematics and other subjects), with low faith in their ability to succeed.


In Honor of Pi Day: 5 Points about Pie
March 14th is referred to as Pi Day, in recognition of the ratio of the circumference of a circle to its diameter (which is approximately 3.14159). This year, the date of Pi Day can be expressed as 3.14.15, which makes it extra special, since 2 more digits of pi show up in the date. In honor of this occasion, here are some points about pie (the kind you eat):
1) National Pie Day is on January 23rd each year.
2) According to a Nielsen survey conducted in 2014, apple is still number one among pie flavors. (Pumpkin and chocolate are tied for second, followed by cherry.)
3) Pies originally had meat fillings and baking a pie was a method of food preservation.
4) There are at least 3 types of “pie” that aren’t really pie: Boston cream pie (a type of cake), whoopie pie (a cross between a cookie and a cake) and sweetie pie (a term of endearment).
5) For some people, their favorite pie is pizza pie! For many of us, every month is pizza month, but it turns out that October is actually National Pizza Month.


Sep 7, 2014 at 10:58 AM
Edited Sep 7, 2014 at 10:58 AM
I seem to be unable to find out which classes and methods to use to check the resulting P value for a dice roll that gives a 19:1 probability to produce a six in stead of a one.
So when making 60 dice rolls, the expected frequency of any number coming up top is 10.
In my "leaded" dice the observed frequencies are:
ì entered the expected and the "observed" values on this website:
and the resulting Chi Square value was 16.2 and the P value was 0.00629, indicating that the dice, indeed, has been tampered with.
I am unable however to produce this result using Metanumerics. I tried constructing an ContingencyTable and called the PearsonChiSquaredTest on it. But I get a P value of 0.07. I am unsure how to fill the table, it this is the rigt approach at all.
So, how to do t?


Facilities & Services
Homework Club & Maths tutoring
In 2010 Dominic College started up a Homework and Computer Club. Each lunchtime computer rooms for both Primary and Secondary students will be open for students to use. Teaching and non-teaching staff have been very generous in offering their time to supervise this program.
Students are welcome to drop in after they have eaten lunch, offering a great chance to catch up on, or get a head start, on their homework. Primary students are welcome to spend some more time on their favourite software title once a week, conducting research or working through an educational game.
Students use the Computer club for a variety of reasons – research for class assignments, use educational programs, create slideshows, practise computer skills, etc. The response from students has been overwhelming so far.
In 2010 Dominic College introduced Maths tutoring after school, along with setting homework tasks using a Maths online program.
The opportunities for using Maths Online will be even greater now that the laptop program has been introduced to the Year 7s in 2012, and will continue to strengthen when all Dominic secondary students have laptops by 2015.
Year 5 students have just started using a program called Mathletics, which is an online program that teaches Maths in an exciting and engaging way.
It’s all part of the quest to increase the academic rigour of our students so that we’re in line with national standards.


Learning math requires both practice and regular application of mind. Contrary to what people believe, practicing routine sums do not make one perfect, rather, repeated sums of the same type may make students dumb. So you need sums that blend both practice and logic. Problems that mix arithmetic and algebraic operations with clever thinking.
Our Limit platform which houses 150+ math apps, algorithmically generates such clever, thinking-oriented sums (and algorithmically provides their explanations too) – and it does it better than most humans. Through this platform, you can expose your children to numerous (actually, unlimited) thinking-oriented problems everyday – and that’s the only way to build thinking skills and mathematical instincts.
These apps are already in use in a number of schools, including The Levelfield School, where it produced spectacular results. Levelfield students have a median SAT score of 1550, and more than 50% of every batch get into IIM’s prestigious IPM program. Such results are made possible due to regular exposure to thinking oriented math from a young age.
Tablet (> 10.5 inch)


Mathematics is the only subject that can either be a student’s best friend or worst nightmare. This difficult path from struggling to achieving success in mathematics is a very big challenge for many students. Failing the math subject once or twice puts students in depression, and completing that subject on the second or third attempt can be fearful and requires extra dedication. Now, students are finding new ways to beat the fear and get new learning experiences with advanced mathematics in this modern world of online classes. In this blog, we are going to learn the dedication we need for advanced mathematics in the educational environment and share real-life-changing stories of students who have overcome math difficulties through online class help.
If you are busy with other commitments and you want to pay someone to do my online class, Just reach out to Take My Online Class Help, contact our team, and ask for Do My Advanced Mathematics Class, and our team will be here to assist you shortly.
Table of Contents
The Struggle with Mathematics
Any student who has struggled with math subjects knows very well about the frustrations of math problems that can’t be solved by those students. Struggle can come due to difficulty with problems, confusion about the formula, or a lack of motivation. The instructor has to teach students math subjects with real-world situations that involve math outside the classroom.
Many fields, like computer science, engineering, and some business-related fields, include mathematics subjects in their fields. Some students find mathematics hectic and discouraging. Now, we will know why you should struggle in mathematics.
- Lack of Understanding
- Stress and Anxiety
- Concentrations and Attentions
- Limited Resources are available.
- Failure fear
Transformative Power with Advanced Math
Advanced math is tougher than basic math and requires a deeper understanding of the concepts. Calculus, Linear algebra, differential equations, and some more are parts of advanced mathematics. Let’s check how advanced mathematics can change student’s learning journeys:
- Increased Problem-Solving Skills: Advanced mathematics helps any student to think critically about any particular problem and develop deep problem-solving skills, which will help you in your career.
- Analytical Thinking: With logical reasoning and analytical thinking, any student can face many difficult problems with confidence.
- Prepares for Other Fields: Advanced math is important for students who want to pursue careers in science, technology, engineering, mathematics, and many other fields.
- Opens Doors for Advanced Education: The success of advanced mathematics helps you open doors to high-level universities and advanced degree programs.
Real-Life Stories with Math Success
To show the changing power of advanced mathematics and online class help, let’s check out the real-life stories of students who overcame their math difficulties and achieved remarkable success in online classes.
Journey of Danny
Danny used to study in high school, where she always had some difficulties with math subjects. Her grades continuously went below average, and she became depressed. When it was her second attempt, she decided to go for the online advanced mathematical class. With a personal math instructor, she started questioning any problem or formula from her teacher, and then finally, she learned much better. She finally found the support she always needed. With her constant consistency, regular practice, and dedicated support, she not only improved her marks but also developed a love for mathematics. Now she feels math is like a game. After high school, Danny took a good mathematical field in college.
Flexibility of Thomas
Thomas also used to study in high school, where he faced many difficult challenges in learning advanced math concepts. He was about to give up on his studies, but then he learned about support from an online personal math tutor. Then, with his instructor’s help, he began to solve difficult math problems. His hard work paid off when he got good grades in his exams. He then chooses a prestigious engineering program. His journey proved that using the right resources can help anyone in their math struggle.
Anxiety of Ella
Ella, in her school days, was always used to feeling discouraged when it came to math subjects. She used to avoid math-related questions. In her college days, she was forced by her family to choose mathematics as her career path, so she decided to get help from online math teachers. After completing difficult problems and with the guidance of experienced instructors, Ella reduced her anxiety and built confidence in herself. That confidence made her the best mathematics student, and after school and college, she became a math teacher.
The Resources and Role of Online Classes
As there is increasing popularity nowadays of STEM-focused learning, many students are taking more and more challenging math courses. And, for some students, this math subject is a real challenge to face, but knowing where to go and asking to understand math and improve their understanding
Resources and Online Classes have played a very important role in these success stories. They provide many benefits, like:
- Explicit instruction
- Conceptual understanding
- Using concepts in Math vocabulary
- Puzzle pieces, math instruction
- Lack of Patience
- Not enough opportunity
For every student, it is not possible to go through the journey of struggling to succeed. Practicing mathematics in your daily routine and using online resources for math assistance can help you more and more confident to get the best marks in your math subject. With the example of Danny, Thomas, and Ella, we have seen, that their success stories are the motivation for us they like them every student can overcome mathematical problems with dedication, consistency, and the right support of online teachers. These difficult math problems are realistic and give students a chance to practice more and more while solving them and providing accurate answers. With these online resources, math will no longer be a source of fear but a path to success in the future. Whether there is any student or any teacher, keep one thing in mind ‘Advanced mathematics will change your life, and these calculations will help you anywhere in your life.’


Odds of winning roulette twice in a row
Find out about the probabilitites of winning with each Same even money bet result in a row On the roulette charts above I have used; ratio odds. Approach roulette with the sober realization that, Strategy is critical if you want to increase your odds of winning. 4 of which you cover twice. When the roulette has hit 5 reds why The only thing in your favour is that you are saying "I can't be wrong twice in a row so I Roulette odds of winning.
Improving Your Odds at Roulette
The answer sounds like, yes, it is rare to see 15 reds in a row, but it is equally rare to see a combination of any 15 color arrangements. It is correct that the different spuns are independent from each other when playing the roulette - however it is not entirely correct that roulette has no memory. All Right Reserved to RouletteStar. Subtract the numerator 5 from the denominator If you know that the roulette is fair, then it doesn't matter if you bet on red or black. The independent events in roulette are analogous to the simple situation of coin tossing. There are a number of ways to display probabilities.
What are the odds of hitting the same number twice on a roulette table?
Of course you do. I've been playing roulette at Bet for years, and I have no intentions of moving. Everyone that has asked me about where's best to play roulette online agrees with me, so that says something in itself. So if you're smart enough to care about the best place to play fair and reliable online roulette , check out the games Bet I know you won't be moving back to your old casino if you've got one after you've had your first real money spin.
Here are a bunch of charts and tables for different probabilities in European roulette that might be useful to know. There's also some handy but not necessarily easy information at the bottom about working out roulette probabilities, plus a little bit on the gambler's fallacy. The following probabilities are for European roulette. Check out the American probabilities page if you're playing on a wheel with the double-zero. How unlikely is it to see the same colour 2 or more times in a row?
What's the probability of the results of 5 spins of the roulette wheel being red? The following chart highlights the probabilities of the same colour appearing over a certain number of spins of the roulette wheel.
The probability of the same colour showing up 4 times in a row is 5. As the graph shows, the probability of seeing the same colour on consecutive spins of the roulette wheel more than halves well, the ratio probability doubles from one spin to the next.
Стесняясь своей выбритой писи, Мальвина поворачивается попкой. жаркого секса. - спросил Малик. 178. Включив музыку погромче, фифа стала в джинсовой юбке и кофте около большой аудиосистемы и начала постепенно раздеваться. - после того как она осталась довольна своей кожей, спросил.
но тем не менее её Большие сиськи не перестали привлекать внимание мужчин, а когда она в мокром топе, то так и хочется снять с неё одежду.
I reworked a section from of my most popular statistics lectures on probability theory and roulette. Below is the article in full. Roulette is a straightforward casino game.
While the wheel is spinning, a ball is released. This ball eventually ends up stopping in a numbered and coloured red or black pocket. You bet on the final resting place of the ball by selecting a number, range of numbers or a colour.
When betting on colours, if you pick correctly, you double your money. A few years ago, I received quite a few spam e-mails with the following tip on how to win at roulette. If you ignore the atrocious spelling and grammar, the basic idea seems to be a good one. Under this system, you double losing bets until you win, that way you will always win an amount equivalent to your first stake.
Casinos have stayed in business over centuries for a reason: These limits expose a huge flaw in our spam-based strategy. But how likely is losing 7 bets in a row?
Put another way, the probability of this happening is 1 in We can now work out the probabilities of making various amounts of profit, once again using the multiplication rule:. How much would you need to win? And what are the odds of this happening? Put another way, 15 out of 16 times, you will exceed a savings account interest rate. But, 1 in 16 times you will leave the casino with nothing. Not even enough to get the 99 bus back over the Tay.
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Revista de Economía del Banco Central del Uruguay, Segunda Época, Vol.21, Num.1.Montevideo, Mayo 2014.
This paper reviews and discusses the application of four non experimental methods to estimate the impact of the full time school program in Uruguay (FTS) on student outcomes in math, reading and science, assessed at age 15 by the international PISA tests. I use ordinary least squares, matching, instrumental variables (IV) and control functions, and I discuss the possible sources of bias that are present in each method. As an exclusion restriction, I use the distance from the center where the student was assessed by PISA, to the nearest FTS. When taking into account selection on unobservables through control functions, I find that students attending FTS improve their math and science test scores by 0.34 and 0.64 of a standard deviation, respectively. The IV estimates do not allow rejecting the hypothesis of null effects. In the case of reading, estimates do not allow rejecting the hypothesis of negative effects.


Certainly one of the questions when planning for the long run is that
you regularly asks in the school program |when preparing to your future is, which you inquires from the school program }: What may be the meaning of foundation in mathematics? Generally in most of the cases, the response may vary from 1 person to the other and to the query is complex. You will locate some of the responses to become catchy.
You’d realize that they are only two types of numbers if you explore the basics https://www.shoqata-studenti.ch/the-incredible-details-into-what-does-in-math-mean-that-people-dont-know-about/ of base in mathematics. But what exactly would be the bottom? And how can you use it ?
Foundation is just an algebraic expression that is utilised to describe the position of number or almost any element in relation to any other part or number. Base can also be expressed in base units. By way of example, a base-ten variety would indicate that a number is 10 points lower than the number.
Base comes from the Latin term”basi” which means base. https://techville.fr/2020/01/21/where-to-find-field-theory-mathematics/ We will usually utilize it to refer to the bottom of any number, As soon as we do foundation addition. So in base 2 inclusion, as an instance, the two base-ten amounts will be referenced as”tens”.
Base it self is also referred to as precent, which is derived from the Latin phrase”praecerum”. Precent could be the bottom of the twelve-tens. It’s also the basis used to figure fractions, that can be fractions which can be multiples of the base (e.g. thirty five separated by 2 would be thirty five times 2 ).
Now that you just know what base is, you can start to comprehend how it can be utilized in mathematics. As a way to compute the derivative of the job, you have to know the derivative of the base. To try it, you want to specify the denominator of this derivative. You will learn that the denominator of the derivative, once you’ve got the denominator.
So now that you just know what’s, you are already able to start to observe the way that it can be used in math. Recognizing that the meaning of a foundation is one thing, but actually deploying it is something.


This area contains the messages from the old Yahoo cadintoshmac group after the port.
1 post • Page 1 of 1
Hello:When the program makes dimensions, it draws a line with arrow points at each end. At times, the points are "inside" the two lines being dimensioned, pointing outwards. At other times (more often) the points are "outside" the two lines, and are pointing in towards the center of the line. How do you control this difference? I've tried "Option > Dimenions" and the Line Ending menu at the bottom of the drawing. Thanks, Jon


School is starting back up. If you have a math wiz in the family, then you’ll be in the market for a new graphing calculator. Casio has you covered. From the very simple to the really advanced.
Pretty in pink! This is your standard scientific calculator. Perfect for middle school. My daughter loves this one because it’s easy to use and well it’s pink.
Casio’s latest standard scientific calculator features new Natural Textbook Display and improved math functionality. FX-300ES PLUS has been designed as the perfect choice for middle school through high school students learning General Math, Trigonometry, Statistics, Algebra I and II, Pre-Algebra, Geometry, Physics.
- Intuitive functions
- Improved math functionality
- Natural Textbook
For the more advance classes Casio has the graphing calculators. They are amazing and do so much! Perfect for Pre-Algebra, Algebra 1 &2, Geometry, Trig, calculus, and so much more! So many options that I’m sure I wouldn’t even use a quarter of what this calculator is capable of. The greatest thing about this calculator is the price. At only $49.99 it’s an affordable option on any budget.
NEW 9750 GII FUNCTIONALITY
New types of regressions
Chi-squared GOF function
9 new probability functions
Pie charts & Bar Graphs
And much more!
New overall design with the same generous screen size that you’ve enjoyed with the 9750GA Plus
Icon-based menu adds to overallintuitive usability
When looking for a calculator there are a couple of things you’ll want to make sure you’re looking for.
Features Make sure you have everything you’re student is going to need.
Durability/Longevity You want a calculator that is build tough. These are going into backpacks and purses and will be banged up a bit. If you buy a calculator that is fragile then you’ll be buying another before the school year is out.
Ease of Use The ideal calculator will be ergonomic and easy to use with a user-friendly button layout and several functions within close reach. The buttons must be easy to read and the display should deliver a clear, high-contrast readout. Reaching the desired formula or symbol should be intuitive and quick.
Support/Warranty Graphing calculators are complex machines and extensive user’s manuals and documentation are often needed to perform specific tasks. Make sure your able to go on-line and get a user manual and customer service.
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Math is everywhere. Counting, adding, subtracting, multiplying, and dividing are done on a daily basis by people around the world – even if they are not conscious about it. Depending upon the profession that a person is in, math may also be used in a more complicated form – such as algebra, calculus and trigonometry. Learning how to solve math problems is a skill that everyone needs in order to be successful. Math is used on the job, to manage a personal checking account, and even to count the quantities of various items in the home or in the office. Not everyone is born a math whiz – which means that people need to know where to get the help when they need it.
There are lots of ways for people to figure out “how to” perform particular math problems. There are training lessons, quizzes, and games that all revolve around math. If someone is not familiar with a particular form of math, regardless of whether they are a student or not, they can turn to the Internet for help. Many people have been able to improve their math skills in a short period of time by studying the how-to guides that are available. When math is used properly, it can tell a person how much of something they have, how long it will take to get somewhere, how to manage a budget, and much more. Regardless of what someone might think in school, math is a subject that will be used again. Those who excel in math are able to get further in life because they have a deep understanding of the mathematical concepts.


JUST HOW DO Casinos EARN MONEY?
Many people that play casino games have no idea just how much there is to learn. In fact, they could not even understand how a simple strategy for a certain kind of casino game works. Learning several basic strategies can make all of the difference in whether you earn at gambling.
For example, in roulette there are the number of winning cards, the minimum and maximum bet, and the payout odds. Casinos use these factors to determine the odds that a person has of winning when they place their bets on a specific casino game. The payout chances determine whether or not you will walk away successful or if you will lose out. Knowing just how these odds are figured out can assist you decide what chances to bet on when you place bets on casino video games.
One of the important considerations for gamblers is the standard deviation. A standard deviation can be an estimate of the value of the random variable, in this the casino sport table. The standard deviation is merely the difference between your expected and your actual outcome. When discussing standard deviation, you should talk with regard to tails and heads. A normal binomial distribution runs on the binomial distribution with mean and typical deviation values, which makes things a little better to recognize.
Normal deviation is not the only thing that helps gamblers make a decision what odds to bet on casino game titles. Another consideration may be the simple game concept, which states that casino game titles are based on random likelihood and that any player’s chances of winning are exactly the same no matter where they sit at the table. House advantage identifies the difference between the probability of a person player at any given desk against the probability of all players at that desk, and this can cause gamblers to vary their bets based on which factors give them an edge.
Property advantage can make the difference between a gain and a loss. Which means that the same amount of people at a table could have the same probability of hitting on a jackpot but someone will always win a lot more than they lose. One example of using random number video games to greatly help gamblers decide what chances to bet on casino video games would be the amount of people at a internet casino who has ever before won or lost, an individual card game. These people may then be used to help gamblers figure out if casino games have a greater house advantage than other games. For example, someone at a progressive slot machine game may have the chances of hitting a crimson jackpot one in three million, but this person hasn’t won a single red or black jackpot in their entire lifetime. Using these folks to greatly help with the mathematics can considerably improve gamblers chances of striking the jackpot.
The final section of the casino game may be the wheel. The wheel takes the winning figures from the essential roulette system and then places them in specific positions on the wheel. These jobs will always change as the odds of all the different combinations which come off the wheel are never exactly the same. In case a casino were to offer the customer the choice of experiencing the steering wheel reset to any place they desired them to place a bet on, it might very well find yourself changing the odds dramatically. The reason being the casino can change the odds depending on how much money is in the pot, mgm 바카라 just how many players are left in the overall game and any other amount of aspects.
Roulette, slots and poker games all have random elements that produce them unique. For that reason they are able to deal with roulette, slots and poker by the use of a wheel. To be able to understand how gambling machines and roulette do the job, you need to know how the odds of each combination is figured out. To carry out that, it is important to look at a number of the math engaged.
Most casinos have a typical deviation that is necessary when they calculate the odds of the various outcomes. Basically, this can be the standard deviation which is the deviation of the average outcome that occurs throughout a random walk from one value to another. When a casino uses normal deviation in calculating their odds, they are basically determining what’s normal behavior. Standard deviation can be used in many several types of gambling games including slots, roulette and blackjack among numerous others. It is the one factor that makes many of these games what they are and why they continue being popular among people even with all these decades.


June 22, 2021, Sofia. Contestants and partners gathered online for the ceremony to announce the winners in the 21st edition of the international programming contest CodeIT , organized by Musala Soft. The President of the Republic of Bulgaria Rumen Radev, under whose patronage the competition is held, made an official address to the guests. The first place in the ranking is for Martin Kopchev – a student in 11th grade at the Highschool of Natural Sciences and Mathematics “Acad. Ivan Gyuselev”, Gabrovo, Bulgaria and part of the Bulgarian national team in informatics.
“Mathematics is the true abstract beauty, and informatics allows us to see this beauty in practice. Dear contestants, you are not just authors of programs and application software. You are creators and you create a new outlook to everyday life, which is also a big responsibility. Because no sphere in our life can function without the digital technologies, and developing complex algorithms, you model social relations. Be inspiring professionals and good citizens!” – shared during the online event the President of the Republic of Bulgaria.
Professor Nikolay Denkov, Minister of Education and Science, added in a video address: “You are changing the life around us by creating new technologies that were unthinkable until recently. I wish you not only to be successful professionally, but also to be better and most helpful to the people around you.”
The event was hosted by Elena Marinova, President and Co-Founder of Musala Soft. “At Musala Soft we believe that in addition to our direct work in building the future of the software industry with customers and partners, we are obliged to give back to the IT community. Giving is deeply incorporated in Musala Soft’s values. And because Olympic blood runs in our veins, our strongest focus in corporate social policy is elite computer science education.”
Final Ranking CodeIT 2020/2021:
1. Martin Kopchev – 11th grade, Highschool of Natural Sciences and Mathematics “Academician Ivan Gyuselev”, Gabrovo, Bulgaria;
2. Emil Indzhev – graduate of the Mathematics Highschool “Baba Tonka”, Ruse, Bulgaria; currently a 3rd year student at Oxford, majoring in Computer Science;
3. Anton Anastasov – graduate of the Highschool of Natural Sciences and Mathematics “Academician Boyan Petkanchin”, Haskovo, Bulgaria, graduated from the Massachusetts Institute of Technology in 2017;
4. Deyan Hadzhi-Manich – 9th grade, Highschool of Mathematics “Dr. Petar Beron”, Varna, Bulgaria;
5. Nemanja Majski – 9th grade, Highschool “Velko Petrovich”, Sombor, Serbia;
6. Atanas Dimitrov – 10th grade, Sofia Highschool of Mathematics “Paisiy Hilendarski”, Sofia, Bulgaria;
7. Viktor Kozhuharov – 12th grade, Highschool “Baba Tonka”, Ruse, Bulgaria;
8. Georgi Petkov – 11th grade, First Private School of Mathematics, Sofia, Bulgaria;
9. Blagojce Pavleski – 3rd year student at the Jahya Kemal College, Skopje, North Macedonia;
10. Aleksander Gubica – 9th grade, Highschool “Velko Petrovich”, Sombor, Serbia;
11. Rumen Mihov – 11th grade, Highschool of Natural Sciences and Mathematics “Atanas Radev”, Yambol, Bulgaria; student at the “Shikovi” school of Informatics;
12. Vedran Bajic – 10th grade, Highschool “Velko Petrovich”, Sombor, Serbia.
Final Junior Ranking CodeIT 2020/2021:
1. Veselin Markovich – 8th grade, Highsool of Mathematics “Dr, Petar Beron”, Varna, Bulgaria;
2. Daniel Koynov – 8th grade, Highschool of Natural Sciences and Mathematics “Nancho Popovich”, Shumen, Bulgaria;
3. Georgi Iliev – 9th grade, Sofia Highschool of Mathematics “Paisiy Hilendarski”, Sofia, Bulgaria;
4. Mihail Mihalev – 7th grade, Highschool of Natural Sciences and Mathematics “Academician Ivan Gyuselev”, Gabrovo, Bulgaria;
5. Boris Angelov – 6th grade, Sofia Highschool of Mathematics “Paisiy Hilendarski”, Sofia, Bulgaria.
Since 2012 Musala Soft invites top gurus in competitive programming to give an inspiring lecture to the finalists. This year they met with Rumen Hristov. He is a contestant from Bulgaria, 6th in the world IOI rankings of all time, graduated from MIT and in the “Forbes” ranking “30 under 30 in the United States”.
Honorary chairman of the jury since the creation of the contest is prof. Krassimir Manev – President of the International Olympiad in Informatics / IOI/ 2014-2017 and Chairman of the Initiative Committee of the First European Youth Olympiad in Informatics (eJOI), Bulgaria 2017 and its president.
Special thanks to our patrons and sponsors who provided the awards and supported us in organizing CodeIT, season 2020-2021.
Patrons – the Bulgarian Academy of Sciences and the Institute of Informatics and Mathematics, Sofia University “St. Kliment Ohridski” and its Faculty of Mathematics and Informatics, Technical University – Sofia and its Faculty of Computer Systems and Technologies, University “Angel Kanchev” – Ruse, University “Professor Asen Zlatarov” – Burgas, Sofia Highschool of Mathematics “Paisiy Hilendarski”, the National Highschool of Natural Sciences and Mathematics “Academician Lyubomir Chakalov”, Mathematics Highschool “Baba Tonka” – Ruse, the Vocational Shool for Computer Programming and Innovations – Burgas, “Electronic systems” Technological School – Sofia, A&B School of Informatics – Shumen; “Shikovi“ School of Informatics – Yambol.
Sponsors – American Foundation for Bulgaria. CIELA Publishing, Janet 45 Publishing House, AMG Publishing, Freckles, Cougar Gaming for Bulgaria, ERP Academy, JOY Optics, Grand Optics, Prestigio, Samsonite – Bulgaria Speedy, Ubisoft Sofia, ZEISS Vision Center.


Mathematics Biennal 2014
The Mathematics biennal is a conference for teachers, pedagogues, headmasters, scientists and other persons interested in maths. The meeting offers updated skills for mathematic teachers at every level, During the biennal topical science is to be presented by national and international scientists. Workshops and lectures are planned to take place during the two-day meeting and pedagogues from different schools will present their work and learning projects through exhibitions.
|Thu Feb 6 - Fri Feb 7 2014||Umeå University|
Organizer: Umeå University
+4670-528 19 65


Technical analysis as apoosed to fundamental analysis, includes analyzing charts and technical indicators like RSI, MACD, moving averages, etc.
It has its uses if the trader or investor is aware of its good and bad points.
One weakness is that its interpretations can be affected if you draw the same charts on a different scale, i.e. arithmetic or semi-log scale. Another potential weakness is that the price and volume of a stock can be manipulated so as to give certain patterns or readings for the other traders.
A) RSI (Relative Strength Index)
The number of days can be varied. In our case we choose 9 days instead of the usual 14 days. The RSI can also be calculated on a weekly or monthly basis. The shorter the time, the more sensitive RSI becomes.
The maximum and minimum levels that the RSI indicator can theoretically go to are 100 and 0. Usually if the RSI is above 70, it is overbought and if it is below 30, it is oversold. These are useful for short-term traders.
An important use of RSI is when there is a divergence between the company's price or a market index and its RSI. A "bullish divergence" signals a short-term bottom while a 'bearish divergence" signals a short-term peak.
Introduction to RSI:
This indicator is also very popular with traders in the future markets. Its formula is:
RSI = 100 - ( 100/1+ rs )
Where rs = average of X day's up closes / average of X day's down closes.


As paperless, online interactions are used more widely, digital signatures can help you secure and safeguard the integrity of your data. By understanding and using digital signatures, you can better protect your information, documents, and transactions.
This is undoubtedly the most accessible book on digital signal processing available to the beginner. Using intuitive explanations and well-chosen examples, this book gives you the tools to develop a fundamental understanding of DSP theory. The author covers the essential mathematics by explaining the meaning and significance of the key DSP equations. Comprehensive in scope, and gentle in approach, the book will help you achieve a thorough grasp of the basics and move gradually to more sophisticated DSP concepts and applications. The book begins with a complete explanation of the often misunderstood topic of periodic sampling. The introduction to the important discrete Fourier transform, and its fast Fourier transform (FFT) implementation, is the most lucid and illuminating explanation available anywhere. You will also find extensive information on both finite impulse response (FIR) and infinite impulse response (IIR) digital filters, as well as coverage of the benefits of signal averaging. In addition, the book demystifies the abstruse topics of the Convolution theorem and complex signals. The practical uses of various binary number formats are also carefully described and compared. Finally, a collection of tricks-of-the-trade used by professionals to make DSP algorithms more efficient will help you apply DSP concepts successfully. 2b1af7f3a8