I did not even use the sheet for that reason. Covariates can also exist in research designs where no independent or dependent variables exist. Psychology Statistics For Dummies Cheat Sheet (UK Edition), Going Beyond Stress: The Psychology of Health. In psychology statistics, research studies which involve collecting quantitative data (any data that can be counted or rendered as numbers) usually require you to collect and store data on a data sheet about several variables. AQA Psych cheat sheet. Click on a series title to see the statistics list of products in the series. All you need is to send us the login details and we will send the price quote. Ordinal: If you measure a variable at the ordinal level then the values on the variable have the measurement property of magnitude only. Choose from 405 different sets of statistics psyc psychology formulas flashcards on Quizlet. See more ideas about statistics cheat sheet, statistics math, statistics. When putting together the psychology statistics you need to report when you’re describing a variable in a report, you need to know which of the three measures of central tendency – the mode, median and mean – you should use. Includes vocabulary and formulas from the entire AP Statistics curriculum. Entails the basics on the approaches, SOCIAL, BIOLOGICAL, COGNITIVE and LEARNING. Statistics Cheat Sheet Statistics Symbols Statistics Help College Hacks Social Science Cheat Sheets Mathematics Psychology Education. Stats Dept courses or Psychology 1900 or OEB 153 or Math 19b). Covers Normal Model, linear regression, probability, experiment design, and hypothesis tests. Psychology Revision Psychology A Level Psychology Resources Psychology Studies Abnormal Psychology A Level Revision English Gcse Revision Thesis Writing Writing Tips. You measure a variable at the ordinal level when the scores in the variable are ordered ranks. This Cheat Sheet helps you out with some basic concepts in psychology statistics. Read more. Be guided by the advantages and disadvantages of each measure. Caratteristiche farmacologiche dei principali antidepressivi. These cheat sheets were collected and scored by an independent scorer on a 10-point scale for However, the mean isn’t appropriate when extreme scores and/or skewness exist in your data set. This type of independent variable is a quasiindependent variable. Ratio: if you measure a variable at the ratio level of measurement, it has the measurement properties of magnitude, equal intervals and a true absolute zero. Data measured at the interval/ratio level: All three measures of central tendency are appropriate. The standard deviation indicates the extent to which the scores on a variable deviate from the mean score. Saved by Candace McCreary. Includes info on how to read and explore data frames, basic statistical functions and operations, programming basics, and plotting with ggplot. Cheat Sheet, Psyc Mid.Childhood - Cognitive Development Cheat Sheet, Piagets theory of cognitive development Cheat Sheet, Psyc Mid.Childhood - Physical Development Cheat Sheet, AP Psychology Ch.6-10 Cheat Sheet Cheat Sheet, Prevent Pressure - The Procrastination Playbook Cheat Sheet, frankl - orang yg mengatasi diri Cheat Sheet, carl rogers - fully functioning human Cheat Sheet, Jung Theory: 12 Common Archetypes Cheat Sheet, Certified Agile Project Manager (IAPM) Cheat Sheet. Statistics for Psychology Students 1. Dependent variables are sometimes referred to as outcome variables or criterion variables. 2 people found … Saved by Cheatography. You may be more interested in studying psychology than in crunching numbers, but knowing psychology statistics is essential if you’re going to make all that research data stack up, and have other people understand it. social psychology and behavior. A dependent variable is usually the variable that you expect to change when you manipulate the independent variable. Within this research design, these variables are covariates. This product is part of for following series. Learn statistics psyc psychology formulas with free interactive flashcards. Psychology infographic and charts. Psychology Statistics For Dummies Cheat Sheet (UK Edition) The order is the same way that I would choose if I were writing a psychology myself. Independent variables are sometimes referred to as predictor variables. In some cases, you refer to variables as independent variables even when you’re not directly manipulating them.. Every semester, psychology students around the country anxiously file into their required, introductory statistics classes. The interquartile range is usually preferable, as it is more informative than the range. As the charts and maps animate for time, the changes in the world become easier to understand. The three main ones are the range, the interquartile range and the standard deviation. I accidentally put a block twice, sorry :(. Independent variables are sometimes referred to as predictor variables. Statistically Figuring Sample Size Choose your answers to the questions and click 'Next' to see the next set of questions. Although some love it, statistics tends to be difficult and anxiety-producing for psychology students (who sometimes refer to it as Sadistics 101).To combat this, publishers have released a flurry of student-friendly textbooks designed to make statistics more … The standard deviation (often abbreviated to Std. Statistics For Dummies Cheat Sheet By Deborah J. Rumsey Whether you’re studying for an exam or just want to make sense of data around you every day, knowing how and when to use data analysis techniques and formulas of statistics will help. Strictly speaking, an independent variable is a variable that you manipulate so that you can study how the changes in the independent variable influence changes in other variables. For example: Where is the center of the data located? How spread out is the data? A cheat sheet for Living and Working With Children, Cheatsheet for chapters 11,12, and 14 of AP Psychology, A brief explanation for psychologists in the following units: social influence, memory, attachment and psychopathology. statistics symbols cheat sheet. The variable’s level of measurement is a classification system that tells you what measurement properties the values of a variable have. Data measured at the interval/ratio level: All three measures of dispersion we have examined are appropriate. Probability and Statistics;Psychology and Business statistics will make you comfortable to use stats if you are in the fields of psychology and business. Statistics Cheat Sheet Basic Statistics Definitions: Statistics – Practice or science of collecting and analyzing numerical data Data – Values collected by direct or indirect observation Population – Complete set of all observations in existence Sample – Slice of population meant to represent, as accurately as possible, that population Jan 17, 2019 - Explore jayabharathi8's board "statistics cheat sheet" on Pinterest. How correlated are the data from two variables? R cheatsheet¶ [This PDF includes useful R functions and syntax for Psych 252. You determine the most appropriate measure of dispersion as follows, depending on the nature of your data: Data measured at the nominal level: Because all three measures of dispersion require data to be ranked or summed, none of them are appropriate for data measured at the nominal level. With our experience you can be assured of good grades and timely submission of all the discussion posts, assignments and tests. Equal intervals: This means that a unit difference on the measurement scale is the same regardless of where that unit difference occurs on the scale. The measures of dispersion you use in psychology statistics show you the spread or variability of the variable you are measuring. Centus statistics, easy to explore, visualize and communicate. Description: An introduction to the techniques of research employed in the study of human behavior. DRAFT: Glanzer and Cunitz (1966) - Memory Stores Cheat Sheet Psychological study investigating two types of memory stores. Traffickers disproportionately target at -risk populations including individuals who have experienced or been exposed to other forms of violence (child abuse and maltreatment, interpersonal violence and sexual The mean is usually preferable. Psychology: Middle Childhood and Emotional & Social Development. Strictly speaking, an independent variableis a variable that you manipulate so that you can study how the changes in the independent variable influence changes in other variables. You psychology have to be a data expert to navigate between different views, psychology your own comparisons, and share your findings. In that respect it was a waste of money for me. Distribution of scores: For the purposes of choosing a measure of central tendency, you need to know whether any extreme scores exist in your data set (often called outliers) or whether the distribution of scores is skewed. Description. However, the standard deviation (or variance) isn’t appropriate when there are extreme scores and/or skewness in your data set. Generally speaking, you classify variables in psychology statistics as independent variables, dependent variables or covariates. After making the payment you leave everything else to us. If you have any problems, or just want to say hi, you can find us right here: Chapter 4: Sensation and Perception Cheat Sheet, Psyc Mid.Childhood - Emotional & Social Dev. Donncha Hanna, PhD is a psychology lecturer at Queen's University Belfast whose primary teaching responsibilities include statistics and research methods. A brief explanation for psychologists in the following units: issues and debates, relatioinships, schizophrenia, aggression. Can be used as supporting evidence for arguments made within the Cognitive Level of Analysis (CLOA) in IB Psychology exam paper questions. ENGLISH (ONE YEAR): • One semester of the English requirement is met with Expos. Data measured at the ordinal level: The mode and the median are appropriate. Mar 17, 2020 - Explore Mark Stansberry's board "Statistics Cheat Sheet AP and College" on Pinterest. The median is usually preferable, because it’s more informative than the mode. A covariate is a broad term used for a variable in a research design that’s neither an independent nor a dependent variable. I thought it would make taking the class a second time in college easier; I was wrong!! Martin Dempster, PhD is a health psychologist and the research coordinator for the Doctorate in Clinical Psychology programme at Queen's University Belfast. The most important information you need to know before taking the Certified Agile Project Manager (CAPM) certification exam, by the International Association of Project Managers (IAPM). A brief explanation for psychologists in the following units: approaches, biopsychology and research methods. The standard deviation is usually preferable. In other words, the dependent variable is the variable that the independent variable affects. Weighing up the advantages and disadvantages of each measure leads you to the following conclusion: the most appropriate measure of central tendency for a variable depends on the level of measurement of the variable and the nature of the distribution of scores within that variable. On cheat sheet exams, both Introductory Psychology and Statistics participants were instructed to prepare a double-sided 8½ × 11 sheet of paper on which they could write as much information as they wanted to use on the exam. statistics cheat sheet ... Counseling Psychology. However, the numbers can have different measurement properties and these determine what types of analyses you can do with these numbers. You measure a variable at the nominal level when you’re using the numbers in the variable only as labels. Pre-Med Cheat Sheet for EPS Concentrators A/Y 1-20. Saved by Gigi Gonzalez. Statistics Cheat Sheet Statistics Symbols Statistics Math Probability Worksheets Chi Square Third Grade Science Developmental Psychology Study Skills Calculus Probability and Statistics Cookbook The cookbook contains a succinct representation of various topics in probability theory and statistics. Statistics Cheat Sheet. Prerequisite: PSYC UN1001, and a statistics course (PSYC UN1610 or the equivalent), or the instructor's permission.. Nominal: This means that a variable has none of the three measurement properties. 45. Statistics for Psychology, 6th Edition. Breve descrizione farmacologica dei farmaci contro il Parkinson. Dev. Students who take two semesters of Expos have met the full requirement of two semesters of English. True absolute zero: The true absolute zero point means that the zero point on the measurement scale is the point where nothing of the variable exists and, therefore, no scores less than zero exist. A cheat sheet for Living and Working With Children. This AP Statistics cheat sheet can help you review for the AP Statistics Exam! 44. PSY 138: Reasoning in Psychology Using Statistics. In some designs you use a covariate to take account of other factors that might influence the relationship between the independent and dependent variable. These are the values that have been scored by participants in the study, and not necessarily the highest and lowest possible scores. the role of statistics in empirical research, and (iii) showing that the sampling distribution of the test statistic is both the bridge between descriptive and inferential statistics and the probability foundation of significance tests. annamclem. or SD) is the average deviation of scores in your data set from their mean score for a particular variable. color-psychology-cheat-sheet… Infographic. See more ideas about physics and mathematics, math formulas, calculus. These three measurement properties enable you to classify the level of measurement of a variable into one of four types. We can also help you with your entire class. In this situation the median is usually best. Therefore, the dependent variable is so called because its value depends on the value of the independent variable (at least in theory). During the course of one semester of introductory psychology and statistics classes, they gave one open-book exam, one cheat sheet exam and one closed-book test. Interval: If you measure a variable at the interval level of measurement, it has the measurement properties of magnitude and equal intervals. The measurement properties that the values in a variable can possess are: Magnitude: This means that you can order the values in a variable from highest to lowest. The interquartile range is the difference between the upper quartile and the lower quartile in a set of ordered scores. A good research design measures these variables so that you can account for their influence. More information... More ideas for you This sheet made an already confusing subject even more confusing. The most common descriptive statistics are in the following table, along with their formulas and a short description of what each one measures. 27 Apr 20. psych. Data measured at the ordinal level: The range and interquartile range are appropriate. The mean score is the average of scores on a variable. See more ideas about statistics cheat sheet, cheat sheets, statistics. Limbic System Working With Children Cheat Sheets Cheating Psychology Study The Unit Programming Create When you record variables on a data sheet, you usually record the values on the variables as numbers, because this makes statistical analysis easier. DRAFT: social psychology Cheat Sheet. Critical Values of the Studentized Range Statistic (Tukey's HSD Critical Values) When you determine the level of measurement of your variable of interest and whether or not there is skewness and/or extreme scores in your data set then you can determine the most appropriate measure of central tendency, as follows: Data measured at the nominal level: Of the three measures of central tendency examined in this chapter, the mode is the only appropriate one as the scores cannot be ordered from smallest to largest in a meaningful way. The three most important measures of dispersion are defined as follows: The range is the difference between the highest score and the lowest score in a variable. psychology statistics cheat sheet, 4 pts. Level of measurement: You need to distinguish between three levels of measurement (nominal, ordinal, and interval/ratio) when choosing a measure of central tendency. ... PLUS • Any statistics course (e.g. In this situation the interquartile range is usually preferable. How to stop feeling pressured and coerced into doing things. Cheatsheet for chapter 6-10 of AP Psychology behavioral statistics cheat sheet, FACT SHEET: Human Trafficking Human trafficking is a public health issue that impacts individuals, families, and communities. Who this course is for: This course is a good fit for those who feel anxious about anything math related and think of themselves as non-math people. Psychology Major. Descriptive Statistics in Psychology Chapter Exam Instructions. This type of independent variable is a quasiindependent variable. AP Psychology cheat sheet for chapters 1-5. statistics to get a feeling for the data. color-psychology-cheat-sheet In some cases, you refer to variables as independent variables even when you’re not directly manipulating them.. P.Lindemann.. School Psychology Social Work Exam Abnormal Psychology. The scores can be ordered from smallest to largest and this is meaningful, however they cannot be added up so the mean cannot be calculated. Lesson 1 - Introduction to Sequence and Series and "The Cheat Sheet for College Students" - YouTube When you conduct your statistical analyses on this data, you need to know what role each variable played in your research design. Mar 10, 2019 - Explore Lords Cooks's board "Statistics cheat sheet" on Pinterest. Very clear step by step instructions. Related tags: A-level Ap 2017 Psych Development. Quartiles are formed by dividing a set of ordered scores into four equal-sized groups. If you searching to test Psychology Books For Psychology Majors And Psychology Statistics Cheat Sheet price. When working with psychology statistics you can classify variables according to their measurement properties.


Diane Liporace has a B.S. degree in Mathematics and an M.S. degree in Computer Science. In 2017, she joined the Department of Mathematics and Computer Science at Drew University as an adjunct instructor teaching Object-Oriented Programming in Java. She believes the Users Group is a great way for students to connect with industry experts and learn how Java is being used to solve real problems.
Before working in academia, Diane was a Staff Level Software Engineer at IBM automating semiconductor manufacturing equipment and processes.
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There is a so-called rule about dating: the youngest age you are supposed to date is half your age plus seven. So, if youre 16, the youngest age you should consider is 15 – because 16 divided by two is eight and 8+7 equals 15. We can write the dating rule as an equation: y = x ÷ 2 + 7 .
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We invite bachelor, master and PhD students studying mathematics or teaching at any University whose seat is in a Western Balcan country and interested in continuing careers in the education of mathematics and science popularisation to apply for participation in Summer School for the Future (STE)M Leaders. Summer School aims to provide students with training in creating STEM content with an emphasis on mathematics and soft skills necessary for the successful organisation of science popularisation events and to promote friendly relations and collaboration among students from Western Balkan countries. Mathematics and STEM subjects are essential for securing economic growth, but the industry and the government sector must recognise the importance of teachers roles in society. Summer School is also training the next generation of teachers to lead this change. The school will be jointly organised by the University of Montenegro, the Mathematical Institute SANU, the University of East Sarajevo, Cyril and Methodius University in Skopje, the University of Vlora and the University of Mostar under the auspices and financial support of the Western Balkan Fund.
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Do you need basic math skills to become a Licensed Practical Nurse (LPN)? In a word: “Yes!”
While it’s true programs, pumps and calculators may do most of the math work for LPNs day-to-day, if you need to treat patients at the scene of an accident or the equipment is down because of a power glitch, you’ll be expected to accurately do required calculations to ensure the health and safety of patients.
All nursing revolves around a few basic math skills – adding, subtracting, multiplying and dividing decimals, fractions and whole numbers, and converting numbers from the English system to a metric one, among them. As Americans, we think in terms of pounds, ounces and inches. Not so in the medical field, where measurements are based upon the metric system and a nurse’s conversions skills come into play.
Those skills are especially important when a nurse is told to administer 750 mg of medication every four hours, but the tablets are 250 milligrams each. Perhaps you must give a patient 7.5 mg, but the vial says “5 mg per cc.” Or, you have to calculate the number of drops to administer per minute if ordered to “give 500 mg over 30 minutes” through an I-V drip. Simple enough…if you know your math! If not, your patient’s safety could be in jeopardy.
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Introduction to Randomness and Random Numbers
RANDOM.ORG is a true random number service that generates randomness via atmospheric noise. This page explains why it's hard (and interesting) to get a computer to generate proper random numbers.
Random numbers are useful for a variety of purposes, such as generating data encryption keys, simulating and modeling complex phenomena and for selecting random samples from larger data sets. They have also been used aesthetically, for example in literature and music, and are of course ever popular for games and gambling. When discussing single numbers, a random number is one that is drawn from a set of possible values, each of which is equally probable, i.e., a uniform distribution. When discussing a sequence of random numbers, each number drawn must be statistically independent of the others.
With the advent of computers, programmers recognized the need for a means of introducing randomness into a computer program. However, surprising as it may seem, it is difficult to get a computer to do something by chance. A computer follows its instructions blindly and is therefore completely predictable. (A computer that doesn't follow its instructions in this manner is broken.) There are two main approaches to generating random numbers using a computer: Pseudo-Random Number Generators (PRNGs) and True Random Number Generators (TRNGs). The approaches have quite different characteristics and each has its pros and cons. Pseudo-Random Number Generators
As the word 'pseudo' suggests, pseudo-random numbers are not random in the way you might expect, at least not if you're used to dice rolls or lottery tickets. Essentially, PRNGs are algorithms that use mathematical formulae or simply precalculated tables to produce sequences of numbers that appear random. A good example of a PRNG is the linear congruential method. A good deal of research has gone into pseudo-random number theory, and modern algorithms for generating pseudo-random numbers are so good that the numbers look exactly like they were really random. back to the menu
The basic difference between PRNGs and TRNGs is easy to understand if you compare computer-generated random numbers to rolls of a die. Because PRNGs generate random numbers by using mathematical formulae or precalculated lists, using one corresponds to someone rolling a die many times and writing down the results. Whenever you ask for a die roll, you get the next on the list. Effectively, the numbers appear random, but they are really predetermined. TRNGs work by getting a computer to actually roll the die - or, more commonly, use some other physical phenomenon that is easier to connect to a computer than a die is.
PRNGs are efficient, meaning they can produce many numbers in a short time, and deterministic, meaning that a given sequence of numbers can be reproduced at a later date if the starting point in the sequence is known. Efficiency is a nice characteristic if your application needs many numbers, and determinism is handy if you need to replay the same sequence of numbers again at a later stage. PRNGs are typically also periodic, which means that the sequence will eventually repeat itself. While periodicity is hardly ever a desirable characteristic, modern PRNGs have a period that is so long that it can be ignored for most practical purposes.
These characteristics make PRNGs suitable for applications where many numbers are required and where it is useful that the same sequence can be replayed easily. Popular examples of such applications are simulation and modeling applications. PRNGs are not suitable for applications where it is important that the numbers are really unpredictable, such as data encryption and gambling. back to the menu
It should be noted that even though good PRNG algorithms exist, they aren't always used, and it's easy to get nasty surprises. Take the example of the popular web programming language PHP. If you use PHP for GNU/Linux, chances are you will be perfectly happy with your random numbers. However, if you use PHP for Microsoft Windows, you will probably find that your random numbers aren't quite up to scratch as shown in this visual analysis from 2008. Another example dates back to 2002 when one researcher reported that the PRNG on MacOS was not good enough for scientific simulation of virus infections. The bottom line is that even if a PRNG will serve your application's needs, you still need to be careful about which one you use. True Random Number Generators
In comparison with PRNGs, TRNGs extract randomness from physical phenomena and introduce it into a computer. You can imagine this as a die connected to a computer, but typically people use a physical phenomenon that is easier to connect to a computer than a die is. The physical phenomenon can be very simple, like the little variations in somebody's mouse movements or in the amount of time between keystrokes. In practice, however, you have to be careful about which source you choose. For example, it can be tricky to use keystrokes in this fashion, because keystrokes are often buffered by the computer's operating system, meaning that several keystrokes are collected before they are sent to the program waiting for them. To a program waiting for the keystrokes, it will seem as though the keys were pressed almost simultaneously, and there may not be a lot of randomness there after all.
However, there are many other ways to get true randomness into your computer. A really good physical phenomenon to use is a radioactive source. The points in time at which a radioactive source decays are completely unpredictable, and they can quite easily be detected and fed into a computer, avoiding any buffering mechanisms in the operating system. The HotBits service at Fourmilab in Switzerland is an excellent example of a random number generator that uses this technique. Another suitable physical phenomenon is atmospheric noise, which is quite easy to pick up with a normal radio. This is the approach used by RANDOM.ORG. You could also use background noise from an office or laboratory, but you'll have to watch out for patterns. The fan from your computer might contribute to the background noise, and since the fan is a rotating device, chances are the noise it produces won't be as random as atmospheric noise. back to the menu Thunderstorms generate atmospheric noise
As long as you are careful, the possibilities are endless. Undoubtedly the visually coolest approach was the lavarand generator, which was built by Silicon Graphics and used snapshots of lava lamps to generate true random numbers. Unfortunately, lavarand is no longer operational, but one of its inventors is carrying on the work (without the lava lamps) at the LavaRnd web site. Yet another approach is the Java EntropyPool, which gathers random bits from a variety of sources including HotBits and RANDOM.ORG, but also from web page hits received by the EntropyPool's own web server.
Regardless of which physical phenomenon is used, the process of generating true random numbers involves identifying little, unpredictable changes in the data. For example, HotBits uses little variations in the delay between occurrences of radioactive decay, and RANDOM.ORG uses little variations in the amplitude of atmospheric noise.
The characteristics of TRNGs are quite different from PRNGs. First, TRNGs are generally rather inefficient compared to PRNGs, taking considerably longer time to produce numbers. They are also nondeterministic, meaning that a given sequence of numbers cannot be reproduced, although the same sequence may of course occur several times by chance. TRNGs have no period.
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Nonlinear multi-wave coupling and resonance in elastic structures
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Nonlinear multi-wave coupling and resonance in elastic structuresKovriguine DASolutions to the evolution equations describing the phase and amplitude modulation of nonlinear waves are physically interpreted basing on the law of energy conservation. An algorithm reducing the governing nonlinear partial differential equations to their normal form is considered. The occurrence of resonance at the expense of nonlinear multi-wave coupling is discussed.IntroductionThe principles of nonlinear multi-mode coupling were first recognized almost two century ago for various mechanical systems due to experimental and theoretical works of Faraday (1831), Melde (1859) and Lord Rayleigh (1883, 1887). Before First World War similar ideas developed in radio-telephone devices. After Second World War many novel technical applications appeared, including high-frequency electronic devices, nonlinear optics, acoustics, oceanology and plasma physics, etc. For instance, see  and also references therein. A nice historical sketch to this topic can be found in the review . In this paper we try to trace relationships between the resonance and the dynamical stability of elastic structures.Evolution equationsConsider a natural quasi-linear mechanical system with distributed parameters. Let motion be described by the following partial differential equations(0) ,where denotes the complex -dimensional vector of a solution; and are the linear differential operator matrices characterizing the inertia and the stuffiness, respectively; is the -dimensional vector of a weak nonlinearity, since a parameter is small The small parameter can also characterize an amount of small damped forced and/or parametric excitation, etc. ; stands for the spatial differential operator. Any time the sought variables of this system are referred to the spatial Lagrangian coordinates .Assume that the motion is defined by the Lagrangian . Suppose that at the degenerated Lagrangian produces the linearized equations of motion. So, any linear field solution is represented as a superposition of normal harmonics:.Here denotes a complex vector of wave amplitudes The discrete part of the spectrum can be represented as a sum of delta-functions, i.e. .; are the fast rotating wave phases; stands for the complex conjugate of the preceding terms. The natural frequencies and the corresponding wave vectors are coupled by the dispersion relation . At small values of , a solution to the nonlinear equations would be formally defined as above, unless spatial and temporal variations of wave amplitudes . Physically, the spectral description in terms of new coordinates , instead of the field variables , is emphasized by the appearance of new spatio-temporal scales associated both with fast motions and slowly evolving dynamical processes.This paper deals with the evolution dynamical processes in nonlinear mechanical Lagrangian systems. To understand clearly the nature of the governing evolution equations, we introduce the Hamiltonian function , where . Analogously, the degenerated Hamiltonian yields the linearized equations. The amplitudes of the linear field solution (interpreted as integration constants at ) should thus satisfy the following relation , where stands for the Lie-Poisson brackets with appropriate definition of the functional derivatives. In turn, at , the complex amplitudes are slowly varying functions such that . This means that(1) and ,where the difference can be interpreted as the free energy of the system. So that, if the scalar , then the nonlinear dynamical structure can be spontaneous one, otherwise the system requires some portion of energy to create a structure at , while represents some indifferent case.Note that the set (1) can be formally rewritten as(2) , where is a vector function. Using the polar coordinates , eqs. (2) read the following standard form(3) ; ,where . In most practical problems the vector function appears as a power series in . This allows one to apply procedures of the normal transformations and the asymptotic methods of investigations.Parametric approachAs an illustrative example we consider the so-called Bernoulli-Euler model governing the motion of a thin bar, according the following equations :(4) with the boundary conditionsBy scaling the sought variables: and , eqs. (4) are reduced to a standard form (0). Notice that the validity range of the model is associated with the wave velocities that should not exceed at least the characteristic speed . In the case of infinitesimal oscillations this set represents two uncoupled linear differential equations. Let , then the linearized equation for longitudinal displacements possesses a simple wave solution,where the frequencies are coupled with the wave numbers through the dispersion relation . Notice that . In turn, the linearized equation for bending oscillations reads The resonance appears in the system as that corresponds to any integer number of quarters of wavelengths. There is no stationary solution in the form of standing waves in this case, though the resonant solution for longitudinal waves can be simply designed using the d'Alambert approach.(5) .As one can see the right-hand term in eq. (5) contains a spatio-temporal parameter in the form of a standing wave. Allowances for the this wave-like parametric excitation become principal, if the typical velocity of longitudinal waves is comparable with the group velocities of bending waves, otherwise one can restrict consideration, formally assuming that or , to the following simplest model:(6) ,which takes into account the temporal parametric excitation only.We can look for solutions to eq. (5), using the Bubnov-Galerkin procedure:,where denote the wave numbers of bending waves; are the wave amplitudes defined by the ordinary differential equations(7) .Herestands for a coefficient containing parameters of the wave-number detuning: , which, in turn, cannot be zeroes; are the cyclic frequencies of bending oscillations at ; denote the critical values of Euler forces.Equations (7) describe the early evolution of waves at the expense of multi-mode parametric interaction. There is a key question on the correlation between phase orbits of the system (7) and the corresponding linearized subset(8) ,which results from eqs. (7) at . In other words, how effective is the dynamical response of the system (7) to the small parametric excitation?First, we rewrite the set (7) in the equivalent matrix form: , where is the vector of solution, denotes the matrix of eigenvalues, is the matrix with quasi-periodic components at the basic frequencies . Following a standard method of the theory of ordinary differential equations, we look for a solution to eqs. (7) in the same form as to eqs. (8), where the integration constants should to be interpreted as new sought variables, for instance , where is the vector of the nontrivial oscillatory solution to the uniform equations (8), characterized by the set of basic exponents . By substituting the ansatz into eqs. (7), we obtain the first-order approximation equations in order :.where the right-hand terms are a superposition of quasi-periodic functions at the combinational frequencies . Thus the first-order approximation solution to eqs. (7) should be a finite quasi-periodic function The conservation of quasi-periodic orbits represents a forthcoming mathematical problem in mathematics, which is in progress up to now ., when the combinations ; otherwise, the problem of small divisors (resonances) appears.So, one can continue the asymptotic procedure in the non-resonant case, i. e. , to define the higher-order correction to solution Practically, the resonant properties should be directly associated with the order of the approximation procedure. For instance, if the first-order approximation is considered, then the resonances in order have to be neglected.. In other words, the dynamical perturbations of the system are of the same order as the parametric excitation. In the case of resonance the solution to eqs. (7) cannot be represented as convergent series in . This means that the dynamical response of the system can be highly effective even at the small parametric excitation.In a particular case of the external force , eqs. (7) can be highly simplified:(9) provided a couple of bending waves, having the wave numbers and , produces both a small wave-number detuning (i. e. ) and a small frequency detuning (i. e. ). Here the symbols denote the higher-order terms of order , since the values of and are also supposed to be small. Thus, the expressions; can be interpreted as the phase matching conditions creating a triad of waves consisting of the primary high-frequency longitudinal wave, directly excited by the external force , and the two secondary low-frequency bending waves parametrically excited by the standing longitudinal wave.Notice that in the limiting model (6) the corresponding set of amplitude equations is reduced just to the single pendulum-type equation frequently used in many applications:It is known that this equation can possess unstable solutions at small values of and . Solutions to eqs. (7) can be found using iterative methods of slowly varying phases and amplitudes:(10) ; ,where and are new unknown coordinates. By substituting this into eqs. (9), we obtain the first-order approximation equations(11) ; ,where is the coefficient of the parametric excitation; is the generalized phase governed by the following differential equation.Equations (10) and (11), being of a Hamiltonian structure, possess the two evident first integrals and ,which allows one to integrate the system analytically. At , there exist quasi-harmonic stationary solutions to eqs. (10), (11), as,which forms the boundaries in the space of system parameters within the first zone of the parametric instability.From the physical viewpoint, one can see that the parametric excitation of bending waves appears as a degenerated case of nonlinear wave interactions. It means that the study of resonant properties in nonlinear elastic systems is of primary importance to understand the nature of dynamical instability, even considering free nonlinear oscillations.Normal formsThe linear subset of eqs. (0) describes a superposition of harmonic waves characterized by the dispersion relation,where refer the branches of the natural frequencies depending upon wave vectors . The spectrum of the wave vectors and the eigenfrequencies can be both continuous and discrete one that finally depends upon the boundary and initial conditions of the problem. The normalization of the first order, through a special invertible linear transformleads to the following linearly uncoupled equations,where the matrix is composed by -dimensional polarization eigenvectors defined by the characteristic equation; is the diagonal matrix of differential operators with eigenvalues ; and are reverse matrices. The linearly uncoupled equations can be rewritten in an equivalent matrix form (12) and ,using the complex variables . Here is the unity matrix. Here is the -dimensional vector of nonlinear terms analytical at the origin . So, this can be presented as a series in , i. e.,where are the vectors of homogeneous polynomials of degree , e. g.Here and are some given differential operators. Together with the system (12), we consider the corresponding linearized subset(13) and ,whose analytical solutions can be written immediately as a superposition of harmonic waves,where are constant complex amplitudes; is the number of normal waves of the -th type, so that (for instance, if the operator is a polynomial, then , where is a scalar, is a constant vector, is some differentiable function. For more detail see ).A question is following. What is the difference between these two systems, or in other words, how the small nonlinearity is effective?According to a method of normal forms (see for example [7,8]), we look for a solution to eqs. (12) in the form of a quasi-automorphism, i. e.(14) where denotes an unknown -dimensional vector function, whose components can be represented as formal power series in , i. e. a quasi-bilinear form:(15) ,for examplewhere and are unknown coefficients which have to be determined.By substituting the transform (14) into eqs. (12), we obtain the following partial differential equations to define :(16) .It is obvious that the eigenvalues of the operator acting on the polynomial components of (i. e. ) are the linear integer-valued combinational values of the operator given at various arguments of the wave vector .In the lowest-order approximation in eqs. (16) read.The polynomial components of are associated with their eigenvalues , i. e. , where or ,while in the lower-order approximation in .So, if at least the one eigenvalue of approaches zero, then the corresponding coefficient of the transform (15) tends to infinity. Otherwise, if , then represents the lowest term of a formal expansion in .Analogously, in the second-order approximation in :the eigenvalues of can be written in the same manner, i. e. , where , etc.By continuing the similar formal iterations one can define the transform (15). Thus, the sets (12) and (13), even in the absence of eigenvalues equal to zeroes, are associated with formally equivalent dynamical systems, since the function can be a divergent function. If is an analytical function, then these systems are analytically equivalent. Otherwise, if the eigenvalue in the -order approximation, then eqs. (12) cannot be simply reduced to eqs. (13), since the system (12) experiences a resonance.For example, the most important 3-order resonances includetriple-wave resonant processes, when and ;generation of the second harmonic, as and .The most important 4-order resonant cases are the following:four-wave resonant processes, when ; (interaction of two wave couples); or when and (break-up of the high-frequency mode into tree waves);degenerated triple-wave resonant processes at and ;generation of the third harmonic, as and .These resonances are mainly characterized by the amplitude modulation, the depth of which increases as the phase detuning approaches to some constant (e. g. to zero, if consider 3-order resonances). The waves satisfying the phase matching conditions form the so-called resonant ensembles.Finally, in the second-order approximation, the so-called “non-resonant" interactions always take place. The phase matching conditions read the following degenerated expressionscross-interactions of a wave pair at and ;self-action of a single wave as and .Non-resonant coupling is characterized as a rule by a phase modulation.The principal proposition of this section is following. If any nonlinear system (12) does not have any resonance, beginning from the order up to the order , then the nonlinearity produces just small corrections to the linear field solutions. These corrections are of the same order that an amount of the nonlinearity up to times .To obtain a formal transform (15) in the resonant case, one should revise a structure of the set (13) by modifying its right-hand side:(16) ; ,where the nonlinear terms . Here are the uniform -th order polynomials. These should consist of the resonant terms only. In this case the eqs. (16) are associated with the so-called normal forms.RemarksIn practice the series are usually truncated up to first - or second-order terms in .The theory of normal forms can be simply generalized in the case of the so-called essentially nonlinear systems, since the small parameter can be omitted in the expressions (12) - (16) without changes in the main result. The operator can depend also upon the spatial variables .Formally, the eigenvalues of operator can be arbitrary complex numbers. This means that the resonances can be defined and classified even in appropriate nonlinear systems that should not be oscillatory one (e. g. in the case of evolution equations).Resonance in multi-frequency systemsThe resonance plays a principal role in the dynamical behavior of most physical systems. Intuitively, the resonance is associated with a particular case of a forced excitation of a linear oscillatory system. The excitation is accompanied with a more or less fast amplitude growth, as the natural frequency of the oscillatory system coincides with (or sufficiently close to) that of external harmonic force. In turn, in the case of the so-called parametric resonance one should refer to some kind of comparativeness between the natural frequency and the frequency of the parametric excitation. So that, the resonances can be simply classified, according to the above outlined scheme, by their order, beginning from the number first , if include in consideration both linear and nonlinear, oscillatory and non-oscillatory dynamical systems.For a broad class of mechanical systems with stationary boundary conditions, a mathematical definition of the resonance follows from consideration of the average functions(17) , as ,where are the complex constants related to the linearized solution of the evolution equations (13); denotes the whole spatial volume occupied by the system. If the function has a jump at some given eigen values of and , then the system should be classified as resonant one In applied problems the definition of resonance should be directly associated with the order of the approximation procedure. For instance, if the first-order approximation is considered, then the jupms of of order have to be neglected .. It is obvious that we confirm the main result of the theory of normal forms. The resonance takes place provided the phase matching conditions and .are satisfied. Here is a number of resonantly interacting quasi-harmonic waves; are some integer numbers ; and are small detuning parameters. Example 1. Consider linear transverse oscillations of a thin beam subject to small forced and parametric excitations according to the following governing equation,where , , , , , и are some appropriate constants, . This equation can be rewritten in a standard form,where , , . At , a solution this equation reads , where the natural frequency satisfies the dispersion relation . If , then slow variations of amplitude satisfy the following equationwhere , denotes the group velocity of the amplitude envelope. By averaging the right-hand part of this equation according to (17), we obtain, at ;, at and ; in any other case.Notice, if the eigen value of approaches zero, then the first-order resonance always appears in the system (this corresponds to the critical Euler force).The resonant properties in most mechanical systems with time-depending boundary conditions cannot be diagnosed by using the function .Example 2. Consider the equations (4) with the boundary conditions ; ; . By reducing this system to a standard form and then applying the formula (17), one can define a jump of the function provided the phase matching conditions и .are satisfied. At the same time the first-order resonance, experienced by the longitudinal wave at the frequency , cannot be automatically predicted.References
1. Nelson DF, (1979), Electric, Optic and Acoustic Interactions in Dielectrics, Wiley-Interscience, NY.
2. Kaup P. J., Reiman A. and Bers A. Space-time evolution of nonlinear three-wave interactions. Interactions in a homogeneous medium, Rev. of Modern Phys., (1979) 51 (2), 275-309.
3. Kauderer H (1958), Nichtlineare Mechanik, Springer, Berlin.
4. Haken H. (1983), Advanced Synergetics. Instability Hierarchies of Self-Organizing Systems and devices, Berlin, Springer-Verlag.
5. Kovriguine DA, Potapov AI (1996), Nonlinear wave dynamics of 1D elastic structures, Izvestiya vuzov. Appl. Nonlinear Dynamics, 4 (2), 72-102 (in Russian).
6. Maslov VP (1973), Operator methods, Moscow, Nauka publisher (in Russian).
7. Jezequel L., Lamarque C. - H. Analysis of nonlinear dynamical systems by the normal form theory, J. of Sound and Vibrations, (1991) 149 (3), 429-459.
8. Pellicano F, Amabili M. and Vakakis AF (2000), Nonlinear vibration and multiple resonances of fluid-filled, circular shells, Part 2: Perturbation analysis, Vibration and Acoustics, 122, 355-364.
9. Zhuravlev VF and Klimov DM (1988), Applied methods in the theory of oscillations, Moscow, Nauka publisher (in Russian)
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To simplify Matrix Algebra calculations.
MAT a1() = CON 'Set all elements of a1() to one
MAT a1() = CON(expr) 'Set all elements of a1() to value of expr
MAT a1() = IDN 'Establish a1() as an identity matrix
MAT a1() = ZER 'Set all elements of a1() to zero
MAT a1() = a2() + a3() 'Addition
MAT a1() = a2() 'Assignment
MAT a1() = INV(a2()) 'Inversion
MAT a1() = (expr) * a2() 'Scalar Multiplication
MAT a1() = a2() - a3() 'Subtraction
MAT a1() = a2() * a3() 'Multiplication
MAT a1() = TRN(a2()) 'Transposition
Array names with the MAT statements may optionally include a set of empty parentheses. The following are both equally valid, but the inclusion of the parentheses improves clarity of the code:
MAT a1 = CON
MAT a1() = CON
Matrix * and INV operations support all
It is the programmer's responsibility to ensure that arrays used with MAT are of the appropriate size and type. All operations involving two or more arrays require that they be of exactly the same size and type, without exception. Failure to adhere causes undefined results. In the interest of execution speed, no error checking is performed at run-time.
Every scalar value denoted here as 'expr' must be enclosed in parentheses. Although Matrix operations tend to imply a two-dimensional array, unless otherwise noted (such as with MAT IDN, *, TRN), MAT may be used with arrays of one to eight dimensions. It is permissible to specify one array for multiple MAT parameters.
MAT array1() = IDN
This establishes array1 as an identity matrix,
with all diagonal elements as 1 and all others as zero. This produces
undefined results if array1 is not a "square" matrix.
Each element of array2 is multiplied by the scalar value of the expr, then assigned to array1.
MAT array1() = TRN(array2())
Transposes the row and columns from array2 to array1. Arrays must be equivalent: array1(5,2) and array2(2,5). Only a square matrix may be transposed to itself.
MAT array1() = INV(array2())
Inverts the array from array2 to array1. Only a square matrix may be inverted. Proof: If array1 is then multiplied by array2, the resulting "array3" will be equal to an Identify Matrix, (MAT array3 = array1 * array2 ' array3 should now be equal to "MAT array3 IDN").
MAT a() = b() * c()
Array multiplication occurs as follows:
' Row Column assumption:
' array [a]l,n = [b]l,m * [c]m,n
FOR i = 1 TO l ' Row [a]l = Row [b]l
FOR j = 1 TO n ' Column [a]n = Column [c]n
a(i,j) = 0# ' # if Double-precision
FOR k = 1 TO m ' Column [b]m = Row [c]m
a(i,j) = a(i,j) + b(l,k) * c(k,j)


Are you fearing the SAT Math area? Youre absolutely not alone. If you have a hard time in this subject, you may have a little bit of anxiety over this portion of the test, despite the fact that youre enabled a calculator for part of it! Thats okay. Understanding what to expect is truly half the battle. Heres what you require to understand before you sit for the exam, how you can prepare, and a couple of places to discover examples of the hardest SAT mathematics questions youll face on test day.
What Does the SAT Math Section Include?
There are 58 total concerns in the mathematics section of the SAT and you have 80 minutes to answer them. The very first part is “no calculator,” lasts 25 minutes, and includes 15 multiple option and 5 grid-ins. The second part allows you to have a calculator, lasts 55 minutes, and has 30 numerous choice and 8 grid-ins. You will have access to particular formulas throughout both sections so you do not require to remember any.
The Math area consists of questions on:
Heart of Algebra. This area can ask questions about direct Equations, charts, linear relationships, functions, word problems, and more.
Additional Topics. A bulk of the questions will fall into one of the areas above, however some will also cover, geometry, complex numbers, and trigonometry.
Passport to Advanced Math. This section covers questions about nonlinear expressions, polynomial aspects, functions, quadratic formulas, and more.
Issue Solving and Data Analysis. This covers ratios and proportions, scatterplots, information reasonings, precents, information collections, and more.
There will be a couple of other concerns in this exam that over geometry, trigonometry, radians,
Tips for Taking the SAT Math Section
Here are a couple of suggestions for taking the SAT Math area:
1. Take Practice Exams
When youve taken a practice exam, review your work. Exist certain areas of the Math portion that you did improperly on? Youll desire to concentrate on those locations before you take another practice test. You might even wish to speak to your math teacher or consider dealing with a tutor for additional assistance if youre truly having a hard time in a particular location of math.
When it comes to the SAT is to take practice examinations, one of the finest things you can do. This will help you get as close to the “real deal” as you potentially can before your official test date. Take them under the same conditions, too. That means no distractions, time frame, no turning pages back to previous areas, and breaks at the appropriate times.
2. Note the Questions Go From Easy to Hard
The SAT Math areas are developed to have the easy questions initially and the hard concerns last. Pacing yourself is essential as youll desire enough time to answer those challenging questions.
If youre lacking time and you havent addressed those difficult concerns, complete what you can and after that guess the rest. There is no charge for guessing if youre seriously on the final two minutes of the area!
3. If Its Not the Calculator Section, You Dont Need a Calculator to Answer it!
The Hardest SAT Math Questions.
If the school is test-optional, your SAT or ACT scores can absolutely have an impact on your admission possibilities– even! If youre curious what schools are searching for in a student and the SAT score you must go for, utilize our College Match tool.
Some trainees reach concerns in the no-calculator part of the SAT exam and think that there need to have been some error. You will not require your calculator on this section.
There are 58 overall questions in the mathematics section of the SAT and you have 80 minutes to address them. Are there certain areas of the Math part that you did badly on? You might even want to talk to your mathematics teacher or think about working with a tutor for additional help if youre truly having a hard time in a specific area of math.
The number one thing you can do to improve your SAT Math area score and deal with those hard concerns is to be prepared. Practicing and understanding what to expect will absolutely help you come out on top, even when its time for your main test date.
Much like appeal is in the eye of the beholder, the “hardest” mathematics concerns will differ from individual to person. Taking a practice test will absolutely assist you determine the locations where you have the most trouble.
Im not sure if you wish to copy/paste pictures of the hardest SAT mathematics concerns into the post, so I offered some links below to be consisted of or to pull extra information from.
Nevertheless, if you wish to see some actual examples of the mathematics questions youll see on either your practice test or the genuine offer, this research study guide from College Board has some excellent examples of tough concerns you may face, as well as additional information on all of the sections.
Are you fearing the SAT Math section? Heres what you require to understand prior to you sit for the examination, how you can prepare, and a couple of places to discover examples of the hardest SAT mathematics concerns youll deal with on test day.


The 14th edition of the Carnival of Math is out there for your pleasure a couple of days ahead of schedule over at Vlorbik on Math Ed. This is an excellent edition with links to a wide variety of worthwhile math blogs at all levels from K-8 through advanced. Similar to a suggestion I had offered in the 10th edition of the Carnival (which I hosted), there is now a call to consider a Carnival of Research Mathematics. Although the consensus back then was to keep one math carnival intact, the idea of splitting it appears to be gaining momentum, particularly since the last couple of carnivals seemed to be weighted more heavily toward math ed. As long as each has enough of a following, I believe this can benefit both ends of the spectrum. I could add more here, but go enjoy the latest Carnival!


Is your child a fan of math? My 10 year old has found it's not her most favorite of subjects, but we seem to be working through it. As I am trying to figure out what math curriculum to use next year, I was introduced to Math Mammoth by Maria Miller. I received the awesome opportunity of reviewing the light blue series for grade 5.
I received files that were easily downloadable to my desktop. Here is what is included in the grade 5 light blue series:
- User Guide Math Mammoth Light Blue
- More info from Math Mammoth
- Bonus Soft-Pak
- Student Worksheets
The student worksheets consist of 5-A and 5-B along with answer keys. 5-A covers:
- The Four Operations
- Large Numbers and the Calculator
- Problem Solving
- Graphing and Statistics
- Fractions: Add and Subtract
- Fractions: Multiply and Divide
It's good to go through the sheets up to 4 times a week. This is our goal for the summer as well to keep our brains sharp.
I like how cutouts are included with this curriculum series. These are used for learning fractions.
There are also cumulative review chapters included in the series. Chapters 1-8 and practice sheets. You can also make extra worksheets. This option takes you to a website where you can generate worksheets for your 5th grader to stay on top of their math skills. Pretty cool!
When it's time to test your 5th grader on math skills they have learned, you can print them out. All 8 chapter tests are included as well as an end-of-year test.
I think I may utilize Math Mammoth through the summer as well as a supplement through our homeschool year next year. I really like it and Kelly seems to not mind it either, haha! She really enjoys fractions! All of the pages are easy to understand. A child can figure it out on their own which is always a plus, but if they are struggling with an area, it's simple for the parent to instruct as well.
How much does this curriculum cost?
- Full set for 5 is $34.
- Full set for 5-A is $17.50
- Full set for 5-B is $17.50
- Supportive Materials are $8.95
What math curriculum do you currently use? Have you ever used Math Mammoth?
Feel free to read other reviews by the TOS Review Crew.


(For brevity's sake, hereafter I will refer to the parent isotope as ).
In many cases, there are independent cues (such as geologic setting or the chemistry of the specimen) which can suggest that such assumptions are entirely reasonable.
This will be discussed in more detail in the section on Gill's paper below.
The "generic" method described by Gonick is easier to understand, but it does not handle such necessities as: (1) varying levels of uncertainty in the X- versus Y-measurements of the data; (2) computing an uncertainty in slope and Y-intercept from the data; and (3) testing whether the "fit" of the data to the line is good enough to imply that the isochron yields a valid age.
The simplest form of isotopic age computation involves substituting three measurements into an equation of four variables, and solving for the fourth.
The equation is the one which describes radioactive decay: If one of these assumptions has been violated, the simple computation above yields an incorrect age.


Happy Pi day
Pi Day is celebrated on March 14th (3/14) around the world. Pi (Greek letter “”) is the symbol used in mathematics to represent a constant — the ratio of the circumference of a circle to its diameter — which is approximately 3.14159. Pi has been calculated to over one trillion digits beyond its decimal point.
Pi (π) is the ratio of the circumference of a circle to its diameter. It doesn't matter how big or small the circle is - the ratio stays the same. Properties like this that stay the same when you change other attributes are called constants.
What happens on Pi Day?
March 14 is Pi Day. It is a day to celebrate the mathematical constant pi (π) and to eat lots of pie. Celebrated in countries that follow the month/day (m/dd) date format, because the digits in the date, March 14 or 3/14, are the first three digits of π (3.14), Pi Day was founded by Physicist Larry Shaw in 1988.
Enjoy the day and make sure to eat some "pie"


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Madan M. Gupta & Liang Jin & N. Homma – Static & Dynamic Neural Networks
Provides comprehensive treatment of the theory of both static and dynamic neural networks. * Theoretical concepts are illustrated by reference to practical examples Includes end-of-chapter exercises and end-of-chapter exercises. *An Instructor Support FTP site is available...
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Adrian Silvescu – Fourier Neural Networks (Article)size 587 KBThe first mathematical model of a neuron was proposed by McCulloch & Pitts.The underlying idea that this model tries to capture is that the response function of a...
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This post is part of a series of weekly found poetry prompts. If you have an idea for a found poetry source, email Senior Poetry Editor Beth Ayer.
The power of the golden section to create harmony arises from its unique capacity to unite different parts of a whole so that each preserves its own identity and yet blends into the greater pattern of a single whole.
— György Dóczi, The Power of Limits
For this week’s prompt, you’ll need to do some math. Wait: hear me out. Math, science, and poetry fit together quite nicely. After all, math explains many common patterns and examples of beauty in nature, and science and math texts have proven to be excellent sources for found poetry. So, please join us in a little experiment.
For this exercise, we’ll refer to two related concepts: the Fibonacci Sequence and the Golden Ratio. Numbers in the Fibonacci Sequence are produced by adding the two previous numbers in the sequence. So, the sequence begins 0+1=1, 1 + 1=2, 1 + 2=3, 2 + 3=5, and continues in that pattern. The Golden Ratio (1.61803398875), based on the Fibonacci Sequence, represents a pattern that occurs in nature, often expressed in a spiral. The proportion not only appears commonly in nature, it has also long been mimicked in art and design. Look at the layout of the page you’re reading right now (unless of course you’re reading on a mobile device): the proportion of the body text to the right side columns is surely based on the golden ratio.
Fibonacci numbers, like many elements found in nature, follow a 1:1.61 ratio – this is what we refer to as the Golden Ratio, and as it forms such a common sight in nature, it feels pleasing to the eye…
You can learn more about these concepts by following the links sprinkled throughout this post. But for the purposes of our task at hand, the above is probably enough background. Let’s get started.
Follow these steps to create your poem:
- Select a book from your shelf.
- Use the Fibonacci sequence to identify the page numbers to which you will refer: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377…
- Turn to the first page and count the number of lines. Divide the total number of lines by the golden ratio (1.61803398875) and round to the nearest whole number.
- The text in the resulting line will be the first line of your poem. So if your page is 25 lines long, you will use line number 15.
- Turn to the next number in the sequence (page 2) and repeat the same process outlined above.
- Once you have recorded all the lines of the poem, it is acceptable to revise by removing words, fixing tenses, and changing punctuation.
- Lines should stay in original order, but it is OK to change line breaks by combining them.
- You may choose not to begin with page 1 of your source text.
- If you come up with an alternate technique for using these numbers, please let us know!
- Please share your poems in the comments. I’ll start by adding the first comment.
Top image by jitze on flickr


Place Value Worksheets Expanded Notation Using Decimals
Expanded Notation Using Decimals Worksheets This Place Value Worksheet Generator Is Great For Teaching Children To Read And Write Numbers With Decimals Using Expanded Notation You May Select 2 3 Or 4 Digit Numbers With Tenths Hundredths Or Thousandths Decimals Number Of Digits In The Number
Expanded Notation Math Worksheets Teachers Pay Teachers
Two Five Question Quizzes Designed To Assess Student Mastery Of Texas Math Teks 4 2b Represent The Value Of The Digit In Whole Numbers Through 1 000 000 000 And Decimals To The Hundredths Using Expanded Notation And Numerals These Are High Quality Perfectly Aligned And Formatted Like The Staar T
Expanded Notation Worksheets Teaching Resources Tpt
4th Grade Texas Math Supports 4 2b Represent The Value Of The Digit In Whole Numbers Through 1 000 000 000 And Decimals To The Hundredths Using Expanded Notation And Numerals Included In This Set 24 Task Cards Answer Key Answer Document And A Gameboard Task Cards 1 12 Whole Numbers Task Card
Expanded Notation Worksheets
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Expanded Notation Quiz Worksheets Teaching Resources Tpt
Your Students Will Be Asked To Find The Expanded Notation Form Of Numbers From The Millions Place To The Hundredths Place Tenths And Hundredths Are Expanded Using Both Fractions And Decimals There Are 24 Self Checking Cards They Can Check Their Own Answers Using The Qr Codes Or Turn In Complet Subjects Fractions Decimals Place Value Grades 4 Th 5 Th 6 Th Types Activities MathWrite Numbers In Expanded Form Printable Math Worksheets
Math Worksheets For Write Numbers In Expanded Form Standard Expanded And Word Form Write Numbers In Expanded Form These Are Expanded Form Worksheets For Converting Numbers From Standard Numeric Notation Into Conventional Expanded Form Where The Place Value Multiplier And The Digit Are CombinedPlace Value Worksheets
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Worksheets For Expanded To Standard Numeric Form The Worksheets On This Page Require The Opposite Skill Of Those In The Previous Section Here A Student Is Given A Value Written In Expanded Form And They Are Asked To Write The Standard Numeric Form Of The Number As The Answer
Standard Expanded And Word Form Dadsworksheets
48 Standard Expanded And Word Form Worksheets Practice Expanded Form Worksheets For Converting Numbers From Standard Numeric Notation Into Expanded Place Value Form Expanded Form Worksheets Will Help Students Understand Place Value Concepts And Be Better Able To Understand The Gaps In Converting Longer Numbers With Zero Place Values Into
Expanded Notation Task Cards Worksheets Teachers Pay
Your Students Will Be Asked To Find The Expanded Notation Form Of Numbers From The Millions Place To The Hundredths Place Tenths And Hundredths Are Expanded Using Both Fractions And Decimals There Are 24 Self Checking Cards They Can Check Their Own Answers Using The Qr Codes Or Turn In Complet
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There isn't anything like a superb story, and nothing like being the person who started a renowned urban legend. Deciding upon the ideal approach route Cursive writing is basically joined-up handwriting. Practice reading by yourself as often as possible.
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| by Dezia Restivo
To arrive at your “key number,” add each digit of the month and the day of your birth; this gives you your number unless it comes to more than 9. If this is the case, add the two remaining digits together. This is now your number. For example, if you were born on November 17th, then add the following digits: 11 and 17 (1+1+1+7=10). Because 10 must be reduced to arrive at one digit, add 1 + 0 = 1. Therefore your “key number” would be 1.
Even when out of town, there are ample opportunities for you to use your initiative. Exercise caution where tempers are concerned. Wear turquoise.


Job Reference: MathsWk DT 007 Job ID 207201961
Job Type: Permanent
Salary: DOE £25000 - £50000
Date Posted: 16th January, 20182018-01-16
Date Closing: 23rd July, 201807/23/2018
Sector(s): Secondary Teacher Jobs, Maths Teacher Jobs
Agency: Castles Education
Are you an experienced Maths teacher or NQT?
Are you looking for a potential leadership and development role as a Maths teacher?
Are you looking for a chance to join an improving school in a successful Maths department?
Can you deliver engaging and motivating Maths lessons to students across all key stages?
If you answered yes to the questions above then we would like to see your CV today!
The school places ambition at the heart of its ethos. It wants pupils to be the best that they can be academically, culturally and socially. It is relentless in the pursuit of excellence in GCSEs. This is a school with an amazing team spirit in the sporting and arts arenas. It builds strong social awareness through charity and community work.
We are seeking an enthusiastic and passionate Maths teacher for an exciting opportunity that will help support and build an inspirational Maths department.
As a Maths teacher working in this school, you will be joining a school that is proud to be at the heart of its local community. It is a school with a strong family feel its aim is to develop students who are;
We require a full-time teacher of Maths who is able to teach Maths across all key stages. You will join a well-resourced and collaborative Maths department in a school where students are well motivated.
The successful Maths teacher will join a vibrant department. You will teach Maths with a healthy and open attitude to progress and change.
The community provides a purposeful learning environment for both students and staff, stressing the importance of creativity, independence, celebration and empathy.
We are fully committed to safeguarding and promoting the welfare of children, younger learners and vulnerable adults and we expect all staff and volunteers to share the same commitment. All positions will be subject to enhanced DBS checks, satisfactory references and will be exempt from the provisions of the Rehabilitation of Offenders Act 1974


Next month is my birthday month. I am so exited.
In Math yesterday, we did this thing called brain benders, and in that, we did “genius testing”, and that was really awesome. Here are the questions:
- How many birth days do the average persons have?
2. A plane crashed on the boarder of New Mexico and Texas, so where do they burry the survivors?
Ans: They survived!
3. There are three apples, you take two away, how many apples do you have?
4.A butcher is five foot ten, so what dose he weigh?
5. An electric train goes south at 71 miles per hour and the wind blows 31 miles north per hour, so which way will the smoke blow?
Ans: There is no smoke!
6. Do they have a Fourth of July in England?
Ans: Yes, they just don’t celebrate it.
7. Some months have 30 days. How many have 28?
Ans: All of them.
8. How many stones did it take to finis the Great Wall of China?
9. A farmer has 17 sheep, and all but nine die. How many survived?
10.How much dirt is in a 6 by 6 by 6 hole?


The Pirates of Fossil Island
Make your own dinosaur pirate and solve math problems to win treasure on the high seas!
For ages 3 and up, our first game focuses on simple arithmetic and counting: addition, subtraction, multiplication, and division.
Don’t worry if this sounds too complicated -- our Learning Engine™ starts easy, tracks progress, and customizes the game's difficulty for each player.
Our Learning Engine™ tracks your kids’ progress and shows them exactly the problems they need to see. As they learn, the game grows with them!
Your kids will choose a character and level up with cool new items as they learn more math! With thousands of different combinations and new items coming out all the time, we’ll keep your kids motivated and coming back for more.
Math Goes Multiplayer
Real math is about collaboration and sharing ideas. With our safe and anonymized multiplayer network, kids can solve math problems with friends and compete for high scores, right on their iPad!


How many bricks do you need?
Let us help you calculate how many bricks you need for your wall area. Just enter your wall area below and select your brick size and we'll estimate the number of bricks you need.
Enter your wall area (square metres - m2)
You can calculate the area of your wall by multiplying the length of the wall by the height (expressed in metres).
Select your chosen brick size from the options below (dimensions in millimetres)
QUANTITY OF BRICKS:
Disclaimer: This Brick Calculator has been provided as a guide only.
Before ordering your bricks, be sure to check the quantity with your bricklayer and add a wastage allowance.


The “now-focusing effect” inevitably leads to a preference for spending over saving.
But can we even process economic numbers correctly?
Sri Humana: So, what shall we discuss today?
Ann: I heard an interesting news story; it said our per-capita income is actually growing.
Garret: Boring. I watched a fascinating horror movie instead.
Sarah: Emily has nightmares, and I can’t sleep all night.
Thomas: To tell you the truth, I do not like horror movies. But judging from the ones I have seen, the whole script usually revolves around some kind of a monster. These horrible creatures rarely have much in common; they’re rather unique. But how about this: suppose someone combined the Predator, the Alien, Godzilla, Dracula and Jason into one “average monster.” What would it look like? I think it would be funny and bizarre.
Now, in your everyday life, you are bombarded with all kinds of average statistics. Journalists use them, politicians use them and your boss uses them.
Average salary, average IQ, average results and of course the average person. The average person on Earth is 1.8 meters tall, has a 110 IQ, earns $5000 per year, has one and a half children, is half Chinese and half Indian, and half man half woman. What a monster!!!
The most dangerous average monsters are the ones in areas where results or outcomes are not equally distributed. Areas like wealth, internet traffic, city sizes, areas destroyed by fire and all sorts of other social phenomena.
Don’t get me wrong, averages do have some meaning and use, but mostly when they’re mentioned in connection with things that are distributed normally. Things like people’s height, health, and school grades. Or the number of sunny days in a year, etc.
For example, consider the average wealth of a random, relatively small group of people. Now add Bill Gates to that same group, and calculate the average again. What happens to the average figure?
Now consider the average IQ of a similar random group. Then add Einstein to the group, and calculate again. How would the average IQ change?
There is a useful tool for measuring variability, but remember it is useful only if your data is distributed normally – for example, the way body part sizes appear among a group of people, with all values falling within a fairly well-defined range. This tool is the metric known as standard deviation. It simply measures how far a particular measurement is found to deviate from the average (mean) measurement, in a particular group. A low standard deviation means that the data points tend to be very close to the mean. A high standard deviation means that the data points are spread over a large range of values, some far from the mean. (If you calculate the standard deviation in a group to be very high, it may mean your average figure is of little or no use.)
Now, don’t worry – we’ll get to how you can use this tool in managing your wealth very soon. First, we’ll look at how to calculate it – then we can put it to work.
Stop believing in “average monsters” and your nightmares might go away.
For the sake of example, let’s imagine you have a small flock of seven chickens, and you sell their eggs (yes, “nest eggs”). You want to find out the average number of eggs each chicken lays each year, and how much variation there is within the group (the standard deviation). You have kept a record of each chicken’s production for the past year, and you are ready to do the math.
Here are the eight steps for calculating standard deviation:
- Organize your data – gather it all together so you can work with it. In this case, get out your record of each chicken’s production.
- Add your data. Find the total number of eggs your whole flock chickens produced. We’ll say it was 980 eggs.
- Calculate the average of your data by dividing the total by the number (count) of records (the number of chickens for which you kept records: 7) This gives you 980/7=140. That means the average number of eggs per chicken was 140.
- Subtract the average number from each record. For example, if Chicken #1 (Betsy) laid 120 eggs, you would subtract 140 from 120. Write that number down, and then go through the same process for the other six chickens.
- Square the above numbers. That is, multiply each of the numbers you found by itself. Betsy’s number would be 20 x 20, or 400. Write that down and repeat the process for the rest of the flock’s numbers from step 4.
- Add up all the squared numbers.
- Calculate the average of all the numbers found in step 5.
- Calculate the square root of the number you found in step 7. The number you find here is the standard deviation.
*NOTE: There IS a shorter and easier way to do this, if you happen to have a spreadsheet app such as MS Excel, and know how to use it. Just create a spreadsheet for your data and use the STDEV function.
In this example, 35 is your standard deviation. That means you can anticipate that if you add a chicken to your flock, you will end up with 140 more eggs in the next year, plus or minus 35 eggs. (That is, you might get as few as 105 or as many as 175, but it’s likely to be closer to 140.) This also assumes that your sample (the records for your seven chickens) is representative of all chickens in the region.
Standard deviation is a widely used metric, especially for evaluating risks. Be careful in using it, though – many people fall into a trap when using standard deviation: they become overconfident about risks in domains which have extreme distributions. (This common mistake actually contributed to the financial crisis of 2008.) So, use standard deviation wisely, and don’t get overconfident about it – especially when using it in the social domain.
Some questions for you:
- Do you consider yourself an average person?
- What is the average day temperature in the Sahara? In Chicago?


Calculations or Calculated Variables provide the means to create calculations based on various data elements. Calculations are most commonly used within a Survey to create a new variable based on survey responses such as 'BAC' or 'AUDIT Score'. However, IMPACT Feedback also provides Calculations in Reports, Messages, and Events. Please see the table below for information about each calculation type.
|Quick Show Condition ||Used for the creation of a variable to use in show logic (item condition). Common uses of the Quick Show Condition are to variables used to hide survey questions (or pages) based on the response to a previous question. |
Use this to create a 'Cannabis Logic' item that will hide subsequent questions about Cannabis if the case responds a certain way to a previous question about Cannabis.
|Conditional Expression||Use this to return one of two possible outputs (either return 'this' or 'that'). The output variable can be another number, a date, text, True/False or another calculation. |
A conditional expression can be used in a report to return the text 'never' for a student's Drinking Days Per Month value instead of '0 days per month' if the student said they have have never drank and entered zero drinks into the two week calendar.
A conditional bucket expression works much like a conditional expression except that in this case the input variable (ie: responses to a survey question) can be broken into various buckets with corresponding output.
A conditional bucket expression can be used to return a risk category based on a Family History Risk Score for use in a report. Risk scores within a set of defined numerical ranges will return a particular risk category: 0-2 returns a risk category of 'Low', 2-4 returns 'Medium', 4-7 returns 'High' and 7+ returns 'Very High'.
|Date Manipulation||Date manipulation adds or subtract from a specified date. |
A date manipulation calculation could calculate the # of days since the case was created/added to the system.
|Date Number Extract||These calculations are used to extract a numeric component (hour, day, year, etc.) from an event within IMPACT Feedback.|
This can be used to return the day of the week a survey was completed for use in a report.
|Formatter||This calculation provides a means for formatting the input variable for display (ie: in a Feedback Report or Message). |
The 'precision' function can be used to round BAC to the desired number of decimals or return a date calculation in a specific format (mm/dd/yyyy),
|Math Expression||Math expression calculations provide a robust solution for computing complex math equations. |
For example, AUDIT Score is calculated by assigning a certain numeric value to each response on the scale.
|Math Function||This calculation type provides the following three options for rounding a numeric value to a whole number. |
|Normative Lookup||Use this to compute normative information typically displayed above normative charts. Normative lookup calculations reference your Organization's norms in order to provide normative percentage or percentile rank to be inserted into the Feedback Report.|


PURPOSE: To improve reliability of piling length determination of piled-up coins by a method wherein a reference of piling length determination made at a wrapping part according to a measured value of the piling length at a piling part is set at an appropriate value.
CONSTITUTION: A controlling means 81 which controls a piling part 2 for piling up coins drawn out one by one and a wrapping part 3 for receiving and wrapping the piled coins is connected with piling length measuring means 82 and 59 for measuring piling length of the piled coins respectively at the piling part 2 and wrapping part 3 and a storing means 86. The storing means 86 stores a piling length x 0 preliminarily set with respect to a measured value x of the piling part piling length, its tolerance range x 0 ±α and divisions of thicker, standard and thinner x 1 , x 2 and x 3 [x 0 -α≤x 1 < x 0 -β≤x 2 <x 0 +β<x 3 ≤x 0 +α]. Further, the storing means 86 stores a plurality of piling length references y 1 , y 2 and y 3 which are preliminarily set with respect to a measured value y of the wrapping part piling length corresponding to the respective values x 1 , x 2 and x 3 , and its tolerance range yi±γ. At this time, γ<α is satisfied. If the measured value of the wrapping part piling length is within the tolerance range of the wrapping part piling length corresponding to the measured value of the piling part piling length stored in the storing means 86, wrapping is carried out.