I get asked a lot what I use them for so I want to share with you some ideas that I had.
One station my kids LOVE to do is sort and count. I just put a bunch of different erasers out for them and they go to work. Simple and really NO prep!
Another very popular math station my students love is Roll to 50. 2 students roll a dice, then put that number of erasers on the grid. When it is all filled up they count and see who had the most. This activity is great for addition and counting. I also made the frames for rolling up to 20 for some students and those who are looking for a challenge can roll up to 100!
Since there are always a few different seasonal eraser styles out at a time, another activity students can do is creating patterns. On this sheet, the students are given the eraser to start with. What they come up with at the end is up to them. You could have them create any kind of pattern they need to work on. I even left 2 rows blank for students to show you how they can create their own kind of pattern.
One last math idea I had was to use the erasers to help build number sense.
You can click here Activity Sheets to get a copy of the sheets. Also, feel free to pin the picture below so you can save these ideas for later.
**** I have now created these activities for ALL the erasers that are found in the Dollar Spot!
Leave me a comment and tell me how you would use these erasers in your classroom. I am always looking for more ideas!


We all know that Maths is an important subject for the students of Singapore. It is a compulsory subject that most students don’t like to study. Students take this subject from their primary school until the end of A-levels. Most students do not like to study this subject because it has tough techniques and sections. It is often a prerequisite of learning popular courses in Engineering as well as commerce universities.
In Singapore, Maths home tuition becomes a basic need of every student. However, as research, there is a steady increase in the number of new topics covers by the maths curriculum. Each new topic in foreign countries taught in greater difficulty and depth.
Learn more about Women’s Education in Bangladesh.
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Me and my friend were just discussing usual kind of things and somehow this came up in conversation. It seemed a simple enough question to ask ourselves but we found ourselves struggling to come up with any regular 3-dimensional shape with only 3 sides. The least we could imagine was four, a simple triangular based pyramid. So we decided to leave it there and I made a mental note to look it up on the internet when I got a chance.
Now i did a very small bit of research before trying to work it out, well actually I say research, i just found a forum online and had a read through, there seemed to be quite a few experts, or knowledgeable people there, which knew a thing or two about geometry and that sort of thing.
Lets try and answer this question in a simpler way first, can you have a regular 2-sided, 2-dimensional shape. So in this question we are looking for a regular 2-dimensional shape, by regular i mean like a square, a pentagon, an octagon. The fewest sides i can imagine a 2-dimensional shape having would be 3, a simple triangle. But you can say you can get a semicircle, where the curved edge counts as 1 side, and the flat edge as the second side. In which case you are then using a 1 dimensional line and a 2 dimensional curve to get your 2 sided object. So we conclude that you can only get a 2-sided, 2-dimensional shape using atleast one 2-dimensional curved line. And by only using 1-dimensional lines we can obtain only a three-sided shape as the least sided shape. Follow that? I’ve pretty lost managed to lose it myself just thinking about how to put it.
So, ignoring curved lines, the minimum sides for a 2-dimensional shape is made of 1-dimensional lines. Now if we think about a simple regular 3-dimensional shape, like say a cube, it is made of 2-dimensional squares. So we can guess that a regular 3-dimensional shape, ignoring curved surfaces, is only made of 2-dimensional surfaces. As a little added extra bit i’m just thinking does that mean that to get to a 4-dimensional shape we would need to make it out of these simple regular 3-dimensional shapes, ignoring curves? Hmmm that is an interesting thought. But impossible for me to imagine, and most humans i would hazard a guess.
So anyway, from there i tried to imagine a regular three-dimensional shape made of triangles…..I couldn’t……I retreated back to the forum. There i found someone had posted something about seeing a 3-dimensional object from one angle you could see 3 sides had to all interact at one point, or something like that i forget exactly what it was. But it got me thinking, when you look at a cube directly onto a corner you see 3 faces which all meet at that corner, so what if you could bend them all round again to interact at a corner on the other side? I couldn’t imagine it with a cube, but i quickly realized i could just think of a rugby ball, except with it having 3 curved surfaces instead of 4. I’d done it! I’d managed to imagine a 3-sided 3-dimensional object. Although i did have to bend the rules a bit, haha.
I think i’ve come to the conclusion that:
- I can’t do research very well at all, and
- There is no 3-sided, 3-dimensional object which only uses 2-dimensional shapes.
I don’t like the use of curved surfaces, because it just feels like cheating, once I could break that invisible rule i kind of set for myself i found i could imagine many things, for example: a two-sided 3-dimensional shape would just be 2 intersecting spheres, and you could either use the non intersecting or intersecting parts to get your shape. And another simple 3-sided, 3-dimensional shape could be a cylinder, but it doesn’t look as nice. There you go, take what you will from that.
Here‘s a link to that forum i so reference. They start talking about hollow 3D shapes aswell, which i just completely ignored for my own purposes.


appropriate reporting formats of logistic regression results and the minimum observation-to-predictor ratio. The authors evaluated the use and interpretation of logistic regression pre-sented in 8 articles published in The Journal of Educational Research between 1990 and 2000. They found that all 8 studies met or exceeded recommended criteria. Key words: binary data analysis, categorical. Regression results are often best presented in a table. APA doesn't say much about how to report regression results in the text, but if you would like to report the regression in the text of your Results section, you should at least present the unstandardized or standardized slope (beta), whichever is more interpretable given the data, along with the t -test and the corresponding significance.
4.15 Reporting the Results of Logistic Regression « Previous page Next page » Page 16 of 18 Our interest here has been not only in the association between ethnic group, social class, gender and exam achievement, but also how the relationship between ethnic group and exam achievement changes as we account for other explanatory variables (like SEC) and interaction effects Example: Logistic regression . If you have conducted a logistic regression, you can describe your results in several different ways. You could discuss the logits (log odds), odds ratios or the predicted probabilities. Which metric you choose is a matter of personal preference and convention in your field Reporting Multiple Regressions in APA format - Part Two Andrew Dart May 4th 2013 Statistics. And so, after a much longer wait than intended, here is part two of my post on reporting multiple regressions. In part one I went over how to report the various assumptions that you need to check your data meets to make sure a multiple regression is the right test to carry out on your data. In this. Writing up your results - Guidelines based on APA style In a results section, your goal is to report the results of the data analyses used to test your hypotheses. To do this, you need to identify your data analysis technique, report your test statistic, and provide some interpretation of the results. Each analysis you run should be related to your hypotheses. And if you analyze data that is. Join former statistics tutor and Walden University graduate, Dr. Zin Htway, for his version of the APA style write-up for the statistical test, Logistic Regression. This video was edited for.
Multiple linear regression is somewhat more complicated than simple linear regression, because there are more parameters than will fit on a two-dimensional plot. However, there are ways to display your results that include the effects of multiple independent variables on the dependent variable, even though only one independent variable can actually be plotted on the x-axis The table for a typical logistic regression is shown above. There are six sets of symbols used in the table (B, SE B, Wald χ 2, p, OR, 95% CI OR).). The main variables interpreted from the table are the p and the OR.. However, it can be useful to know what each variable means
For binary logistic regression, the format of the data affects the deviance R 2 value. The deviance R 2 is usually higher for data in Event/Trial format. Deviance R 2 values are comparable only between models that use the same data format. Deviance R 2 is just one measure of how well the model fits the data Binomial Logistic Regression using SPSS Statistics Introduction. A binomial logistic regression (often referred to simply as logistic regression), predicts the probability that an observation falls into one of two categories of a dichotomous dependent variable based on one or more independent variables that can be either continuous or categorical SPSS Simple Linear Regression Tutorial Published March 11th, The figure below is -quite literally- a textbook illustration for reporting regression in APA format. Creating this exact table from the SPSS output is a real pain in the ass. Editing it goes easier in Excel than in WORD so that may save you a at least some trouble. Alternatively, try to get away with copy-pasting the (unedited.
If you want to report results from multiple regressions, you can use the above format. If you clearly label each column, you will be able to refer to this table in your text when comparing regression results and conducting your analysis. For example, the table below reports four different regressions In the regressions below, the researcher is interested in the individual characteristics of. Logistic regression does not have an equivalent to the R-squared that is found in OLS regression; however, many people have tried to come up with one. There are a wide variety of pseudo-R-square statistics (these are only two of them). Because this statistic does not mean what R-squared means in OLS regression (the proportion of variance explained by the predictors), we suggest interpreting. To report your findings in APA format, you report your results as: F (Regression df, Residual df) = F-Ratio, p = Sig You need to report these statistics along with a sentence describing the results. In this case we could say: The results indicated that the model was a significant predictor of exam performance, F(2,26) = 9.34, p = .001. Coefficient
With simple linear regression the key things you need are the R-squared value and the equation. e.g., Number of friends could you might also want to report the regression equation, either in normal equation form or in a table that gives the intercept and the unstandardised coefficients. ANOVA With one-way ANOVA you need to find the following in the SPSS output: the F value, the p-value. . Scoot the decision variable into the Dependent box and the gender variable into the Covariates box. The dialog box should now look like this: 3 Click OK. Look at the statistical output. We see that there are 315 cases used in the analysis. The Block 0 output is for a model that includes only the intercept. SPSS Stepwise Regression - Example 2 Published February 28th, 2017 by Ruben Geert van den Berg under Regression. A large bank wants to gain insight into their employees' job satisfaction. They carried out a survey, the results of which are in bank_clean.sav. The survey included some statements regarding job satisfaction, some of which are. The data held in the file cancer.sav is from a study reported by Brown (1980) and are commonly cited in texts considering binary logistic regression. The prognosis for prostate cancer is based upon whether or not the cancer has spread to the surrounding lymph nodes. In this classic study Brown et al (see Brown, 1980) explored the following separate indicators for lymph node involvement in a.
This quick start guide shows you how to carry out linear regression using SPSS Statistics, as well as interpret and report the results from this test. However, before we introduce you to this procedure, you need to understand the different assumptions that your data must meet in order for linear regression to give you a valid result. We discuss these assumptions next Interpretation and APA writing template for the Standard Multiple Regression Results Above: A standard multiple regression analysis was conducted to evaluate how well high school grade point average and verbal SAT scores predicted college GPA. The linear combination of high school GPA and verbal SA Reporting Statistics in APA Style A Short Guide to Handling Numbers and Statistics in APA Format . The material in this guide is based on the sixth edition of the publication manual of the American Psychological Association: American Psychological Association. (2010). Publication manual of the American Psychological Association (6th ed.). Washington, DC: Author. Report The Results of All.
. 2 Guidelines for APA Style 1. Identify reason for analysis 2. Identify analysis 3. Report results 4. Report effect sizes 5. Report means. You would report these results in the standard format for reporting ANOVA. To do this, you can use the formula: F simple linear regression, when you have multiple predictors you would need to present this information for each variable you have. You might also want to include your final model here. So, in this case we might say something like: A simple linear regression was carried out to. I am trying to figure out the best way to report the results of a logistic regression in an APA paper. My understanding is that the odds ratio is the most important for interpretation so I don't think I should report the Beta. For significance, do I state the Wald like I would in a comparison (e.g. t(N-2) = #.##, p < .##). Thanks Hierarchical regression This example of hierarchical regression is from an Honours thesis - hence all the detail of assumptions being met. In an undergraduate research report, it is probably acceptable to make the simple statement that all assumptions were met. 3.2.2 Predicting Satisfaction from Avoidance, Anxiety, Commitment and Conflict Prior to conducing a hierarchical multiple regression. Reporting ordinal regression results. Thread starter ABN; Start date Nov 7, 2018; A. ABN New Member. Nov 7, 2018 #1. Nov 7, 2018 #1. Hi all - some help with reporting results of ordinal regression please: I have two group of variables (two separate groups of independent variables) and one ordinal dependent variable. I ran an ordinal regression for each group separately. After allot of work.
Presentation of Results A multinomial logistic regression was performed to model the relationship between the predictors and membership in the three groups (those persisting, those leaving in good standing, and those leaving in poor standing). The traditional .05 criterion of statistical significance was employed for all tests. Addition of the predictors to a model that contained only the. Module 5 - Ordinal Regression You can jump to specific pages using the contents list below. If you are new to this module start at the Introduction and work through section by section using the 'Next' and 'Previous' buttons at the top and bottom of each page. Be sure to tackle the exercise and the quiz to get a good understanding. Objectives 1. Understand the principles and theories underlying. Regression results are often best presented in a table. APA doesn't say much about how to report regression results in the text, but if you would like to report the regression in the text of your Results section, you should at least present the unstandardized or standardized slope (beta), whichever is more interpretable given the data, along with the t -test and the corresponding. An Introduction to Logistic Regression Writing up results Some tips: First, present descriptive statistics in a table. Make it clear that the dependent variable is discrete (0, 1) and not continuous and that you will use logistic regression. Logistic regression is a standard statistical procedure so you don't (necessarily) need to write out the formula for it. You also (usually) don't need to. Reporting a single linear regression in apa 1. Reporting a Single Linear Regression in APA Format 2. Here's the template: 3. Note - the examples in this presentation come from, Cronk, B. C. (2012). How to Use SPSS Statistics: A Step-by-step Guide to Analysis and Interpretation. Pyrczak Pub. 4
Reporting Results References Hypothesis testing in psycholinguistic research Typically, we make predictions not just about the existence, but also the direction of e ects. Sometimes, we're also interested in e ect shapes (non-linearities, etc.) Unlike in ANOVA, regression analyses reliably test hypotheses about e ect direction and shape withou Recommendations are also offered for appropriate reporting formats of logistic regression results and the minimum observation-to-predictor ratio. The authors evaluated the use and interpretation of logistic regression presented in 8 articles published in The Journal of Educational Research between 1990 and 2000. They found that all 8 studies.
Reporting Results of Multiple Logistic Regression Models Depending on the Availability of Data Richard M. Mitchell, Westat, Rockville, MD ABSTRACT This paper discusses a process of developing multiple logistic regression models based on the availability of data, as well as the presentation of corresponding results. The process was developed for an individual patient data meta-analysis (IPD-MA. The results of binary logistic regression analysis of the data showed that the full logistic regression model containing all the five predictors was statistically significant, ᵡ2 = 110.81, df =11, N= 626, p<.001 indicating that the independent variables significantly predicted the outcome variable, low social trust. The results of the data.
For all regression analyses, some report of effect size should be given for the overall model (such as R2) as well as for the individual predictors (such as converting the F ratios or t ratios associated with each predictor in the final equation to an effect-size r). We recommend reporting both the unstandardized B and the standardized β. Linear regression requires a numeric dependent variable. The independent variables may be numeric or categorical. Hierarchical regression means that the independent variables are not entered into the regression simultaneously, but in steps. For example, a hierarchical regression might examine the relationships among depression (as measured by some numeric scale) and variables including. Tip: if you're interested in taking your skills with linear regression to the next level, consider also DataCamp's Multiple and Logistic Regression course!. Regression Analysis: Introduction. As the name already indicates, logistic regression is a regression analysis technique. Regression analysis is a set of statistical processes that you can use to estimate the relationships among variables In logistic regression, we solve for logit(P) = a + b X, where logit(P) is a linear function of X, very much like ordinary regression solving for Y. With a little algebra, we can solve for P, beginning with the equation ln[P/(1-P)] = a + b X i = U i. We can raise each side to the power of e, the base of the natural log, 2.71828 This gives us P/(1-P) = ea + bX. Solving for P, we get the. 2. Summarise regression model results in final table format. The second main feature is the ability to create final tables for linear (lm()), logistic (glm()), hierarchical logistic (lme4::glmer()) andCox proportional hazards (survival::coxph()) regression models.The finalfit() all-in-one function takes a single dependent variable with a vector of explanatory variable names (continuous.
Multilevel Logistic Regression Analysis Applied to Binary Contraceptive Prevalence Data Md. Hasinur Rahaman Khan and J. Ewart H. Shaw University of Warwick Abstract: In public health, demography and sociology, large-scale surveys often follow a hierarchical data structure as the surveys are based on mul-tistage stratiﬁed cluster sampling. The appropriate approach to analyzing such survey. Reporting regression : Multiple linear regression was carried out to investigate the relationship between gestational age at birth (weeks), mothers' pre-pregnancy weight and whether she smokes and birth weight (lbs). There was a significant relationship between gestation and birth weight (p < 0.001), smoking and birth weight (p = 0.017) and pre-pregnacy weight and birth weight (p = 0.03. The APA style manual does not provide specific guidelines for linear mixed models. Additionally, a review of studies using linear mixed models reported that the psychological papers surveyed differed 'substantially' in how they reported on these models (Barr, Levy, Scheepers and Tily, 2013). It depends greatly on your study, in other words
While logistic regression results aren't necessarily about risk, risk is inherently about likelihoods that some outcome will happen, so it applies quite well. Clinically Meaningful Effects . Now what's clinically meaningful is a whole different story. That can be difficult with any regression parameter in any regression model. The odds ratio is an effect size you can use to choose a. Logistic regression will accept quantitative, binary or categorical predictors and will code the latter two in various ways. Here's a simple model including a selection of variable types -- the criterion variable is traditional vs. non-traditionally aged college students and the predictors are gender, marital status, loneliness and stress. Analyze à Regression à Binary Logistic predictors. The results section of an APA format paper summarizes the data that was collected and the statistical analyses that were performed. The goal of this section is to report the results without any type of subjective interpretation What to report? What a statistics program gives you: For a simple regression (one independent variable), statistics programs produce two estimates, a (the constant term) and b (the linear coefficient), for the parameters α and β, respectively. Each estimate has an associated t-value (along with its degrees-of-freedom, df) and p-value, for the test that the corresponding parameter is zero Logistic Regression In reporting logistic regression output it is important to provide enough information for readers to gauge the substantive significance as well as the statistical significance. Readers have difficulty interpreting the unstandardized B estimates and noting which is statistically significant does little to help the reader know which, if any, is substantively significant. For.
This post describes how to interpret the coefficients, also known as parameter estimates, from logistic regression (aka binary logit and binary logistic regression). It does so using a simple worked example looking at the predictors of whether or not customers of a telecommunications company canceled their subscriptions (whether they churned) reported as (APA, 2001). All statistical symbols are reported in italics: N, SD, M, p, Mdn, r, df, etc. This is true whether they appear in the body of the journals or tables. This section covers specifically how APA style is used to report statistical information or results in various forms in a journal. A smaller font size (10) will be used. In interpreting the results, Correlation Analysis is applied to measure the accuracy of estimated regression coefficients. This analysis is needed because the regression results are based on samples and we need to determine how true that the results are reflective of the population. The correlation analysis of R-Square, F-Statistics (F-Test), t.


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The work perfect rectangle (2003) is a configuration of glass plates that follow the mathmatical principle of the "perfect square". This principle was discovered in 1978 by the Russian mathematician A. J. W. Duijvestijn and describes the division of a square into the smallest number of different smaller squares. The smallest number possible is 21, without any square being repeated.
This most simple division was executed by Carsten Nicolai in his work perfect square (2004). Alternatively he has also done the work perfect rectangle, which has an aspect ratio of 33:32 (it is made of only 9 squares) and comes close to the square ideal thus being a perfect rectangle.
By the spiral layering of the glass plates (up to 6 on top of each other) an additional, complex visual structure occurs which elevates the composition to three dimensions. In its aesthetic form this composition of different layers of glass plates remind of computer storage media and captivates with its visual complexity and multifaceted reflections.


Caracterización de la distribución de los valores P de las pruebas paramétricas en poblaciones normales
Additional Document Info
Hypothesis test are widely used in data analysis but, in general, the random nature of p value is not consider in such applications. Power function and p-value probability distribution are strongly related, this relationship should be a component in both hypothesis testing conclusions and sample size calculation. However, this is not the case, possibly due of to two factors: first many people ignore the random nature of p-value and second there is a lack of information in the subject. Some papers introduced some characteristics of p-value distribution as mean value and median, but such values were not obtained for every parametric test in normal populations. This paper contains a full characterization of p-values probability distribution for both one and two sided hypothesis test for parameters in one or two normal populations. P-value probability distribution and their percentiles are presented, emphasizing in median value. Additionally the paper introduces approximate criteria for calculating both distribution function and percentiles, and highlight the relationship between power function and p-value.


Image Credit: Igor Sokalski Getty Images
At least 3,700 years ago, Babylonian mathematicians approximated the ratio of a circle’s circumference to its diameter. They inscribed their answer, the first discovered value of pi, on a humble clay tablet: 25/8, or 3.125. Now Carl-Johan Haster, a theoretical astrophysicist at the Massachusetts Institute of Technology, has managed to do almost as well: in a study uploaded to the preprint server arXiv.org, he measured pi to be about 3.115.
In the intervening years, researchers have calculated the true value of the ratio to a modest 50 trillion decimal places with the aid of powerful computers (you probably know how it starts: 3.141592653 … and on into infinity). Haster’s approximation of it may be a couple of millennia behind in terms of accuracy, but that fact is of little relevance to his real goal: testing Einstein’s general theory of relativity, which links gravity with the dynamics of space and time.
Continue to the full article on Scientific American, “Pi in the Sky: General Relativity Passes the Ratio’s Test” by Daniel Garisto.


Statistical data analysis tools
Go&to&the&data&table&and&click&on&the&data&analysis&tool&& from&the&listof&tools,&choose&descriptive&statistics:& excel_stats_nicar2013docx. Access health services research data, statistics, surveys, and tools this site provides access to several nyc tools for statistical analysis, including. Using the data analysis tools although excel is a fine spreadsheet, it is not a statistical data analysis package in all fairness. An introduction to statistical data analysis (summer 2014) so, if you feel resistance against learning about these tools, think about the fact that.
Easy access to juvenile court statistics (1985-2014) lets users access data on juvenile court processing of more this data analysis tool. Learn how to collect your data and analyze it, figuring out what it means, so that you can use it to draw some conclusions about your work. A plethora of statistical modeling tools are available in the market providing various matlab provides functionalities for statistical data analysis and modeling.
Excel has several data analysis tools included through an analysis toolpak add-in these tools can quickly produce complex engineering or statistical analyses of your. Data analysis is the process of systematically applying statistical and/or logical techniques to describe and illustrate, condense and recap, and evaluate data. List of statistical packages statistics outline statisticians glossary (hpc) data structures and data analysis tools for python in python and cython. Make your data sing we look at 22 free tools that will help you use visualization and analysis to turn your data into informative, engaging graphics. Education data analysis tool (edat) download nces survey datasets in various statistical software formats customize your dataset by selecting a survey, population.
Lesson 12 - to determine what statistical methods to use for specific situations types of data, examples, analysis, minitab commands, and conditions. Use the analysis toolpak for complex, statistical analyses in excel foe windows if the data analysis command is not available, you need to load the analysis toolpak. 6 basic statistical tools a multitude of different statistical tools the basic assumption to be made is that a set of data, obtained by repeated analysis. Statistical analysis is a very useful tool to get approximate solutions when the actual process is highly complex or unknown in its true form.
Statistical analysis handbook a comprehensive handbook of statistical concepts, techniques and software tools by dr m j de smith. Top 52 free statistical software: list of 50+ open source statistical software statistical software are programs which are used for the statistical analysis of the. Statistics about - crime and victims, drugs and crime, criminal offenders, the justice system in the united states, law enforcement, prosecution, courts and. Orange – a visual programming tool featuring interactive data visualization and methods for statistical data analysis, data mining.
Additional resources to the toolkit tool developed in microsoft excel that will automate analyses of data quality metrics (for countries that do not have dhis 2. Statistical tools and data for program has developed statistical methods and associated software tools for the analysis and reporting of cancer statistics. Statistics & data analysis the sas ® system provides extensive statistical capabilities, including tools for both specialized and enterprise.


Many kids aren't too keen in learning math. Math could be a tedious process for most kids. A study shows that learning math for kids would be much better if done with movement.
A study shows that engaging children in math class could help them understand it better. By having children use their bodies in math class, they perform much better. This has been the findings of a study made by the University of Copenhagen's Department of Nutrition, Exercise and Sports.
The study has looked at how different ways of teaching math to children might help children in learning math better. The study has shown that when children engage their bodies more, there have been improvements in learning. The study has also found that children learn better with individualized instructions.
Movement makes children learn better, as observed by head researcher Jacob Wienecke. He is an associate professor from the University of Copenhagen. The study has shown that lower intense physical activities can have much impact on how children learn. An earlier study has shown that children learn much when engaged in intense physical activities.
The study has shown that physical activity has been beneficial on kids while learning math. Scores have generally improved. Improvement has been has much as 7.6 percent, and tests have four more correct answers than the average.
Children who benefited most from physical activity are those who are average to highly developed abilities in math, according to the University of Copenhagen's site. Children who did not do well in math prior to the study did not see any advantage in it. Wienecke has said that individual instruction should also be considered, especially in children who are falling behind.
The research is focusing next on which areas of the brain are being used while physical activity is done while studying. A study would also be made on what the effects of movement are on other skills such as reading, as Science Daily reports. The study has shown that movement while learning math has much benefit for children.
Learning math would be more effective if movement is involved as well. Learning math is much better with movement, as a study has seen. Preschoolers are also found to learn better when taking naps.


Redneck Engineering Exam
1. Calculate the smallest limb diameter on a persimmon tree that will support a 10 pound possum.
2. Which of the following cars will rust out the quickest when placed on blocks in your front yard?
a. '66 Ford Fairlane
b. '69 Chevrolet Chevelle
c. '64 Pontiac GTO
3. If your uncle builds a still that operates at a capacity of 20 gallons of shine per hour, how many car radiators are necessary to condense the product?
4. A pulpwood cutter has chain saw that operates at 2700 rpm. The density of the pine trees in a plot to be harvested is 470 per acre. The lot is 2.3 acres in size. The average tree diameter is 14 inches. How many Budweiser Tall-Boys will it take to cut the trees?


A pie chart is a circular chart divided into wedges that represent the proportions of a whole. Pie charts are used to show the distribution of data. Most of the time, a pie chart is used as a graphical representation of data in which the percentage or relative size of each item is displayed as a slice of a pie.
Pie charts are used to display how much of a whole is taken up by different items. They are often used to compare proportions, for example, in survey results. If you’re interested in learning more about pie charts, keep reading to learn more about creating a pie chart in Excel, when to use them, and whether there are any worthy alternatives to using this type of chart.
How to Create a Pie in Excel
To create a pie chart in Excel, you will need to have at least two pieces of data that you would like to graph on your personal computer. The first step is to enter the data into two columns in Excel. Label one column “Category” and the other “Quantity.” In the Category column, list the different categories for your data.
In the Quantity column, list how many items fall into each category. Once you have entered your data, select Insert > Pie Chart from the menu bar at the top of your screen. A new pie chart will appear on your worksheet with default settings. Excel will automatically assign colors and formatting to your chart based on the type of data you have entered.
If you would like to customize your chart, click on any part of it to select it. Once it is selected, various options will appear in the ribbon at the top of your screen (the toolbar across the top). From here, you can change things like font size and color, add titles or labels, change how percentages are displayed, and more. You can also drag and drop individual slices around on your chart to rearrange them however you like.
When to Use a Pie Chart
There are a few different occasions when a pie chart can be useful. One example is when you want to compare different values. For instance, if you want to know what percentage of your income goes towards rent, food, and transportation, you could use a pie chart to compare these values.
Another example is when you want to show how a whole is divided into parts. For example, if you want to show how the United States is divided into states, you could use a pie chart. This could also be used to show the different types of people who live in a certain area. Finally, a pie chart can be used to show a trend over time. For example, if you wanted to show how the number of people who identify as LGBTQIA+ has changed over time, you could use a pie chart to show this trend.
How to Read a Pie Chart
When looking at a pie chart, it is important to first understand what the graph is trying to show. In most cases, a pie chart is used to show how a certain percentage of a whole is divided up between different categories. For example, imagine that you are a manager at a grocery store. You want to know how much money your store makes from different product categories.
To find this out, you might create a pie chart that shows the percentage of total sales each category makes. The most important thing to remember when reading a pie chart is to look at the percentages, not the numbers.
This is because the numbers on a pie chart can be misleading. For example, imagine that your store sells 100 items in total. If the pie chart showed that the store made $10 from selling apples, it would seem like apples are a very important product for the store. However, if you look at the percentages, you would see that apples only account for 10 percent of the store’s sales. This is why it is important to always look at the percentages when reading a pie chart.
Alternatives to Using a Pie Chart
There are a number of alternatives to using a pie chart to display data. Some of these alternatives include bar graphs, line graphs, and scatter plots. Bar graphs are a great way to compare data between different categories. They can be used to compare, for example, the percentage of men and women who voted in an election.
Bar graphs can also be used to compare data over time. For example, you could use a bar graph to show how the percentage of people who voted in an election changed over time. Line graphs are a great way to show how data changes over time.
For example, you could use a line graph to show how the percentage of people who voted in an election changed over time. Line graphs can also be used to show how two different pieces of data are related. For example, you could use a line graph to show how the number of people who voted in an election corresponds to the number of people who live in the state.
Scatter plots are a great way to show how two different pieces of data are related. For example, you could use a scatter plot to show how the number of people who voted in an election corresponds to the number of people who live in the state.
Hopefully, this guide has been useful in helping you create a pie chart, learn how to read one properly, as well as explore some alternatives.
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On histograms and kernel densities (I) histogram kernel density matplotlib Jun 17, 2016 Histograms and kernel densities are ubiquitous in data analysis. At a exploratory stage, we want to know about the variables’ distribution. You can quickly check some descriptive statistics like the mean, variance, percentile and kurtosis. Or, to have a clear picture, you can plot histograms or kernel densities. While histograms are quite intuitive to understand, I find that kernel densities are less so. This need not be the case. It turns that both distributions plots are closely related. As a bonus, a good understanding of kernel densities goes a long way. This is key for other topics as kernel regression and causal inference techniques, like matching. Let’s start by proposing a random variable with a given distribution. We will talk about Unfortunately, most of the time we are not given a distribution. We just have some data samples. In this case, a histogram or a kernel density is needed to determine how does the distribution look. Suppose, for what follows that we have taken a 1000 samples from variable A histogram is basically putting these values in some boxes, better known as bins. These bins are equally ranged intervals. Basically what is happening under the hood is that data is sorted according to which bin belongs to. Then, to reflect how much data is collected in the bin, heights are correspondingly assigned. I wrote the following code to make equally sized bins given some input data and the selected bin width. Diclaimer 1: I just wrote this code for didactic purposes if you want to plot histograms check histogram plotting in matplotlib. Diclaimer 2: Properly selecting the bin width is an art of its own, and has important implications when trying to spot your data’s distribution. Disclaimers away, here is some code that will create the bins, according to the bin width selected. def data_bins(array, binwidth): """Creates binwidths according to the number of the width given.""" bands =  j = 1 stop = False while not stop: x_0 = np.amin(array) beginning = x_0 + (j-1)*binwidth end = x_0 + j*binwidth bands.append((beginning, end)) if end > np.amax(array): stop = True j += 1 bands = np.array(bands) return bands The easiest way to figure out what this is doing is by imagining we are given all the range of the data and we want to perform some cuts. These cuts are of a special kind, however, as they will be of equal length. The next step is to put the data in the right bins and assign a particular height according to how much data is within that bin. def obs_in_bin(array, binwidth): """"Puts the observation in its corresponding bin, according to the specified bin width.""" num_per_bin =  cal_bands = data_bins(array, binwidth) for bands in cal_bands: num_per_bin.append(np.sum((array>= bands) & (array < bands))) num_per_bin = np.array(num_per_bin) freq = num_per_bin / (len(array)*binwidth) return freq, cal_bands An important thing to remember is that this is not a frequency chart, i.e. the height of the bar does not give us the probability of observing a value within that range. Remember that the histogram is trying to approximate the density of the variable. Plotting our results only takes one easy step: freq_bin, cal_bands = obs_in_bin(ran_num, 0.25) fig, ax = plt.subplots() for i in range(len(cal_bands)): ax.bar(cal_bands[i], freq_bin[i], 0.25) plt.title("Histogram") Here is the graph for a bin width of 0.25: Now that we know more about histograms, it will be easier to figure out what kernel densities are.


Illinois schools will administer the Partnership for Assessment of Readiness for College and Careers (PARCC) assessment beginning in April. These assessments are fully aligned to the K-12 Illinois Learning Standards in English/Language Arts and Mathematics and emphasize academic rigor, critical thinking, problem solving and college and career readiness for all students. The . . .
To Parents and Community Members: You are invited to attend the following Public Information Forums regarding The Princeton Elementary April 4, 2017, Referendum. March 21, 2017 - 7:00 PM - Logan Jr. High March 30, 2017 - 7:00 PM - Jefferson Elementary We look forward to sharing facts relative to the referendum with you at these times.
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The Briefing Book consists of slides showing results from the 2012 NSSME, which can be drawn upon for creating presentations about K–12 science and mathematics education. It follows the structure of the Report of the 2012 National Survey of Science and Mathematics Education, and consists of 13 sets of PowerPoint slides. The “Study Overview” describes the study design, instruments, and response rates. It also includes an acknowledgment slide that should be included in any presentation utilizing Briefing Book slides. The remaining sets of slides correspond to chapters 2–7 of the 2012 NSSME report, with two sets of slides for each chapter (one for science and one for mathematics).
Information on using the Briefing Book can be found in:
The significance calculator described in the introduction is linked below:
Significance Calculator for Percentages (XLSX, 15K)
|Teacher Background and Beliefs||Science||Mathematics|
|Science and Mathematics Courses||Science||Mathematics|
|Factors Affecting Instruction||Science||Mathematics|


Bayesian inference is a powerful tool for probabilistic model calibration and inverse problems. UQ[py]Lab offers a flexible and intuitive way to set-up and solve Bayesian inverse problems.
The reliability-based design optimization (RBDO) module offers a set of state-of-the-art algorithms to solve various types of optimization problems under probabilistic constraints. They include:
On top of these well-known algorithms, the modular design of the RBDO module allows the user to set up customized solution schemes by combining all of the reliability, surrogate modeling, and optimization techniques available in UQLab.
Support vector machines (SVM) come from machine learning and allow one to build predictive models from data. In the context of uncertainty quantification, SVM for regression (SVR) can be used as surrogate models of complex simulators using designs of computer experiments. SVM for classification (SVC) can be used in the context of reliability analysis.
Polynomial Chaos-Kriging (PC-Kriging) associates the global approximation behavior of polynomial chaos expansions and the local accuracy of Kriging to provide a highly accurate surrogate model at low computational costs.
Canonical low-rank approximations (LRA) are a powerful alternative to polynomial chaos expansions that are particularly effective in high dimension.
Gaussian process modeling is a flexible and robust technique to build fast surrogate models based on small experimental designs
When the performance of a system is affected by uncertainties on its characteristics and/or its environment, reliability can be assessed by computing probabilities of failure.
UQLab offers state-of-the-art reliability algorithms and a powerful modular framework
for active learning reliability.
Probabilistic modelling lies at the core of uncertainty quantification. Full support for complex probabilistic models based on copula and marginal representation. Powerful data-driven inference module.
Sensitivity analysis can identify the driving factors that most influence the response of a model
Polynomial chaos expansions (PCE), one of the most powerful and versatile surrogate models available today


|An Anytime Algorithm for Computing Inconsistency Measurement
|Year of Publication
|Ma, Y, Qi, G, Xiao, G, Hitzler, P, Lin, Z
|Karagiannis, D, Jin, Z
|Knowledge Science, Engineering and Management, Third International Conference, KSEM 2009
Measuring inconsistency degrees of inconsistent knowledge bases is an important problem as it provides context information for facilitating inconsistency handling. Many methods have been proposed to solve this problem and a main class of them is based on some kind of paraconsistent semantics. In this paper, we consider the computational aspects of inconsistency degrees of propositional knowledge bases under 4-valued semantics. We first analyze its computational complexity. As it turns out that computing the exact inconsistency degree is intractable, we then propose an anytime algorithm that provides tractable approximation of the inconsistency degree from above and below. We show that our algorithm satisfies some desirable properties and give experimental results of our implementation of the algorithm.


This video demonstrating the Dzhanibekov effect in the microgravity of the space has intrigued me into simulating the effect myself. Dzhanibekov effect, also known as the tennis racquet theorem or the intermediate axis theorem is the phenomenon caused when rigid body with three principal axes is rotated along an axis near to its intermediate axis. When a rigid body is rotated along such an axis, the rotation is not stable as shown in the video below. Though numerical methods are used to solve the dynamics in the current post, a more analytical approach is taken in the book Classical Mechanics, Goldstein.
Lagrangian method is used to formulate the dynamics of the rigid body. The derivation is available in the Mathematica notebook in this repository. The derived dynamics is verified by the conservation of energy check and is shown below.
On the other hand, the same system is simulated in C++ and Fortran to compare the computation time and accuracy of the implementations. For these comparisons, none of the libraries are included, only array manipulations are used in both languages. A fixed-step fourth-order Runge-Kutta method is written to integrate the equations of motion. The implementations in both languages are available here. The result of the simulation can be seen in the video below:
These simulations are done on a system with the following specifications:
Processor : 4x Intel(R) Core(TM) i5-4210U CPU @ 1.70GHz
Memory : 3944MB (2797MB used)
Operating System : Ubuntu 16.04.6 LTS
Number of cores used: 1
The time and accuracy for ten simulation trails are considered for the data presented in the table. Max error is defined as the absolute maximum percentage change in the energy of the system.
Comparison between C++ and Fortran:
The percentage change in the energy of the system with the iteration steps for the simulation in Fortran90 is shown below.
The percentage change in the energy of the system with the iteration steps for the simulation in C++ is shown below.
The compilers used are g++ and gfortran for codes written in C++ and F90, compiled without the use of any optimisation flags. Fortran is superior not just in execution speed but also in maintaining the accuracy in its computations. I suppose this has to do with the way floating-point operations are handled in Fortran vs C++. Although C++ is now a common tool for most of the engineers, it is always worth mentioning that when it comes to speed and accuracy Fortran beats C++ some times as in this case.


3 edition of College math found in the catalog.
1993 by Whittier Publications, Inc .
Written in English
|The Physical Object|
|Number of Pages||202|
Basic College Mathematics, 3rd Edition by Julie Miller and Molly O'Neill and Nancy Hyde () Preview the textbook, purchase or get a FREE instructor-only desk Edition: 3.
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What is the optimization?
The optimization is a mathematical/numerical tool that can solve a complex problem in various fields. After the design variables for a target system are defined, the objective and constraint functions can be expressed in terms of the design variables. Through iterations, the optimization algorithm updates the design variables to extremize (maximize or minimize) the objective function while satisfying the constraint functions. For example, let us assume to optimize a beam structure under the given geometric and loading boundary conditions. Then, compliance minimization with a mass constraint provides the optimal structure, as shown below.
A example of a MBB beam
We implement the fundamental principle of multidisciplinary engineering through the computational analysis and determine the optimal design for a real-world system through the design optimization. The current research areas are 1) mobility , 2) electromagnetic , and 3) biomechanical systems. Our ultimate goal is to propose innovative systems which can enhance human and vehicular mobility.


The study of statistical mechanics in curved geometries has recently gained an increasing amount of attention. Particularly the Ising model in negatively curved spaces has been studied as a mean to understand exotic crystals, soft-matter and field theories in Anti-de Sitter spaces. We analyze the Ising model on in the hyperbolic plane as well as 2+1-Anti-de Sitter (AdS) space using high temperature series-expansion and Monte-Carlo simulations. While series expansions have been performed on the hyperbolic plane before, we study a wider class of hyperbolic lattices and go to much higher order, allowing us to analyze the dependency of critical phenomena on the magnitude of curvature. In the past Monte Carlo methods have been difficult to use as the curvature lead to severe boundary effects which persist even for large system sizes. We overcome this problem by constructing families of closed 2D surfaces of increasing area and compactified AdS spaces of increasing volume, akin to periodic boundaries in euclidean space. It has been discussed into which universality class the Ising model in hyperbolic space falls. Our results strongly support that it falls into the mean-field universality class.


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Solution manual for A Survey of Mathematics with Applications 9E Allen R. Angel, Christine Abbott. Dennis C. Runde
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Solution Manual for A Friendly Introduction to Analysis 2/E 2nd Edition Witold A.J. Kosmala
Solution Manual for Mathematics with Applications In the Management, Natural, and Social Sciences 11/E 11th Edition Margaret L. Lial, Thomas W. Hungerford, John P. Holcomb, Bernadette Mullins
Solution manual for Linear Algebra with Applications, 5/E Otto Bretscher
Solution Manual for Discrete Mathematics for Computer Scientists Cliff L Stein, Robert Drysdale, Kenneth Bogart
Solution Manual for A Friendly Introduction to Number Theory, 4/E 4th Edition Joseph H. Silverman
Solution Manual for Precalculus Enhanced with Graphing Utilities Michael Sullivan, Michael Sullivan III
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On this day 116 years ago, Charles Lutwidge Dodgson, otherwise known as Lewis Carroll, died at 66 following complications from pneumonia.
Mathematician Dodgson was known in geometrical circles (…triangles?) for his in-depth work with logical mathematics and algebra, amongst others.
However, he’ll be best remembered for his work under his pen-name, publishing the unforgettable ‘Alice’s Adventures in Wonderland’ and her subsequent tales that followed.
Rest In Peace, Lewis Carroll.


This is an activity which will help your Algebra 1 or Algebra 2 students with practice when graphing parabolas in vertex form. The worksheet can be used as a homework assignment or assessment activity. Students are asked to identify the axis of symmetry, the vertex, they use a given substitution point and state the reflected point needed to create three points to sketch the parabola. This activity is a part of my UNIT 4 BUNDLE. An answer key is provided.
✎ Use the activity in groups
✎ Use the activity as a review exercise prior to assessing students
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Section 5.1 Graph Quadratic Functions in Vertex Form
A2.5.6 Describe the characteristics of a quadratic function (maximum, minimum, zero values, y-intercepts) and use them to solve real world problems


Ja. Jeg fandt det!
Dicte would be proud. I had been looking for causality to the mammography trial in the two Swedish counties of Dalarna and Ostergotland, but the culprit turned out to be Malmo, across the way from Denmak. Ironically, Malmo was fingered by lead author of the Two-County trial, Laszlo Tabar.
Tabar argued in the BMJ that the Malmo trial shouldn't be used to determine the value of mammography screening because between 70% and 74% of women invited to the trial actually had a mammogram and some 24% of women who were not invited had a mammogram.
We can write down the following system of equations, where A is the probability of dying from breast cancer conditional on getting mammography screening and B is the probability of dying from breast cancer without mammography screening.
0.7*A + 0.3*B = 63/21088
0.24*A + 0.74*B = 66/21195
Plugging these equations into Mathematica we get.
A = 0.00291
B = 0.00317
While the intent-to-treat analysis suggest a 4% reduction in death from breast cancer associated with mammographic screening. Accounting for the actual take up rate suggests an 8% reduction. Note that none of this accounts for sampling variation and is only presented for illustrative purposes.
Now this analysis also assumes that everyone who took up mammography screening is the same as those that didn't take up the screening, excepting for the fact that they took up mammography screening. This is plainly not true.
To be continued....


Reza Abazari* and Mehrdad Lakestani Pages 477 - 483 ( 7 )
Background: Medical ultrasonic images are usually degraded by a special kind of noise called ’speckle'. The speckle noises usually have an effect more on edges and fine details of an ultrasound images which lead to reduction in their contrast resolution consequently create difficulties in the diagnosis of illnesses.
Methods: In this paper, to reduce the speckle noise of medical ultrasound image, we have proposes a denoising approach by using ’discrete shearlet transform' based on pseudo-polar fast Fourier transform. The mathematical structure of present method is briefly discussed. To illustrate the efficiency of proposed approach, the experimental results of synthesis of some real Ultrasound images are considered.
Results: Experimental results illustrate that proposed approach can obtain better performance in terms of Peak Signal To Noise Ratio (PSNR) for ultrasound image denoising. Our numerical tests include a series of computer-simulated and in MATLAB experiments.
Discrete shearlet transform, fourier transform, image denoising, PSNR, threshold, ultrasound Image.
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz


ASQ CEO Paul Borawski writes in February's blog: "How can we, those who understand, use, and love science and technology, pass it along? For those outside of the U.S., how is STEM taught and encouraged in your country?". When I was in elementary school, math and science were not my favorite subjects. I had a hard time understanding the logic. I have always been a top student throughout my school years, but something had to happen to change my views on math and science in order to keep it that way. My parents did a great job in encouraging me and my sister to do well in school without enforcing it on us. My father graduated from the top rated technical university in Turkey so he definitely loved math and science. He is one of those people who can hold hundreds of phone numbers in his memory for years! In 6th grade, I was challenged even more in math class as it was getting harder to comprehend. I was feeling upset about this so I approached my parents for some help. My father said to me, "If you give me an hour of your time, I guarantee you will get it", and that's exactly what happened. That "one hour" changed everything for me. I was also lucky to have great math teachers in later years. My father's love and passion for math and science led the way for me to become an engineer and I thank him for that. His teachings were simple and easy to understand. There is no benefit in complicating math in early stages of education. If children get the basics right, everything else will make more sense.
I had the opportunity to attend senior year in high school in the U.S. and I witnessed the challenge students were facing in math and science. I asked myself why there is a lack of interest. Again, the answer that I found was that students were missing the basics. What I decided to do was to help students and start tutoring on basics. I pretty much continued to do this throughout my college years. Remembering the past, one of my friends ended up getting A's in college algebra after a couple math sessions. I strongly believe that if teachers can simplify math for students, there will be more interest. Also, showing students the magic of math surrounding our lives, will encourage them to pass it along to their classmates. If a student is good in math and science, why not ask him/her to volunteer in tutoring other students? That way, passion and knowledge is shared and students' confidence elevates.
University of North Texas, where I graduated as an engineer, hosted a great program called DC BEST during my undergrad years. Students from different schools in the area compete against each other by showing off their creations "robots". You won't believe the level of teamwork, excitement, passion and creativity coming out of these young students. As their website states, " Engineers and other technical professionals from local industries serve as team mentors who advise and guide students through the design and construction of their machines". http://robotevents.com/robot-competitions/best/ Isn't it a great way of encouraging younger generations in math and science and preparing them to become the next superstars of engineering and technology?
The future of STEM is promising. As parents, teachers, mentors and professionals, we can do better in developing technical skills among younger generations by focusing on the basics and keeping it fun!


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Limit Theorem (CLT). The latter may lead to a Large Deviation Principle (LDP) if the probability of visiting a non-typical state is exponentially small and we can come up with a precise formula for the exponential rate of convergence as the size of the system goes to in nity. In this introduction we attempt to address four basic questions: 1.
Stochastic processes: Stochastic process, Queueing theory, Brownian motion, Poisson process, Convergence of random variables, White noise: Amazon.es: Source.
Wed 28.1.2015: transition functions, construction of Markov processes from transition functions, definition of martingale; Fri 30.1.2015: properties of supermartingales, Upcrossing inequality, Doob's maximal inequalities, path properties of supermartingales; Wed 4.2.2015: Martingale convergence theorem, Feller processes and stopping times.See also Supplementary lists. These lists include items which are somehow related to statistics however are not included in this index: List of statisticians; List of important pu.Renz, Ouchti, El Machkouri and Ouchti and Mourrat have established some tight bounds on the rate of convergence in the central limit theorem for martingales. In the present paper a modification of the methods, developed by Bolthausen and Grama and Haeusler, is applied for obtaining exact rates of convergence in the central limit theorem for martingales with differences having conditional.
The conditions of convergence of continuous processes are analogous to those mentioned above for discrete time (see ). The basic instrument for proving the convergence of procedures of stochastic approximation is the theorem on the convergence of non-negative supermartingales (see Martingale).Read More
Comparing this result with many other convergence theorems, we find that is requires X to be a martingale instead of just a submartingale. I assume this must have some reason, i.e. this result does not hold for submartingales.Read More
For example, a representation theorem of set-valued martingales was proved by Luu by means of martingale selections (141). Convergence theorems of martingales, sub- and supermartingales under various settings were obtained by many authors, Korvin and Kleyle (119), Papageorgiou (169, 170, 171), Hess (85), Wang and Xue (218), Li and Ogura (131) and (133). Also there are many more works of.Read More
In complex analysis, the Hardy spaces (or Hardy classes) H p are certain spaces of holomorphic functions on the unit disk or upper half plane.They were introduced by Frigyes Riesz (), who named them after G. H. Hardy, because of the paper ().In real analysis Hardy spaces are certain spaces of distributions on the real line, which are (in the sense of distributions) boundary values of the.Read More
Martingale difference sequence Last updated May 16, 2019. In probability theory, a martingale difference sequence (MDS) is related to the concept of the martingale. A stochastic series X is an MDS if its expectation with respect to the past is zero.Read More
Limit theorem: reproduce a proof with an adaption from discrete to continuous time 4 Uniform martingale convergence of Radon-Nikodym derivatives of a convex set of probabilities.Read More
In probability theory, a martingale is a model of a fair game where knowledge of past events never helps predict the mean of the future winnings. In particular, a martingale is a sequence of random variables (i.e., a stochastic process) for which, at a particular time in the realized sequence, the expectation of the next value in the sequence is equal to the present observed value even given.Read More
Definitions of hardy space, synonyms, antonyms, derivatives of hardy space, analogical dictionary of hardy space (English).Read More
In probability theory, the central limit theorem (CLT) establishes that, in some situations, when independent random variables are added, their properly normalized sum tends towar.Read More


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When we talk about employing a strategy based on statistics against slots, your first thought might be one of confusion: I thought slot you play today wins were totally random? While that’s true, slots have been around long enough now for us to know a thing or two about some statistics around slots.
The probability you’re going to win with slots is something that’s determined by a random number generator and the number of symbols on each reel in slots. The generator in slots comes into play with whether or not you win, depending on whether it creates a winning combination of symbols or not.
Employing a strategy based on statistics against slots might appear an impossible endeavor, but there are some tricks to help spins work in your favor. For instance, the number of possible combinations can be calculated – just multiply the number of symbols on each reel. So three reel slots? Seven symbols. That means 7x7x7=343. That’s 343 combinations.
It’s easy to calculate the odds of winning with slots too. With slots, to calculate your odds of winning just divide the number of winning combinations with the number of combinations that are possible. It’s complicated, however, to come up with a concrete formula to win with slots and get a great return.
Part of why it’s so difficult is because all of these slot calculations don’t really mean anything when the online slot machine odds are what dictates who wins, when. It does make sense wins with slots are determined like this, however. Different winning combinations offer different prizes in slots, and some of the highest are from winning certain puzzles in slots.
When it comes to playing slots, there is one simple slot strategy to always bear in mind. Know the rules, get an idea of what your odds of winning are, and find out the expected slots payout. Be sure to have fun, and make sure you quit slots while you’re ahead.
So if you win, for example, £200, cash out £100 and play the rest. Have an amount of money, and decide if you lose it, you’ll immediately quit the game. By also making sure you play just for the fun of it, any losses with slots won’t be taken too harshly.
More is sometimes better when you’re choosing the number of coins to play per spin in slots. Max out whatever the online slot machine allows for, rather than playing with singular coins. This way, you can boost your chances of winning a better prize in slots and the value will also be higher than expected.
You could also play one coin at a time until you make some money, and opt-out, when you want to so your money, goes further. How you play slots is of course, up to you, but hopefully the above is helpful when you’re employing a strategy based on statistics around slots.


NonEuclid is a Software Simulation offering Straightedge
and Compass Constructions in Hyperbolic Geometry (a geometry of Einstein's
General Relativity Theory and Curved Hyperspace) for use in High School
and Undergraduate Education.
This web site provides the platform independent,
NonEuclid software (written in 100% pure Java) together with a 25 page,
illustrated, hypertext introductory explanation of Hyperbolic Geometry.
NonEuclid has moved.
The new site is: http://math.rice.edu/~joel/NonEuclid/


Improve your chances of winning Lotto!
Hello lotto friends, today I’m going to talk about the only universally accepted method of potentially winning the lotto:
“To win the Lotto, you must first have a Lotto entry”
We all know it, every reasonable adult around the globe understands it, you simply can’t win the lotto if you don’t have an entry! So surely the following maths apply:
Universal Formula to improve your Chances
1 entry = 1 chance to win
2 entries = 2 chances to win
3 entries = 3 chances to win
The more entries you have the more chances you have of winning. It’s like throwing a dice, if I’m trying to land on a 6 and I have 1 dice, my chance of hitting a six is 1 chance out of 6 possibilities. But if I have 6 dice my chances are dramatically improved!
A great lottery coming up on 14th May is the Australian Powerball. 4 lines will cost you $10.20 and potentially land you a Prize pool of $15 MILLION AUD and of course you can follow the formula above and grab a couple of entries and potentially improve your chances!
Have fun and play responsibly


USC Aiken Hosts STEM Friday for High Schoolers
Aiken, SC (12/12/2018) — High school juniors and seniors throughout the CSRA took part in STEM Friday at the University of South Carolina Aiken.
The event helps introduce students to STEM fields of study and careers.
"Our region's workforce is steeped in STEM-related fields," said Dr. Chad Leverette, interim dean of the college of science and engineering at USC Aiken.
"We have a responsibility to help prepare the future STEM leaders in our state, region and nation. We hope STEM Friday sparks some interest in these important fields."
Almost 150 students who attend public or private high schools or who are homeschooled in the area attended the event. They visited with USC Aiken professors and students in psychology, mathematics, engineering, computer science, chemistry, physics, biology and geology. Many took part in interactive experiments.
"We had a 500 percent increase in STEM Friday attendance this year, showing the interest in STEM and USC Aiken," Leverette said.
For more on the next STEM Friday, go to: https://www.usca.edu/cofse/stem-friday/


Besides the “meaning of life” question, this could be one of mankind’s greatest mysteries. I would imagine every single person reading this has asked themselves this very question at least once in their lives. Are we, as inhabitants of Earth, alone in the Universe?
I’m not very religious at all (don’t @ me), but I am not against anyone following any religion. Seriously, why would anyone care what another person’s religious views are? Anyway, I suppose that anyone who is religious has a vastly different view on this subject than I do, which is fine. Honestly, you might be right and I might be waaaay fucking off on my ideas, but to each their own.
I’m certainly not a math expert, but some quick Google dot com search returns some interesting numbers. Estimates vary quite a lot but most of the numbers I came across are between 200 and 400 billion stars, or suns. With estimates of 17% of those planets in the Milky Way being the right size, and at the right distance from their sun. That comes in at roughly 17 billion possible earths.
Let’s throw out half of those, since the two earth-size planets in our solar system are Venus and well Earth of course. With Venus being uninhabitable due to its surface temperature being more than 400 degrees. So that puts us at 8.5 billion possible earth-like planets. You can’t deny math, right?
I know those are some huge numbers, and I am NOT a numbers guy, so let’s round down to make it easier for me. The numbers are telling me that there are 8,000,000,000 chances for life to kick start and flourish like Earth has. I like the sound of that.
That, of course, isn’t even taking into account the possible planets rotating around the 2 to 4 billion stars in each of the estimated 100 billion other galaxies. Ok, now the math is getting too complicated for me. That’s a lot of math and I was told that there would be no math!
I’m going to side with math on this one (X-Files music). Besides, what’s actually scarier? Having galactic neighbors, or being all alone?


Sudokuro Sudoku & Kakuro Games for Nintendo DS
Sudokuro contains 1,500 hand-crafted Sudoku puzzles and an unlimited
number of automatically Sudoku puzzles, and over 5,000 Kakuro puzzles.
Players may enter data either with buttons or the Nintendo DS stylus,
and the game also features text recognition. With three levels of
difficulty for each game, and a simple 2x2 Sudoku mode especially
designed for children, the whole family can enjoy playing Sudokuro.


The once-a-decade United States Census provides a fascinating teachable moment for students of all grade levels, intersecting social studies, mathematics and other disciplines in concrete ways. The U.S. Census Bureau’s Statistics in Schools program is offering free, teacher-designed resources at census.gov/schools that connect with various academic areas, including math, geography, history and more. There are resources specific to the 2020 Census, broken down by grade-level, including pre-K and English Language Learner targeted information, as well as engaging state-by-state facts, videos and maps to help engage students.
MEA is committed to ensuring a “Complete Count” for our state. Everything from federal funding for critical children’s resources to Michigan’s representation in Congress depends on an accurate count of residents. Visit mea.org/census for resources and updates.


Aidan amazes me everyday with what he knows. Out of the blue he will say something that I didn't "teach" him and he just picked it up. It is cool when those moments happen as it can be a little harder for kids like Aidan to learn incidental language. This is a video of Aidan counting to 5, using his book that has a number on each page and a picture on the opposite page. I got it for him for Christmas and we have looked at it maybe 1-2 times a week. We tend to count objects quite a bit but he sees the actual numbers less frequently, maybe 1-2x a week. I was shocked and amazed when he picked up the book and said each number on the page.
I'm that mom
9 years ago


A Control-variable Regression Monte Carlo Technique for Short-term Electricity Generation Planning
(English)Manuscript (preprint) (Other academic)
n the day-to-day operation of a power system, the system operator repeatedly solves short-termgeneration planning problems. When formulating these problems theoperators have to weigh the riskof costly failures against increased production costs. The resulting problems are often high-dimensionaland various approximations have been suggested in the literature.In this article we formulate the short-term planning problem as an optimal switching problem withdelayed reaction. Furthermore, we proposed a control variable technique that can be used in MonteCarlo regression to obtain a computationally efficient numerical algorithm.
Probability Theory and Statistics Control Engineering
Research subject Physics, Electrotechnology
IdentifiersURN: urn:nbn:se:lnu:diva-61573OAI: oai:DiVA.org:lnu-61573DiVA: diva2:1083540


The following Graph operators are defined for both the generic and user-derived Graph types:
Graph& operator=(const Graph& g); int operator==(const Graph& g) const; int operator!=(const Graph& g) const;
The following assignment and equality operations are then legal:
g2 = g1; // g1 and g2 are previously declared Graphs if (g2 == g1) ... ; if (g2 != g1) ... ;
When one Graph is assigned to another, the newly-assigned Graph includes the same Vertices and Edges as the original Graph. Two Graphs are equal if and only if they include exactly the same Vertices and Edges.
We'll see, as part of the discussion of Graph Algorithms in the section, ``Traversals'', an example of when the Graph assignment operator is quite useful.


Tuesday, February 22, 2011
Pain de mie with whole wheat flour
We really enjoyed both the pain de mie and the toast bread from Hamelman's Bread, but because I like to feed my family whole grains, I was eager to try adding whole wheat flour.
When hubby requested that I make chicken noodle soup and grilled cheese sandwiches (with pain de mie, of course!) during his parents' visit, I decided it was the perfect time to try it with whole wheat.
I had a big breakthrough with this recipe, too. I used Hamelman's instructions on baker's math to rescale the recipe, and for the first time, I feel like I actually understood what I was doing. Having struggled with getting the straight pullman pan corners, I decided to try 3 pounds of dough in the pan this time. I scaled the recipe for 3 pounds and was on my way!
I followed Hamelman's pain de mie recipe, but used half whole wheat flour (actually part white whole wheat and part whole wheat, finishing up two bags of flour that I had in the cupboard). The only problem was with my scale (again!): right as I started pouring water, my scale turned off (GR!), so I ended up with too much water and had to put in extra flour to compensate. I think I ended up with more than 3 pounds of dough. And then I forgot about the bread while it was doing its final proof and came to find it had exploded out of the sides of the pan! We really struggled to get the lid off, but finally did. I punched down the dough, reformed it, and put it back in the pan.
The next challenge was that this last (unexpected) rise happened during bed time, so it overproofed a little again. I ended up with not only square corners, but square corners with an extra T at the top. Closer...at least I discovered that I really could get square corners. :P
Anyway, the bread was delicious and the grilled cheese sandwiches were the best ever. Next time I'll try it with just slightly under 3 pounds of bread, but will still use at least 50% whole wheat.


Mathematics and art may seem like two completely different fields, but when they come together, something truly amazing is created. From the intricate patterns in historical architecture to the designs on a quilt, mathematics plays a significant role in creating beauty. One such branch of mathematics that focuses on the creative aspect of visually manifesting mathematical expressions is geometry.
Geometry has been used throughout history to create some of the most beautiful patterns and designs. Take, for example, the historical architecture of Wells Cathedral, Alhambra Palace in Spain, and Sheikh Lutf Allah Mosque in Iran. These structures showcase the intricate designs created using geometry. But how are these designs created?
At Working Men’s College, we recognize the connection between maths and creativity. That’s why we encourage our students to explore the world of Islamic and other geometric patterns. In today’s post, we’ll take a closer look at Islamic patterns and how they are constructed.
Islamic patterns are created using repeated circles, squares, pentagons, and other polygons. These shapes are combined to create intricate patterns with a central motif – the Star. The star is created by dividing a circle into equal parts, and it is the foundation of all Islamic decorations.
In our first session, students recreated a motif/pattern from the Alhambra Palace using eight-fold symmetry. They learned how to draw the motif from a circle and then traced and transferred the design to create a masterpiece. This activity not only taught them about geometry and Islamic patterns, but it also allowed them to be creative and express themselves through art.
It is fair to say that Mathematics and art go hand in hand. Geometry is just one example of how mathematics can be used to create beauty. By exploring Islamic patterns and other geometric designs, students can develop their creativity while also learning valuable maths skills. So, next time you admire a beautiful pattern or design, remember that it was likely created using mathematics.


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