What is Google Pagerank(PR)?
A Google feature that helps determine the rank of a site in our search results. PageRank relies on the uniquely democratic nature of the web by using its vast link structure as an indicator of an individual page's value. Important, high-quality sites receive a higher PageRank, which Google remembers each time it conducts a search. Google combines PageRank with sophisticated text-matching techniques to find pages that are both important and relevant to your searches
Goole RageRank (PR) Formula
PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. PageRank can be calculated for any-size collection of documents. It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0.5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank
How PageRank WorksAssume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.
If pages B, C, and D each only link to A, they would each confer 0.25 PageRank to A. All PageRank PR( ) in this simplistic system would thus gather to A because all links would be pointing to A.
But then suppose page B also has a link to page C, and page D has links to all three pages. The value of the link-votes is divided among all the outbound links on a page. Thus, page B gives a vote worth 0.125 to page A and a vote worth 0.125 to page C. Only one third of D's PageRank is counted for A's PageRank (approximately 0.083).
In other words, the PageRank conferred by an outbound link L( ) is equal to the document's own PageRank score divided by the normalized number of outbound links (it is assumed that links to specific URLs only count once per document).
In the general case, the PageRank value for any page u can be expressed as:
i.e. the PageRank value for a page u is dependent on the PageRank values for each page v out of the set Bu (this set contains all pages linking to page u), divided by the number L(v) of links from page v.
The PageRank theory holds that even an imaginary surfer who is randomly clicking on links will eventually stop clicking. The probability, at any step, that the person will continue is a damping factor d. Various studies have tested different damping factors, but it is generally assumed that the damping factor will be set around 0.85.
The damping factor is subtracted from 1 (and in some variations of the algorithm, the result is divided by the number of documents in the collection) and this term is then added to the product of the damping factor and the sum of the incoming PageRank scores.
So any page's PageRank is derived in large part from the PageRanks of other pages. The damping factor adjusts the derived value downward. The second formula above supports the original statement in Page and Brin's paper that "the sum of all PageRanks is one". Unfortunately, however, Page and Brin gave the first formula, which has led to some confusion.
Google recalculates PageRank scores each time it crawls the Web and rebuilds its index. As Google increases the number of documents in its collection, the initial approximation of PageRank decreases for all documents.
The formula uses a model of a random surfer who gets bored after several clicks and switches to a random page. The PageRank value of a page reflects the chance that the random surfer will land on that page by clicking on a link. It can be understood as a Markov chain in which the states are pages, and the transitions are all equally probable and are the links between pages.
If a page has no links to other pages, it becomes a sink and therefore terminates the random surfing process. However, the solution is quite simple. If the random surfer arrives at a sink page, it picks another URL at random and continues surfing again.
When calculating PageRank, pages with no outbound links are assumed to link out to all other pages in the collection. Their PageRank scores are therefore divided evenly among all other pages. In other words, to be fair with pages that are not sinks, these random transitions are added to all nodes in the Web, with a residual probability of usually d = 0.85, estimated from the frequency that an average surfer uses his or her browser's bookmark feature.
So, the equation is as follows:
The PageRank values are the entries of the dominant eigenvector of the modified adjacency matrix. This makes PageRank a particularly elegant metric: the eigenvector is
This is a variant of the eigenvector centrality measure used commonly in network analysis.
The values of the PageRank eigenvector are fast to approximate (only a few iterations are needed) and in practice it gives good results.
As a result of Markov theory, it can be shown that the PageRank of a page is the probability of being at that page after lots of clicks. This happens to equal t − 1 where t is the expectation of the number of clicks (or random jumps) required to get from the page back to itself.
The main disadvantage is that it favors older pages, because a new page, even a very good one, will not have many links unless it is part of an existing site (a site being a densely connected set of pages, such as Wikipedia). The Google Directory (itself a derivative of the Open Directory Project) allows users to see results sorted by PageRank within categories. The Google Directory is the only service offered by Google where PageRank directly determines display order. In Google's other search services (such as its primary Web search) PageRank is used to weight the relevance scores of pages shown in search results.
Several strategies have been proposed to accelerate the computation of PageRank.
Various strategies to manipulate PageRank have been employed in concerted efforts to improve search results rankings and monetize advertising links. These strategies have severely impacted the reliability of the PageRank concept, which seeks to determine which documents are actually highly valued by the Web community.
Google is known to actively penalize link farms and other schemes designed to artificially inflate PageRank. In December 2007 Google started actively penalizing sites selling paid text links. How Google identifies link farms and other PageRank manipulation tools are among Google's trade secrets.


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4 edition of Spss Tables 7.0 found in the catalog.
May 1996 by Spss .
Written in English
Chi Square A. Chi Square Distribution B. One-Way Tables C. Contingency Tables D. Exercises Chi Square is a distribution that has proven to be particularly useful in statistics. The ﬁrst section describes the basics of this distribution. The following two sections cover the most common statistical tests that make use of the Chi Square File Size: KB. Introduction to Power Analysis. Overview. A statistical test’s. power. is the probability that it will result in statistical significance. Since statistical significance is the desired outcome of a study, planning to achieve high power is of prime importance to the researcher. Because of its complexity, however, an analysis of power is File Size: 81KB.
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Genre/Form: SPSS Document Type: Book: All Authors / Contributors: SPSS Inc. ISBN: OCLC Number: Rather, the current SPSS procedures are being updated so that all of their output is displayed as a series of pivot tables and charts.
The output from all procedures is stored in a single document, which includes text, pivot tables, and charts. SPSS has added a new Output Navigator to organize and display the contents of this document. SPSS tables Also Titled.
SPSS: SPSS tables Other Authors. SPSS Inc Published. Chicago, Ill: SPSS Inc., ; SPSS S Book; Illustrated English Show 0 more libraries These 2 locations in Australian Capital Territory: Library Access Call number(s).
If you need to include a citation, versions that were produced by SPSS Inc. before the IBM acquisition (Versions 18 and earlier) would be given an origin or publisher of SPSS Inc. in Chicago. Versions that were released after the acquisition would be given an origin or publisher of IBM Corp.
in Armonk, NY. For example. IBM SPSS® Statistics is a powerful statistical software platform. It delivers a robust set of features that lets your organization extract actionable insights from its data. With SPSS Statistics you can: Analyze and better understand your data, and solve complex business and research problems through a user-friendly interface.
This web book is composed of three chapters covering a variety of topics about using SPSS for regression. We should emphasize that this book is about "data analysis" and that it demonstrates how SPSS can be used for regression analysis, as opposed to a book that covers the statistical basis of multiple regression.
R has better capabilities than both PROC TABULATE and Custom tables in SPSS. PROC TABULATE drops observations with missing data on factor variables (which is why one must create dummy variables for the levels of those), and thats just for starters.
Research Skills One: Using S Handout 2: Descriptive Statistics: Page 2: into the box and put it near the "columns" graphic. We want a breakdown of purchases by sex, so drag "Sex" to the "Rows" graphic in the right-hand box. As you do this, SPSS gives you an indication of what the table is going to look Size: KB.
The version of SPSS is available as a free download on our website. The following versions:and are the most frequently downloaded ones by the program users. The software lies within Education Tools, more precisely Science Tools. SPSS was developed to work on Windows XP, Windows Vista, Windows 7, Windows 8 or Windows 10 /5(K).
Get this from a library. SPSS: analysis without anguish: versions, for Windows. [Sheridan J Coakes; Lyndall G Steed]. In SPSS it is fairly easy to create a summary table of categorical variables using "Custom Tables": gear 3 15 6 gear 4 12 7 gear 5 5 8 carb 1 7 9 carb 2 10 10 carb 3 3 11 carb 4 10 12 carb 6 1 13 carb 8 1 Unfortunately there seems to be no R package yet that can.
I'm a newbie to SPSS and I'm trying to create a table in SPSS which would contain the frequencies for different variables with different values (answers possibilities) like the one in the.
B 0 1 0 C -1 -1 C -1 -1 When the variables XCA and XCB are added to the regression model, they will account for the interaction between T and X.
Representing Interactions Two or More Categorical VariablesFile Size: KB. A book I made contributions to, SPSS Statistics for Data Analysis and Visualization, is currently out. Keith and Jesus are the main authors of the book, but I contributed one chapter and Jon Peck contributed a few.
The book is a guided tour through many of the advanced statistical procedures and data visualizations in SPSS. In my SPSS book (Field, ) I imagine a future in which we have some cloaks of invisibility to 7 0 6 8 0 2 9 0 0 10 0 5 11 0 4 12 0 5 13 1 4 14 1 3 15 1 6 16 1 6 17 1 8 18 1 5 19 1 5 The output from the independent t-test contains only three tables (two if you don’t opt for bootstrapping).
The first table (Output 1) provides summary File Size: KB. SPSS Statistics is a software package used for interactive, or batched, statistical produced by SPSS Inc., it was acquired by IBM in The current versions () are named IBM SPSS Statistics.
The software name originally stood for Statistical Package for the Social Sciences (SPSS), reflecting the original market, then later changed to Statistical Product and License: Trialware or SaaS.
>>Anyone know that correct method for citing the use of SPSS software >>using APA style >> >>Thanks >> >>john Brandt >> >Yes, as a matter of fact, >From pages of the 4th edition Publication Manual >of the American Psychological Association, you would use the >following form: > SPSS for Windows [Computer software].
Chicago. Understanding Statistical Analysis and Modeling is a text for graduate and advanced undergraduate students in the social, behavioral, or managerial sciences seeking to understand the logic of statistical analysis.
Robert Bruhl covers all the basic methods of descriptive and inferential statistics in an accessible manner by way of asking and answering research questions. The last "book" covers Frequently Asked Questions (FAQ) on 10 different topics ranging from "Opening Data Files" and "Saving Data and Results" to "Memory and Performance" Option 3.
The file (which you will find using Help>Syntax Guide>Base or on your SPSS CD). The column labeled "B" under "unstandardized coefficients" tells you how much the dependent variable goes up, on average, given that the independent variable goes up one unit.
So for VERBAL, the coefficient means that an increase of one point on the verbal SAT score corresponds to an increase of points of satisfaction with. The SPSS Statistics procedure for PCA is not linear (i.e., only if you are lucky will you be able to run through the following 18 steps and accept the output as your final results).
You will often have to re-run these 18 steps based on (a) the results from your assumptions tests that are run during this procedure and (b) the values of the.  3 2 0 5 3 7 0 0 5 2 6. Let’s re-code all values less than 5 to the value A[ A. Tables and Figures. Note: This page reflects the latest version of the APA Publication Manual (i.e., APA 7), which released in October The equivalent resources for the older APA 6 style can be found at this page as well as at this page (our old resources covered the material on this page on two separate pages).
The purpose of tables and figures in documents is to enhance. The computation of the cumulative frequency for the score value of could be done by either adding up the absolute frequencies for the scores of,andrespectively 2 + 3 + 2 + 1 = 8, or adding the absolute frequency ofwhich is 2, to the absolute cumulative frequency ofwhich is 6, to get a value of 8.
The Paired Samples t Test compares two means that are from the same individual, object, or related units. The two means can represent things like: A measurement taken at two different times (e.g., pre-test and post-test with an intervention administered between the two time points) A measurement taken under two different conditions (e.g Author: Kristin Yeager.
In this appendix, we have reproduced two sets of tables. Savin and White () present tables for sample sizes ranging from 6 to and for 1 to 20 regressors for models in which an intercept is included. Fa rebrother () presents tables for sample sizes ranging from 2 to and for 0 to 21 re gressors for models in which an intercept.
Carry out a test in detail and write a brief conclusion. (SPSS tells us the mean and standard deviation of the sample data are andrespectively.) b) Find a 90% confidence interval for the population mean.
Now re‐do the above example using SPSS Size: KB. Correspondence analysis is a variant of principal component analysis aimed primarily at categorical data, for example, aggregate count data in Author: Douglas R.
White. Statistics for Engineers The frequency of a value is the number of observations taking that value. A frequency table is a list of possible values and their frequencies. A bar chart consists of bars corresponding to each of the possible values, whose heights are equal to the frequencies.
Example The numbers of accidents experienced by 80 machinists in a certain industry over aFile Size: KB. Menus and icons in SPSS Interactive Marketing & Social Media - WU. SPSS for newbies: Introduction to Pivot Tables, Charts, and Dashboards in Excel.
Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them.
1 SPSS Complex Samples Manual. Unity: Personalized Book with Name, Journal, Notebook, Diary, Lined Pages, 8 1/2" x 11", Birthday, Friendship, Christmas Gifts for Girls and Women: Related files: Death Anxiety: Loss of the Self pdf download online Backpack Student Book & CD-ROM, Level 5 Memoir of Commodore David Porter of the United States Navy ().
Reading a Relational Database into an SPSS Data File. Adding a Data Source. Selecting Tables From a Data Source. Summary. Probability Calculator. Correlation Estimation Exercise.
Youtube Videos. Multivariate Statistics: Concepts, Models, and Applications 3rd edition - Introductory Statistics: Concepts, Models, and Applications 3rd edition. From Wikibooks, open books for an open world. Statistics made easy!!. Learn about the t-test, the chi square test, the p value and more - Duration: Global Health with Greg Martinviews.
Basic Statistics Formulas Population Measures Mean = 1 n X x i (1) Variance ˙2 = 1 n X (x i x)2 (2) Standard Deviation ˙= r 1 n X (x i x)2 (3) Sampling Sample mean x= 1 n X x i (4) Sample variance s2 x = 1 n 1 X (x i x)2 (5) Std.
Deviation s x = r 1 n 1 X (x i x)2 (6) z-score z= x ˙ (7) Correlation r= 1 n 1 Xn i=1 (x i x) s x (y i y) s y (8 File Size: KB. • SS T = as before (squared difference between each score and the grand mean) • SS BG = SS T - SS WG • SS WG = for each participant, difference between their individual scores and their mean, squared and summed • SS M = the squared difference between each condition mean and the grand mean multiplied by the number of subjects, summed • SS R = SS WG –SS M (the File Size: 1MB.
The usual way is "multiple dichotomies" i.e. dummies. Another alternative is "multiple responses". In this case, you establish first what is the maximum number of simultaneous choices per person (perhaps the individual choosing the largest number chose 7 out of the 10 options presented).
If the maximum number of choices per person is k, you create k. SPSS for Windows Advanced Statistics Update Documentation for other add-on modules (e.g., Tables, Trends, Categories, Lisrel) are also available.
Documents may be purchased though the local bookstore, or directly ordered from Prentice Hall (/). SPSS family [electronic resource] SPSS Australasia] [North Sydney, N.S.W Wikipedia Citation Please see Wikipedia's template documentation for further citation fields that may be.
Define response rate, and discuss some of the current thinking about response rates. Describe what a codebook is and what purpose it serves. Define univariate, bivariate, and multivariate analysis. Describe each of the measures of central tendency. This text is primarily focused on designing research, collecting data, and becoming a.Use the simple set of options in Figure 2, to run a basic reliability analysis.
Click on to return to the main dialog box and then click to run the analysis. Figure 2 Interpreting the Output SPSS Output 1 shows the results of this basic reliability analysis for the fear of computing Size: KB. SPSS нь MS DOS дээр суурилсан байснааWindows хангамжтай болохдоо , гэсэн хэдэн хувилбарыг дамжинбайрлалт, зохион байгуулалтын хувьд улам боловсронгуй болон шинэчлэгдсээр байна


Create makeshift rulers using miscellaneous objects. Start by looking for random objects around the house, starting in the garage. In your wallet, you have dollar bills that are close in size to rulers. The average bill is at least half a foot and easy to fold into the pocket, so it is the ideal choice.
Another important item to use is a credit card along with a cell phone. Write down the measurement of each object and save each one as a makeshift ruler.
First, know the different types of measurements that are commonly used. From the smallest to the largest, there are millimeters, centimeters, inches and feet. Think of the general lengths for each type of measurement. Then, think of objects you own that are equivalent to these lengths.
For instance, the average pen is the equivalent of nearly five inches, which is nearly half a foot. In total, a foot is twelve inches or one third of a yard. You want to list all of the common items that equal the length of a foot. Also, look for items that equal the length of a yard if you need to make a longer measurement.
You will find it easier to use items that already exist instead of creating your own. It takes too much time to create a ruler out of paper and pencil marks. The main point is to use items that are already lying around for your convenience.


Each paper published in journal of mathematics research is assigned a doi ® number, which appears beneath the author's affiliation in the published paper. A guide to writing mathematics dr kevin p lee introduction this is a math class why are we writing there is a good chance that you have never written a paper in a. Abstract in recent times, due to the improvement of internal cylinder flow analysis technology with computational fluid dynamics (cfd), the prediction accuracy of. Topics of interest for computational mathematics, computational geometry & statistics conference – cmcgs 2018. Jaylon curtis from trenton was looking for computational geometry + thesis allan hill found the answer to a buy research papers onlinecourse work.
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Discrete & computational geometry and real algebraic geometry the journal also accepts papers with a distinct geometric springer for research. The journal seeks high quality original papers of both a research and an the highest quality in computational mathematics american mathematical society. Discrete & computational geometry and real algebraic geometry the journal also accepts papers with a distinct geometric flavor in springer for research. Free geometry papers, essays, and research the development of modern architecture - with the interaction between the development of computational. View computational geometry research papers on academiaedu for free.
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Some research topics in applied mathematics the paper [b2] introduced a this problem can also have a strong computational component. Computational geometry is a forum for research in theoretical and applied aspects of computational geometry the journal publishes fundamental. On this page you ca get sample pages of a research paper research paper topics pertaining to algebra research paper topics pertaining to geometry. Click here click here click here click here click here this amazing site, which includes experienced business for 9 years, is one of the leading pharmacies.
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Calculate the Molarity describes the relationship between moles of a solute and the volume of a solution. Nov 30, 2020 Calculating concentration in mol dm-3. 1. What is the molarity of a solution prepared by dissolving 0.15 mole of ammonia in enough distilled Calculating the Number of Moles in a Solution. Titration to know and then the calculation.
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Provningsgasens molvikt. av T Maunula · 2018 · Citerat av 9 — gothenburg studies in educational sciences 410. Students' and Teachers'. Jointly Constituted. Learning Opportunities. The Case of Linear Equations. 30 juli 2016 — Concentration of copper in digestate from digester 5 (D5) and 27 Figure 17.
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2008-06-04 2018-08-29 Most commonly, a solution ‘s concentration is expressed in terms of mass percent, mole fraction, molarity, molality, and normality. When calculating dilution factors, it is important that the units of volume and concentration remain consistent.
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Calculate moles of NaCl in solution solution n = c × V c = 0.10 mol L V = 250.00 L Convert volume in mL to volume in L: V(L) = V(mL) ÷ 1000 · Calculate mass of The molar concentration unit [mol/ L (M)] is a conventionally widely used as concentration method. Compound, Molecular formula, Molecular weight, Purity The molarity equation can be rearranged to solve for moles 19 Mar 2021 Figure 4.5.1: Preparation of a Solution of Known Concentration Using a Solid Solute. Example 4.5.1: Calculating Moles from Concentration of The concentration is assumed to be molarity (mol/L or mmol/mL).
equation-06. To solve for the
Aug 22, 2019 MOLAR MASS tells how much 1 mole of the formula unit weighs.
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, To av C Liu · 2005 · Citerat av 11 — where C is the molar concentration and I) is the diffusion coefficient for the water vapor-air at the condensate surface and Vh is the mole fraction of water vapor at the evaporation Equation (9) is the formula used in theoretical calculations.
M = n V, where n is the number of moles and V is the volume in litres. The formula for calculating molar concentration, known as molarity, is the total moles of the solute divided by the total amount of the solution in liters. Molarity is sometimes indicated by an M, which means moles per liter.
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Solution. Using the definition of molarity, we have. equation-06. To solve for the Aug 22, 2019 MOLAR MASS tells how much 1 mole of the formula unit weighs.
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Learning Opportunities. The Case of Linear Equations. av L Bartek · 2020 — According to Paritosh et al (2017) the VFA concentration in AD acid, with molecular formula C2H4O2 and molecular weight 60 g/mol, the. 30 juli 2016 — Concentration of copper in digestate from digester 5 (D5) and 27 Figure 17. Volatile solids reduction calculated with the mass balance equation (MBE) a substance amount of 43,7 moles of methane for 1 Nm3 of methane. The molar ratio allows for conversion between moles of one substance and moles of another.
moles quiz - Test - Wordwall
CO2. [mole fraction]. O2. [mole fraction] τ [s]. 460. 1035 8263 0.108. reaction rate constant, mole. 1-a-b.
Moles are used to measure small amounts of atoms and molecules because they *Molar Concentration Calculation of the molar concentration of a solution.


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There are draws in EuroJackpot from March 23, , to November 12, So, in the case of 3-oddeven, we multiply 0. The calculation shows that a 3-oddeven combination occurs approximately times in draws.
Using the same computation for the rest of the odd-even patterns, we come up with the completed comparison graph below:. The agreement between prediction and the actual results only proves that the EuroJackpot game follows the probability dictate.
Math does not lie. This also indicates that when playing a Eurojackpot game, you have the power to choose the combination that follows the behavior of a random lottery game. The Eurojackpot game favors the 3-oddeven and 2-oddeven groups; consequently, most winning combinations belong to these groups.
According to probability theory, this expectation will happen because a random lottery game spreads the probability fairly between odd and even numbers. For example, not all combinations belonging to 3-oddeven have a favorable success-to-failure ratio.
One example of this is the combination. Based on our understanding of probability, a straight combination such as cannot be a good choice since a truly random game distributes the probability across the number field.
Therefore, a random lottery draw will not favor a combination with pure low numbers. Therefore, grouping the number field into odd and even numbers will not be sufficient.
We have to include low and high numbers in the calculation process. This integration ensures that the probability is spread fairly across the number field and thus provides accurate information for decision-making.
Generated by Lotterycodex calculator. These Lotterycodex templates will tell you accurately which combinations will dominate the Eurojackpot game.
As a Eurojackpot player, you should buy tickets with combinations that frequently occur in a lottery draw. These dominant templates are the ones with favorable success-to-failure ratios. Remember that buying tickets is the only way to increase your odds of winning.
But buying tickets randomly is not an effective method. Mathematically speaking, a lottery wheel gives you the mathematical advantage of trapping the winning numbers. Read on: Lottery Wheel: A Clever Mathematical Strategy That Works. Using the Lotterycodex calculator as a lottery wheel, the program will help you make informed choices as it separates the dominant from the rare groups, making number selections easy.
Read on: Lottery Calculator: A Mathematical Guide Beyond Number Selection. As a lottery player, you aim to know how to win Eurojackpot. You should use the templates that will lead your way in that direction. Based on the above table, template 1 dominates the Eurojackpot game, and according to the law of large numbers, template 1 will continue to show dominance even after draws.
There are millions of combinations in EuroJackpot. How do you know you choose a combination with a favorable success-to-failure ratio? Do you know how to win Eurojackpot? I welcome your opinion.
Please join and add value to the conversation. Share a specific strategy that works for you in the EuroJackpot game. To improve your chances of winning the Eurojackpot, you should use combinatorics and probability theory instead of statistics. Probability theory, on the other hand, helps calculate the success-to-failure ratio for each combinatorial group, aiding you in making more informed decisions when selecting lottery numbers, thus potentially offering you more favorable shots.
I do not support common lottery myths and superstitions but emphasize a rational, mathematical approach to playing the lottery. In a random lottery game, superstitious beliefs or myths cannot influence the outcome.Eurojackpot is a transnational European lottery launched jacklot March As jaackpot Marchthe european jackpot participating europsan the lottery are: Croatia  Czech Republic eiropean,  Denmark all free slot machines Estonia jackkpot,  Finland   Germany  Slotocash free spins no deposit Iceland jafkpot Italy all free slot machines Latvia  Lithuania  Netherlands  Norway  Poland SlovakiaSlovenia Spain  and Sweden. The goal is to match 5 correct numbers out of 50 plus another 2 supplementary numbers out of another 12;  the odds of winning the jackpot are , The lottery draw takes place every Tuesday and Friday at local time in Helsinki. Up to January 31, the Eurojackpot lottery had a 'rolldown' clause: in case the jackpot is not won for 12 consecutive draws, the 13th draw will be subject to a rolldown whereby if no winner is able to match all 7 winning numbers, the jackpot is paid out to the next winning tier where a winner is available. Draws eurlpean place eurppean All free slot machines and are held european jackpot Helsinki, Finland. Europena well as Italy, Eurojackpot is available to play in Croatia, Czech Republic, Denmark, New casinos, Finland, Germany, Hungary, Iceland, Latvia, Lithuania, the Netherlands, Norway, Poland, Slovakia, Slovenia, Spain and Sweden. Eurojackpot can be played online or through an authorised retailer. Follow these simple steps on how to play:. Each entry into the draw consists of five main numbers from 1 to 50, and two Euro numbers from 1 to Match all five main numbers and both Euro numbers to win the jackpot.


How to apply the Golden Ratio in Design
The quickest way to apply the golden ratio in design is using the rule of thirds, dividing an area into equal thirds both vertically and horizontally, the intersection of the lines will provide a natural focal point for the shape.
Photographers are taught to place their key subject on one of these intersecting lines for a pleasing composition, the same principle can be used in the design.
Although the rule of thirds can be applied to any shape, if it is applied to a rectangle with proportions approximately 1: 1.6, it comes very close to a golden rectangle, which makes the composition all the more pleasing to the eye.
To apply it to any design, you have to make sure that the ratio of the design area is 1: 1.61, or multiplying the height or with of an area by .618
Making a grid is the basis for any great design, is a way of organizing content on a page, using any combination of margins, and guides.
There are different methods and proportions, the golden ratio is probably the most famous and used in art; we will study its history and how to apply the Golden Ratio in Design.
Table of Contents
What is the the Golden Ratio
The golden section or ratio is a mathematical relationship found in nature that can be used to create aesthetically harmonious compositions.
It is roughly equal to the ratio 1: 1.61 and it is commonly illustrated by the fibonacci spiral or golden rectangle.
The golden section is closely related to the Fibonacci sequence. The Fibonacci sequence results from adding the consecutive numbers in a sequence:
1 + 1 = 2, 2 + 1 = 3, 3 + 2 = 5, 5 + 3 = 8, 8 + 5 = 13
Each term is the sum of the previous two.
Mathematicians have studied the golden ratio because of its unique and interesting properties founded in nature.
Mathematicians have established the golden ratio as an irrational mathematical constant, approximately:
This relationship means that two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to (=) the ratio of the larger quantity to the smaller one.
Construction of the Golden Rectangle
A golden rectangle can be constructed with only a ruler and a compass using this technique:
- Construct a simple square
- Draw a line from the midpoint of one side of the square to an opposite corner
- Use that line as the radius to draw an arc that defines the height of the rectangle
- Complete the golden rectangle
History of the Golden Ratio
Since ancient times, man has studied or theorized about aesthetics, proportions, beauty, nature or the human body, everything seems to be made by patterns, and these patterns could determine whether or not an element is beautiful.
Ancient Greek mathematicians first studied what we now call the golden ratio because of its frequent appearance in geometry. Some studies of the Acropolis, including the Parthenon, conclude that many of its proportions approximate the golden ratio.
Plato, Michelangelo or Leonardo have been creating theories that determine that objects, elements, visual compositions, sculptures, etc. that are created according to certain principles, determine that they are more aesthetic or comfortable to look at, that they use a “natural” visual language that they make them appear better or prettier in our eyes.
The modern history of the golden ratio starts with Luca Pacioli’s Divina Proportione of 1509, which captured the imagination of artists, architects, scientists, and mystics with the properties, mathematical and otherwise, of the golden ratio.
Salvador Dalí explicitly used the golden ratio in his masterpiece, The Sacrament of the Last Supper.
The dimensions of the canvas are a golden rectangle. A huge dodecahedron, with edges in golden ratio to one another, is suspended above and behind Jesus and dominates the composition.
In 2003 Weiss and Weiss came on a background of psychometric data and theoretical considerations to the conclusion that the golden ratio underlies the clock cycle of brain waves. In 2008 this was empirically confirmed by a group of neurobiologists.
In 2010 the journal Science reported that the golden ratio is present at the atomic scale in the magnetic resonance of spins in cobalt niobate atom
Examples of Golden Ratio in Design
Golden Ratio is widely used in logos. In the following examples the text or the dimensions are apparently based on proportions of the golden ratio
If we measure the sides of our credit or debit cards, we will notice that the relationship between their sides is. the golden number.
When the credits card were designed, they thought of giving it “ideal” dimensions.
Measuring the height and width of a credit card, we will see that they measure 85.60 X 53 mm. Well, if we do the division 85.60 / 53 it gives us the result 1.61, which is practically the value corresponding to the golden number
Maybe when the firs cards were made the designers never though of the golden ratio, and the size could be simply explained in that we humans tend to perceive dimensions that are based on the golden ratio as esthetically pleasing.
A card size that looked pleasing may have been chosen from others , and we found it pleasing because it was close to the golden ratio.
How to apply Golden ratio in Design
Let us use as example the ratio for the header of a web page. As a basis we will use a document of 1024 x 768 pixels.
We multiply the height by .618
768 x .618 = 474.624
That will be our measure for the content. The difference (293.38) will be the measure of our header.
In Web design is more difficult to implement because of the difference in the resolutions of the users monitors, but you can use it to design boards, Magazine advertisements, etc.
There are a few tools across the Internet that does a good job of finding the golden ratio
- Golden Ratio Calculator
- Kevin Cannon’s Golden Ratio Calculator. He also has a golden ratio widget.
- Adobe Exchange Search: Golden Spiral This golden spiral can be used to work out perfect proportions


Mathematical models help assess risk, but woe betide those who think math can predict stock market gains and losse Together, the math and magic of marketing may do more to advance how companies identify, attract, and retain customers
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Financial mathematics not only have a direct effect on the innovation of financial instruments and financial markets operate efficiently, but also for the company's investment decision-making and evaluation of project research and development (such as real options) and risk management in financial institutions has been widely used  The tasks like promoting a product online, use of social media platforms, following different methods of direct and indirect marketing, door to door sales, sending e-mails, making calls, providing the number of schemes like 'Buy one get one free', 'Flat 50% off', offering discounts on special occasions, etc. are all done on the basis of simple mathematical concepts
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Linear Regression is one of the popular algorithms in Machine Learning and perhaps in the statistic community as well. In this post, I will dive you into the math behind linear regression and how it actually works. I hope you are aware of equations, not any high-level linear algebra or statistics, and a little bit of Machine Learning also.
Table of contents
- Why is the name Linear Regression?
- Assumptions in Linear Regression
- Model Representation
- Loss function in Linear Regression
- Optimization: Gradient Descent
- Overfitting and Underfitting
- Bias-Variance tradeoff
- Case Study on Boston House Prediction Dataset
Linear Regression is studied to understand the relation between the output variable(y) and the input variables(X). If there is only one input variable then we called it Simple Linear Regression and for more than one input variable, it is referred to as Multiple Linear Regression.
A Machine Learning regression problem can be viewed as finding the real value of the output variable(y) given input features(X). So the model is trained to find out the relation between output and input. The model will try to learn the statistical relationship between the variables, not the deterministic relationship. In the deterministic relationship, one variable can be perfectly expressed as others like converting student marks into percentages given CGPA. In the case of a statistical relationship, one variable cannot be perfectly expressed as another. For example, determining the relation between the price of the flat and area of flat.
Before we go into the mathematical background of Linear regression let’s try to build the intuition with the help of real-world problems. Let’s say we want to predict the age of the person based on the weight and we have the following data with us.
If we plot the above 2-D data then it will look similar to the following:
The whole aim of the Linear Regression is to find the best line (In 2-D) through all the points that can minimize the error. The best-fitting line is called a regression line. In higher dimensional data we called it a regression plane.
Now If I ask you which of the above is the best line through all the points?
One can intuitively say that the line in figure 2 is the best line through all the points. As you can see the red line is much closer to all the points than the remaining 2 lines in other figures.
I hope now you have a high-level idea of the Linear Regression model and what it actually does. In the next, I will go step by step into a little bit of maths.
3. Why is the name Linear Regression?
The linear regression was found a lot of years ago and is studied by different researchers in different ways. The name linear is there because it is borrowed from the linear model. A linear model is one that assumes the linear relationship between the output variable(y) and input features(X). The term regression is because it solves the regression problem in ML.
This is how the name is given Linear Regression. More generally we can say that y(output) is calculated from the linear combination of X(inputs).
4. Assumptions in Linear Regression
In order to understand how to use linear regression in practice, we must understand the assumptions of it. The assumptions are as follows:
It describes a condition in which the error term (which we want to minimize by the model) is similar across all the values of independent variables X. If there is no specific pattern observed in the data then we called it heteroscedasticity. The most convenient way to check whether data is homoscedastic or heteroscedastic is to plot the scatterplot between the residual values and the predicted values.
4.2 Linear relationship:
By this assumption, there is a linear relationship between the output variable(y) and input features(X). This can be validated by using the scatterplot between the features and output.
4.3 No Multicollinearity:
Multicollinearity occurs in the data when the input features are highly interrelated with each other. The heatmap is used to determine the correlation between each feature. This value lies between 0 and 1. 0 indicates that the particular two features are not correlated to each other and exactly the opposite goes for 1.
4.4 Multivariate normal distribution:
The error produced by the model while predicting the values follows the normal distribution.
4.5 Autocorrelation between the errors:
This assumption is mostly applicable to the time series data. When the current value of the residual is dependent on its previous value then we can say that there exists the autocorrelation between the residuals.
However, now we have seen most of the assumptions of the linear regression that one has to keep in mind while building the regression model. These assumptions make sure that the linear model gives us the best possible result.
5. Model Representation:
Let’s try to recall the example that we have discussed in section 2 of predicting the age given the weight of the person. The equation of the straight line can be represented as follows:
y=mx + c
Where y = Output variable
m = slope of the line
X = input feature and
C = Intercept
In Machine Learning we rewrite the above equation as follows:
y^ = W1X1 + W0
Where y^ = Predicted output
Xi = input
W0, W1 = Parameters of the model
The above equation we saw is only when we have one input variable and one target variable. But the real world has more than 2 dimensions. So our changes to
Where fi = input features and 1<= i < m
f0 = 1
Wi = Parameters of the model
m = dimensions of the data
We can think of different values of Wi as the weight of each feature or influence of the different features on the output. If for a particular feature the W = 0 means that feature doesn’t have any effect on the output produced. Therefore it indirectly removes the influence of that particular input on the model.
6. Loss function in Linear Regression
The different values of the weights (W0, W1, ………, Wm) give us a different line in 2-D and different hyperplanes in m-dimensions. But how did the model come to know which line or hyperplane is the best fit for the data? Even how the model compares 2 different lines or hyperplanes.
Because of this reason, we introduce a loss function called Squared Loss. The mean squared loss defines how close yi to actual point ytrue.
For each point, the data we define a loss a follows:
Where yi^ = Predicted value
yi = Actual value
By squaring we are getting rid of the negative values in case there is any.
We sum over all the errors produced by the model for all the points and take the values of the weights that line which minimizes the error. The mathematical equation for it can be represented as follows:
This is also called an Ordinary Least Square Method.
7. Optimization: Gradient Descent
Gradient descent is an optimization algorithm used for optimizing the parameters in order to reduce the given loss function.
In the case of linear regression, it does by adjusting the weights of the features. Firstly it randomly initializes the weights then it adjusts weights in such a way that the squared error is minimum. The squared loss is calculated for each pair of input and output data points. A learning rate (alpha) is used to determine the step size on each iteration throughout the procedure.
I have another blog that explains the GD in more detail. You can refer to it by the below link for more information (link here).
8. Overfitting and Underfitting
Overfitting is the condition when the model learns each and every small detail of training data which impacts the performance of the model on the completely unseen data.
Underfitting is a state in which the model learns nothing is not generalized well for the unseen data. The underfitting for the regression model can be simply the mean of the target variables.
The below 2 figures gives a clear idea of underfitting and overfitting in the linear regression model.
9. Bias-Variance tradeoff
How to find the best model?
The answer is depending on the model at hand we try to fit the model between overfitting and underfitting often called a good fit. As you might know, the aim of the whole Machine Learning model is to develop a generalized model that lies between high bias and high variance. Finding whether a model suffers from high bias or high variance is another responsibility of the developer.
Regularization is the technique of penalizing the magnitude of the coefficient of the model. In regularization, we keep all the features the same number of features but the magnitude of the coefficient of it.
But how can we reduce the magnitude of the coefficient? For this purpose, we have a different regression that uses regularization to overcome this. They are Ridge regression, Lasso regression, and elastic net regression. I have covered all this technique in a different blog post. For more information, you can refer to Logistic Regression, Ridge regression, Lasso regression, and Elastic Net regression.
In this post, we have learned the concepts of linear regression as well as the maths behind it. Also, we have applied linear regression on real-life datasets. So I hope you are now able to relate the concepts that we have learned with the case study.
Thanks for reading! If you liked the blog then let me know your thoughts in the comment section.


Educational Youth Programs
Ages 6 - 13
Youth Camp Juliena is a week-long summer camp for kids ages 6-13 that are Deaf or Hard of Hearing. Through fun activities, campers form lasting friendships and acquire valuable leadership, team-building, social, and communication skills. Activities include: Arts & Crafts, Swimming, Movie Nights, Campfires, and more!
High School Students
STEM Hands is a week-long residential camp for high school students interested in Science, Technology, Engineering, and Math (STEM). Students will get to stay in college dorms for the week while working on projects, doing research, and taking tours of different STEM facilities in Atlanta.


I have always been a math and science girl. There is just something about those subjects that click for me, and I loved those classes the most. In middle school, I was a part of a program at our local university that encouraged young girls to embrace the Science, Technology, Engineering and Mathematics (STEM) programs.
This continued into my life as I became a math and science teacher. I thoroughly enjoyed teaching math to my accelerated high school students, especially when the light bulbs went off in their heads. It was even more exciting when those students continued on into STEM programs themselves!
I am completely honored to be running the Glass Slipper Challenge this month with the Teaching and Learning Collaborative, a group that embraces the STEM programs, and encourages girls to participate in these subject areas. Together, we are the PI-rate Princesses! (A little math humor for you.)
As I continue to fundraise for this amazing cause, I have a great opportunity for you! Not only will your donations provide innovative and high-quality professional development for educators (resulting in amazing programs for students in the STEM areas), but you will also be entered for a fantastic drawing!
For every dollar that you donate to the Teaching and Learning Collaborative, you will get an entry into my PANDORA charm giveaway! I have specifically chosen the color charm, which encompasses the signature color of one of your favorite Disney Princesses! (The winner will get to choose the color.) You must donate at least $10 to be entered and if you have already donated, you will be included in the giveaway as well.
Donate at the link below and you will be entered to win. Donations must be made by February 18, 2016.
The Teaching & Learning Collaborative is a 501c3 nonprofit organization. Donations are deductible. Additional documentation can be provided for those interested. To be entered in the giveaway, donations must be $10 or more. The PANDORA charm winner will be chosen after February 18, 2016, notified by email and will choose the color charm they would like.


Dear Parents and Guardians
Back-to-school sales are in full swing. It might be a good idea to get a jumpstart on other shoppers and get your student a calculator and math supplies while they are still in stock.
We suggest students have the following for all math classes at Elk Ridge Middle School:
– Three ring binder
– Lots of pencils (We learn from our mistakes!)
– Loose leaf paper
– Earbuds (to use when watching lesson videos)
– Calculator (see below)
We strongly recommend that each student have their own calculator to assist with practice assignments and to reduce the number of items that are shared in class. Here are links showing the calculators that are used in each class:
Math 8, Sec. 1, & Sec, 2 Calculator (These classes start using calculators the first week of school.)
Math 7 Calculator (Math 7 does not use calculators until 2nd quarter, but they are cheaper now.)
Elk Ridge will have a calculator rental program, but availability is limited. (Rental information will be forthcoming.) With the emphasis on not sharing supplies and Friday distance learning, it would be a good idea to get a calculator sooner rather than later.
Please contact your student’s math teacher if you have questions or concerns.
Elk Ridge Math Department


I have been homeschooling Brielle for the last two school years. One of her most difficult subjects has been math. Although she is 16 years old, she studies 3rd and 4th grade work in all subjects, except math. She is only doing first grade math work and it is a constant struggle.
Lately, however, Brielle has been kicking some serious butt in math!
I have no idea what changed. I haven’t been doing anything majorly different with her in math. And yet she FINALLY seems to be getting the concepts of simple addition and subtraction facts and has mastered each to 11.
I am so proud and excited for her! (And happy to moving on to bigger numbers after two years of doing the same facts over and over again!)


Vedic Maths is the fastest calculating system. One can calculate 10 times faster than conventional method. The simplicity of Vedic Mathematics means that calculations can be carried out mentally (though the methods can also be written down). There are many advantages of using a flexible, mental system. Pupils can invent their own methods, they are not limited to the one 'correct' method.
This leads to creative, confident and intelligent pupils. Vedic maths is the need of hour due to increasing competition. Research is being carried out in many areas including the effects of learning Vedic Maths on children; developing new, powerful but easy applications of the Vedic Sutras in geometry, calculus, computing etc. It's place of origin is India.


When you're looking for a math tutor in Gainesville, Florida, you want somebody who can help your son or daughter get to grips with a tricky subject and start enjoying schoolwork again. At Sylvan, we appreciate that different students have different needs, which is why we offer you the choice of three great math programs that boost both confidence and academic results: personal math tutoring, Math Edge and math homework help. We make sure our programs are aligned with college and career readiness standards, which means the skills your child develops at Sylvan will make a big difference at school —and beyond! So whether it's conquering algebra, understanding geometry or the extra guidance young math whizzes need to advance to the next level, all you have to do is get in touch with your nearby Sylvan center in Gainesville.
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Congratulating and commending the Kansas Academy of Mathematics and Science.
JPN: Journal Page Number
|Thu 17 Mar 2011||Senate||Enrolled on Thursday, March 17, 2011||382|
|Wed 16 Mar 2011||Senate||Adopted without roll call||366|
|Wed 16 Mar 2011||Senate||Introduced||365|
2013. Powered by KLISS. Rendered: 2013-05-23T22:55:26. Head Rev No: 346362


Hi, Welcome back to learn aptitude. Today we are going to look take a look on Problems on Trains. As you can see in any aptitude examination, you can find at least one Train based problem. In this post you will get various basic Problems on Trains. So lt’s get started.
1. Unit Conversion Formula
Conversion is a simple problem that you may face in the every Train based problems. The conversion problems are to convert Km/Hour to Meter/Sec or Meter/Sec to Km/Hour.
So when the question is to convert KM/Hour to Meter/Second then we have to multiply by 5⁄18 , and when the question asking to convert meter/sec to Km/Hour then multiply by 18⁄5 .
- ‘A’ Km/Hour = A × 5⁄18 M/Sec
- ‘B’ m/Sec = B × .18⁄5 Km/Hour
Q.1 Convert 54 Km/Hr to M/Sec?
Solution: 54Km/Hour= 54 × 5⁄18 =15 m/Sec
Q.2 Convert 50 m/Sec to Km/Hr?
Solution: 50 m/Sec= 50 × 18⁄5 =180 Km/Hr
2. Time and Distance Formula
The most important formula to solve Problems on Trains is Time and Distance formula. So just Remember this formula and your rest work is done.
Let Distance covered by the train =d
and the time take by the train = t
Hence Speed of the Train ‘s’=
Q. A train is 500m long and its speed is 100m/Sec. Find the time taken by the train to cross a poll.
3. Train with an object
In this type train has to cross an object like platform, Tunnel or Bridge etc. To solve this type of problem we have to use the following concept.
Let the length of the Train = L1, and the length of the Tunnel/Platform/ Bridge = L2 and time taken to cross the bridge = t and speed= s.
When the train completely, cross the object the total length = L1 + L2
Hence the Speed (S) =
Q.3 A train is 200m long and is running at 72 Km/Hour. At what time it will pass 100mt long, bridge?
Q.4 A train is 200m long and is running at 72 Km/Hour. At what time it will pass 100mt long, bridge?
Q.5 A train 200m long is running at the speed 30Km/Hr. Find the time taken by the train to pass a poll near it?
Theory of Relativity on Train Problems
There are two types of theory of relativity.
- Two Trains Moving Opposite to each other
- Two Trains Moving in the same Direction
4. Two Trains Crossing Each Other in Opposite Direction
Let’s assume two trains T1 and T2 of length L1 and L2 respectively. Two trains are moving in the opposite direction to each other.
Train T1’s speed is v1 and train T2’s speed is V2.
Here we have to calculate the time taken by the two train to cross each other completely.
In our case the two trains have to cross each other’s length i.e L1+L2 distance.
Let’s assume that you are travelling on a train with a speed of 80Km/Hr. You just see another train passing you at a speed of 30Km/Hr. You feel that the opposite train is moving faster than your train. While your train is moving at a faster speed. This is happening due to the addition of speed of both the train. You feel the speed of 70+30= 100Km/Hr.
Similarly in our case speed will be considered as V1+ V2
∴ Time (t) =
Q. Two Trains A and moving to each other at a speed of 42Km/Hr and 48 Km/Hr to each other respectively. The length of train A is 137 meters and the length of train B is 163m. How many times they will take to cross each other?
(A) 12.0 Sec
(C) 7.2 Sec
(D) 6.3 Sec
5. Two trains moving in the Same Direction
Let’s assume train T1 and train T2 of length L1 and L2 are moving in the same direction at a speed of V1 and V2 respectively.
Here also the length will be = L1+ L2
Let’s assume you are travelling in a train at a speed of 50Km/Hr and you find another train is moving in the same direction at the same speed. You will feel that two trains are not moving. This is due to subtraction of speed.
Similarly, in our case the overall speed can be calculated by subtracting the both train’s speed.
Speed= V1 – V2
∴ Time (t) =
Q. Two Trains A and moving in the same direction at a speed of 72Km/Hr and 54 Km/Hr to each other respectively. The length of train A is 100m and the length of train B is 120m. How many times they will take to cross each other?
(A) 48 Sec
(B) 46 Sec
(C) 42 Sec
(D) 49 Sec
Answer: (B) 46 Sec
Solution: L1= 100m
V1= 72 Km/Hr, V2= 54Km/Hr
As two trains moving in the same direction so Relative Speed of train V= V1- V2 = 72-54 = 18 Km/Hr= 18 × 5⁄18= 5 m/ Sec
T= (100+120)/5= 44 Sec
Problems on Trains
Q.1 A train is 150m long running on a train line at a speed of 68kmph. In what time it will cross a horse running at a speed of 8Km/Hr in the same direction?
(A) 15 Sec
(B) 14 Sec
(C) 9 Sec
(D) 12 Sec
Q.2 A train is running at 54Km/Hr speed and it takes 20 Sec to pass a Tonnel. Next it takes 12 Second to pass a Woman walking at 6Km/Hr in the same direction in which train is running. Find the length of the Tunnel?
This is one of the most important Problems in Trains section.
Answer: (A) 140 m
Solution: Relative speed of train with respective to the Woman= (54-6)Km/Hr = 48 Km/Hr= 48 × (5/18) = (40/3)m/Sec
When the train will pass the Woman, the train will cover its own length with Relative speed.
∴ Length of the train = Speed × Time = (40/3) × 12= 160m
Speed of Train = 54 Km/Hr = 54 × (5/18) = 15 m/Sec
When the train will cross the Tunnel, it will cover tunnel length along with its own length.
Let the Tunnel Length be x
Speed = (Tunnel Length + Train Length) / Time
⇒20 = (x+160)/ 15
⇒ x+ 160 = 20 × 15
⇒ x= 300 – 160
⇒ x = 140
∴ The length of the Tunnel = 140m


- Do musicians have higher IQs?
- How does the Pythagorean theorem relate to music?
- What side of the brain do musicians use?
- Are singers more intelligent?
- What country did Pythagoras live in?
- What is the role of mathematics in music?
- Does piano help with math?
- Who has the highest IQS?
- When was Pythagorean tuning used?
- What did Plato say about music?
- Is there a connection between math and music?
Do musicians have higher IQs?
– Musicians show higher general intelligence (FSIQ), verbal intelligence (VIQ), working memory (WMI) and attention skills than non-musicians..
How does the Pythagorean theorem relate to music?
Pythagoras is attributed with discovering that a string exactly half the length of another will play a pitch that is exactly an octave higher when struck or plucked. Split a string into thirds and you raise the pitch an octave and a fifth. Spilt it into fourths and you go even higher – you get the idea.
What side of the brain do musicians use?
rightThe ability to produce and respond to music is conventionally ascribed to the right side of the brain, but processing such musical elements as pitch, tempo, and melody engages a number of areas, including some in the left hemisphere (which appears to subserve perception of rhythm).
Are singers more intelligent?
Whether in tune or not, singing cultivates human development, with kids profitting most from the activity. Those who sing also get sick less soften, a study shows.
What country did Pythagoras live in?
What is the role of mathematics in music?
Mathematics also plays a pivotal role in musical harmony. Essentially, harmony is the combination of musical sounds as perceived by the ear and is analyzed in terms of math based concepts such as frequency, pitch, and chord progression. Mathematics is also deeply interwoven with the western notion of musical scale.
Does piano help with math?
Playing the piano improves your mathematical ability Notes and rhythms, as well as music theory, are based on math. … Studies have shown that students who play an instrument usually perform better in math tests than students who don’t.
Who has the highest IQS?
Marilyn vos SavantWriter Marilyn vos Savant (born 1946) has an IQ of 228, one of the highest ever recorded. Someone with a “normal” intelligence will score somewhere around 100 on an IQ test. To meet someone with an IQ approaching 200 is certainly impressive. Vos Savant has lived a quiet life since childhood.
When was Pythagorean tuning used?
16th centuryThe so-called “Pythagorean tuning” was used by musicians up to the beginning of the 16th century.
What did Plato say about music?
Plato said that “music is a moral law. It gives soul to the universe, wings to the mind, flight to the imagination, and charm and gaiety to life and to everything”.
Is there a connection between math and music?
Music involves creating patterns of sound, whereas Mathematics is the study of patterns. Research has found out that popular pieces of music have definite mathematical structures that are less evident in others. These patterns appeal to our innate desire for mathematical rhythm and patterns.


Mathematics at St. Patrick’s
Subject Leader: Mrs Mulrooney
Our vision is to produce confident mathematicians who know and understand the purpose, relevance and importance of maths in their everyday life. We want our children to be number confident and able to make a valued contribution for themselves, the community and the world. Our aim is to provide quality first teaching in mathematics, which sets high expectations for all pupils. We will support all pupils to ensure that they are able, where possible, to master an age appropriate curriculum.
Intent and Implementation
Mathematics is a creative and highly inter–connected discipline that has been developed over centuries, providing the solutions to some of history’s most intriguing problems. It is essential to everyday life, critical to science, technology and engineering and necessary for financial literacy and most forms of employment. A high quality mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject. (National Curriculum 2014).
Mathematics at our school is based on the National Curriculum for Mathematics for year groups 1 to 6. The Early Years Foundation Stage Framework informs mathematical learning in the Early Years Foundation Stage. These programmes of study are used to give a balanced and broad curriculum to all of our pupils; this includes the statutory and non-statutory aspects of the curriculum and EYFS framework.
At St Patrick’s Catholic Primary Academy, we aim to provide a mastery approach and to deliver high quality Mathematics education for all our pupils in order for them to develop a sense of enjoyment and curiosity about the subject through our ‘Curriculum Drivers.’ We want our pupils to engage in rich experiences which allow them to think critically and enhance their resilience. They will be provided with opportunities to develop their skills in fluency, reasoning and problem solving as stated in the aims of the National Curriculum for Mathematics.
Our aims in the teaching of mathematics are:
- to promote enjoyment of learning through practical activity, exploration and discussion;
- to develop confidence and competence with numbers and the number system;
- understand the four operations and be able to calculate both mentally and by using formal written methods;
- be able to recall an increasing number of facts over time;
- to develop the ability to solve problems through decision-making and reasoning in a range of contexts;
- to develop a practical understanding of the ways in which information is gathered and presented; to explore features of shape and space, and developing measuring skills in a range of contexts;
- to help children understand the importance of mathematics in everyday life.
As well as the three aims outlined in the National Curriculum (DfE, 2014):
- to become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
- to reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language.
- to solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.
Our Curriculum Design
We believe that the vast majority of children can succeed in learning mathematics in line with
It is achievable for all. We have high expectations and encourage a positive ‘can do’ mindset towards mathematics in all pupils, creating learning experiences which develop children’s resilience in the face of a challenge and carefully scaffolding learning so everyone can make progress
The whole class is taught mathematics together, with the expectation that every child will master the key concept, whilst some will work more deeply on challenging tasks
Deep and sustainable learning – lessons are designed with careful small steps, questions and tasks in place
The ability to build on something that has already been sufficiently mastered – pupils’ learning of concepts is seen as a continuum across the school
Conceptual and Procedural Fluency – teachers move mathematics from one context to another, using objects, pictorial representations, equations and word problems.
There are high expectations for pupils to learn times tables and key number facts and have a true sense of number. They are encouraged to think whether their method is appropriate, reliable and efficient.
Differentiation is used in many forms, such as the amount of time that pupils will spend using concrete resources or pictorial representations to grasp concepts. It will be seen through targeted questioning and the feedback and scaffolding individual pupils receive in class as they work through problems.
Challenge through greater depth – teachers set tasks to deepen knowledge and improve reasoning skills within the objectives of their year group.
The ability to reason about a concept and make connections – pupils are encouraged to make connections and spot patterns between different concepts
Precise mathematical language, often used in ‘stem sentences’, is used by teachers so that mathematical ideas are conveyed with clarity and precision
Sufficient time is spent on key concepts, to ensure that learning is well developed and deeply embedded before moving on
Problem Solving is central to apply their understanding