Why do I need number sense? Mathematics is an emotional word. For some people it conjures up images of sitting in rows, trying to find answers to pages of ‘sums’ and an overwhelming sense of failure. For other people it is a thing of beauty, something we use everyday and which we are all amazing at. You might like to ponder which emotion resonates with you, but while you do, let me tell you that everyone is fantastic at mathematics – it’s just that some people don’t’ think they are!
A huge part of mathematics is about playing with numbers. We call this number sense. We all have number sense, but sometimes we can forget about it or think we have ‘lost’ it. Number sense is about having a feel for numbers. It is about spotting patterns and making connections. It is not about figuring out the answer quickly. In fact, number sense is less about the answer and more about understanding what we are doing and why it works.
Just imagine a classroom filled with learners who are curious about numbers, who love to solve problems in more than one way, who are encouraged to discuss the problem with their peers and swap what they have noticed or what they are wondering about. These learners love a problem that they cannot yet solve. They know they can use facts that they know to work out questions they haven’t yet solved. One of the reasons they exhibit these mathematical characteristics is that they know mathematics isn’t about being right or wrong, it is about making sense of numbers. Eventually we might discuss the answer (in fact I often give learners a question and the answer at the same time to avoid any anxiety around finding the answer), but first we stop, pause and think; What do we notice? What could we try first? What does my friend think?
As teachers we can’t always insist our learners love mathematics, or feel confident with it, but we can set tasks that enable them to develop their number sense. Here are four tips that will help you to develop number sense with your learners:
Use manipulatives to expose the structure of mathematics. Manipulatives (physical objects) such as bead strings, ten frames and counters are essential for revealing the structure of mathematics. For example, using counters in an array to show what 4 x 5 looks like helps us to teach that multiplication is additive (we could use a different manipulative to show that multiplication is also multiplicative).
2. Design tasks for learners to work on
Design tasks which enable learners to solve them in different ways. One of my mantra’s is ‘one problem, five different ways’. Open ended tasks allow learners to think. If a question is closed (e.g. what is the answer to 3 + 7?), there is limited room for thinking, but if we ask what two numbers could be added together to sum to 10, we have opened up possibilities, and also invited learners to think how they might approach this question.
3. The equals symbol =
The equals symbol means balance, not ‘here comes the answer’. Too often questions are presented with the equals sign towards the end of the question (e.g. 3 + 4 = ?). This gives a false impression that it is the signal to work out the answer. But learners need to understand that the quantity on either side of the equals symbol need to balance. So, it doesn’t matter where the equals symbol appears (e.g. 10 = 4 + ?).
4. Fact finder
If you know one fact, you know lots more! This is often a surprise to learners, but once we show them how facts connect to each other, they realise they actually know a lot more than they thought they did! For example, if you know that 4 x 5 = 20, you also know that 5 x 4 = 20, or 20 ÷ 4 = 5 and so on.
Alison Borthwick is a consultant, guest author and writer for Thirsty Scholars Partnership. Alison has written our recently launched courses * Primary Maths: Developing Number Sense with your Learners.


Measurement error in the Worldwide Governance Indicators is discussed in Party Systems and Country Governance on pages 31-33 and in the associated footnotes.
As described on those pages, the creators of the WGI data estimated that the standard errors ranged from ±0.18 to ±0.23 for five indicators in 2007 and was ±0.26 for the sixth, Political Stability. Typically, standard errors are doubled (i.e., ±0.18 becomes ±0.36) to insure that an observed WGI score is significantly different from the observed score at the standard leve of 95 percent confidence. For this student exercise, we propose the looser criterion of (roughly) one standard deviation, which implies that we are only 68 percent confident that differences between the predicted and observed scores are significant. Relaxing the criterion for this project results in identifying more countries to select for study. We believe that the value of the project comes more from doing the research using countries that interest students.
Apart from measurement error, there is also prediction error, reflected by the standard error of the estimate (SEE), which is the standard deviation of the mean of the squared residuals (deviations around the regression line). If the SEE = 0, the prediction is perfect with no residuals or deviations from predicted values. Thus the SEE incorporates not only measurement error for the variables in the regression equation but also the adequacy of the theory that underlies the regression equation. Not reported in Party Systems and Country Govenance, the standard error of the estimate associated with equation 9.1 is 0.56. Given that the purpose of the research project is to determine underachievers and overachievers based on factors that are not in the equation, using the SEE seems inappropriate.


Math, 28.10.2019 17:29
Inverse or direct 1. the amount of water to the space that water did not occupy in a particular container. 2. the area of the wall to the amount of paint used to cover it. 3. the time spent walking to the rate at which the person walks. 4. the time a teacher spends checking papers to the no. of students. 5. the age of a used car to its resale value.


AB models and microsimulations JAS-mine provides a unique tool for both microsimulations and large-scale agent-based applications. Dynamic microsimulations are computer models aimed at applying specific processes (such as ageing, educational choices, labour market events, household formation, etc.) to a representative sample of a given population, in order to forecast its evolution or understand the distributional impact of some policy of interest. While some processes might be deterministic (such as ageing, or pension eligibility), other processes are stochastic (such as mortality, or retirement choices) and are generally estimated in the data. Agent-based models (ABM) also take an initial population and simulate it forward in time. The main differences between the two approaches can be traced down to the following: (i), microsimulations are more policy-oriented, while agent-based models are more theory-oriented; (ii) microsimulations generally rely on a partial equilibrium approach, while agent-based models are most often closed models. The initial population in an agent-based model is typically not meant to reproduce a real population of agents: for example, in a labour market model with firm creation all individuals might be initiated as unemployed, or randomly employed. The focus is on the emergence of aggregate patterns from the interaction of the individual agents, with the aim to replicate some observed stylized fact (business cycle fluctuations, for instance). Accordingly, the value of the parameters that drive the processes are chosen ad-hoc, or only roughly calibrated with real data. However, in their struggle to replace dynamic stochastic general equilibrium (DSGE) models, agent-based models are becoming more empirically oriented. At the same time, microsimulations are becoming more complex, by including more behavioural responses and general equilibrium feedbacks. If the two approaches retain different goals and perspectives, from a mathematical and computational perspective they are identical. Both agent-based models and microsimulations are recursive models, where the number and individual states of the agents in the system are evolved by applying a sequence of algorithms to an initial population. As with computer-based simulations, they face the problem of reproducing real-life phenomena, many of which are temporally continuous processes, using discrete microprocessors. For a more in-depth analysis, see: Richiardi M (2013). The missing link: AB models and dynamic microsimulation. In: Leitner S., Wall, F. (eds). Artificial Economics and Self Organization. Springer, Lecture Notes in Economics and Mathematical Systems, vol. 669, Berlin.


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r_true = k1 * r + k3 * r**3 + k5 * r **5
where r_true is an idealised angular distance from the optical axis and r is the measured distance. k1 is the scale at the centre of the field, usually quoted in arcsec/mm.
WFCAM and VISTA are no exception and prior to on-sky measurements being available, ray-tracing enables an estimate of the expected field distortion to be made.
The above figure shows the non-linear distortion (ie. % scale change) expected for WFCAM as a function of wavelength. For VISTA there is negligible variation with wavelength and the following figure shows the tabulated K-band distortion, (red splodges), with an "r-cubed" fit superimposed (green circles).
In the K-band WFCAM and VISTA will have scales, ie. k1 values, of 22.30 and 17.09 arcsec/mm respectively. The term due to k5 is usually negligible and until real sky data is available is not worth pursuing, since other similarly sized distortions may be present. Rearranging the preceding equation to a more convenient form gives
r_true = r' * (1 + k3/k1**3 * r'**2) = r' + k * r'**3
where r' is the measured distance from the optical axis in arcsec using the k1 scale. If we convert all units to radians the "r-cubed" coefficient is conveniently scaled (in units of radians/radian**3 - honest!) and has values of 76.1 and 42.5 in the K-band for WFCAM and VISTA respectively.
[Measurements on real WFCAM data indicate that this coefficient is more like -50.0, ie. apart from the sign and magnitude it was about right. Note that subsequent numbers for WFCAM have been updated to correspond to the real on-sky values.]
Although this type of distortion generally presents no problem for accurate calibration of individual pointings, it can lead to various complications when stacking data taken at various locations, eg. dither sequences. This is caused by the differential non-linear distortions across individual detectors being comparable to, or larger than, the pixel size of the detector. In these cases stacking involves resampling and interpolation of some form. While these are inevitable in combining pointings to form contiguous tiled regions, they may be avoided at earlier stages, such as stacking individual detector dither sequences, by suitably limiting dither offsets and thereby both simplify and speed up the data processing.
The following figures demonstrate the level of this optical distortion over the field of view.
For WFCAM the non-linear term introduces a (pincushion/barrel) distortion amounting to roughly 10 arcsec from the centre to the edge of the 0.8 degree diameter field, denoted by the blue circle.
For VISTA the corresponding numbers are a distortion of around 25 arcsec at the edge of the 1.67 degree diameter field, denoted by the blue circle.
We can quantify this effect in a more useful manner by forming
dr_true/dr' = 1 + 3k * r'**2
which describes the local change in relative pixel scale as a function of radial distance. For example, for WFCAM at around 0.45 deg radius, the second term is about 1.0% in size (ie. 3x the radial distortion value shown in the earlier plots). This means that a 10 arcsec shift in the centre corrsponds to a 10.1 arcsec shift at the outer corners of the arrays. The majority (~90%) of this distortion occurs across individual detectors. Therefore, even after re-registering the detector centre, there would still be a distortion at the +/-0.05 arcsec level across it.
To first order the size of this effect clearly scales as the size of the offset (though of course the pattern induced depends on the direction). Confining dither offsets (and microsteps) to within +/-5 arcsec of a target centre (a reasonable practical compromise of various constraints) would enable nonlinear resampling for "dither" stacks of each detector to be avoided for WFCAM but possibly not for VISTA. Of course tiling contiguous regions by filling in the gaps between detectors with additional pointings will always involve non-linear resampling as will large offset pattern dither sequences.
(1 + k r'**2).(1 + 3k r'**2) =~ (1 + 4k r'**2)
or in other words roughly 4x the linear scale distortion.
At the corners of the field WFCAM has a worst case (K-band) linear scale distortion of about 0.3% leading to photometry systematics due to this effect of at most ~1.2% relative to the centre, and can probably be safely ignored for most applications. If required it is also feasible for this correction to be factored in with the "mesostep" correction for scattered light photometric systematics. To illustrate the effect the following colourful image shows the systematics in photometry that would arise from a standard WFCAM 4 pointing tile.
The systematics vary from 0% in the centre up to 0.5% lighter shades of green, through purple and red at 1.0% to yellow, 1.5% in the corners. The field of view shown is roughly 0.8 deg x 0.8 deg. The exposure map below shows how this relates to the final field.
Grey-green equates to 1; puprle 2; and yellow 4.
For VISTA however, the scale distortion at the edge amounts to some 0.8% - 0.9% implying worst case photometry systematics of order 3.5% from centre to edge of field.
Given that tiling of 6 pointings to create a "uniform" contiguous coverage of the 1.67 degree diameter field is likely to be the baseline mode of operation for VISTA, further modelling is required to see if the resultant systematics are large enough to warrant special attention during pipeline processing and at the mosaicing stage. Stacking individual detector dithers is not a problem (other than needing to cope with non-linear astrometric distortions). The next colourful image shows the systematics in photometry arising from a standard VISTA 6 pointing tile.
The systematics vary from 0% in the centre up to 1% lighter shades of green, through purple and red at 2-2.5% to yellow, 3% toward the corners. The field of view shown is roughly 1.2 deg x 1.5 deg. The exposure map below shows how this relates to the final field.
Green equates to 1; grey-green 2; purple 3; red; 4 and yellow 6.
CTYPE1 = 'RA---ZPN' / Zenithal polynomial projection CTYPE2 = 'DEC--ZPN' / Zenithal polynomial projection CRPIX1 = 3914.68291287068 / Reference pixel on axis 1 CRPIX2 = 2958.23149413302 / Reference pixel on axis 2 CRVAL1 = 325.5563 / Value at ref. pixel on axis 1 CRVAL2 = 0.2084674 / Value at ref. pixel on axis 2 CD1_1 = -1.4011089128826E-6 / Transformation matrix CD1_2 = -9.2625825594913E-5 / Transformation matrix CD2_1 = -9.2750922381494E-5 / Transformation matrix CD2_2 = 1.31362241659925E-6 / Transformation matrix PV2_1 = 1.0 / coefficient for r term PV2_3 = 220.0 / coefficient for r**3 termand is the style we are proposing to adopt for both WFCAM and VISTA.


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A space relationship generally defines how a subject is positioned in space relatives into a reference photo. If the research image is significantly larger than the thing then the ex – is usually depicted by an ellipse. The ellipse could be graphically represented using a allegoria. The parabola has comparable aspects into a sphere around july plotted over a map. Whenever we look directly at an raccourci, we can see that it is shaped in such a way that all of it is vertices make up excuses on the x-axis. Therefore an ellipse could be thought of as a parabola with one target (its axis of rotation) and many parts of orientation on the other.
There are several main types of geometric diagrams that relate areas. These include: the area-to-area, line-to-line, geometrical engineering, and Cartesian structure. The fourth type, geometrical engineering is a little not the same as the other forms. In a geometrical engineering of a set of parallel right lines is utilized to stipulate the areas in a model or perhaps construction.
The primary difference between area-to-area https://herecomesyourbride.org/mexican-brides/ and line-to-line is that a great area-to-area relative relates just surface areas. This means that you will find no space relationships included. A point over a flat surface can be viewed a point within an area-to-room, or an area-to-land, or a room to a place or terrain. A point over a curved surface can also be regarded as part of a room to place or element of a room to land regards. Geometries like the ring and the hyperbola can be considered element of area-to-room relationships.
Line-to-line is normally not a spatial relationship but a mathematical a person. It can be defined as a tangent of geometries on a single collection. The geometries in this relationship are the region and the edge of the area of the two lines. The space relationship of these geometries is given by the mixture
Geometry plays an important purpose in vision spatial associations. This enables the understanding of the three-dimensional (3D) world and it gives all of us a basis for learning the correspondence regarding the real world as well as the virtual environment (the electronic world is actually a subset for the real world). A good example of a visible relationship is a relationship among (A, M, C). (A, B, C) implies that the distances (D, E) will be equal when measured out of (A, B), and that they maximize as the values from the distances reduce (D, E). Visual spatial relations can also be used to infer the parameters of a model of real life.
Another application of visual space relationships certainly is the handwriting research. Fingerprints still left by numerous people have been used to infer different aspects of someone’s personality. The accuracy of them fingerprint analyses has advanced a lot over the past few years. The accuracy of those analyses could be improved further more by using electronic methods, particularly for the large samples.


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The second round of Who Wants to Be a Mathematician is now complete, and we are delighted to be able to announce the four students, who will be taking part in the UK final next month:
- Zaka Ahmed from King Edward VI Aston, Birmingham
- Jordan Baillie from St Maurice’s High School, Cumbernauld
- Jingyi Guo from Concord College, Shrewsbury
- Paul Scarr from Whitley Bay High School, Newcastle
These four teenage mathematicians beat over 1,000 other students from across the UK to win a place in the live final in London on November 28th, hosted by stand-up mathematician Matt Parker. The UK winner will then go on to compete in the Grand Final in Baltimore at the Joint Mathematics Meeting, the world’s largest gathering of mathematicians, where they will pit their mathematical wits against the regional winners from across the US and Canada. The overall champion will win $10,000, to be shared between the student and their school.
Good Thinking would like to thank the American Mathematical Society for inviting UK students to participate in this international mathematics competition.


This article is part of a series of educational articles that describe some of the advanced concepts implemented in Option Samurai’s option scanner. In this article, we will focus on the Expected Value. We aggregated more information on our tutorial page.
What is Expected Value
Expected value is a statistical measure that tries to predict the strategy’s value, assuming you could have executed it many times at different dates but with the same prices/distances, etc. It is calculated by summing the payout at expiration multiplied by the probability of that payout.
The expected value is derived from: Stock price, option prices, Implied volatility, time to expiration, the distance of strikes from the last price, dividends, and risk-free rate. Usually, you aim to have the highest expected value possible, as it indicates a statistical edge.
Example: Expected Value of put spread
In this example, we will see how the Expected value is calculated on a bull put spread. This spread is built with a short put (strike A) and a protective long put (strike B) where both options have the same expiration and A>B.
We can divide the spread into 3 ranges:
- Maximum profit range (where the price is greater than A) – Range 1 in the example
- Maximum loss range (where the price is lower than B) – Range 2 in the example
- Between A and B the spread will show profit or loss that is linear changing depends on the stock price – Range 3 in the example
To calculate the expected value we add:
- The probability of being above A * max profit (positive)
- The probability of being below B * max loss (negative)
- For the area between A and B, we use log-normal distribution and multiply it by the payout.
The sum of the 3 components is the Expected value.
How to use Expected value:
After explaining what is expected value we get to the most important part: How can we use it to find better trades.
1. Filter according to Expected value
This is the most prominent and powerful way to use this value. With our option scanner, you can instantly find only the profitable trades according to the expected value, in real-time. This means that you only analyze trades where you have a statistical edge. This saves you time and, in the long run, helps your edge compound.
You can also set the expected value filter to be more than $100 or any other value to account for commissions and unexpected scenarios and even increase your edge.
2. Find optimal trade (Sort descending)
After getting your results, you can sort by expected value to compare different strikes, expiration, and tickers to find the optimal trade when taking into considerations all the different variables (profit, loss, liquidity, growth, trend, sentiment, IV, etc).
The sorting helps you manage your time more efficiently by looking at the trades with the highest edge first – meaning the optimal trade first. An Important note – The fact that the EV is positive, doesn’t mean you will necessarily make a profit, it is just indicating there is an edge in this trade in your favor.
3. Create a ratio using expected value
A more advanced way to use expected value would be to create a custom ratio unique to your trading style. The best way to do it is to export the results to excel using our export feature.
After you have all the data in excel you can start playing with it. Some ratios for example:
- Expected value / Max loss – This ratio combines EV (higher is better) and Max loss (lower is better). sorting the trades according to this ratio takes into account the worst-case scenario when you analyze a trade
- Expected value * IV rank (if credit strategy) or Expected value / IV rank (for debit strategy) – This ratio combines the EV with the Implied Volatility rank. It means that trades with high IV will get precedence if it is a credit strategy, and Low IV trades will get precedence if it is a debit strategy.
- Expected value * Growth rate – This ratio combines the EV (higher is better) with the fundamental measure of the company expected EPS growth (higher is better). This combines 2 measures from different ‘domains’ and gives precedence to higher growth
You can, of course, create more ratios that fit your style: Divide by days to expiration (EV per day), use PE (see how expensive the stock), div yield, and much more.
The expected value is a statistical measure that tries to predict how profitable a strategy will be. It uses the market conditions, such as: option prices, implied volatility, stock price, dividends, and more to give a dollar amount of the expected profit (or loss) of the strategy.
Though the expected value gives a dollar value, it does not mean that this will be the profit from the trade. It is better to think of the EV as an integrated edge in the trade. Over many similar trades, you are expected to collect this edge and increase your profits.
You can use the Expected value to:
- Filter trades that have positive EV and have an edge.
- Sort by EV to save time and compare trades
- Create your own custom ratios that will help you to uncover the trades that best fit you.
We have more advanced features in Samurai, Such as:
- Implied Volatility suite – Read the knowledgebase article here.
- Unique features section in the knowledgebase
- Read about the edge of using IV percentile and backtests we did
(The article was originally published on Dec 13, 2017, and updated since.)


This calculator helps you calculate your monthly mortgage payments based on your loan amount, interest rate, tenure, and other factors. You can use this tool to find out how much you need to pay each month to repay your home loan.
Formula for EMI Calculation
P x R x (1+R)^N / [(1+R)^N-1] where-
P = Principal loan amount
N = Loan tenure in months
R = Monthly interest rate
The rate of interest (R) on your loan is calculated per month.
R = Annual Rate of interest/12/100
If rate of interest is 7.2% p.a. then r = 7.2/12/100 = 0.006
For example, If a person avails a loan of ₹10,00,000 at an annual interest rate of 7.2% for a tenure of 120 months (10 years), then his EMI will be calculated as under:
EMI= ₹10,00,000 * 0.006 * (1 + 0.006)120 / ((1 + 0.006)120 – 1) = ₹11,714.
The total amount payable will be ₹11,714 * 120 = ₹14,05,703. Principal loan amount is ₹10,00,000 and the Interest amount will be ₹4,05,703
Calculating the EMI manually using the formula can be tedious.
Property Nonstop’s EMI Calculator can help you calculate your loan EMI with ease.


The aim of the School of the Physical Sciences is to contribute to our understanding of the physical world through excellence in observational, theoretical and experimental science and to extend quantitative, qualitative and combined methodologies to address problems in the fields of biology, technology, medicine, social science and the humanities. In pursuit of these goals, the School coordinates objectives in research, teaching and infrastructure.
The School of the Physical Sciences comprises:
The Faculty of Mathematics including: Applied Mathematics and Theoretical Physics (DAMTP) and Pure Mathematics and Mathematical Statistics (DPMMS).
The Isaac Newton Institute of Mathematical Sciences is also part of the School.
The Faculty of Physics and Chemistry including: Chemistry, Institute of Astronomy, Materials Science & Metallurgy and Physics (Cavendish Laboratory).
The Faculty of Earth Sciences and Geography including: Earth Sciences and Geography (including the Scott Polar Research Institute).
The Council of the School of the Physical Sciences
Formal representation on the Council of the School, the School's most senior decision-making body, is outlined in Chapter VIII of the University's Statutes and Ordinances.
Current Council of the School membership »
Further School-level committees with formal Terms of Reference are:
Graduate Education Committee
Undergraduate Education Committee
Equality and Diversity Forum
The above committees all report to the Council of School. There are also a number of working groups and fora that provide the focus for discussions.
Useful links on the School's website:


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10x10 Grid Paper Teacher Resource 3 Teacher Resource 4 Summative Assessment Answer Key 1. What is a repeating pattern? A repeating pattern is a set of shapes that are repeated over and over again.
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Welcome to math lab today you're on your journey to discover decimal multiplication you are provided with some 10 by 10 graph paper a lab observation sheet and some color pencils look carefully at your ten by ten graph paper the vertical lines are in green and the horizontal lines are in red eat small square right here I will mark the small square represents one out of 100 which is nothing but 0.01 to represent 0.1 or 1 by 10 on your graph sheet shade 10 squares vertically or 10 squares horizontally how will you represent 0.3 on your graph sheet yes you can shade 30 squares vertically or 30 squares horizontally remember 0.3 is nothing but 30 by hundred or 3 by 10 now suppose if we shade the entire graph paper what do we represent we represent one that is nothing but 100 out of 100 to multiply 0.8 into 0.9 follow these instructions first shade 80 squares vertically using a light color pencil next shade 90 squares horizontally using another color pencil can you identify the squares that are common to both 72 squares out of 100 are common to both and hence 0.8 into 0.9 is equal to 0.72 to multiply 2 into 0.2 follow these instructions take 2 10 by 10 graph papers as each of graph paper represents one shape the entire graph sheet vertically using a light color pencil to multiply by 0.2 you will shade 20 squares using another pencil horizontally so right here we have shaded 20 squares in each graph paper so what do we find the number of squares that are common to both so each graph paper has 20 out of 100 squares common is it not equal to 40 out of 100 which is nothing but 0.4 this gives the product of two into 0.2 to multiply 1.3 into 0.4 follow these instructions you can represent 1.3 by shading vertically a whole graph paper and 30 squares in another graph paper by using a light color pencil now 2 x 0.4 you will shade horizontally 40 squares in both the graph papers in another color pencil can you identify the product have fun discovering multiplication of decimals


Initial appearance: November 7, 2010
Last updated: July 31, 2020
A curtate cycloid curve is generated as shown in the following diagram, drawn by David Cohen of Cohen Musical Instruments and which appeared in his American Lutherie article "Curtate Cycloid Arching"1:
Violin makers and guitarmakers first became interested in these curves for purposes of arching profiles of carved plate instruments following publication of an article by Quentin Playfair2 in which he compared these curves to arching profiles of golden age violins. They don't really model the arching curves of violins well at all3 but they are nice looking curves and are readily rendered (curves that more realistically model those of Cremonese violin arching profiles can be found here).
The parametric equations for calculating locations of points on a curtate cycloid curve are:
x = aφ - b sin φ
y = a - b cos φ
a is the radius of the circle;
φ is the phase, 0 to π;
b is some displacement from the center of the circle;
As you can see, the equations yield coordinate values as functions of phase φ. For purposes of generating graphs or graphic curves, it is highly desirable to be able to generate points using a fixed x interval. And for purposes of generating a series of contour lines approximating an arched surface or for generating instructions to a CNC machine for cutting an arched plate, it would be convenient to have a series of points that used a fixed y interval (contour interval).
Here is how these parameters relate to a typical transverse arching profile:
The generated curve is shown in black in the above drawing. It should be obvious how to mirror a piece of the start of the curve to form the recurve area, and how to mirror the whole thing to get a profile for the right side of the plate too.
Note that the x or y interval is specified implicitly. When requested to generate a list of points for a half curtate cycloid curve with a fixed x interval, the calculator uses (the length - the x offset) divided by (the number of points - 1) as the x interval. When requested to generate a list of points for a half curtate cycloid curve with a fixed y interval, the calculator uses (the total height - the Y offset) divided by (the number of points - 1) as the y interval.
You can specify the format you want for the output. The calculator will generate a tab delineated .csv file for use by a spreadsheet, a .dxf file containing a polyline representing the specified curve in default units for use by CAD drawing software, or an .svg file containing a polyline representing the specified curve in default units for use by artistic drawing software. The calculator will also generate a coordinate list output in a popup window. If you specify this be sure to allow popups for this website. The coordinate list is output as a list suitable for copying to the clipboard and then being pasted into a spreadsheet or other program for further use.
Here's the calculator which generates a list of points for a half curtate cycloid curve:
Cohen, D. “Curtate Cycloid Arching”
American Lutherie #96, p. 26.
Playfair, Q. “Curtate Cycloid Arching in Golden Age Cremonese Violin Family Instruments” CAS Journal, Vol. 4 ( No. 7 (Series II)), pp. 48-58.
Mottola, R.M. “Comparison of Arching Profiles of Golden Age Cremonese Violins and Some Mathematically Generated Curves” Savart Journal, Vol. 1 ( No. 1)


we are pleased to announce the monthly online seminar “Diff.-Equations
and Singularities”, which will hopefully bring together people from
different mathematical fields like analysis, differential and computer
algebra, or differential topology who have an interest in singularities
of functional equations.
The monthly seminar talks are introductory and survey talks accessible
to people having different mathematical backgrounds. The next talk is
given by Prof. Francois Boulier on 6th of May, 17:00 CET.
For more information please see our webpage:
Please register (in advance) to receive the Zoom details which are
necessary to attend the meetings. The registration link is
which can also be found on the webpage.
With kind regards,
Sebastian Falkensteiner, Jorge Mozo Fernández, Alberto Lastra, Alexey
Remizov, Werner Seiler, Matthias Seiß
Online Seminar “Diff.-Equations and Singularities”


I was “happily” reading my calculus textbook, reading about the arc length integral, when I saw this picture of circles with inscribed polygons approximating their respective circles. I quickly took a picture, sent it to Yang, and told him that the picture shows the relationship between nondistinction and infinite distinction.
Zhuangzi wrote that assigning attributes, or distinguishing, is like turning the circle into a square. The circle is considered to be boundless in having no corners and is meant to be a representation of nature. So by distinguishing nature, one becomes bound to their perceptions of nature.
The Effect of Infinite Distinction
Yet, what the picture shows is the effect of infinite distinctions on nature. Through assigning an infinite amount of attributes, one can come to an unbounded perspective of nature (and an unbound mind). By complexity or simplicity, one can singularly come to unboundness. This is strange, considering that the two are total opposites but come to the same end. But it does make sense because one ideal has to have another, opposite one. Note that regular distinction isn’t in the discussion because it surely won’t lead to sagehood or unboundness.
Which one: Nondistinction or Infinite Distinction?
People usually say, about nondistinction, that it is impractical but agreeable. I spoke to my philosophy professor about this topic and he asked me for the reason why nondistinction is the way to go instead of distinction. I didn’t know the answer and I’m not sure if I know it now. But, my intuition tells me that, between nondistinction and infinite distinction, simplicity and complexity, that the former’s path is less long than the latter’s path (similar to ignorance or omniscience; which one takes more to attain fully). This is not to say that nondistinction is easier, but rather both are very difficult yet nondistinction seems more practical, given the alternative. At least western thinkers know how they can come to unboundness, by infinite distinction.


The Petit Menhir Workshops
Petit Menhir has teamed up with three great teachers to offer you educational cards to use with our wooden game. Get these workshops for free together with your order via fun print-at-home cards!
Petit Menhir Workshops: the concept
The concept is quite simple: reproduce the figures imagined by our three star teachers using our little menhirs!
The educational benefits are numerous and vary according to the different workshops. Fine motor skills, dexterity, memory, geometry, concentration and many others!
These workshops are particularly appreciated by the youngest players who do not yet have the ability to build complex towers, as most of the figures are in two dimensions and do not require finding the points of balance.
Dexterity Workshop with LilouTeach
Objective: train dexterity, geometry and 3D representation.
Creativity Workshop with Maicresse Camille
Objective: stimulate creativity and train hand-eye coordination.
ABC Workshop with Cocon Schooling
Objective: learn the ABC in a fun way.


There is a pervasive cultural attitude against mathematics, but it is actually a mind-blowing tool for analyzing and predicting the world around us—and far beyond. We asked mathematicians Edward Frenkel and Po-Shen Loh, and physicists Michio Kaku, Michelle Thaller, Janna Levin and Geoffrey West to explain the wonders of math.
West explains the rule of ‘quarter-power scaling’ in biology—there is a mathematical equation that predicts how much food an organism needs to eat to survive and it’s remarkably consistent, whether you’re looking at ladybugs, cats, elephants, and even trees and flowers. Math underpins our lives in incredible ways.
Infinitesimal calculus—the math that describes how moving bodies change over time—turns out to predict not just phenomena on Earth but far out in the universe. The 11-dimensional math used by physicists turns out to predict the exact results of particle physics experiments. Humanity is on an incredible journey with mathematics and every day it opens up the world and universe in eye-opening ways.


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There isn't anything like a superb story, and nothing like being the person who started a renowned urban legend. Deciding upon the ideal approach route Cursive writing is basically joined-up handwriting. Practice reading by yourself as often as possible.
Research urban legends to obtain a concept of what's out there prior to making a new one. You are still not sure the radicals have the proper idea. Naturally, you won't use the majority of your ideas. If you've got an idea for a tool please inform us. That means you can begin right where you are no matter how little you might feel you've got to give. You are also quite suspicious of any revolutionary shift. In earlier times you've stated that the move of independence may be too early.
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Hello guys , today I went up to the recruiting office and talked to the guys there. I just got my GED in the mail and I told them I wanted to see about joining and told them that I have the GED, to my surprised he said that's fine and said I'm good to go , I just need to score higher than 50 on the ASVAB.
He then offered me a practice ASVAB test , which caught me off guard , but I said ok screw it lets take it. 30 Min later I was finished and got a score of 64. I told him what fields I wanted to go in ( computers , network ect... ) he said if I score the same on my main test I'd have options for 3 different computer jobs.
I was pretty damn happy , so I told him I'd take a week and study a little more then take it. He took down my info and said he will call me next Monday about taking the test on Tuesday.
So , I went home , and picked out a couple of jobs I'd really like. Here they are...
94F - Computer/Detection Systems Repairer
15W - Unmanned Aerial Vehicle Operator
25FF - - Network Switching Systems Operator-Maintainer
By the time of the test , I'll have at least 5 jobs picked out. So I guess this is where the questions come in.
1. How good did I do on my practice? I know it's only the 4 main subjects , but is that a decent score , should I score higher than 50 ?
2. Those 3 jobs require , 105 in aptitude area EL and/or 105 in aptitude area SC , are those line scores hard to come by?
3. Any other jobs I'm missing ? You see what I'm interested in , any other suggestions ?
4. On the 94F I see under requirements (Successful completion of one year of high school algebra and general science) now , I finished my GED and the Math portion did have algebra on it. Does that count at all or will I not qualify for that job ?
Well , it seems those are the only questions I really have right now , I got a ASVAB for Dummies app on my Iphone I've been looking over , it seems like it will help a little. Sorry about the long story , I just wanted to make sure you knew where I was at right now.
Hoping to see some replies soon!


Climbing Power Formula
I came across an interesting formula yesterday that may be used to predict how much power is necessary to climb a given hill on a bike. It's from Allen Lim, PhD. Allen has a long list of accomplishments related to power-based cycling the most notable of which is consulting with Floyd Landis. Floyd credits Allen with determining what he would have to do powerwise to win the now infamous stage 17 of the 2006 Tour de France. I haven't talked with Allen in some time and no longer have his email address after a computer crash this past fall so I haven't been able to confirm what I'm about to show you. But it seems to work so I suspect it's right.
Dr. Lim's formula to estimate the power necessary to climb a hill:
bike + rider weight (kg) x 9.8 x elevation gain (meters) / time (seconds) = power (watts). Add 10% for rolling and air resistance.
So yesterday I tested it. I climbed a known one-mile hill and captured the data on my power meter. Here are my metrics from that climb:
Weight of my Cervelo Soloist with 1 water bottle - 8.18kg
Body weight with winter clothes, shoes, etc - 74.55kg
Elevation gain (est based on average 5% grade) - 78.87m
Time to climb hill - 312 seconds
Plugging all of these into the formula and adding 10% predicts that it would take me 225 watts to climb this hill. The actual was 218. Remarkably close, especially when you consider that I am estimating the elevation gain and there is some variation between power meter readings.
Of course this formula could be used to figure out how long it would take you to climb a given hill in a race at a certain power output by simply rearranging the formula components. You could also use it to figure out how much faster you would climb a hill if you reduced your total system weight by a given amount but kept power the same.
Interesting stuff. If Allen sees this I hope he comments.


We’re back after the holidays, and our first episode of the new year discusses some math and computer science topics that will come up frequently in future episodes.
We discuss graphs first, which are a data structure used to store relationships between objects. You’ve probably heard the term “social graph” used to describe the friendships in a social network like Facebook or Twitter. These structures pop up frequently in computer science, the natural sciences, and in other areas. I give an example of when a graph might be useful, and try to clarify when it may not be useful.
After graphs, we go to a specific subset of graphs, called trees. Whereas a graph can look like a spider’s web, or a grid of streets, all trees look very similar - much like a family tree or an org chart of a large company. I discuss when and why trees are appropriate.
Finally, we discuss computational complexity and algorithm analysis. These topics come up frequently when writing code to solve interesting problems. Computational complexity theory is the study of classifying problems by their complexity (in terms of run time, memory used, etc). Algorithm analysis is concerned with finding the amount of time, memory or other resources needed for an algorithm, usually as a function of the size of the input. Together, these tools allow for structured reasoning about the complexity of problems, and what problems are feasible or unfeasible, given our current understanding and current hardware. Interestingly, “hard” math problems that can not be solved by our current computing resources are actually the foundation for secure internet communication - cryptographers rely on what are called trap-door functions to create secure encryption algorithms.
I hope you all enjoy the episode, and I will talk to you soon!


Just as we had higher order derivatives with functions of one variable we will also have higher order derivatives of functions of more than one variable.
complex number z^2 = i-1? | Yahoo Answers
Download GPU-Z 2.16.0 - softpedia.com
The standard normal distribution is a normal distribution with a mean of zero and standard deviation of 1.Paramount Pictures has announced the released date for the follow up to the 2013 apocalypse thriller World War Z, which starred Brad Pitt as a family man recruited to prevent the zombie apocalypse.
Another Road also known simply as Shin Budokai 2 is the second Dragon Ball Z release on the PSP.Here are all the two-letter words and three-letter words that are acceptable for use in Scrabble(R).
Math 21a Graphs in Space Spring, 2009
Dragon Ball Z - Shin Budokai 2 (Europe) ISO < PSP ISOsIf you noticed there are two z-tables with negative and positive values.
22561 - Testing the equality of two or more proportions
Comparing Two Proportions | STAT 414 / 415If a z-score calculation yields a negative standardized score refer to the 1st table, when positive used the 2nd table.Consequently, the p-value for the two-sided Z test is the same as for the chi-square test.
Distributions and Probabilities - StatPacZ-test for testing equality of variance is used to test the hypothesis of equality of two population variances when the sample size of each sample is 30 or larger.Found 50 2-letter words with Z for Scrabble, Words With Friends, WordHub, and Crosswords.
Browse this comprehensive list of two-letter words with Z to find your best possible play.
World War Z 2 Writer Teases New Storyline For SequelThese changes should revolutionize scores, making the Q and Z much easier to play.The team at A two Z Windows and Doors Calgary knows you want a trusted partner who will walk you through every step and take care of the little details.
Solutions for assignment 3 - UCLA
Normal Distribution Problems with Solutions - analyzemath.com
Tangent Planes and Normal Lines - LTCC OnlineHow do you find the two numbers by using the factoring method, if one number is seven more than.
Math 21a Gradients & Level Surfaces Spring, 2009
Plants vs. Zombies™ Garden Warfare 2 - Official SiteFor some reason your suggested change could not be submitted.A one-tailed probability is used when your research question is concerned with only half of the distribution.
SYSTEMS OF EQUATIONS in THREE VARIABLES
The time taken to assemble a car in a certain plant is a random variable having a normal distribution of 20 hours and a standard deviation of 2 hours.I have included the TWL (Tournament Word List), a standard North American list which is used by a lot of online Scrabble-type sites, followed by the more extensive international SOWPODS list.When this is the case, we write and solve a system of equations in order to answer questions about the situation.
Statistical Tables t Distribution - Department of StatisticsWe can define a new function F(x,y,z) of three variables by subtracting z.This article describes the formula syntax and usage of the Z.TEST function in Microsoft Excel.Here we assume that we obtained a sample mean, x and want to find its p value.
Click below to download the free player from the Macromedia site.It is the probability that we would obtain a given sample mean that is greater than the absolute value of its Z-score or less than the negative of the absolute value of its Z-score.For a given hypothesized population mean, x, Z.TEST returns the probability that the sample mean would be greater than the average of observations in the data.The Z-transform can be defined as either a one-sided or two-sided transform.


Sensorial exercises are designed to isolate and sharpen each of the five senses and heighten the child’s sense of spatial relationships. The materials have a built in control of error enabling the children to correct their own mistakes. Some of the sensorial activities include the Tower of Cubes, trinomial cubes, binomial cubes, geometric solids, and sound boxes.
Montessori students may choose what they would like to work with each day. There are many items of work out on the shelves, each carefully arranged and in the kept in the same place every day.
A Montessori student shows how to choose and use the work in the classroom properly.


- Invariant Bayesian Inference in Regression Models that is robust against the Jeffreys-Lindleys Paradox
- Journal of Econometrics
- Volume | Issue number
- 123 | 2
- Number of pages
- Document type
- Faculty of Economics and Business (FEB)
- Amsterdam School of Economics Research Institute (ASE-RI)
We obtain the prior and posterior probability of a nested regression model as the Hausdorff-integral of the prior and posterior on the parameters of an encompassing linear regression model over a lower-dimensional set that represents the nested model. The Hausdorff-integral is invariant and therefore avoids the Borel-Kolmogorov paradox. Basing priors and prior probabilities of nested regression models on the prior on the parameters of an encompassing linear regression model reduces the discrepancies between classical and Bayesian inference, like, the Jeffreys-Lindley's paradox. We illustrate the analysis with examples of linear restrictions, i.e. a linear regression model, and non-linear restrictions, i.e. a cointegration and an autoregressive moving average model, on the parameters of an encompassing linear regression model.
- go to publisher's site
If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library, or send a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible.


Descriptive Statistics means describing the main features of a data in a quantitative manner. It is summary of sample and observations. These summaries are summary statistics or easy to understand graphs. There is a big difference between descriptive statistics and inductive statistics. We can say that descriptive Statistics is used to shrink the sample size or in other words it can be used to summarize the sample. Hence, we can say that the basis of descriptive Statistics is not probability. When a data is presented in a conclusive manner the descriptive Statistics are also presented with the inductive statistics. To illustrate this we can say that, if we want to conduct a population survey there is basically table which has the sample size, demographic area, clinical characters like age, proportion of sex etc. The measures used for description of data are of central tendency. These measures include the mean, the median and the mode and measures of dispersion include standard deviation, kurtosis and skewness. For example runs scored in cricket is a descriptive Statistics that gives us a summary about the game or the player as a whole. This number is calculated as follows: Number of runs scored by a player/total number of runs scored by the team.
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Elucidating the genetic code
is a postdoctoral fellow at the Ontario Institute for Cancer Research, working on computational deconvolution of tumour gene expression profiles. He has become involved in Software Carpentry through the UK's Software Sustainability Institute. His research interests are in scientific computing, specifically in computational inverse problems, numerical linear algebra, and the numerical solution of PDEs.Jaime Ashander is a population biologist who develops theory on the consequences of trait change for population dynamics, and methods to infer population processes from genomic and phenotypic time series. Camille Avestruz is a Ph D candidate and NSF Graduate Research Fellow in the Physics Department at Yale University.
is a Data Scientist at Fino Consulting in NYC, where he applies statistical and machine learning approaches to projects in the education and energy sectors.
He was always interested in science so he wound up becoming a full time researcher in particle physics, and has recently transitioned to the field of data science.
is a Ph D student at the University of Queensland working on vaccine target identification from the genomes of Streptococcal fish pathogens.
is a computational biophysicist who uses modeling and simulation to understand how proteins move small molecules across the cell membrane. in Biophysics at the University of California, Berkeley and is currently a Research Assistant Professor in the Department of Biological Sciences at the University of Pittsburgh.
He is one of the core developers of the open source, Weighted Ensemble Simulation Toolkit (WESTPA) and spends most of his days building computational tools and crunching data for the good of science using python. works at the intersection of applied mathematics, software engineering, and application domains as diverse as adaptive optics, semiconductor lithography, and ice-sheet modeling.


If I was meeting with Ingrid's grandmother I would first start off with the positive. I would let her grandmother know that she did a great job on her social studies, science and reading comprehension scores. We would talk about how these subject areas are where Ingrid really shines.
I would then address math concepts where Ingrid scored as average. I would discuss how she is preforming in the class in math concepts and let her know that we will work to keep Ingrid at this level as well as improve in this subject area.
We would then talk about spelling and math computation, where Ingrid tested at below average. I would let Ingrid's grandmother know what we will be doing in the classroom to help Ingrid improve those scores. We would also review how Ingrid was doing in my class with these concepts to make sure that she was not just having a problem with standardized testing. I would also suggest working an extra 15 minutes a day at home on these concepts. I would refer her to this website http://www.kidsspell.com/ where Ingrid could play games on the computer to help with her spelling. This would be a fun website for Ingrid to practice her math computation skills. http://www.coolmath4kids.com/ I would emphasize to Ingrid's grandmother to try to work practice in without overwhelming the student. I would let her know that I will be monitoring her progress and communicating with her regularly.


Theory behind Harmonic Pattern Detection techniques
Harmonic patterns have very strong connection with Fibonacci numbers and Elliot Wave theory. Fibonacci numbers are much simpler than Harmonic Patterns. Harmonic Pattern uses more rigid rules in identifying the trend reversal patterns than Fibonacci number. Naturally Harmonic Patterns have more predictive power than simple Fibonacci numbers. Elliot Wave theory is much more complex for average traders. Elliot Wave theory suffers a lot from subjective counting rules and it is very difficult to apply in real trading environment. Harmonic Pattern Trading strategy can serve very well for both beginners and sophisticated traders in any financial markets. They are profitable if properly used.
The most widely used research method behind Harmonic patterns are the ratio and frequency studies. Unlike other quantitative description such as mean, standard deviation or median, ratio is insensitive to the scale. Therefore, both large pattern and small patterns can occurs under the same pattern category. The frequency is the key metrics determining the significance of the patterns from historical study. The frequency studies on various financial markets including equity, forex and future showed that several patterns are very strong trend reversal indicators. At least, couple of dozens of such patterns were reported officially and unofficially. However, not all the patterns have equal predictive powers.
Our Harmonic Pattern Detection Software including Harmonic Pattern Plus and Scenario Planner can detect 11 Harmonic Patterns with most predictive power including:
- Alternate Bat
- Deep Crab
- 5-0 patterns
- 3 Drives pattern
Pattern Matching Error and Pattern Matching Accuracy
As harmonic pattern detection and statistical geometric pattern detection share a lot of common knowledge, we uses some established concepts from statistics, econometrics and other financial theory for our harmonic pattern software. Firstly we introduce the concept of pattern matching error. The pattern matching error is the error or difference between the detected pattern and the reference pattern in the text book. The pattern matching error simply represent how closely the detected patterns are matching to the reference pattern in the text book. Some traders might doubt why we don’t introduce the reverse concept of pattern accuracy (pattern accuracy = 1 – pattern matching error) instead of pattern matching error. Simply speaking, it is because it is the industrial standard to report the error than accuracy in many financial and statistical organization. But the difference between pattern matching error and accuracy is none. You need to get used to convert pattern matching error to pattern matching accuracy for your financial trading.
There are many error metrics or loss function can be used for pattern matching error for harmonic patterns including MSE (Mean Squared Error), RMSE (Root Mean Squared Error), MDE (Mean Absolute Error), MAPE (Mean Absolute Percent Error). We list some of common error functions for your better understanding:
To provide the universal measure of pattern matching error regardless of pattern types and their size, we uses MAPE (Mean Absolute Percent Error) in our Harmonic Pattern Software. To help more clear understanding of our users, we present full formula for our pattern matching error, MAPE:
As the pattern matching accuracy is equal to 1 – pattern matching error, Harmonic pattern with smaller MAPE represents the cleaner and more beautiful pattern. Both our Harmonic Pattern Plus and Harmonic Pattern Scenario Planner will report MAPE to traders. Traders can use this MAPE metrics to fine tuning entry and exit timing for their trades. Also remember that both Harmonic Pattern Plus and Harmonic Pattern Scenario Planner have the ability to reply historical pattern from your charts for your complete strategy development.
Pattern Matching Accuracy vs Success Rate
One common mistake for traders is to take pattern matching accuracy (= 1 - pattern matching error) as success rate of the pattern. This is quite misleading and traders must not confuse between pattern matching accuracy and success rate. Pattern matching accuracy represents how closely the detected pattern are matching against the reference pattern from the text book. Pattern matching accuracy will tell you how much the shape of the detected patterns are like the reference pattern traders know. Normally the detected patterns are expected to have MAPE less than 10%. However, we often observe that some patterns are as ugly as having MAPE 25%, but they still have quite good predictive power.
On the other ends, Success rate represents how many times the patterns were successfully predicted the trend reversal in historical data. The success rate is highly subjective to pattern itself. For example, Shark pattern and butterfly pattern have different success rate. Our harmonic pattern software is well designed for you to study the success rate of each patterns and to improve your trading skills. Although we have pointed the difference between patterns matching accuracy and success rate by their definition, both also have strong connection too. For example, you will less likely to make a mistake in your trading when you spot the patterns with smaller MAPE in your charts. Because the pattern with large MAPE might indicate that the pattern is still immaturely formed, therefore the price might continue to move in the trend direction instead of tuning.
Further note on Pattern Matching Error and Accuracy
As we described, there are quite bit of mathematics used to describe how closely the detected harmonic patterns are matching against the ideal patterns. We did it by taking industrial standard approach. For professional traders and investors, this can be very usual things they come across in their trading floor everyday. Although there are little bit of theory to digest, traders are not necessarily need to know the math behind our pattern detection theory. Therefore, our harmonic pattern software can be used for any level of traders including beginners. So feel free to give a go with our harmonic pattern software. Traders just need to know that smaller MAPE (%) for the detected pattern indicates that the detected pattern is more close to ideal or perfect patterns from the text book.


Normal quadratic equation is a 2nd-degree polynomial and the equation for a straight figure 4: a linear and an exponential model fit to the same x y data. In this section we will look at solving exponential equations and we will won't work because we don't know how to write 9 as a power of 7. And so forth, where is the taylor polynomial of the degree n for the exponential function at we show the graphs of the exponential function along with the first. Deciding polynomial-exponential problems, published by acm 2008 article power series and linear difference equations sergei a.
Linear, polynomials, exponential, and power functions linear, polynomial, and exponential functions polynomial functions have the best continuity properties. Functions exp (f(x)) by differentiation, or by expanding the exponential into a power where ci(n) is a polynomial of degree n in r with integer coefficients, and. Linear, polynomial (degree =2) and exponential are by far the most common used growth rates for incrementals the reason is that they.
Some of the most famous rules of the calculus of derivatives: the power rule, the sum rule, the constant multiple rule, and the number e defined. This article is complete as far as it goes, but it could do with expansion, in particular: it seems that the proof would apply to x k , x ∈ r without. The degree (for a polynomial with one variable, like x) is: the largest exponent of that variable polynomial more examples: 4x, the degree is 1 (a variable.
This is an extremely brief, and perhaps poorly done, explanation of how to do the basic power rule for derivatives as well as the derivative of. Regard the exponential function as the unique solution to the initial value problem f the main reason why the exponential grows faster than a polynomial is. The function p(x) = x3 is a polynomial here the “variable”, x, is being raised to some constant power the function f(x)=3x is an exponential function the variable.
Fit exponential models in curve fitting app or with the fit function curve fitting app creates the default curve fit, polynomial change the model type from. Cannot be computed in time exp(o(n)), and the same is true for computing the number of all out the existence of polynomial-time algorithms under standard complexity-theoretic loops then p(x) = pergx is a polynomial of degree d ≤ n. Using the duality between polynomials and formal power series, we first show how decomposition of polynomial-exponential functions from values finally, we. How do you calculate power, exponential, root, polynomial, logarithm and linear values and how do you convert trigonometric functions into.
Using excel in calculations with the exponential function 1 parabolas we call polynomials of the second degree parabolas or quadratic functions one can. Exponential growth dominates polynomial growth we prove here that lim xao xe bx=p ror any a pand b 1 for example, lim xao x100000000. Free exponential equation calculator - solve exponential equations step-by-step.


Operators are symbols that perform operations on variables and values. Based on the class of operator used, they can be adapted towards different applications.
Arithmetic operators are used to perform simple arithmetic operations.
||computes remainder||5%2 =1|
||floor division (will not return floating point numbers||5//2= 2|
x = 5 y = 7 z = x + y print(z)
Comparison operators are used to check conditions and compare two numbers or variables.
||Checks if two numbers are equal||x == y|
||checks if two numbers are not equal||x != y|
||checks whether a number is less than another||x < y|
||checks whether a number is greater than another||x > y|
||checks whether a number is less than or equal to another||x <= y|
||checks whether a number is greater than or equal to another||x >= y|
x = 5 y = 7 if (x<y): print('Y is greater')
Assignment operators are used to assign a value to a variable.
|=||a=8||a is assigned the value of 8|
|+=||a+=8||this is useful in case of an iterative operation; similar functions can be defined for other arithmetic operators|
x = 5 x += 10 print(x)


Quiz To Drive you Mad (Answers here) (U)
1) Some months have 30 days, some have 31. How many months have 28 days?
2) In the USA a man gave one son 10 cents and another son was given 15 cents. What time is it?
3) If you had only one match and entered a room in which there was a kerosene lamp, an oil heater, and a woodburning stove, which would you light first?
4) There is a house with four walls. Each wall faces south. There is a window in each wall. A bear walks by one of the windows. What color is the bear?
5) Is half of two plus two equal to two or three?
6) Do they have a 4th of July in England?
7) How many animals of each species did Moses take aboard the Ark with him?
8) How far can a dog run into the woods?
9) What is the significance of the following in the USA: The year is 1978, thirty-four minutes past noon on May 6th.
10) Is it legal in California for a man to marry his widow's sister?
11) If a farmer has 5 haystacks in one field and 4 haystacks in the other field, how many haystacks would he have if he combined them all in the center field?
12) What is it that goes up and goes down but does not move?
13) I have in my hand only 2 US coins which total 55 cents in value. One is not a nickel. What are the coins?
14) A farmer has 17 sheep. All but 9 died. How many did he have left?
15. Divide 30 by 1/2 and add ten. What is the answer?
This quiz reprinted from here: http://www.angelfire.com/blues/zahidhomepage/


Outgoing Erasmus+ Student Mobility for Studies 2 semesters (1st Cycle studies, 2nd Cycle studies, 3rd Cycle studies): Natural sciences, mathematics and statistics(ISCED 05)
NB! Please verify that the mobility direction is correct before you apply.
|Academic field||Natural sciences, mathematics and statistics (ISCED 05)
|Type||Erasmus+ Programme Countries (2nd cycle studies, 3rd cycle studies), 2 semesters|
|Nominal duration||~10 months|
|Study language||combined English/Italian|
2nd Cycle of studies
studia trzeciego stopnia
English / Italian B1
A motivation letter must be added to your application.


Redskins. That's how many.
1.84269 x 631694.853 / square root of half a banana = a lot?
if i'm in the tent, none. i would eat them all. yum.
how big is the tent? are these jumbo or mini marshmallows? are we accounting for mallow squishing? argh. I hate math. Lets just eat s'mores instead.
as many as the licks it takes to get to the center of a tootsie pop
Depends on the size of the tent and the marshmallow. For example, the Stay Puft Marshmallow Man probably can't fit into a tent of any size.I really like Ghostbusters.
What Tim said.
I think the correct answer is 26-24 marshmallows in Texas stadium. Booyah bitches.
That almost sounds like the dirtiest question ever.
The question is flawed as you haven't defined any of the criteria necessary! Let's see if I can help you out some. I think the original question was if you could fit a ton of marshmallows in a 10x10x5' tent wasn't it? Do I really need to break down the math like I did on Saturday night over the camp fire? ;)
At least 5 marshmallows.
i still think we should call kraft and conduct an experiment. then we can have the largest s'mores making/eating party ever. a dream come true. who's with me?or maybe we should just ask the cows, cows, cows in a truck. i bet they know.
Is this like one of those jellybeans-in-a-jar guessing games? Where if you guess the right number to get all the jellybeans?! Whoever wins better stock up on graham crackers and chocolate.
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November 23rd is Fibonacci Day, an annual holiday that honours one of the most influential mathematicians of the Middle Ages - Leonardo Bonacci.
November 23rd is celebrated as Fibonacci Day because when the date is written in mm/dd format (11/23), the digits in the date form a Fibonacci sequence.
One of the beauties of the Fibonacci sequence is that the series is evident all over the natural world. Petal arrangements in flowers, the ordering of leaves in plants, the shell of the nautilus, the DNA molecule and even hurricanes show patterns that correspond to the sequence.
1, 1, 2, 3, 5, 8, 13, 21, ...
To celebrate the day in school we will have lessons about the sequence in maths. In art, students will learn how the golden section and the Fibonacci numbers are evidenced in works of art. In music students will look at how the keys on the piano link to the Fibonacci numbers. Around school there is also a Fibonacci hunt, with a prize draw for students who find the first 8 terms of the sequence. With the challenge of finding any teachers that have a room number that is part of the Fibonacci sequence.


Explore STEM During Spring Break
Are you a student in grades 3-12 who is interested in Science, Technology, Engineering, and Math? Do you have any free time during spring break? If so, the Purdue University Extension invites you to join them for two mornings of exploring STEM through hands-on stations!
Activities will include 3D printing, coding, robotics, circuits, construction sets, and much more!
Dates: March 31 and April 1
Time: 9:00 am - noon
Location: Hendricks County 4-H Fairgrounds
Cost: $25 for one child ($22 for second child, $20 for third child)
There is no cost for parents to participate with children.


CBM Calculator Description
Absolutely free utility to calculate your consignment volume (CBM) & weight according to expected container.
1. Easy to use windows interface
2. Maintain history of calculations
3. Exact volume calculation upto 6 decimal places
4. Graphical presentation of volume and weight
5. Dimensions can be used in following unit of measurements
CBM Calculator Screenshots
Screenshots are not available currently.
What's New in CBM Calculator 1.0.0
Release notes are not available currently.
CBM Calculator Requirements
No additional system requirements.


Welcome to 3rd Grade!
I am so excited you are in my class and I cannot wait to see what the year has in store for us! We will be reading a lot of books, learning new math concepts, doing experiments and learning all about the world around us!
We will not be having spelling tests this year. Instead, we will be doing word work in our classroom every day. Note cards may be sent home each nine weeks to practice words you may be unfamiliar with.
The only other homework I assign is practicing your math facts. We will take multiplication quizzes throughout the year. Becoming fluent with your facts will help you with problem solving and prepare you for the 4th grade.


Math 111 - Trigonometry
This course is no longer offered. Talk to your academic advisor to see which course is the best option for you.
- To help students obtain basic trigonometric concepts by way of an integrated approach.
- To promote problem-solving and critical thinking skills through the application of trigonometric concepts to common situations.
- To enhance learning and understanding of trigonometric concepts through the integrated use of graphing calculators.
- To promote and utilize the “Rule of Four”: All concepts are explored algebraically, numerically, graphically and in context with applications.
PPL 50+ or MCLG 88+ or SAT I MSS 590+ or ACT MATH 24+ or Math 112 or Math 113.
The following course materials are required for Math 111:
- Pearson MyMathLab Access
- Graphing Calculator -- Certain models of graphing calculators are allowed, while others are forbidden. Information can be found here.


The Forward Kinematics for the left leg of the Quadbot have been formalised, using modified Denavit-Hartenberg parameters and axes conventions.
I also made a simple Python applet to verify the maths and visualise the leg’s poses. I used Tkinter and three Canvas widgets to show orthogonal views.
The reason I am testing the maths in a quick Python program is that I want to be able to port them easily over to Arduino, as my latest aim is to drop the Raspberry Pi and A-Star 32U4 LV Pi expansion module (shown in some of the latest CAD models) in favour of trying out an ArbotiX controller. A benefit with the latter is that I wouldn’t need a Dynamixel-to-USB converter (e.g. USB2AX) or separate motor power supply.
Next up will be to work out the Inverse Kinematics.
|2||pi/2||29.05||0||th_2 – 34|
|3||0||76.919||0||th_3 + 67.5|


The name ‘Sekolah Rendah’ for primary schools in the state should be changed or rebranded to create emphasis on the subjects of science, technology, engineering and mathematics (STEM).
Minister of Education, Science and Technological Research Dato Sri Michael Manyin said the word ‘rendah’ is a clear indicator of what the national education syllabus is doing to deprive students of interest in STEM subjects.
“During the formative years of a child, if we do not inculcate (in them) the interest (in STEM) and not teach them the right and proper way, it will kill their interest. This needs to be reversed,” he told a press conference after launching the state-level National Science Week 2018 at the Sarawak State Library (Pustaka Negeri) here yesterday.
He said if the interest in STEM subjects is already killed at primary school level, there is no way for a student to cope at the secondary school level.


Knowing Your Rate Of Interest Could Help You Save Cash
You need to know how your interest rate is calculated and understand how to calculate it yourself before you take out a bank loan.
There are many different practices banking institutions used to determine rates of interest, and every technique shall replace the number of interest you spend. You will better understand your loan contract with your bank if you know how to calculate interest rates. In addition will likely be in a much better place to negotiate your rate of interest.
When a bank quotes you mortgage loan, it is quoting what is called the effective interest rate, also referred to as the percentage that is annual (APR). The APR is significantly diffent compared to the stated interest rate, because of the effects of compounding interest.
Banking institutions might also connect your rate of interest to a standard, usually the prime interest. In the event your loan includes this kind of supply, your rate of interest shall differ, dependent on changes in this standard.
Determining Interest on a One-Year Loan
In the event that you borrow $1,000 from the bank for just one year and have now to pay $60 in interest for the 12 months, your reported interest is 6%. Here is the calculation:
Effective Rate on an easy Interest Loan = Interest/Principal = $60/$1000 = 6%
Your apr or APR is equivalent to the rate that is stated this example while there is no substance interest to think about. It is a easy interest loan.
Meanwhile, this loan that is particular less favorable in the event that you maintain the cash for the reduced time period. For instance, if you borrow $1,000 from the bank for 120 times and also the interest stays at 6%, the effective yearly rate of interest is significantly greater.
Effective price = Interest/Principal X Days in the(360)/Days Loan Is Outstanding year
Effective price on that loan with a Term of significantly less than One 12 months = $60/$1000 X 360/120 = 18percent
The effective interest rate is 18% as you just have utilization of the funds for 120 times in place of 360 times.
Effective Rate Of Interest for A discounted loan
Some banking institutions provide reduced loans. Discounted loans are loans which have the attention re payment subtracted through the principal prior to the loan is disbursed.
Effective price for a discounted loan = Interest/Principal – Interest X times within the 12 months (360)/Days Loan is Outstanding
Effective price on a loan that is discounted $60/$1 https://yourinstallmentloans.com/installment-loans-az/,000 – $60 X 360/360 = 6.38percent
As you can plainly see, the effective interest rate is greater on a discounted loan than for an interest loan that is simple.
Effective Rate Of Interest With Compensating Balances
Some banking institutions need that a business that is small for a company financial loan hold a stability, known as a compensating balance, making use of their bank before they’re going to accept financing. This requirement helps make the rate that is effective of greater.
Effective price with compensating balances (c) = Interest/(1-c)
Effective rate compensating balance = 6%/(1 – 0.2) = 7.5 % (if c is just a 20 % compensating balance)
Effective Rate Of Interest on Installment Loans
Many customers have actually installment loans, that are loans which are paid back with a group range re payments. Many auto loans are installment loans, as an example.
Unfortuitously, probably the most confusing interest levels that you are going to hear quoted on a financial loan is the fact that for an installment loan. Installment loan rates of interest are usually the interest rates that are highest you will come across. Utilising the instance from above:
Effective price on installment loan = 2 X Annual # of payments X Interest/(complete no. of re re payments + 1) X Principal
Effective rate/installment loan = 2 X 12 X $60/13 X $1,000 = 11.08per cent
The attention price about this installment loan is 11.08%, when compared with 7.5per cent in the loan with compensating balances.


In an era when the performance by American students in math and science lags behind the rest of the world, while those skills are becoming more important, it’s good to have a place to get your child the help they need. Now, Ann Arbor’s Vera Chiu and Grace Wang have opened a local franchise of Mathnasium, a California-based chain of math-only tutoring centers with a unique, effective approach to teaching. “We provide a tailor-made learning plan based on [students’] needs and what they know and don’t know,” says Chiu, who has a PhD in genetics from U of M. Mathnasium centers give a strong math foundation using a curriculum developed by educator Larry Martinek. Martinek’s approach is rooted in developing what Mathnasium calls “number sense,” which, as Chiu describes it, lets students “understand math not just mechanically, but conceptually.” Mathnasium offers programs for children from pre-kindergarten through high school. Students generally attend two or three times a week for about an hour, and receive one-on-one attention from an instructor. For children bored or intimidated by math, Mathnasium’s unconventional approach is just the ticket. “We have a lot of fun built into it,” Chiu says.
2111 Packard Rd., Ste. C. 734-769-5666. www.mathnasium.com


There are a whole load of lotteries available online for players of every taste and, when it comes to picking a favourite, U.S Powerball is up there for many. This game has been played since 1992! Famed for its sizable jackpots (the highest of which was an astounding $1.586 billion) it’s no wonder around 292,201,338 players turn up for at 10:12 PM every Wednesday and Saturday. If you’re looking to earn the big bucks, you certainly can’t get better than this, the world’s most exciting lottery.
As can be expected from a lottery which begins at $40 million, though, winning a lottery like this isn’t the easiest. In fact, to gain that much-coveted money, players must match five white balls out of 69, and one red Powerball out of 26. Those are extreme odds, hence why game organisers increase the jackpot by $10 million with every draw. The odds are all worth it if you win millions and millions of dollars.
Still it’s by no means an impossible goal, as some astounding winner stories attest. The best way to win is, of course, to play in the first place. Some top US Powerball players also use specific techniques, such as calculating due numbers, to increase their chances of a win.
While no one can predict a Powerball draw (if only), some theories do suggest that certain patterns appear in the balls which make it possible to at least increase the odds. By taking a look at the average historic number of draws for each Powerball number, then, some players attempt to foresee which are due. These are opposed to overdue or not due numbers, which are either rare picks or numbers which haven’t yet been drawn enough to warrant a noticeable pattern.
When it comes to US Powerball play at the moment, for example, due numbers are as follows -
Statistically, it's liable that each of these numbers is less than ten draws away from being drawn. If you're at a total loss as to which numbers to select for your next ticket, then, these could each be worth your attention.
Of course, this isn't the only way to predict how to pick lottery numbers for the upcoming US Powerball draw. Along the same vein, many players also rely on a hot and cold number system. This system also looks at the likelihood of drawing a specific number but from a slightly different angle. Instead of considering when a ball is next likely to appear, these players will consider how many times balls are drawn, and thus pick 'hot' numbers which appear more often.
Other methods include lottery prediction software and also avoiding multiples of numbers in one ticket. Die-hard players even devise their own mathematical formulas for success.
As anyone would expect, there's no official stance on whether methods like these work for getting players any closer to the desired jackpot. After all, the only guaranteed way to do that is to play in the first place!