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In this video, I talk about a simple rule that can be of immense help in understanding how advanced calculations work in Tableau – if you properly understand the Golden Rule, you are well on your own way to figuring out how any advanced table calculation or LOD calculation actually produces the result.
Here is the gist of the video:
Before you understand the Golden Rule, you need to understand one more fundamental idea that is crucial in the reporting world: Level of Detail or granularity.
We can understand Level of Detail of a report by comparing it to the level of detail we see on a Google Map as we zoom in and out. As we zoom in, we see more detail and as we zoom out, we see less detail – the same thing applies to a report/chart. As we add more dimensions, we see more detail and as we remove dimension, we see less detail. Hence, Level of Detail is nothing but the combination of dimensions on the report.
But what does a Dimension mean for the database? What does the database do when you add one more Dimension to your report?
For the database, Dimension are equivalent to Filters. As you add a Dimension, the database adds a Filter. If you have 3 dimensions on your report, then the database has to add filters on each of the 3 dimensions to calculate the value of a cell in your report.
Hence, here is the Golden Rule: For each cell/mark,
- Find the Filters i.e. Level of Detail
- Apply the Filters
- Then do the Calculation e.g. SUM
In one-line, it can be written as “Filters THEN Calculation“
From this video onwards, I am not going to be producing a text version immediately. It is difficult for me to find large chunks of time to produce the videos and to write the text version. But as I find time, I will come back and update the post to have the text version – for now it is only going to be videos. I hope you find them to be of value.


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I was so obsessed by this problem that I was thinking about it all the time - when I woke up in the morning, when I went to sleep at night - and that went on for eight years.
About Up Went
The definition of a good mathematical problem is the mathematics it generates rather than the problem itself.
Mathematics Mathematical Rather
Always try the problem that matters most to you.
Matters You Problem
I really believed that I was on the right track, but that did not mean that I would necessarily reach my goal.
Did Really Track
Pure mathematicians just love to try unsolved problems - they love a challenge.
But the best problem I ever found, I found in my local public library.
Library Public Best
However impenetrable it seems, if you don't try it, then you can never do it.
Then Never However
I don't believe Fermat had a proof. I think he fooled himself into thinking he had a proof.
I grew up in Cambridge in England, and my love of mathematics dates from those early childhood days.
Up Grew Early
I had this rare privilege of being able to pursue in my adult life, what had been my childhood dream.
Had Being Privilege
I loved doing problems in school.
Fermat said he had a proof.
Had Proof Said


Ok, the powerball lottery of tomorrow, Jan 13th, 2016. Some of the math has been already done here and there. So I was thinking another approach: Lets assume that a couple of Forbes-listed guys likes to play lotto in this favorable situation.
Think Gates and Buffet, or any of your preferred top ten or whatever corporations they own, or the corporations themselves (This is also considered by Andy Kiersz).
According numbers in “is-the-powerball-lottery-profitable“,
the total ticket cost is, at 2$ each number, $584M -$93.4 (prices) – $175M (self-jackpot) = 280M. And the jackpot price is 1.3 billion. Share between both players, it is still 650M
IRS tax is not problem for them, the corporations have an army of lawyers taking care of it, it is irrelevant for them, and same with other expenses as buying some lottery franchise, workers, management etc.
So should they play? Well, obviously yes if they are the only two players. They are still going to get $370M worst case. This is not very interesting.
What about two weeks ago, when the prize was only $528M? Sharing the price they get $264M, less than the cost of the, er, “ticket”. So they are into a sort of
snowdrift or chicken game, (or hawks, doves or whatever bird you like):
G Passes G buys ticket B Passes 0, 0 0, 248M B Buys 248M, 0 -16M, -16M
(the numbers come from the differences 528-280=248 and 264-280=-16)
With pure strategies there are two situations with Nash equilibrium: either (G Buys, B Passes) or the reciprocal. In such situations, nobody has
incentive to change his move. But this fact is not help to decide what to play, specially
in a situation without memory of the previous games.
There is also a mixed equilibrium. Consider the
mixed strategies where G and B decision of buying the game has a
probability p, q, respectively. So G’s expectation of benefit is
p(1-q) 248M – p q 16M
and if B sets his mixed strategy to q= 248/264 = 0.9394 then G’s expectation is
zero independently of q. And same exchanging the roles.
Warning: I have an issue here: if I want to look for evolutionary stable strategies, I’d think I should set p=q, differentiate the above expectation, and look for extremes, and then I get p=q=124/264=0.4697. Obviously this value of (p,q) is not a Nash equilibrium because one player can move p fully up to 1.0 and get a benefit from it. But it is better: in the long run it gets about 58M of benefit for each player in average, instead of zero. Cooperation emerging from symmetry?
So, should G and B just throw a random number and then decide to play only if this
number is less than 0.9429? At least it looks rational.
Does it get more interesting with more players? Not a lot more, because the realistic number of tickets sold is estimated to be equivalent to three or four billonaire players. Well, lets see For a 1.3B jackpot to be unprofitable, we
need at least five, so that 1300/5 – 280 = -20 < 0. Lets say we have
other three players from the top 20 (hey, looking at the list there are some
math-minded guys in fact: Brin, Page, Bezos… rational enough to proceed
via game theory :-). Regrettably the calculation of the mixed strategy
becomes more complicated: we need to consider five separate probabilities
and the fact that we have situation with zero to five people sharing
I think we could do a guess by assuming that the equilibrium solution sets everybody
to an expectation of zero losses (and zero benefit). This really works in the
previous case, setting p=q and asking p ( 248M – p *260M) = 0, but I am not sure about generalizing. Well, if we do, we ask
0= p^5 (1300/5 – 280)
+ 4 p^4(1-p) (1300/4 – 280)
+ 6 p^3(1-p)^2 (1300/3 – 280)
+ 4 p^2(1-p)^3 (1300/2 – 280)
+ p (1-p)^4 (1300 – 280)
to wolfram alpha, we see that there is only a root between zero and one:
p = 0.92857…
So the mixed strategy could be to play only if rnd() < 0.92857. Of course if the other four players adhere to this strategy, it is true that the extant player gets zero losses (and zero benefit) for any mixed strategy he chooses.
Again, consider two weeks ago, when we only had $528M in the jackpot. Then
0= p^5 (528/5 – 280)
+ 4 p^4(1-p) (528/4 – 280)
+ 6 p^3(1-p)^2 (528/3 – 280)
+ 4 p^2(1-p)^3 (528/2 – 280)
+ p (1-p)^4 (528 – 280)
I am not sure what those solutions mean. It is clear that if the players were able to
coordinate they could choose to form a cartel, only one of them playing each
week and thus extracting the same benefit but only at the cost of one “full ticket”. If
they are able to evolve to such understanding, this is a topic for
Evolutionary Game Theory. But then, as I said in the red warning above, we perhaps want to define stability from the derivative of the expectation function across the diagonal.


2 edition of Synthetic geometry found in the catalog.
Robert Franklin Jolly
|Statement||by R. F. Jolly.|
|The Physical Object|
|Number of Pages||140|
In many modern expositions of synthetic geometry, Playfair’s axiom (John Playfair, –) is chosen as that postulate instead of Euclid’s parallel postulate Post Playfair’s axiom states that there is at most one line parallel to a given line passing through a given point. Originally published by Yeshiva University in and reissued by Dover Publications in , this may be the only book devoted solely to the history of analytic geometry. Within pages, it provides wide-ranging coverage of this theme.
to yield geometric ones, and vice versa. In geometry we get at the properties of the conic sections by means of the properties of the straight line, and cubic surfaces are studied by means of the plane. [Figure 1] FIG. 1 [Figure 2] FIG. 2 1/5(1). Thanks for A2A, George. However first read a disclaimer: I've never been comfortable with Euclidean geometry, and, actually, I had even dislike for this sort of math. So my geometric knowledge is fairly limited and lacking coherency. Moreove.
integration of traditional synthetic geometry, coordinate geometry, and transforma-tional geometry is seen throughout the text and students learn to appreciate the interdependence of those branches of mathematics. The intent of the author is to make the book of greatest service to the average student using thorough explanations and multiple. The book discusses elementary problems dealing with plane analytical geometry. The text presents topics on the axis and intervals on an axis and coordinates on a straight line. The book also defines what a rectangular Cartesian coordinates in a plane is, the division of an interval in a given ratio, and shows how to calculate the area of a.
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Synthetic Differential Geometry (London Mathematical Society Lecture Note Series Book Synthetic geometry book - Kindle edition by Kock, Anders. Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Synthetic Differential Geometry (London Mathematical Society Lecture Note Series Book ).5/5(1).
Projective Synthetic Geometry in Lady Frieda Harris’ Tarot Paintings and in A. Crowley’s Book of the Law Written by Claas Hoffmann. It was in when the English magician Aleister Crowley wrote the the Book of the Law.
It was dictated by a praeter-human intelligence calling itself. Synthetic geometry is the kind of geometry for which Euclid is famous and that we all learned in high school. Modern synthetic geometry, however, has a more logically complete and consistent foundation. In this chapter the pattern of this foundation will be adapted, informed by the previous physical considerations, to develop a synthetic system File Size: KB.
item 3 Elementary Synthetic Geometry by George Bruce Halsted (English) Hardcover Book F - Elementary Synthetic Geometry by George Bruce Halsted (English) Hardcover Book F.
$ Free shipping. No ratings or reviews yet. Be the first. Genre/Form: Sayings: Additional Physical Format: Online version: Jolly, R.F. (Robert Franklin), Synthetic geometry. New York, Holt, Rinehart and Winston . Calculus And Analytic Geometry - Free download Ebook, Handbook, Textbook, User Guide PDF files on the internet quickly and easily.
What is synthetic geometry. Could you provide a short (i.e. a paragraph or two, not much longer) explanation in general elementary terms. In particular, I hope to be able to understand the contrast between synthetic and analytical (invariant-theoretic?) approaches in the end.
Wikipedia's definition is a bit too advanced for me. Get this from a library. Synthetic geometry of manifolds. [Anders Kock] -- "This elegant book is sure to become the standard introduction to synthetic differential geometry.
It deals with some classical spaces in differential geometry, namely 'prolongation spaces' or. Elementary Synthetic Geometry of the Point, Line and Circle in the Plane by Nathan Fellowes Dupuis, first published inis a rare manuscript, the original residing in one of the great libraries of the world.
This book is a reproduction of that original, which has been scanned and cleaned by state-of-the-art publishing tools for better. Parts of the book. Most of the basic notions of synthetic diﬀerential geometry were al-ready in the book; the main exception being the general notion of “strong inﬁnitesimal linearity” or “microlinearity”, which came into being just too late to be included.
A small Appendix D on this notion is therefore added. This is a book in the tradition of Euclidean synthetic geometry written by one of the twentieth century's great mathematicians. The original audience was pre-college teachers, but it is useful as well to gifted high school students and college students, in particular, to mathematics majors interested in geometry from a more advanced standpoint.
UCD Maths Support Centre Geometry and Trigonometry - Synthetic Geometry These videos are designed for both the Higher and Ordinary Level Mathematics courses, except the one with an asterisk, which is only designed for the Higher Level Mathematics course.
Axiomatic geometry is a modern phrase used to describe synthetic geometry, probably cooked up by some educator who didn't think that the term "synthetic" was a good choice, and wanted a more meaningful expression.
The link in the lead is actually correct in the following sense - the link is on axiomatic and should point to an article that talks.
The logical foundations of analytic geometry as it is often taught are unclear. Analytic geometry can be built up either from “synthetic” geometry or from an ordered ﬁeld. When the chosen foundations are unclear, proof becomes meaningless.
This is illustrated by the example of “proving analytically” thatFile Size: KB. In general, mathematical theories can be classified as analytic or analytic theory is one that analyzes, or breaks down, its objects of study, revealing them as put together out of simpler things, just as complex molecules are put together out of protons, neutrons, and example, analytic geometry analyzes the plane geometry of points, lines, etc.
in. Synthetic geometry definition is - elementary euclidean geometry or projective geometry as distinguished from analytic geometry. Official Book Trailer - " Geometry Problems. Solutions to "Geometry in Figures" by A.
Akopyan" or you just find Geometry exciting, this book might be just for you. This banner text can have markup. web; books; video; audio; software; images; Toggle navigation.
I am looking for a rigorous book on both 2d and 3d euclidean geometry, and also how analytic geometry can be developed from synthetic geometry. I haven't really found such a book yet. I would be very glad if someone could reference such a book.
upper level math. high school math. social sciences. literature and english. foreign languages. Find many great new & used options and get the best deals for Elementary Synthetic Geometry of the Point, Line and Circle in the Plane by N. F. Dupuis (, Hardcover) at the best online prices at eBay!
Free shipping for many products!Synthetic Geometry The original study of geometry is now called synthetic to distinguish it from the analytic geometry of coordinate systems, which developed much later.
In the area of synthetic geometry, the book focuses on the Pythagorean Theorem and on similar figures—figures that are stretches or shrinks of each other by the same factor in.Project Maths Strand 2 - Synthetic Geometry - Constructions The constructions listed below are prescribed by the Project Maths Syllabi with the relevant levels and certificates detailed on the left.
On the right are links (when viewed online) for video, animated and document resources to assist understanding and practice. C I d C C y JC Hi er File Size: 1MB.


This project required us to create a Grasshopper model that allows for parametric control of objects. I created a simple model that includes a geometry arranged on a grid, along with an attractor point that resizes the geometry.
I began by setting up a Square Grid and attaching sliders. The first slider controls the distance between grid points, and the second and third slider controls the number of rows and columns.
The next step was inserting a Distance variable, and this will determine the distance between the grid points and a floating point. This floating point was created in Rhino and linked in Grasshopper. Then I put in a Division variable which will cause objects near the attractor point to decrease in size.
The final step in the Grasshopper model was to define the geometry at each grid points. I inserted a Polygon definition that has the grid points and the attractor point variables. The polygon includes a slider plugged in to change the shape (number of sides) of the polygons.
Examples of final images created after baking the Grasshopper model and filling in the geometry in Adobe Illustrator.
13x13 grid, 3-sided geometry and attractor point in the lower left corner.
16x16 grid, 50-sided geometry (circle), grid spacing was condensed, attractor point in bottom right corner.


We follow the White Rose Mathematics Strategy at Woodlands, which is derived from the current National Curriculum.
Calculations are taught according to the Woodlands Primary Academy Calculation Policy, which has an emphasis on high expectations with most of the formal calculations experienced by the end of Year 4. We have a concrete, pictorial and abstract approach to Mathematics, which allows pupils to manipulate, number physically, moving on to drawing pictures and diagrams to represent their calculations before working in the abstract of number. This is a fluid approach allowing pupils to move back and forth, as their needs require, to help them grasp the fundamental conceptual understanding of Mathematics.
We have a strong emphasis on problem solving and reasoning at Woodlands with children focussing on the core calculations in their arithmetic sessions allowing them to explore maths deeply in their main Mathematics lesson. Our pupils are continuously challenged to prove or disprove key theoretical ideas in maths to allow them to fully engage with what they are learning. They are also expected to articulate their thoughts around core methods to demonstrate their understanding. As a result of this approach, Maths at Woodlands Primary Academy is full of energy, exploration and engagement.
Maths vision statement
At Woodlands, we believe the language of mathematics is universal. Our aim is to give our children the foundation blocks for opportunities in the future and to develop a secure subject knowledge, enabling them to apply it to reasoning, problem solving and real-life situations. This is delivered by developing a deep understanding of maths through a concrete, pictorial and abstract approach. Our approach to maths helps our children to embed a deeper understanding of maths as children understand what they are doing rather than just learning to repeat routines.
Our children begin their Maths journey in our Nursery where they begin to develop their mathematical thinking through play and exploration in a stimulating environment. In Reception the children continue to develop these skills with the addition of a formal maths lesson. Throughout the Reception year the children work towards the end of year Curriculum Goals (which are based on the Educational Programmes in the EYFS Statutory Framework) and are assessed against the Early Learning Goals at the end of the year. Through daily maths lessons, Years 1-6 experience the three aims in the National Curriculum (fluency, reasoning and problem solving) to develop their deepening understanding of a concept. As a result, our children develop a positive mindset and attitude towards maths and their confidence in maths shines through.
At Woodlands we use the White Rose scheme of learning and its supporting materials as well as other reputable resources. Children use Times Tables Rockstars at school and have the option to access it at home to reinforce their learning.
Staff are continuously assessing where pupils are and, through live marking, misconceptions can be addressed. Possible misconceptions are also identified when planning.
Our Maths Subject Leaders, Mrs Stubbins and Miss Jowett, are passionate about maths and can be contacted if you wish to find out more about our vision for maths at Woodlands.


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ü Understand ratios and rates
ü Apply ratios and rates in real-world and math problems
ü Add, subtract, multiply, and divide multi-digit numbers and decimals
ü Find common factors and multiples
ü Understand the meaning of fractions and be able to add, subtract, multiply, and divide fractions
ü Find the percent of a number
ü Understand the meaning of negative numbers and be able to locate them on a number line
ü Recognize opposite signs of numbers and understand them as having opposite values. Use in real-world contexts (e.g., temperature above/below zero, above/below sea level, credits/debts).
ü Understand ordering and absolute values of numbers
ü Graph coordinate points on a coordinate plane in all four quadrants
ü Recognize statistical questions to collect data. Display numerical data on a number line, including dot plots, histograms, and box plots. Summarize numerical data.
ü Use variables to represent two quantities in a real-world problem that change in relationship to one another, writing expressions and equations.
ü Generate and identify equivalent expressions applying properties, including the distributive property.
ü Solve one step equations.
ü Analyze the relationship between the dependent and independent variables in tables, graphs, and equations.
ü Find the area of triangles, special quadrilaterals, and polygons in real-world and mathematical problems.
ü Understand and find volumes.


Determine Your Odds regarding Winning the Lotto Mega Millions Powerball
Do know how to calculate chances of earning the lottery, including the Florida Lotto? You can compute each set regarding odds for each different lottery activity you play. Along with the assistance of any small hand placed calculator or with the free online car loan calculator on your personal computer, you simply multiply typically the numbers together plus add one division process when “the order” of the selected numbers is just not expected for a specific lottery game.
Exactly what you “need to be able to know” could be the range of total golf balls that the being successful numbers are attracted from….. would it be fifty nine, 56, 42, 49, or 39? If there is a new secondary drawing intended for the single additional ball, such as the “red ball” with Powerball or even the Mega Millions’ “gold ball” you need to know how many projectiles will be in this group too. Are there 49 or 39?
It doesn’t issue if it does not take California, Ohio, Texas, PENNSYLVANIA or NJ Lotto. This strategy or even formula gives you the actual odds. Florida Lottery is 6/53. New York Lottery is definitely 6/59. The Kansas Lottery, Massachusetts Lottery, Wisconsin Lottery, and the State associated with Washington Lottery hold a 6/49 lottery numbers ratio. Illinois Lottery includes a 6/52.
Once you have got this info Mua Vietlott Online qua App Zalopay correctly throughout front of you along with your calculator within hand, you can start functioning the formulas. You need to choose five regular tennis balls and another extra basketball correctly matched in order to the winning drawn numbers to succeed the multi-million dollar jackpot that a majority of involving us dream about winning someday.
Inside the first example there are 56 balls in the particular first group plus 46 balls throughout the secondary group. In order to be able to win the Lottery jackpot it is advisable to match almost all these balls (5 + 1) specifically, but not actually so as. The Florida Lottery’s Super Lotto Plus is 47/27. The big drum is definitely spinning with the particular initial section of the drawing. You have a 1/56 chance to be able to match your quantity to this 1st ball.
With a single ball removed following your first number have been drawn, you now have got a 1/55 chance of matching one other one of the numbers to typically the second ball attracted. With each attracted number a ball is removed cutting down the number regarding remaining balls by a total of one.
The odds of you properly matching the amount on the 3 rd ball to end up being drawn is right now 1/54 from your complete number of tennis balls remaining in typically the drum. With the third ball eliminated from the carol and sitting using the other two succeeding numbers, your likelihood of correctly matching the fourth ball is reduced to 1/53.
This is why each time the ball is launched from the drum the odds are usually reduced by one. You started using a 1/56 opportunity, then with every new winning quantity it is decreased to 1/55, 1/54, 1/53, and together with the fifth golf ball you have chances of 1/52 appropriately matching this 5th winning number. This can be the first part involving the mixture of how to calculate the odds of winning the lottery, including the Florida Lottery.
Now take these kinds of five odds symbolizing the five being successful numbers (1/56, 1/55, 1/54, 1/53, plus 1/52). The “1” on top of the fraction symbolizes your one and even only chance in order to correctly match the drawn number.
Today you in order to calculator and multiply all top numbers (1x1x1x1x1) equal one (1). Next you grow all the base numbers (56x55x54x53x52). Correctly entered and multiplied you discover the total is 458, 377, 920. The newest fraction becomes 1/458, 377, 920. This is a 458 million to one probability to win. In the event that you where required to pick the numbers within order just such as they can be drawn, in that case these would get the odds towards you to earn this Pick 5/56 ball lottery sport.
Fortunately or however, you aren’t required to pick the amounts in the actual order they are drawn. The other phase of the solution will reduce the particular odds, which enables you to match these five being successful numbers in virtually any order. In this specific step you are going to grow the number of balls drawn — five (1x2x3x4x5). Along with calculator in palm you see that this total equals a hundred and twenty.
To give you the right to choose your several matching numbers within any order, you create these chances by dividing 120/417, 451, 320. A person definitely need a calculator for this one. 120/458, 377, 920 drops your probabilities of winning this kind of lottery to 1/4, 819, 816. They are over 3. 5 million to one particular odds against you of winning this Pick 5/56 ball lottery game.
In case this were typically the Mega Millions Lottery, you need in order to add the “gold ball” to these types of five winning sketched balls as a way to get the Multi-Million Buck Jackpot. The only platinum ball is calculated as a 1/46 chance of corresponding it correctly, plus since you happen to be pulling just one amount it has in order to be an specific match. Again, you only have of which “1” chance to do it right. Today you should multiply 3, 819, 816 by 46.
Grab your calculator and do the multiplication. Your final chances against you succeeding the Mega Hundreds of thousands Jackpot are calculated to be a hundred seventy five, 711, 536 or clearly stated a hundred seventy five million, 711 1, 000, 5 hundred 36 thirty-six to one (175, 711, 536 to 1). You now know exactly how to calculate chances of winning the particular Mega Millions Lottery.
The Powerball Lottery calculations are based on a 1/59 for the 1st five white golf balls and 1/39 to the “red” power basketball. The first collection of multipliers is 59x58x57x56x55. This party totals 600, 766, 320. Now separate 600, 766, 360 by 120 (1x2x3x4x5). Your new total is 5, 006, 386. There is a 1/39 opportunity to catch the particular “red” ball. 39 x 5, 006, 386 gives an individual the true odds involving winning the Powerball Jackpot, namely 195, 249, 054 in order to 1.
Another five +1 Lottery that seems to get everywhere in the particular United states of america is the “Hot Lotto” which offers a 39/19 count number. It is enjoyed in 15 various States. DC Lottery, Delaware Lottery, Florida Lottery, Iowa Lottery, Kansas Lottery, Maine Lottery, Minnesota Lottery, Montana Lottery, New Hampshire Lottery, Brand new Mexico Lottery, Northern Dakota Lottery, Ok Lottery, South Dakota Lottery, Vermont Lotto, plus the West Las vegas Lottery. The last odds of succeeding the minimum $1 Million Jackpot is 12, 939, 383 to 1.
A Pick 6/52 ball Lottery game formula looks such as this: (1/52, 1/51, 1/50, 1/49, 1/48, 1/47) for some sort of total of fourteen, 658, 134, 4 hundred divided by 720 (1x2x3x4x5x6) for the odds of 1/20, 358, 520. Your possiblity to win the 6/52 Lottery is above 14. 5 thousand to one to earn, such as the Illinois Lotto.
The Hoosier Lottery that uses In State’s nickname, bears a 6/48. The state of michigan Lottery is 6/47, Arizona Lottery in addition to Missouri Lottery will be 6/44, Maryland Lottery is 6/43, plus Colorado Lottery will be 6/42. Compare this to the Sarasota Lottery.
A Go with 5/39 ball Lottery game formula looks like this: (1/39, 1/38, 1/37, 1/36, 1/35) for an overall of 69, 090, 840 divided by 120 (1x2x3x4x5) with regard to the odds of 1/575, 757 of being successful the Jackpot such as the Illinois Little Lotto. Various other States using the identical 5/39 lottery numbers include the NUMERICAL CONTROL Lottery, Georgia plus Florida Lottery Imagination 5, and Tennessee Lottery’s Pick a few. Virginia Lottery’s Money 5 carries a 5/34 range.


Special Session on "Advances in Single-Objective Continuous Parameter Optimization with Nature-inspired Algorithms"
Aims and ScopesSingle-objective continuous parameter optimization problems amount to find the minima (or maxima) of a scalar objective function which accepts a vector of real numbers as the argument. Such problems are ubiquitous in the diverse domains of science and technology. Most often in black-box optimization scenarios, the gradient information of the function is unavailable and the problem becomes even harder as the function possesses non-ideal characteristics such as non-convexity, ruggedness, ill-conditioning and so on. This makes the direct applicability of the mathematical programming methods infeasible very often. With the huge advancements made in computational resources over the past few decades, the field of nature-inspired algorithms for solving such problems has been growing at a spectacular rate now. Objective of this special session is to report the recent advances made in solving complex multimodal and multi-dimensional optimization problems (most often without any regular mathematical structure) with the application of swarm and evolutionary metaheuristics. Analytical studies on function features and landscape investigation are also welcome.
We encourage the prospective authors to test their proposed algorithms/algorithmic variants on the recently developed benchmarking suites for the IEEE CEC (Congress on Evolutionary Computation) competitions on real parameter optimization. The authors may also use a collection of real world continuous parameter optimization problems proposed for the CEC 2011 competition. Please see the following URL for further details: http://www.ntu.edu.sg/home/epnsugan/index_files/cec-benchmarking.htm. We also encourage the authors to validate their results through suitable (and preferably non-parametric) statistical tests.
Topics of Interest
Papers must present original work or review the state-of-the-art in the following non-exhaustive list of topics:
- Particle Swarm Optimization (PSO) and its advanced variants.
- Differential Evolution (DE) and its advanced variants.
- Covariance Matrix Adaptation Evolution Strategies (CMA-ESs).
- Artificial Bee Colony (ABC) and other honey bee inspired algorithms.
- Real coded Genetic Algorithms (GAs).
- Hybrid and memetic algorithms for continuous search spaces.
- Ensemble Strategies for Evolutionary Algorithms (see http://www.ntu.edu.sg/home/epnsugan/index_files/EEAs-EOAs.htm for some pioneering contributions).
- Parameter control and adaptation in evolutionary algorithms.
- Neighborhood-based search operators.
- Multi-population and distributed search techniques.
- Learning based techniques for continuous parameter optimization.
- Analysis of function features and fitness landscapes for continuous optimization problems.
- Swagatam Das, Indian Statistical Institute, India.
- P. N. Suganthan, Nanyang Technological University, Singapore.
- Janez Brest, University of Maribor, Slovenia.
- Roman Senkerik, Tomas Bata University in Zlin, Czech Republic.
- Rammohan Mallipeddi, Kyungpook National University, Republic of Korea.


"One small step for a man-one giant step for mankind" - Neil Armstrong
This S.T.E.M. lesson is designed to encompass many of the math skills the students learned throughout the school year. Students will also make connections and reflections on how rockets affect their daily lives. Students will build their own prototype rocket mostly from scratch. Most of our everyday life depends on rockets. Satellites were launched by rockets which send signals back to earth for our GPS systems, televisions, and cell phones. They even help send images back so we can predict the weather and see what countries are doing around the world. The model rockets are launched just like the real ones: with electrical ignition, a launching tower, countdown and recovery system.
"For every action there is an equal but opposite reaction." - Isaac Newton
PA Standards:M6.A.1.4.1: Model percents (through 100%) using drawings, graphs and/or sets (e.g., circle graph, base ten blocks, etc)
M6.B.2.1.1: Use or read a ruler to measure to the nearest 1/16 inch or millimeter.
M6.B.2.2.1: Find the perimeter of any polygon (may include regular polygons where only the measure of one side is given – same units throughout).
M6.B.1.1.1: Determine and/or compare elapsed time to the minute (time may cross AM to PM or more than one day).
M6.E.2.1.1: Determine/calculate the mean, median, mode and/or range of displayed data (data can be displayed in a table or line plot – use whole numbers only up to 2 digits).
M6.E.1.1.3: Display data in frequency tables, circle graphs, double-bar graphs, double line graphs or line plots using a title, appropriate scale, labels and a key when needed. Circle graphs for open-ended items must show a center point and tic marks.
M6.C.1.1.3: Identify and/or determine the measure of the diameter and/or radius of a circle (when one or the other is given).


Curtin Mathematics Research Scholarship
Applications accepted at any time
About this scholarship
Curtin University has a scholarship opportunity for a PhD student to participate in an ARC Future Fellow Project " Novel nonlinear functional analysis methods for singular and impulsive boundary value problems ". The project aims to develop innovative functional analysis theories and methods to study various complex nonlinear boundary value problems with particular focus on singular and impulsive problems. The PhD research students are expected to participate in the project with focus on nonlinear analysis and computational methods for some complex initial boundary value problems involved.
- Future Students
- Postgraduate Research
- Permanent Humanitarian Visa
- Australian Permanent Resident
- International students
- Australian Citizen
- New Zealand Citizen
- Merit Based
Maximum number awarded
The successful candidate will receive a stipend of around $25,500 per annum which will be indexed for the duration of the award. This scholarship shall be for three years with a possible maximum extension of up to six months.
If the successful candidate is an international student, the scholarship shall cover the tuition fees for the duration of the award.
Eligible students must have or expected to have:
- 1st class honours degree or equivalent level of attainment such as a Master degree
Conditions that need to be met to keep your scholarship
Satisfactory HDR annual progress
Changes to enrolment
Full time study only
How to apply
Expressions of interest are sought from applicants:
- with a background in mathematics or related disciplines;
- who have an interest in nonlinear functional analysis, applied mathematics, differential equations and their applications.
Please send your initial expression together with your CV via email to
Dr Lishan Liu , email L.Liu@curtin.edu.au
Prof YH Wu, email firstname.lastname@example.org
Need more information?
Please select base content


“I saw an opportunity to teach and train science, technology, engineering and math knowledge and skills through creative methods”.
Company : TalentS
Country : Saudi Arabia
Interest : Education & Exhibits
Selection Year : 2013
Partners : Saeed Saeed
Website : TalentS
About the company TalentS is working to improve the quality of science, technology, engineering, and math (STEM) education throughout Saudi Arabia. TalentS has developed creative, hands-on, and engaging methods for teaching STEM at robotics competitions and science fairs. The entrepreneurs are now applying their expertise to additional STEM-related learning opportunities, including managing STEM museums, designing exhibits, organizing corporate social responsibility events, and training teachers and students.


Jordan finds teaching to be extraordinarily fulfilling. With a keen interest in both English and mathematics, she enjoys being able to share her knowledge and skills with her students. What draws her to math is the opportunity for collaboration in this specific area, and the engagement that comes from working together to solve difficult problems and sharing attempted solutions to eventually piece together difficult and complex concepts. Her focus in English comes from a personal appeal to studying humanity and the human language through literature. She feels it is a subject that allows people to engage their creative mind in a way that still incorporates critical thinking.
Jordan is currently working toward a Bachelor of Science degree with a major in general math, and a minor in English. Her goal is to pursue further a degree in education, and plans to become an educator with a focus on both English and mathematics.


What are Math Mini Courses from A+ Interactive Math
Math Mini Courses are multimedia lessons, just like the primary math programs available through A+ Interactive Math, designed to teach a particular math concept in a coloring and engaging animated video lesson. The entire program is online, accessible through any computer via streaming. The lessons are interactive and contain quizzes and tests. Grading and tracking are automatic and within all the courses. Full text versions of the lessons are provided if you do not want to do them online and there are printable worksheet sand tests for extra practice and offline work.
There are 20 Math Mini Courses available to choose from and they are for all math levels beginning through middle school. Some of the math mini courses available include: Counting and Identifying Numbers (1st-3rd), Place Value and Number Combinations (1st-3rd), Elementary Geometry (1st-4th), Advanced Fractions (4th-8th), Measurements and Conversions (2nd-6th), and Percentages (5th-8th) to name a few.
How We Used Math Mini Courses
We received 2 math mini courses for our review – Time Math Mini Course and Money Math Mini-Course. We used both of these with our 1st grader. He likes online work so we thought this might be a good fit for him. He is doing a regular math program but we thought that an intensive review and deeper study of Time and Money would be good.
The Time Math Mini Course has 20 lessons and each is about 20 minutes long for us. There is a short, interactive lesson about what is being studied followed by questions to ensure understanding. The lessons cover topics like days, weeks, months, and year, converting time to day, weeks, months and years, the four seasons, second, minutes and house, converting time, digital and analog clocks, adding different units of time, and elapsed time.
You can read the full list of the course contents by clicking here.
The Money Math Mini-Course has 18 lessons and each is about 20 minutes in length. Each lesson is interactive and is followed by a quiz to test retention of the topic covered. The lessons covers topics in understanding the identity of the coins, understanding their worth, converting one set of coins into other likes nickels, dimes and quarters into pennies, counting coins up to a dollar, counting dollars and coins, comparing money, converting money into decimal points, making change, money games, family budging, calculating commission and sales prices, and interest rates. Some of the later topics seems a little advanced for my 6 year old but we will see how he does when we make it there. I am considering using this as a review for my 5th grader if advanced lessons in budgeting, commision and interest rates seem good.
You can see a complete course contents for the Money math Mini course by clicking here.
What We Thought of Math Mini Courses
My son liked the frog that was in each of his courses that you press to submit your answer and fireworks at the end of the lesson highlighting your grade. He really didn’t know if his grade was good or not because we don’t emphasize that a lot in our school at his age but he definitely liked the fireworks surrounding it.
I liked that, if the student misses a question they get a second chance to guess it in most cases and then, if they do not get it right, the explanation of the answer is provided in a teaching model on the screen.
The Teacher/Parent Dashboard is very intuitive and allows you manage your courses and your students. So, if you have multiple students doing different level mini courses, or even the full A+ Interactive Math course, you can manage it in the Parent/Teacher Dashboard. Then, for each student and each course you can view the interactive lessons with quizzes, view the lessons in pdf format, view printable worksheets and tests, view reports, parent/teacher controls, and a “how to get started” video.
I liked that you can check the reports and view each section that has been completed or what sections are in progress within the courses sorted by student. The Parent/Teacher Controls allows you to add extra time to your child’s test time, which I think is a great feature. You can check the scores on their worksheets or how many of the online quizzes they are getting right as well as view a cumulative average of their work within the course.
The student can view several of these charts within their dashboard as well, though mine didn’t really look at those. The person teaching the lessons has a pleasant voice that speaks slowly; however, I thought it was not very animated. I mean, like the voice inflexion wasn’t very dramatic so sometimes it seemed almost monotone, but this was only in places. My son didn’t seem to mind though. However, he did NOT like that the course asked questions within the interactive lesson but left very little time to answer out loud. So he would become frustrated because the “teacher” would say “Do you know what what the 12th month is?” then there would be a pause for an answer, but it was rarely enough time for him to think of the answer so he would get frustrated. I realize that they are trying to make sure that the lesson doesn’t take so long but maybe having the child pause to give the answer or giving a little more time would be good.
My son didn’t like doing the worksheets offline, but that is a nice option. He liked doing them online better. He made through the lessons fine, taking about 20 minutes per lesson unless he got stumped on something. I like that the lessons end so the student can work independently and knows when the lesson is over. However, it would be nice if the lessons became highlighted or checked off in the left sidebar instead of having to mark them at the top of the lesson. My son is not a good reader yet so he didn’t see this and it was confusing at first that he had completed a lesson but it wasn’t marked completed. I did like that if the lesson was completed (and you had marked it properly) and you clicked on lesson, a popup box told you you had done the lesson already.
I liked that these lessons are short, manageable, and available on a particular topic that might require a new way of presenting a topic or some extra work to grasp. I think this is a great way, and economical, to work on an individual math subject like fractions or percentages. I think this would be a very valuable supplement to any math program if the student needed some extra help and a fresh explanation for the subject.
Learn more about mini courses, which there are 20 available and range from $9.99-$19.99 per year per student, which is really quite affordable.
You can read my review, Filling in the Gaps with A+ Interactive, from 2015 on their Adaptive Placement Test and Individualized Lesson Plan and their 2nd Grade full curriculum review from 2013. And see what the rest of the TOS Review Crew had to say about the Math Mini Courses from A+ Interactive Math that they used by clicking the banner below.


New Ideas Into What Is Elimination in Math Never Before Revealed
The Basics of What Is Elimination in Math That You Will be Able to Learn From Starting Immediately
Understanding how to calculate proportions is a fundamental portion of our day-to-day lives! They include math difficulties and sums dependent on the extensive curriculum standards of each grade. The minimum grade is what I should find. When they finish, I’ll ask the class to analyze their work to find out if the students arrived at the exact answer. Math can be challenging but it isn’t hard. Some people wouldn’t be able accept that the subject Math is straightforward.
In math and in real life, when you’re working with decimal numbers, you will encounter an expression you may simplify. De Morgan’s laws stay valid within this Heyting algebra. Throughout many future lessons within this course for Linear Algebra, you will see that row reduction is among the most significant tools there are when working with matrix equations. write my essay Nevertheless, the true presence of the subject math is to earn things from complicate to simple. We’ve used many of these math symbols in some specific circumstance. Take a minute to refresh your Gaussian elimination skills if you should.
I believe your style is fine, and the algorithm looks nice and short. The new interface is fantastic and the extra functionality takes it to a brand-new level. I’m not considering the algorithm. You are just about to learn to address a system of equations using the elimination system. The substitution procedure is among the strategies to fix a system of linear equations. Within this lesson, you are going to learn a technique which can be utilized to fix all systems of linear equations.
There’s an endless number of solutions for this system. book review If you multiply all sections of the equation by the LCM, it doesn’t impact the solution. However, in addition, there are systems of equations which don’t have any solution. You may select three distinct varieties of problems where there’s no solutions, one solutions, or an endless number of solutions.
The point is that, within this format, the system is easy to fix. So there are 3 cases to look at. I will ask that every student solve the system with a different method. Such a system is known as inconsistent.
The Pain of What Is Elimination in Math
The question isn’t about how many more so it isn’t about difference. In rather simple word issues that relationship usually involves merely one of the four primary operations. This exponential equation enables us to locate your salary after any range of years at work, provided that nothing else alterations. And be sure you understand just precisely what the challenge is in fact asking for. This issue isn’t about the difference.
This number may be a suitable answer to a WeBWorK question. Provided that each step along the way is correct, you will develop the exact same answer. There’s a significant difference between believing and expecting. It is an easy matter to demonstrate that the summit angles are congruent.
It is all dependent on the expression. The elimination system is where you truly eliminate one of the variables by adding the 2 equations. Second-order elimination is called the E2 reaction.
That is the reason why it is essential that you comprehend what every one of these symbols is used for. The symbol or2 is called the Laplacian. You must multiply one of the equations by a number that lets you line up coefficients with the very same absolute value for a single variable. You’ve solved all your variables. This is called eliminating the variable.
The issue then becomes a linear equation with only one variable, that may be solved as described above. However, Richardson proved that there is not any algorithm to choose whether two closed-form expressions define the exact same function. Your like terms are the terms with a typical variable.
Want to Know More About What Is Elimination in Math?
A disadvantage when compared with the single-elimination format is that at least twice the quantity of matches need to be conducted. You should not presume that your mean is going to be one of your initial numbers. This observation calls for a different proof, but it’s simple enough. You will likely recognize quite a few of those. You’re going to be expected to understand the quantity of days in a calendar year, the variety of hours in every day, and other essential units of measure. Make certain that you work through them as a way to practice.
What Is Elimination in Math Secrets
If that is how it is, then matrix is reportedly in row echelon form. If they don’t cross, then we’ve got parallel lines, and there is not going to be any answer for x and y. To use the elimination method, you always need each equation arranged’ in the exact same way, so that if the equations are stacked in addition to each other, like terms wind up in the exact same column. Now utilize backslash and have a peek at the residual.
The element in the very first row of the very first column is 1, which differs from zero and then, it’s employed as a pivot. The final result is 0 iff a variety of the diagonal entries are 0. This can be accomplished by subtracting the exact first row from the second row. It’s feasible for the Championship finals to be set by only a single match in the event the W Bracket winner defeats the L Bracket winner. Add another column to the conclusion of the matrix.
The Appeal of What Is Elimination in Math
Please don’t hesitate to reach out to me in case you have any extra questions about this. To begin with, we’ll earn a critical note. If we would like to eliminate the x-term, we ought to make sure we have a constructive and a negative of exactly the same term.
This informative article explains a number of those relationships. This new software is really a help. We hope this page will be quite helpful to students who are attempting to find meaning of some symbols. Thanks for the use of this page.


Me and mathematics have never gotten along. Ever.
I have a condition called Dyscalculia. Dyscalculia is a learning difficulty in which the individual has difficulty with arithmetic, comprehending numbers, and learning numerical skills. To put it simply, it’s like having dyslexia, but with numbers instead of words.
In primary school, I realised that I saw mathematics differently to my peers. As they were furiously scribbling their workings and calculations on the sheet, I sat there for an hour on the first question. I couldn’t tell you that 10 was greater than 7. Why 675 looked like 657. Or, work out a percentage or fraction to save my life. I assumed that I was just terrible at maths; it was one of those things. After all, you hear people say they “can’t do maths” all of the time. But, I couldn’t help but feel stupid.
When it came to GCSE maths, it was even more of a struggle. At first, I put it down to my own efforts. Was I trying hard enough? Maybe I just need to revise more? I even went as far as getting a maths tutor. But, no matter how much my tutors/teachers tried to help me, how many past papers I did, how much practise I put in; nothing did the trick. It wasn’t until I saw an educational psychologist in sixth-form that I was diagnosed with Dyscalculia. I felt a great sense of relief; I finally had an answer.
Dyscalculia hasn’t only affected my academic career, but other areas of my life. Take driving for instance. It’s taken almost four years to learn to drive. That’s not because I’m a terrible driver (I’ve been told I’m a brilliant one!), but because it takes me longer to grasp things. It’s also affected jobs, especially when it comes to handling money. There are times when I’ve been ridiculed and humiliated by others because of my Dyscalculia, but I haven’t let it stop me. It’s just about finding a way that works for you.
Having Dyscalculia doesn’t make you stupid. I achieved 3 A*’s at A-Level, I’m doing a degree I adore, I won Student of the Year in my First Year, and I’ve stepped into my dream job. I’m living proof that anyone can do it!


Emmeke Aarts published her paper on statistical solutions for the analysis of dependent data in Nature Neuroscience.
In neuroscience, experimental designs in which multiple observations are collected from a single research object (for example, multiple neurons from one animal) are common: 53% of 314 reviewed papers from five renowned journals included this type of data. These so-called ‘nested designs’ yield data that cannot be considered to be independent, and so violate the independency assumption of conventional statistical methods such as the t test. Ignoring this dependency results in a probability of incorrectly concluding that an effect is statistically significant that is far higher (up to 80%) than the nominal α level (usually set at 5%). We discuss the factors affecting the type I error rate and the statistical power in nested data, methods that accommodate dependency between observations and ways to determine the optimal study design when data are nested. Notably, optimization of experimental designs nearly always concerns collection of more truly independent observations, rather than more observations from one research object.


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A 8000kg engine pulls a train of 5 wagons, each of 2000kg, along a horizontal track. If the engine exerts a force of 40000N and the track offers a friction force of 5000N, then calculate:
(a) The net accelerating force:
(b) The acceleration of the train; and (c) The force of wagon 1 on wagon 2.
Answer Open The Answer In App
Given : Mass of engine M=8000 kg Mass of each wagon m=2000 kg Frictional force acting in backward direction f=5000 N (a) : The net force acting on the train F ′ =F−f=40000−5000=35000 N
(b) : Let the acceleration of the train be a ∴ F ′ =(5m+M)a 35000=(5×2000+8000)a ⟹a=1.944 ms −2
(c) : External force is applied directly to wagon 1 only. The net force on the last four wagons is equal to the force applied by wagon 2 by wagon 1. Let the acceleration of the wagons be a ′ 35000=(5m)a ′ ⟹35000=10000×a ′ Acceleration of the wagons a ′ =3.5 ms −2 Mass of last 4 wagons m ′ =4×2000 kg ∴ Net force on last 4 wagons F 1 =8000×3.5 =28000 N Thus force on wagon 2 by wagon 1 is 28000 N.
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When you play Online Slot, the game relies on the random number generator (RNG) to determine the results of each spin. The RNG constantly selects numbers between 0 and 4 billion per second. When you press the ’spin’ button, the software finds a random number that corresponds to the order of symbols on the reels at the moment of the spin. The math module in the game software then translates this into a result that is displayed on the screen. This process is also monitored by gambling regulators to ensure that players cannot manipulate the outcome of a spin.
In the past, there were slight chances of tricking slot machines by tracking the order in which the machine displayed symbols or manipulating the lever. However, this is not the case anymore as modern slots are programmed to be completely random. Moreover, the RNG used by online casinos and mobile apps is tested by independent laboratories to ensure their fairness.
There are many different types of Online Slots available to players, ranging from simple and basic video slots to branded ones based on popular movies, television shows, games or sports teams. Many of these games have varying paylines, jackpot sizes and maximum winning amounts. Players can increase their odds of winning by playing with all paylines activated.
Another way to maximize your win potential is by playing a progressive slot. These slots feature a jackpot prize that grows every time someone makes a bet. This prize can be triggered in various ways, including through the winning of a bonus feature or the scatter symbol.