On Twitter and Reddit, calls from students to #rescoreJuneSAT
After Campbell Taylor scored a 1470 on the SAT in March, the rising senior knew he was just 20 points shy of the score he needed to qualify for a top scholarship at Mississippi State University - his first-choice for college.
So the 17-year-old resolved to take the test again in June and spent the intervening months buried in SAT preparation books and working with tutors. Taylor awoke at 7:30 a.m. Wednesday and checked his latest score online. The results were disappointing: He received a 1400.
He missed one more question overall in June than in March but his score, he said, dropped precipitously. And in the math portion of the exam, he actually missed fewer questions but scored lower: Taylor said he got a 770 in March after missing five math questions but received a 720 in June after missing just three math questions.
Other high-achieving high school students faced the same conundrum when results of the June SAT were released earlier this week - their scores were lower than previous results, despite missing the same number of questions or even fewer. They’ve taken to Twitter and Reddit, arguing the scale used to score the June SAT was unfair and could jeopardize students’ scholarship or college admission prospects and may force many to pay another registration fee to retake the exam.
Taylor broadcast his gripe on Twitter, posting on Wednesday: “I, along with thousands of other high school students have been cheated out of a rightful SAT score given the College Board’s decision to harshly curve down the June 2018 SAT test. We deserve a true score and for our tests to be reconsidered under a FAIR scale.”
He closed with the hashtag: “rescoreJuneSAT.”
The College Board, which oversees the test, issued a statement addressing the furor: “We want to assure you that your scores are accurate. While we plan for consistency across administrations, on occasion there are some tests that can be easier or more difficult than usual.”
The company uses a statistical process called “equating” to try to ensure that a test taken one day can be compared to a test taken on another day. The number of questions a student correctly answers is matched to a scaled score, according to the College Board.
One wrong answer on a test given one day could equal two or three wrong answers on a more difficult version given another day, the company said.
But students argued the College Board should not have administered a test that varied so much in difficulty compared to other versions.
Marguerite Saunders, 17, said she answered 51 of 58 questions correctly on the math portion of the exam in March and received a 740. In June, she said she successfully answered 54 out of 58 questions and received a 700.
“It’s not the most accurate representation of my math ability and the whole reason people take the SAT is to have an accurate representation,” she said.
Saunders, a rising high school senior in the District of Columbia, said she doesn’t disagree with the College Board’s use of equating but questioned “why they would release the test in the first place.”
Leslie Rives, a parent in Kennedale, Texas, said her son’s score dropped by 20 points in June - to 1390 - despite answering six more questions correctly than he did in March. Rives said her son, a rising senior, is now considering whether he’ll retake the test. He hoped that a higher score in June would boost his chances at more competitive schools, she said.
“It was so disheartening,” Rives said. “This one test could potentially just change this year of college admissions.”


When viewing wall quantities by category, there are Area of Formwork and Area of Formwork for Strutting High. I am wondering what is the difference between them.
Area of Formwork: Calculate the area of formwork to the whole wall.
Area of Formwork for Strutting High: Calculate the area of formwork to the wall part exceeding 3.5m.
Condition: Wall thickness = 0.2m, height = 5m, length = 6m, and the starting height to calculate strutting high = 3.5m.
Area of Formwork: quantity for whole wall (5m) = (6 + 6) * 5 = 60
Area of Formwork for Strutting High: quantity for wall part (height > 3.5m) = (6 + 6) * 1.5 = 18
3) Measurement Settings:
The quantity is calculated based on the option for Method for calculating strutting high.


GoldSpot Discoveries’ utilizes a quantamental approach to investing.
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Heating and cooling degree days are calculated by using the average temperature for the day, the high + low, and subtracting the average or mean temperature from the number 65 for heating degree days or subtracting 65 from the average for cooling degree days. The number 65 is used as the base number because most buildings and homes would be most comfortable and energy efficient at our around 65 degrees.
Example: On a summer day the high was 90 and the low 70. The average is 80. 80 (average) - 65 (base) = 15 cooling degree-days. It reflects how much power people should be using on the average to cool, in this case their homes/businesses. Take those daily cooling degree days and you can have daily/monthly or annual averages


By Iain T. Adamson
Offers a proper description of set concept according to the Von Neumann-Bernays-Godel axiomatic strategy utilizing the concept that of periods. Covers the root of the speculation, kin, ordinals, cardinals, and the axiom of selection. Paper. DLC: Set concept.
Read or Download A Set Theory Workbook PDF
Best logic books
During this publication top students supply state of the art overviews of methods to the formal expression of data constitution in normal language and its interplay with basic rules of human cognition and conversation. They current severe money owed of present knowing of the way features of grammar, reminiscent of prosody, syntax, morphology, semantics, and pragmatics, engage within the packing and unpacking of knowledge in conversation.
This ebook examines many features of flood threat administration in a complete method. As hazards depend upon chance and vulnerabilities, not just geophysical instruments for flood forecasting and making plans are provided, but additionally socio-economic difficulties of flood administration are mentioned. beginning with precipitation and meteorological instruments to its forecasting, hydrological versions are defined of their purposes for operational flood forecasts, contemplating version uncertainties and their interactions with hydraulic and groundwater types.
This booklet includes chosen papers from the Colloquium in Honor of Alain Lecomte, held in Pauillac, France, in November 2007. the development used to be a part of the ANR undertaking "Prélude" (Towards Theoretical Pragmatics in line with Ludics and Continuation Theory), the court cases of which have been released in one other FoLLI-LNAI quantity (LNAI 6505) edited by means of Alain Lecomte and Samuel Tronçon.
This publication constitutes the refereed lawsuits of the ninth foreign Symposium on sensible and common sense Programming, FLOPS 2008, held in Ise, Japan, in April 2008. The 20 revised complete papers awarded including three invited contributions have been conscientiously reviewed and chosen from fifty nine submissions. The papers are equipped in topical sections on constraints, positive mathematics, based kinds, rewriting, software transformation, common sense and lambda-calculus, kinds, and debugging.
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Ifwe denote the elements by the numbers 1,2,3,4,5,6, 7, 8, then the following are the combinations of2 (or, more simply, pairs) that can be generated from them 12 13 I 4 2 3 2 4 25 34 35 3 6 4 5 4 6 4 7 1 5 I 6 2 6 3 7 4 8 2 7 3 8 1 7 2 8 5 6 5 7 5 8 6 7 68 78 1 8 We can see very well that the number of these pairs is (from right to left) 1+2+3+4+5+6+7 On the other hand we might have argued that any element can be paired with the remaining 7, so the 8 elements would yield 8 x 7 pairs; but we have counted every pair twice, first when we were pairing the first term and then when we were pairing the second.
Susie said this instead of 1+2+3+4+5+6+7 She said 4 instead of 1, that is 3 more. But she also said 4 instead of 7, that is 3 less, and these equal out. In the same way it is true that 4 is 2 more that 2, but it is 2 less than 6 and so these too equal out. ' I had to give Eve her due; I could never have explained it so well myself. These little unprejudiced researchers make some extraordinary observations. 'It's like an exercise book,' exclaimed Mary, another little pupil. ' Pure interest was guiding these little researchers.
So the numbers in the Pascal Triangle occur as coefficients of descending powers of lOin the expression of the powers of 10 + 1. The second term in 10 + 1 is 1, and every power of! is still 1 (since 1 X 1 = 1), and so it does not appear that the powers of the second term come into the expression at all. But we can smuggle them in in the following way: 1IS = 1331 = 1000 + 300 + 30 + 1 = 1 X 103 + 3 X 102 X 1 + 3 X 10 X 12 + 1 xis We see that while the powers of the first term decrease, the powers of the second term increase.


5 edition of The Mathematics of surfaces found in the catalog.
The Mathematics of surfaces
|Statement||edited by J.A. Gregory.|
|Series||The Institute of Mathematics and Its Applications conference series ;, new ser., 6, Oxford science publications|
|Contributions||Gregory, J. A., Institute of Mathematics and Its Applications.|
|LC Classifications||QA571 .M38 1986|
|The Physical Object|
|Pagination||x, 282 p. :|
|Number of Pages||282|
|LC Control Number||86196680|
Because the sine waves repeat, it will loop back to the same shape every two seconds. Display 2D functions with a grid. The abstract machine, called TIGRE, exhibits reduction rates that compare favorably with previously reported techniques. We don't need to repeat that code for each individual function. In physical simulation, one breaks the world down into little pieces that are represented as large vectors.
In general, studying the rules and ideas of mathematics can help us understand the world better. We'll make it possible to display multiple and more complex functions. Book recommendation: Numerical Recipes in C: The Art of Scientific Computing William Press, Saul Teukolsky, William Vetterling and Brian Flannery The Mathematics of surfaces book University Press [this is a very valuable reference but is not normally used as a textbook] Sampling Theory and Signal Processing Over and over in computer graphics we represent some object such as an image or a surface as a collection of numbers that are stored in a regular two-dimensional array. Professor Cohn's lucid and insightful book presents an ideal coverage of the subject in five parts. A circular cone locus of a line crossing a circle, and passing through a fixed point, the apex, which is outside the plane of the circle is an algebraic surface which is not a differentiable surface.
Finally, some techniques for solving difficult equations make use of random numbers to estimate their solutions. Spectral Sequences I have now returned to an earlier plan of having this material be an extra chapter of the Algebraic Topology book, rather than a separate book. This book explores generalizations and specializations in these areas. Certainly when researchers carry out studies using human subject, they require statistical methods in order to perform the analysis of the data. Bracewell McGraw Hill Matrix Equations There are a wide variety of problems that come up in computer graphics that require the numerical solution of matrix equations.
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Topology 4 Its result can by The Mathematics of surfaces book to set the point's Y coordinate, instead of using explicit math. The study of number theory usually focuses more on the structure and behavior of the integers rather than on the actual foundations of numbers themselves, and so is not listed in this subsection.
In fact, in this case, linear equivalence may move an intersection point out to infinity. A good understanding of sampling theory is important if we are to use and to control the quality of such representations.
If the function is differentiablethe graph is a differentiable surface. Nevertheless, physics and mathematics are closely tied to one another in several areas within computer graphics. The title of the book is likely to change before it is published since the current title may not give a good idea of the contents.
Every differentiable surface is a topological surface, but the converse is false.
Display 2D functions with a grid. Topology 17 For further information or to download the part of the book that is written, go to the download page.
Using deduction is what makes mathematics thinking different from other kinds of scientific thinking, which might rely on experiments or on interviews.
The result will be a function that doesn't just slide as time progresses, it changes its shape. Some problems that need matrix techniques include: finding the best position and orientation to match one object to another one example of a "least The Mathematics of surfaces book problemcreating a surface that drapes over a given collection of The Mathematics of surfaces book with minimal creases thin-plate splinesand simulation of materials such as water or cloth.
Whenever we do this we are creating a "sampled" representation of the object. The theory starts to diverge from that of algebraic surfaces when we try to ensure linear equivalent divisors give the same intersection index, this would be used, for example in computing a divisors intersection index with itself.
By finding general rules, mathematics solves many problems at the same time as these rules can be used on other problems. There are also many diagrams to aid the reader in understanding the material.
Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics by Justin Solomon - CRC PressUsing examples from a broad base of computational tasks, including data processing and computational photography, the book introduces numerical modeling and algorithmic design from a practical standpoint and provides insight into theoretical tools.
Borwein - DocServerThe desire to understand Pi, the challenge, and originally the need, to calculate ever more accurate values of Pi, has challenged mathematicians for many many centuries, and Pi has provided compelling examples of computational mathematics. To make that easy, assign the current result to an y variable before returning it.
Appendices have been added giving the calculation of the stable rational homology, a proof of the Group Completion Theorem, and the Cerf-Gramain proof that the diffeomorphism groups of most surfaces have contractible components.
We can make do The Mathematics of surfaces book retrieving its value only once, before the loop, storing it in a variable. Evolutes, involutes and cycloids are introduced through Christiaan Huygens' fascinating story: in attempting to solve the famous longitude problem with a mathematically-improved pendulum clock, he invented mathematics that would later be applied to optics and gears.
In classical geometrya surface is generally defined as a locus of a point or a line.“This is the first textbook on mathematics that I see printed The Mathematics of surfaces book color. This book is not a usual textbook, but a very well written introduction to differential geometry, and the colors really help the reader in understanding the figures and navigating through the text.
this book will surely serve very well for students who want to learn differential geometry from the ground up no Brand: Springer International Publishing. Useful appendices accompany the text, providing hints and solutions to these exercises and also a sketch of how the treatment can be modelled within a conventional topology course for more advanced students.
The book can be regarded as an example of the emerging discipline of mathematics education, as well as being about surfaces. $\begingroup$ I know Forster's book quite well, having taught out of a good portion of it a few times.
It is extremely well-written, but definitely more analytic in flavor. In particular, it includes pretty much all the analysis to prove finite-dimensionality of sheaf cohomology on a compact Riemann surface.Note: Pdf are based on reference standards.
However, formatting rules can vary widely between applications and fields of interest or study. The specific requirements or preferences of your reviewing publisher, classroom teacher, institution or organization should be applied.“This is the first textbook on mathematics download pdf I see printed in color.
This book is not a usual textbook, but a very well written introduction to differential geometry, and the colors really help the reader in understanding the figures and navigating through the text. this book will surely serve very well for students who want to learn differential geometry from the ground up no Brand: Springer International Publishing.Useful appendices accompany ebook text, providing hints and solutions ebook these exercises and also a sketch of how the treatment can be modelled within a conventional topology course for more advanced students.
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Forex Trading is a global trading and exchange market. This focuses on the trading of foreign monies and does have an effect on exchange rates and currency value. There are skills that are essential for trading in the foreign exchange market. One of those skills is a solid working knowledge of math.
Being good at math is helpful with Forex trading because of the intense mental math that is used with every trade. Being able to quickly run the mental correlations between the two numbers that are presented together will make each trade go faster and smoother.
It is not necessary to be a math genius or even have advanced math knowledge such as calculus. The math that will be a greater benefit to you will be your foundational math facts and mental math. If you are trying to get started with Forex trading and aren’t sure your math skills are up to the task, don’t worry. We are going to talk about the math needed, what Forex really is, and what other skills are valuable for your trading.
Do You Have To Be Good At Math for Forex Trading?
While it is true that having strong math skills overall, you don’t have to be a mathematician to be a successful Forex trader. It is helpful to like math and enjoy working with numbers because you will be staring at sets of numbers all day.
Even though you don’t have to be great at math for this type of trading, if you struggle with numbers and correlations, you might want to have a refresher course in math facts and mental math. There are also essential math guides that have been designed just for Forex traders. These can be helpful to teach you what you need to know when it comes to trading on the foreign exchange market.
Along with math skills, it is also helpful to be able to analyze the trades that you are trying to complete. Many people that are skilled in math are also excellent when it comes to the analysis of facts and numbers. These two skills go hand in hand.
The analysis part of math will help you decide if the trade is a positive or negative correlation, as well as whether or not the trade should happen. Without the ability to quickly analyze the trade and do mental math, trading will be difficult and tedious. But these skills can be learned.
High School and College math is something that most of us would like to never revisit; however, for Forex Trading, there are certain skills that you learned that will come in handy. One of those skills is correlations. Correlations teach us how to compare efficiently two numbers as well as seeing how they relate and interact with each other. With Forex Trading, the name of the game is looking at two different currencies and gleaning how they are relating to each other—otherwise known as the exchange rate.
When we look at what an exchange rate between two countries is, we are looking at the product of a correlation. Having a working understanding of correlations is a useful math skill if you are going to work with the Foreign Exchange Market.
There is no way to count the number of times we have been told by a math teacher that we need to know our math facts. Not reference a paper but know them by heart and be able to recall them easily.
Foundation math facts are used daily in Forex Trading. If you have efficient or instant recall of addition/subtraction and multiplication/division on a high level, then your job will be easy. If you struggle with math facts but still want to work in Forex Trading, then you should sharpen up those skills.
Other Skills Needed for Forex Trading
Besides the need for math and analytical skills, there are some other skills that are imperative when it comes to Forex trading. These skills pair well with mental math and analysis to make the job of trading on the foreign exchange market smoother and less stressful. The great thing about these skills is that they can all be learned.
There is not a skill needed for Forex trading that is a natural-born gift. While some people may just naturally enjoy doing these things and are good at them, anyone can put in the time and acquire these skills.
Excellent organization and record-keeping skills are a must when it comes to a job like Forex trading. Knowing what was traded for what and when is imperative in an environment where the pieces are constantly moving and changing.
While it is possible to be a Forex trader without keeping the records of what has happened or how trade was completed, it will benefit you in the long run as a trader. Like we mentioned earlier, analysis is one of the key skills needed for this type of job. Much of Forex trading is the strategy and finding something that works well.
This is only accomplished by being able to see what has been done before and finding the pattern. When you understand what you have done and the ways you could have done it better, you can then begin to grow as a trader and will become truly profitable.
Record keeping and organization is the key to unlocking your potential as a Forex trader.
Understanding of Foreign Exchange
If you are going to work with the Foreign exchange market as a trader, then you should probably understand the Foreign exchange. You don’t need to go into it as a rookie and know everything. You certainly won’t understand everything. The important thing is to have a basic understanding and working knowledge of what the foreign exchange does.
Doing a job without understanding who you are working for, why you are doing what you are doing, or even what you are doing is going to be miserable. This is the knowledge that you can gain quite easily with an internet search and some reading.
You will need to learn and understand the language that is used in Forex trading. There is Forex specific wording that can leave you confused if you don’t know what it means. Take the time to educate yourself if you want to work in Forex trading.
Persistence and Focus
Any kind of financial trading is going to be a test of focus, persistence, and mental fortitude. With a volatile global market, it is understandable that there will be good days and bad days. A good Forex trader has to have the ability to be rational, stay focused, and be resilient. When it seems like it is all going to fall apart, the trader can’t fall apart too. It is important to find a solution.
It is also important to keep your cool under pressure. Losing control or stressing out when a trade is not going the way you thought it would won’t help anything. However, if you stay focused and calm, you will find a solution. This is a skill that, like the others, can be learned.
Having mental math and analysis skills will go a long way in Forex trading. While it is good to have a foundational understanding of business math, there are other skills that are important for a trader to have. All of these skills work together to help successful traders working on the Forex trading market.


What’s Actually Happening with What Is a Radical in Math
The set of all of the entities in the order essays present context is known as the universal set, or simply the universe. Your work, and what exactly you do each and every day, is a fantastic place to get started. Everyone would agree that there’s an appearance to the area of form and it is quite real in its effects.
Western thought particularly, and human thought in general, makes much of the idea of causality. Generally mathematical usage, however, term isn’t restricted to additive expressions. In the majority of circumstances each symbol provides the exact clear, precise meaning to each reader, irrespective of the language they speak.
If you would like more precision, think about using or instead, with the precise arguments. It’s often beneficial to combine functions to generate different functions. A good example of this kind of algorithm is that of surveying all feasible alternatives.
The Meaning of What Is a Radical in Math
You’d need to be stupid or inside a deep, self-decieving denial over basic biology not to find this. Numerical analysis offers an important example. Actually, mathematics encompasses a wide assortment of skills and concepts.
Using What Is a Radical in Math
The Equity Project is currently trying to tackle teacher burnout and boost retention. In addition, I believe HE CREATED the full Universe. Colleges want to accept pupils who’d love to be there.
33, by way of example, does not have any square aspects. A Product of Two Radicals With the Same Index Number In different words, whenever you are multiplying two radicals that possess the exact index number, you can write the item below the identical radical with the frequent index number. A square root is understood to be a number which when multiplied by itself gives a true non-negative number referred to as a square.
Failure can turn into an excuse to stop. From that point, you can end up in prison. That means you might take a look in case you enjoy.
No one wants to dip into each chapter, searching for a specific topic. What a wonderful step-by-step explanations. With a principal subject, the composition will have focal point where you will develop the rest of the paragraphs.
The Upside to What Is a Radical in Math
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The level of difficulty of solving discrete programming problems is dependent on the existence of a massive number of local extrema. It will permit you to check and see whether you experience an understanding of these kinds of problems. A true breakthrough at the moment.
Not one of these requires a calculator, though you may discover that a calculator enables you to look at your answer. At this time you don’t carry out the conventional algorithm in your head. The player that supplies the appropriate answer first wins both cards.
I would like to give you some examples. Here are some examples below.
In typical scenarios the range of local extrema is extremely large. The inversion vector doesn’t appear to get a similar advantage, but it’s widely used anyway. However, it’s important to confirm the solution in the original equation to be certain it checks, as it might not be an actual solution.
Declining mathematics scores are the ever-present culprits in most of these educational problems. In addition, I believe HE CREATED the full Universe. Examples from various other nations.
No one wants to dip into each chapter, searching for a specific topic. What a wonderful step-by-step explanations. Each topic has a great number of examples to comprehend the applications of concepts.
The main reason for this strange rule is it’s that which we will need to do in order to keep each of the fundamental rules consistent. There are two fundamental cases to be concerned about. In Case 2, there’s it.
So try to remember that if you’re graphing your points. You are able to check these inequalities in your graphing calculator to make certain they’re correct. Simplifying Use this calculator if you just desire to simplify, not tackle an equation.
The presentation is going to take a thematic strategy, which might vary each term. Here are some examples below.


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These skills are rooted in algebra, geometry, statistics and other topics.
In total, the online academy has more than 20,000 closed-captioned videos and material covering more than 5,000 topics.
After selecting one, you can set the lowest and highest numbers to appear in the questions, as well as the number of questions on the worksheet.
It takes a click to generate an accompanying answer sheet.
The library contains manipulation tasks targeted to students from pre-kindergarten to grade 12.
For example, a grade 6 geometry activity involves using geoboards to illustrate area, perimeter and rational number concepts. The website lists skills, such as telling time and the order of operations.
Created by Utah State University, the online library’s goal is purely to engage students.
Specifically, it’s to help teachers provide students with more activities.
Math Goodies also appeals to diverse learners by featuring free puzzles, articles and word problems to complement the lessons.
You can use the website to create custom worksheets, too.
The resources target students from kindergarten to grade 12, including printable rulers and measurement conversion tables.
You can pair them with Teacher Vision’s lesson plans, but you must be a registered user to access them.
Regardless, you can access relevant lessons from teachers across the United States.


Why the Dow Will Hit a Million, Eventually
At an event earlier this month, Warren Buffett, one of the most successful investors of all time, revealed his prediction that the Dow Jones industrial average (DJIA) will be “over 1 million” in 100 years.
With the DJIA currently sitting at about 22,400, is it even reasonable to think that the stock market could grow that much? Growth from the current value of the Dow to 1 million would represent an increase of about 45 times over. My first impression was that a value of 1 million for the Dow is very high, and Mr. Buffett must be either confused or overly optimistic to put forth such a prediction.
But since this prediction came from someone who clearly has a good understanding of investments and the stock market, I decided to check out the math behind this prediction to see if it makes sense.
An important part of Warren Buffett’s prediction is the “in 100 years” part. One hundred years is a long time, and although it may be surprising, Warren Buffett’s prediction of the Dow topping 1 million is actually quite reasonable given the historical performance of the market. In fact, the prediction of the Dow reaching 1 million in 100 years may even be conservative.
Here’s the math
Let’s look at what kind of growth rate would be required for the Dow to reach 1 million in 100 years. As I mentioned, the Dow would need to grow by 45 times its current value. When thinking about investment growth, it is informative to look at the growth in terms of the number of doublings that would be required.
2n = 45
n ln(2) = ln (45)
n = ln(45) / ln(2)
n = 3.81 / 0.693
n = 5.5
So the market value would need to double 5.5 times from its current value to reach 1 million. Let’s look at this in the form of a table to make sure it makes sense:
|# of Doublings||Resulting Dow Value|
|0 doublings||22,400 (current Dow)|
|6 doublings||1,433,600 (Dow over 1 million)|
From the table above, you can see that doubling the current Dow five times yields 716,800, and doubling six times yields over 1 million, so the number of doublings for the Dow to reach 1 million must be somewhere in between. Our estimate of 5.5 doublings makes sense.
So the Dow would need to double 5.5 times in 100 years — or in other words, it would need to double every 18.2 years: 100 years / 5.5 doublings = 18.2 years to double.
The next step to checking out Mr. Buffett’s prediction is to figure out what rate of growth would be required for the value of the Dow to double every 18.2 years.
For a quick estimate, I turned to the “Rule of 72.” The Rule of 72 is a handy approximation to find how many years it will take an investment to double — simply divide 72 by the annual rate of growth. I flipped the Rule of 72 formula around to check the rate of growth required:
72 / growth rate = years to double
72 / growth rate = 18.2 years
Solve for growth rate:
72 = 18.2 x growth rate
growth rate = 72 / 18.2 = 3.96 percent annual growth
So the “Rule of 72” approximation tells us that an annual growth rate of 3.96 percent would be required to double the Dow every 18.2 years, which is the rate of growth needed for the Dow to hit 1 million in 100 years.
If you don’t want to settle for an approximation, or if you are just geeky in a cool sort of way, you can do a more exact calculation:
2P = PeYr
2P = Pe(18.2)r
ln(2) = 18.2r
r = ln(2) / 18.2
r = 0.038 or 3.8 percent
The approximation from the Rule of 72 matches pretty closely with the exact calculation, so it seems we have nailed down the rate of growth that is required for the Dow to reach 1 million.
It turns out that that an annualized growth rate of 3.8 percent is well within the historical growth rate of the stock market over the past 100 years. The average rate of return from the stock market is typically considered to be as high as 7 percent.
Of course the stock market does not march steadily along at an average rate of growth year after year. The market swings up and down from day to day and follows longer upward and downward trends during bull and bear markets. But over the long haul, the average trend for the stock market has been upward at a rate of well over 3.8 percent average growth over the past 100 years.
In addition to the mathematical consideration of the rate of growth required for the Dow to reach 1 million in 100 years, another consideration is whether the world’s people and natural resources will continue to sustain economic growth over the next 100 years. With development of exciting new technologies and emerging global markets to drive growth, it seems reasonable that the stock market could keep going up.
So it looks like Mr. Buffett’s thinking makes good sense as usual, and the prediction of the Dow 1 million makes perfect sense.


Christos Athanasiadis, University of Athens, Greece; László Babai, The University of Chicago, USA; Eiichi Bannai, Kyushu University, Japan; Louis J. Billera, Cornell University, USA; Anders Björner, Royal Institute of Technology, Sweden; Aart Blokhuis, Technical University of Eindhoven, The Netherlands; Andries E. Brouwer, Technical University of Eindhoven, The Netherlands; Jonathan Brundan, University of Oregon, USA; Robert Calderbank, Duke University, USA; Peter J. Cameron, University of St. Andrews, U.K.; Philippe Delsarte, Universite catholique de Louvain, Belgium; Ira M. Gessel, Brandeis University, USA; Chris D. Godsil, University of Waterloo, Canada; Ian P. Goulden, University of Waterloo, Canada; Curtis Greene, Haverford College, USA; Philip J. Hanlon, Dartmouth College, USA; Wilfried Imrich, Montanuniversität Leoben, Austria; Alexander Anatolievich Ivanov, Imperial College London, U.K.; David M. R. Jackson, University of Waterloo, Canada; Jeff Kahn, Rutgers University, USA; Gil Kalai, Hebrew University, Israel; Thomas Lam, University of Michigan, USA; Brendan D. McKay, Australian National University, Australia; Isabella Novik, University of Washington, USA; Cheryl E. Praeger, University of Western Australia, Australia; Christophe Reutenauer, Université du Québec à Montréal, Canada; Richard P. Stanley, Massachusetts Institute of Technology, USA; Dennis W. Stanton, University of Minnesota, USA; John Stembridge, University of Michigan, USA; Koen Thas, Ghent University, Belgium; David G. Wagner, University of Waterloo, Canada.
This is the home page of Algebraic Combinatorics, a mathematics journal currently owned by its Editorial Board and Editors-in-Chief.
It is dedicated to publishing high-quality papers in which algebra and combinatorics interact in interesting ways. There are no limitations on the kind of algebra or combinatorics: the algebra involved could be commutative algebra, group theory, representation theory, algebraic geometry, linear algebra, Galois theory, associative or Lie algebras, among other possibilities. The combinatorics could be enumerative, coding theory, root systems, design theory, graph theory, incidence geometry or other topics. The key requirement is not a particular subject matter, but rather the active interplay between combinatorics and algebra.
Algebraic Combinatorics adheres to the principles of Fair Open Access.
The journal acknowledges the support of the Foundation Compositio Mathematica.
The journal will be a member of the Mersenne Center for Open scientific publishing and published using its platform, developed by Mathdoc in France (University of Grenoble, CNRS).
The manuscripts should be submitted via the editorial platform of the journal. Before submitting, an account has to be created by the author on this platform.
The usual submission format of an article is the PDF format. If the article is accepted for publication, all source files (tex or latex, bibtex, illustrations) will be required from the author. Authors are encouraged to prepare their article in the standard LaTeX class amsart.cls.
The journal does not typically publish new proofs of known results. To avoid overconcentration of topics, submissions from authors who have another paper under review are discouraged.
Last changed 2018-01-09.


A leafstalk the footstalk of a leaf connecting the blade with the stemHaving three sides especially three plane sides as a threesided stem leaf petiole peduncle scape or pericarpThe continued stem or midrib of a pinnately compound leaf as in a rose leaf or a fern.
A particular representation of the data set in shrinked form is known as the stem and leaf plotThis statistical plot makes it possible for you to display the data set values in graphical charts for a better interpretation.
A stemandleaf plot is a chart tool that has a similar purpose as the histogram and it is used to quickly assess distributional properties of a sample the shape of its probability distributionThe specific advantage of the stemandleaf plot over a histogram is that the stemandleaf plot aside from showing the distributional properties.
A stemandleaf plots in statistics is a device for presenting quantitative data in a graphical format similar to a histogram to assist in visualizing the shape of a distributionThe stem usually consists of the digits in the greatest common place value of each data while the leaves contain the other digits of each item of data.
Question Use a stemandleaf plot to display the data which represent the scores of a biology class on a midterm exam75 85 90 80 87 66 82 88 95 91 76 80 86 92 94 68 75 91 94 87 76 91 85 99 Determine the leaves in the stemandleaf plot belowKey 33 33 Exam Scores 6 7 81 9 What.
Aug 13 2020nbsp018332Once this is installed we can use the following code to create a stemandleaf plot for our dataset import stemgraphic create stemandleaf plot fig ax stemgraphicStemgraphic x The number in the red box at the bottom of the plot displays the minimum number in the dataset 32The number in the red box at the top of the plot displays.
Before we move ahead let it be clear that you have to understand a few terms that are related to this statistical analysis.
The crossword clue Leaf and stem jointsWith 5 letters was last seen on the January 01 1961We think the likely answer to this clue is AXILSBelow are all possible answers to this clue ordered by its rankYou can easily improve your search by specifying the number of letters in the answer.
Each solver will come with clear instructions on how the solver should be usedAlso some calculators will have available videos that will help you to proceed if you are having troublesStemandLeaf Plot Maker InstructionsThe following graphical tool creates a StemandLeaf on the data you provide in the box below.
Example quot32quot is split into quot3quot stem and quot2quot leafMore Examples Stem quot1quot Leaf quot5quot means 15Stem quot1quot Leaf quot6quot means 16Stem quot2quot Leaf quot1quot means 21The quotstemquot values are listed down and the quotleafquot values go right or left from the stem valuesThe quotstemquot is used to group the scores and each quotleafquot shows the individual scores within each group.
Get an instant layout of stem leaf plot along with other basic statistical terms with the help of this free stem and leaf plot calculatorYes if you want to comprehend the calculations involved in the process then you are just a couple of clicks away with the assistance of this stemplot maker.
In a stemplot left side entries are called stems and the right side entries are called leavesIn figure above the stems are tens here 5 represents 50 6 represents 60 and so on and the leaves are actual valuesStems and leaves may be labelled as millions thousands ones tenths etc.
Jan 03 2022nbsp018332Step 2 Identify the stemsFor any number the digit to the left of the rightmost digit is a stem.
Marsh plants usually consist of multiple leaves distributed along a central stem.
Mar 11 2022nbsp018332Joins A Leaf To A StemThe crossword clue Joins a union with 4 letters was last seen on the March 11 2022We think the likely answer to this clue is WEDSBelow are all possible answers to this clue ordered by its rankYou can easily improve your search by specifying the number of letters in the answer.
May 05 2021nbsp018332A stemandleaf plot is a type of plot that displays data by splitting up each value in a dataset into a stem and a leafThis tutorial explains how to calculate the mean median and mode of a stemandleaf plot.
May 09 2019nbsp018332Procedure to make stemandleaf plot Separate each observationdata into a stem which will consist of all except rightmost digit and leaf the rightmost digitLeaf must have only one digit while stem can have as many digits as possibleWrite the stem in a vertical column with smallest at the top but in Python you will get largest at the.
Nov 04 2019nbsp018332Stemandleaf plots provide an ataglance tool for specific information in large sets of dataOtherwise you would have a long list of marks to sift through and analyzeYou can use this form of data analysis to find medians determine totals and define the modes of data sets providing valuable insight into trends and patterns in large data sets.
On this page you will understand the meaning of stem and leaf plotsYou will also get to know how these are plottedYou will be further introduced to another type of stem and leaf plot called the twosided or back t back stem and leaf plotWe’ll also make Stem and Leaf Plots to display data distributions with the help of a few examplesIn the given examples you’ll get to know how to organize the data and to use the stemandleaf plot concept to obtain answers to interesting questions.
Once you have verified that there are no questions regarding the use of the applet pass out the Worksheet to accompany quotStemandLeaf PlotsquotWalk the students through entering the data and finding the mean median and mode for problem number 1Have the students finish the worksheet.
Solution Step 1 Find the least number and the greatest number in the data setThe greatest number is 31 3 in the tens place The smallest number is 12 1 in the tens place Step 2 Draw a vertical line and write the digits in the tens places from 1 to 3 on the left of the line.
Statistics and Probability questions and answersThe accompanying specific gravity values describe various wood types used in constructionConstruct a stemandleaf display using repeated stemsEnter numbers from smallest to largest separated by spacesEnter NONE for stems with no valuesComment on any interesting features of the display.
Stem And Leaf Plots Sample Math Practice Problems The math problems below can be generated by MathScoreCom a math practice program for schools and individual familiesReferences to complexity and mode refer to the overall difficulty of the problems as they appear in the main programIn the main program all problems are automatically.
Stem and leaf plots are one such way of representing data in an easier and convenient wayStem and leaf plots have several advantages that make them very handy for the purpose of analyzing large sets of data easily.
The range of a data set is the difference between the smallest value and the greatest value in the data setA stemandleaf plot is a way of organizing data values from least to greatest using place valueUsually the last digit of each data value becomes the quotleafquot and the other digits become the quotstemquot.
The stem and leaf plot is a plot used to represent numerical data by showing its distributionEach numerical data value is split into a stem the first digit or digits and a leafThe stem is the first digit or digits while the leaf is the last digitThe stem and leaf plot is used when your data is not too large about 15150 data points.
The Stem and Leaf plot is a way of organizing data into a form that makes it easy to see the frequency of different valuesIn other words we can say that a Stem and Leaf Plot is a table in which each data value is split into a stem and a leafThe stem is the lefthand column that has the tens of digitsThe leaves are listed in the righthand column showing all the ones digit for each of the tens the twenties thirties and forties.
The winding or twining stem of a hop vine or other climbing plantA plant having a woody durable stem but less than a tree a shrubTo shoot or divide into branches or subdivisions as the stem of a plantThe point where the base of the stem of a plant arises from the root.
This free online software calculator computes the Stemandleaf Plot for a univariate datasetThe parameter scale can be used to expand the scale of the plotA value of scale2 will cause the plot to be roughly twice as long as the defaultEnter or paste your data delimited by hard returnsSend output to Browser Blue Charts White.
Copyright © 2021 Zilong Laboratory Machinery Company All rights reserved sitemap


Arts Education Belongs in Every School
Alyse is a student at Elizabeth Freese Elementary School in San Diego who loves to dance.
Her favorite subject is math.
California Arts Council grant recipient the Malashock Dance Company is there to make sure both of Alyse’s passions stay strong.
Malashock’s Math in Motion program, explains managing director Molly Puryear, was developed in response to student’s creeping doubt of their mathematical abilities as they grow. Through dance, MIM teachers offer kids a tangible, kinetic connection to math, boosting their confidence to self-express and solve equations.
“Dance and math are my two favorite things, so being able to combine those two together makes me really happy,” said Alyse.
“Dance and math are my two favorite things, so being able to combine those two together makes me really happy.”
— Alyse, student
As an arts supporter, we know you get it. You understand the relationship between the arts and academics, and the importance of programs such as Math in Motion. Yet less than 40 percent of all California students currently receive any kind of arts education in school.
The latest data from Create CA shows that arts participation in our schools has improved, but we’re still not where we need to be. Students who need the social and academic benefits of arts instruction the most — low-income students, English-language learners — are the ones most likely to be denied access.
Smart needs art, and every dollar counts. Do your part for keeping creativity inside California’s classrooms. Between now and October 15, make a donation of $1 or more to the Keep Arts in Schools Voluntary Tax Contribution Fund. 100% of your tax-deductible contribution is applied to arts education programming supported by the California Arts Council.
By making a contribution, you’re making a difference. You can help more grantees like the Malashock Dance Company bring arts experiences to more kids like Alyse.
After all, we’re in need of creative math whizzes like her for many tax seasons to come.
About Voluntary Contribution Funds
A voluntary contribution is an election made by the taxpayer to designate amounts on their tax return to charitable funds. A contribution of $1 or more is permitted in whole dollar amounts. Voluntary contributions are permitted as charitable contributions (in the year following the contribution) on the Federal Schedule A. For more information, visit the California Franchise Tax Board Voluntary Contribution Funds webpage..


Effective Focal Length (EFL) is the focal length affected by the camera’s crop factor. The numbers in the lens’ manual show some focal length values that this particular lens can use. For instance, 15-30mm means that the lens can be anywhere from 15 mm 30 mm. Of course, that explains it, right? Let’s take a closer look at all these terms.
The “Crop Factor” is the ratio of a given sensor to the standard 35mm sensor, also known as a full-frame sensor. This element determines the actual or equivalent angle of view and hence visible area of the lens on the given camera.
A lot of photographers with the two most common sensor crop factors: 1.6x for Canon, and 1.5x for Nikon and others. But let’s have a look how is this number calculated and how does it affect your final photo.
Crop Factor Calculation
So, the clue is the diagonal dimension of the sensor. The crop factor is the ratio on the full-frame diagonal to the diagonal of the sensor we calculate. Pythagorean theory will help us to calculate the diagonal knowing both horizontal and vertical sides of the rectangle.
c = √(a2 + b2)
The dimensions of the full-frame sensor are 24mm and 36mm. Therefore, the crop factor formula gives us √(242 + 362) = 43.27mm
Nikon Crop Factor Calculation
To find a crop factor of any given sensor, we need to calculate the diagonal. In case of the amateur level, Nikon DSLR cameras the dimensions are 23.6mm x 15.6mm.
√(23.62 + 15.62) = 28.29mm
So the crop factor is 43.27 / 28.29 = 1.53, rounded down to 1.5 for convenience.
Canon Crop Factor Calculation
Using same logic and Canon specs we can quickly calculate its crop factor.
√(22.22 + 14.82) = 26.68mm
43.27/26.68 = 1.62, rounded down to 1.6 for convenience.
Effective Focal Length Calculation
The standard focal length is what the manufacturer writes on the lens. But the crop factor affects it. So, the effective focal length is the actual resulting value that the lens has on the camera with the crop factor adjustments. For your reference, sometimes it is called Effective Focal Range.
Have a look at the image.
As you can see with the same physical focal length F, the angle a2 is smaller than a1. This fact means that on the cropped sensor you actually see the narrower area through the viewfinder. In reality, this narrow fielf of view effect is the same effect as if you zoomed in a little bit. And so this virtual zoom in focal length is the effective focal length. Hopefully, it clarified things instead of making them even fuzzier.
Focal Length Formula
And finally, we made it to the magic formula that will help you to understand what your lens is capable of.
EFL = FL x CF
In other words, Effective Focal Length is equal to Focal Length multiplied by the Crop Factor. As simple as that. For instance, if you have a lens 24-70mm, then the actual, effective focal length on the amateur Nikon camera with crop factor = 1.5 will be 36-105mm. This focal range increase naturally affects the angle of view because the longer the focal length, the narrower the angle.
In other words, the 24mm lens with the 24mm set as current focal length delivers 36mm on the camera with 1.5 crop factor. This fact is neither good nor bad. For a landscape it can be bad, rendering your wide lens not as wide. As opposed to the telescopic lens, where it increases your reach. 300mm turns into 450mm, which is an incredible level up.
Common Crop Factors
The table below shows some common crop factors for the modern cameras. With those values, you can easily calculate the effective focal length and know your photographic equipment better.
|Sensor Size||Sensor Dimension||Crop Factor|
|Medium Format||53.7mm x 40.4mm||0.64|
|Medium Format (cropped)||43.8mm x 32.9mm||0.79|
|Full Frame 35mm (all FF cameras)||36mm x 24mm||1|
|APS-H (Canon)||27.9mm x 18.6mm||1.3|
|APS-C (Nikon DX, Sony, Pentax)||23.6mm x 15.6mm||1.5|
|APS-C (Canon)||22.2mm x 14.8mm||1.6|
|1.5″||18.7mm x 14mm||1.9|
|4/3″||17.3mm x 13mm||2|
|1″||12.8mm x 9.6mm||2.7|
|2/3″||8.8mm x 6.6mm||3.9|
|1/2.3″||6.17mm x 4.55mm||5.6|
This Wikipedia article has a wider list of sensors. I’m sure with the new knowledge you can now easily calculate all crop factors you need.
Wow! Excellent technical information, but makes my head spin….
hi Terry, thanks. Did you find it hard to understand?


For decades, slot games have held a dominant position among the games of chance. Their popularity stems from a variety of factors: ease of use, brevity, and privacy, but perhaps the most important aspect of slot design is its mathematical layout. This parametric configuration is a secret kept by most slot producers, which, unfortunately, means that most players do not know how to interpret it.
Most modern slot machines have a computer that determines the odds of winning each spin by multiplying the probability of hitting a particular symbol on a reel by the number of symbols on the machine. This process is often referred to as “weighting”, which allows the manufacturer to create a disproportionate number of wins and losses for a given set of symbols. It also limits jackpot sizes by limiting the number of possible combinations.
In order to maximize the chances of winning on a slot game, it is necessary to understand the mathematics behind the system. This involves basic multiplication and division skills, so that players can quickly calculate the probability of hitting a specific combination. Moreover, it is essential to choose the right slot in relation to your bankroll. This will ensure that you are playing for a long period of time and not just chasing quick wins. This approach will also help you to avoid making costly mistakes that could cost you your entire bankroll. It is also recommended to find a site that offers free slots play, as this will allow you to practice your skills without risking any real money.


waltersm at telusplanet.net
Mon Feb 21 21:54:05 PST 2005
Hello Shawn Grover and others on the list,
I am now about 41% the way through the absolute beginner's guide to c, and the
last four chapters went very quickly as I saw the ways that I did certain
things in Fortran and Assembler are easily done in c, such as incrementing
and decrementing registers, with the added feature of post incrementing
versus pre incrementing and post decrementing versus pre decrementing
The things that were done in the text brought back memories of my computer
course at SAIT between 1970 and 1976 with two years off in the middle to pay
off the student loan, and the extra two years I took repeating failed courses
due to relapses of my schizophrenia.
My previous knowledge from my computer courses enabled me to absorb some of
the concepts a little faster than someone who had never graduated from a two
year computer program.
At the rate I am now going I should complete the "absolute beginner's guide to
c" in about 10 more days.
Then I have the other 13 c books and three c++ books to study.
In the not too distant future I expect to be able to write a c program to
solve exp(x +jy) = x + jy where j = square root of -1.
Even if C does not have complex number functions, I could still do the complex
number calculations using the rules of complex multiplication, division,
addition, subtraction, and exponentiation using real number operations.
For example, exp(x + jy) = exp(x)*cos(y) + j*exp(x)*sin(y).
And (x1 + jy1)*(x2 + jy2) = (x1*x2 - y1*y2) + j*(x1*y2 + x2*y1)
All solutions of exp(x + jy) = x + jy come in complex conjugate pairs, a thing
which I discovered myself, but which someone who had taken advanced analysis
says is true of all analytic functions f(x + jy). That is the solutions to
any equation of the form f(x + jy) = x + jy occur in complex conjugate pairs
if f is analytic.
I was able to find three complex conjugate pairs of solutions to exp(x + jy) =
x + jy, but I misplaced the solutions and the programmable calculators on
which I did them are worn out. Unfortunately I have not replaced those
However, when I learn the transcendental functions sin(x), cos(x), tan(x),
exp(x) in c, I should be able to solve those equations and perhaps find more
complex conjugate pairs of solutions.
I was able to prove that there are infinitely many solutions to exp(x + jy) =
x +jy, but of course, with round off errors we can only find a find a finite
number of those solutions.
Anyone who has successfully passed first year calculus can prove that exp(x) =
x has no solution in the real number field. But there are infinitely many
complex conjugate pairs of solutions in the complex field.
I expect to be able to start solving those equations using numerical methods
and c in perhaps a couple of months.
Michael Walters - clug two tier member and member of the programming special
More information about the clug-progsig


But one very important thing that I learned from this course is that
the reason for teaching Math is not teaching Math itself.
And that Math is a tool for the
1. development of intellectual, logical reasoning, spatial visualization , analysis & abstract thought
2. development of numeracy, reasoning, thinking , and problem solving skills
3. opportunities of creative work and moment of enlightenment & joy.
This statement is profound! If I do not get the goal correct, the effort that I am putting in is futile. If it means that I have to rethink my teaching philosophy and unlearn everything about teaching pre-school math, i will. In this hi-tech world whereby mathematical problems and computational skill can be easily solved and accomplished by pressing a few buttons on the keyboard. What is there left for us to do?
Our belief will determine our actions. So
let's crack some heads,
let's kill some brain cells,
let's out wit each other, and
let's have some fun!
From Tr Anita


Our intent is to develop pupils who can…
Become fluent in the fundamentals of mathematics;
can solve problems by applying their mathematics. (National Curriculum 2014)
Click here to view the Key Instant Recall Facts (KIRFS) overview.
How do we promote learning in Maths?
At St John’s Church School we know that mathematics is important in everyday life. We all enjoy maths and can succeed if we:
Work hard to become fluent.
Push ourselves to reason.
Don’t give up when problem solving is challenging.
Whole school Curriculum Overview for Maths.
“I love helping Tiny the tortoise when he gets his maths wrong!” Rebecca Y2
“I love active maths and winning Motty in Friday assembly!” Sam Y4
What does Maths look like at St John's?
We want all children to enjoy mathematics and to experience success in the subject. We follow a mastery approach where all pupils are taught to their year group expectation with challenge for the more able and support for those who need it. We are committed to developing children’s curiosity, as well as an appreciation of the beauty and power of mathematics.
Fieldhead, Off Leymoor Road, GOLCAR, Huddersfield, HD7 4QQ


Check out our collection of color-by-number printable worksheets for children. Find and print these coloring pages to help children practice skills such as numbers.
paint by numbers: an interactive coloring book for children. This mathematical game teaches children to recognize numbers and solve simple mathematical examples.
In addition, this program develops memory, attention, imagination and logical skills. Color by Number has several images including: back to school color by number, car and boat color by number, cat and dog color by number, Halloween and Christmas color by number, etc. Children will improve their number recognition skills as they identify and match each number with its corresponding color using a color and number key to color the image according to the instructions given. Printable color by number worksheets allow children's imaginative power as they color recognizable objects and things to create a beautiful work of art.
Coloring by number involves children learning about different numbers, distinguishing different colors by their names, and finding the right color tone that matches each number.


February 14, 2015 is application deadline for Akamai Internship Program Summer 2015Posted on Feb 3, 2015 in Education
Paid internships at Hawaii observatories and companies for students at community colleges and universities in Hawaii, and students from Hawaii studying on the mainland. The Akamai Internship Program is an amazing opportunity to get work experience. Some of the students get the opportunity to work at NELHA. More than 100 Akamai interns are now in science and tech jobs. Accepted students will be matched with a mentor and project in fields that include: engineering, computer science, electronics, IT, astronomy, physics, math, biology, chemistry, and aquaculture.
Application Deadline: February 14, 2015
Begin your online application here.


Combat Basics Edit
Two basic numbers determine the result of a battle: the attack power and the defense power.
The easiest to compute is the attack power: it is just the attack value of each type of attacking troop multiplied by their quantity. A 1000 berserkers have an attack power a_1 of 50 * 1000 = 50,000, while a 1000 knights have an attack power a_2 of 90,000. Together their power is a_tot = 140,000.
The attention of the defending troops is evenly split among the attacking troops according to their attack power. So if 1,400 rangers are defending against the attack above, 500 will be defending themselves against the berserkers (a_1/a_tot of all rangers), while 900 against the knights (a_2/a_tot). The same happens if we add 1,400 guardians.
The defense power against the berserkers will be the defense value of each type of unit times the number of units focused on the knights, i.e. a value d_1 of 500 * 40 (rangers) + 500 * 30 (guardians) = 35,000. Same for the knights: d_2 = 54,000. The total defense power is therefore d_tot = 89,000.
The attacker wins if the attack power is greater than the defense power, he loses if the opposite event occurs.
What about the number of kills? The defenders get the same percentage of losses for every troop: a_tot/d_tot if they win, the square root of this ratio if they lose. The resulting ratio must be multiplied by the battle intensity (cf. note). In our example the defenders lose: if we are talking abount an assault they lose .5 * sqrt(140/89) = 62.71 of their troops.
The losses among the attackers depend on the troop type. In our case (only one troop per category) the losses are as follow: the berserkers lose *d_1/a_1* of their troops if they win, its square root if they lose and we take always into account the battle intensity. So the death rate among berserkers is .5 * 35/50 = 35, among the knights .5 * 54/90 = 30.
- Note:* The *battle intensity* is 50 for assault, scout or boss, 10 for the attacker if the boss dies, 1 for the defender of a plunder, 10% for the rest.
Numbers after the decimal point mean chance of an additional death.


STEM is an acronym for the fields of Science, Technology, Engineering and Mathematics. As part of their name STEM also referred to various institutions and initiatives to promote these relevant specialist areas/scientific disciplines.
Science, Technology, Engineering and Mathematics (STEM) refers to four major areas of study that are responsible for most innovation in modern society.
Michael Klein commented on the government's efforts to bring more female students in STEM disciplines:
Quote: «German original:
- Trotz aller Werbung für MINT-Fächer, trotz aller Girls' Days, aller Versuche, Frauen für das zu begeistern, was als Männerberuf gilt und wie wir von Genderisten wissen, ist alles, was mit Männern in Verbindung steht, schlecht, gewalttätig, kühl, egoistisch und logisch-rational, trotz all dieser Versuche, ist der "Uni-Run" weiblicher Studierende auf MINT-Fächer bislang ausgeblieben.
- Despite all the advertising for STEM disciplines, despite all Take a Girl Child to Work Days[wp], all effort to inspire women for what is considered to be man's job and as we know from genderists, that is anything that has to do with men is considered poor, violent, cold, selfish, and logical-rational, despite all these attempts, the "Run" to female students on STEM disciplines at universities has so far failed.» - Michael Klein
- Alternative Math - Short Film - Ideaman (September 19, 2017) (Size: 9:07 min.)


Group Theory And Chemistry Download eBook PDF/EPUB
45 Chapter 3 Symmetry and Group Theory Chapter 3 deals with the fundamentals of the formal system used in this research, group theory. All basic constructs used in the research and based in group theory are presented here: group... Group Theory is a branch of the mathematical field of algebra. One important application, the theory of symmetry groups, is a powerful tool for the prediction of physical properties of molecules and crystals.
Symmetry Tutorial Point Groups
1 m.sc (chemistry) semester-i (course i) (inorganic chemistry) lectures-60 max. marks-80 note: i. ten questions will be set by the examiner selecting two from each unit.... This provides the essential tables (character tables, direct products, descent in symmetry and subgroups) required for those using group theory, together with general formulae, examples, and other relevant information.
CHEM 673 Symmetry and Group Theory in Chemistry
Group Theory is a mathematical method by which aspects of a molecules symmetry can be determined. The symmetry of a molecule reveals information about its properties (i.e., structure, spectra, polarity, chirality, etc…) messages from the body their psychological meaning pdf In group theory, the elements considered are symmetry operations. For a given molecular For a given molecular system described by the Hamiltonian Hˆ , there is a set of symmetry operations Oˆ
Symmetry and Group Theory ChemistryABC
Group Theory is a mathematical method by which aspects of a molecules symmetry can be determined. The symmetry of a molecule reveals information about its properties (i.e., structure, spectra, polarity, chirality, etc…) ccie routing and switching version 5 books pdf The presentation here is short, and limited to those aspects of symmetry and group theory that are directly useful in interpreting molecular structure and spectroscopy. Nevertheless I hope that the reader will begin to sense some of the beauty of the subject. Symmetry is at the heart of our understanding of the physical laws of nature. If a reader is happy with what appears in this book, I
How long can it take?
Group theory ETH Zürich
- Tables for Group Theory Portal IFGW
- Symmetry and Group Theory ChemistryABC
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Symmetry And Group Theory In Chemistry Pdf
Chem 64 Problem Set 2: Molecular Symmetry and Group Theory 1. SA chapter 4: Exercises 4.1-4.6 and 4.11; Problems 4.1 and 4.2 [For exercise 4.3f (BF4 –) beware of a typo in the solutions manual: this ion is tetrahedral.] [For Exercise 4.2, see Strauss page 54. The question asks if an S4 axis is present, but the manual doesn't answer it for parts a and b. Since there is an Soo axis in the Dooh
- Part II Chemistry 2009–10 Course B7: Symmetry and Perturbation Theory Symmetry Ali Alavi c University of Cambridge 2010
- This provides the essential tables (character tables, direct products, descent in symmetry and subgroups) required for those using group theory, together with general formulae, examples, and other relevant information.
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- 1.3 Summary of Symmetry Operations, Symmetry Elements, and Point Groups. symmetry point group for that molecule and the group specified is denoted Cn. When additional symmetry elements are present, Cn forms a proper subgroup of the complete symmetry point group. Molecules that possess only a Cn symmetry element are rare, an example being Co(NH2CH2CH2NH2)2Cl2+, which …


Dr Leonardo Bottolo is a Reader in Statistics for Biomedicine at the University of Cambridge and a fellow at The Alan Turing Institute. He received his PhD in Methodological Statistics from the University of Trento, Italy, in 2001. Before joining the University of Cambridge, he was appointed Senior Lecturer in Statistics in the Department of Mathematics, Imperial College. He worked as a postdoc in the Mathematical Genetics group, University of Oxford and at the Institute of Mathematical Sciences, Imperial College.
Dr Leonardo Bottolo’s goal is to develop scalable Bayesian models and design their efficient software implementations to tackle the problem of statistical and machine learning in large, diverse and complex data sets that are standard in modern molecular biology, for example, single-cell RNA-sequencing (scRNA-seq) and single-cell Assay for Transposase-Accessible Chromatin with high-throughput sequencing (scATAC-seq) and biomedicine, for instance, data collected in neurodegenerative diseases, multilocus imprinting disturbances and mitochondrial and cardiovascular diseases.
- Ochoa, E., Lee, S., Lan-Leung, B., Renuka, D., Ong, K.K., Radley, J.A., Pérez de Nanclares, , Martinez, R., Clark, G., Martin, E., Castanos, L. Bottolo, L., and Maher, E. (2021). ImprintSeq, a novel tool to interrogate DNA methylation at human imprinted regions. Accepted Genetics in Medicine.
- Ruffieux, H., Fairfax, B., Nassiri, I., Vigorito, E., Wallace, C., Richardson, S., and Bottolo, L. (2021). EPISPOT: An epigenome-driven approach for detecting hotspots in molecular QTL studies. American Journal of Human Genetics, 108(6):983-1000
- Bottolo, L., Banterle, M., Richardson, S., Ala-Korpela, M., Järvelin, M-R., and Lewin, A. (2021). A computationally efficient Bayesian Seemingly Unrelated Regressions model for high-dimensional Quantitative Trait Loci discovery. Journal of the Royal Statistical Society: Series C. 70(4):886-908
- Alexopoulos, A., and Bottolo, L. (2020). Bayesian Variable Selection for Gaussian copula regression models. Journal of Computational and Graphical Statistics, 30(3):578-593
- Zhang, X., …, Bottolo, L., and Ware, J. (2020). Disease-specific variant pathogenicity prediction significantly improves clinical variant interpretation in inherited cardiac conditions. Genetics in Medicine, 23: 69-79.
- 2019 – (Co-I) MRC Research Grant (£ 1,175,347) with Johnson (PI), E. Petretto (Co-I), P. K. Srivastava (Co-I), ICL, S. Sisodiya (Co-I), M. Thom (Co-I), UCL: “An integrated systems-level framework for deciphering multidrug-resistant epilepsy”.


Contributing Author: Mrs. Monica Davis, Rockbridge Academy Upper School Math Teacher
“When I step into my classroom each day, I hope to convey to my students a little more of what math truly is: an act of worship and a way to think God's thoughts after Him.”
At some point during my freshman year of college, I began to dread the inevitable question that occurs while making polite conversation with someone you just met:
"So, what are you majoring in?" The question itself was not what bothered me as much as the responses I received after my answer: "I'm a math major."
The reactions certainly ran the gamut. Some were flattering: "Wow! You must be so smart!" Some played off the typical stereotypes: "Do you just sit in the basement of the math building solving problems and inhaling chalk dust all day?" Some I simply did not know how to respond to: "I don't know how you do that. I hate math so much!" The worst response though, was one occasionally levied by the humanities majors at my staunchly classical, liberal arts college: "I don't think I could handle doing something so utilitarian all day. I prefer the liberal arts."
As the poor people who told me this discovered, nothing starts me on a rant faster than the accusation that math is not a liberal art. There is so much about math that is not utilitarian in the slightest. In my Abstract Algebra class, for example, we studied number systems in which 3x2 = o (this is true in modulo 6). In Real Analysis, we learned about two different sizes of infinity: countable and uncountable. My all-time favorite class was Non-Euclidean Geometry; this is a perfectly consistent, completely valid geometry in which rectangles do not exist! While all of these subjects have applications in advanced science, studying them is as much a liberal art as studying The Brothers Karamazov. Dostoevsky even uses non-Euclidean geometry in this work as an illustration as he lays out his solution to the problem of evil in the world.
To be fair to those innocent humanities majors who provoked my rant, there is a lot of math that is utilitarian. I also took four semesters of Calculus in which I described the path of projectiles using vectors. I took probability and a mathematical economics class in which we studied supply and demand functions and talked about optimizing production while reducing cost. You see, math is really quite strange. It is simultaneously the most applicable and the most abstract subject. It is incredibly practical and also something that many people do "just for fun." Math has unlimited applications and yet is one of the most pure forms of abstract thought.
This is why, despite the occasional disparaging remark about my subject, I loved being a math major. I delighted in immersing myself in a subject with such variety and beauty. As much as I may have loathed the question, "What are you majoring in?" I loved the question, "Why did you decide to major in math?" My answer to the "why" question is always the same: math gives us a glimpse into the mind of God. Through math, we see the order and logic that God as the master designer has built into the universe. We see the character of God reflected in math, especially His consistency, transcendence, and creativity. Math shows us God's sovereignty as we learn how He superintended each step in the development of the subject throughout history. Ultimately, the beauty and nature of math reflects the beauty and nature of the God who created math.
When I step into my classroom each day, I hope to convey to my students a little more of what math truly is: an act of worship and a way to think God's thoughts after Him. The math faculty at Rockbridge is committed to communicating this vision of math as a means to glorify God. This is what it means to teach math Christianly.
Monica Davis, has now been teaching for seven years with the math faculty at Rockbridge Academy in Crownsville Maryland. She earned her B.A. in 2013 from Hillsdale College, Hillsdale, Michigan. Article is republished here with her permission.


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Models for Vehicular Traffic on Networks
By Mauro Garavello, Ke Han and Benedetto Piccoli
This book presents a theory of modeling, analyzing, computing, and optimizing traffic flows on networks. It provides comprehensive and self-contained descriptions and analyses on the widely used conservation law models for dynamic traffic flows on networks.
Multiscale Modeling of Pedestrian Dynamics
By Emiliano Cristiani, Benedetto Piccoli and Andrea Tosin
This book presents mathematical models and numerical simulations of crowd dynamics. The core topic is the development of a new multiscale paradigm, which bridges the microscopic and macroscopic scales taking the most from each of them for capturing the relevant clues of complexity of crowds.
Modeling, Simulation, and Optimization of Supply Chains: A Continuous Approach
By Ciro D’Apice, Simone Göttlich, Michael Herty and Benedetto Piccoli
This book offers a state-of-the-art introduction to the mathematical theory of supply chain networks, focusing on those described by partial differential equations.
Introduction to the Mathematical Theory of Control
By Alberto Bressan and Benedetto Piccoli
This book provides an introduction to the mathematical theory of nonlinear control systems.
Traffic Flow on Networks
By Mauro Garavello and Benedetto Piccoli
This volume is devoted to macroscopic models for traffic on a network, with possible applications to car traffic, telecommunications and supply chains.
Optimal Syntheses for Control Systems on 2-D Manifolds
This monograph is the first devoted to optimal syntheses in control theory and focuses on minimum time on 2-D manifolds.


Understand Your Chances Of Winning The Lottery In 5 Minutes Flat
Most lottery players don't really understand their chances of winning the lottery.
Because normally, understanding it all takes more maths than most of us ever did at school. And more thinking than we do in an average day at work!
So no college degrees needed for our explanation!
Table Of Contents:
Starting With Toast
We won't bore you to death with statistics and formulas - you hate that right? So let's keep it fun, OK?
You're making breakfast. And as a result of your half open eyes and carpet slipper shuffle - you trip - catapulting your toast across the room..!
So, what is the chance it will land 'butter side down'?
OK, so assuming 'sods law' is not at play in this particular universe, there are 2 sides the toast can land on. I think we can safely agree then that it's a '1 in 2' chance of butter side staining your carpet...
This time you were 'lucky', it was dry side down.
That's lesson 1 done. Relieved..?
Picking Your Toast Up...
You bend, pick your toast up, blow most of the hair and grime off it - and return it to your plate (why not, 5 second rule..?).
Just as the dog barrels into your legs on route to a serious barking at the mailman. Your bleary eyed dismay watches your toast take off for a second time...
So what are the chances it will stain your carpet this time?
If you said '1 in 2', well done, you've already got lesson 2 down.
(And this is way more important than you might think)
Not sure why?
There are still 2 sides to your toast. And still only one of them has some butter on it. That means there is still a 1 in 2 chance of a grease mark on your carpet!
The fact your toast fell 'dry side down' the first time will NOT make it any more or less likely that it will be butter side this time.
Clearly it's your lucky day, it was dry side again. Just be thankful you didn't choose cornflakes today.
So, previous results do not affect the future. That's lesson 2. Easy stuff this probability theory!
What's This Got To Do With My Chances Of Winning The Lottery?
OK, let's start talking balls ("you already were...").
If there was a really dumb lottery that had only 2 balls. And they drew out just 1 of them to pick the winner. What would your chances of winning be?
Yes, it's the toast example in glorious lottery 3D. Which means, your chances of winning are 1 in 2.
And of course, it means if ball 1 was picked last week, the chances of it being picked this week are just the same. Ball 2 didn't suddenly become more likely because it didn't come out last week.
More Balls Please!
Right. So what happens if we add another ball?
Pretty easy right? Our odds now change to '1 in 3'. Because we are still picking out 1 ball, but there are now 3 balls to pick from.
OK. So what if we draw 2 balls out of 3...
Ouch. That got harder. It sounds like it might be '2 in 3' - but it isn't.
Just to prove it to you. If you think about it a bit more (don't worry, it's nearly time for a coffee break!), here are all the possible combinations that can be drawn:
|Ball 1||Ball 2|
But wait a second. Did you spot it? When we're talking about your normal lottery draw, it doesn't matter what ORDER the balls are drawn in, so long as they match the ones on your ticket - right?!
So, if you look a little closer at those numbers in the table, you can see that 01, then 02 is exactly the same result as 02 then 01! If your numbers were 01 and 02 you'd hit the jackpot for either of those.
So there are actually 2 ways of drawing every result, 01 first then 03 - or 03 first then 01 etc.
Confused yet? Waddya mean 'no'! ;-)
You have now found the secret formula for working out your chances of winning the lottery!
No, really! You have.
You worked out there were 6 possible ways the balls could be drawn. And you worked out that there were 2 ways each set of results could be drawn - because it didn't matter what order the balls were in for you to win.
The only thing you didn't do was to divide the 6 possible results by the 2 ways of drawing them. Which gives the correct answer - a '1 in 3' chance of winning.
You may now call yourself a student of lottery statistics and probability. Nice one.
Even More Balls!
Let's get dangerous. We're going to jump up to a 4 number lottery with 3 balls drawn. Ooooooh. (Patience eager student, 49 balls shall come to those who wait!).
OK. So if you write down all the possible combinations that can be drawn, how many are there?
Oh, alright, I'll do them for you...
|Ball 1||Ball 2||Ball 3|
OK. So there's 24 combinations. Now look closely, like before. How many times is each set of numbers repeated? How many times, for example, can you see balls 01, 02 and 03 but in any order?
I make it six times.
So with your magic formula, that means we divide 24 possible combinations by 6 ways to draw each set of numbers.
Which gives us 4. Or a '1 in 4' chance of this jackpot.
Look What Happens When We Add One More Ball
So let's still draw out 3 balls. But now from a total of 5 balls.
Even I'm not going to write all those combinations down. But I will let you in on a nifty way to discover how many there are, for any number of balls.
All you have to do is this: 5 x 4 x 3 = 60 ways.
Eh, how did that work!?
Easy. You start with the highest numbered ball, in this case 5. And keep multiplying by the next smaller numbered ball. For as many balls as you are drawing out.
So, if you were drawing 2 balls out of 3, like our example we did earlier. Well that's just 3 x 2 = 6. Which is exactly what we worked out, the long way!
Or, for 3 balls out of 4, it's 4 x 3 x 2 = 24, which is also the same as we worked out above.
Nifty isn't it!
But How Many Combinations Are There In A Real Big Lottery?
Most of us play a lottery with 49 different balls, and 6 balls get drawn.
Everything works the same way. Just be ready for some big numbers!
We just do the same as before: 49 x 48 x 47 x 46 x 45 x 44 = 10,068,347,520.
That's a big number and an awful lot of combinations. But don't forget that it doesn't matter what order the balls are drawn in!
Here's our second big time saver.
It would take forever just to write all these combinations down. Then trying to figure out how many times combinations are repeated would be a very long and dull day.
When you can simply do this: 6 x 5 x 4 x 3 x 2 x 1 = 720.
You can maybe spot where that little shortcut came from.
It's 6 balls to be drawn, multiplied by 5 left to draw, then 4 left etc.
But let's double check this against our answer above. When we drew 3 balls we worked out the combinations were repeated 6 times didn't we? Which is 3 x 2 x 1.
Easy when you know how.
That lottery statistics diploma is nearly in the bag!
So What, Then, Are My Chances Of Winning The Lottery?
Here's where the magic finally happens. Because you've pretty much already worked it out.
We just take the big number, and divide it by the smaller one! Or in other words divide the number of different possible combinations, by the number of ways they can be repeated.
So it's 10,068,347,520 divided by 720.
Which comes out to '1 in 13,983,816'.
And that's why you don't win the jackpot every week!
Well done for staying awake this far. If you've had less than 3 cups of coffee, I'm impressed!
How To Increase Your Chances
So now you know how tough the odds are, I suppose you now want to know how to make it easier to win?
One way is to play less often but play the same number of tickets/combinations overall.
That's right, 10 combinations played in a single draw have a better chance than 5 combinations played in two draws. Same cost to play, but slightly better odds!
That might make your head hurt just a little. The math certainly will so that's one for another day :-).
Just bear in mind it is only slightly better. And playing once a year is definitely not nearly as much fun as playing once a week. So don't go crazy on this one!
The other (obvious) way to increase your chances is... buy more tickets.
It's easy to see that if you buy two tickets, you double your chances. So that 1 in nearly 14 million, becomes 2 in 14 million instead (because you bought 2 of the 14 million possible combinations). Which is also the same as 1 in 7 million.
Wahay, now you're gonna win big. ;-)
Don't forget though, that there are also prizes for matching 5 numbers out of 6, or 4 numbers. Or even just 3.
So your chances of winning the lottery aren't quite as bad as they look. Still pretty grim for the jackpot though!
But the fact is that even just one ticket has an infinitely better chance than no ticket at all :-)
Congratulations on becoming an Expert in Lottery Statistics and Probability.