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关键词: 计算流体力学(CFD), 数值模拟, 模型确认, 认知不确定性, 概率盒
Abstract: With the emergence of new computer technologies, Computational Fluid Dynamics (CFD) numerical simulation has been extensively implemented in many areas such as aerospace, national defense, ship hydrodynamics, wind power, and water conservancy. CFD numerical simulation provides effective decision-making and validation methods for complex fluid analysis of equipment, model parameter evaluation, and aerodynamic optimization design. Existing CFD simulations are conducted under the premises of deterministic mathematical models, fixed physical parameters, and fixed boundary conditions. Due to the complexity of physics and cognitive biases of human beings, there are, however, many potential uncertain factors with different representation forms in CFD, such as model parameter uncertainty, numerical dispersion, and model form uncertainty, resulting in a great challenge to the credibility of CFD simulation results. This article elaborates on the uncertain factors encountered in CFD, and provides a comprehensive discussion on the mainstream model validation metrics. We focus on the model validation metrics under epistemic uncertainty, including several metrics under the interval theory and probability-box theory. The NACA0012 airfoil flow problem is leveraged to demonstrate the effectiveness of the model validation metrics under various uncertainties in CFD.
Key words: Computational Fluid Dynamics (CFD), numerical simulation, model validation, epistemic uncertainty, probability-box


Definition of Surjections
1. surjection [n] - See also: surjection
Click the following link to bring up a new window with an automated collection of images related to the term: Surjections Images
Lexicographical Neighbors of Surjections
Literary usage of Surjections
Below you will find example usage of this term as found in modern and/or classical literature:
1. Real Analysis by Andrew M. Bruckner, Judith B. Bruckner, Brian S. Thomson (1997)
"In the setting of Banach spaces, bounded linear transformations that are surjections are always open. This fact is known as the open mapping theorem and is ..."


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Looking out for number one has become synonymous with egocentricity and selfishness but it has a deeper connotation. It turns out that number one takes inordinate precedence – the actual integer not the self!
Let’s say you examined a large set of numbers – anything as diverse as, say, the heights of buildings, animal populations, census statistics; shopping bills; etc. – basically any big number set. If the sample is large enough you would expect the statistics to produce completely varied results and if you examined the first digit (1-9 on each line – ignoring arbitrary zeros at the start) you would expect each number to be represented proportionately 11.1% of the time (or 1 in 9 times).
But time after time this is not what shows up in reality. The proportional frequency of each first digit overwhelmingly favours number one (30% of the time). Even more bizarrely, the numbers 1-9 decrease in frequency in perfect sequence; with numbers 7-9 appearing as the first digit far less often. This declining order occurs so uniformly across any large number set that a mathematical formula has been devised to demonstrate the expected proportion of numbers beginning with the leading digit.
The first person to truly appreciate this was the mathematician Simon Newcomb when he noticed that his book of maths calculation tables was frayed more in the earlier pages than towards the back. People performed more calculations using numbers that began with lower digits!! Much later Frank Benford noticed the same pattern and proved the theorem – hence the phenomenon is now called Benford’s Law.
But a mathematical law must have a universal application – the law of gravity applies everywhere, for example, and not just in selected places. So if Benford’s Law truly is universal then it must apply to every large data set. There is growing evidence that it does. However, the data set must be sufficiently large to eliminate contaminants – clearly there are no politicians in the Dáil whose age begins with 1 and there are only 10 lotto numbers beginning with 1. These data sets are too constrained and are not universal enough to satisfy Benford’s Law.
Rather than simply having academic interest this curiosity has very real practical implications; it can detect fraud! It turns out that financial data fits neatly into the theorem. For those who may be minded to falsify financial accounts or tax returns your sequencing of numbers can leave tell-tale signs of irregularity. When creating numbers we have a tendency to use too many 5’s; 6’s and 7’s, for example, and not enough 1’s and 2’s. Applying Benford’s law an auditor or detective could easily uncover the untruths and, of course, in the modern world of high-speed computers the sequencing of digits can be accomplished in double-quick time. However, evidence of inconsistencies does not prove fraud but highly unlikely number sequences certainly warrant further investigation.
MMPI has applied the law to share prices but has so far failed to find any predictive sequencing. Pity that!


An easy way to execute complicated functions in Simulink is to use the Embedded MATLAB Function block. When you insert one of these blocks it creates a MATLAB file that is contained within the Simulink model block. The issue with this block is that only a subset of the full MATLAB language is available within an Embedded block. The simple solution to this problem is the function eml.extrinsic which sets certain functions to execute externally.
[outputa outputb] = myfunction(inputa, inputb);
The function names within the extrinsic call will be set to run within MATLAB instead of Simulink. Now functions like tf and ss can be used!
Another Embedded MATLAB tip is to use ‘*1i’ to represent complex numbers. (This is mentioned in the MATLAB documentation but looks like ‘li’.)


Use Subheadings– but do not use more subheadings than listed below Introduction ● Signpost reader to the contents of your essay Campaign Overview ● Identify the campaign you are focusing….
To be eligible for the UK. Marine Corps, a woman must have a height between 58 in. and 73 in.
Women have normally distributed heights with a mean of 63.6 in. and a standard deviation of 2.5 in. (based on data from the UK National Health Survey). i. Find the percentage of women who satisfy the Marine Corps height requirement. ii. If the requirement is changed to exclude the shortest 1 % and the tallest 1 %, find the heights that are acceptable. iii. If nine women are randomly selected, find the probability that their mean height is between 63.0 in. and 65.0 in. d) Assuming that TV replacement times have a mean of 8.2 years and a standard deviation of 1.1 years, find the probability that 50 randomly selected TV sets will have a mean replacement of 7.8 years or less.


Casino Game Abilities
You can find currently three main categories of casino games available: card games, video poker games, and electronic casino games. Video poker video games are played by one person at a time and don’t require the participation of internet casino staff to play. These game titles are ever more popular among non-gamers because they’re relatively easy to learn and play. They also have a tendency to offer a more competitive playing experience than most other games are.
Blackjack is just about the best-known card game in the world, and once and for all reason. Blackjack is often the initial casino game members are introduced to and is an excellent introduction to the more challenging games that the casino gives you. When you are playing blackjack at an on the web casino, you will find that you have the best odds of winning when you come to bet. That’s as the house continually has blackjack cards, and the lowest possible house edge (or advantage) is two per card. The lower your chances of getting an advantage increase, the better off you’re. The minimum bet amount is definitely lower than the maximum bet amount, therefore the lower you are ready to go with an individual card, the better off you’re.
Another simple blackjack strategy is by using basic statistics to analyze the way the blackjack player could be behaving. One such statistic is named the binomial distribution also it compares the winning probability of blackjack with the chances of picking a range in the set, up to specified restriction. The binomial distribution plots the probability as a work of the number of successes and failures. For example, the standard deviation can be used to plot the data points for each 100 hands played. The typical deviation uses a normal curve to plot the info points to enable you to see the range of actions and how it differs with the amount of successful plays and the length of each successful have fun.
Blackjack players could make use of the typical deviation to estimate the casino’s odds of winning more money in the favorite games. Standard deviation is most useful in studying the random distribution of the outcomes of gaming occasions, like spins on roulette wheels or spins on slots. It can also be used to review the behavior of the odds in non-stop jackpots on slots and video poker machines. One casino identifies these as “montee video games,” because players can win multiple prizes simultaneously over many fingers.
The random distribution of the outcome of casino slot machines is similar to the odds of hitting the jackpot in slots. When players place bets, they take the chance that the modern casino will hit a jackpot. If you are gambling with a 10-part slot machine game, then the best odds which can be given to you’d be if you get yourself a hit every time with among your bets. But, because you don’t know what’s the best payout will be, you won’t know whether you’re getting the very best odds on slot machines or not.
To study the real odds at playing slot game titles, a player should multiply the total amount wagered as well as the casino’s expected payout for each spin. For instance, in case a person is betting ten cents about the same spin, the casino’s envisioned payout per spin is $.10. With this number, the player can perform a quick computation to determine the amount wagered, multiplied by the likely payout to get the casino’s true probability of winning. Then, he can multiply that number by the amount of times he really wants to bet and find if he gets a winning bet every time. In this manner, the player can calculate his chances of winning without having to depend on the numbers generated by the machine.
In roulette and blackjack, players need to follow a strategy of matching the amount of opponents that come up with a specific number. A good player should do this consistently to improve 바카라 사이트 his chances of winning. This can be the same in playing other gambling house games such as craps and baccarat. It needs strategic thinking, which is part of the real skill component.
Overall, playing casino games online is better because it includes a lower house edge than slots games. Nevertheless, both roulette and slots game titles have the tendency to create larger jackpots. Additionally, there are casino games online that use random amount generators for drawing numbers. As compared to these, the home edge is smaller in modern casino games on the web.


ChallengeIf you want to strain your brain to drain, consider the NJ Math League Contests.
Contenders do not have to like mathematics, but have to love it.
Contenders do not have to work hard, but have to work smart.
Contenders do not have to do things perfectly, but have to do them right.
Contenders do not have to show their best, but have to give their best.
After all, in NJ Math League, contenders do not measure their values because their values measure them.Count your values while your values count for you. Take the challenge.Dr. Rivera


ES 101 Section 6 EKG Analysis Homework # 3
Per our class discussion on 9/26/2001, take your EKG data and do a 2, 3,or 4 point differentiation. Find the minimum slope (maximum negative value.) Determine the number of QRS complexes in your data if you use .8 and if you use .6 of this value as a trigger. Plot on a single graph two complexes of EKG data with the slope and trigger value overlaid.
Report: a. number of QRS complexes, average heart rate
b. give me a copy of your plot, reasonably labeled.
c. discuss your results.


Multiple linear regression is an extension of simple linear regression used to predict an outcome variable (y) on the basis of multiple distinct predictor variables (x). With three predictor variables (x), the prediction of y is expressed by the following equation: y = b0 + b1*x1 + b2*x2 + b3*x3
R makes it very easy to fit a logistic regression model. The function to be called is glm() and the fitting process is similar the one used in linear regression. In this post, I would discuss binary logistic regression with an example though the procedure for multinomial logistic regression is pretty much the same.
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Binary, Multinomial, and ordinal logistic regression models are some examples of the robust predictive methods to use for modeling the relationship between non-normal discrete response and the predictors. This study looks at several methods of modeling binary, categorical and ordinal correlated response variables within regression models.
The significance of variables, including; maximum value of welding power, electrode force, zinc coating, power drop, and so on, was examined and the multinomial logistic regression model was estimated using the significant variables. The accuracy of the predictive model for weld quality was estimated to be 96.4%.
See full list on stats.idre.ucla.edu
The LOGISTIC statement performs power and sample size analyses for the likelihood ratio chi-square test of a single predictor in binary logistic regression, possibly in the presence of one or more covariates. All predictor variables are assumed to be independent of each other.


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We are going to utilize the cross product calculator and dot product of vectors to explore equations of planes and lines. Vector functions have a consequence of a vector function of an input . It’s technically not as a vector, so it instead ought to be thought of as a way of using arithmetic of vectors having a point from the aeroplane since a position vector can’t be interpreted.
In instances such as this, any two specified points online may most likely have its own place vector cross product calculator. We can define L(t) for a vector-valued function that maps the input signal to the output vectors L(t). In 2 dimensions, the equation may seem as a lineup equation.
We use t because it is the parameter, or indicator of every point at stake. T is utilized by us since there’s a point often labelled from the time in which a thing is situated in the point. In instances like this, b is a fixed point (place vector) online cross product calculator and that is the cross product calculator between two points at stake, or even the continuous slope vector at stake. Let’s view the equation of the line through the points P1 and P2. We have our incline, so we are ready to choose any of these points at stake.
The main reason the vector cross product equation calculator of the line is used is as it generalizes. We can do the identical thing for 3 different lines. 1 we receive our first points. Contemplating any aeroplane, there needs to be a vector n vertical to each vector v parallel to your aeroplane. Let us see the equation of this plane with routine going through the point on the aeroplane. We could put the equation to practical form. We have to form two vectors like cross product and dot product linking one of these points, to get the equation of the plane through three non-colinear points. P1P3.
These vectors are either parallel to the aeroplane, so the product will give a vector that’s normal, that would be certainly to both u and v, and so perpendicular to the plane. Using the things in a different order may produce a vector, no matter how the type will be precisely the exact same. We can detect the equation of a plane given.
In case you’re a baseball fan, this ERA calculator or cruncher is directly in your ballpark. It finds the estimation of the Earned Run Average – a metric that gauges the viability of a pitcher in a significantly more precise manner than a basic success to-lose proportion. Peruse on to gain proficiency with the standards of this measurement – what is ERA in baseball, and how to figure the ERA of a discretionary player. Also, in the article underneath you can locate a short synopsis of baseball history, a depiction of the most famous baseball association – Major League Baseball, and some specialized data about a baseball field and a polished ash. At long last, you’ll get an opportunity to investigate the MLB ERA heads of the most recent 10 years.
What is ERA in baseball?
To lay it out plainly, ERA is a proportion of a pitcher’s viability. It considers his exhibition over each of the nine innings yet additionally takes the time he has been pitching.
By definition, it is the mean of gained runs surrendered by a pitcher for every the absolute of innings pitched (9 for an ordinary game, 7 for softball, and 6 or 7 for youth baseball match-ups). In the event that any guarded blunders happen during the game, the run is viewed as unmerited and isn’t considered for ERA computations.
For the most part, the lower the ERA score, the better. The most minimal profession acquired run normal in history is 1.82, held by Ed Walsh, who played from 1904 to 1917. After the difference in rules post-1920, the least vocation ERA score currently has a place with Mariano Rivera (2.21), who played baseball in years 1995–2013.
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Part 3 of our conversation with Deborah Ball, professor at University of Michigan School of Education.
Here is a transcript.
– Welcome to PLtogether Lounge Talks. I’m Adam Geller, founder and CEO of Edthena. Today we’re talking with Deborah Ball. She is a researcher, a professor at the University of Michigan School of Education, the founder of Teaching Works and another role, which many of you know her for, but really relevant to what we’re talking about today. A practicing math teacher. Deborah thanks so much for joining us for Lounge Talks.
– Good to see you Adam.
– Good to see you as well. Well, today I wanna talk a little bit about math. Folks know you as a math scholar and someone who has a lot of opinions about how to teach math. So let’s you know, I guess you know, the math curriculum is very big. There’s a lot that we can definitely not get to the whole curriculum and in 10 minutes, but you know, if I’m a math teacher and I’m thinking about, okay, all my kids are at home all my students are at home. How should I be thinking about adapting what I’m teaching? Like, how do I pick and choose? You know, if I’m teaching third grade, how should I be prioritizing?
– That’s a great question, Adam. And I’ve been trying to think about this and I wouldn’t pretend to have answers for this, for sure. But I think there’s some opportunities right now that we might wanna take. I think that most of us who have been around for a while and been teaching for a while have seen the curriculum in the elementary school and certainly the other levels just get layered with more and more and more, very little ever leaves the curriculum and everyone talks about how more things just get added. This is probably a moment to take a step back and think about what are the things that really could get more kids hooked in to enjoying math to thinking mathematically what are the opportunities here and I can say one thing that trying to stuff, the regular curriculum, whatever that is, in our schools, stuffing into zoom is probably a recipe for disaster on a number of fronts, and I don’t wanna dwell on that right now because the reasons why in the immediate we probably tried to do that. But if, as we think forward, I think there’s other kinds of opportunities. For example, we often know that for children to engage in some pretty significant mathematical problem solving, that takes time and in school, we’re often so pressed for time, you have a math period in a math class, and it’s followed by some other class. And there’s just isn’t the time that it takes to do what we call persevering in mathematics. But, you know, here we have an opportunity to consider some problems that kids could work on over a longer period of time and come back together on zoom or asynchronously to think about how the problem is working out. And there another is a collection of such problems that are pretty easy to get into, but not simple to finish, that I’ve seen from the work that I do with children, children get really engaged in including children who have found themselves as not being interested in math. I’ll give you one example, that is pretty straightforward and kind of simple on the surface, but is of kind of example, it might not sound all that exciting, but I’ve seen kids really take off on it. And it’s as simple as this write equations for time. So, you know, kids will start off, if they’re a little, they’ll write things like, you know, eight plus two equals 10. And then, you know, they start writing things, and sometimes a little bit of a nudge, they realize, oh, like, it doesn’t have to be adding, I could subtract, but within moments, and depending on the age, and what kinds of tools they have to bring to bear, they’re trying to see like, what kind of fancy things can they write with, like multiple numbers in it or different operations, and the more sort of arithmetic and other calculational tools they have at their disposal, like factorials, or, you know, any number of things, they can become more and more intricate. Pretty quickly, kids of many ages begin to realize like, hey, this is gonna go on for a while, which raises a really interesting question like, you know, is there a finite number of solutions to this problem? Well, you know, actually there isn’t. And we don’t give kids very many experience with solving problems that have infinitely many solutions and grappling with the infinite is actually something children get into. So this is the kind of problem that a teacher could set up for a group of children in her class or even a broader group. They could go off and work on it, they could come back together, there could be a little bit of provoking like, hey, you know, has anybody tried new problems that involve division? Or has anybody tried any problems where they see a pattern where they think they can generate a lot more? And we’ve worked on these kinds of problems with children in the summers and the summers, often we work with children who have begun to think of themselves as not good at math. But they get hooked into these problems and begin to realize there’s just a whole different way of thinking. So what I’m arguing in part is there’re problems that have a lot of space in them that depending on the tools kids have, they have many different things they can do. They take time to do in school time is not our friend often but you know, at home time looks pretty different. And these are also interesting problems because many of them contain opportunities to practice very ordinary skills of mathematics. But the bigger picture of the problem is something a lot more fundamental, like the idea of solution space that’s infinite. You can also think of problems that have no solutions. And I can give you many other examples. But this is a moment to consider problems that have a lot of math packed into them, but aren’t actually quite so easy to do in school and would work quite well for a range of credit levels of current academic skill, and would allow kids to stretch and not hit the ceiling right away, not trip, but be able to expand both their sense of like playfulness, but also development of ideas.
– So I think you kind of mentioned the idea of students during the summer and that kind of space of in some ways less, at least the students feel like it’s less structured learning. And now it’s like endless Summer for them, right, like of lots of opportunity for less structured learning. If I’m a teacher, and I teach math, and I’ve tuned in, and now you’ve of whetted my appetite for this type of problem it’s okay if not, but is there something I should google or phrase that helps me find problems that are like this one that you just described? If it’s not something that I have as part of, my resources already?
– Yeah, that’s a really good question. I don’t know that there’s a single site. But over the last, you know, a few decades, you know, math reform kind of comes in comes and comes and comes. So depending on whether you’ve taught, you know, five years, 10 years, 20 years, you’ve seen these cycles come around, they have different names. But going back as far as even the 1970s there were some really interesting problem books that were called something like basic skills with a problem solving orientation. I don’t think that’s quite what it was called. But it was, you know, in the era of basic skills, a guy named Robert Works and edited a whole bunch of problems that I ended up kind of learning when I was a very beginning teacher and realizing oh, like these can be adapted out the train problem, which I’m not gonna go into right now a problem that we’ve done every summer with kids very complicated problem that has no solutions. Originally born out of a very simple problem that Robert Works suggested, which involved trying to figure out whether it was possible to create all the sums out of a very small set of numbers. There’re problems that they’d been around, I think one has to kind of Google problems with them many solutions or problems with no solutions. Another source of the comprehensive school mathematics program, which was a curriculum in the 1980s, developed in the 70s and into the 80s and 90s. It’s still around, not very many districts used it, but it has very non-standard sorts of problems, that if you do the crosswalk to the Common Core, or whatever the standards are in your locality, easy to make that mapping. But what’s interesting about these problems is that they’re what I would consider the layered they have basic skills, and then they have basic concepts, but they involve a question that or a stuck kind of point or something where you can be like see something from a different angle so that the same time you’re doing some basic drill, you’re actually doing things that are far more interesting and not everything’s numerical. It’s also useful to be thinking about problems that are outside the space of letter number and calculation like problems involving space and pattern, problems involving probability. Like most people never get opportunities to really think like, how do you know how likely something is and their dice problems where you get really caught off guard about what the likely outcome is. So I think building some kind of like, collective space to collect these problems. We don’t need thousands of these problems. We need like 50 to 100 for now, I mean, it’s better to curate a few really good problems that kids can get hooked into. And that at least is one opportunity, things that take kids some time that they actually get interested in. And I think that is something for us to think really hard about rather than worrying about whether every single piece of the current curriculum we work with gets somehow managed to be transmitted to home. I think that’s not a recipe for helping kids. You know, feel like they enjoy mathematics, learn things not sort of get stuck. I think we really have to flip and use this opportunity definitely.
– It’s kind of like in science, you know, there’s this whole category of problems, discrepant events. And I, you know, as a science teacher, you learn, that’s the name for that problem set. So I think I was not a math teacher but I think if I was listening to that I heard there’s a whole category of problems called problems without solutions that I should go be looking for some very helpful before we wrap up this conversation, you know, kind of sticking in this realm of thinking about the learning at home, and adapting the curriculum and picking certain problems. Is there an example of how teachers could create learning opportunities about math that they couldn’t, for lack of a better word assigned, but have to do with going out and exploring the world? Are there any examples of that? I mean, you know, at a really young age could be count the trees in the park or something simple, right? If you’re really just at the counting phase, but I’m not curious more at that middle or later elementary where there might be something where you, you go out and you explore and you collect data, which seems like a valuable skill to be developing.
– Yeah, you’re actually kind of bringing up two different trains of thought here. One would be creating collections of things. And that leads to interesting questions about categorization and structure mathematical structure is one of the key practices in the Common Core. And I think for a lot of us, when that got introduced, we were uncertain, like, what does that mean for little kids to identify mathematical structure? If you have a collection of things or a set of problems and kind of think what structures are that you could create like categories or things that seems similar, there are things you can do with collections that you can try to figure out like what’s similar within this collection? What’s different a little kids could think about that. You can try to think about what does it mean to compare collections? And that took me to another kind of thinking that you’ve raised for me and that question, which is, we don’t spend enough time thinking about what this sort of basic question of how much or how many what that question is about when we ask it a little kids, we’re always assuming accounting type of answer. But we asked questions about how much or how big or how many were all kinds of different measurements, for example, is it more or less cold today? Is it you know, is something taking up more space than something else? Is something longer than something else? Is something taller is something more numerous? And we know from Piaget that kids mixed so sometimes they think something’s more because it takes up more space. There’s a lot of playing around with questions of comparison of quantity and measure, you know, what does it mean for something to be later than something else? That’s also a measurement, measurement of time, volume, weight, these are all different kinds of measurement. And with a little bit of just sitting back and thinking many, many people could be stimulating children to ask many more questions about find something that’s more than something else. What makes you say it’s more? And open your mind to think that they might not be comparing number but they might be comparing how much space something picks up or how much it weighs or how long it takes to carry it somewhere and invite children to think of lots of different ways to compare, in some sense, the question how much or how big among and think of reasons for that, which that gets you mathematical reasoning, it opens the space of what measurement actually means. But I do think that for this to happen outside of school, teachers might have to have the space to be able to be released from thinking they’re just taking their curriculum and putting it into zoom into meetings for kids, and thinking, are there some things that are worth spending a little time on that they could explain to families and that kids could kind of have some time and space to think about, and I wouldn’t worry so much that the kids are going to, fall behind this, in fact would give kids an opportunity to be enriched mathematically in ways we often don’t give them time for.
– Listening to you, I feel, my understanding of math education constantly stretched and I realized how much my experience of it as a science educator does not prepare me to be in front of students to teach math because yeah, I mean, well, but, you know, I think here you’re bringing up some really valuable examples of ways that teachers can adapt and create these kind of rich learning opportunities that are centered in you know, for talking about elementary level like math concepts that can involve the parents can involve going out in the real world, but still tie back to those key skills and in some ways translate from the kind of, you know, the academic way of describing it as you did into the, in some ways to still version that’s gonna get sent home to parents as like, hey, it’d be great if you did this, and this and this with your students and the next two weeks, and then, you know, let’s have them come back and talk to each other about that experience. So I think you’ve, you know, you kind of broaden what ways to think of what’s possible. A fast talk but we will continue together in just a moment, Deborah Ball thank you so much for joining us for another PLtogether Lounge Talk. If you’re joining us for the first time, you can listen to more conversations at pltogether.org. Deborah, thanks again for joining us.
– Thank you Adam.


The State Education Department has taken a number of steps to provide tools, resources, and support for the implementation of the Common Core and the new evaluation system. They have worked closely with the authors of the standards to identify and explain the 12 instructional shifts essential for successful implementation of the Common Core. Attached are some helpful web sites with educational data tools that support data driven instruction in the classroom. Most resources are posted on EngageNY.org to support this hard work:
- Tri-State Rubric & Review Process - A rubric constructed by the Tri-State collaborative (MA, RI, NY) to help teachers and principals determine the quality, rigor, and alignment to the Common Core of curricular materials;
- Common Core Toolkit - A compilation of many Common Core aligned tools and resources that span assessment and curriculum and can be used as part of professional development workshops;
- NY Math Emphases - Guidance about which content should be the major focus math areas for your students in each grade-level. (As you know, the assessment will prioritize the major work of each grade. This document highlights what that major work is – and could also be a helpful tool for explaining the Common Core in math to parents and others.);
- Curricular Exemplars - Exemplars in both ELA and Math to help serve as a guidepost for what Common Core aligned curricular materials can look like;
- Video Series - Professional development videos that present the instructional shifts in ELA and Math required by the new standards through conversation with David Coleman, a leading author of the Common Core and the incoming President of the College Board;
- NY State 3-8 Assessment Sample Items - Approximately 12 sample items for each grade level and subject, which include multiple choice, short constructed response, and extended constructed response; and
- Common Core Aligned Curriculum Maps for ELA and Math - Draft curriculum maps for ELA and Math, grades K-5, which help outline how the Common Core can be taught over the course of the academic year.


BSc (Hons) Mathematics and Physics
Write to us for more information
This full-time programme lasts four years. The first two years are a combination of the core modules taken on both the BSc in Mathematical Sciences and the BSc in Applied Physics at UL.
In these first two years the fundamental aspects of physics and mathematics are established. Physics subjects will include topics such as Mechanics, Waves, Light, Thermal Physics, Electromagnetism and Modern Physics, which covers the scope of current basic understanding in physics. In addition, more applied subjects are optics and semiconductors, which are essential to modern technology.
During the spring semester of the third year, a period of co-operative education (industry placement) gives you practical experience in a relevant work environment. It is organised by the University’s Department of Co-operative Education in collaboration with representatives from various industries, both in Ireland and abroad. Students are interviewed by company representatives. Upon selection, they are offered full-time employment during the Co-operative Education period and are paid at a competitive rate.
During the final year a project is undertaken which allows for an in-depth analysis of a particular problem. This also gives students interested in postgraduate research the opportunity to conduct exploratory research into a potential research topic.
- Common entrance
- Waves / Light / Modern Physics
- Semiconductor devices
- Calculation 2
- More linear algebra
- Introduction to Probability and Statistics
- Linear analysis methods
- Vector analysis
- Ordinary Differential Equations
- Modern Physics
- Thermal Physics
- Introduction to numerical analysis
- Partial Differential Equations
- Quantum Mechanics
- Physics of solids
- Introduction to Fluid Mechanics
- Complex analysis
- Atomic / molecular / laser physics
- Numerical solutions for PDE
- Linear Algebra 2
- Probability models
- Cooperative education
- Solid State Physics 1
- Mathematics of natural phenomena
- Perturbation technology. and asymptotics
- Math and Physics Project 1
- Nanotechnology 1
- Modern measurement physics
- Solid State Physics 2
- Dynamic systems
- Mathematical model
- Math and Physics Project 2
- Nanotechnology 2
- Medical Instrumentation
Employability skills of this degree
- Design and conduct observational and experimental studies.
- Analyze and interpret data, find patterns and draw conclusions.
- Dealing with abstract concepts.
- Present mathematical arguments and conclusions with precision and clarity.
- Advanced arithmetic and analysis of large amounts of data.
- Logical thinking.
- Arithmetic: mathematical models, interpreting and presenting information graphically and using mathematics to find solutions to scientific problems.
- IT skills, including specialist software packages and some programming.
- Attention to detail.
- Communication: conveying complex ideas and using technical language correctly.
- Applicants will require a baccalaureate degree officially translated into English.
- IELTS 6.0 or higher (or internationally recognised equivalent).
- TOEFL 580 (paper-based) or 90 (online).
- UL has approved the use of the Duolingo English Test (DET) as a temporary measure for 2021/2 admission (due to test center closures). The minimum requirement will be a DET score of 110. An interview may be required along with this for certain programs.
Applicants must possess at the time of enrolment the prescribed Certificate of Completion (or an approved equivalent) with a minimum of six subjects which must include: two H5 (Higher Level) grades and four O6 (Ordinary Level) grades or four H7 (Higher Level) grades. Subjects must include Mathematics, Irish or another language.
In addition, applicants must have a minimum grade of O3/H7 in Mathematics and a grade of H4 in any of the following: Agricultural Sciences, Applied Mathematics, Biology, Chemistry, Physics, Physics with Chemistry.
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Statistical Computing 2
This website contains teaching materials for part of the second computing unit of the taught component of the Computational Statistics and Data Science (COMPASS) PhD programme. The source for this website is available here. The website for the first computing unit can be found here.
The material provided here focusses on how
R can be interfaced with
C++ via the
Rcpp package. More specifically, we guide the students through the following steps:
Rcpppackage for easier/safer integration between
Rcpp sugarfor performing standard statistical operations in
performing numerical linear algebra computation via the
C++code in an
Some of the chapters contain programming exercises, focussed on exploiting the
Rcpp family of packages to speed-up statistical computations.
- Allaire, J.J., Eddelbuettel, D. and François, R., 2018. Rcpp Attributes. Vignette included in R package Rcpp, URL http://CRAN.R-Project.org/package=Rcpp.
- Chambers, J.M., 2017. Extending R. Chapman and Hall/CRC.
- Eddelbuettel, D., 2013. Seamless R and C++ integration with Rcpp. New York: Springer.
- Eddelbuettel, D. and Balamuta, J.J., 2018. Extending R with C++: A Brief Introduction to Rcpp. The American Statistician, 72(1), pp.28-36.
- Eddelbuettel, D. and François, R., 2010. Rcpp syntactic sugar.
- Eddelbuettel, D. and Sanderson, C., 2014. RcppArmadillo: Accelerating R with high-performance C++ linear algebra. Computational Statistics & Data Analysis, 71, pp.1054-1063.
- Matloff, N., 2015. Parallel computing for data science: with examples in R, C++ and CUDA. Chapman and Hall/CRC.
- Wickham, H., 2014. Advanced r. Chapman and Hall/CRC.


Kids learn many things at home nowadays before they join preschool or any play schools at an early age. They learn reading and writing numbers and the alphabet from their parents. Writing numbers can be a challenging activity for the kids in preschool and kindergarten. However, some secret tips will ease how to teach your kid to read and write numbers. That means we can train them how to count the numbers and make them learn how to write the same. Let’s understand how to teach your kids to read and write numbers using simple tricks.
As we all know, one of the first and foremost lessons we teach our kids is how to count numbers. This task is similar to opening the doors to mathematics, and understanding numbers is a necessary skill to conquer the subject in the early years of a kid’s education. Numerous approaches can support kids to feel confident in reading or counting numbers alone while teaching. It’s essential to prove the ability to count/read/write numbers and help them build an understanding of numbers that will help kids evolve mathematical skills in the coming days. Teaching to read and write numbers doesn’t have to be challenging. You need to be patient and follow an engaging approach to train your kids about reading and writing numbers so that they will be excited to learn more with enthusiasm.
Below are the few tricks that help you teach your kids to write and read numbers.
1. Start your lesson with the formation of numbers
Make your child understand the formation of numbers using simple shapes like curves, lines, circles, etc.
2. How to start writing the number
Train your kid to write numbers by starting from the top portion of the number.
3. Use number stories
Sharing some exciting stories will help kids pronounce numbers in a sequence and understand how much the number indicates. For example, counting figures will be a simple task to explain to them about counting and understanding numbers.
4. Count and write numbers
Use some playing things or fingers to make kids understand the count of numbers. Fold your fingers, start counting unfolded fingers, and write the numbers each time. In this way, we can teach them numbers from 0 to 10 quickly. This is a well-known technique to teach kids some basic addition and subtraction in maths. Also, we can use toys and rhymes to make them understand counting.
5. Write numbers in different places
ou can teach your kids to write numbers by making them observe number shapes in various places. For example, by writing them on paper, writing numbers on a floor using some colours, etc.
Apart from the above-mentioned tricks, there exist multiple techniques to teach kids to read and write numbers. Many of us know that kids will grasp things by hearing and seeing something more comfortable to pronounce. Thus, we can use the technology to show them some fun rhymes and videos on numbers to make them understand effectively. Besides, you can use some workbooks that help kids read and write by seeing some pictures. In this way, we can use a number of simple tricks to teach kids writing and reading numbers in an easily understandable way.


Report CopyRight/DMCA Form For : Proofs And Mathematical Reasoning University Of Birmingham
1 Introduction 6,2 Mathematical language and symbols 6. 2 1 Mathematics is a language 6,2 2 Greek alphabet 6. 2 3 Symbols 6,2 4 Words in mathematics 7,3 What is a proof 9. 3 1 Writer versus reader 9,3 2 Methods of proofs 9. 3 3 Implications and if and only if statements 10,4 Direct proof 11. 4 1 Description of method 11,4 2 Hard parts 11,4 3 Examples 11. 4 4 Fallacious proofs 15,4 5 Counterexamples 16,5 Proof by cases 17. 5 1 Method 17,5 2 Hard parts 17,5 3 Examples of proof by cases 17. 6 Mathematical Induction 19,6 1 Method 19,6 2 Versions of induction 19. 6 3 Hard parts 20,6 4 Examples of mathematical induction 20. 7 Contradiction 26,7 1 Method 26,7 2 Hard parts 26. 7 3 Examples of proof by contradiction 26,8 Contrapositive 29. 8 1 Method 29,8 2 Hard parts 29,8 3 Examples 29, 9 1 What common mistakes do students make when trying to present the proofs 31. 9 2 What are the reasons for mistakes 32,9 3 Advice to students for writing good proofs 32. 9 4 Friendly reminder 32,c University of Birmingham 2014. 10 Sets 34,10 1 Basics 34,10 2 Subsets and power sets 34. 10 3 Cardinality and equality 35,10 4 Common sets of numbers 36. 10 5 How to describe a set 37,10 6 More on cardinality 37. 10 7 Operations on sets 38,10 8 Theorems 39,11 Functions 41. 11 1 Image and preimage 41,11 2 Composition of the functions 42. 11 3 Special functions 42,11 4 Injectivity surjectivity bijectivity 43. 11 5 Inverse function 44,11 6 Even and odd functions 44. 11 7 Exercises 45,12 Appendix 47,c University of Birmingham 2014. Talk to any group of lecturers about how their students handle proof and reasoning when. presenting mathematics and you will soon hear a long list of improvements they would wish for. And yet if no one has ever explained clearly in simple but rigorous terms what is expected it is. hardly a surprise that this is a regular comment The project that Agata Stefanowicz worked on. at the University of Birmingham over the summer of 2014 had as its aim clarifying and codifying. views of staff on these matters and then using these as the basis of an introduction to the basic. methods of proof and reasoning in a single document that might help new and indeed continuing. students to gain a deeper understanding of how we write good proofs and present clear and logical. mathematics Through a judicious selection of examples and techniques students are presented. with instructive examples and straightforward advice on how to improve the way they produce. and present good mathematics An added feature that further enhances the written text is the. use of linked videos files that offer the reader the experience of live mathematics developed by. an expert And Chapter 9 that looks at common mistakes that are made when students present. proofs should be compulsory reading for every student of mathematics We are confident that. regardless of ability all students will find something to improve their study of mathematics within. the pages that follow But this will be doubly true if they engage with the problems by trying. them as they go through this guide,Michael Grove Joe Kyle. September 2014,c University of Birmingham 2014,Acknowledgements. I would like to say a big thank you to the Mathematics Support Centre team for the opportunity. to work on an interesting project and for the help and advice from the very first day Special. gratitude goes to Dr Joe Kyle for his detailed comments on my work and tips on creating the. document Thank you also to Michael Grove for his cheerful supervision fruitful brainstorming. conversations and many ideas on improving the document I cannot forget to mention Dr Simon. Goodwin and Dr Corneliu Hoffman thank you for your time and friendly advice The document. would not be the same without help from the lecturers at the University of Birmingham who took. part in my survey thank you all, Finally thank you to my fellow interns Heather Collis Allan Cunningham Mano Sivanthara. jah and Rory Whelan for making the internship an excellent experience. c University of Birmingham 2014,1 Introduction, From the first day at university you will hear mention of writing Mathematics in a good style and. using proper English You will probably start wondering what is the whole deal with words when. you just wanted to work with numbers If on top of this scary welcome talk you get a number of. definitions and theorems thrown at you in your first week where most of them include strange notions. that you cannot completely make sense of do not worry It is important to notice how big difference. there is between mathematics at school and at the university Before the start of the course many of. us visualise really hard differential equations long calculations and x long digit numbers Most of us. will be struck seeing theorems like a 0 0 Now while it is obvious to everybody mathematicians. are the ones who will not take things for granted and would like to see the proof. This booklet is intended to give the gist of mathematics at university present the language used and. the methods of proofs A number of examples will be given which should be a good resource for further. study and an extra exercise in constructing your own arguments We will start with introducing the. mathematical language and symbols before moving onto the serious matter of writing the mathematical. proofs Each theorem is followed by the notes which are the thoughts on the topic intended to give. a deeper idea of the statement You will find that some proofs are missing the steps and the purple. notes will hopefully guide you to complete the proof yourself If stuck you can watch the videos which. should explain the argument step by step Most of the theorems presented some easier and others. more complicated are discussed in first year of the mathematics course The last two chapters give. the basics of sets and functions as well as present plenty of examples for the reader s practice. 2 Mathematical language and symbols,2 1 Mathematics is a language. Mathematics at school gives us good basics in a country where mathematical language is spoken. after GCSEs and A Levels we would be able to introduce ourselves buy a train ticket or order a pizza. To have a fluent conversation however a lot of work still needs to be done. Mathematics at university is going to surprise you First you will need to learn the language to. be able to communicate clearly with others This section will provide the grammar notes i e the. commonly used symbols and notation so that you can start writing your mathematical statements in. a good style And like with any other foreign language practice makes perfect so take advantage. of any extra exercises which over time will make you fluent in a mathematical world. 2 2 Greek alphabet, Greek alphabet upper and lower cases and the names of the letters. 2 3 Symbols, Writing proofs is much more efficient if you get used to the simple symbols that save us writing long. sentences very useful during fast paced lectures Below you will find the basic list with the symbols. on the left and their meaning on the right hand side which should be a good start to exploring further. mathematics Note that these are useful shorthands when you need to note the ideas down quickly In. general though when writing your own proofs your lecturers will advise you to use words instead of. the fancy notation especially at the beginning until you are totally comfortable with the statements. if then When reading mathematical books you will notice that the word implies appears. more often than the symbol,c University of Birmingham 2014. A alpha N nu,gamma O omicron,E epsilon P rho,Z zeta sigma. H eta T tau,theta Y upsilon,I iota phi,K kappa X chi. lambda psi,M mu omega,Table 1 Greek letters,Quantifiers. universal quantifier for all,existential quantifier there exists. Symbols in set theory,intersection,or proper subset. composition of functions, Common symbols used when writing proofs and definitions. if and only if,is defined as,is equivalent to,or such that. E or contradiction,or end of proof,2 4 Words in mathematics. Many symbols presented above are useful tools in writing mathematical statements but nothing. more than a convenient shorthand You must always remember that a good proof should also include. words As mentioned at the beginning of the paper correct English or any other language in which. you are literate is as important as the symbols and numbers when writing mathematics Since it is. important to present proofs clearly it is good to add the explanation of what is happening at each. step using full sentences The whole page with just numbers and symbols without a single word will. nearly always be an example of a bad proof, Tea or coffee Mathematical language though using mentioned earlier correct English differs. slightly from our everyday communication The classic example is a joke about a mathematician. c University of Birmingham 2014, who asked whether they would like a tea or coffee answers simply yes This is because or in. mathematics is inclusive so A or B is a set of things where each of them must be either in A or in B. In another words elements of A or B are both those in A and those in B On the other hand when. considering a set A and B then each of its elements must be both in A and B. Exercise 2 1 Question There are 3 spoons 4 forks and 4 knives on the table What fraction of the. utensils are forks OR knives, Answer Forks or knives means that we consider both of these sets We have 4 of each so there. are 8 together Therefore we have that forks or knives constitute to 11 of all the utensils. If we were asked what fraction of the utensils are forks and knives then the answer would be 0. since no utensil is both fork and knive, Please refer to section 10 where the operations on sets are explained in detail The notions or. and and are illustrated on the Venn diagrams which should help to understand them better. c University of Birmingham 2014,3 What is a proof, The search for a mathematical proof is the search for a. knowledge which is more absolute than the knowledge accu. mulated by any other discipline,Simon Singh, A proof is a sequence of logical statements one implying another which gives an explanation of why. a given statement is true Previously established theorems may be used to deduce the new ones one. may also refer to axioms which are the starting points rules accepted by everyone Mathematical. proof is absolute which means that once a theorem is proved it is proved for ever Until proven. though the statement is never accepted as a true one. Writing proofs is the essence of mathematics studies You will notice very quickly that from day. one at university lecturers will be very thorough with their explanations Every word will be defined. notations clearly presented and each theorem proved We learn how to construct logical arguments and. what a good proof looks like It is not easy though and requires practice therefore it is always tempting. for students to learn theorems and apply them leaving proofs behind This is a really bad habit and. does not pay off during final examinations instead go through the proofs given in lectures and. textbooks understand them and ask for help whenever you are stuck There are a number of methods. which can be used to prove statements some of which will be presented in the next sections Hard. and tiring at the beginning constructing proofs gives a lot of satisfaction when the end is reached. successfully,3 1 Writer versus reader, Kevin Houston in his book 2 gives an idea to think of a proof like a small battle between the. reader and the writer At the beginning of mathematics studies you will often be the reader learning. the proofs given by your lecturers or found in textbooks You should then take the active attitude. which means working through the given proof with pen and paper Reading proofs is not easy and may. get boring if you just try to read it like a novel comfortable on your sofa with the half concentration. level Probably the most important part is to question everything what the writer is telling you. Treat it as the argument between yourself and the author of the proof and ask them why at each. step of their reasoning, When it comes to writing your own proof the final version should be clear and have no gaps in. understanding Here a good idea is to think about someone else as the person who would question. each of the steps you present The argument should flow and have enough explanations so that the. reader will find the answer to every why they might ask. 3 2 Methods of proofs, There are many techniques that can be used to prove the statements It is often not obvious at. the beginning which one to use although with a bit of practice we may be able to give an educated. guess and hopefully reach the required conclusion It is important to notice that there is no one ideal. proof a theorem can be established using different techniques and none of them will be better or. worse as long as they are all valid For example in Proofs from the book we may find six different. proofs of the infinity of primes one of which is presented in section 7 Go ahead and master the. techniques you might discover the passion for pure mathematics.


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Math majors already know that their academic course is great for a career in finance, statistics, accounting, and academia. But what if you don’t want to do any of those things? You don’t need to change your major to find a job you actually want. In fact, there are many jobs for math majors out there that — at first glance — don’t seem to involve much math. Check out these six surprising jobs for folks with math degrees, and get ready to wow employers with your number skills!


Solutions and investigations. for the first time. Students will be emailed their login details nearer the time. The Junior Mathematical Olympiad is a follow- on round to the Junior Mathematical. There are two papers.
Mathematics - Grade 12 past question papers and memos. If you& x27; d like to chat with someone about audiobook the Maths Challenge. This page contains Mathematics Grade 12.
there is the opportunity for students to take practice Challenge pdf papers which will allow you to see how it works and get. Junior Mathematical Challenge archive Try online Challenges. award thresholds - online JMC Gold 102+.
was of easy to moderate level for the students with Standard Maths while for those with Basic Maths. The Junior Maths Challenge will run in a slightly different format this year and will run online. simply call us onor email. Forreasonsofspace, thesesolutionsarenecessarilybrief. Maybe you would like to learn more about one of these.
J admin Cowley students from 7R1. which has meant I spent part of last week printing papers & answers to create folders. but provisionally 29th June.
Olympiadand IMCpapers. although with any luck such errors will be noted in the relevant solutions. and sixth form students in England and Wales.
Dates of this year& x27; s follow- on rounds. Maths Challenge; Maths Enrichment; Australian Intermediate Mathematics Olympiad;. AMO paper with solutions here.
Results should be available by early August. An important aim with the Final Round is for learners to interact with others in the context of mathematics - mathematics is a social activity and we. for most of the problems. Unlike the Junior and Intermediate challenges. This paper assesses the. download past papers.
Senior pdf download Maths Challenge Advice Booklet. while the second part will be held ebook on Wednesday junior maths challenge 2020 paper magazine May 12. If you have found our materials valuable.
Grades 4- 5 learners write the Junior paper and Grades 6- 7 learners write the Senior paper. Through participation. download past papers and solutions The following materials are copyright UK Mathematics Trust and may be used in accordance with our policy on the use of intellectual property. Junior Maths Challenge - year 8.
paper maths challenge junior magazine. The Junior Mathematical Challenge is a 60- minute. MathWorks Math Modeling.
10 in Section A and six in Section B. Junior Mathematical Challenge Paper. multiple- choice competition aimed at students across the UK. please consider making a donation to support our work.
past papers and solutions. I explain question 18 from the. the challenge will take place online with Cowley students taking the challenge on Wednesday 1st July at 11 00am.
The Mathematical Association runs the Primary Maths Challenge and the PMC website http. This year she& x27; s decided to use only past papers. We cannot guarantee grading if papers have not arrived by Friday May 28. Only answers are charged.
although younger students may also take part. There were no follow- on rounds due to Covid- 19. students experience what it& read x27; s like to work as a team to tackle a real- world problem under time and resource constraints. epub Jul ; Norman Cuello Barroso. JUNIOR MATHS CHALLENGE GRADE BOUNDARIES. I explain question 25 from the.
Mathematics Standard. Challenge is a contest for high school juniors and seniors in the U. precision of thought.
and understood the solutions. The following is a list of Primary School Revision Papers Mid T. Teachers in home- schools are eligible to register as school co- ordinators and run our competitions.
CBSE has conducted the two different Maths papers. free pdf My year 7 daughter has begun her 12 week countdown to the UKMT. akin to those faced by professional mathematicians. We did not find results for. Paper 1 and Paper 2. The problems on the Junior Mathematical Challenge are designed to make students think.
Did all the intermediate papers up to. Announcement of Results. ALL GRADE 12 MATHEMATICS EXAM PAPERS. Subo on Year 1 Past Paper.
Date to confirmed later. CBSE Class 10 Maths exam was conducted on 12th March. and fluency in using basic mathematical techniques to solve interesting problems.
The last time this happened was in. Can get 22- 25 on most intermediate maths challenge papers and 17- Télécharger 20 on the senior ones. termediate Maths Challenge- Thursday 6th Feb. is a two- hour competition consisting of 16 problems. The last time it happened in a non- palindromic year was 2020 in 1982.
CBSE Class 10 Maths Paper. 8R1 and 8B1 will take part in the. any incorrect answer in the SMC will lose you a mark.
AQA A- level Maths Autumn Exam 7357 Paper 1, 2, Exam Discussion Edexcel A- Level Mathematics - Pure Maths 1 - 7 October. Return of Papers to the Organisers. and will next happen in. Any errors in the questions have not been corrected.
Click to DOWNLOAD the papers for FREE of charge. but I& x27; m te that the Questions and Solutions available here are as they were presented to schools. Application Process Now Closed -. UKMT junior maths MT Junior maths challenge is a paper taken by the top students in year 7 and 8 every year i. Grading for the competition begins during the University mid- semester break.
Time is of the essence. junior maths challenge. and Western Cape. This mathematics competition is for students in years 9 to 11. Chithambara Maths Challenge Exam postpone until further notice; Recent Comments. The first part of the competition will be sat on Wednesday April 14.
Try online Challenges. Check spelling or type a new query. is hosted as a bolt- on to https. We did not find results for. Junior Maths Challenge- Thursday 30th April. The Papers are for all Provinces.
The usual deductions for incorrect answers to questions 16 to 25 were not applied. Download past papers and solutions The following materials are copyright UK Mathematics Trust and may be used in accordance with our policy on the use of intellectual property. You can buy collections junior maths challenge 2020 paper magazine of older papers and solutions through our shop. the Junior Maths Challenge was held online due to the COVID- 19 pandemic. this study will highlight the challenges mathematics teachers face in inculcating higher- order thinking skills among students. Junior Maths Challenge boundaries so high.
Registered home- schools. AMC past papers in PDF format Order free PDF versions of AMC. It encourages mathematical reasoning. Learners have 90 minutes to solve 15 challenging mathematical problems. T T United Kingdom Mathematics Trust junior maths challenge 2020 paper magazine Junior Mathematical Challenge Tuesday 30 April.
You can also check the analysis and review. is the 36th year of this highly successful Competition. AMO paper and solutions junior maths challenge 2020 paper magazine Download the.
Junior Mathematical Challenge ran by the UK Mathematics Trust.
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Perhaps you’ve heard of it: Pi Day. The day when math enthusiasts across the country celebrate March 14, or the first 3 digits of Pi.
This year marks a significant celebration: The first five digits will be represented on 3.14.15 as well as the next five at exactly 9:26:53 am. So, in what will be a once-in-a-lifetime event for most of us, the first 10 digits of Pi will correspond to the date and time this Saturday.
I caught wind of this news a few weeks ago, so I’ve already purchased a commemorative t-shirt. After all, what’s a special event without a souvenir, right?
I imagine that we’ll hear the news of babies born at the exact second of Pi Day 2015. And bakeries across the nation are celebrating with special pies of Pi. My daughter is trying to memorize the first 100 digits of Pi for a contest they’re holding at school. Think we’ll have a Google Doodle for Pi Day?
Regardless, check out some of the fabulous Pi events I unearthed in our region and beyond:
- There’s a Pie-Eating Flash Mob in downtown Hickory NC from exactly 9:26 a.m. to 9:36 a.m. Their tagline? “Come to the Geek Side… We have Pi”
- Love beer AND pie? Check out Port City Brewing Company in Durham. They’ll be pairing beers with matching pies from 3 pm to 6 pm.
- Over in Greensboro, they’re hosting a Pie Auction to benefit Cakalak Thunder Drum Corps from 6 pm to 8 pm.
- Happen to be in NYC? Join the National Museum of Mathematics in Madison Square Park for a countdown and free pie! The museum will have lots of fun Pi Day activities for young and old.
- In Ann Arbor, MI, they’ll be having a 3.14 mile Pi Day Celebration run
- There are two fancy Pi Day celebrations in the San Francisco Bay area
- If you’re in DC, there are a ton of restaurants offering Pi Day specialties and events.
Need a pie recipe? Try one of these 13 Irrational Pie Recipes.
Remember: Pi Day is not for Squares.


If you may demonstrate a good history of repaying loans on time (and therefore you’ve got great credit scores), you’re going to get lower APRs on virtually every sort of loan. Many financial loan lenders will provide you with different offerings and deals. You’re able to take loans against your current property or take a normal home loan.
Women are now nearly all borrowers of such loans, along with nearly all college students. Simple interest is the interest that’s earned on the principal quantity of money over a specific amount of time.
The mortgage business is a comparatively new concept in India and is chiefly called the housing finance market. https://grademiners.com/term-papers Especially with long-term loans, most each periodic payment is an interest expense, and you merely pay off a little part of the balance. The insurance provider can provide you any and all details about the policy so long as you’re the person who owns the policy or the person on which the insurance was written.
Depending on the eligibility, you can secure a specific quantity of credit. After 20 or 25 decades of payments below this plan, your remaining balance might be forgiven. The most length of the loan is 20 decades.
For instance, you can observe the substantial effect of earning a down payment a lot more significant that with an automobile loan. You may also print or plot a payment program. The loan payment formula shown https://www.irif.fr/~epit/ is used for a typical loan amortized for a set period of time with a fixed pace.
Within the previous 50 decades there have been several large shifts in American higher education. With a couple of exceptions, all those marks were from student loans. That means you can say our day starts with the idea of maths.
In the majority of the scenarios, you don’t refinance your loan on a yearly bases, so you might want to understand what the rate of interest is for each period. Along with the above modules, the course includes a selection of non-modular activities, covering curriculum subject wisdom and expert practice. It emphasizes the use of the graphing calculator as a learning tool and as a means to obtain solutions.
The closing costs vary based on the area and the kind of loan. The gure below represents the distance covered by a vehicle within a given amount of time Find the typical speed of the vehicle in kilometres per hour. You will devote a substantial period of time on placement.
Candidates within this program are expected to demonstrate content knowledge, pedagogical knowledge and techniques, professional expertise, and professional dispositions to be qualified to enter student teaching or internship placements. Students will acquire advanced knowledge and techniques in mathematics, and paper editing service the capability to use them to tackle complex problems in quite a few situations.
Among the insights supplied by mathematical modeling is that essentially the exact mathematical or statistical structure can on occasion model seemingly different circumstances. Firstly, a lot of factors in the equations stay unaccounted for. Statistical Inferencedevelops your understanding of mathematical approaches to statistical inference, an area where the skills of hypothesis testing, estimation and prediction are employed in an increasing number of authentic world fields in addition to in research design.
There is an assortment of factors that help determine the sum of home loan you are able. The formula used to figure loan payments is precisely the same as the formula used to compute payments on a normal annuity. There are assorted types of loan forgiveness programs out there.
Finding the Best Loan Mathematics
Students will justify their last figures. It is an essential key in today’s business and industries. Loan mathematics are just like an annuity.
Failure to keep academic integrity won’t be tolerated. These standards concentrate on English Language Arts and Mathematics to be able to be certain that students possess the skills essential to succeed in the rest of the subjects. Furthermore, you’ll have a profound understanding of Mathematics and be well placed to have a leadership role in school.
If you click Start Monitoring, you may keep dropping PDFs in that folder and the application will automatically convert them into JPGs provided that the program is open. Disbursement is usually dependent on the stage of completion of the undertaking. A postbaccalaureate program is notTEACH-Grant-eligible if it’s provided by means of a school which also provides a bachelor’s degree in education.
Looking at amortization is extremely helpful if you would like to fully grasp how borrowing works. Calculators are perfect for obtaining a quick answer. Personal loans aren’t eligible.


for 0 < x <= 1 uses Taylor series expansion Our unit tests suggest that the accuracy of the Exponential Integral function is correct up to 13 floating point digits. Return Complex Returns sqrt(a2 + b2) without underflow/overflow. Parameters double x The value to evaluate. Return double The logistic function of p. navigate here
Sign in using Search within: Articles Quick Answers Messages home articles Chapters and Sections> Search Latest Articles Latest Tips/Tricks Top Articles Beginner Articles Technical Blogs Posting/Update Guidelines Article Help Forum Article The constants DBL_MIN and double.MinValue are different because they are minimizing over different ranges. I have to use erf / erfc function, but I did not find it under Math. Return double General Harmonic number.
C# Erfc Function
Please look here for a custom solution. Parameters int t The Harmonic number which needs to be computed. more stack exchange communities company blog Stack Exchange Inbox Reputation and Badges sign up log in tour help Tour Start here for a quick overview of the site Help Center Detailed double BetaIncomplete(double a, double b, double x) Returns the lower incomplete (unregularized) beta function B(a,b,x) = int(t^(a-1)*(1-t)^(b-1),t=0..x) for real a > 0, b > 0, 1 >= x >= 0.
double BesselI1(double x) Returns the modified Bessel function of first kind, order 1 of the argument.
We have tested this implementation against the arbitrary precision mpmath library and found cases where we can only guarantee 9 significant figures correct.
Chebyshev polynomial expansions are employed in each interval.
He has over 15 years programming experience in Basic, Fortran, C, C++, Matlab, and C#, specializing in numerical computation methods, algorithms, physical modeling, computer-aided design (CAD) development, graphics user interface, and
Copy inline float nearbyint(float _X) restrict(amp); inline double nearbyint(double _X) restrict(amp); Parameters_X Floating-point valueReturn ValueReturns the rounded integer value.nearbyintf FunctionRounds the argument to an integer value in floating-point format, using the
Copy inline float modf( float _X, _Out_ float* _Iptr) restrict(amp); inline double modf( double _X, _Out_ double* _Iptr) restrict(amp); Parameters_X Floating-point value_Iptr (out parameter) The integer portion of _X, as a
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Why are Car Batteries still so heavy?
See Stand-alone error function for details of the algorithm.This code is in the public domain.
Return double The lower incomplete (unregularized) beta function.
Any gotchas? The range is partitioned into the two intervals [0, 2] and (2, infinity). The numeric limit constants for doubles look deceptively like C counterparts, but are not the same. Function names are capitalizations of traditional names, with a few exceptions.
Copy inline float fmodf( float _X, float _Y) restrict(amp); Parameters_X The first floating-point argument._Y The second floating-point argument.Return ValueThe remainder of _X divided by _Y; that is, the value of _X A&s Formula This number should be between 0 and 1. double Factorial(int x) Computes the factorial function x -> x! Parameters double z The argument of the gamma function.
Check out my blog or send me a note. With more than twenty years of computer programming experience, he has published several papers in physics journals.Bibliographic informationTitleNumerical Methods, Algorithms and Tools in C#AuthorWaldemar Dos PassosEditionillustratedPublisherCRC Press, 2016ISBN1420007602, 9781420007602Length598 pagesSubjectsScience›Physics›Mathematical & double Binomial(int n, int k) Computes the binomial coefficient: n choose k. For example, C# has no error function erf(x).
Inverse cumulative distribution function is calculated by using the InvNormalDistribution subroutine. Chebyshev polynomial expansions are employed in each interval. C# Erfc Function Thanks for the article! functions in math class and this Erf func share|improve this answer edited Apr 3 '14 at 10:49 answered Apr 3 '14 at 10:43 kudra 94112 add a comment| up vote 0
He also describes various methods for approximating integrals and special functions, routines for performing statistical analyses of data, and least squares and numerical curve fitting methods for analyzing experimental data, along http://winnsecurityproducts.com/error-function/integral-of-error-function.html MPFR source is available from www.mpfr.org. asked 2 years ago viewed 1464 times active 3 months ago Upcoming Events 2016 Community Moderator Election ends in 2 days Visit Chat Linked 2 Does anyone know of a .NET The author discusses alternative ways to obtain computer-generated pseudo-random numbers and real random numbers generated by naturally occurring physical phenomena.
The book clearly explains practical chart and graphics methods and their underlying algorithms. Downloads page Delphi Delphi version. Our unit tests suggest that the accuracy of the Gamma function is correct up to 13 floating point digits.
Numerical Methods, Algorithms and Tools in C# presents a broad collection...https://books.google.com/books/about/Numerical_Methods_Algorithms_and_Tools_i.html?id=dFHvBQAAQBAJ&utm_source=gb-gplus-shareNumerical Methods, Algorithms and Tools in C#My libraryHelpAdvanced Book SearchBuy eBook - $100.76Get this book in printCRC PressAmazon.comBarnes&Noble.comBooks-A-MillionIndieBoundAll sellers»Numerical Methods, Algorithms
Parameters double x The value to compute the bessel function of. You probably want to add using System; at the top of your files so you can just type Math rather than System.Math every time you need to call a method. double ExponentialIntegral(double x, int n) Computes the generalized Exponential Integral function (En). It's very good that you pointed out that double.Epsilon doesn't represent the value of epsilon as in numerics usual.
Complex Hypotenuse(Complex a, Complex b) Numerically stable hypotenuse of a right angle triangle, i.e. (a,b) -> sqrt(a^2 + b^2) Parameters Complex a The length of side a of the triangle. Introduction to Numerical Solutions Generate and add keyword variations using AdWords API Introduction to .NET Window Tabs (WndTabs) Add-In for DevStudio SAPrefs - Netscape-like Preferences Dialog AngleSharp Comments and Discussions in computer science and engineering along with a Ph.D. weblink If that isn't sufficient, then there books such as Abramowitz and Stegun, which is a 40 year old handbook of mathematical functions that's still regarded as a important reference.
Return double The logarithm of the Euler Beta function evaluated at z,w. Functions in System.Math follow .NET naming conventions, and so start with capital letters. Return double The upper incomplete regularized gamma function. Return double The inverse error function evaluated at given value.
The C constant DBL_EPSILON is the smallest positive double precision number x such that 1 + x does not equal 1. Our unit tests suggest that the accuracy of the Gamma function is correct up to 14 floating point digits. Some of the missing functionality can be filled in easily. for value > 0 double Gamma(double z) Computes the Gamma function.
Conclusions In summary: Math functions are members of the System.Math class. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. */ #region Constants const double tiny = 1e-300; const Copy inline float ldexpf( float _X, int _Exp) restrict(amp); Parameters_X Floating-point value, mantissa_Exp Integer value, exponentReturn ValueReturns _X * 2^_Explgamma FunctionComputes the natural logarithm of the absolute value of gamma of double ExponentialMinusOne(double power) Numerically stable exponential minus one, i.e.
The range is partitioned into the two intervals [0, 8] and (8, infinity). Parameters double z value to evaluate. p - 0.5 : Math.Sqrt(-2 * Math.Log(1 - p)); r = q * q; x = (p < ierfp_low) ? (((((c * q + c) * q + c) double BesselI0MStruveL0(double x) Returns the difference between the Bessel I0 and Struve L0 functions.
Return double A value value! Return double The Euler Beta function evaluated at z,w. double StruveL1(double x) Returns the modified Struve function of order 1.


Sprinkler K-factor is based on the following formula:
The real meaning of K-factor is that the flow in gpm can be discharged from the nozzle when the pressure is 1 psi.
While K-factor is used in calculation in other units like that in SI system, the K-factor of a nozzle, such as a sprinkler, a measuring orifice, or even any outlet of a pipe, must be converted to a value based on the units of flow and pressure in such calculation.
The following table offers such conversions:
In Hazen-Williams formula, flow is proportional to pressure to 1.85-th power, and thus K-factor is slightly different from that calculated by the above formula.
In flow testing and sprinkler system calculations using Hazen-Williams formula, K-factor is calculated using the following formula:
A K-factor calculated based on this formula is 45 times of the value calculated based on flow in L/s and pressure in kPa:
If bar is use for SI calculations, K-(L/s-bar) is 1/10 of K-(L/s-kPa), i.e. 4.5.


PDF Studio comes with precision measuring tools that can be used to measure the distance, area, and perimeter of objects within the PDFs. Various unit types (i.e. pt, mm, in, ft, m, etc…) can be set and is displayed next to the measurement. Each tool can also be calibrated to match the scale within the PDF for accurate measurements. Once placed, measurements can be modified by dragging any of the vertices on the measurement and the values will be updated accordingly.
PDF Studio offers advanced settings when using measuring annotation tools:
- Set separate X & Y calibration values
- Add comments to the measurement value
- Snap to content for precise location
- Always use fixed angles
Available Measurement Annotations:
The Distance Measurement Annotation is used to calculate the length a single linear measurement.
The Perimeter Measurement Annotation is used to calculate the length of all sides of a shape or a multi-segment line.
The Area Measurement Annotation is used to calculate the area of a given shape.


|A measure of the total gain/loss expressed as a percentage of invested capital.
|A measure of risk adjusted performance relative to a benchmark. A fund that produced the expected return for the level of risk assumed has an Alpha of zero. A positive Alpha shows that the manager produced a return greater than expected for the risk taken while a negative Alpha indicates the converse. Essentially a proxy for the fund managers skill.
|A standard against which an investment is measured. (The BTopFX Index data from Barclay Hedge is used here for comparison purposes.)
|A measure of an investments’ volatility relative to the benchmark. It is a measure of risk. A beta of 1 means that the investment is as volatile as the benchmark while betas’ greater than 1 or lesser than 1 reflect volatilities higher than or lower than the benchmark respectively.
|The year over year growth rate of an investment over a specified period of time. It is a notional number that depicts the rate at which an investment would have grown if it grew at a steady rate.
|A measure of downside risk that focuses on returns that fall below a minimum threshold. Used to calculate the Sortino Ratio.
|is the degree to which exceptional values, much larger or smaller than the mean, occur more frequently (high kurtosis) or less frequently (low kurtosis) than in a normal distribution. It measures the tail-heaviness of the distribution.
|calculated by dividing the compound annual growth rate (CAGR) of a fund since inception by its biggest draw-down. The higher the ratio, the better the risk-adjusted returns.
|The maximum decline from peak to trough before a new high is achieved.
|Modified Sharpe ratio
|A measure of the mean return per unit of risk for investments exhibiting asymmetric distributions. Calculated by dividing the excess returns by the modified value at risk (mVaR)
|Modified Value at Risk (mVaR)
|quantifies the risk of an investment with a given confidence level for return distributions that are asymmetric (non Gaussian).
|Price Interest Point. It is the smallest price change that a given exchange rate can make (e.g. If the EUR/USD moves from 1.4050 to 1.4051 then that means that exchange rate went up 0.0001 or 1 pip).
|(** Normal Distribution Skewness = 0 **) A measure of symmetry – or lack of symmetry. Skewness can be either negative or positive. Data points skewed to the left of the mean are negatively skewed while those to the right are positively skewed.
|A variation of the Sharpe ratio which differentiates harmful volatility (volatility caused by negative returns) from volatility in general.
|A representation of the risk associated with a given investment. A statistical measure of the variability of the returns.
|An index that tracks the monthly performance of a hypothetical $1000 investment.