Mathematics information for online study; you can learn about mathematics and related subjects, self-study and e-Learning courses about mathematics.
Mathematics is the science that deals with the logic of shape, quantity and arrangement. Math is all around us, in everything we do. It is the building block for everything in our daily lives, including mobile devices, architecture (ancient and modern), art, money, engineering, and even sports. Since the beginning of recorded history, mathematic discovery has been at the forefront of every civilized society, and in use in even the most primitive of cultures. The needs of math arose based on the wants of society. The more complex a society, the more complex the mathematical needs. Primitive tribes needed little more than the ability to count, but also relied on math to calculate the position of the sun and the physics of hunting. Mathematics is not about answers, it's about processes. Let me give a series of parables to try to get to the root of the misconceptions and to try to illuminate what mathematics IS all about. None of these analogies is perfect, but all provide insight. Other mathematicians hate to admit it, but when you get right down to it, math is about numbers. Of course it involves logic, spatial relations, proofs, all sorts of things. But that’s not the heart of it. Math is the study of numbers in all their fascinating aspects and manifestations. But since that’s so mundane - people can actually understand the definition - it just doesn’t sound mysterious enough for many mathematicians. "Mathematics is the art of giving the same name to different things." -Henri Poincaré. I would define mathematics as the study of structure divorced from context.
In mathematics, we study various structures: numbers, groups, geometric objects, etc. We study their patterns and figure out how they work and interconnect. I would make the argument that anything existing in the universe and anything that can be cooked up by the human mind that has some sort of structure to it can be studied mathematically. Of course, what one might argue is that disciplines like physics, chemistry, and biology do the same thing: they search for the physical patterns and structures that exist out in the world. What is the key difference between these pursuits and mathematics? The key is that in all of the above-mentioned physical sciences, any problem that you consider has a certain context, a certain specific interpretation. An oscillating pendulum is not the same thing as a vibrating string which is not the same thing as a spring with a mass attached to it. However, from a mathematical point of view, all of these systems are essentially the same thing. Once you strip away all of the physical details and particular context of a problem, what remains is its mathematical content. The beauty of this is that by considering things so abstractly, you begin to see connections that you would not otherwise recognize. The motion of a pendulum, a string, and a spring are all described using sinusoidal functions. That same periodic behavior might be observed just as well for sound waves, and light waves, and ocean waves. When you have a perspective this broad, you can begin by looking at a problem one way, flip it around, realize that you can contextualize it in a completely different way, and then start using the tools of a seemingly unconnected theory to solve your problem.
History of Mathematics
In Babylonia mathematics developed from 2000 BC. Earlier a place value notation number system had evolved over a lengthy period with a number base of 60. It allowed arbitrarily large numbers and fractions to be represented and so proved to be the foundation of more high powered mathematical development. Number problems such as that of the Pythagorean triples (a,b,c) with a2+b2 = c2 were studied from at least 1700 BC. Systems of linear equations were studied in the context of solving number problems. Quadratic equations were also studied and these examples led to a type of numerical algebra. Geometric problems relating to similar figures, area and volume were also studied and values obtained for p. The Babylonian basis of mathematics was inherited by the Greeks and independent development by the Greeks began from around 450 BC. Zeno of Elea's paradoxes led to the atomic theory of Democritus. A more precise formulation of concepts led to the realization that the rational numbers did not suffice to measure all lengths. A geometric formulation of irrational numbers arose. Studies of area led to a form of integration. The theory of conic sections shows a high point in pure mathematical study by Apollonius. Further mathematical discoveries were driven by the astronomy, for example the study of trigonometry. Several civilizations — in China, India, Egypt, Central America and Mesopotamia — contributed to mathematics as we know it today. The Sumerians were the first people to develop a counting system. Mathematicians developed arithmetic, which includes basic operations, multiplication, fractions and square roots. The Sumerians’ system passed through the Akkadian Empire to the Babylonians around 300 B.C. Six hundred years later, in America, the Mayans developed elaborate calendar systems and were skilled astronomers. About this time, the concept of zero was developed.
Prehistoric people must have used simple arithmetic. However when people became civilized mathematics became far more important. Proper record keeping was essential. In Iraq a people called the Sumerians counted in sets of 60. We still divide hours into 60 minutes and minutes into 60 seconds. We also divide circles into 360 degrees. There were a number of great Indian mathematicians during this era. Among them were Aryabhata (c. 476-550) and Brahmagupta (c 598-670). A Persian named Al-Khwarizmi was also a famous mathematician. He lived in the early 9th century. He wrote about Indian numerals and algebra. In the 19th century Carl Friedrich Gauss (1777-1855) made contributions to algebra, geometry and probability. Charles Babbage (1791-1871) is called the father of the computer because he designed a mechanical calculating machine he called an analytical engine (although it wasn't actually built in his lifetime). Babbage was assisted by another great mathematician called Ada Lovelace (1815-1852). George Boole (1815-1864) created Boolean algebra. Meanwhile in 1801 William Playfair (1759-1823) invented the pie chart. (Florence Nightingale did not invent the pie chart although she did use them). John Venn (1834-1923) invented the Venn diagram.
Mathematics as Science
Many others will answer this question by referring to the various definitions and associations that come with the word 'science'. However, these are not even consistent between languages as English, German, Swedish, Japanese, Mandarin, all have words for Science that are not 1:1 matches.
If Math would be seen as something that assists Science, then mathematicians would be degraded to assistants. No good. So, while the test/verify/measure/model paradigms in Science quite don't apply to Math, I prefer thinking of Math’s as a part of Science for mentioned reasons. Traditionally, the development of physics, which is a science, was paralleled with the refinement of the mathematical techniques employed to handle the mathematizing way of the (theoretical) method in physics. This gives rise to two different approaches to mathematics (since up to the mid-1950s the most influential science to mathematics apart from mathematics itself was physics) a pure and an applied one. Content wisely, both approaches can encompass the same branches of mathematics, e.g., Lie Group Theory, which can be further developed from a pure approach, can also be instrumental zed and further developed in order to meet the needs of physicists who investigate symmetries in their theories or that study symmetries of solution spaces to e.g. Partial differential equations.
If we look on mathematics as an imaginary world with no connection to reality, we can still do science. Let's call that "Platonic mathematics." If instead we claim that mathematics is nature's language, then we can explore nature through mathematics, and again, its legitimate science. Let's call that "natural mathematics."
The kind of mathematics having no essential connection with the physical world. I say "essential connection" because links between nature and esoteric mathematical notions spring up in unexpected places, like the surprising connection between locusts and prime numbers.
The kind of mathematics arising from the uncanny efficiency with which mathematics describes nature.
In this article we will explore science derived from both Platonic and natural mathematics.
Foundation of Mathematics
The content of a theory, describing its model(s), is made of components which are pieces of description (concepts and information, described in 1.3). A theory starts with a choice of foundation made of a logical framework and an initial version of its content (hopefully rather small, or at least simply describable). The components of this initial version are qualified as primitive.
The study of the theory progresses by choosing some of its possible developments: new components resulting from its current content and that can be added to it to form its next content. Any other possible development (not yet chosen) can still be added later, as the part of the foundation that could generate it remains. Thus, the totality of possible developments of a theory, independent of the order chosen to process them, already forms a kind of «reality» that these developments explore. it is a misconception to think that natural structures in mathematics have simplest or best definitions and the same applies to the axioms for mathematics itself. The definition requires you to specify some sort of theoretical computer such as a Turing machine, but this is completely arbitrary. There are lots of alternatives that are equally good and all you can do is show that they are all equivalent. What makes concepts interesting and useful in mathematics is not how good their base definition is, but rather their universality. You may think the best definition of PI is in terms of a circle, but it could also be defined in terms of infinite series or the period of functions obeying simple differential equations. What makes PI so interesting is that it comes up all over mathematics, not just in geometry. This is what we mean by universality. So mathematics itself also has many different starting points but they all lead to the same thing. Some starting points or axioms may be more convenient given our current preferred mathematical interests, but they are not really more fundamental than any other starting point that leads to the same body of mathematical ideas.
Pure and Applied Mathematics
Applied mathematics seeks to produce tools to help us understand the physical world. Pure mathematics does not. There are some really great answers here, so I'm not sure if I can really add to this, but I am going to try. Hopefully I don't sound like too much of a broken record. Applied mathematicians are typically motivated by problems arising from the physical world. They use mathematics to model and solve these problems. These models are really theories and, as with any science, they are subject to testify ability and falsifiability. As the amount of information regarding the problem increases, these models will possibly change. Pure and applied are not necessarily mutually exclusive. There are many great mathematicians who tread both grounds. German Mathematics soon outstripped the French, with Gottingen becoming the center of a golden age of Mathematicians. The terms pure mathematics and applied mathematics seem to have been invented in the 19th century, but they really aren't two different kinds of mathematics. The distinction is more of intent than of content. Any applied mathematics contains pure mathematics, and any pure mathematics may have been or may be applied sometime in the future. The applications are to some kind of science. Mathematics that is studied with the intent to be applied to natural science, biological science, or social science can be called applied mathematics. Scientists use a lot of mathematics in their work. If a scientist develops some new mathematics in the course of studying science that could be called applied mathematics. If that same scientist goes a little further studying that mathematics without the intent of applying it, you could call that pure mathematics. There are many problems pursued by pure mathematicians that have their roots in concrete physical problems – particularly those that arise from relativity or quantum mechanics. Typically, in a deeper understanding of such phenomena, various “technicalities” arise (believe me when I tell you these technicalities are very difficult to explain). These become abstracted away into purely mathematical statements that pure mathematicians can attack. Solving these mathematical problems then can have important applications.
Pure mathematics is simply mathematics considered without regard to applications outside of mathematics. It may or may not have been applied. It may or may not be applied sometime in the future. The French solved a lot of the problems of the time, mostly in probability, but the Germans solved problems that didn't exist, but were going to be vital as the 20th Century started. Notably the Mathematics behind relativity had been worked out, as had general solutions involving abstract algebra. New technologies such as radio and electricity required Mathematics that wasn't based on things you could see. Numbers themselves turned out to be a whole lot more complicated and Math’s moved into non-numerical fields (Boolean algebra and Graph theory) Pure Math’s at its heart is a quest for truth, it has an almost mystical element. Pure Math’s is the equivalent of a mystery tour, you could end up anywhere, but the point of a journey is not the destination. That is pure math. Applied mathematics occurs when we search for a collection of axioms and conclusions which help us describe the physical world. Much of mathematics is based on such quests. Indeed, due to the historical nature of mathematics being applied to these quests, a large portion of our body of mathematical theory is related to the physical world, right down to the axioms that we use. This is one reason why so much that mathematicians produce ends up being useful.
The Fields Medal
The Fields Medal is one of the most recognized prizes given to mathematicians who have achieved something great during their career. The official title for this prize is the International Medal for Outstanding Discoveries in Mathematics and it is given out once every four years to up to four mathematicians under the age of 40.
This prestigious prize is actually presented by a king – the King of Norway – to a mathematician who is outstanding in their field of study.
Wolf Prize in Mathematics
The Wolf Foundation of Israel awards six different prizes each year and one of them is the Wolf Prize in Mathematics. This prize has been awarded since 1978 and it is also a very prestigious honor to receive one in the fields in which they are given.
One of the newer prizes in mathematics is the Chern Meda, which began recognizing lifetime achievements for mathematicians in 2010, is awarded every four years. It is given out at the International Congress of Mathematicians and it includes a prize of $250,000. The first recipient in 2010 was Louis Nirenberg and the 2014 winner was Philllip Griffiths.


Don't forget that you can see lots of other stuff that we've been up to if you check out our videos in the video resources centre.
Year One Video Resource Centre
We have been looking at the work of the artist Mondrian who was famous for his paintings using squares and rectangles. Check out more of our Mondrian work in the Video Resource Centre which can be found in the 'Children' menu.
In maths we have been learning about sequences, patterns and putting things in order. We made up a sequence and our partner had to continue it.


How Does A RESIDENCE Edge Appear?
You can find generally three major categories of casino games: casino table video games, hand-held gambling products, and random variety games. Internet casino gaming machines, including slot machines, pachinko, and video poker equipment, are usually played by one person at the same time and don’t require the participation of gambling house staff to play. Hand held gambling devices, including keno equipment and roulette tables, are played out by several individuals concurrently, while random variety games are played in teams or pools.
Every casino game includes a unique strategy for dealing with loss and winning. While all video games follow a mathematical release of probability, not all strategies follow an identical framework. In a casino activity, the probability an object will come into a specific position is called the standard deviation. For example, in the standard deviation, the sum of all of the possible outcomes is the number of times a normal distribution will undoubtedly be drawn. The deviation could be thought of as the sum of all possible results, where the denominator may be the expected value of any end result.
Slots are a special casino video game that uses the same concept of regular deviation in its random effects. In a typical slot machine game, the jackpot is really a fixed amount, which can’t be changed, whether utilized by the casino or players. Whenever a slot participant wins a jackpot, he gets to claim his share of the prize money, called the bonus. The size of the bonus, or quantity of coins in the “pile” may also vary, but for purposes of simplicity, the same concept of standard deviation applies.
Once all individuals have been paying in their winnings, the last of the money in the pot goes to the casino with the best expectancy. This is also called the “dividend”. At the end of each game session, the casino takes one (1) from each one of the pots in succession. That’s the total amount of money in play; the casino will divide the winnings among its individuals. Each player has the best probability of winning the dividend, consequently she pays the gambling house for the distribution of the funds.
Two other types of casino games available in land-based casinos are roulette and craps. Both work with spread betting to look for the probability of a win. Unlike slot machines, craps can use various bets, including both funds and credit. Roulette uses a wheel to find out odds, while slot machines use fixed odds. Much like slots, however, the casino might want to pay out some of the winnings to the winner, or to the house.
Another popular choice for casino video games is table games. Three of the very most popular are blackjack, baccarat, and craps. Blackjack is played on a single table with a dealer, baccarat uses two tables and craps runs on the single table and multiple people. Each of these games have their very own best odds of winning. The odds for each game will undoubtedly be listed on the precise casino’s site.
When players place bets, the gambling establishment deducts a certain amount from the total wagered 인터넷바카라 and then adds that total the player’s winnings. The gambling house takes care of the rest. This keeps the home edge, or percentage of gains, at the very least.
Alternatively, the house edge may be the casino’s way of “overcharging” its customers with more money than they likely to pay. In the case of roulette and baccarat, which means that the casinos take a higher percentage of winnings compared to the fair share. With slots, the home edge can be hugely high because they are games of chance. Some of the slot machines in a casino might not even spin the numbers. On the other hand, because a lot of people like to gamble with slots, the casinos add them in all of these casinos to “shore up” their very own casinos. Therefore, when you play a slot machine you are actually “playing” the slots as the house border benefits the casinos.


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Tuesday, June 18, 2013
2:07 pm, Wednesday, December 26, 2012 -- On the recent opening day of New York City's new Museum of Mathematics, or MoMath as it is called, a colorful spherical toy was being enjoyed by kids of all ages in the midst of all sorts of high tech, user-friendly exhibits with decidedly mathematical themes.
To be exact, in tongue-twisting if...
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Bingo is not just a game for senior citizens to joyfully play in bingo halls. I don’t know about you, but I enjoy a good bingo game from time to time. Did you know that using bingo games in the classroom can be a fun way to review? When I started creating classroom resources for my Teachers Pay Teachers store, bingo games were one of the first things that I created. Why? My students enjoyed playing bingo and didn’t even realize that in the midst of the fun that they were having, they were reviewing what I taught. Here’s how I use bingo games in my classroom…and you can do the same. Trust me, your students will beg you to play!
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Currently, I use bingo games in my classroom as a form of review for math concepts. I typically save my bingo games for Fun Fridays. In my classroom, I don’t teach a new lesson on Fridays. Instead, we quiz on the lessons taught during the week. After the quiz, my students do math stations while I meet in small groups. Sometimes we forego the math stations in favor of projects or games like Bingo.
The bingo games that I create require students to make their own bingo cards which really adds to the fun. Depending on the type of Bingo game, my students can solve the problems first and then assemble their bingo cards. For example, the three digit addition bingo game above would take too long to play if my second grade students had to solve each problem when I called out the sums. So, the students solve each problem first and then they cut out the problems for their bingo cards.
Bingo games aren’t just for math review. Bingo games can be used to practice sight words, nonsense words, geography, history, and much more.
And of course, I love to use bingo games to celebrate holidays. I teach in Louisiana, so we celebrate Mardi Gras in February. My students love playing Mardi Gras Bingo. These games are quick and easy for almost any grade. Quick tip: If you’re playing bingo with your students and they can’t read yet, you could also display the words using your document camera. I also have easier bingo games called BOO games. The BOO games are great for PreK and Kindergarten.
What do you think about using bingo games in your classroom? Do you currently use bingo or some other type of game to review in your classroom? Let me know in the comments below.
- CALLING ALL FIRST AND SECOND GRADE TEACHERS! Join me and a great group of other fabulous 1st and 2nd grade teachers in my Facebook group, Taming First & Second Grade. We have great discussions and you can gain some much needed inspiration.
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Contact Theresa le Roux on 0213702500Beautiful Gate is a South African non-profit organisation based in the township of Lower Crossroads, Philippi, Cape Town. We are working hard to make sure that more than 1000 learners can have a bright future - filled with hope! Studies show that less than 43% of learners take Mathematics and less than 32% take Science to Grade 12, while all of the top 100 scarce skills and high demand occupations in South Africa require Mathematics and Science Proficiency. Through a focus on improving each child's academic abilities in Maths, English and Science, as well as Business subjects at the high school level, our hope is that we will raise a generation of children who will find or create employment in South Africa! Join our Ride for Hope team in 2017!
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To link to the entire object, paste this link in email, im or document to embed the entire object, paste this html in website to link to this page, paste this link in email, im or document. Sudoku - a graph theoretic problem graph theory is the study of graphs which are mathematical structures used to model pairwise relations between objects from a certain collection graphs are among the most ubiquitous models of both natural and human-made structures. Algorithms, graph theory, and linear equations in laplacians 3 by a measure of the size of s when we measure the number of vertices in s, we obtain the isoperimetric number of s. 3 patent big data analysis using graph theory big data can be defined as various descriptions by academic and industrial fields in statistics, big data is focused.
Graph theory has experienced a tremendous growth, one of the main reason for this phenomena is the applicability of graph theory in other disciplines such as physics, chemistry, biology, psychology, sociology and theoretical computer science. Re: graph theory phd post by djysyed » fri dec 22, 2017 8:01 am i was under the impression not to try talking to them about their papers unless you were writing thesis level papers prior to applying. Isoperimetric inequalities and the alexandrov theorem 2013 undergraduate honors thesis adviser: simon brendle stanford university probability and graph theory.
Graph theory thesis writing service to help in custom writing a master's graph theory thesis for a master thesis degree. Research papers of graph theory 1984 essay thesis writing assignment of economics education review abbreviation love is universal essay supplemental essays. In this thesis, we focus on graph polynomials that have only real roots polynomi-als with only real roots arise in various applications in control theory and computer.
Postgraduate research topics in pure mathematics graph theory and number theory, and experience in computing (thesis project. Graph theory work through the khan academy tutorial on graph representation - after working through each part take the quiz to check your understanding and then complete the challenge. A thesis in this area would study manifold theory and the theory of matrix groups the only prerequisites for this topic are calculus, linear and abstract algebra one goal is the classification of some families of lie groups.
Math/stats thesis and colloquium topics • propagation of viruses in networks (a graph theory / dynamical systems problem) sabermetrics. Master thesis finding and analyzing social networks in unstructured web log data using probabilistic the required theoretical background on graph theory is covered. In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objectsa graph in this context is made up of vertices, nodes, or points which are connected by edges, arcs, or lines.
Graph theory is the area of mathematics that examines the characteristics of graphs a graph is a set of points called nodes or corners, connected by lines, called arcs or edges a graph is a set of points called nodes or corners, connected by lines, called arcs or edges. Graph theory, the vertices of a simple connected graph represent the locations of the radio transmitters, or radio stations, with the labels of the vertices corresponding to channels or frequencies assigned to the stations. In mathematics and computer science, graph theory is the study of graphs: mathematical structures used to model pair wise relations between objects. What are the current areas of research in graph theory dear friends there is anothe area of graph theory called neutrosophic graph theory this theory is geeneralization of classical graph.
Graph theory essays: over 180,000 graph theory essays, graph theory term papers, graph theory research paper, book reports 184 990 essays, term and research papers available for unlimited access. This is a list of graph theory topics, by wikipedia page see glossary of graph theory terms for basic terminology examples and types of graphs amalgamation. Research papers on graph theory development situational leadership dissertation times new roman or arial essays phd dissertation or thesis numbering bressay ferry times to mackinac literature based dissertation on fgm inc (nasa pagbasa ang pagasa essays) english language is the key to success essay dissertations help usa research paper on legalizing marijuana recreational main difference.


There are some situations where the xy=k formula may not be the best choice to provide the best possible execution for traders. For example, this is the case for pairs of tokens with an exchange rate that rarely deviates from 1:1.
In cases like these, stableswap AMMs are much more capital-efficient than their constant product counterparts, since they amplify liquidity to facilitate trades around the 1:1 target exchange rate.
How Stableswap Invariant Pools Work
Stableswap pools are the middle ground between constant product pools and constant price pools. A constant price pool is similar to a constant product pool, but uses a constant sum formula Rx+Ry=k, resulting in a constant price ∆x / ∆y = 1.
The stableswap invariant algorithm uses an amplification parameter (A) that determines how close the stableswap curve should be to the constant product curve; an amplification value of 0 (A = 0) achieves results identical to the constant product pool algorithm; higher values of A push the curve closer to the constant price curve, resulting in lower slippage for exchange rates close to 1:1.
The formula for the stableswap invariant works by combining terms representing the constant product and constant sum formulas. It's using the constant D to represent the total number of tokens in the pool when token X and token Y have an equal price, and A represents the amplification parameter. The formula can be written as:


Distilled Book Insights: 5 Key Insights from "The Ten Equations That Rule the World - And How You Can Use Them Too" by David Sumpter
Have you ever wondered how the world operates beneath its complex, chaotic, and intricate surface? Hidden within the complexities of our surroundings, there's a powerful force - a handful of simple mathematical equations that govern everything, from the spread of diseases to the growth of plants to movements of financial markets and more.
That's what this book, "The Ten Equations That Rule the World: And How You Can Use Them Too" explores, and here are five of the core insights from this book:
1. The world is governed by a small number of mathematical equations: Whether you know it or not, our world plays by the rules of mathematics, most of the time anyway. The profound equations that shape our world often remain hidden, buried deep within the intricate systems that surround us. Yet, understanding these fundamental mathematical principles gives us the ability to unravel the mysteries that of the world around us. And by exploring and understanding these equations, we open the door to a world of insight, providing us with a clearer lens through which to understand our surroundings. That said, the equations aren't static. They change and evolve over time, just as the world does.
2. Curiosity Matters More than You Realize: Our world is a treasure trove of captivating phenomena, waiting to be explored and explained through the lens of mathematics. And you cannot do that without being curious. Even for this reason alone, it makes sense to cultivate your curiosity and ask questions about how the world works. Challenge yourself to find answers and explore the underlying mathematical patterns and principles that govern natural phenomena and everyday events. By nurturing your curiosity, you'll get closer to understanding the mysteries of the world around you.
3. Perseverance Pays Off: Learning mathematics can seem like a confusing and tough task, but remember that to have deeper understanding of the world around you, you need to be persistent. Don't be frustrated if you don't understand a concept right away. Embrace the journey of learning, because with consistent practice and determination, you'll be able to master even the most challenging mathematical puzzles (and any other concept you want to demystify). Each step you take brings you closer to unlocking the secrets of the universe. Some things might not make sense right away, but digging deep and persevering will get you to the understanding you want, and need.
4. Embrace Your Creativity: Even though it might seem like it, mathematics is not a rigid box. The reality is that it is a versatile tool that can be used in different ways to solve problems, including solving problems creatively. Sticking to binary definitions isn't the point, the point is to look beneath the surface and stretch the boundaries, because that's what will help you understand better, and do more. Think outside the box, innovate, and pioneer new solutions that can transform the way you interact with the world.
5. Empower Yourself through Mathematics: As you dive deeper into the world of mathematics, you'll find yourself equipped with a formidable ally - the ability to make better decisions. Armed with insights you can get from mathematical principles, you'll be able to navigate life's struggles, challenges and intricate situations with more confidence and understanding. Mathematics can empower you to understand complex situations better, assess risks better, and can also help you make better and more informed decisions.
And in case you are wondering about the equations, here are the 10 equations mentioned in the book:
The SIR model
The Black-Scholes equation
The Lotka-Volterra equations
The Navier-Stokes equations
The Schrödinger equation
The Einstein field equations
The Boltzmann equation
The Ising model
The Fibonacci sequence
The Mandelbrot set
Like it or not, the world is full of hidden mathematical equations - equations that come together to create the magnificent tapestry of our existence. And that's not a bad thing, because it gives you a clear path to better understanding things that otherwise seem too convoluted. Through the power of mathematics, you can better decipher the language of the universe, and even get better at self-discovery and empowerment.
Mathematical equations can be confusing, but they can help you make your life easier and better. Persevering in your quest to understand them will get you the insights you want, and the ten equations mentioned above are a good place to start.
Don't shy away from things just because they seem complicated. Ignore that instinct, and explore them instead. Because that is what will help you move forward faster, and better.


Colorful Tree Fractals in Flex
October 13, 2008
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So, in my continuing series of simple Flex examples, I am posting an example of how to build mathematically generated Fractals. In this app, we have a button, a color picker, a numeric stepper, and of course, our friend the Canvas.
To use the example, choose a “trunk” color from the color picker, and click somewhere in the Canvas (which is pretty much the entire stage). It will call a function that will draw the tree. This function is iterative, meaning it calls itself over and over again to create the proper number of branches, etc. At each iteration, it will also make the color more ‘green’, and the line weight one pixel smaller. We pass in a few seed variables to get it started, including an initial direction (pointing straight up), the initial color, and an X and Y coordinate to start at. The last variable we pass in also dictates how think the trunk should be (and therefore setting how many iterations deep the function should go).
Again, you can view 100% of the source code of this application by clicking on the image above and running the app, right clicking, and going to View Source. I encourage comments on the example and code — let me know if this is useful at all! This app should be a good example on some of the math and graphics functions in Flex. There is also a demonstration on how to break up an RGB value and modify it programmatically, in addition to recursive functions.
Hope you have fun, and enjoy! I think I only have one more example based on math stuff, so if that bores you, there is other cool stuff to come!
Edit: Be careful with the "trunk size" or the number of iterations. Slower PC’s have a hard time with numbers larger than 10. Only choose a number > 13 if you have a really slick pc.


Common sense media editors help you choose best math games, websites, and apps for kids quality games and apps make practicing math fun. Use this list of top 5 apps that will help students learn and enhance understanding of algebra. Read reviews, compare customer ratings, see screenshots, and learn more about algebra touch download algebra touch and enjoy it. Join aaron quigley for an in-depth discussion in this video, algebra touch, part of ipad apps for educators.
Top tech for everything from factoring to functions explore this awesome algebra apps and websites top picks list of 14 tools curated by common sense. This app can scan and solve math equations instantly in a textbook and display the answer instantly — similar to apps that scan barcodes and takes. Practice algebra app solve online algebra 1 problems including polynomials, combining like terms, adding and subtracting polynomials. Explore carolann cormier's board apps math algebra on pinterest | see more ideas about maths algebra, app store and high school maths. 3 matrix algebra and applications 31 matrix addition and scalar multiplication 32 matrix multiplication 33 matrix inversion 34 game theory 35 input-output models. Download and install latest version of mathpapa - algebra calculator app for free at freeppstop ratings, user reviews, direct apk files download links.
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Alaska performance scholarship courses that qualify for the aps algebra 1 algebra 2 geometry trigonometry. Abstract algebra theory and applications thomas w judson stephen f austin state university august 16, 2013. The dirac equation, as the relativistic equation that describes spin 1/2 particles in quantum mechanics can be written in terms of the algebra of physical space (aps. Aps 2_2s_2016_subespaço gerado_base_dimensão_resumidopdf — pdf document, 326kb.


Well, why not? The usual answers boil down to either an appeal to arithmetic intuition (e.g. treating division as repeated subtraction, you can never subtract zero to get anywhere) or definition (you can't divide by zero because zero is defined not to have a multiplicative inverse, i.e. "because I said so"). But the former is mathematically naïve and the latter is unsatisfyingly circular. So let's dig in to why we want to define zero out of division.
I added a light theme to the site.


The Odds of Winning a Slot
When you play slot, it’s important to remember that the odds are a big part of the game. Understanding these odds can help you make better decisions about how much to bet and which machines to choose. It’s also helpful to know that you can’t always win, so don’t get discouraged if you lose sometimes.
The Odds of Winning
To understand the odds of a slot machine, you need to know how a random number generator works. The RNG generates a combination of symbols that appear on each reel, then shuffles them around until the screen shows a mix of matching and non-matching symbols. If enough of these match on active paylines and start from the left or right, the machine will pay out a prize according to the payout table.
The house edge of a slot machine is how much the casino will win on average over time from a bet. This is determined by the probability that a particular outcome will occur, which you can calculate by multiplying the total number of possible outcomes by the likelihood of each one occurring.
When you’re looking for a slot, the pay table is a key piece of information that can help you make better decisions. It can help you identify what kind of machine you’re playing, how many paylines it has, and whether there are any bonus features that can boost your winnings. You’ll usually find the pay table displayed at the bottom of a slot machine or in a pop-up window on some online versions.


Queuing models are important tools for studying the
performance of complex systems, but despite the
substantial queuing theory literature, it is often necessary
to use approximations in the case the system is nonmarkovian.
Phase type distribution is by now
indispensable tool in creation of queuing system models.
The purpose of this paper is to suggest a method and
software for evaluating queuing approximations. A
numerical queuing model with priorities is used to
explore the behaviour of exponential phase-type
approximation of service-time distribution. The
performance of queuing systems described in the event
language is used for generating the set of states and
transition matrix between them. Two examples of
numerical models are presented – a queuing system
model with priorities and a queuing system model with


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Math is everywhere, it is present in almost, if not every aspect of your life. Whether it is a lucky number, or numbers at work or when you start calculating how much leggings you are buying ;). The most amazing fact is that Math is the same in every country, that's why Math is the Universal Language of the world. We created these Universal Math Skull leggings, which you can wear anywhere, anytime and anyplace.
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Most of the students show poor performance in mathematics. This thing becomes the cause of stress not only for the students but also for their parents. That’s why both teachers and parents are looking for ways to improve the score of the students in mathematics. Before finding these ways, we should try to know the factors that are becoming the cause of the lower score of the students in mathematics. First, they show a negative attitude while learning mathematics. Secondly, some students don’t understand mathematics because their teachers are not using the appropriate method to teach mathematics. The lack of self-belief is also becoming the cause of the lower grades of the students in mathematics. After analyzing the possible ways that are becoming causes of the lower grades of the students in mathematics. Here, experts of a PhD dissertation writing service will discuss the top five ways to improve the score of the students in mathematics.
- Engage In The Class:
Most of the students can’t understand the basic mathematic concepts because they don’t show engagement in the class. Therefore, the first step to improve the score in mathematics is to increase the engagement rate in the class. To engage in the class, they can follow various tips. First of all, they should try to attend all the classes. If they will miss some classes, they can’t understand the next lecture. Secondly, they should try to pay attention to the class during lecture and try to participate in the classroom discussions. It will be helpful for them to clear all the concepts about the lecture. Thirdly, they should try to take careful notes during the lectures. These notes will be helpful for them to solve homework questions. At last, you should also attend your class with a positive attitude.
- Boost Your Grades With Homework And Tests:
If you want to get the best grades in mathematics, you will have to show good performance in the homework, tests and final exams. To boost your grades with homework and tests, you should follow some essential tips. First of all, you should find a quiet place to solve the homework questions. It will be helpful for you to focus on your homework. Secondly, you should try to submit all the assignments before the deadline. If you will not submit the assignments, you will not get the grades of these assignments. Thirdly, if some math questions are difficult for you, you should try to give some extra time in understanding these questions. Fourthly, if you are struggling to understand some math concepts, you should start to teach these topics to others.
- Work Through Math Concepts:
By working through math concepts, you can also improve your grades in mathematics. To work through math concepts, you can also follow various tips. First, you should write out all the steps to solve the math questions on the paper. These steps will be helpful to you to solve the problems. Secondly, if you are facing some problems in understanding a specific mathematical concept, you should try to solve some extra examples. Thirdly, you should try to make it relatable with real-life problems. To make it relatable with real-life problems, you should apply the mathematic concepts with real-world problems. At last, you should master the first mathematical concept before moving to the next.
- Learn The Basic Skills:
If you are struggling to learn the advance concepts in mathematics, it means that you don’t have command on the basic mathematical skills. Therefore, the best way to learn advance mathematical skills is to learn these basic skills. To learn basic mathematical skills, you should follow some essential tips. First of all, you should try to understand the basic concepts in mathematics. Secondly, you should try to go over new concepts by practising the problems. Thirdly, you can also solve the extra problems to learn basic mathematical problems. At last, you will have to apply mathematical concepts to the real world.
- Analyze And Understand Every Mistake:
When you will practice lots of mathematical problems to learn new concepts, you will make some mistakes. Some students lose heart after making these mistakes. As a student, you should learn that these mistakes will be helpful to you to understand the mathematical concepts thoroughly. After making these mistakes, you should try to analyze these mistakes. During this analysis, you should try to know why you have made this mistake. When you will analyze and understand every mistake, you will never try to make this mistake while solving the problems in the exams. If you will attend the exam without practice, you will make these mistakes in the exam paper.


Calculus: An Applied Approach, Eighth (8th) Edition with Student ... Calculus: An Applied Approach, Eighth (8th) Edition with Student Solutions Manual: 9780547198019: Amazon.com: BooksHoughton Mifflin Calculus Solutions Manual - This book actually shows you how to go from problem in your calc book to the answer(s). Gives solutions to ALL problems. However odds are infront of book and evens are in back I dont understand why its not just all together.. Delegation strategies for the NCLEX, Prioritization for the NCLEX, Infection Control for the NCLEX, FREE resources for the NCLEX, FREE NCLEX Quizzes for the NCLEX, FREE NCLEX exams for the NCLEX, Failed the NCLEX - Help is here. In contemporary education, mathematics education is the practice of teaching and learning mathematics, along with the associated scholarly research. Researchers in mathematics education are primarily concerned with the tools, methods and approaches that facilitate practice or the study of practice; however, mathematics education research, known on the continent of Europe as the.
Dear Twitpic Community - thank you for all the wonderful photos you have taken over the years. We have now placed Twitpic in an archived state.. BibMe Free Bibliography & Citation Maker - MLA, APA, Chicago, Harvard. Our collection of Math Resources has multiple pages designed for teaching within specific grade bands. You'll also find valuable collections of support and.
Definition. A matrix is a rectangular array of numbers or other mathematical objects for which operations such as addition and multiplication are defined. Most commonly, a matrix over a field F is a rectangular array of scalars each of which is a member of F. Most of this article focuses on real and complex matrices, that is, matrices whose elements are real numbers or complex numbers. Couple other things to note – most of the compensation for Oracle executives (and this seems true at most companies) is in the form of equity rather than straight salary.. Are your students ready for the Common Core math exams? You can find out by using Benchmark Now!, a free online tool from Naiku for Grades 3-High School.It is designed to help identify students' knowledge and skills with professionally developed assessments using questions from Houghton Mifflin Harcourt’s Assess2Know® Benchmark Item Bank..
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Amidst acute geopolitical flux, the study of grand strategy is necessary for scholars and strategists alike. As a framework for scholarship, it trains attention on the highest-order questions of international relations: why, how, and for what purposes states.
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Teaching Methodology – Singapore Centre
Mathematics has been often considered a “difficult” subject. Some students have a tendency to be extremely worried about Maths. Hence, as a specialised mathematics coaching centre, it is our priority and duty to make students realise that “mathematics can be interesting and fun”.
As part of our regular class room teaching we continuously look at ways to make the classes interesting and encourage active student participation.
We adopt the following approach in our classes:
- Organise quizzes on different topics
- Foster critical thinking
- Encourage students to think out of the box and look at different strategies to solve a particular problem
- Reward the students
- Special attention is paid to students who require extra guidance in certain areas
For learning Mathematics, hands-on problem solving is very important. The student has to solve numerous problems on paper and pencil to gain confidence over the subject. As part of our teaching methodology, students are given online assignments which they need to complete on a regular basis within a fixed time period. Our aim is to enhance the ability of students to approach problems in a disciplined manner and ingrain time management skills.
As teachers our aim is to make the students understand the concepts. Once the student is able to grasp the concept, problem-solving is easy. To develop a strong foundation in maths, we provide course material with practical examples; show real-life examples where certain mathematical concepts learnt are used; and encourage students to identify more such scenarios. These methods are used to make the maths sessions interesting, help remove the “fear factor” which is often associated with this subject and at the same time enable students to excel in school and Board examinations.


What does the golden ratio mean? One of the common questions in the field of plastic surgery. The golden ratio is a geometric and numerical ratio used in mathematics and art, as it is believed to give the most harmonious and beautiful dimensions. This ratio also applies to the ideal human figure, when the proportions of the body and face are equal to the golden ratio, the ideal figure of the human body is obtained.
How is the Golden Ratio Measured?
As for the question of how to measure the golden ratio in plastic surgery, It is measured by taking the ratio of the length of the face to the width, the ratio of the length from the wings of the nose to the tip of the chin to the distance between the middle of the lip and the tip of the chin, the ratio of the distance from the outer point of one eye to the outer point of the eye opposite to the horizontal length of the lip, the ratio of the distance between the lip and the eyebrow connection To the long part of the nose, the ratio of the distance from the hairline to the wings of the nose to the distance from the wings of the nose to the tip of the chin, the basic calculations that help achieve the golden ratio of the face, for a more symmetrical and beautiful face
Golden Ratio Measures:
Plastic arts and architecture attempt to achieve beauty by following the laws of harmony in nature, these mathematical patterns are also used to calculate the ideal proportion in the human body. This principle of harmony, which is quite evident in ancient Egyptian inscriptions and ancient Greek and Roman artwork, is based on the number Phi 1.618. Measurements of the golden ratio are as follows, the ratio of the height of the whole body from the floor to the navel gives the number Phi. The ratio between the elbows and the wrists of our arms gives the Phi number, and the ratio of the elbow to the shoulder of the entire arm from our wrists to the shoulders is the Phi number.
Required Surgeries to Capture the Golden Ratio
The cosmetic procedures that are applied to the face that does not achieve the golden ratio are called the cosmetic procedures with the golden ratio. In short, all the cosmetic procedures for the face with the golden ratio are also called Profiloplasty. Through it, the face as a whole is evaluated. while performing plastic surgeries within the framework of the golden ratio; Care is taken to ensure that structures such as the forehead, eyebrows, nose, cheek, chin, lips, neck and ears take their perfect shape and correspond to each other. If you are asking about the procedures that are performed during the golden ratio facelift, they differ from one person to another, as procedures such as rhinoplasty, orthodontic treatments, dental implants, Hollywood smile and many other facial plastic surgeries necessary to achieve the golden ratio can be applied.
How Much Does It Cost to Have a Golden Ratio Face?
The cost of the golden ratio operation varies according to the person’s condition, as it, as we mentioned, can include a group of facial surgeries. The average Golden Ratio operation in Turkey for 2023 is $3000.”
You can contact HealDone for information about golden ratio surgeries and to make an appointment, and you can find answers to all your questions about the treatment process.


In part 1 I introduced this concept and in part 2 I determined my Opening Day team. But to answer the question regarding how such a team would do gave me a lot of trouble, and took a different turn than I expected.
Initially I believed I could use a simple WAR calculator to see just how well my players would do and use that guide to determine the team’s fate. Yet to figure those factors out I would need to calculate a player’s OPS and slugging percentage as well as a pitcher’s ERA. So my first order of business was determining about how many plate appearances each player would get; thus, I made a matrix covering the nine starting positions and also determined how many starts and relief appearances each pitcher would make. From there I calculated the rest of the statistics based on the players’ real-life numbers and some overall averages.
Using my team’s starting lineup and their WAR, this is the comparison to the Orioles 2018 lineup.
|2019 WAR||SotW team||Pos.||Baltimore||2018 WAR|
|1.5||A. Wynns||C||C. Joseph||0.3|
|2.0||T. Mancini||1B||C. Davis||-2.8|
|2.3||J. Schoop||2B||J. Schoop||1.3*|
|1.5||P. Florimon||SS||M. Machado||2.9*|
|7.5||M. Machado||3B||R. Nunez||1.2*|
|1.5||C. Mullins||CF||A. Jones||0.2|
|-0.3||L.J. Hoes||RF||J. Rickard||0.4|
|0.9||C. Walker||DH||M. Trumbo||0.3|
|2.9||E. Rodriguez||SP||D. Bundy||0.1|
|2.7||Z. Davies||SP||A. Cashner||0.6|
|3.1||D. Bundy||SP||A. Cobb||1.1|
|0.9||S. Brault||SP||K. Gausman||2.2*|
|1.0||P. Bridwell||SP||D. Hess||0.7|
|0.8||Z. Britton||CL||B. Brach||0*|
|1.1||J. Hader||RP||M. Castro||1.3|
|1.3||M. Givens||RP||M. Wright||-0.1|
|-0.8||E. Gamboa||RP||T. Scott||-0.1|
|31.1||Total WAR||Pos.||Total WAR||10.5|
But the one thing about WAR is that it’s a relatively inexact science. Still, using the simple WAR calculators for pitchers and batters, I came up with a team WAR of 32.3 for my mythical 40-man roster. That turns out to be 21 wins better than the 2018 Orioles (meaning 68 wins) and nearly 25 fewer wins than the Red Sox, which would compute to an above break-even season with 83 wins. To me, that was a little too much of a range.
So I tried a different way. Since I had figured out most of the main batting stats in order to define OPS and slugging percentage for the hitters, I decided to treat the pitchers the same way and figure out the batting stats against them. Once I had those numbers, I pored over about two decades’ worth of team batting stats to determine the closest parallels to runs scored based on average, on-base percentage, slugging percentage, and OPS, numbers which I averaged together to determine projected totals of runs scored and runs allowed, which then allowed me to figure out a Pythagorean win-loss record that’s relatively accurate – most teams finish within a few games of their Pythagorean record.
On that basis, my team would finish with a surprisingly good record of 72-90. I say surprisingly because it would finish near the bottom of both the batting and pitching rankings; then again, these align well with the rankings of the 2018 American League teams as five teams finished with fewer than 72 wins and this team generally laid in the bottom third statistically. Presumably it would be a rather strong bullpen that carries my team if they get an early lead.
One other thing all this calculation allowed me to do was change the roster somewhat. (This was reflected in the posts as I did the statistics before the second post where I selected the team.) In one instance, Christian Walker was not a full-time DH but was ticketed for AAA – however, in figuring out his season he had a bat that was too good to send down in comparison to my outfielders – so he stayed. And since his real-life MLB experience has mostly come as a pinch-hitter he’s a natural DH. Other players got more starts than originally envisioned because they were the best player I could put out there despite not being “established.” I also took the propensity for injuries into account so several of my players missed time on the “disabled list” and others were “called up” to replace them. For example, Pedro Florimon has been an injury magnet the last few seasons so in my mythical campaign he missed some time, enabling Manny Machado to slide over to short and placing utility players at third. Players who are well short of a full season are usually considered to be injured for a portion of it.
So I have not only answered my question, but I’ve also created a projected set of statistics (set in pretty much the same fashion as Baseball Reference lays out statistics) for each player based on a weighted formula of previous seasons and levels – thus, a guy who played at AAA a lot has his numbers adjusted a few ticks lower where appropriate. Raw rookies took a bit of a pounding from this, but if I continue to update these numbers they will settle in closer to their eventual MLB norms. It also gives me the fun of seeing how numbers will compare to real life as 2019 progresses.
(One note: for players who have retired I simply used their previous 4 active seasons, disregarding the layoff factor. It was as if they were still playing.)
This was a very fun and challenging exercise – but since I still have the numbers I could do it again for next spring as new players join the SotWHoF. It will actually be easier since I gave the now-retired players a courtesy cup of coffee (maybe a latte in a couple cases) in this mythical season but won’t feel the need to in 2020, unless I get in a positional pinch. (For example: if Michael Ohlman doesn’t find a team this year I still need him as a third catcher unless a guy like onetime SotW Wynston Sawyer gets the call.)
But consider this as you watch the 2019 season unfold and see how bad my projections are: at least free agency won’t break up this team! Thanks for playing along.


3. Find the Fake (Counterfeit) Coin set ?
There are 5 sets of coin (10 coins in each set). All coins weight 25gms (say) each except the coins in one set which weigh 2gm more (each). You have a digital weighing machine which can be used only once.
How do you determine which set of 10 coins is of higher weight?
Note: Basic assumption holds good.
Read it and post your answers as reply to the post. I will be adding my answer if there are no correct answers after 10 replies.


YEAR 1'S NEWSLETTER
This half term we have been covering the following-
Maths- We have started to work with numbers to 20 and have be counting to 20, writing numbers to 20, comparing numbers, ordering numbers, looking at number patterns, add by counting on, subtract by counting back, subtract by subtracting in 1s, subtract from 10 and have learnt some addition and subtraction facts. We are able to recognise solids/shapes, group shapes and make patterns. We have compared height and length, measure using things and body parts.
English- We have focused our writing around The Gingerbread Man and The Three Billy Goats Gruff. We will learn the stories by heart and then write them with our own different ending. We will learn when to use capital letters, use and and because to write longer sentences and will use the sounds that we have learned in phonics lessons to support our spelling. We will also learn to use interesting vocabulary to excite our reader. We will continue to read in a group and individually every week.
RE- We will learn about Jesus through stories.
Science- Our focus will be on materials and their properties.
DT- We have designed a getaway vehicle for The Gingerbread Man and will make a floating boat for The Billy Goats.
PE- We have been exploring balance through floor work and using the equipment.
We will continue to alternate Music (Mr Baxter) and French (Mrs Hopwood) lessons each week.
We have had a Gingerbread Man Decorating Party to celebrate the end of our work.
There will be some homework sent home for the half term. This will have an element of choice and we will send you a guidance sheet home to help you help your children. We will also be assessing the children on their phonics knowledge this will be instead of individual reading.
Please feel free to ask any questions!


The solution contains all real numbers. You’ve accessRestricted access. Now, the way to solve the problem gets transparent.
Because the debut of slope is normally accompanied by the capability to over here graph a line, start off with the financial small business example first. The above Ven diagram can be employed to demonstrate how various sorts of quadrilaterals relate to one another. There are just two parts of information that are important to solving this dilemma.
The Unexposed Secret of What Is an Inequality Math
Ploughs are utilized to ready the ground when large tracts of land are required for growing crops like wheat, barley and rye. For instance, a government may want to be aware of the normal number of children under the age of 12 that are malnourished in the nation, in the exact same way an organization may want to understand the typical number of workers working that have stress disorders. There’s inequitable funding for schools in lots of places throughout america of america.
Among the absolute most helpful things that you can do as a way to find God’s love is to meditate with distinctive devotees. The exact first tip required for an extremely very good relationship is there ought to be equality between the couple. On occasion, things just need a little period of time to become used to.
1 important consideration to bear in mind is that there’s often more than one viable model. You might opt to take to the streets and take part in a demonstration. Two fingers pointing at exactly the same moon.
The Properties of Inequality will arrive in handy when you wish to address problems. Financial Samurai isn’t a typical personal finance website. Trigonometry of a suitable triangle.
It’s paper writing the best program ever. They can practice this worksheet to better their abilities. Student isn’t sure he or she found the right solution.
The What Is an Inequality Math Chronicles
An empty set includes no elements. Either side of the equation corresponds to a side of the balance. Subtractb from either side.
A circle is only a round straight line with a hole in the middle. ECB are congruent because they are vertical angles. As stated earlier, slope is something which is essential to be in a position to calculate.
Details of What Is an Inequality Math
A system of inequalities has more than 1 inequality statement that has to be satisfied. The very first, largely mathematical explanation means income inequality. You may select which kind of inequality and the sort of numbers to utilize in the issues.
The aim is to place an inequality sign at the middle support of the scale to earn a true mathematical sentence. You may select which type of inequality and the type of numbers to utilize in the difficulties. The key thing about inequalities is there are multiple possible solutions.
A scale may also be employed to demonstrate inequalities. In case the statement is correct, the number is a way to solve the equation or inequality. In case the identical quantity is added to every side of an inequality, the outcomes are unequal in the exact same purchase.
If you take a close look at the remainder of the data and exclude the outlier, you notice it’s in the form of a normal distribution. Often you would like to reduce several measurements of something to a single value, because that’s simpler to handle and understand than the comprehensive distribution, and you’re o.k. with the information loss. The optimal solution would be to discover the ordinary household incomes of both counties and compare them with each other.
In the event the typical deviation is quite huge then the statistician may claim that the dispersion in salary is quite huge and thus the prosperity claim of the nation ought to be viewed with suspicion. You are able to receive a fairly good idea about the full set of information by calculating its mean. You shouldn’t have the ability to predict the error for any specific observation.
The Do’s and Don’ts of What Is an Inequality Math
The very first rule, nevertheless, is comparable to that used in solving equations. The comprehension of each term enables students to take important actions in laying the appropriate foundations for algebra. It’s occasionally required to fix this variety of equation for one of the letters as soon as it concerns the others.
Statistics assumes your values are clustered around some central price. It is also related to probability in many ways, so you may like to take a workshop on probability and statistics to explore more about the relation between the two topics.
The calculator has the capability to do calculation with letters (literal calculation), this function makes it possible for you to group, collect the conditions of an expression to acquire a reduced type of this expression. The skills utilised in graphing linear inequalities are essentially the very same as the ones needed for graphing linear functions. What’s more, equations are extremely intuitive, but a number of the arithmetic of inequalities is quite unintuitive.
Or, you might begin a site publicly denouncing the wealthy and powerful. You’re encouraged to incorporate a teaching statement as a portion of the on-line application. Altering the type of an answer isn’t necessary, but you ought to be able to recognize whenever you have a proper answer though the form is different.


Students majoring in this program develop a strong mathematical background in a mathematics core following the guidelines of the National Council of Teachers of Mathematics and the Mathematical Association of America. Graduates of this program are prepared to teach mathematics at the secondary level. These students will receive a Bachelor of Science in Mathematics Education and a minor in K-12 Education Technology. Graduates of this program will also be prepared to use the computer as a tool in both the learning and teaching of mathematics. All DSU teacher education graduates earn a K-12 Educational Technology Endorsement.
System-wide General Education Requirement (30 Credits)
One of these credits are met when completing MATH 123 as part of the system general education. Additional electives may be completed in the math program electives and/or the K-12 educational minor.
Yearlong Residency / Student Teaching
Teacher candidates complete a yearlong residency / student teaching capstone experience during the final two semesters prior to graduation. Placements are made in districts with which the College of Education has a formal partnership and whose personnel are trained in the co-teaching model. Out-of-area placements are not granted for the yearlong residence / student teaching experience. Requirements for licensure vary from one state to another. If you are interested in professional licensure, please check with the appropriate licensing body in the state where you intend to practice. The US Department of Education link will help you learn more about certification in your state.
Students planning to obtain certification and teach outside of South Dakota are encouraged to take


We have been learning about doubling and halving in reception 1, and the mathematical language too. Today we kept doubling the number of biscuits we had for snack until we had 16 ( which is one of the teen numbers we practise everyday)…
…Then we had to find a partner to share our biscuit. This meant we had half each. Maths at snack time is such fun!
Today we used the balance scales to weigh and measure. We now know if we want to balance the scales we need to have the same amount of weight on each side. If one side is heavier the bowl will go down and the lighter bowl will go up. We used lots of mathematical language during this activity.
Zoo2U came to us in Nursery and Reception .The Meerkat was one of several animals we looked at and stroked .The Meerkat was very friendly and he loved Ivy so much, he fell asleep on her lap !
We talked about how animals belong to different groups and we found out that we are all mammals!
Two weeks ago we planted Sunny, our class sunflower in the woods. We measured her after a week and she had grown 5cm, this week she had grown another 3cm.
We know that Sunny needs sun, soil and water to grow, so when we visited her on Thursday we gave her a watering can full of water. Next week we will take our ruler and measure her again.
Last week we spent the week using lots of mathematical language to measure objects. We measured the children and put them into size order, we cut ribbons the same length as the children and then put them into size order to name just a couple of our activities!
This week in maths we have been using mathematical language to talk about weighing the ingredients to make cakes. We got to eat them at snack time….and silence descended on the room for 20 seconds as every last climb was eaten!
In Reception we have lots of tricky words to read and write. To help us learn the words Mrs Ogden thinks of lots of interesting ways to help us. Today she wrote the words on our snack time bananas, and we couldn’t eat our banana until we read a word (luckily everyone could!)…we thought she was monkeying around but she was serious!


guesses, since fewer data points existed. The best formula proposed thus far is:
Two values have been proposed for the M constant. The first, and most often quoted, is (-11/3). This generates a graph which matches the TNG Tech Manual almost exactly, and swoops off to infinity quickly after that The second, derived by Sharon Collicutt, has M = 1.502. This includes the “lost data point” given on page 111 of the Tech Manual, the speed of Warp 9.9997.
The M = -11/3 value works for W 9. The M = -1.502 value works for W 9 and W = 9.9997, but misses the other new data points by a fair margin.
The TNG Tech Manual indicates that Mike Okuda has an actual formula, within an Excel spreadsheet on his Macintosh, but no-one has reported seeing it to r.a.st.tech. “Our solution was to redraw the warp curve so that the exponent of the warp factor increases gradually, then sharply as you approach Warp 10. At Warp 10, the exponent (and the speed) would be infinite...”
Note that none of the above formulas have an increasing exponent. Given the description, I attempted some simple formulas, on the hunch that Rick and Mike wouldn’t bother with anything really fancy. is the right shape, but is very off for anything above 7 or so.
So here’s a new formula by Pete Carr that matches the integral Warp 1-9 values exactly:
This has the advantage of being both accurate and simple, and has a rising exponent. However, it does not match at all for values over Warp 9! So there is probably something more that we’re missing. A few more terms in the exponent, perhaps?
Figure 1. Warp Speed/Power Graph
Figure 1 is an ASCII version of a graph from the TNG Tech Manual.
The part of the graph above the ??? is speculation, and is just to show that as W 10, velocity and power infinity.
“Future TNG scale” (TNG "All Good Things..."): ?!?!?
Quoted in this episode is the speed Warp 13, and Riker later indicates “maximum warp”. While we haven’t a clue how fast these are, they’re presumably faster than Warp 9 on the TNG scale, and necessarily slower than Warp 10 on the TNG scale (since TNG Warp 10 is infinite speed). A few possibilities present themselves:• Warp 10 - 13+ are shorthand for Warp 9.x. One possibility is that 9.90 is called Warp 10, 9.91 is called Warp 11, etc.
• New warp technologies provide at least 13 power usage minima between c and infinite speed, instead of the 9 possible with old warp technologies.
Please see Warp and Subspace, Continued, page 12.


Hi! I'm a Senior Researcher at NEC Labs America, where I develop algorithms for natural language understanding and (formerly) digital pathology. Highlights include leading systems for fact extraction and verification (Team Papelo), and the e-Pathologist system for automatic analysis of biopsy images (Japanese overview here).
In 2015 I launched Group Ring, a web platform facilitating easier reading and discussion of mathematical articles, as a self-funded, self-developed startup.
I was a COE Researcher (postdoc) at the Kyushu University Faculty of Mathematics in Fukuoka, Japan, in 2006-2007, where I contributed to the Infty Project for optical character recognition of mathematical documents. I also worked in Tokyo in 2009-2010 to assist development of e-Pathologist.
See my publications page.


As if I wasn't tracking enough data already, I've decided to use Jack Daniel's Mileage Training Point system. The reationale behind the system is that not all running was created equal. For example, we can run hours and hours of easy pace running each week, but we can only tolerate a fraction of that time doing intervals. J.D. has designed a table that assigns a point value for every minute of training at a given intensity. The intensity used as a key can be either the %VO2max or %MaxHR. I prefer to use the pace (%VO2Max) but I'm sure using the HR would give the same results. According to J.D., typical weekly totals range from 50 for a beginner to over 200 for an elite runner.
The values I use are:
Recovery pace: 0.2
Easy pace: 0.25
Marathon pace: 0.45
Threshold pace: 0.6
Interval pace: 1.0
Repetition pace: 1.5
In the book, the table is much more detailed and I can't imagine maintaining a by-the-minute log in a spreadsheet, but I usually know what my workout is supposed to be and I can use that to get a value that is probably close enough to the "actual" value.
Example: Typical hill workout 1.5 miles warmup (15 minutes easy) + 6 x (2 minutes hill + 2 minutes rest) + 1.5 miles cooldown (15 minutes easy)
This translates to: 15*0.25 + 6*(2*1.5+2*0.25) + 15*0.25 = 28.5 points in 54 minutes
If we compare this with a slow run of the same duration we get: 54*0.25 = 13.5 points, not even half the point value of a quality workout. Of course, we can only survive a couple of quality workouts a week without overetraining so we can't just limit ourselves to interval workouts.
By matching the HR or effort to other activities such as swimminf or cycling, one could keep track of the global quality of his (or her) weekly training.
The reason I decided to try this is that I want to be able to keep track of the "effectiveness" of my training. Looking at the point value of a workout, I see that if I have to drop a hill or interval workout, I lose more than double the training value of a Base run. I'm trying to build a decent spreadsheet on Google Docs but it's not really ready so I won't burden you with it, but as you can see, this is not rocket science.
Obviously, keeping track of all those numbers doesn't make me a better running Training does. But I'm willing to try anything that help me understand why I should suffer through the HELL of hill sprints and other quality workouts. I'm not a fast runner, yet I run faster than most because I'm willing to suffer. Hopefully this will help me make the most out of my training.


Intervention for children with learning difficulties or additional needs
' 1 -1 ' and 'Small Group' Tutoring is available for children from Prep - Year 8 in English and Maths.
Keeping up with the expectations in reading, writing, and maths can be a challenge for some children. Large class sizes, distractions and background noise can all contribute to some 'falling behind'.
If your child requires assistance in any of these areas, contact us today to discuss your child and we can tailor a program to suit their needs.
Locations and times are arranged to suit family commitments and busy lifestyles.
Fees are $80 per hour, payable by cash, direct deposit or through your NDIS provider.
' 1 - 1 ' Tutoring is available Mon-Fri by appointment
We have one 'Small group' Maths Tutoring class for Years 5-8, available on a Sunday morning
9.30am - 10.30am in person or via skype.


My name is Lisa-Marie Sihler and teach 6th-grade math. I am a graduate student of James Madison University. I graduated in 2012 with my Bachelor's of Science and in 2013 with my Master of Arts in Teaching in Elementary Education, PreK-6 with an Algebra I endorsement.
This is will be my 9th year teaching. I taught 4th grade for 2 years at Sandy Hook Elementary School in Strasburg, VA, taught 8th grade math for 2 years at Peter Muhlenberg Middle School in Woodstock, VA, and taught 5th & 6th-grade math for 4 years here at DMIS. This will be year 5 as a DM General!
I have worked with children with social, emotional, physical and learning disabilities. I have taught students on the autism spectrum, with ADD/ADHD, with emotional disorders, with cerebral palsy, and ELL students.
I was born in Germany and had several thrilling abroad experiences in Hong Kong, Zimbabwe, and South Africa. I currently live with my 2.5 year old son & my ball pythons Pumpkin and Pi.


MathTD is an educational mobile game that I'm currently working on. The idea is to combine tower defense and math flashcards. Well, not a full tower defense but a portion of its mechanics which will be explained in the next section.
You and your enemy will each have a single tower. Both sides will have 2 main goals:
- Attack the enemy
- Defend your base
In order to attack the enemy base and to defend your own base, you have to summon warriors; think of Age of War but instead of earning money to hire mercenaries, you have to answer math questions.
Every correct answer will summon a warrior that will die for you. To make it a little exciting, every wrong answer will summon an enemy warrior. On top of that, there will be a timer that when it runs out - wait for it - an enemy warrior will spawn.
With these mechanics, players will be encouraged to solve the math problems as fast as possible. At least, that is the plan.
Lose Conditions and Level Progression
I'm planning to make things simple. Warriors will act more like bullets rather than actual warriors having long fights. That means, when opposing warriors hit each other, both will die. If a warrior hits the opposing base, it will die and the base will lose 1 hit point. You lose when your base is out of hit points.
On the other hand, if you manage to deplete the enemy base hit points then you will move on to the next level. For the level progression, I'm simply thinking of increasing the digits of the given numbers. For example, on each level your have to add two numbers randomly chosen between:
- Level 1: 10 to 99
- Level 2: 100 to 999
- Level 3: 1000 to 9999
- Level N: 1EN to 1E(N+1) - 1
I'm also thinking of decreasing the timer duration as the level advances.
That's it for now. I have other ideas for my game but I'm still deciding if I will implement it. As I've mentioned earlier, I want this game to be simple so I'm trying to refrain myself from adding too many features.


Meet Emmet Penney. He is a student at Bennington College, and my son. He is taking a class with a rising young math star (if mathematicians have a star system) Jason Zimba. They are researching alternative ways math can be taught and hope to discover why so many kids struggle with math in America. It’s a bold undertaking. I have asked Emmet to blog about it. He agreed and his first submission follows:
In my math class at Bennington we’re looking to find out why people hate math and what can be done about it. The class is taught by maverick mathematician Jason Zimba. The goal of the class right now is to collect data about the education system and math. Part of the data collection process involves guest speakers to talk with our class. We prepare questions for them to read on our wikipage (link posted below) before they come in and begin a dialogue. Thus far, all guests have been from the Bennington community. 1) Ryan Moran, our first guest and a senior at Bennington, brought up an interesting point that learning computer languages, or “logic languages” is much like learning verbal languages; the more languages you know, the easier it is to absorb more. Ryan’s ideas on why people hate math was broken into two parts: 1) The key events are early in one’s education; 2) It’s due to the teaching methods, which make people computers or in any case don’t engage people in rich thoughts – organic thoughts – thoughts that help people make sense of their life and world – not necessarily concrete or practical thoughts.
Ken Himmelman, the Dean of Admissions at Bennington, came into talk to our class and shared ideas with us on why kids don’t respond well to math: 1) Math education is like a “Math Frat,” with an odd type of hazing, “You have to do it because I had to do it!”; 2) This “hazing” comes in the form of rote memorization of key concepts, similar to how foreign languages are taught. I found the parallels between these points and Ryan’s points very interesting. Our next visitor will be Joe Holt, a computing teacher at Bennington whose popular Code Critique class has an unusual structure. We’ll be asking him about his experience with math education among other things. I’ll keep you posted on our progress.


Parents, we are now just about half way done with 1st Grade. It's been a really good year as we've grown to 21 students in the class. The kids have grown so much since entering the classroom. They've become readers and they have learned how to add and subtract. I am so excited about how far these kids have gone.
I get asked a lot about what can we do at home to help. It really depends on your child. First, make sure they know all the letter sounds. Next, work on sounding out words. Then read...and read...and read. Memorize the sight words that I send home. Read the two books every night that I send home. Practice adding and subtracting at home. Flash cards for math and the sight words are always a great way for the children to learn..
Look for the Thursday folder on Thursday. Please take out the kids papers, sigh the paper on the left and then return the folder with just the one paper inside. We go to the library every Thursday. We have PE every Wednesday and Friday so it's a good idea to wear sneakers on those days. I let the kids bring snack every day.
I am so excited about the future with these children. I see them getting smarter every day. Ask them if they need any school supplies (crayons, pencils, glue sticks). Get them headphones for Ipads if you can. Message me anytime you want on the Talking Points app. Let's start the year off doing everything we can to get the kids ready for 2nd Grade.


Ever wondered how it’s possible you can talk to your phone and it’s actually giving relevant answers?
The answer is: Neural networks. A computer technology which works very similar to the human brain. And makes it possible for computer software to learn from example data (data sets).
How is this done?
It’s not easy. In the end it’s all about statistics and statistical analysis. One specific statistical analysis technique is the most important: Regression analysis.
Imagine the following dataset, consisting of x and y values:
Based on the data above, what would the y-value be when x = 18? The correct answer is: 36. Why?
Take a look at the data set and notice it’s simply doubling the data for x to get the y-value.
This is high school math and not very complicated.
We say y is a function of x.
In formula form: y=2x.
Now, let’s have a look at a real world example:
As you may notice, there’s no ‘fixed’ model. The data points are scattered around the real function. The function in this case is just a ‘best fit’ in the data set.
As you see, the function is a straight line. We therefore say it’s linear. This type of regression analysis is called ‘linear regression analysis’.
Below other ‘real world’ examples:
As you might see, the two examples above are non-linear. Both are plotted logarithmic. The number e, which is the base number for natural logarithms. By adjusting one or more of the axes to logarithmic is a common way of displaying logarithmic functions to display the functions in a nice way.
You may be able to think of even more complicated functions, such as quadratic, multi-dimensional or trigonometric. They all exist and are applied in machine learning.


Several track parameterizations are used in DELPHI. During the track reconstruction, TER and TKR forms are used (stored in the TE and TK TANAGRA banks respectively). For track extrapolation and fitting, the EXX form is used. The perigee parameters define the track at its point of closest approach to a reference point (usually the origin). Because the reference point is implicit, only five parameters are required. The other parameterizations also define the distance from the origin (in either or ) at which they apply. It is the perigee parameters and their weight matrix (inverse covariance matrix) that are stored on the DST and used in most of the subsequent analysis.
The parameters are the cylindrical position coordinates and are the Cartesian position coordinates (in cm). The cylindrical forms are used mostly in the barrel and the Cartesians mostly in the endcaps. and are, respectively, the polar and azimuthal track directions at the specified point. is the azimuthal angle, relative to a radial track ( ). All angles are in radians.
The particle's momentum components are given by
is the geometric impact parameter, whose magnitude gives the distance from the origin (or other reference point) to the perigee, the point of the track's closest approach in the plane. The sign of is positive if the track passes to the right of the origin, when looking along (see figure B.1).B.1
For lifetime studies, it is often convenient to use another signing convention: the lifetime-signed impact parameter. In this case, a positive sign is assigned if the track intersects the direction vector (often estimated from the thrust axis) of a presumed decaying particle in front of the reference point (usually the beamspot or reconstructed primary vertex). For a large boost, the average lifetime-signed impact parameter is proportional to the decay lifetime . Since we can reconstruct the vertex directly, this method and the lifetime signing convention are not used in this thesis.Tim Adye 2002-11-06


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HONITON COMMUNITY COLLEGE
"Success for All"
Nurturing an ambition to succeed
From the satisfaction of solving a new problem to the sense of intrigue felt when encountering the patterns which pervade the subject, there is something for everyone. Mathematics has a great deal to offer students of all abilities. Qualifications in mathematics are highly sought-after by employers. The five year programme leading to GCSE keeps this in mind whilst seeking to illuminate the subject in its own right.
The “Revisit & Extend” nature of our curriculum ensures regularity of review and provides natural opportunities for students to consolidate as well as extend their skills.
Years 7 & 8
Starting with the four operations – addition, subtraction, multiplication and division – the path toward abstract problem-solving begins here. At the same time as students increase their fluency with the language of the subject, they gradually develop confidence in using mathematics to tackle a variety of challenges from across the discipline.
Students build on their work in years 7 & 8 to develop their existing abilities in some areas and build a whole new set of skills in others. Preparation for Key Stage 4 is the focus here and building solid foundations to build on going forward.
Key Stage 4
The foundation tier of GCSE Mathematics (grades 1 - 5) provides an emphasis on the essentials of the subject, along with an introduction to problem-solving, especially in practical situations. The higher tier (grades 4-9) develops a wider and more abstract repertoire. At this level students encounter demanding areas of the subject and use their abilities to solve problems of greater complexity.
Key Stage 5
A-Level Mathematics offers the intellectual challenge and abstract elegance for which the subject is renowned. But a great deal more is in store for students as they encounter powerful and far-reaching applications. The course is fully examined at the end of the two years and consists of pure mathematics alongside statistics and mechanics. Mathematics naturally complements many other A-level subjects and provides an essential grounding for anyone interested in the scientific or technological world.


Department of Mathematics, Statistics and Computer Science
The courses of mathematics were introduced in the Deptt. of Physical Sciences in the year 1960 along with the establishment of the university. The department was established in the year 1968 by the name Deptt. of Mathematics and Statistics which was latter renamed as Deptt. of Mathematics, Statistics and Computer Science in the year 1998. Earlier basic thrust of the department was to teach various undergraduate/ postgraduate programmes of the university. Department introduced computer usage in the university with acquisition of TDC-12 in 1973. Presently department offers M.Sc. (Maths), M.Sc. (Agricultural/Statistics) and Ph.D. (Maths) programmes. The research thrust areas are fluid mechanics, functional analysis, reliability theory, approximation theory, pattern recognition, Artificial Intelligence, Neural Network, applied statistics and sampling theory. The Department is rigorously pursuing the development of Mathematical and Statistical models for predication of agricultural production, disease surveillance and financial stock analysis. Computer-Assisted Teaching method is being followed in the Department. 6 Professors, 1 Associate Professors, and 2 Assistant Professors at present serve the Department.
Department has about 200 computer programmes in FORTRAN for Mathematical and Statistical modeling. 16 VT-220 terminals are connected with LINUX based Super Server . One Pentium server and 15 PCs are connected on LAN for PG students and 10-Desktop PCs are for UG students
Besides the University Central Library, Department has its own library consisting of about 200 books of Mathematics, Statistics & Computer Science.


We took the afternoon to do this, and it cost $20/adult and $15/child. If you added $1/person each, you could also visit the rest of the Science Centre. And I’m glad we did – we breezed through the Shark exhibit in about 20 mins – and it felt like we just donated some cash for nothing.
Given that the kids mainly liked to see the Great White shark, the rest of the exhibits were passable but boring, and once they had seen the life-sized cast of the Great White, the show was over. So time spent at ‘Planet Shark’ exhibit – 20 mins max. Time spent in the Science Centre proper – over an hour.
Thankfully the Science Centre had loads more entertaining and educational exhibits for all ages – I liked the Mathematics exhibit, where you could learn about the history of Maths, or how Mathematical equations could be found in nature, e.g. in the nautilus (the golden ratio). I learnt something new today too – Euler’s number. Lovely stuff!


Crayon Factory Math: Real-World Addition & Subtraction
I don’t know about you, but as a kid I LOVED watching How It’s Made on the Discovery Channel, and my favorite clips from Mr. Rogers were always when he showed how something was made! Even now as an adult (and being married to a manufacturing engineer), I can’t help but watch these when they show up on my recommended videos.
Kids are constantly seeing final products, and most of the time they have no idea how those things got there, yet they are fascinated by the process! I put this lesson together after being mesmerized by watching crayons be made in a factory, and my students loved it! I’m all about making lessons applicable to real life where possible, and factories are places where math is used every day. Rather than get bored of more worksheets to practice our long addition and subtraction, I decided to have students think through some more challenging problems.
I kicked the lesson off by watching this youtube video:
The entire time kids were “ooh”-ing and “aaah”-ing. They didn’t even complain when I handed them a worksheet! We worked through the first problem together, discussing what kind of word problems they were solving. I told students that each problem builds on the previous ones, so they should look at their answer from another problem if they aren’t sure which numbers to use.
My students really improved their critical thinking when I had them work through this activity and think about what the question was actually asking. They collaborated to figure out which information they needed to use to solve each problem, and they practiced more complex addition and subtraction problems at the same time!
Try this with your students and download the Crayon Factory Math worksheet by clicking the button below!