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Like being a Mathematics graduate, you should have a basic understanding of maths and mathematics and some maths and physics classes too, where you will study at college. Certainly one of the greatest aspects https://english.csuci.edu/program/sampleessay.htm of this issue is that it permits the pupils to develop a base to succeed in every aspects of math. As a grad, the pupils can have the edge of increasing their performance by simply taking Math-Physics classes, that have a bigger concentration of investigation. The attention of those development and study classes are going to be that they are attempting to solve a specific issue.
The course does not require complex math abilities as well as the problem with this specific subject matter is that the students might have to work hard to improve their mathematics skills and develop their creative thinking skills, such as for instance problem solving, and greater skill , imagination . At the close of the program, pupils will need to take your last examination to prove they have accomplished the eligibility. That really is indeed students will be in a position to find their location that they would like.
The Themes are a Blend of Physics and Mathematics. Z pupils can focus on two subjects such as calculus, algebra, trigonometry, geometry, and figures. In the physics fields of astronomy, chemistry, and physics, Physics students may concentrate on the other hand.
The students will probably soon be learning lots of different theories of physics as well as the way in which they relate solely with mathematics, while taking the school classes. The Physics students will participate in experiments, simulation construction, and utilize computation to solve the equations. It’s critical for your pupils to fully grasp why the quantities that are different must be treated as mathematical items or either number. These notions are required to solve issues.
Another important gain of Math-Physics is the fact it has got the power to help develop skills in each one the topics such as archery, that could save a lot of time and money. Being a grad, you will be able to discover your Mathematics and Profession skills are successful and you can easily discover which subjects that you ought to concentrate in, to be able to excel in your field.


Love maths and have a cute baby? Then treat your baby to this super cute babygrow with the mathematical symbol Pi. It would also make a lovely gift for a maths loving friend with a new baby boy or girl.
Our baby vests are 100% cotton and made in the UK. They have poppers at the bottom for ease of dressing and envelope style shoulders. We recommend that our baby clothes are washed inside out at 30 degrees and iron on the reverse. Please do not tumble dry.åÊ


03 Nov Math Team @ Princeton University
On November 3rd , 2018. TEECS Math Counts Team participated competition at Princeton University. There were around 250 students from all 6th to 8th grade participating at the Competition.
TEECS Math Counts Team won first place in Circuit station from 4 different stations. (Popcorn, Toothpicks, Triumphant Triplets, Circuit) and also team member 6th grade student earned the top10 Place in the All Grade Categories.
Congratulations to Mr.Tong all the team members.
Math Contest is a nationwide math coaching and competition program for middle-school students. Math Contest promotes student interest in math by making math achievement challenging, exciting, and prestigious.


On Saturday the 27th of October Wallsend Public School and our P&C will be hosting a school fete. The fete will be held at Wallsend Public School with the purpose of raising much needed funds for our STEM (Science, Technology, Engineering and Mathematics) programs.
STEM is about the skills required to learn science, technology and mathematics, and how engineering and design processes are used to achieve an outcome or goal. During these lessons and programs, students identify a problem and are encouraged to think critically and creatively to find a solution. Through these inquiry-based approaches students are equipped with the necessary skills to succeed in future workplaces.


Don't spent hours writing a program for some programmable calculator while MtrxCal can perform the same calculations with just a few simple lines. Don't waste time trying to find the right maximum and minimum values for plotting your functions. Just let MtrxCal use its build-in auto-scaling feature. The syntax for adding two values and adding two matrices containing hundreds of values is the same. Define a range like x=[-6:0.1:6] and calculate the sinus of this matrix like y=sin(x). Now you can just plot all the values with the command plot(y) or plot the power of y using the command plot(y.^2)
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Regardless of the student or age, we aim to foster critical thinking and problem solving skills that are appropriate for the course yet universal in application. We seek to develop a sense of fluency in working with numbers, graphs, and aesthetic appreciation for mathematics as an art rather than a science. Math is more than a tool to be used by other disciplines, and by showing the beauty in the subject, students can appreciate it more fully.Mathematics Department Mission Statement
The vision for this course is to explore baseball and statistics. Most boys are familiar with baseball and have watched or played it for years. There is a great opportunity to explore many concepts of elementary statistics through the lens of baseball. Baseball offers us an opportunity to explore the following concepts of mathematics/statistics: distributions, probability, graphs, expectations. We will also explore how the game has changed through the years and get an introduction to programming in R, a statistical software package widely used in baseball analysis.
This course completes the study of the syllabus for the AP exam in BC Calculus. The course begins with a review of the derivative and its applications. The course then covers additional applications of differential calculus, the definite integral and its applications, computation of antiderivatives, series, and Taylor’s formula, and some work on solving simple differential equations. All students are expected to take the AP exam.
Number theory is the study of the most basic properties of the whole numbers. Its goal is to answer questions like “How many prime numbers are there? How many ways can you factor a whole number? How can you find the greatest common divisor of two numbers?” On the other hand, cryptography is the study of how to send information that can be read only by the intended recipient. One of the remarkable discoveries of the 1970s was the discovery that these two seemingly unrelated disciplines were in fact entwined and that safe and secure cryptographic methods required the use of number theory. The purpose of this class is to provide an introduction to number theory, an historical overview of cryptography and then discuss how the seemingly abstract methods of number theory have profound application in cryptography.
Offered at Roland Park Country School, Graph theory and game theory is a topics course designed to extend students’ problem-solving skills by exposing them to a vast array of mathematical ideas. Students will explore the power of mathematics beyond and outside of the traditional pre-calculus/calculus sequence. Students will study a variety of networking applications such as Euler circuits, Hamilton circuits and traveling salesman problems, and scheduling using critical paths. Additional course topics include: matrix applications, probability and odds, permutations and combinations, and a selection of problems and strategies from traditional game theory.
Offered at The Bryn Mawr School, discrete mathematics answers the "when will I ever use math" question. Discrete mathematics has applications in a wide and diverse range of interesting fields, including architecture, interior design, art, business, transportation and scheduling, politics and government, city planning, international policies, economics, sports, entertainment, and computer security. In this course, topics covered will include matrices and Markov chains, graph theory, linear programming, optimization, voting methods, game theory and fairness, and codes and cryptography. Students will be researching new mathematical ideas and practicing new mathematical techniques, as well as completing projects and written assignments to investigate specific applications of discrete mathematics.


I havenpercent27t received my babypercent27s birth certificateThey involve Python implementations of various dynamic programming algorithms such as Viterbi, Forward-Backward, and CKY, as well as machine learning algorithms such as MLE and EM. HW1: FSAs/FSTs: recovering spaces and vowels HW2: English pronunciation, part-of-speech tagging as composition, Katakana-to-English (back)transliteration The HMM has four main algorithms: the forward, the backward, the Viterbi, and the Baum–Welch algorithms. Readers can ﬁnd the four algorithms for a single observation sequence inNguyen and Nguyen(2015). The most important of the HMM’s algorithms is the Baum–Welch algorithm, which calibrates parameters for the HMM given the observation data. Algorithm 3 Nesterov’s accelerated gradient g t Ñq t 1 f(q t 1 hmm t 1) m t mm t 1 +g t q t q t 1 hm t cal momentum, and Hessian-Free  algorithms for conventionally difﬁcult optimization objectives. 2.2 L 2 norm-based algorithms  present adaptive subgradient descent (Ada-Grad), which divides h of every step by the L 2 norm Genetic Algorithms , also referred to as simply "GA", are algorithms inspired in Charles Darwin's Natural Selection theory that aims to find optimal solutions for problems we don't know much about. For example: How to find a given function maximum or minimum, when you cannot derivate it?Python is a programming language that lets you work more quickly and integrate your systems more effectively. There's considerable literature on graph algorithms, which are an important part of discrete mathematics. Graphs also have much practical use in computer algorithms.Gradient descent is an optimization algorithm that works by efficiently searching the parameter space, intercept($\theta_0$) and slope($\theta_1$) for linear regression, according to the following rule: @Mohammed hmm going back pretty far here, but I am pretty sure that hmm.t(k, token) is the probability of transitioning to token from state k and hmm.e(token, word) is the probability of emitting word given token. Looking at the NLTK code may be helpful as well.
Safari screenshot full page macAlgorithm 3 Nesterov’s accelerated gradient g t Ñq t 1 f(q t 1 hmm t 1) m t mm t 1 +g t q t q t 1 hm t cal momentum, and Hessian-Free  algorithms for conventionally difﬁcult optimization objectives. 2.2 L 2 norm-based algorithms  present adaptive subgradient descent (Ada-Grad), which divides h of every step by the L 2 norm Forward algorithm History. The forward algorithm is one of the algorithms used to solve the decoding problem. Since the development of... Algorithm. Instead, the forward algorithm takes advantage of the conditional independence rules of the hidden Markov... Smoothing. In order to take into account ... (Hidden) Markov model tagger •View sequence of tags as a Markov chain. Assumptions: –Limited horizon –Time invariant (stationary) –We assume that a word’s tag only depends on the previous tag (limited horizon) and that his dependency does not change over time (time invariance) –A state (part of speech) generates a word. We Baum-Welch expectation maximization algorithm Then recalculate P(xd|M, θ) for all observed data in the learning set (use Forward, Backward, or Forward/Backward to do this) Rinse & repeat . . . Successive iterations increase P(data) and we stop when the probability stops increasing signiﬁcantly (usually measured as log-likelihood ratios). Dec 06, 2016 · This package is an implementation of Viterbi Algorithm, Forward algorithm and the Baum Welch Algorithm. The computations are done via matrices to improve the algorithm runtime. Package hidden_markov is tested with Python version 2.7 and Python version 3.5.
Savage 110 tactical stockHere, the algorithm determines the threshold for a pixel based on a small region around it. So we get different thresholds for different regions of the same image which gives better results for images with varying illumination.forward_algorithm() - Calculate sequence probability using the forward algorithm. This implements the forward algorithm, as described on p57-58 of Durbin et a…The Forward-Backward Algorithm (4:27) Visual Intuition for the Forward Algorithm (3:32) The Viterbi Algorithm (2:57) Visual Intuition for the Viterbi Algorithm (3:16) The Baum-Welch Algorithm (2:38) Baum-Welch Explanation and Intuition (6:34) Baum-Welch Updates for Multiple Observations (4:53) Discrete HMM in Code (20:33) The HMM algorithm set (Forward Backward, Baum Welch and Viterbi) is quite easy to implement. ... (Python 3.7) for HMM implementing. ... we use hidden Markov model which is based on statistical ... Mar 18, 2018 · Now let’s switch gears and see how we can build recommendation engines in Python using a special Python library called Surprise. In this exercise, we will build a Collaborative Filtering algorithm using Singular Value Decomposition (SVD) for dimension reduction of a large User-Item Sparse matrix to provide more robust recommendations while ...
Xd mod 2 laser•The information flows, in general, in the forward direction Input layer: Number of neurons in this layer corresponds to the number of inputs to the neuronal network. This layer consists of passive nodes, i.e., which do not take part in the actual signal modification, but only transmits the signal to the following layer. I've talked about Markov chains, hidden Markov models, and the Viterbi algorithm for finding the The algorithm to do this with is called the forward-backward algorithm. So we have our hidden Under the assumption we're using MATLAB or Python, something with proper matrix and array...class hidden_markov.hmm (states, observations, start_prob, trans_prob, em_prob) ¶ Stores a hidden markov model object, and the model parameters. Implemented Algorithms : Forward algorithm: P(Z k, X 1:k) Figure 3.3: HMM showing two time slices, k-1 and k To compute this probability distribution, we will try to split the joint distribution term into smaller known terms.


Yes, today is when Father's get to calculate their Darwinian fitness, which is how many copies of your genes you've passed on to the next generation. With only one F1 the Phactor has an obvious DF of 0.5. However it's not actually that simple. You see the Phactor on average shares a 0.5 genetic heritage with each of his sisters, so on average 0.25 of my genes were passed on to each of their six offspring. Wow! Thanks to my sisters my DF has gone up to 2.0. Now things start to get a lot trickier. As yet, none of us are grandparents. But our parents each had siblings with whom they shared a 50% genetic heritage. And they had children, cousins. Of course your parents also had cousins who had kids too. So again a fraction of each of their genes are shared by the Phactor, but now the math is getting to the point where without another cup of coffee no attempt will be made to figure this out. So there you have it. Happy Father's Day. You have a DF of at least 0.5.


Two weeks ago, I posted two SAT-style Quantitative Comparison questions. This week, I am posting the solutions (sorry, I know it's a bit late).
If we let the radius of the inner circle be r and the length of segment BC be s such that the radius of the outer circle is r+s, then we can express all the quantities that we are interested in in terms of r and s.
The length of arc CE is:
¼(2π(r+s)) = ½πr + ½πs
The length of arc BD plus the length of segment DE is:
¼(2πr) + s = ½πr + s
The length of segment CB plus arc BD plus the length of segment DE is:
s +¼(2πr) + s = ½πr + 2s
When comparing each pair of terms, the ½πr cancel each other out. Because s is a length, we know that s>0, which means that ½πs is always greater than s, but is always less than 2s. In terms of answering the quantitative comparison questions, this means the answer to the first question must be A and the answer to the second question must be B.
Put another way, if you are walking around a 90 degree arc (such as from point C to point E), it will always be faster to walk around the outer arc than to walk to an inner arc, traverse it, and return to the outer arc. What is particularly interesting is that this is true regardless of the radius of the inner arc.
Now before you start taking the outside edge of every curve, note that this only holds true for arcs less than a certain size. For example, what if it you were traversing a semicircle instead?
The length of the outer arc would be:
½(2π(r+s)) = πr+πs
The length of the two straightaways plus the inner arc would be:
s +½(2πr) + s = πr + 2s
Because πs is greater than 2s, it makes more sense to walk to the inner arc when walking around a semicircle! So where is the breaking point? This can be determined by letting x be the fraction of the circle to traverse and setting the two path lengths equal to one another and solving for x:
x(2π(r+s)) = x(2πr) + 2s
2πxr+2πxs = 2πxr + 2s
2πxs = 2s
πx = 1
x = 1 / π
Plugging that into Google Calculator, we see that x is ~0.318, so once you're walking more than a third of the way around a circle, it makes more sense to move to the inner arc.
I thought that this would make a great SAT question for several reasons. First, and most importantly, this is a quantitative comparison question that does not have any numbers, yet its answer is not D! I'm pretty sure that most students hated geometry (so sad!), so when they come to something like this, it's pretty easy to throw up one's hands and declare the question unsolvable. Of course such a student would be incorrect...
Also, this question is resistant to some common SAT-solving techniques. For example, for geometry questions where the figure is to scale (such as this one), The Princeton Review will tell you to make small marks on your answer sheet so you can use it as a ruler, but because this problem involves arcs, that is of little help. Another common SAT tip is to redraw the diagram, exaggerating r or s, but if you play around with that, you can probably convince yourself that there are cases where one quantity is larger than the other, but it's hard to say conclusively that it holds true for arbitrary values of r and s.
That means the only ones who will be answering the question correctly are those who can do the math. Isn't that how it should be?


We all know that converting weight to other units is a necessary skill, right? Well, if you’re looking to convert pounds to kilograms, you’ve come to the right place. In this article, we will teach you how to convert 7 pounds into kg using simple and easy-to-remember steps. This will help you when shopping for groceries, measuring ingredients, and more. So read on and learn how to convert weight quickly and easily!
What is kg?
One pound is equal to 0.4536 kg.
How to Convert 7 Pounds of Weight to Kilograms
There are a few methods one can use to convert pounds to kilograms. One is to use the weight in pounds and divide it by 2.2, which will give you the kilograms. Another way is to use the mass in kilograms and divide it by 6.2, which will give you the pounds.
What are the Benefits of Converting 7 Pounds into kg?
There are many reasons to convert pounds to kilograms. One reason is that kilograms are the internationally accepted unit of weight. When you convert pounds to kilograms, you are basically converting them into a physical measurement that is easier to work with. Additionally, when you convert pounds to kilograms, you can more accurately track your body weight over time.
Here are some of the benefits of converting pounds to kilograms:
1. Easier To Track Your Body Weight Over Time. One of the main benefits of converting pounds to kilograms is that it makes it easier to track your body weight over time. When you convert pounds to kilograms, you are essentially creating a physical measurement that is easier for you to work with. This means that you can see how your body has changed over time and whether or not you are achieving your goals.
2. Conversion Is Essential For International Use. Another benefit of converting pounds to kilograms is that it is an essential part of international use. When talking about weights and measurements, kilograms are the internationally accepted unit of weight. This means that when communicating with people from other countries, using kilograms is a much more accurate way to do so than using pounds.
3. More Accurate Than Pounds When It Comes To Physical Measurements such as BMI and Waist circumference. One final benefit of converting lbs into kgs is that it can be more accurate when measuring BMI (Body Mass Index) and waist circumference. Do both BMI and waist circumference measures use grams as their
convert from 350 pounds to kg?
To convert 350 pounds to kilograms, divide the weight in pounds by 2.2. This will give you the kilograms per pound.
How to convert 260lbs to kg?
There is a basic equation for converting weight from one unit to another:
Weight (pounds) = Kilograms
In order to convert 260 lbs to kg, you would use the equation listed above. Once you have calculated the pounds in kilograms, you would then divide that number by 2.2 to find the equivalent number in stones.
How to convert 100 pounds into kg
There are a few methods for converting pounds to kilograms, but the most common is to divide by 2.2. For example, if you weigh 100 pounds and want to convert that into kilograms, you would divide 100 by 2.2 which would give you 62.5 kilograms as the result.
Examples of pounds to-kilograms calculations
Pounds to kilograms can be calculated in a variety of ways. Here are some examples:
-To convert pounds to kilograms using the basic rate, divide the number of pounds by 2.2.
– convert pounds to kilograms using the metric rate, divide the number of pounds by .454.
-To convert pounds to kilograms using the U.S. Customary measurement, divide the number of pounds by 4.54.
What is the conversion rate for kg to pounds?
There is no one-size-fits-all answer to this question as the conversion rate for kilograms to pounds will vary depending on the weight and measurement of both objects. However, a rough estimate would be 1 kilogram (2.2 pounds) = 0.45 pounds.
hope you like this review we are continuously sharing educational data.


Hello~My name is Julia Carlesso I have been married for 26 years. We have 3 children, 2 sons and a daughter, ages 21, 19 and 15. We have 1 cat and 2 hermit crabs. My oldest son and daughter attend the University of Detroit-Mercy. My youngest son plays hockey and soccer. I just do my best to keep up with them. :)
I attended the University of Michigan-Dearborn where I got my Bachelors Degree in Elementary Education with a Math major. I have also earned my Masters and Education Specialist Degrees at Oakland University.
I taught at Wolfe Middle School 1995-2012 at that point I moved to Crothers. Since at Crothers I have taught second and third grade.
I have set up a Google Classroom. Visit the website classroom.google.com and click on the + button to join a class. Our class code is 4ra7fbk. Hope to see you there! :)


How to Calculate Your Pledge
Preparing your pledge is as easy as 1, 2, 3!
Step 1: Calculate your tithe.
We are exhorted in scripture to bring to Lord 10% of all of our increase. Increase includes all of our wage income and profits from business and investment. To calculate your tithe, simply add up all of the your projected “increase” for the year and multiply that by 0.1.
Example: I will earn $37,000 in wages this year. 37,000 x 0.1 = 3,700. So my tithe (for the year) will be $3,700.
Step 2: Calculate your offering.
Your offering is any amount you give above the tithe. There are 2 approaches to offering. You could set an additional percentage (i.e. 2% more) or you can give a set amount (i.e. $500 more). Calculate or set your offering amount.
Example: Continuing with the $37,000 amount from above, I will give 2% of my earning as offering. 37,000 x 0.02 = 740. So my offerings (for the year) will be $740.
Step 3: Combine your tithe amount and your offering amount.
Add your tithe and offering amount together. This is your vision pledge.
Example: A tithe of $3,700 and an offering $740 will combine this way (3700+740 = 4,440). So my total pledge (for the year) is $4,440. This is the amount I will write on my Vision Fund Pledge Card.


What is 5.25 as a decimal?
Step-by-Step Solution 5.25% = 0.0525 in decimal form. Percent means ‘per 100’. So, 5.25% means 5.25 per 100 or simply 5.25/100. If you divide 5.25 by 100, you’ll get 0.0525 (a decimal number).
In respect to this, what is 5.25 as a fraction?
The decimal number 5.25 is equal to the fraction 21/4.
Furthermore, what is 9.5% as a decimal? 9.5% = 0.095 in decimal form. Percent means ‘per 100’. So, 9.5% means 9.5 per 100 or simply 9.5/100. If you divide 9.5 by 100, you’ll get 0.095 (a decimal number).
Keeping this in view, what is 5.25 as a percent?
What is 0.5 percent as a decimal?
28 Related Question Answers Found
What is 2.75 as a fraction?
NOW THIS FRACTION CAN BE REDUCED BY DIVIDING BOTH NUMERATOR & DENOMINATOR BY 25. 11/4 WHICH IS AN IMPROPER FRACTION. 11/4=2 3/4 IS THE SAME ONY THIS IS A MIXED FRACTION WHICH IS ALSO=2.75 WHICH IS WHERE WE STARTED.
What is 3.25 as a fraction?
Answer and Explanation: The decimal 3.25 would be written a couple of different ways as a fraction: 3.25 = 3 1/4 as a mixed number. 3.25 = 13/4 as an improper fraction.
What is 2.625 as a fraction?
Example: Convert 2.625 to a fraction Multiply 0.625/1 by 1000/1000 to get 625/1000. Reducing we get 5/8.
What is 3.75 as a fraction?
3.75 in fraction form is 15/4.
What is 5.25 as a whole number?
Pre-Algebra Examples Find the number in the whole number place 5 and look one place to the right for the rounding digit on the right side of the decimal point 2 . Round up if this number is greater than or equal to 5 and round down if it is less than 5 .
What is 5.75 as a fraction?
As we have 2 numbers after the decimal point, we multiply both numerator and denominator by 100. So, 5.751 = (5.75 × 100)(1 × 100) = 575100.
What is 9.5 as a percent?
What is 9.5 as a fraction?
Step-by-Step Solution As we have 1 numbers after the decimal point, we multiply both numerator and denominator by 10. So, 9.51 = (9.5 × 10)(1 × 10) = 9510.
How do I turn fractions to decimals?
To convert a fraction to decimal, we divide the numerator by the denominator using long division and to convert a fraction to percent, we convert the fraction to decimal and the decimal to percent. To convert a percent to decimal or fraction, we divide the percent by 100 and reduce the fraction.
What is 16% as a decimal?
Since there are 2 digits in 16, the very last digit is the “100th” decimal place. So we can just say that . 16 is the same as 16/100.
What is 7.5 as a fraction?
Step by Step Solution So, 7.5/100 = (7.5 x 10)/(100 x 10) = 75/1000. Step 3: Simplify (or reduce) the above fraction by dividing both numerator and denominator by the GCD (Greatest Common Divisor) between them. In this case, GCD(75,1000) = 25.
What is 8% as a decimal?
Percent to decimal conversion table
What is 7.5 As a decimal?
Step-by-Step Solution 7.5% = 0.075 in decimal form. Percent means ‘per 100’. So, 7.5% means 7.5 per 100 or simply 7.5/100. If you divide 7.5 by 100, you’ll get 0.075 (a decimal number).
How do you write percents as a fraction?
To convert a Percent to a Fraction follow these steps:
- Step 1: Write down the percent divided by 100 like this: percent 100.
- Step 2: If the percent is not a whole number, then multiply both top and bottom by 10 for every number after the decimal point.
- Step 3: Simplify (or reduce) the fraction.
How do you convert to a decimal?
To convert fractions to decimals, look at the fraction as a division problem. Take the top number, or the numerator, of the fraction and divide it by the bottom number, or the denominator. You can do this in your head, by using a calculator, or by doing long division. For example, ¼ is just 1 divided by 4, or 0.25.
What is 9% as a fraction?
Decimal to fraction conversion table
What is 4% as a fraction?
Answer and Explanation: 4 percent in fractional form is equal to 1/25. Percent literally means out of 100. To convert percent to fractions, we divide the given percent value


A collection of some of our greats, Brahmagupta who studied the works of Aryabhatta, Latadeva, Varahamihira and others. He wrote the Brahmasputa Siddhanta and Khanda Katkaya transmitted by the Arabs. I’ll show that later. Solutions of linear and quadratic equations and the rules for zero operations, positive and negative numbers. Trignometric tables and in Astronomy he said that Moon is closer to the Earth than the Sun. And he solved this equation which is a very famous equation in literature. More than in this time frame he had the complete solution to the set of equations which the westerners refer to as the Pell’s equation. And even greats like Oiler and others were clueless on how to solve this and eventually after about a 100 years of trying Europe was able to solve this 1000 years after Brahmagupta had already solved it.
Bhaskara-I who wrote these works. Zero, positional arithmetic, approximation for sine. There is a very famous approximation that Sin x can be represented by this kind of expression. Very, very famous. Even today we use this and he is the one who invented that. Bhaskara II lived in Bijapur, Bijapur northern Karnataka and he went to Ujjain and became the Head of Department of Astronomy over there. An instance of people moving across the country and working in different places. He wrote Siddhanta Shiromani and he appears to have also got the elements of differential calculus. He computed precession like I told you. This statement he made. “At the highest point the instantaneous speed is zero”. This is an assertion of the Calculus of variation, where at the highest point the rate of change is zero. That is a property I use even today for living in optimization and fields like that. So I owe it all to this very famous scientist. One of my most famous favorite scientists from ancient India – Bhaskara II.
Madhava of Sangamagrama (Trissur), all these expressions that you see, this infinite series are attribute to him. So he is the one who invented this and much, much more. Founder of Kerala school of Astronomy and Mathematics. Infinite series, Calculus, Trignometry. Iterative solution of nonlinear equations, something I do for a living even today, originated with him. We typically think Newton is the one who talked about iterative solution for nonlinear equations. But it turns out that he was the one who did these things. George Joseph Geevarghese, professor and he says that Madhava’s math was transmitted to Europe a century before Newton by the Church and these are some of the alumni of the school.
Featured Image: – http://www.famous-mathematicians.com/madhava/


The Mathematics Department has a cohesive team of Mathematics teachers, working closely together and being supportive of one another in order to bring out the best in our students. We take pride in creating success stories and have expectations to meet high standards of performance.
To ignite in our pupils a passion for Mathematics and develop their latent potential in the subject so that they are able to appreciate it in real-life applications.
Our students have done us proud in last year’s National Examinations, with good distinction rates over the last 3 years.
O and N Level Results
|2017||4 Exp||A Maths||100||60.5|
Annually, the department organises training workshops for passionate students who are interested in competitive mathematics. As an extra-curricular activity, the training workshop stimulates purposeful discussions amongst the students as well as prepares them with higher-order problem-solving heuristics. The topics discussed do not just complement the MOE Mathematics syllabus, they also develop the students’ creative thinking skills and deepen their understanding of certain concepts. From Secondary 2, students also take part in the Singapore Math Olympiad (SMO) and Singapore & Asian Math Olympiad (SASMO) competitions. Our strengths lie in giving students numerous opportunities to demonstrate their passion for mathematics.
Within the school curriculum, our students are always yearning for more and eager to tackle new challenges. Hence, all Secondary 3 Express students take Additional Mathematics as a subject, and selected 3NA and 3NT students take up cross-level Mathematics at a higher level (NA students study Express Maths, and NT students study NA Maths).


General purpose parallel computations on GPU devices
What We Do
GPU devices offer amazing parallel processing capabilities. Our team deals with the development and practical application of new algorithms and data structures that allow to fully use the computing power of modern SIMD (Single Instruction Multiple Data) coprocessors. Our results find applications in data compression, information searching and indexing, graph processing, genomics and many others.
,,New data intensive algorithms and structures for GPU processors''
National Science Centre, Sonata (decision: DEC-2012/07/D/ST6/02483) – 36 months
Budget: 433.400 pln
,,Computational cluster for genomical mathematics and computer science''
Budget: 100.000 pln
,,A system for efficient time series creation from textual data''
Budget: 190.550 pln
New data intensive algorithms and structures for GPU processors
The goal of the project is to design new or adapt existing parallel structures and algorithms for multi-core general purpose graphic processing units. Among results we expect significant acceleration of existing solutions and enlargement of processed volumes of data. Scientific hypothesis proposes that this goal may be achieved with popular GPU devices and personal computers.
The project will be focused on highly attractive algorithms devoted to data intensive applications. Conducted literature studies and analysis of many implemented algorithms for GPUs showed a need of creating universal and consistent design of structures and algorithms for graphical devices including current trends in processors’ evolution. In the project we shall analyze solutions for MOLAP and time series databases. Results evaluation and load testing which will be performed with real-life data will allow to fine tune algorithms and structures to graphical devices requirements.
Because of the nature of the proposed research, the work method envisages performing the following tasks: design of theoretical foundations of a parallel-enabled algorithm for vector processor architecture; design of a prototype library focused on particular GPU processor limitations; implementation of a working prototype and efficiency measurements; prototype optimization in order to achieve maximum efficiency; publishing of results.
All the research will be performed with the equipment available at the Faculty of Mathematics and Information Science WUT, using PC workstations or professional computational nodes in a server-room. The results will be statistically analyzed according to the following factors: scalability of an algorithm or a data structure when the data volume changes, importance of acceleration according to a similar CPU based solution, effective time, memory, memory transfer and parallel core complexity.
The need for computations, and data volumes to be processed, grows rapidly, even processors with streaming capabilities and parallel cores are often unable to run calculations with the necessary efficiency. Supercomputers which can be found in computational centres are both too exotic and expensive to become common. The answer to these issues are computational cards built upon multicore graphics cards which outperforms classical CPU processors. What is missing are new representations of data structures and methods of processing them, which will enable efficient programming of algorithms working within the specific limitations of a GPU. By developing new data structures and new operations utilizing all available cores the project will open up new possibilities of using graphics cards in many fields of science, where drastic efficiency improvement of data processing is crucial. The expected impact of the project will enable popular personal computers in analysis.
A system for efficient time series creation from textual data
2019 Krzysztof Kaczmarski, Albert Wolant. GPU R-Trie: Dictionary with ultra fast lookup. Concurrency and Computation: Practice and Experience 31(19). John Wiley & Sons, Inc. 2019.
2018 Krzysztof Kaczmarski, Albert Wolant. Radix Tree for Binary Sequences on GPU. In: Wyrzykowski R., Dongarra J., Deelman E., Karczewski K. (eds) Parallel Processing and Applied Mathematics. Parallel Processing and Applied Mathematics 2017. Lecture Notes in Computer Science, vol 10777. 2018. Springer, Cham
2017 Krzysztof Kaczmarski,Piotr Przymus. Fixed length lightweight compression for GPU revised. Journal of Parallel and Distributed Computing. Elsevier. September 2017. DOI: doi.org/10.1016/j.jpdc.2017.03.011
2016 Krzysztof Kaczmarski, Paweł Rzążewski, Albert Wolant: Parallel algorithms constructing the cell graph. Concurrency and Computation: Practice and Experience 29(23). John Wiley & Sons, Inc. 2016.
2015 Krzysztof Kaczmarski, Pawel Rzazewski, Albert Wolant: Massively Parallel Construction of the Cell Graph. Parallel Processing and Applied Mathematics Volume 9573 of the series Lecture Notes in Computer Science pp 559-569
2014 Krzysztof Kaczmarski, Piotr Przymus, Pawel Rzazewski: Improving High-Performance GPU Graph Traversal with Compression. ADBIS 2014:201-214
2014 Piotr Przymus, Krzysztof Kaczmarski, Krzysztof Stencel: A Bi-objective Optimization Framework for Heterogeneous CPU/GPU Query Plans. Fundam. Inform. (FUIN) 135(4):483-501 (2014)
2014 Piotr Przymus, Krzysztof Kaczmarski: Compression Planner for Time Series Database with GPU Support. T. Large-Scale Data- and Knowledge-Centered Systems (TLSDKCS) 15:36-63 (2014)
2014 Joanna Porter-Sobieraj, Sebastian Cygert, Daniel Kikola, Jan Sikorski, Marcin Slodkowski: Optimizing the computation of a parallel 3D finite difference algorithm for graphics processing units. Concurrency and Computation: Practice and Experience (CONCURRENCY) 27(6):1591-1602 (2015)
2013 Piotr Przymus, Krzysztof Kaczmarski: Time Series Queries Processing with GPU Support. ADBIS 2013. Volume 241 of the series Advances in Intelligent Systems and Computing pp 53-60. Springer-Verlag. ISBN: 978-3-319-01862-1
2013 Piotr Przymus, Krzysztof Kaczmarski: Dynamic Compression Strategy for Time Series Database Using GPU. ADBIS 2013. New Trends in Databases and Information Systems Volume 241 of the series Advances in Intelligent Systems and Computing pp 235-244. Springer-Verlag. ISBN: 978-3-319-01862-1
2013 Piotr Przymus, Krzysztof Kaczmarski, Krzysztof Stencel: A Bi-objective Optimization Framework for Heterogeneous CPU/GPU Query Plans. CS&P 2013:342-354
dr Krzysztof Kaczmarski
inż. Artur Niewiadomski
inż. Stanisław Piotrowski
Have a Project in Mind?
Please get in touch with the head of the group.


Data analysis is an important aspect of several functions such as economics, accounting, management and finance. Data analysis employs several tools – statistical and mathematical tools being one of them. Averages is one such mathematical analysis tool. It is essentially a single value that summarizes or represents a set of values. An average can have different meanings in different applications.
This article looks at meaning of and differences between two types of averages –simple average and weighted average.
Definitions and explanations
As the name suggests, simple average of a set of values is determined by dividing the sum total of all the values by the number of values in the set.
The formula of simple average can be expressed as follows:
Simple average = (Total of x1 + x2+x3…..+xn)/n
- x = values in the set
- n = number of values in the set
For example, say ABC Inc. has 5 different items in its stock and wishes to know the average price of its stock. The simple average can be calculated as below:
|Sr No||Stock item name||Cost price (in USD)|
|No. of items||5|
|Simple average (Total/no.of items)||11.80|
The main benefit of simple average is its ease of calculation. A drawback of simple average method is however that it may not be an accurate representation of an average especially if values in the set have varying importance attached to them.
Thus, simple average is an effective method to calculate the average of a set of values in which each value is of equal importance. In other cases, use of weighted average may be more accurate, as detailed below.
Weighted average is a means of determining the average of a set of values by assigning weightage to each value in relation to their relative importance/significance.
The formula of weighted average can be expressed as follows:
Weighted average = (Total of x1w1+ x2w2+x3w3…..+xnwn)/(Total of w1 +w2+w3….+wn)
- x = values in the set
- w = weightage of each value in the set
- n = number of values in the set
For example, let’s continue the same example as above. While ABC Inc has 5 different items in its stock, they are present in different quantities in stock. The quantities in which they are present will become the ‘weights’ and thus a weighted average calculation would be more accurate to calculate the average price of its stock. The weighted average can be calculated as below:
|Sr No||Stock item name||Cost price (in USD)
|Quantity in stock (in kg)
[A * B]
|Weighted average (Weighted cost/total of weights)||10.69|
As can be seen, the weighted average cost arrived at differs from the simple average cost due to the introduction of quantities in the data set.
Weighted average method is opted for when values in a set are all not of equal importance. Thus, by taking into consideration the relative importance of each value, the weighted average method seeks to equate all the values comprised in the set. This makes weighted average method a more complex but more accurate calculation method than simple average.
Difference between simple average and weighted average
The difference between simple average and weighted average has been detailed below:
- Simple average is the average of a set of values calculated with each value being assigned equal importance or weightage.
- Weighted average is the average of a set of values calculated by giving weightage to the relative importance of each value.
2. Formula numerator
- In simple average calculation, the numerator of the formula is the sum total of all the values in the set.
- In weighted average calculation, the numerator of the formula is the sum total of – the values in the set multiplied by the weightage assigned to each value.
3. Formula denominator
- In simple average calculation, the denominator of the formula is the total number of values in the set.
- In weighted average calculation, the denominator of the formula is the sum total of all the weights assigned to the values in the set.
4. Weights assigned
- In simple average calculation, weights are not assigned to each value.
- In weighted average calculation, weights are assigned to each value in relation to their specific importance/relevance.
5. Useful when
- Simple average calculation is useful in simpler data analysis when all values are equally important. It is more relevant in simple mathematical analysis.
- Weighted average calculation finds more relevance in accounting and financial calculations such as – weighted average cost of inventory, weighted average cost of capital.
6. Indication of
- Simple average is an indication of arithmetical mean or center point of the set of values.
- Weighted average on the other hand does not necessarily indicate this. It would be more tilted towards the values which have been assigned a greater weight in the set.
7. Ease of calculation
- Simple average is easier to calculate.
- Weighted average is more complex to calculate than simple average.
- Simple average is a less accurate method of average calculation especially in more complex sets of data.
- Weighted average considers the relative importance of all values and thus is a more accurate representation of the average of a set.
Simple average versus weighted average – tabular comparison
A tabular comparison of simple average and weighted average is given below:
|Average of values computed by assigning equal importance/weightage to each value||Average of values computed after taking into account the relative importance/weightage of each value|
|Total of all values||Total of weighted values (i.e., total of values after assigning importance/weightage to each value)|
|Number of values||Total of weights assigned to values|
|Weights are not assigned||Weights are assigned to values|
|Used in simple data analysis situations where each value is of equal importance or weightage||Used in relatively complex data analysis situations where each value requires a significantly different importance or weightage|
|Arithmetical mean or center point||Titled towards the values with greater importance or weightage|
|Ease of calculation|
|Easy to compute||Complex as compared to simple average|
|Less accurate||More accurate as compared to simple average|
Conclusion – simple average vs weighted average:
Both simple and weighted average methods are acceptable methods of calculating the average of a set of values. However, it is primarily their utility in various applications that separates them. While simple average is more useful in simple mathematical calculations, weighted average has a wider range in accounting and financial applications. This makes weighted average a more relevant analysis tool for business applications.


Is it humanly possible to turn your brain into a calculator and give answers as fast as a calculator can? Yes, it is, we have already seen the instance of the legend and genius Shakuntala Devi. She has awed the world with her incredible and bizarre talent to calculate mathematics mentally. For an ordinary human being, calculating the square root of a 100 digit number can be a mammoth task without a calculator. These calculations are simply a cake walk for a mathematical prodigy. For Shakuntala Devi, these feats were just as easy as calculating “2+2=4” and thus, she became the human calculator.
The 21-year-old student from Hyderabad studying at St. Stephen’s College won the Mental Calculation World Championship at Mind Sports Olympiad and earned the tag of the world’s fastest ‘human calculator’. This title was once acquired by Shakuntala Devi herself. Neelakanta Bhanu Prakash already holds 50 national and 4 international records. He defeated Scott Flansburg in the year 2016 after winning the fastest human calculator title.
The event was conducted virtually and saw participants from Greece, Germany, UAE, UK, and 9 other countries. There were 30 participants between the age group of 15 and 30 years who participated to become the fastest human calculator. Prakash said, “Child is an art. But he develops a fear of maths because we have tested them too often on tasks we don’t mean anything to them. Playing with numbers actually is fun. I want to bring back India its past glory to mathematics. India has some of the finest brains and faculty. We must help many excel more in mental arithmetic than what we have achieved so far.”
The newly labeled human calculator has opened up his start-up by the name ‘Exploring Infinities’ and has already initiated work with the Government of Telangana. The start-up has already made more than 700 hours of content from classes 6 to 10. These prodigies are the face of future India who will represent the future generation in all spheres of life. What a moment of pride and joy for all the Indians, we have another mathematical prodigy!


How many minutes in a week? We come up with a lot of interesting questions in our heads when we’re sitting around doing nothing. We begin to think creatively while also being curious. If you work in an office, you’ll be thinking about the long hours you put in each week or year.
How many minutes in a week?
Have you ever pondered how many minutes there are in a day, how many seconds in a day, or how many minutes there are in a month? How many seconds are there in a month? How many minutes are there in a week? You’d also like to know how many minutes you spend on each activity over the course of a week.
How many minutes are there in an 8-hour day, and how many minutes are there in a week?
This page will answer all of your questions regarding how many minutes are in an hour, how many minutes are in a day, how many minutes are in a week, and how many seconds and minutes are in a day, month, and year. A second is the most fundamental and smallest unit. A minute is made up of sixty seconds. As a result, all other units, such as nanoseconds, minutes, and hours, are generated by the second. As a result, it is a necessary value for assuming time.
On the other hand, 60 seconds equals one minute, regardless of how many minutes there are in a year or how many minutes there are in a day. One hour is equivalent to sixty minutes, while one day is equal to 24 hours. The rotation of the earth on its axis causes this procedure to occur.
How Many Seconds in an Hour?
How many minutes does it take to make a year? Calculating how many hours in a week is basic and straightforward. Multiply 60 minutes by 24 hours to get the total time. Then double the result by 30 days. 60*24*30, for example, and then multiply by 12 months. As a result, 60 minutes will equal 518,400.
Converting how many minutes in a week is the inverse. A week may last 52 months or less, but you will never lose more than 215 hours every month.
Week Minutes or Minutes:
The second is the SI time base unit. 1.6534391534392E-6 minutes equals 0.0166666666667 seconds. It’s important to keep in mind that rounding errors can occur, so double-check the data frequently. This website will show you how to convert between the number of minutes in a week and the number of weeks. Fill in the units in the form with your numbers.
Date difference of calendar days:
You might also want to know how many days are between two dates on the calendar. Use the date calculator to find out how old you are in days or to calculate the length of an event. A minute is a 1/2-hour and 60-second time unit. (See the second leap for certain unusual minutes in a week of 59 seconds or 61 seconds.)
A week is a period of time that is more than a day but shorter than a month. In most current calendars, notably the Gregorian calendar, the week is seven days long, making it the most extended conventional time unit with a set number of days. It is frequently used as a time unit, despite the fact that it has no direct astronomical basis.
Converting hours to minutes is as follows:
We frequently need to know how many minutes it will take to complete a task in hours. This website provides a useful online calculator for converting this type of time measurement unit at any moment.
How many hours a week is that possible?
Week one has a duration of 7 * 24 = 168 hours. One hour is equal to 0.005952 weeks, for example. It’s the equivalent of 336 hours over the course of two weeks. As a result, two hours equal 0.0119 weeks.
Stages of management:
The week and the hour are two completely distinct times. In a company, there are many management stages—every hour, every month, every day, every week, and so on. Experts are in charge of the phases of time management in order to keep a plan and tactics in place. There is, of course, a hierarchy of importance. Managers of time schedulers have possible employment orders as well as primary tasks and paths to complete these activities.
Levels of observation:
The monitoring levels vary significantly throughout the course of an hour, a day, a week, or a month. A manager does each type of management task while maintaining suitable goals. Time managers are in charge of the company’s output in order and have well-defined responsibilities. Most firms have a lot of people who share a lot of experience and close contracts.
All systems are maintained to a high standard:
Complete maintenance of all systems is time management. Senior managers and officers are terms used to describe specialists. These individuals are the ones that organise and maintain the company’s engine. Managers, for example, in a bank, make decisions that influence the entire company. These gentlemen don’t just plan their activities for the year; they also implement a business strategy and run a firm to carry it out. In a week, how many minutes are there? How many minutes in a week? How many minutes in a week? How many minutes in a week?
Also read: eToro Login


Math at Home builds the knowledge and skills of home care providers, teachers, and parents to help them:
Set up environments that promote math literacy
Facilitate math activities and lessons for young children
Learn about mathematical concepts necessary for teaching young children
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A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the area of the signal board?
(i) Traffic signal board is in the shape of equilateral triangle. Let name it ABC.
Side of equilateral triangle ABC = a units (given)
Perimeter of equilateral triangle i.e., 2s = a + a + a = 3a
(ii) Perimeter of this equilateral triangle = 180 cm
a + a + a= 180 cm
3a= 180 cm
The triangular side walls of a flyover has been used for advertisements. The sides of the walls are 122 m, 22 m and 120 m (see fig.). The advertisement yield an earning of ` 5000 per m2 per year. A company hired one of its walls for 3 months. How much rent did it pay?
Let sides of triangular side walls of fly- over in metres are a, b and c.
a = 122 m, b = 22 m and c = 120 m
Perimeter of triangle,
2s = (122 + 22 + 120) m
There is slide in a park. One of its side walls has been painted in some colour with a message ‘‘KEEP THE PARK GREEN AND CLEAN’’, (See Fig.). If the sides of the wall are 15 m, 11 m and 6 m, find the area painted in colour.
Sides of coloured triangular wall are 15 m, 11 m and 6 m.
Perimeter of this triangular wall;
2s = (15 + 11 + 6)m
Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm.
Sides of a triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540 cm. Find its area.
Given that the sides of triangle are in the ratio of 12 : 17: 25.
Let sides of triangle in cm are 12x, 17x and 25x.
Perimeter of triangle =540 cm (given)
12x + 17x + 25x=540 cm
x =10 cm
Now sides of triangle are
12x = 12 × 10 = 120 cm
17x = 17 × 10 = 170 cm
and 25x = 25 × 10 = 250 cm
An isosceles triangle has perimeter 30 cm and each of the equal sides is 12cm. Find the area of the triangle.
Perimeter of an isosceles triangle = 30 cm
12 cm + 12 cm + Third side = 30 cm
A park, in the shape of a quadrilateral ABCD, has ∠C = 90°, AB = 9 m, BC = 12 m, CD = 5 m and AD = 8 m. How much area does it occupy?
In Fig., if we join
BD, we observe that diagonal BD divides quadrilateral ABCD in two triangles (i) Right triangle BCD and (ii) ABD.
In rt. BCD, rt. angle is at C.
Therefore Base; CD = 5 m
and Altitude, BC = 12 m
Area of quadrilateral ABCD
= Area (BCD) + Area (ABD)
= 30 m2 + 35.4 m2
= (30 + 35.4) m2
= 65.4 m2
Hence, area occupied by the quadrilateral is 65.4 m2.
Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.
Radha made a picture of an aeroplane with coloured paper as shown in Fig. Find the total area of the paper used.
A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28cm, find the height of the parallelogram.
A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, grass of how much area of grass field will each cow be getting?
Let rhombus shaped field be ABCD.
Therefore its each equal side;
AB = BC = CD = DA
= 30 m
and let its longer diagonal AC = 48 m, Diagonal
AC divides the rhombus in two congruent triangles.
(i) ABC and (ii) ACD. As we know that area of two congruent triangles are equal.
Therefore area (ABC) = area (ACD)
Now it is enough to find the area of ABC whose sides are AB = BC = 30 m and AC = 48 m Perimeter (2s) of ABC = (30 + 30 + 48) m
2s = 108 m
An umbrella is made by stitching 10 triangular pieces of cloth of two different colours (See Fig.) each piece measuring 20 cm, 50 cm and 50 cm. How much cloth of each colour is required for the umbrella?
Sides of each of 10 triangular pieces of two different colours are 20 cm, 50 cm and 50 cm.
A kite is in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 8 cm and sides 6 cm each is to be made of three different shades as shown in fig.
How much paper of each shade has been used in it ?
Let ABCD be a square whose each sides is a cm
AC = BD = 32 cm
In rt. ABC,
A floral design on a floor is made up of 16 tiles which are triangular, the sides of the triangle being 9 cm, 28 cm and 35 cm (See Fig.). Find the cost of polishing the tiles at the rate of 50 p per cm2.
A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The nonparallel sides are 14 m and 13 m. Find the area of the field.
Let ABCD be a field in the shape of trapezium.
Parallel sides AB = 10 m
and CD = 25 m
and Non-parallel sides; AD = 13 m
and BC = 14 m
Draw BM DC
also draw BE || AD so that ABED is a
BE = AD = 13 m
and DE = AB = 10 m
Now in BEC,


“If you know mathematics, it can help you make wise decisions.”
That’s the philosophy behind Gregory Foley’s teaching and research—and the spirit through which he serves as the Patton College of Education’s Robert L. Morton Professor of Mathematics Education.
Morton (BSED ’13, LHD ’68) graduated from Ohio University in 1913. Alumni Gateway did not exist, but Morton embodied the virtues etched on that landmark in everything he did as an OHIO alumnus. He returned to his alma mater as a faculty member in 1918 and embarked on a 42-year career devoted to the teaching of mathematics as a means of changing lives.
Morton’s legacy can still be seen and felt on the Athens Campus—in the lecture hall that bears his name and in the professorship he endowed 45 years ago.
Foley credits Morton’s philanthropy with allowing him to work more closely with graduate students, collaborating on professional development for math teachers and evolving curriculum designed to ensure a successful transition from high school mathematics to college courses.
Through that work, Foley and his students are building communities—within Ohio University and with local school teachers—and impacting the field of mathematics education. An article Foley co-authored with a student and an Athens County math teacher was featured in the April 2018 issue of the official journal of the National Council of Teachers of Mathematics.


What are SATs?
SATs are statutory assessments carried out by all state schools. They assess how your child’s abilities compare nationally with other children in the same year group.
Your child will be assessed at Key Stage 1 (KS1) during Year 2, at age 7.
Further SATs testing takes place at Key Stage 2 (KS2), when your child will take part in National Curriculum tests in English, maths and the new grammar test at the end of Year 6 (usually age 11).
Schools are not required to publish 2021/2022 Key Stage 2 outcomes.
The data below shows the outcomes for 2018/2019 Key Stage 2.
* For a pupil to achieve the expected standard in reading and maths they must achieve a scaled score of 100+ in the corresponding tests.
* For a pupil to be working at greater depth in reading and maths they must achieve a scaled score of 110+ in the corresponding tests.
The average scaled score at Leconfield Primary School for reading is 102.1
The average scaled score at Leconfield Primary School for maths is 104.0
* Average progress made in KS2
National average progress is always 0. Schools that make less progress receive a negative number rating, schools that make more progress receive a positive rating.
Average progress in reading -3.91
Average progress in writing +0.66
Average progress in maths – 2.55
Guidance and further information to help you analyse the data that the government report in the school and college performance website.
Please click the link below to view our performance on the ‘compare school and college performance website:


دوشنبه 4 اردیبهشت 1396
نویسنده: Angela Boyd
Task Design In Mathematics Education: an ICMI study 22 by Anne Watson
Task Design In Mathematics Education: an ICMI study 22 Anne Watson ebook
Publisher: Springer International Publishing
Buy Mathematics Education journals, books & electronic media online at Springer. Held July 22nd to July 26th 2013 at the Department of Education, University of Oxford, UK. Call for papers and dissemination of discussion document April 2012. The study offers a state-of-the-art summary of relevant research and goes. Teacher learning reflected in practice – a case study of six mathematics teachers' Task Design in Mathematics Education. ICMI Study 22: Task Design in Mathematics education. Choose from a Task Design In Mathematics Education an ICMI study 22. Task Design The Study Chairs are Anne Watson and Minoru Ohtani. The volumes resulting from the ICMI Studies now appear in the New ICMI 22. This book is the product of ICMI Study 22 Task Design in Mathematics Education. ICMI Study 22, Jul 2014, Oxford, United Kingdom.


Game Design: The Clue Connectionon July 20, 2012 at 2:32 pm
Some time back, I sat down and tried to figure out how Treasure Mountain! worked, because I really liked the problem-solving, clue-acquisition, and exploration concepts in the game. Right before my lunch break, I realized that the gameplay is based on (or inspired by) Clue of all things. It was the number of clues that gave it away.
I’m still trying to work out the particulars, but I think I’ve figured out the basic pattern to determining how many objects there are, and how they’re connected to one another. I still haven’t worked out how there are more or less objects with “shared values” to the main one, except that maybe some are deliberately left empty.
What got me started was realizing that by having some of the Clues reflects fewer of the objects, they could have more clues while also reducing the number of necessary objects. I started with Clue and worked backwards. Clue has nine rooms, six suspects, and six murder weapons, for a total of three hundred twenty-four combinations.
I figured, since there were only nineteen searchable objects in Treasure Mountain!, that having the number of clues would be a good place to start. If you have three quantities, three adjectives, and four nouns, you only thirty-six combinations, which is much closer to nineteen. It’s almost twice as many. Which got me thinking.
The problem with having 3x3x4=36 objects, means that if you’re going to play the game where partially-correct guesses reward the player (and encourage further exploration), then your minimum number of “partials” is going to be approaching ten. At most, Treasure Mountain! give you half that many.
So I had to think about it some more. Some quantities didn’t apply to all the objects. Small/large doesn’t apply to things like trees or flags, which are either all large or all small. Numbers, like groups of one to three, or four to six, don’t apply to the same objects. Trees and bushes may be found in groups of one to three, but mushrooms, flags, and flowers can be found in groups of up to six.
Obviously, there’s more to it. And some math involved. *snerk*


OT — Tapered Increaser
- Used when a pipe diameter change is required.
- Materials Available: 304/ALZ, 316/ALZ, 304/304, 316/316
- A = Smaller Diameter
- B = Larger Diameter
- C = Installed Length = [(B-A) 2] +2 (see Note 1 below)
- Example: Installed Length for 12VSI304-18OT equals [(18-12)2] + 2 = 14".
Ordered Part Includes:
OT, plus one two-piece Outer Jacket, and one VB for smaller diameter. Fiber insulation provided for IVSI models.
- Installed length shall not be greater than longest available straight pipe length (see page 7) for each diameter.
- K = N [1 -(A/B)2]2
- where N = 0.47 for one step OT
- N = 0.53 for two step OT


Multi step math word problems
Use after delta lesson 15 multistep word problems the student text includes some fairly simple two step word problems some students may be. Word problems here is a list of all of the skills that cover word problems these skills are organised by grade, and you can move your mouse over any skill name to. Pick your strategies carefully keep answering correctly to become a word problem master and win a virtual prize.
Printable worksheets and lessons wayne's coin collection step-by-step lesson- wayne exchanges and gives away coins how many does he have left. Word problem worksheets for 3rd-grade math word problems are an essential part of the grade 3 common core standards these will help young students. Use estimation to solve multi-step word problems involving addition, subtraction, multiplication, and division. Lesson nys common core mathematics curriculum 21 5•6 lesson 21: make sense of complex, multi-step problems and persevere in. Objectives ccss math: operations & algebraic thinking 3oad8: solve two-step word problems using the four operations represent these problems.
Quiz theme/title: multistep word problems description/instructions to solve a problem, you need to make several decisions one way to approach a problem is to. A three-page printable worksheet with worked examples, guided practice, and independent questions on solving multi-step word problems this worksheet is 1. Solving math word problems can be fun and sometimes frustrating some are easy, while others require a few steps use this interactive.
Engaging standards-aligned learning resources and realistic test practice learn and practice 'multi step word problems' and explore hundreds of other free math and. Are your students struggling with solving multi-step word problems this simple process breaks down the solving complicated problems into 3 easy steps. Fun math practice improve your skills with free problems in 'multi-step word problems' and thousands of other practice lessons. Browse and read multi step math word problems multi step math word problems follow up what we will offer in this article about multi step math word problems.
Solve each of the multi-step word problems on this page problems contain basic numbers of 20 or less each problem can be solved without knowledge of multiplication. Grade 6 multi-step word problems | grade 6 ccss math multistep word problem ,operations & algebraic thinking worksheets. Math word problems including single- and multi-step word problems with addition, multiplication, subtraction, division and other math topics.
Math worksheet free multi step equations worksheets solving 8th grade four practicing writing and one all operations word problems two equation mixed v print how to.
- Multi step word problems for grade 5 showing top 8 worksheets in the category - multi step word problems for grade 5 once you.
- Particularly in multi-step mathematical situations, reading comprehension can hinder the child's skill in solving a word problem having him or her read the question.
- Multi-step word problem unit grade 4 in this unit you will find: ๏a complete, comprehensive unit plan ๏12, two-step word problems and solutions.
- Browse and read multistep math word problems worksheets multistep math word problems worksheets where you can find the multistep math word problems worksheets easily.
- Multi-step word problems multi-step word problems independent practice worksheet multiple operations word problems keywords: grade 4 core math.
The best source for free multistep worksheets math daily reviews creator two step problems (multiply then divide. After searching for some multi-step word problems on the internet, i could not find any that were hard enough to match the north carolina homework questions that my.


Getting motivated to pay off credit card debt can be a challenge knowing that you only need to make a minimum payment to get by but let’s help put things into perspective. Did you know that consumers can pay off a 30-year mortgage faster than their $5,525 in credit card debt when making only the minimum payments? It’s true - we’ve done the math.
According to Experian, the average balance on consumer credit cards in 2021 was $5,525 and 40.7% of those consumers carry a balance on their cards from month to month. At a quick glance, these numbers don’t seem so bad. In fact, the percentage of consumers who carry over balances each month is at an all-time low. Unfortunately, the truly concerning part is how much these people will pay for this debt without thinking twice about the real cost.
Here’s a riddle, what do the numbers 443, 37, and 10,380 have in common? It will be the approximate 443 months, 37 years, and $10,380 in interest each consumer will pay for their $5,525 in credit card debt. Did you just think how is that even possible? Are they really paying double their principal balance in interest? Let’s take a look at some of the math.
According to the Federal Reserve, the average credit card annual percentage rate (APR) in 2021 was approximately 16%. Most credit card companies require 1%-3% of your principal balance paid down each month plus interest charges - we’ll use 2%. Let’s assume consumers only make the minimum payment and don’t add any additional debt.
To get the daily interest rate, use the APR and divide it by 365 (for the days in a year). Take that figure and multiply it by the current balance to get the daily periodic rate.
(APR / days in year) * current balance = daily periodic rate
(0.16 / 365) * 5,525 = $2.42 daily interest
You can calculate the monthly payment by multiplying the daily periodic rate and the number of days in the billing cycle.
daily periodic rate * number of days in billing cycle = monthly payment
$0.24 * 31 = $75.08
Repeat these steps 442 times to get your total interest paid or use this super easy (and free) online calculator that even provides you with a payment schedule.
Now, if these figures don’t motivate you to pay off your credit cards every month, I always recommend looking at the amount of time it takes you to earn that money. If you make $15/hour, it will take you 692 hours to pay only the interest owed on your credit card. Get help to create better habits and book your appointment with KJ Dykema, MRFC® today to pave your path to financial freedom.
Johnson, A. (2021, September 10). The average credit card balance is $5,525. here's what you need to know. CreditCards.com. Retrieved January 2, 2022, from https://www.creditcards.com/credit-card-news/credit-card-debt-statistics-1276/


Morning Maths Videos
At school, our pupils usually practise key mathematics skills (place value, addition, subtraction, multiplication and division) for around ten minutes each morning. We have now created online videos so that the children can do this work at home. These videos include questions that are answered by a teacher with explanation. There will be a link to each day’s video in the year group work section of the school website. The concepts covered are hugely important and we would like the children to complete the morning maths work each day at home. If your child struggles with the concepts, recording the workings written by the teacher day after day will really help them to improve. Once concepts are understood, the aim is accuracy, and finally accuracy with speed. Daily practice is extremely helpful with building this accuracy.


I am fast becoming a lover of data! This week, I have been engaged in on-entry assessment in areas of literacy and numeracy for Pre-Primary levels. Today's numeracy assessment addressed counting, partitioning and subitising.
In addition to the value to the classroom teacher in terms of differentiating teaching and learning, for a novice like me, conducting assessment was an incredibly useful experience. It allowed me to observe the limitations or areas of error common across this stage level; it illuminated the 'big ideas' of mathematics and their logical centrality to curriculum and planning; and it allowed me to see the natural progression of skills and knowledge as children progress in their learning.
Conducting these assessments inspired me to do some more research into data-driven teaching. Using the APST as a scaffold, I intend to make data-informed teaching a cornerstone of my practice.


Need to do a simple math problem in Excel? Do you know how to create a basic formula?
This How-To Article shows you how to do some basic math in Microsoft Excel.
1. Click the cell in which you would like to place the answer to the math problem.
2. Type the following: =10+10.
Tip: Replace the two "10" numbers with the numbers you want to find the answers to. You can also change the operation of the formula. That is: you can change the "+" sign to "-", "*" (multiplication), or "/" (division). You can also enter algebraic type formulas in the cell.
3. Press the "Enter" key.
4. The answer to the formula you just entered will be shown in the cell.
Tip: You can change the "10" and "10" to the names of cells. (Example: =A1+A2) This will allow you to modify the contents of cells A1 and A2, and the sum of the cell which has this formula in it will update automatically.
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Using a CD Calculator
CD calculators are very easy to use and can be very helpful in figuring out how much interest you will earn on a certificate of deposit. To help you figure out the rate of return on your certificate of deposit investment all you have to do is enter the CD deposit amount, the term of the CD, the CD interest rate and how interest will be compounded, daily, weekly, monthly or annually.
The more frequently interest is compounded the higher the overall return and annual percentage yield will be. Here is an example to give you a better idea.
$100,000 deposited in a 12 month CD with an interest rate of 5.00% compounded daily will have an APY of 5.127%. Earning $5,126.74 in interest.
$100,000 deposited in a 12 month CD with an interest rate of 5.00% compounded annually will only have an APY of 5.00%. Earning $5,000 in interest, $126.74 less then a CD that has interest compounded daily.
This is the power of compound interest, earning interest on top of interest. $100,000 deposited in a 5 year CD with the same interest rate above compounded daily will earn $28,400.31, compounded annually will only earn $27,628.13, a difference of $772.18.
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Now these games are essentially all games with observable actions. The term appeared in publications starting about 1988 in the work of e Maskin and Tirole 2001): Markov-Perfect Equilibrium, MPE). Alternatively, using the earlier terminology of the differential (or difference) game literature, the equilibrium is a closed- In game theory, a subgame perfect equilibrium (or subgame perfect Nash equilibrium) is a refinement of a Nash equilibrium used in dynamic games.A strategy profile is a subgame perfect equilibrium if it represents a Nash equilibrium of every subgame of the original game. a pair of equations that express linear decision rules for each agent as functions of that agentâs continuation value function as well as parameters of preferences and state transition matrices. In this lecture, we teach Markov perfect equilibrium by example. a pair of Bellman equations, one for each agent. (SPE doesnât su er from this problem in the context of a bargaining game, but many other games -especially repeated games- contain a â¦ Markov Perfect Equilibrium The Markov Perfect Equilibrium (MPE) concept is a drastic re nement of SPE developed as a reaction to the multiplicity of equilibria in dynamic problems. A strategy profile Ï is a MPE for a tug-of-war if it is both a SPE and Markovâ¦ It is used to study settings where multiple decision-makers interact non-cooperatively over time, each pursuing its own objective. Browse our catalogue of tasks and access state-of-the-art solutions. relevant" state variables), our equilibrium is Markov-perfect Nash in investment strategies in the sense of Maskin and Tirole (1987, 1988a, 1988b). We use Markov-perfect equilibrium (cf. Since the pathbreaking paper Stochastic Games (1953) by Shapley, people have analyzed stochastic games and their deterministic counterpart, dynamic games, by examining Markov Perfect Equilibria, equilibria that condition only on the state and are sub-game perfect. A Markov perfect equilibrium with robust agents will be characterized by. It is the refinement of the concept of subgame perfect equilibrium to extensive form games for which a pay-off relevant state space can be readily identified. Markov perfect equilibrium is a refinement of the concept of Nash equilibrium. The term appeared in publications starting about 1988 in the work of economists Jean Tirole and Eric â¦ A Markov perfect equilibrium is an equilibrium concept in game theory. A Markov perfect equilibrium is an equilibrium concept in game theory.It is the refinement of the concept of subgame perfect equilibrium to extensive form games for which a pay-off relevant state space can be readily identified. We will focus on settings with â¢ two players The agents in the model face a common state vector, the time path of which is influenced by â and influences â their â¦ Get the latest machine learning methods with code. Markov perfect equilibrium is a key notion for analyzing economic problems involving dy-namic strategic interaction, and a cornerstone of applied game theory. Informally, this means that at any point in â¦ No code available yet. big companies dividing a market oligopolistically.The term appeared in publications starting about 1988 in the economics work of Jean Tirole and Eric Maskin .It has â¦ I would like to know if there are analog equilibrium â¦ A Markov perfect equilibrium is a game-theoretic economic model of competition in situations where there are just a few competitors who watch each other, e.g.
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An ancient knowledge unlocks the mysteries of the Universe as well as the secret of market behaviour.
CAN AN ITALIAN MATHEMATICIAN'S 13th century discovery really make you money? Most professional traders would agree. Fibonacci was an obscure mathematician born into a family of merchants who wrote a number of texts, which played an important role in reviving ancient mathematical ratios. One of these timeless ratios is the foundation for behavioural technical analysis. It is the Golden Ratio first mentioned by philosophers such as Aristotle of ancient Greece and known by builders of the Egyptian pyramids.
This ratio was demonstrated with many examples from nature in his mostimportant text known as Liber Abaci, written in 1202. In this book, Fibonacci detailed the mathematics and revealed the mysteries behind the construction of the ancient pyramids of Egypt. He proved that the Golden Ratio was applied by the engineers, developers and building contractors to every stage of pyramid construction.
What is more amazing is that the finished pyramids were in actuality manifestations of golden ratios.
The Golden Ratio is the heart of Fibonacci analysis. It is based on the ratio 1.618. And is based on the number sequence, which is known as the Fibonacci sequence: 1,1,2,3,5,8,13,21,34,55,89,144 and so on.
Each number is added to the preceding number. For example 1 +1 =2, 2+1 = 3, 3+2 = 5.
As the sequence expands, dividing two consecutive numbers will give the ratio .618, the reciprocal of the golden ratio 1.618. For example, dividing 89/ 144 = .618.
WHAT IS THE SIGNIFICANCE OF THIS RATIO?
It is found in nature in the structure of flowers. The sunflower is a good example. The seeds are distributed over the flower's disk in Fibonacci numbers. The human body has 1000s of Fibonacci ratios and numbers. For example, our hands have five fingers and three joints in each finger, which are Fibonacci numbers.
The Golden Ratio can also be found in the shells of soft-bodied mollusks such as snails and oysters. The Golden Ratio patterns on their shells reflect the changes in their annual growth rates. Application to stock markets also show this Fibonacci growth pattern
FIBONACCI AND NATURE
The Fibonacci sequence can be found in the universe. Each arm of a galactic spiral has a logarithmic shape, which conforms to Fibonacci numbers. Nature finds it easiest both to structure itself and grow in a manner specified by the Fibonacci sequence. In fact DNA is structured in a Fibonacci sequence.
Nature implants in all living organisms the Fibonacci sequence. Trees and plants exhibit this Fibonacci growth pattern as branches and leaves grow one at a time.
THE MARKET AS A LIVING ORGANISM.
As markets reflect the hopes and fears of human beings, it is reasonable to say the Fibonacci sequence of numbers and the golden ratio could be found in markets.
Fibonacci math works through crowd behavior. A rally builds a common structure of participation. When it finally ends and starts to unwind, shareholders try to predict how far price might fall before the underlying trend resumes. The unconscious mind first sees the proportional one-third retracement as a good reversal point. New buyers do emerge here, but the subsequent bounce often fails through the prior intermediate low. This terminates the crowd's greed phase and begins a period of reason.
W D GANN'S 50% RULE.
The great master trader and multimillionaire W. D. Gann described in 1930 a trading rule that can be applied to get rich.
It was after he had gone to India to study the secrets of numerology from prominent wizards and gurus. From this instruction he gained wisdom about the mysteries of human nature and how they could be measured and applied to earning profits in the market.
When he returned from India to the US he applied these methods to his trading and became more rich.
It was the 50% rule. He advised to wait for markets to make new highs and correct 50% from these highs and then buy. He also mentioned the .618 level as a buying opportunity. He also advised to place a stop loss level under the swing low.
Conceptually this is a powerful method and is in fact used by most professional swing traders as it defined a small risk under the Fibonacci retracement with the opportunity of a large profit to be taken at the swing high.
This article is an introduction to the power of Fibonacci. It works because it is founded in human behavior and emotion, just like swing trading. I suggest you use your MetaStock Fibonacci retracement tool and apply it to your trades. It should improve your results.


- Lambda Calculi | Internet Encyclopedia of Philosophy
- The Lambda Calculus
- Proof Polynomials
- An encyclopedia of philosophy articles written by professional philosophers.
Crossley2 fdwa, jncg cs. Many people have Many people have done such work. First-Order Constrained Lambda Calculus. The constraints can be used passively for restricting the range of variables and The constraints can be used passively for restricting the range of variables and actively for computing solutions of goals. Here we present an extension of that calculus obtained by adding existential quantifiers and new rules for handling the new terms. This avoids the problem of shared variables and gives a very smoothly working language.
We present a proof of the Church-Rosser property and the denotational semantics of the whole calculus. Disjunctive Constraint Lambda Calculi. Earlier we introduced Constraint Lambda Calculi which in- tegrate constraint solving with functional programming for the simple case where the constraint solver produces no more than one solution to a set of constraints. We now introduce We now introduce two forms of Constraint Lambda Calculi which allow for multiple constraint solutions. Moreover the lan- guage also permits the use of disjunctions between constraints.
Untyped constrained lambda calculus.
SBV is a deep inference system that extends the set of logical operators of multiplicative linear logic with the non commutative operator Seq. We prove that the cut elimination holds on SBVr. SBVr and its cut free subsystem BVr are complete and sound with respect to linear lambda calculus with explicit substitutions. Completeness and soundness follow from simulating linear beta-reduction with explicit substitutions as processes. The role of the new renaming operator of SBVr is to rename channel-names on-demand. This simulates the substitution that occurs in a beta-reduction. Despite SBVr is a minimal extension of SBV its proof-search can compute all boolean functions, as linear lambda-calculus with explicit subst Categorical semantics of the call-by-value lambda-calculus.
Lambda Calculi | Internet Encyclopedia of Philosophy
Lambda calculus and intuitionistic linear logic. Higher - Order linear ramified recurrence. An infinitistic feature of classical logic Frege, the Law of Non-Contradiction, and Intuitionism'. Technically, the matter is more or less implicit in my earlier notes. There is a notable surprise, however, as regards the said correspondence. At a very basic level, thus. Moreover, if we take seriously the genuinely classical double-negation isomorphism, in proof-theoretical terms as in Chrysippus, Frege etc.
As an immediate side-effect, every genuinely classical tautology using explicitly the LNC in its proof admits of infinitely many distinct [equationally non-equivalent] witnesses i. It makes that substitution operation is complex to be analyzed. To overcome this drawback, explicit substitution systems are proposed. They bridge the gap The objective of the proposed system is to integrate the high volume of data along with the important considerations like monitoring a wide array of heterogeneous security.
When a real time cyber attack occurred, the Intrusion Detection When a real time cyber attack occurred, the Intrusion Detection System automatically store the log in distributed environment and monitor the log with existing intrusion dictionary. At the same time the system will check and categorize the severity of the log to high, medium, and low respectively. After the categorization, the system will automatically take necessary action against the user-unit with respect to the severity of the log. The advantage of the system is that it utilize anomaly detection, evaluates data and issue alert message or reports based on abnormal behaviour.
A survey of recent research in logic. First, we simplify the final step of the proof by First, we simplify the final step of the proof by following the left reduction strategy directly in the resource calculus, avoiding to introduce an abstract machine ad-hoc. We also introduce a groupoid of permutations of copies of arguments in a rigid variant of the resource calculus, and relate the coefficients of Taylor expansion with this structure, while Ehrhard and Regnier worked with groups of permutations of occurrences of variables. Finally, we extend all the results to a non-deterministic setting: by contrast with previous attempts, we show that the uniformity property that was crucial in Ehrhard and Regnier's approach can be preserved in this setting.
Concept-Relation Algebra. Extension of lambda calculus applied on graph theory. It is meant to compute the functional relation between distant nodes in graphs called "concept-relation" graphs. Can be used to superseed linear algebra, fuzzy logic and cloud Can be used to superseed linear algebra, fuzzy logic and cloud clustering. The numerals are defined as follows:. Successor, addition, multiplication, predecessor, and subtraction can also be defined as follows:.
As in the case of the booleans, an example of using the successor and addition functions will help show how these definitions functionally capture arithmetic. The arithmetical functions defined above clearly fit this description. Recall that a combinator is a term with no free variables. In particular, Y as defined before, is a fixed point combinator, since.
In the exposition of booleans, connectives such as and , or , et cetera, were given in a very general formulation. They can also be defined more concretely in terms of true and false in a manner that may be closer to capturing their truth tables.
In the paper, Church defined plus , mult , and minus somewhat differently than presented here. The predecessor function was originally defined by Kleene, in a story which will be discussed in section 4. The most striking feature of this definition, which will be discussed in more depth in what follows, is that it defines an intuitive notion effective calculability with a formal notion.
In this sense, some regard the thesis as more of an unverifiable hypothesis than a definition. In what follows, we will consider, in addition to the development of alternative formulations of the thesis, what qualifies as evidence in support of this thesis. In short, a function which has an algorithm that calculates its values will be effectively calculable and any effectively calculable function of one natural number has such an algorithm. Church offers a second notion of effective calculability in terms of provability within an arbitrary logical system.
The history of this particular version of the thesis has no clear story.
The Lambda Calculus
Kleene allegedly realized how to define the predecessor function as given in the previous section: Kleene had earlier defined the predecessor function using an encoding of numerals different from those of Church while at the dentist for the removal of two wisdom teeth. For a first-hand account, see Crossley [, p p. According to Barendregt [, p. In fact, lambda definability must coincide with intuitive computability. But I did not, Church did. Alan Turing, in his groundbreaking paper also published in , developed the notion of computable numbers in terms of his computing machines.
Thus, he claims to have captured the intuitive notion of computability with computability by Turing machines. While Turing may believe that his machines are closer to the intuitive notion of calculating a number, the fact that the three classes of functions are identical means they can be used interchangeably.
This fact has often been considered to count as evidence that these formalisms do in fact capture an intuitive notion of calculability. For a detailed analysis of many misinterpretations of the thesis and what it does imply in the context of the nature of mind, see Copeland . In a famous lecture addressed at the meeting of the International Congress of Mathematicians in , David Hilbert proposed 23 problems in need of solution.
The second of these was to give a proof of the consistency of analysis without reducing it to a consistency proof of another system. At a conference, Hilbert posed three problems that continued his general program. Turing proceeds by defining a formula of one variable which takes as input the complete description of a Turing machine and is provable if and only if the machine input ever halts.
Therefore, if the Entscheidungsproblem can be solved, then it provides a method for proving whether or not a given machine halts. But Turing had shown earlier that this halting problem cannot be solved. For a thorough discussion of computation in physical systems and the resulting implications for philosophy of mind, see Piccinini . Kleene  offers in chapters 12 and 13 a detailed account of the development of the Church-Turing thesis from a figure who was central to the logical developments involved.
Kleene  also discusses Turing computability. The halting problem, as outlined above, however, takes an arbitrary machine and an arbitrary input. We now define a set of types and a new notion of term that incorporates this idea. In many programming languages, base types include things such as nat , bool , etc. This set can be countably infinite for the purposes of proof although no programming language could implement such a type system.
- Language Regulation in English as a Lingua Franca: Focus on Academic Spoken Discourse.
- Lambda Calculi?
- Questions tagged [combinatory-logic]?
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The simply typed terms can then be defined as follows:. This formal system does not permit other application terms to be formed. Seen in this light, the strongly normalizing property states that one cannot write a non-terminating program. Clearly, then, this is a somewhat restrictive language. One can readily see that simple types correspond directly to propositions in this fragment of propositional logic modulo a translation of base types to propositional variables.
The term then corresponds to a proof of the proposition. In the simply-typed case, the correspondence can be fleshed out as:. Table 1. As was mentioned, the Curry-Howard correspondence is not one correspondence, but rather a family. The main idea is that terms correspond to proofs of their type.
An encyclopedia of philosophy articles written by professional philosophers.
There are thus many variations of the proofs-as-programs correspondence. See the following notes section for many sources exploring the development of more complex correspondences. That programs represent proofs is more than an intellectual delight: it is the correspondence on which software verifiers and automated mathematical theorem provers such as Automath, HOL, Isabelle, and Coq are based. These tools both verify and help users generate proofs and have in fact been used to develop proofs of unproven conjectures.
Shane Steinert-Threlkeld Email: shanest stanford. History a.


What does it take to create a video game, line up rhythms like the best DJs, or design a roller coaster that produces the biggest thrills? In Design Zone, you can go behind the scenes and see how video game developers, music producers, roller coaster designers and other creative problem-solvers use math to do the amazing things they do. Design Zone explores mathematical concepts like patterns, variables, scale, slope, and ratios used by artists, architects, engineers, musicians and other innovators.
Each thematic area will draw you into compelling scenes of music production, videogame development, and extreme sports. Here you can design your own experiences and solve real world challenges while discovering that math isn’t just a subject in school—it’s a fundamental, creative tool that we can use to design and invent!