Discriminant Analysis Presentation
|Introduction to Discriminant Analysis|
|Discriminant analysis is a statistical technique used to classify objects or cases into two or more pre-defined groups based on a set of predictor variables.|
It is commonly used in various fields, including social sciences, marketing, and finance, to understand the factors that differentiate groups and make accurate predictions.
The goal of discriminant analysis is to find a linear combination of predictor variables that maximally separates the groups.
|Types of Discriminant Analysis|
|Linear Discriminant Analysis (LDA): This is the most commonly used form of discriminant analysis. It assumes that the predictor variables are normally distributed and have equal covariance matrices across groups.|
Quadratic Discriminant Analysis (QDA): Unlike LDA, QDA relaxes the assumption of equal covariance matrices and allows for different variances and covariances across groups. It is more flexible but requires a larger sample size.
Regularized Discriminant Analysis (RDA): RDA is a modified version of LDA that handles situations where the number of predictor variables is larger than the number of observations. It uses regularization techniques to prevent overfitting.
|Assumptions of Discriminant Analysis|
|Normality: Discriminant analysis assumes that the predictor variables are normally distributed within each group. Deviations from normality can affect the accuracy of the classification.|
Linearity: It assumes that the relationships between the predictor variables and the discriminant function are linear. Non-linear relationships may require alternative methods such as non-linear discriminant analysis.
Homoscedasticity: Homoscedasticity assumes that the variances of the predictor variables are equal across groups. Violations of this assumption may lead to biased classifications.
|Steps in Discriminant Analysis|
|Data Preparation: Collect and clean the data, ensuring that it meets the assumptions of discriminant analysis (e.g., normality, linearity, homoscedasticity).|
Variable Selection: Choose the predictor variables that are most relevant for classification. This can be done using techniques like stepwise selection or expert knowledge.
Model Estimation: Estimate the discriminant function coefficients using maximum likelihood estimation or other appropriate methods.
|Interpretation of Discriminant Analysis|
|Discriminant Function: The discriminant function represents the linear combination of predictor variables that maximally separates the groups. It can be used to classify new cases into the appropriate groups.|
Discriminant Loadings: These coefficients indicate the relative importance of each predictor variable in discriminating between groups. Larger loadings suggest stronger discriminatory power.
Wilks' Lambda: This statistic measures the overall significance of the discriminant analysis. A smaller value indicates a more significant discrimination between groups.
|Benefits of Discriminant Analysis|
|Predictive Power: Discriminant analysis helps predict group membership based on the given predictor variables, allowing for accurate classification of future cases.|
Variable Importance: It identifies the most important predictor variables that contribute to group differentiation, aiding in understanding the key factors driving the classification.
Data Reduction: Discriminant analysis can reduce a large number of predictor variables to a smaller set of discriminant functions, simplifying the analysis and interpretation.
|Applications of Discriminant Analysis|
|Market Segmentation: Discriminant analysis is widely used in marketing research to identify segments of customers based on their purchasing behaviors, demographics, or psychographic characteristics.|
Credit Risk Assessment: Discriminant analysis helps financial institutions assess the creditworthiness of applicants by classifying them into high or low-risk categories based on financial indicators.
Medical Diagnosis: Discriminant analysis assists in diagnosing diseases by classifying patients into different diagnostic groups using various medical measurements.
|Limitations of Discriminant Analysis|
|Assumption Sensitivity: Discriminant analysis relies on several assumptions, such as normality and linearity, which may not always hold in real-world datasets.|
Overfitting: In situations where the number of predictor variables exceeds the sample size, overfitting can occur, leading to poor generalization and inaccurate predictions.
Multicollinearity: High correlations among predictor variables can affect the stability and interpretability of the discriminant function coefficients.
|Discriminant analysis is a powerful statistical technique used for classification and prediction tasks.|
It helps understand the factors that differentiate groups and make accurate predictions about new cases.
By identifying important predictor variables and simplifying complex datasets, discriminant analysis provides valuable insights across various domains.
|References (download PPTX file for details)|
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This free course, Teaching mathematics, has been designed for non-specialist mathematics teachers of 8 to 14 year olds, teaching assistants, home schoolers and parents and draws on the established provision of mathematics education at The Open University. It can also be used as Continuing Professional Development by individuals or groups of teachers. The authors have many years’ experience of teaching mathematics in the classroom and in Initial and Continuing Teacher Education.
This course aims to develop your understanding of the mathematical content covered in the middle school years and effective strategies and approaches to the teaching and learning of this content. Through your studies you will begin to understand how children in this age group learn mathematics and the common misconceptions which they may experience.
After studying this course, you should be able to:
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Ok, so most of us don’t like Math, but it is important to understand the various methods that can be used when discussing curvature. Specifically the supposed curvature of the ball we are told we live on. Jon Le Bon does a great job of breaking down the mathematics behind the various methods of calculating such curvature, using Geometry, Trigonometry and Algebra.
Part I: Introduction
Part II: Geometry – simple method for calculating expected drop on a circle.
Part III: Trigonometry – calculating expected drop on a sphere using triangles.
Part IV: Calculating Obstruction


Remember basic arithmetic from school? These work just like those.
|+$a||Identity||Conversion of $a to int or float as appropriate.|
|-$a||Negation||Opposite of $a.|
|$a + $b||Addition||Sum of $a and $b.|
|$a - $b||Subtraction||Difference of $a and $b.|
|$a * $b||Multiplication||Product of $a and $b.|
|$a / $b||Division||Quotient of $a and $b.|
|$a % $b||Modulo||Remainder of $a divided by $b.|
|$a ** $b||Exponentiation||Result of raising $a to the $b'th power.|
The division operator ("/") returns a float value unless the two operands are integers (or strings that get converted to integers) and the numbers are evenly divisible, in which case an integer value will be returned. For integer division, see intdiv().
Operands of modulo are converted to int before processing. For floating-point modulo, see fmod().
The result of the modulo operator
% has the same sign
as the dividend — that is, the result of
$a % $b
will have the same sign as $a. For example:
echo (5 % 3)."\n"; // prints 2
echo (5 % -3)."\n"; // prints 2
echo (-5 % 3)."\n"; // prints -2
echo (-5 % -3)."\n"; // prints -2


If ever you have a doubt on byte code of an image or size of an image, this is how it calculates of it.
Every image consists of blocks called pixels. As we all know data is always stored informs of bits. So even pixels will consume some bits of memory. For suppose we have only white and black 0 represents white and 1 represents black. So each of these pixels consume one bit of memory. For example: we have an image of size 100X200 pixels.
So total amount of memory in bits is 100*200*1=20,000 bits
A byte is equal to 8 bits.
So total amount of memory in bytes is 20,000/8=2500 bytes.
Now if you want to have shades of grey , definitely we must increase the bits of memory for a pixel. Say we have given 2 bits of memory for a pixel, we can store 4 shades of grey.
00 represents white
11 represent black
01 represents light grey
10 represent dark grey
For example: we have an image of size 100X200 pixels .
Total memory =(100*200*2)/8=5000 bytes
The Similar way if you allocate 3 bits per pixel, we can have 8 shades of color.
000 represent White
001 ,010,011,100,101,110 represent various shades of grey
111 represent black
Total memory =(100*200*3)/8=7500 bytes
From above 3 observations, we can easily derive a formula.
n bits can produce 2^n patterns (2 to the nth power)
Total no of colors= 2^bits (2 to the power bits per pixel).
4 shades of colors=2*2 which is 2 bits per pixel
8 shades of colors=2*2*2 which is 3 bits per pixel
16 shades of colors=2*2*2*2 which is 4 bits per pixel
32 shades of colors=2*2*2*2*2 which is 5 bits per pixel
64 shades of colors=2*2*2*2*2*2 which is 6 bits per pixel
For a general image representation, we need 256 colors. So
256 shades of colors=2*2*2*2*2*2*2*2 which is 8 bits per pixel


Welcome to Year 1! Here are just a few snapshots of life in year 1 at Birchwood Avenue!
Year 1 C
This half term our topic is Paws, claws and Whiskers. We have been reading a variety of texts about big cats and how their habitats change across different continents. We also looked at the different home pets you can have and decided that Mrs Di-Bella should have school pet that we can all play with!
In DT we were able to build animal enclosures and had to plan it first to think about what our animals would need in their homes, whether that be water, food, toys or a shelter.
In maths we continued with our daily counting in 2's, 5's and 10's and we used our knowledge to learn how to multiply and divide. We also learned how to half and quarter, shapes, everyday object and amounts of a number.
This half term we learned about splendid skies. We found out about all different kinds of weather and compared our climate to that of Spain. We especially enjoyed reading Mrs Mopples washing line and writing our own version of the story.
We read the blue balloon and used it as inspiration for our own balloon launch. We can't wait to find out how far our balloons have travelled. We predict that they will go all the way to the seaside or even the North Pole!
In maths we have been using numbers up to 50 in lots of ways, counting, representing adding and subtracting. We feel much more confident when using tens and ones now.
We read a rhyming story and decided to investigate rhyme. We thought of lots of rhyming words and created rhyming strings. Then we played a pairs game where we worked together to find the pairs.
As part of our topic on transport we found out all about boats. We thought about different designs and created our own using paper. We added decoration and features such as a captain or a mast. Then we tested them by floating them in a bowl of water.
We have been adding and subtracting this term. When we were confident in our subtracting we played a game in pairs. We both started at 20 and rolled a dice to find the amount we should subtract. The first one to 0 was the winner!
In one world week we learned a Russian dance.Look at us go!
YEAR 1 C
This half term year 1's topic is 'Planes Trains and Automobiles' . We have been learning about road transport and designing our own eco friendly car. We have also been looking at air and rail transports comparing the differences we can see. In Maths we have been learning how to add and subtract number and sometimes using pictorial representations.
This half term year 1's topic is 'Bright lights Big City'. We will be learning all about our capital city London and the famous buildings it has. We will be learning about the Queen and her royal family and what it is like to be a tourist in London.
Sorting maths- the children had a range of objects and had to decide how they would sort them. They then had to explain their choices.
1:1 correspondence- the children used 1:1 correspondence to investigate whether groups of objects were the same or different.
Walking the map- the children walked over London before planning a route that allowed them to see different sights and testing that their route worked.


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There is more than one method of dividing fractions. Multiply Decimals Worksheets Math Worksheet Multiplying Word ... #205107. I love using task cards in my classroom because you can use them in so many different ways. 1) 10 5 2) −24 12 3) −20 −2 4) −300 −20 5) 65 5 6) −66 −6 7) 75 −15 8) −56 −14 9) 102 −17 10) −72 −4 11) 153 ÷ 17 12) 12 ÷ −3 13) 48 ÷ 6 14) −120 ÷ −20 15) 306 ÷ 18 16) −65 ÷ 13 -1-©l 92h0 k1p2 r aKVuTt6a0 ASCoEfgt 7wLagrje I bL vLkCL. Usually, I have students complete task cards with a partner on the 3rd or 4th … Smash the 11+ exams with EdPlace! So we have make 10 6. => Learn more Practice file answer key. Canadian curriculum grade 5 math worksheets. Decimals: recurring decimals Video 96 Practice Questions Textbook Exercise. The second expression includes parentheses, so hopefully you will remember that the negative sign also gets squared. Integers. As understood, execution does not recommend that you … Verify your answer with the answer key provided in the worksheet. In particular, you need to get used to timing yourself and sticking to strict time limits. British scientists invented . 122. You also have to pay attention to the signs when you multiply and divide. See more ideas about integers, multiplying and dividing integers, dividing integers. Was able to skip a bunch of pre req classes, so thank you. *TIP: Be familiar with these formulas so won’t waste time looking them up. The following 7th standard Go Math Answer Key and Practice book covered all chapters with a detailed explanation by expert math educators. This page will show you how to use the quadratic formula to get the two roots of a quadratic equation. The easiest and most commonly taught way is to “invert and multiply.” Dividing fractions – invert and multiply. Here are a few reasons why students must practice with 7th Grade Go Math Practice cook and Answer key, they are as follows: 1. More printable math worksheets. Preview Print Answers: Answer, Find, and Shade (2 in 1) Multiplying and Dividing Integers. Become an BoostBase subscriber for … -4/2= -2 The signs are different (negative 4 and positive 2), so the answer is negative. Chapter 1; Chapter 2; Chapter 3; Chapter 4; Chapter 5; Chapter 6; Chapter 7; Chapter 8; Chapter 9 ; Chapter 10; Index; Learning Objectives. Topic#3 Multiplying and Dividing Integers. Practice adding negative and positive integers on a number line. REVIEW: Multiplying and Dividing Integers Find the product or quotient. 7 33 1 − 6 5. Students will practice multiplying and dividing two, three or four integers in this fun self-checking maze activity. Go Math Answer Key for Grade 7: Want to master in mathematics subject? Volume Power Point 1/3/13. 2. You get the pdf Notes-and-Practice, Answer-Key and the Dorito-Man notes too! The purpose of providing the Go Math Grade 7 Answer Key Chapter 2 Multiplying and Dividing Integers is to make the students understand the concepts in a simple way. Fraction definitions to practice and remember. Key to Fractions Workbooks. Just check your signs to make sure that your final answer is correct. • Adding, Subtracting, Multiplying, and Dividing Integers, Decimals, and Fractions • Using measurement systems • Problem Solving Skills Instructional Activities Step 1 Review different units of measure and when to use each one. When we are solving exponents, these operations are used altogether in combination. Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. This is similar to the rule … How to solve difficult Math problems easily? 1 Find each product. Dimensional analysis Video 97 Practice … Accuplacer Math: Quantitative Reasoning, Algebra & Statistics Placement Test Exam Information. These differentiated worksheets are suitable for Year 6 children working at different levels of ability. 3. Rounding makes numbers easier to work with. To find the answer to the riddle, add and subtract positive and negative numbers. I took my PERT test this afternoon and got a 139! 1 2(1) 3 1(1, 1) 19. Writing Linear Equations Involving Graphs. Oct 7, 2019 - Explore Rocio Santos's board "multiplying and dividing integers" on Pinterest. Note: Use the / key where you mean "divide." Includes 13 regular problems and 2 word problems. There are four basic math operations: addition, subtraction, multiplication, and division. What is rounding and why do we do it? The key to remembering this is to follow the order of operations. For complete access to thousands of printable lessons click the button or the link below. 3 • (27) 5 2 • (27) 5 1 • (27) 5 0 • (27) 5 (21) • (27) 5 (22) • (27) 5 Unit 3 Review for test Power point. 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Oct 7, 2020 - Teachers ~ You'll LOVE using this to introduce and teach Multiply and Divide Integers with and your students will catch on super quick and enjoy the Dorito-Man strategy for learning the Integer-Rules. Fill in the boxes to the right, then click the button to see how it’s done. Here's a large number line that you can cut out, assemble, and hang on your classroom wall. 2. You can avail Go Math 7th Grade Answer Key online on aplustopper.com in pdf format. If you use numbers, you can be sure. Students multiply similar shapes together. Use the formula sheet as your guide. These math worksheets provide practice for multiplying fractions. For example: This multiplication table features negative and positive integers ranging from negative four through positive four. 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Problems in Algebra I solve with graphing calculator, science powerpoint 4kids, Simplifying Square Roots That Contain Variables, manual entering of quadratic formula on the TI-89, solve for a given variable worksheets, hardest math problem in the world ?. Book 1 teaches fraction concepts, Book 2 teaches multiplying and dividing, Book 3 teaches adding and subtracting, and Book 4 teaches mixed numbers. Using and Applying Decimal Numbers up to 3 Decimal Places PREVIEW WORKSHEET. 13(-3) = -39 Multiply: (-5)(-8). Understand and Apply Division of Decimal Numbers to Solve Problems PREVIEW WORKSHEET. If correct, a check mark appears beside the answer; if wrong, an X will appear. Middle School Mathematics concepts are clearly explained in a stepwise manner by the award-winning mathematics educators and prepared Go Math Grade 7 Answer key. Chapterwise HMH Go Math Answer Key for Grade 7 can make your learning easier and improve mathematical thinking. 12:50 21 Jan 21 . Then describe any patterns you notice. We offer highly targeted instruction and practice covering all lessons in 6th Grade Math. The key Fibonacci ratio of 61.8% is found by dividing one number in the series by the number that follows it. Students find pairs of congruent shapes, and add the numbers inside of them. Welcome Back. Lauren Chipman. Yes, you can secure much better by solving Go Math Grade 7th Answer Key as you will be aware of tricks and tips to solve different math problems. Solve each word problem by multiplying decimals to the tenths and hundredths place by single digit numbers. For at least some of your practice, you should answer questions under test conditions. ; number line drawna. We both like the way the concepts and theorems are being explained and reinforced through examples. Ask students which unit of measure you would use to find…: • Length of a pencil? TRIVIA IN MATH, calculating lcm in c++ source code, adding, multiplying and dividing integers grade 8, free math sums for sixth graders. For example, 4_ 7 is a rational number, as is 0. In Company 3. Note this page only gives you the answer; it doesn’t show you how to actually do the division. Please login to your account or become a member and join our community today to utilize this helpful feature. View Premium Worksheets . They must answer … It’s good for checking your answers. Here are two examples: If a house is 4 meters and 3 centimeters tall we would say it’s 4 meters tall. Yes, it really is that easy! Includes problems with and without wholes, and with and without cross-cancelling. 1 2( 1) 3 5( 1, 5) 21. …There are two rules for multiplying…and dividing integers. FLUENCY AND SKILLS PRACTICE Name: LESSON 11 GRADE 7 LESSON 11 Page 1 of 2 Understanding Multiplication with Negative Integers Practice multiplying negative integers. Integer operations puzzle displaying top 8 worksheets found for this concept. Point to Point explained solutions available in Grade 7 Go Math Solution Key pdf are designed in a systematic way as per the latest curricula. Middle School Go Math 7th Std Answer Key provides all chapters questions and solutions with detailed explanations. Integers are positive and negative whole numbers. Teach students about comparing, ordering, adding, subtracting, multiplying, and dividing basic integers. Multiplying and Dividing Integers practice Correct online Day 4 Tuesday Quiz #2 10/4 Students will demonstrate understanding of + / - / x / ÷ of rational numbers through a check up quiz ATN Check Up pg. Saved by Free Math Worksheets. GRE math questions cover a wide range of topics including arithmetic, algebra, geometry, and data interpretation. Decimals: ordering Video 95 Practice Questions Textbook Exercise. Topic#8 and #9 PowerPoint. What has 13 hearts, but no other organs? Dividing Decimal Numbers by 10, 100, 1000 and Multiplying by an Integer PREVIEW WORKSHEET. 2 2( 2) 3 7( 2, 7) y … At the top of this worksheet, there are many shapes with positive and negative numbers in them. Fraction Multiplication Fraction Division. Type the answer for each multiplication or division problem. For each sentence, fill in the blank line to demonstrate your knowledge of integers. Or, check out our collection of Multiplying and Dividing Fractions Worksheets, which are perfect for helping children put their knowledge into practice. Then match the letters with the answers. It is a fairly straightforward process. Answers to adding and subtracting integers 1 4 2 2 3 3 4 2 5 4 … Multiplying and dividing decimals by 10, 100 & 1000. View Premium Worksheets . In this section, you will learn the operations of multiplication and division of integers. Plus each one comes with an answer key. Sai is a Geometry student in the school and I was looking for Geometry tutoring sites that can help him reinforce what he is learning and get the concepts correctly in his head. 8 ⋅ (−5) = −40 −12 ÷ (−3) = 4 Key Concept and Vocabulary Visual Model 4 ⋅ (−2) = (−2) + (−2) + (−2) + (−2) Name _____ factors product dividend divisor quotient Multiply and divide. For instance, suppose you're not sure if "half of (the unknown amount)" should be represented by multiplying by one-half, or by dividing by one-half. Each book has a practice test at the end. Start now for free! Download Go Math Grade 7 Answer Key Chapter 2 Multiplying and Dividing Integers for free. Answer: In adding two integers with same sign add their absolute value and keep the common sign. Don’t worry—Magoosh is here to help! Write the positive and negative numbers in order, from least to greatest. We consider these … Answer Key. This will allow you to eliminate outlying answers right away. Teach students about comparing, ordering, adding, subtracting, multiplying, and dividing basic integers. When you multiply two negative numbers or two positive numbers then the product is always positive. Solving HMH & Math practice Go Math Answers and practice books for Grade 7 improve your mathematical understanding level. Multiplying Dividing Integers Worksheet And Worksheets ... #205105. Crewton Ramone's equivalent fractions, games, and video. Showing top 8 worksheets in the category - Multiplication And Dividing Integers. You get the pdf Notes-and-Practice, Answer-Key and the Dorito-Man notes too! When adding two integers with opposite sign subtract the smaller absolute value from the larger and keep the sign of the number with the larger absolute value. The correct maze path requires students to compute 14 problems. … Grade 7 HMH Go Math – Answer Keys. This packet helps students practice multiplying positive and negative numbers (a skill that is essential for algebra and is very often challenging for students!). Quickly access your most used files AND your custom generated worksheets! Enhancing your Math skills and logical ability is very essential for scoring better marks in the exams and it can be possible by our conceptual Go Math Answer Key for Grade 7. Dividing fractions worksheets with two fraction division. Add the positive and negative numbers together. Our premium worksheet bundles contain 10 activities and answer key to challenge your students and help them understand each and every topic within their grade level. Works well as independent practice, homework or even something to leave with the substitute (answer key … CCBC Math 081 Multiplication and Division of Integers Section 1.5 Third Edition 9 Pages 43 1.5 Multiplication and Division of Integers In the previous two sections, you learned two operations on integers: addition and subtraction. Practicing and solving the Go Math Middle School Answers is the best way. Topic#5: Number Properties. Having a good grip on the primary concepts of Maths helps you a lot to grasp the topics involved in middle school concepts. … 2.6 Multiply and Divide Integers Game 2..6 XP Timed Math Facts 2.6 Grade or No Grade Multiply and Divide Integers 2.6 Integers Jeopardy 2.6 Fruit Shooter Integer Multiplication 2.6 Integers: Adding, subtracting, multiplying, dividing 2.6 Kahn Academy - Multiplying Integers tutorial 2.6 Multiplying Positive and Negative Numbers video Integer worksheets contain a huge collection of practice pages based on the concepts of addition, subtraction, multiplication, and division. What was the change in the … 4th through 6th Grades. 1. Multiplying equivalent fractions. Where can I get Go Math Grade 7 Answer Key Pdf Online? *TIP: Read the answer options before you read the math test questions. The GRE math practice questions in this post will help you identify which areas you need to work on and how well you’re prepared for the exam. Multiplying And Dividing Decimals Worksheets Pdf The best ... #205106. Use the TAB and SHIFT+TAB keys, or the mouse, to move between problems.


But a distant observer is any observer outside of the event horizon.
The crucial point here is to understand that a coordinate system is basically the “point of view” of a specific observer – in the case of Schwarzschild coordinates, that would be a stationary observer very far away from the black hole. All observers agree that the in-fall happens in a finite amount of proper time; what differs are only the coordinate times. This isn’t simply a case of what the distant observer sees, from their perspective it’s always possible to for an object to accelerate away. The proper time however, i.e. what a clock physically records as it falls, is buy a essay paper
quite finite, even in Schwarzschild coordinates, as shown below.The physical event takes place regardless of which coordinate system you choose, it’s not a frame-dependent object. The proper distance from some shell r1 down to the event horizon, in Schwarzschild coordinates, isThe proper time this in-fall takes, still in Schwarzschild coordinates (geometrised units), isBoth of these – proper distance as well as proper time – are finite. In other words an object can never reach the event horizon until you do, and you can’t until another object does, and so on.The Schwarzchild coordinates do tell us something about the geometric length of a world-line extending towards an event horizon. I’m not talking about a hypothetical observer at infinite an distance, I’m talking about a real observer at any distance from the horizon. Yes I know the difference between coordinate dependent time and proper time, I’m also well aware of what a change in coordinate systems can do in regards to how time is measured and what it most definitely can’t do.The time interval between events and the order in which they occur is an arbitrary choice of how you choose to measure the system but if an event does occur in one coordinate system then it’s a physically real event that happens in every coordinate system (although the event may be outside of the coordinates used it will be in that coordinate system).
This is what the Schwarzschild coordinates clearly show any coordinates that allow an object to reach an event horizon in a finite amount of proper time are in direct contradiction to this coordinate system. What is not finite is the coordinate in-fall time for a Schwarzschild observer, which corresponds to what he measures on his own clock that remains stationary infinitely far away from the event horizon. Simply put, the Schwarzschild observer never sees anything reach the horizon (he just sees it slowing down, dimming, and being red-shifted to invisibility), but the test particle itself still reaches it in finite time, as demonstrated above.
If you want to be absolutely sure, you can also explicitly calculate the in-fall geodesics from the geodesic equation, and then integrate up to obtain their geometric length. There is no contradiction. therefore no amount of proper time on any watch allows an object reach the horizon. This measurement is equivalent to the geometric length of a radial geodesic, so it being finite means that things do indeed reach and cross the horizon, even though a Schwarzschild observer never sees that happening. The proper distance from some shell r1 down to the event horizon, in Schwarzschild coordinates, isThe proper time this in-fall takes, still in Schwarzschild coordinates (geometrised units), is I don’t doubt the result of the equations you’re using, I doubt their applicability to this situation.
The proper time it takes for something to fall to the event horizon (and onwards into the black hole) is finite and well defined. The Schwarzchild coordinates do indeed tell us something about the geometric length of a world-line extending towards an event horizon. So yes, an event that does not happen for one observer may indeed happen for another observer – because we are in a curved spacetime.There is no contradiction here either, because the in-fall time as measured by a co-moving clock is a proper quantity, i.e. something that all observers agree on, whereas the infinity of the Schwarzschild observer is merely an artefact of the coordinate system, and hence observer-specific.To put it succinctly, in order to check whether the horizon can be reached in a finite amount of time, you need to look at a watch in free fall, not at a watch stationary at infinity.
That is incorrect, see the maths in the last post. This is done in (e.g.) T. The coordinate in-fall time diverging to infinity for Schwarzschild coordinates physically means that such observers never see/measure anything reach the horizon.However, Schwarzschild coordinate time does not tell us anything about the geometric length of a world line extending down to the horizon. But it does happen from the perspective of the in-falling observer himself, and it does so in finite time.
The geometric length of the world lines is finite. Do note though that Schwarzschild coordinate measurements do not correspond to anyone’s physical clock or ruler in the real world.P.S. Time dilation and length contraction on the other hand are observer-dependent quantities, and both diverge at the horizon in the case of Schwarzschild observers. In curved space-times, “time” is a purely local concept, so a far-away clock cannot tell us anything about what happens locally at the horizon, or at any point in between.Understanding the difference between coordinate quantities and proper quantities is absolutely crucial in General Relativity.
Post by Markus Hanke:This is a very common misconception, but it is wrong. It tells us that due to time dilation and length contraction, the world-line is infinite in length before ever reaching the horizon No. So an object can never reach an event horizon from any distance under any amount of acceleration, gravitational or otherwise. Also see Baez (2nd paragraph) for a plain-text explanation : What happens to you if you fall into a black holesP.S. But that does not necessarily mean that everyone can observe, measure, or calculate that event. it never ever happens from the perspective of a distant observer Correct.
As expected, the result – i.e. proper time – matches the expressions given earlier, and is quite finite. But a distant observer is any observer outside of the event horizon. Strictly speaking, a Schwarzschild observer does not even exist in the real world, the coordinate time is simply a bookkeeping device, and does not correspond to anyone’s physical clock reading.See Taylor/Wheeler “Exploring Black Holes” chapter 3, as well as Misner/Thorne/Wheeler “Gravitation” chapter 31, for the precise derivation and physical justification of the above expressions. It’s just that the Schwarzschild observer at infinity cannot see, measure, or calculate it using his own clocks and rulers, since his notions of time and space or not the same as the ones locally at the event horizon.Let’s look at this in more detail.
Posts by Markus Hanke: It takes takes an infinite amount of proper time in Schwarzchild coordinates for an object to reach an event horizon No, it takes an infinite amount of coordinate time for the Schwarzschild observer, meaning that he never sees or measures anything reaching the horizon. Using equations derrived from the perspective of a distant observer, the proper time required on their clock for any object to reach the horizon is infinite (so is the distance in space because of length contraction but sticking with time is fine to keep it simple). This is not a contradiction – they are both right, since measurements of time and space are purely local quantities. If we examine the point of view of an observer in free fall towards the black hole, then we will find that the horizon is reached – and crossed – in a finite amount of time, as measured by a co-moving clock.
The proper measurements on the other hand correspond to what a clock and ruler physically measure when they actually travel along the free-fall geodesic, which is of finite length – all observers agree on this, including the Schwarzschild observer.Since both the above expressions are covariant quantities, if they are finite in one coordinate system, they are finite in all coordinate systems.So, while the Schwarzschild observer argues that – according to his own clock – the in-falling test particle never reaches the horizon, a clock co-moving with the particle disagrees, and reaches the horizon in a finite time as given above. Changing between two valid coordinate systems doesn’t allow an event that can never happen in one to happen in another. Since Schwarzschild observers are by definition infinitely far away from the horizon, it is not really a surprise that their coordinate in-fall time diverges.
It can’t be anything to do with the distant observer accelerating away from the horizon in order to maintain a constant distance as opposed to the falling object only being under gravitational influence because if a distant observer were to fall towards the black hole they still could never observe the closer object reaching the horizon.It can’t be possible for a falling observer to reach the event horizon from the perspective of a more distant falling observer either because the more distant observer could accelerate away and the closer object would have to reemerge from inside the horizon. Apologies for the bad formatting of the maths above, the LaTeX rendering isn’t brilliant on this old forum software. if an event does occur in one coordinate system then it’s a physically real event that happens in every coordinate system An event is physically real regardless of any coordinate system. It tells us that due to time dilation and length contraction, the world-line is infinite in length before ever reaching the horizon. The coordinate labels are an arbitrary choice. The Schwarzchild coordinates are valid though and show that time dilation and length contraction approach infinity at the horizon.A coordinate system that allows an object to cross the event horizon is in direct contradiction to the Schwarzchild coordinates.
If an event never occurs in one coordinate system than it never happens in any coordinate system.It takes takes an infinite amount of proper time in Schwarzchild coordinates for an object to reach an event horizon (proper time as in the time measured on the distant observer’s watch) so it never ever happens from the perspective of a distant observer. That means however long the black hole hole exists for, it can never be too late for an object to escape and therefore no amount of proper time on any watch allows an object reach the horizon.If it were possible to reach an event horizon from the perspective of a falling observer then at what point does the Schwarzchild coordinate system become invalid, how close to the event horizon? Schwarzchild coordinates must always be invalid if this is the case and it’s just a matter of degree, they can’t suddenly stop working at a certain distance. See the expressions in the last post, and refer to the sources I quoted for their detailed derivation and explanation. It takes takes an infinite amount of proper time in Schwarzchild coordinates for an object to reach an event horizon No, it takes an infinite amount of coordinate time for the Schwarzschild observer, meaning that he never sees or measures anything reaching the horizon.
The proper time however, i.e. what a clock physically records as it falls, is quite finite, even in Schwarzschild coordinates, as shown below.The physical event takes place regardless of which coordinate system you choose, it’s not a frame-dependent object. How close to the black hole does an observer have be in order to ‘see’ an object crossing the horizon? It doesn’t make any difference how close it is.No matter how long a black hole lasts for, it will never be enough time for an object to reach the horizon from a distant observer’s perspective.
It’s just that the Schwarzschild observer at infinity cannot see, measure, or calculate it using his own clocks and rulers, since his notions of time and space or not the same as the ones locally at the event horizon.Let’s look at this in more detail. Fliessbach, “General Relativity”.


6 Nimmt! / Take 5! is a counting card game designed by Wolfgang Kramer in 1994 and published by Amigo Spiele. The French version is distributed by Gigamic. This game allows 2–10 players who start with ten randomly numbered cards. These are played in simultaneous turns onto four card stacks with the goal of limiting the number of points (in the form of Bulls’ Heads distributed among the cards) you’re forced to take. Each player attempts to play their cards without laying their 6th card on a stack, as this results in a penalty of collecting all cards in the stack. Each card indicates penalty points with the number of bull heads on top of the card. After any player reaches 66 points the player with the least penalty points wins.
The game is sometimes called 6 who loses!, Take 6!, Category 5, or the original German name. The game can take from 2 to 10 players. The game’s suggested minimum age is 10 years, and lasts on average about 45 minutes. The game consists of multiple rounds (typically 3–4) with cumulative scoring, each taking 10–15 minutes. It is possible to just play a single round as self-contained game.


Pre-primary school teachers’ approaches to mathematics education in Finland
Author(s): Camilla Björklunda (email@example.com)
Source: Journal of Early Childhood Education Research; Vol 4(2), p. 69-92.
Full text: PDF
Abstract: The purpose of this small-scale study is to examine Finnish pre-primary teachers’ approaches to mathematics education. Qualitative analyses from six in-depth interviews reveal different strategies and goals. The teachers describe themselves as the facilitating participant, express that mathematics should be framed in playful settings, and assume that it is to be learnt indirectly. The study discerns different pedagogical goals for mathematics education, such as working on counting procedures, preparing for the next school level, building for a better future, and teaching for mathematical literacy. These constitute the teachers’ pedagogical approaches to early mathematics education. Context is experienced as influencing their practice, together with an overall aim to foster a positive attitude towards mathematics. This is discussed in relation to the teachers’ current practices and the contextual framework in which education is conducted.
Author-Supplied Keywords: Finland, mathematics, teaching, pre-primary education
ISSN-L: 2323-7414 online
Author Affiliation: aUniversity of Gothenburg, Sweden


Cryptography consultants are considerably skeptical of the method’s scalability, however aren’t ruling out the potential for success both.
In line with a current paper, Chinese language researchers claimed to have found a novel technique to interrupt the Rivest–Shamir–Adleman 2048 bit (RSA-2048) signing algorithm current in blockchains and different safety protocols. RSA is a cryptographic method that makes use of a public key to encrypt info and a non-public key to decrypt them.
Breaching the RSA-2048 algorithm requires, just like different algorithms within the RSA numbers household, discovering the prime elements of a quantity with 617 decimal digits and 2048 binary digits. Specialists estimate that it will take extraordinary computer systems 300 trillion years to interrupt an RSA-2048 encryption key. Nevertheless, Chinese language researchers mentioned of their paper that the encryption could possibly be inversed with a quantum pc with 372 qubits, or a fundamental unit of data appearing as a proxy for computation energy.
Compared, the newest IBM Osprey quantum pc has a processing capability of 433 qubits. Beforehand, consultants calculated that factoring RSA-2048 with quantum computer systems using Shor’s algorithm (a quantum factoring technique) would require 13,436 qubits.
Not like classical computer systems that function on a binary foundation of 0 or 1, quantum computer systems make the most of quantum bits that may tackle infinite states at temperatures of -273°C (-459.4°F), achieved through the use of liquid gasoline coolants. Thus, the quantum pc is ready to map out all attainable options to a cryptographic drawback and try them all of sudden, rising effectivity on an astronomic scale.
As advised by American cryptographer Bruce Schneier, Chinese language researchers seem to have combined “classical lattice discount factoring strategies with a quantum approximate optimization algorithm” that efficiently factored 48-bit numbers utilizing a 10-qubit quantum pc. “And whereas there are all the time potential issues when scaling one thing like this up by an element of fifty, there aren’t any apparent boundaries,” Schneier commented.
Safety professional Roger Grimes additionally added:
“Apparently what occurred is one other man who had beforehand introduced he was capable of break conventional uneven encryption utilizing classical computer systems…however reviewers discovered a flaw in his algorithm and that man needed to retract his paper. However this Chinese language crew realized that the step that killed the entire thing could possibly be solved by small quantum computer systems. In order that they examined and it labored.”
Schneier additionally warned that the algorithm depends on a recent factoring paper authored by Peter Schnorr, the place its algorithm works nicely with small bits however falls aside at bigger sizes, with no tangible clarification. “So if it is true that the Chinese language paper is dependent upon this Schnorr method that does not scale, the strategies on this Chinese language paper will not scale, both,” Schneier wrote.
“Basically, the good wager is on the brand new strategies not working. However sometime, that wager shall be flawed.”
Quantum computer systems are additionally restricted by operational elements akin to warmth loss and the requirement of a posh -273°C (-459.4°F) cooling infrastructure. Thus, the variety of nominal qubits required to inverse cryptographic algorithms is probably going far larger than theoretical estimates.
Though researchers haven’t but finished so, the methodology could possibly be theoretically replicable to different RSA-2048 protocols utilized in informational know-how, akin to HTTPS, e-mail, net searching, two-factor authentication, and so forth. Ethereum (ETH) co-founder Vitalik Buterin beforehand said his long-term objectives for embody making the blockchain quantum resistant. Theoretically, this includes forking the community to make the most of a higher-order encryption algorithm that might require larger qubits to interrupt.
Cointelegraph editor Jeffrey Albus contributed to this story.


Is Math Related to Science? You Bet! The word “Math” is applied in a large amount of places however it seems individuals prefer to confuse the two words.
So what will be the connections involving Math and Science? Effectively that may be a very good question.
The answers are far more than you could possibly ever envision. Irrespective of whether you like it or not, there’s Math related to Science. With that becoming said, let’s examine some details connected to Math and how it affects Science. The fact is that Math is important to Science.
Have you ever attempted to understand your math capabilities? best essay writers Did you come across yourself feeling frustrated? Had been you unable to even comprehend the formula that you just have been trying to figure out? If this describes you, it likely means which you have math skills which can be out of date. The top solution to go about understanding your math abilities should be to discover a teacher that could assist you function through a number of the problems that you are obtaining with Math.
Learning math can be difficult and Math connected challenges typically take patience. However, within the meantime you will discover a couple of things which you can do to have some practice. Start out by deciding upon a web-based class for Math. On-line classes are an excellent way to take some practice tests and to acquire some practice with distinctive mathematical difficulties.
Take Math related quizzes, these will test your simple Math capabilities. Also, remember that any difficulty which you need to resolve have to have a answer. This indicates that you’re going to possess to practice solving complications with multiple variables.
It may possibly take some time to master a number of the larger degree of math ideas, but immediately after a number of weeks, you’ll be able to recognize patterns and solutions which can be superior than those you had at the beginning. Plus, youwill have far more self-assurance inside your math expertise. Also, you might notice a difference in your grades and also you will begin to acquire an idea as to why they may be going up.
Is Math Related to Science? As you may know, math is very important to each Math and Science. This implies that Math is really a vital part of any course that may be created to teach an individual tips on how to make use of the sciences.
This is exactly where you’ll discover math courses in Meals Science. https://www.buyessay.net/ These courses help people today from around the globe understand to improve their food science skills. Men and women that are wanting to learn about meals security, nutrition, and making far better food choices will benefit from enrolling in a Food Science class.
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The best mathematicians of the Turkic world gathered in Astana
The 6th Congress of the Turkic world mathematical society was held in Astana.
More than 500 people, including about 100 prominent scientists from 20 countries, attended the event. The congress sections covered all major areas of mathematics. Within four days, scientists discussed topical issues such as algebra and mathematical logic, geometry and topology, theory of function, differential equations and mathematical physics, history and methodology of mathematics teaching of Turkic peoples.
Also a meeting of the Mathematical Society of the Turkic-speaking countries was held during the Congress. A new composition of the society was elected there. The participants unanimously elected Academician Bakhytzhan Zhumagulov as President of the Mathematical Council of Turkic-Speaking Countries for the next term and determined the venue of the next Congress. It was decided that the 7th Congress of the Turkic world mathematical society will be held in Uzbekistan. Following the results of the Congress, leading scientists and young mathematicians who made a significant contribution to the development of mathematical sciences were awarded diplomas.
It should be noted that Congresses of the Turkic world mathematical society are held once in three years. The first Congress was held in Turkey in 1999.
Welcome to the official portal of the International Turkic Academy!


Apache OpenOffice Math Bot
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The Department of Mathematics, Science and Computers (JMSK) is an academic support department that offers courses in Mathematics, Engineering Science and Computers at Sarawak Kuching Polytechnic. JMSK is responsible for handling the teaching and learning of several core courses such as:
Engineering Mathematics 1
Engineering Mathematics 2
Engineering Mathematics 3
The courses are offered to students of the Department of Civil Engineering, Department of Electrical Engineering, Department of Mechanical Engineering, Department of Petrochemical Engineering, Department of Information and Communication Technology and Department of Commerce.
JMSK accentuates on the importance of the quality of teaching and learning to achieve the quality objectives aimed at producing holistic, entrepreneurial and balanced students.


Quick tips on how to maximize your score in a standard 90 turn multiplayer game.
Scoring formula is (Territory + HappyCitizens*2 + ContentCitizens + Specialists) * Difficulty.
The total of all your per-turn scores is divided by the number of turns played so far to get your actual game score. I.e. your actual score is the average of your per-turn scores.
There are 3 kinds of water tiles: coastal, sea, and ocean. Coastal and sea do count twd territory.
You have a size 4 city without temple and granary, sitting in grassland. It will grow every 5 turns. Assuming you have two units policing the city and 0 lux, you will have 4 content citzens.
Your score first five turns are (9 territory tiles + 4 content citzens ) * 3 (regent difficulty) = 39 points. Once your city grows one pop., scoring will go to 42 points per turn.
Total average points in 10 turns: 40.5 points.
If two citzens were kept happy, average score would be 46.5.
If instead a temple is pop-rushed “eating” two citzens, the score would be as follows:
- First five turns are (9 territory tiles + 2 content citzens) * 3 = 33 points.
- After five turns, the population will grow and the border will expand on another 12 tiles. The score then will be (21 territory tiles + 3 content citzens) * 3 = 72.
Total average points in 10 turns: 55.5 points.
Pop-rushing temple for 2 citzens will payback after 6 turns (soon after the city border expands).
A size 6 city and no expanded borders with two happy citzens and two unhappy will generate (9 for territory, 4 for two happy citzens + 2 content + 0 happy)*3 = 45 points per turn.
If two citzens are turned into entertainer – assuming the city can still will keep its population – will generate (9 for territory, 8 for four happy citzens + 2 specialists)*3 = 57 points per turn.
In order to maximize your score – you should follow the following order:
- A. Maximize territory.
- B. Maximize the number of happy citzens, either by lux or by specialists (entertainers).
In practical terms:
- A. Build new cities, as further apart from possible as it can be. Keeping your capital locked at size 8 with zero grow may be great for production, but your score will be better if you get some more cities out of it. Also, planting cities very close will not maximize your score.
- B. Pop-rush temples – even if they cost more population.
- C. Read the game – if it seems like you additional scoring will be needed, start expanding ASAP. Planting a city (even if it stays size 1) on turn 60 will equal to 10 points at the end of the game. A city planted 15 turns after will be worth 5 only points at the end.
- D. Before lose all your gold by turning lux slider up, consider turn citzens into entertainers. This may add a couple of points at the end.


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100 Year Study: Girls Outperform Boys
Girls have gotten better grades than boys for 100 years, and yes, even in math and science.
To find this, researchers from Canada reviewed more than 300 studies on students from between 1914 and 2011. Researchers found that internationally, for a century, girls have outperformed boys in all of their classes.
Researchers say, "We didn't expect to find that girls did better at math and science as well. The girls did better whatever you give them." Researchers note, however, that the girls outpaced the boys in language and reading classes farther than they outpaced boys in math and science.
(Image: Time Magazine)
More info HERE


The procedure for determining the results of the tournament is described in the rules.However, in connection with a large number of questions about what a rating is and how it is calculated, I want to dwell on this point in more detail.
The main criterion for assessing the success of a team in a tournament is the number of points it has received. For each correct answer, the team receives 1 point. Thus, the number of points is the number of correct answers. Often there are situations where by the end of the tournament several teams get the same number of points. In this case, the places in the standings are distributed according to the rating.
A rating is an auxiliary parameter that takes into account the complexity of the questions. There are two types of rating: the rating of the question and the rating of the team. The question rating is equal to the number of teams that answered this question incorrectly. The team rating is equal to the sum of the ratings of the questions to which this team gave the right answers.
Let’s illustrate this with an example. Suppose that 5 teams take part in the tournament, and 10 questions were asked.
The “+” sign indicates the correct answer, the “-” sign is incorrect
As can be seen from the table above, teams N2 and N4 scored the same number of points. In this case, it is necessary to take into account the rating.
The first question was answered incorrectly by three teams (in column 1, three signs are “-“), because its rating is ramen 3. The second question was answered correctly by all the teams and its rating is 0. On the third – three incorrect answers, the rating is ramen 3. And so on.
After that, we determine the ratings of the teams. Team 1 answered correctly questions 1, 2, 4, 7, 8, 9, 10. Therefore, its rating is 3 + 0 + 1 + 2 + 2 + 1 + 4 = 13. The second team answered correctly questions 2, 3, 4, 5 and 8, and its rating is equal to 0 + 3 + 1 + 3 + 2 = 9, respectively. Similarly, for team 3, the rating is 0 + 3 + 2 + 1 = 6, for teams 4 and 5, the ratings are 3 + 0 + 1 + 2 + 1 = 7 and 0 + 1 + 3 + 4 + 2 + 1 = 11, respectively.
Thus, the places in our hypothetical tournament, taking into account the rating, were distributed as indicated in the “Place” column.
The “glasses-rating” system was developed more than 10 years ago, it has been successfully tested in many adult and children’s tournaments in many cities and is widely used at present. Its convenience lies in the fact that the complexity of the issue is determined, firstly, for the playing teams, and, secondly, automatically. This approach allows you to more adequately place the teams in the standings according to their game power.
Polozov A.A. Encyclopedia rating: economy, sport, society / AMKarminsky, A.A.Polozov, S.P. / M. Economics and Life. 455 s


November 11-12 2023
The datathon is a weekend-long competition where you are challenged to solve real-world challenges using techniques in machine learning, AI, and data science. We'll present three challenges, and you'll have to choose one. Typically, you'll be asked to find solutions to specific problems using some datasets. Apart from this, there will be non-mandatory workshops and activities to get relaxed and meet new people!
Our event will take place in UPC's School of Mathematics and Statistics, located in C/ Pau Gargallo 14, Barcelona. You can find a map here!
You will have access to classrooms to work with your own laptop. We will provide you Wi-Fi and food.
The event will start on Saturday November 11 at 9h when we will present the challenges.
You'll be able to work for 32 hours. The event will end on Sunday 12 at 17h, with a closing ceremony where we'll announce the winners.
All students are allowed to attend! Some data analysis or coding skills might be useful, but not required to participate. In fact, there will be a special prize for rookies!
We will provide you with meals, Wi-Fi and some nice swag. And of course, it's completely free!
Watch last edition's official video!


The motivation behind nearly all writing is to communicate. With the end goal to communicate well, you should consider both what you want to communicate, and to whom you plan to communicate it. This is no less valid for mathematical writing than for any other type of writing. The primary goal of mathematical writing is to assert, utilizing carefully developed logical conclusions, reality of a mathematical statement. Careful mathematical readers don't assume that your work is all around established; they should be persuaded. This is your first goal in mathematical writing.


The 4 Most Unanswered Questions about Tips
A calculator is an electrical device that is used to perform mathematical calculations. The old calculators were mechanical. These mechanical calculators are being replaced by the electronic calculators. The invention of the internet also led to the creation of the online calculators. An online calculator is a software that is used to perform all the tasks that can be performed by the most recent scientific calculators. The use of the online calculators is common among the businesspeople and students as well. The use of the calculators make the calculators quite easy. The utilization of the online calculators is increasing. A lot of factors have contributed to this. One of them is the benefits that are associated with the use of the online calculators.
One can enjoy several advantages following the use of online calculators. A few of the numerous benefits of the online calculators are as follows. The first and most obvious advantage is convenience. The calculation of the complicated calculations has been made convenient by the use of the online calculators. Today, there is the internet connectivity almost everywhere. To use the online calculator, you only need an internet connection. One can use the online calculator anytime. In whichever place you are, you can use the online calculator.
It also eases the use of the online calculator. The use of the online calculator is not as complicated as other people may think. The knowledge of the manual calculator is enough to enable anyone uses the online calculator to perform certain calculations. Additionally, the online calculators are characterized with the help button or a manual to assist its users. This manual play a very important role. The ease of using is an important advantage.
The ability of the online calculators to perform all they type of calculations is their other advantage. Similar with the normal calculators, these calculators can practically perform any type of calculation. One can use the online calculators to calculate house loans, property taxes, income tax benefits, insurance among others. The businesspeople, as well as the students, can use the online calculators conveniently. Additionally, there are usually no costs of using the online calculators. As stated above, you only need the internet connection and a device to connect to the internet to access the online calculators. This one of the fundamental advantages that are enjoyed by those people who use the online calculators.
Last but not least, the online calculators are characterized by a user-friendly interface. The online calculators have an interface that is not complicated. The other benefit of the interface is that it is user-friendly. The buttons of the online calculators are arranged the same way as those of the normal calculators. Viewing the buttons on a screen instead of touching them is a slight difference.


Whatever number of players you choose, each player will play the same number of matches. Most times, it is best to choose a number that you can evenly divide by 4. Then each player plays every round, and no one needs to pass. In addition, all players will play with all other players exactly 1 time, and against all other players exactly 2 times. The same applies with 1 more player (5, 9, 13 ...) but then all players will skip one turn. For all the other number of players, each player does not play with or against all other players. But the number of matches is the same for everyone.


The innate parallelism of quantum computers is very powerful for constrained optimization problems — problems where you can count the possible solutions, but the number of them grows extremely rapidly with the size of the problem.
Research efforts to build quantum computers are poised to help solve a number of massive data processing and analysis problems due to become an issue in the middle of the next decade as the Deep Underground Neutrino Experiment and the High-Luminosity LHC begin to operate.
Scientists are working on algorithms to simulate the interactions of fermions (particles of matter) and bosons (force-carrying particles) using qubits of quantum computers.
The Fermilab computing community is now pursuing a program to leverage quantum computing to solve problems in data analysis and theoretical calculations.
Theoretical scientists are developing mathematical models that simulate quantum computing systems — and then mapping quantum physics systems onto those models.


In this article, I’m going to give you a complete roadmap on how to become a Data Scientist with only free courses and resources.
So you’re probably thinking that you need a Masters or Phd from a top university to become a Data Scientist. In a way, it is true that having a master’s or a doctorate in this context from a very large university will open doors for us in the field of data science and machine learning.
But you really don’t need any degree to become a Data Scientist, let me explain how to do it.
How to become a Data Scientist
There are 5 steps to becoming a Data Scientist, they are:
- Learn Python.
- Learn math (linear algebra and statistics)
- Learn Data Science Libraries of Python.
- Learn SQL.
- Build a Project
1 – Learn Python
Python is a great language for data science, now there will be people who say, to learn R or Matlab instead of python. Don’t listen to them. Yet one day you may need to learn R and Matlab.
But for starters, Python is the best choice for me, because external library support for data science and machine learning is better and easier in python.
And luckily, in the following link, you will be still able to find all the materials.
This is a collection of free Python courses that should give you enough knowledge to start learning data science tools.
2 – Learn math (linear algebra and statistics)
Data science is the application of mathematics to data. If you don’t know math, you’ll struggle with data science. You can start learning math for data science using Numerical Python and Statistics .
This is a course provides an introduction to using Python to learn linear algebra. It is designed for people who have no (or little) previous exposure to Python or to linear algebra.
Also, with this free EDX course you can learn :
- Data collection, analysis and inference
- Data classification to identify key traits and customers
- Conditional Probability-How to judge the probability of an event, based on certain conditions
- How to use Bayesian modeling and inference for forecasting and studying public opinion
- Basics of Linear Regression
- Data Visualization: How to create use data to create compelling graphics
3 – Learn Python Libraries
The Python libraries are absolutely fantastic. If you don’t know what a library is, it’s basically something you can add to python, which gives python a lot more functionality.
There are great libraries for data science you should learn:
- Numpy (for linear algebra)
- Pandas (for statistics and data manipulation)
- Matplotlib (for data visualization)
- Learn all data science topics
After learning all these libraries, you can start working on your own projects. You can search the internet to download the datasets for your practice.
You can download the datasets from https://catalog.data.gov/dataset.
And, this is a collection of free Python Libraries courses that should give you enough knowledge to start.
Also, check these two free course from kaggle :
4 – Learn SQL
Data is everywhere. In fact, it is at the heart of newer disciplines such as Data Science and Data Analysis.
It’s essential learn how to manipulate relations using relational algebra operators, and apply these theoretical concepts to a widely used language: SQL , allowing you to interact with relational databases!
Here is a special collection of courses that teaches you enough SQL to start as a data scientist.
Also, I suggest these two free course from kaggle :
5 – What is next ?
Build a Project :
I feel the best thing after learning any course actually in the programming space is to build a project.
I find that I learn better through project-based learning. Learning to program can be stressful sometimes, but having a project to develop as you program could really help re-enforce what you have learned.
Register on Github :
Here you can share your projects with everyone in the world.
The idea is to create a good portfolio of your projects at Github, so people know what you do and how good you are at programming.
Try to upload at least one project each month to Github, so that when employers ask for your contribution to a project, you can impress them with your skills.
After taking the courses above and build some projects, you will be ready to apply for the jobs. You will find many opportunities where you will be a good fit.
Have Question ? ask here


The Developmental Math Lab: Help Starts Here!
Spring 2016 Hours:
- Monday: 9:00 a.m. - 4:00 p.m.
- Tuesday: 9:00 a.m. - 5:15 p.m.
- Wednesday: 9:00 a.m. - 4:00 p.m.
- Thursday: 9:00 a.m. - 5:15 p.m.
- Friday: 11:00 a.m. - 1:00 p.m.
The last day that the Developmental Math Lab is open for the Spring 2016 Semester is Friday, May 13th. Remember to check out the tutorials for final exam review materials in the Student Resources section of this website.
Good luck on finals!!!
What math classes does the lab support?
The Developmental Math Lab supports Math 090, Math 091, and Math 081.
Do I need an appointment to get help?
No, it is a walk-in lab, so no appointments are needed.
How do I earn extra credit?
Just come into the lab and get help, then ask a staff member to sign your extra credit sheet. Don't have a sheet? Just ask for one!
What if I need help and the Developmental Math Lab is closed?
Supplementary worksheets and accmpanying recorded explanation sessions, as well as exam reviews and accompanying video recordings are available on this website. Just click on the tab, "Student Resources" on the left hand side of this page.
Also, you can get help in the Math Lab upstairs (room 2813A) or in the Learning Skills Center when they are open.
For additional information, feel free to contact, firstname.lastname@example.org


This wooden numbers puzzle makes learning to count fun! Puzzles help your child develop problem solving and fine motor skills. These chunky wooden puzzle pieces are easy for little hands to grasp and the bright colors teach numbers in a multi-sensory way.
The name of each number and symbol is printed on the corresponding cutout space on the board so your little recognizes the words, too. Includes the symbols for plus, minus, multipication/times, division and equals so after you master the numbers, you can work on math, too.
Finished puzzle measures 11.75″W x 8.75″H x .85″D
Recommended for ages 3+


In accordance to ADEK Policy (44), GES has an open approach to admitting students from different customs and races. Special care is taken to correctly place students so as to have every opportunity to achieve at their fullest potential.
Admission to all levels / grades is entertained from February of the previous academic year. The number of available seats for each level is estimated based on available statistics. Expression of interest for admission is accepted in the prescribed format.
Students seeking admission to the school will sit a placement assessment to determine their performance level so that appropriate educational support may be provided. These placement assessments will be in the form of:
- Baseline assessments: English, Mathematics and Science
- Specialised Subject assessments for students entering IGCSE/AS/A Level
English is the language of instruction for all the core subjects of English, Mathematics and Science as well as the CIE subjects.


Maths in school used to be easy when we were young. What I used to like about it is that everything just had one solution (the only solution), everything clicked, and worked and was perfectly designed to work that way.
Then years passed and little by little maths started becoming more complicated. But still one solution. If you know the calculations, you would get to it. You just needed to know the way.
With this passing of time, we were also introduced to other type of maths: the maths of life. These are similar in a way. They get harder as we progress: we add, substract, divide and multiply people situations, experiences, happenings in our lives, whether good of bad. Sometimes these maths get so complicated that we have no clue of how we got to the final result. And on top of it, we don’t even know whether it is the right result.
But, I found that there is at least one calculation in the maths of life that is extremely simple, easy to remember and easy to understand.
We only need to know how to do one thing: sharing.
It does the trick, it always works. Have you noticed that when we share something good it gets multiplied? Good times increase their effect when shared.
Also, if we share a bad moment with someone, doesn’t it get better? The negative effect of it gets divided by two.
Did you do the math? Good times are improved when shared, the bad times are reduced when shared.
Try sharing, it works every time.


The Virgin Islands Department of Education, St. Thomas-St. John District, will hold its annual STEAM Week, Tuesday, May 16 to Friday, May 19, 8:30 a.m. daily, at the UVI Sports & Fitness Center on the University of the Virgin Islands St. Thomas Campus.
This year’s theme is “Pushing the Threshold” and will feature a wide selection of Science, Technology, Engineering, Art and Mathematics (STEAM) projects from public, private and parochial schools across the district. On STEAM Day, which is Friday, May 19, attendees will enjoy a host of interactive educational activities and displays created by students and local vendors. The event is free and open to the public
STEAM Week 2017 Schedule:
Technology (K-12th grades) — Tuesday, May 16
Science and Math (K-6th grades) — Wednesday, May 17
Science and Math (7th-12th grades) — Thursday, May 18
STEAM Day (4th-8th grades) — Friday, May 19


Let’s make a few concepts clear.
In a computer system, bit is the smallest unit of data storage in the computer, representing binary bit. A binary bit can represent 0 and 1 states.
At the same time, the computer stores and interprets information in bytes, and stipulates that a byte is composed of eight binary bits, that is, one byte is equal to eight bits (1byte = 8bit).
The video rate of a camera is the number of data bits transmitted per unit time. Generally, the unit we use is Kbps, that is, k bits per second, how many kilobits per second. For example, 3000kbps, that is, 3000kbits per second, that is, 375 bytes.
In hard disk storage, theoretically, 1TB = 1024gb, 1GB = 1024MB, 1MB = 1024KB.
But in fact, for convenience, manufacturers such as hard disk storage industry define 1TB = 1000GB, 1GB = 1000MB, 1MB = 1000KB. In addition, some space in the hard disk will be occupied by firmware program, so the actual size of 1TB hard disk is 931GB.
Well, with the above knowledge, let’s calculate the size of the surveillance video, that is, the size of the video file per unit time multiplied by the time. Unit time (s) file size (byte) = bitstream (BPS) ÷ 8. 24 hours a day video file size = (bitstream ÷8) × 60 × 60 × 24。
For example, for a 1080p, H.265 encoded network camera, the general reference code stream is 2000kbps, then the hard disk space required for this camera to record 24 hours a day is 2000 ÷ 8 × 60 × 60 × 24=21.6GB。 If the bitstream is 1000kbps, the video file size of one day is 10.8GB, the bitstream is 5000kbps, and the file size is 54gb. In order to facilitate the fast calculation, we can roughly remember that the bitstream value (kbps) × 100 is the amount of hard disk space (GB) occupied by the video 24 hours a day, which is convenient for memory and fast for calculation. Of course, if you need accurate data, you can calculate according to the above formula.
Furthermore, many security product service providers now provide their own online video hard disk storage space calculation tools. The calculation methods and principles are basically based on the above analysis. Some options include H.265/H.264 encoding, resolution and other options. In fact, through these options, we can determine the bit stream value of the built-in camera step by step. If we know the bit stream of the camera, we don’t have to be so troublesome.


This is my hypothesis, in a ‘perfect’ world where each team would remain unchanged over two seasons, for example, would the points earned in the first season give a reliable enough measurement of performance so as to aid the football bettor to predict outcomes in the second season. The objective being to make a profit.
One important factor is the current scoring system of 3 points a win, a point for a draw and (obviously) no points for a loss. What about a team who consistently draw, in a season they would earn 38 points. Another team who win half of their games and lose the other half would earn 57 points. So, does the points system accurately rate teams abilities?. If it does why do the teams above have such a difference in points?.
As an example, comparing two performance figures for an upcoming match inufabet ติดต่อ the second season may give figures such as 60 points for one team and 50 points for the other, these figures being supplied from the final league table results for the first season. It’s clear that these two figures alone would not be sufficient to make an accurate assessment of the resulting game.
The possibility I’ve tried so far is:-
Compute an average goals scored per match for each team individually, then computing a standard distribution of goals for that team. Then combine the two team’s distributions giving prices for all combinations of results. Comparing the computed results against bookies odds would highlight ‘generous’ offers.
Other factors such as home advantage needs considering therefore two distributions per team (for home and away) may need consideration.
Football is an unpredictable game too, some teams consistently do well against another team and so on. In each case the factor may require the prediction to be tweaked.


Mark B. Case, Ph.D.
|Title||Professor of Mathematics|
|Background||B.S., United States Coast Guard Academy|
M.S., Rensselaer Polytechnic Institute
Ph.D., University of Rhode Island
|Office||Aquinas Hall, Room 302|
Research Advisor for Senior Capstone Projects:
Small Boat Inventory Modeling, U.S. Coast Guard Atlantic Area Command, 2011.
Statistical Analysis of the Physical Fitness Examination at the United States Coast Guard Academy, U.S. Coast Guard Academy, 2010.
Assessing Waterway Risk, U.S. Coast Guard Atlantic Area Command, 2009.
An Economic Order Quantity (EOQ) Analysis for the Coast Guard Exchange System, U.S. Coast Guard Headquarters, Exchange System Branch, 2008.
HH-60 Helicopter T700 Engine Optimization, U.S. Coast Guard Aviation Repair and Supply Center, 2007.
Cocaine Seizure Analysis, U.S. Coast Guard Headquarters, Office of Law Enforcement, 2006.
Patrol Boat Readiness, U.S. Coast Guard Research & Development Center, 2005.
Third Level Quality Control Analysis of the Smith Hall Weather Station, U.S. Coast Guard Academy, Department of Mathematics and Department of Science, Marine Science Section, 2004.
U.S. Coast Guard HH-65 Transition Course Student Output, U.S. Coast Guard Aviation Training Center, Mobile, AL, 2003.
An Analysis of Skills Based Assignments and the Effects on the Enlisted Workforce, U.S. Coast Guard Headquarters, Office of Workforce Forecasting & Analysis, 2002.
Professor Emeritus, U.S. Coast Guard Academy, 2014
U.S. Coast Guard Meritorious Service Medal for service as Chair, Department of Mathematics, U.S. Coast Guard Academy, 2011.
U.S. Coast Guard Academy Alumni Association Distinguished Faculty Award, 2008.
U.S. Coast Guard Meritorious Service Medal for service as Associate Dean of Academics, U.S. Coast Guard Academy, 2002.
Institute for Operations Research and the Management Sciences (INFORMS)


The Archives of Roy Daysh
Roy Daysh - Former Joint Head Boy and Mathematics Master
Notable former pupil, joint Head Boy with John Cole and mathematics master, Roy Daysh, has died at the age of 85.
John was captain of cricket, Roy was captain of hockey. He joined the RAF in 1945, retiring in 1965 to train as a teacher, and he returned to teach maths at Prices, until his retirement in about 1990. He was a staunch Old Pricean, and held various positions including that of Treasurer. Hear Roy reciting Olly's Prayer "Support us O Lord...."
Roy's son, Michael, supplied this wonderful photograph of John Cole, John Suggate and Roy in 1945.
Michael Daysh has also added the following:


Area is the number of square units inside of a shape. We typically find the area of a shape that is two dimensional like a floor, or a piece of carpet, or a piece of land. Since the area is measuring the number of square units inside of the shape, the units must be written as squared units ex: Many of the area formulas require you to know the height of the shape.
The student does not recognize the trinomial as the product of two binomials. Examples of Student Work at this Level The student attempts a mathematically incorrect approach to finding the area. For example, the student: Questions Eliciting Thinking What type of figure is given?
Can you tell me the formula used to determine the area of this figure? What kind of expression is used to describe the area? What kind of expression is used to describe the length? How should these expressions be related? Instructional Implications Review the area formula for a rectangle using the symbols A for area, l for length, and w for width.
Tell the student to write this formula on his or her paper. Ask the student to identify the two parts of the area formula that are given and to write them underneath the corresponding parts of the formula. Discuss the operation that relates the length and the width in the area formula and how the length and the width can be considered factors of the area.
Since one binomial factor is given, he or she only need determine the missing binomial factor. Provide the student with more practice and experience multiplying and factoring polynomials. Guide the student to recognize factorable polynomials based on their structure.
Be sure the student understands that the factored and expanded forms of a given polynomial are equivalent, but one form might be more useful in a given problem setting. Also, be sure the student understands that not all polynomials are factorable. Examples of Student Work at this Level The student: Attempts to factor the trinomial but makes an error.
Questions Eliciting Thinking Is there a way other than division to determine the missing factor for a trinomial?
If you use a set of parentheses instead of w in your equation, could you figure out what goes in the parentheses?
Did you check your answer by multiplying the two factors? Did you get back to your original trinomial? Are your signs correct? Ask the student to check his or her factorization by finding the product of the factors and then comparing the result to the original trinomial.
Got It The student provides complete and correct responses to all components of the task. Instructional Implications Challenge the student to write an expression for the width of the rectangle if the given trinomial represented the perimeter of the rectangle.kcc1 Count to by ones and by tens.
kcc2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1). kcc3 Write numbers from 0 to Represent a number of objects with a written numeral (with 0 representing a count of no objects).
kcc4a When counting objects, say the number names in the standard order, pairing each object with one and only. By dividing both the sides by 2, the equation changes to 9 = l + w, or l + w = 9.
STEP 3: Think of the possible dimensions the rectangle can have if the sum of the length and width equals 9 ashio-midori.com, it is given that area of the rectangle has to be greater than 18 sq.
cm. Nov 26, · The area of the rectangle is 35cm squared if the bottom and top of the rectangle are x+2 and the left and right side equals x, what is 1)expression of rectangle in terms of x 2)quadratic equation of the situation 3)solve the quadratic equation to find x any help would be appreciated:)Status: Resolved.
Free Rectangle Area & Perimeter Calculator - calculate area & perimeter of a rectangle step by step System of Equations System of Inequalities Basic Operations Algebraic Properties Partial Fractions Polynomials Rational Expressions Sequences.
Matrices & Vectors. Matrices rectangle-calculator.
en. Follow @symbolab.
Related Symbolab . We can use the area of another rectangle to explain what happens when you multiply two binomials.
Example The area of the rectangle can be calculated by the use of the distributive property. Guide the student to interpret the expression 8x + 4 in terms of x, the width of the rectangle.
Provide a value of x, and have the student use the expression 8x + 4 to calculate the perimeter of the rectangle. Ask the student to describe what the expression indicates about using the width to calculate the perimeter.


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Learn what Linear Discriminant Analysis is, and how to apply Linear Discriminant Analysis in R.
The Wilcoxon signed-rank test is a non-parametric statistical test to compare two related samples. Learn how it works, and how to run it in R in this tutorial.
Probability is used to quantify the randomness of a model's behavior. In this article, we'll go over the basics of probability including probability functions, random variables, sample and event spaces, addition and multiplication laws, the binomial distribution, conditional probability, expected value and odds to probabilities.
Statistics is a mathematical science including methods of collecting, organizing and analyzing data in such a way that meaningful conclusions can be drawn from them. Learn the basics of inferential and descriptive statistics in our tutorial.


Paul James Football Select System
The vendor advises that he has made some really good profits by following this simple and effective method and now you can do the same.
"Ever wondered why the bookmaker always wins? Simple, because they have the mathematics stacked in their favour. You can buy systems based on statistics, check the team news, back a team because they look stronger than their opponents and many other contributing factors that help you decide to make a bet. You look at all these attributes, but you are missing one key ingredient â€“ the mathematics". This method explains the mathematics and shows you how to take advantage of this in order to make profitable bets.
Files included with this product
- Paul James Football Select
Paul James Football Select
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You will need Adobe Reader to view PDF's. Get it here >


Business measurements involve the use of mathematical strategies to make decisions in commercial organisations. They require analysis of business costs including raw materials, shrub & machines, rent, earnings, marketing, organization expenses, storage and curiosity.
There are a number of ways to decide the cost of your business, from simple back-of-the-napkin math to complicated Exceed formulas. A lot of methods depend on sales volume level, while others give attention to future income and cash flow multiples.
The first step to determining the value of your organization is to compute your seller’s discretionary return (SDE). This includes all pretax, noninterest cash as well as any kind of employee party, charitable contributions or one time buys.
Next, calculate your break-even point. This really is a key fiscal tool intended for small businesses and can be used to determine how many systems of item you need to promote to cover all of the production costs.
It also helps you determine how lengthy it will take your business to reach their break-even level and start turning www.businessrating.pro/business-calculation-methods-understanding-them-for-effective-management/ a profit. It also assists you predict how much you can charge for your services or products.
Lastly, work out how much you will spend to roll-out your business. Estimation business bills for the first 3 to half a year of operation.
Your startup company costs range from one-time things like equipment, furniture and fixtures, charges, permits and licenses, preliminary inventory and supplies. In addition , you should account for constant expenses such as payroll, insurance and fees. Generally, these kinds of should be computed monthly.