Did you know there is a quick hack using which you can calculate the time period in which your investment will be doubled, tripled and quadrupled? Do you want to know how fast can your money grow with different asset classes like PPF, Mutual funds, Bank FDs, etc.? Using hacks Rule of 72, Rule of 114 and Rule of 144, you can arrive at the answer. The Rule of 72 gives you an estimate of the number of years it will take to double your money in a particular investment, the rule of 114 gives you an estimate of the number of years to triple the investment amount, the rule of 144 gives you an estimate of the number of years to quadruple the investment amount.
How to calculate number of years to double using the Rule of 72?
You need to divide the number 72 by the rate of return of the asset to know the time it would take you to double your investments.
How to calculate number of years to triple using the Rule of 114?
You need to divide the number 114 by the rate of return of the asset to know the time it would take you to triple your investments.
How to calculate number of years to quadruple using the Rule of 144?
You need to divide the number 144 by the rate of return of the asset to know the time it would take you to quadruple your investments.
Let’s take an example for Bank fixed deposits (FDs)
Almost all banks provide Fixed Deposits ranging between 7 days to 10 years tenure. The interest rates vary from one bank to another depending upon the tenure. Bank FDs between 7 days to 10 years will give between 3% to 7%.
Suppose a person wants to invest ₹10 lakhs in Bank fixed deposit. So, assuming a bank FD offering an interest rate of 6.5% p.a., the formula is applied as below:
Rule of 72
= 11.08 years
Rule of 114
= 17.54 years
Rule of 144
= 22.15 years
So, an investment of ₹10 lakhs in a bank FD will get doubled (i.e.₹20 lakhs) in approx. eleven years, triple to ₹30 lakhs in approx. 18 years and quadruple to ₹40 lakhs in approx. 22 years.
Using the same formula, period for other asset classes to double, triple and quadruple is as follows:
**The expected rate of return is considered based on historical averages.
With this DIY formula, investors can very easily find out the time their investments would take to double, triple or quadruple their money.
Also, as we can observe that the time period required for tripling and quadrupling goes on reducing due to the effect of compounding, which is also known as the ‘Eighth Wonder of the World’. Hence, it is always advised to stay invested for a longer term and reap the benefits of this wonder.
We hope the information so presented was useful.
To know more on the topic as well as to start investments please feel free to contact:
Team Richvik – +91 9324609115
Contact us: firstname.lastname@example.org


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ExperienceAs a tutor, I structure my sessions towards working with my students to understand their problems with a particular subject. Then together, we work to overcome the missing link. I assist students in many subjects. Biology, Math, and test prep are my specialties. I have previous experience in tutoring, primarily during my time at Boston University, where I worked for a group that assisted underprivileged students in learning Algebra. I have also been employed as a marine biologist, where I have worked with a variety of different people and volunteer groups.I am available to teach students in a variety of subjects, including: Elementary Math, Middle School Math, Pre-Algebra, Algebra 1, Biology, Life Sciences, Ecology, Science for 3rd grade to 8th grade, Writing, and English. For Test Prep, I work with students in ACT Math, ACT Reading, ACT English, SAT Math, SAT Verbal, SAT Critical Reading, and the GRE.I graduated with high honors from Boston University. There, I earned a B.A. in biology, with concentrations in Ecology and Conservation Biology. I have also returned to school to pursue my master's in Ecology.When I'm not working, I love to hike, do yoga, read, cook, and improve my mind by taking online courses.
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Hello there 🙂 from this lesson we are going to discuss about various types of operators used in Java. You already know most of these operators because they are in your elementary school mathbook. Let’s see.
They are easy to understand! But DON’T skip this lesson as well! You have to have a very clear understanding about them.
Remember the binary operators you have learnt in school? Addition +, subtraction –, division /, multiplication x things 🙂
Binary operators always operate between two numbers only.
Eg: 3+2 so two numbers. What about 3+2+5 there also what we actually did was 3+2=5 first and then 5+5. Isn’t it??
Alright. So now we have the same operators in Java as well.
They are used to do operations between two numerical types such as byte, int, long, double….
Followings are the symbols used in Java;
|Addition||+||23+4.5, x+1, x+y|
|Subtraction||-||2-3, x-53, 34-y-x|
|Multiplication||*||2*y, x*2*y, x*x, 2*x+y|
|Division||/||3/2.0, 10/2, x/y|
The modulus operator of x%y gives the remainder when x is divided by y. So, 30%7 is 2 and 50%2 is 0.
There is one important thing you should remember. When two ints are divided like 7 / 2, then, unfortunately you won’t get 3.5 as the answer. You will get 3 just by omitting the decimal points.
This is because integers cannot have a decimal part. So,
if you want to have the correct answer, you have to make one of the two numbers in to decimal number. Just REMEMBER that!!
Eg: 7 / 2.0 or 7.0 / 2 or 7.0 / 2.0
These operators have a precedence rule. The ones with higher precedence will operate first.
*, / and % have the same precedence.
+ and – have the same precedence. But they have a lower precedence than the other three.
The ones with the same precedence will operate from left to right.
Eg: 3 + 20 / 5 * 3 – 8 % 3
The answer is 13.
What happens here? Let’s see the operators with higher precedence. / → * → %. Though + is occurred first, it won’t start first.
The one which operate first is /. So 20/5 = 4.
Then this 4 is multiplied by 3. 4*3 = 12.
Now the expression is something like this.
3 + 12 – 8 % 3
The next – operator is skipped and 8 % 3 is operated. 8 % 3 is 2. So now the expression is,
3 + 12 – 2
Finally, the + and – operators are going to work from left to right.
3 + 12 = 15 and 15 – 2 = 13.
The relational operators will compare two entities according to a condition and gives either true or false according to the condition. That is, the output is a boolean value.
For example, x >= y checks whether x is larger than or equal to y and gives either true or false using the values of x and y.
If x = 10 and y = 8 then, x >= y means 10 >= 8. It’s true. So the output is the boolean value true.
Other than this >= condition, there are many other types of conditions. OK. we’ll see.
Let’s take two variables x and y.
- x>y means x is larger than y
- x >= y means x equals or larger than y
- x<y means x is less than y
- x<=y means x is less than or equals y
- x!=y means x is not equal to y
- x==y means x equals y
** NOTE : See, instead of single = mark, we have used == that is, two equals. Really why this is done because the single = mark is for the assigning statement in variables.
Eg: int x = 10; → assigning 10 to x.
But x == 10 → used to check whether x equals 10. If it is not 10, false is given out. If x is 10, true is given out.
This will be more clear when we do the lesson, if statements.
There are three boolean operators, AND, OR and NOT.
So here is the explanation about them…
|| – OR operator
When there are two relational operator conditions, this operator is used to give the true output either one of them is correct.
(a>120 || a<0) means that “either a is larger than 120 OR less than zero………” Either one of the conditions is true, the output will be true.
&& – AND operator
This operator gives true only if BOTH conditions in the left and right of it are true.
(a>10 && b<20) means, “if a is larger than 10 AND b is less than 20…..” BOTH of those conditions have to be true to output true. If any condition is false, then the whole output is false.
! – NOT operator
NOT is used to change the true state in a condition to false or false into true.
If !(age<18) is given, the way of getting the result is as follows:
If age is less than 18, then true will be given out. The ! operator will inverse this output. So ultimately, if age is less than 18, false will be given out as the net result.
!(age<18) means that “age is NOT less than 18”. This gives the same meaning as “age is larger than 18”. That is, (age>18) Isn’t it?? 🙂
Updating a variable
Increment and decrement by 1
In the next tutorials, you will frequently find this;
if x is a variable,
x = x +1;
x = x-1;
These types of operation are usual in programming. So you have short methods to represent them.
x++; / ++x; is same as x = x+1;
x–; / –x; is same as x = x-1;
Combined assignment operators
These are somewhat similar to the previous operators. Here, the shortcuts for doing arithmetic operations and updating the variables are illustrated.
- x = x + 2; is equal to x += 2;
- x = x – 3; is equal to x -= 2;
- x = x / 50; is equal to x /= 50;
- x = x % y; is equal to x %= y;
- x = x && y; is equal to x &&= 2;
Type Cast Operators
If you want to change the type of some data in a variable, you can use the type cast operator.
Eg: Let x be a variable of type int.
Suppose x has to be a random integer between 1 and 10.
To generate a random decimal number between 0 and 1, there is a method called Math.random(); But it will just generate a number between 0 and 1. Not a whole number!
So in order to make it a number between 0 and 10, you can of course multiply it with 10.
10*Math.random() will now generate a number between 0 and 10.
But, again, note that, this may not be an integer. For example, if Math.random() generates 0.54, then, 10*Math.random() will form 5.4 which is not an integer.
So in order to eliminate this decimal part and make it an integer, use the type cast operator (int).
Now we can assign it to x.
x = (int) (10*Math.random()); will generate a number from 0 – 9. NOT including 10. If you want to include 10 as well, just do this,
x = (int) (10*Math.random()) + 1;
Remember, using the parenthesis before 10 is compulsory.
Because, the type-cast operator has a higher precedence than *. So, if we forgot the brackets, (int) 10 will execute first. That will be 10 itself.
Then 10*Math.random() is again, a decimal number. Wrong Wrong!
Ooh….End of a long lesson 🙂 In the next lesson, we are going to learn how to give basic input when running a program


TASM hosts events in the summer, fall, and spring consisting of a business meeting and presentations from the Texas Education Agency at all events, and professional learning opportunities in the fall and spring. TASM sponsors these events throughout the year with the goal of providing affordable, quality professional learning from thought leaders in the national arena supporting mathematics education and, more specifically, leaders in mathematics education.
How to Access Your Registration and Invoice
This year’s Spring Conference will be February 22-23, 2024..
Last day to register is February 12! Registration can be canceled up to 7 days before the event. At that time, final numbers must be submitted to the Hilton and no refund will be issued.
Affiliate Conferences & Events


04 Sep Mathematics Practice Specifications
The math curriculum within the school is a significant aspect for a student’s future education.
It has to be educated to the child in a young age so he will be able to learn to understand mathematical concepts and formulas. This can improve their capability to find mathematics later on.
Mathematics in school should involve a very good introduction to math by age . The significance of learning to address issues on newspaper and with objects is essential. A young child should be able to count to 10 until he/she could perform the addition or subtraction. He or she should also be in a position to distinguish among negative and positive amounts.
In elementary math class, the youngster should be able to recognize each semester in the term”inclusion”. When he/she does this, she should have the ability to subtract and add. As of this phase, the child needs to likewise be in a position to recognize the gap between a positive amount and a negative range. The child needs to be able to discover the formulation for addition, subtraction, and multiplication.
After the youngster reaches grade degree in basic mathematics, he/she should have formulated a overall comprehension of the concept. He/she ought to know that several is either a positive or negative range and that they are employed in different tactics in math class. The scholar should also know that addition, subtraction, and multiplication are used when you are multiplying or dividing a number. A student should also be able to recognize the conditions”quantity”amount mixture”.
At a sure point in basic mathematics, students ought to be in a position to apply that concept in his/her daily life. That is, they ought to be able to solve issues by themselves. Now, they should know what they need done and at which they’ve placed the bits. A student must find a way to address problems with a specific aim in mind, including having the grade they analytical essay sample desire to get a test.
Mathematics ought to be heard in the first possible time. It is not simply critical for students to acquire fantastic grades in mathematics, it is also critical for them to get a solid base for later studies in math. When mathematics is heard at the first possible moment, it’s much easier for a child to retain it within the class of time.
Learning math in school is a continuous course of action. Students needs to practice the stuff over and over repeatedly that he/she can apply it correctly in your own lives. Whilst the child becomes better , he/she will find a way to do harder troubles. And the notions will grow more concrete. So that the youngster can use these in true to living.
The youngster’s learning process additionally enables the baby to acquire the abilities and confidence he/she needs to succeed in life. Because the child progresses in math, he/she will build up the capacity to problem solve and also have the self confidence to solve complex troubles. This self confidence may permit a child to solve problems independently and without any outside assistance. Math is a critical part of a child’s living and has to be educated from the early years in these education.


This calculator calculates your monthly payment for an adjustable-rate mortgage (ARM) loan, given a loan amount and loan terms. Payments on an adjustable-rate mortgage are fixed for an initial period and are usually adjusted annually after the initial period. For example, a 3/1 ARM loan would have a fixed rate for the first three years and be readjusted once a year thereafter.
The interest rate on an adjustable-rate mortgage loan is usually reset on the loan's anniversary date. To calculate the new rate, a spread, or margin, is added to a widely used index rate.
Two widely used index rates are the yield on 1-year constant-maturity U.S. Treasury bills (CMT) and the 11th District Cost of Funds Index (COFI), published by the Federal Home Loan Bank of San Francisco.
Your monthly payment increases or decreases with a change in the loan interest rate. Because loan payments change periodically, adjustable-rate mortgages are not for every homeowner.
Adjustable-rate mortgage loans usually have a periodic and lifetime cap that limit how much the interest rate can change in one period and the maximum interest rate during the lifetime of the loan, respectively.


Marc Brendel, Wolfgang Marquardt:
An algorithm for multivariate function estimation based on hierarchically refined sparse grids
Computing and Visualization in Science, 2009, 12(4), 137-153
An adaptive function estimation approach is presented to recover an unknown, multivariate functional relation from noisy data. Using a sparse grid combination approach, both discretization and Tikhonov regulariza- tion need to be selected appropriately to resolve func- tional details whilst suppressing measurement noise. An initially coarse, multivariate grid is adaptively refined using sensitivity analysis, creating a sequence of hierar- chically refined grids. The problem of choosing a multi- dimensional discretization level is thus transformed to the identification of a suitable refinement step, giving rise to a nested approach for the selection of both dis- cretization and Tikhonov regularization. Validation on multivariate test functions shows good approximation results.
Multivariate regression, function estimation, sparse grids, discretization, regularization, L-curve, cross validation


Ipad App Review - Quick Math+
Thu 16 October, 2014
Quick Math+ is a simple to use maths app, which allows children to practise their mental arithmetic skills. It works by asking children simple questions, which they answer by drawing the number needed using their finger. The children work against the clock, which builds in a competitive element straight away, something that children seem to relish. It has a good level of differentiation, as each set of questions has four difficulty settings.
Available for: iOS
Producer: Shiny Things
Cost: (QTY 1-19) – £0.69 (QTY 20+) – £0.34 – Costs are correct for the Apple UK education VPP store at the date posted (they are currently on sale)
Version Reviewed: iOS
Activity ideas: Maths Starters, Maths Speed Challenges and Arithmetic league tables.
Example Usage: Here is a screen shot of the game used in the lesson below.
Lesson Plan: Here is a lesson plan for a ks1 Maths lesson, which introduces the symbols for greater than, less than and equal to.


KELLY'S READING and
Make Learning Fun!
Are you tired of watching your child struggle to learn how to read? Does it break your heart to hear your child say they hate math? It doesn’t have to be this way!
Learning is fun and your child will discover this at Kelly’s Reading and Math Club. We get results quickly and kids build skills and confidence without spending hours toiling away on worksheets and educational apps. Most importantly, we have fun! Every child is celebrated for their own unique learning style and abilities. Kids leave Kelly’s Reading and Math Clubs feeling good, confident, and excited about the next opportunity to learn. Join us in the learning fun!
Hi! I’m Kelly Michelle Dharamshi, M. Ed., OCT. I have taught in a variety of classrooms over my 20-year teaching career in the Toronto District School Board and York Region District School Board. I’ve worked with children in elementary schools in primary, junior, and special education classrooms. I have a Special Education Specialist and I love working with a diverse group of learners.
My approach to reading instruction is based on the science of reading and it is strength-based and student-centred. This means that student strengths, personal interests, and preferences are at the centre of each lesson.
My approach to math instruction comes from my own experience as a child with extreme math anxiety. The connection between math and social-emotional learning is the foundation of every Math Club. Like, reading instruction, math instruction is built around student interests and preferences.
Teaching is individualized and celebrates the learning styles of each student. Learning is NOT one-size-fits-all and I am so grateful that I have the opportunity to celebrate individual learners through The Reading and Math Clubs.
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A Beginner's Guide To Discrete Mathematics Download ->->->-> DOWNLOAD (Mirror #1)
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Maths Worksheets Level 3
Price: £14.99 (Excluding VAT at 20%)
Age Group: General
Order Number: 13025
A collection of worksheets graded according to ability. It comes in two photocopiable books covering skills and knowledge, one at level 2 and the other at level 3. The worksheets are in an attracive illustrated style that will appeal to Junior pupils. Both books contain 40 worksheets which cover work on numbers, calculations, data and space.


Cognitively Guided Instruction (CGI) is a professional development program based on an integrated program of research focused on (a) the development of students’ mathematical thinking; (b) instruction that influences that development; (c) teachers’ knowledge and beliefs that influence their instructional practices; and (d) the way that teachers’ knowledge, beliefs, and practices are influenced by their understanding of students’ mathematical thinking. Using CGI strategies is an effective way of implementing the Iowa Core Curriculum for Mathematics at the elementary level.
Studies have consistently demonstrated that Cognitively Guided Instruction (CGI) students show significant gains in problem solving. These gains reflect the emphasis on problem solving in CGI classes. Learning to understand the development of children’s mathematical thinking can lead to fundamental changes in teachers’ beliefs and practices. These changes were reflected in students’ learning.
The goals of CGI are:
- Analyze story problems and number sentences to determine their mathematical demands and recognize student responses in terms of cognitive development.
- Assess students’ thinking and design problems that will develop students’ understanding of concepts and skills.
- Facilitate discussions that provide a window into children’s thinking, strengthen children’s ability to reason about arithmetic, and build their capacity for algebraic reasoning.
- Use open and true/false number sentences to develop students’ understanding of mathematical concepts and skills.
In CGI professional development, elementary school teachers learn a framework for how children learn the concepts of number and operations and algebra. Teachers work to integrate this framework with their mathematical instruction. CGI is not a curriculum. The knowledge teacher gain in a CGI workshop enhances how they implement any curriculum. CGI teachers understand how their students think about mathematics and how children in general understand mathematics. CGI teachers know how to use what their children currently understand to plan instructional activities for these students. CGI teachers also understand what children need to learn about mathematics in elementary school so they will have a firm foundation upon which they can learn more advanced mathematics.
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Dec 23, 2019 – Mathematical Drawing Software – Draw mathematical illustration diagrams … Mathematical Drawing Software, Free Examples and Templates Download … the creation of mathematical geometry illustration, optics drawings, …
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Abacus Geometry Draw The program is used in conjunction with Microsoft Word to produce documents containing geometrical diagrams, Size: 1.1 MB
Mar 27, 2012 – Geometry Master free download. … Geometry Master 3.0 is a Geometry Help software that enhances Geometrical, Spatial and Drawing skills …
Jul 7, 2009 – The interface includes drawings of each scenario and the formulas involved in the calculation.
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Sum of angles identities
6th September 2020
Recently whilst revisiting trigonometry I came across a neat way of proving the sum of angles identities shown below:
I have used these formulas a number of times in the past to solve problems but I had not thought much about how they came to be. It was not until I learnt the proof I will describe on this post that I finally acquired a solid intuition about what these equations mean.
We will only need two of the right-angled triangle definitions for this proof to work: sine and cosine of an angle.
From the image we can derive the two definitions:
- or written in terms of the opposite side:
- or written in terms of the adjacent side:
Draw a rectangle with a right triangle inside as shown in the image.
Assume the hypotenuse of the triangle is of length 1. We name the angle on the bottom left as and work out the lengths of the opposites and adjacent sides of the triangle using the definitions.
We now shift our attention to the triangle that emerged at the top left of the rectangle. We name the angle on the bottom left as and use the definitions to find the length of the opposite and adjacent sides of the triangle, having a hypotenuse of length .
To find the length of the sides of the triangle in the top right, we need to use the angles we currently know and the properties of right triangles. If we focus our attention on the corner of the red triangle touching the top of the rectangle, we can see that we have 3 angles that add up to 180°.
We can find the angle on the left by computing . Then we have a angle from the red triangle. And finally, as all these angles add up to 180° we can find the angle on the right by computing .
With and the hypotenuse of the right-angled triangle on the top right, we can calculate the length of the opposite and adjacent sides using the definitions of sine and cosine with the angle and having a hypotenuse of length
There are only two steps remaining to reach the goal of obtaining the lengths of all sides of the rectangle. Moreover, The right-angled triangle at the bottom will give use the remaining lengths.
Given that the bottom left corner of the triangle forms an angle of 90°, we can define the angle corresponding to the corner of the bottom triangle as .
Having the right angle and the angle described above, the remaining angle of the bottom triangle is equal to .
Now we can find the remaining lengths of the sides of the rectangle by calculating the opposite and adjacent sides of the bottom triangle using the definitions of sine and cosine with the angle .
Having found the total lengths of all four sides of the rectangle, we can use the fact that parallel sides have the same length to draw the following equivalences.
Equating the top and bottom sides:
Equating the left and right sides:
The equations above can be rewritten to reveal the sum of angles identities as shown earlier:
Trigonometry is a fundamental topic on mathematics as well as a prerequisite to subjects like calculus, physics or linear algebra. Having a good understanding of the trigonometric identities allows us to identify when these relations can be used in scenarios where angles are involved, such as when working with vectors in space. Luckily it is relatively easy to visualise trigonometric relations as we can draw triangles and other basic geometric shapes which allows to obtain intuition by using visual proofs.
- I highly recommend watching this excellent video from the YouTube account blackpenredpen where the instructor goes through this proof step by step on a whiteboard.
- Additionally the Wikipedia article about trigonometric identities is a good place to learn in more detail about the sum of angles and other identities.


Hypotrochoid Art Set
Turn math into art. Classic Hypotrochoid Art Set traces out hypotrochoid and epitrochoid curves turning math into beautiful art.
Hypotrochoid Art Set - At a glance
- Traces out hypotrochoid and epitrochoid curves turning math into beautiful art.
- Simple to use, yet creating unique and original drawings.
- A creative and appreciated toy for children of all ages.
More about the product
Turn math into art. This Classic Hypotrochoid Art Set traces out hypotrochoid and epitrochoid curves creating art from something that is originally advanced math. If you are interested in the details then: "A hypotrochoid is a roulette traced by a point attached to a circle of radius r rolling around the inside of a fixed circle of radius R, where the point is a distance d from the center of the interior circle."
Why we like it
Are you still with us? We thought we lost you in the definition of the hypotrochoid above. Well done, if you made it this far we are happy to provide you with our personal opinion on this original art set. In Givensa we try hard to find useful products that serves a purpose and we want to offer something a bit different compared to what you find in your everyday toy store. We also let our own kids try out all the products to get real feedback on how they like them.
In a world filled with iPads and a dozen TV channels with cartoons there is a lot of competition for the attention of the children but in our experience these kind of creative toys are what keeps their interest the longest. We know this is one of those toys that will not easily be thrown away and therefore we have chosen it for our selection of original toys here at Givensa.
It is also good to know that...
- Set contains 2 hypotrochoid templates, each with 3 gears plus red green and blue pens
- A funny, creative and beautiful way to combine math and art.


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Round to the nearest tenth. 2. SALT Lecretia uses a small funnel as shown below to fill her salt shaker. Find the volume of the funnel. Round to the nearest tenth. 1 2 in. 0.5 in. 4. PAPERWEIGHT Marta bought a paperweight in the shape of a cone. The radius was 10 centimeters and the height 9 centimeters. Find the volume. Round to the nearest ...
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31 cm, m, 4. Find the length of the indicated side. to 2. Find the measure of the indicated angle, to the nearest tenth of a deglvc. N the nearest tenth 16 mm 15.6 cm 102.3' a 31.6 47.6 108.50 3. Solve each triangle Round ansu.ers to the tenth, if LPQR, ZR r = 6.3 cm. C) In Al-MN. LM 5.6m. 10.4 cm, m, 5. the Of the to the nearest tenth of a ...
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Find the volume of each pyramid or cone. Round to the DATE Student Edition Pages 649—653 nearest tenth. 11m 15 in 17 in. 17 in. 2.4 m 9.9 in. 14 in. 15 cm 14 cm 9 cm 7. r ctangular pyramid: length, 8 cm; width, 7 cm; height, 9 cm 8. s uare pyramid: length, 25 mm; height, 30 mm 9. circular cone: radius, 12 yd; height, 18 yd
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Find the diameter of a circle if the circumference is 8 cm. Round to the nearest tenth. 9.2 in. 706.5 cm2 2 Find the diameter of a circle if the circumference is 24.5 m. Round to the nearest tenth. 8.3 m The largest living thing on earth is a California sequoia tree named the "General Sherman." The circumference of its trunk is about 82 ft.
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1Traveltime, Riptide, Abide, Comfortable Shoes, Most Comfortable Shoes, Shoes, Shoes for women, Shoes in wide widths Round your answer to the nearest tenth. a. none of these b. 42.4 in. 2c. 17.3 in. d. 21.2 in.2 ____ 15. A sign is in the shape of a rhombus with a 60° angle and sides of 9 cm long. Find its area to the nearest tenth. a. 70.1 cm 2b. 3.9 cm c. 7.8 cm2 d. 35.1 cm Cherry punch strain wikileafSo, using metric rulers, we can measure lengths to the nearest centimeters and nearest millimeters. Meanwhile in foot/inch rulers we can measures to This means that the measurement is accurate up to a centimeter. Usually objects like pens, bottles, tennis rackets, rulers and so on have lengths that...Round to decimal places Wave length λ: * 10^9 m, Gigameters 10^6 m, Megameters 10^3 m, Kilometers m, Meters 10^-3 m, Millimeters 10^-6 m, Micrometers 10^-9 m, Nanometers 10^-12 m, Pikometers 10^-15 m, Femtometers Send mail with attachment in php code


Here is what is covered in this section :
What is it?
The independent t-test is also called the two sample t-test, student’s t-test, or unpaired t-test. It’s an univariate test that tests for a significant difference between the mean of two unrelated groups.
The hypothesis being tested is:
- Null hypothesis (H0): u1 = u2, which translates to the mean of sample 1 is equal to the mean of sample 2
- Alternative hypothesis (HA): u1 ≠ u2, which translates to the mean of sample 1 is not equal to the mean of sample 2
If the p-value is less than what is tested at, most commonly 0.05, one can reject the null hypothesis.
Independent t-test Assumptions
Like every test, this inferential statistic test has assumptions. The assumptions that the data must meet in order for the test results to be valid are:
- The independent variable (IV) is categorical with at least two levels (groups)
- The dependent variable (DV) is continuous which is measured on an interval or ratio scale
- The distribution of the two groups should follow the normal distribution
- The variances between the two groups are equal
- This can be tested using statistical tests including Levene’s test, F-test, and Bartlett’s test.
If any of these assumptions are violated then another test should be used.
Data used in this example
The data used in this example is from Kaggle.com and was posted by the user Web IR. The link to the data set is here. The data set contains the sepal and petal length and width of various floral species. We will be testing to see if there is a significant difference in the sepal width between the species Iris-setosa and Iris-versicolor which are variables “sepal_width” and “species” respectively.
Let’s import pandas as pd, the data, and then take a look at what we will be working with!
To make the code in the next steps a bit cleaner to read, I will create 2 data frames that are subsets of the original data where each data frame only contains data for a respective flower species.
Independent t-test Example
One needs to import scipy.stats for the following steps! The library matplotlib.pyplot is being imported the graphs can be exported.
Before the t-test can be conducted, one needs to test the assumptions. First to test for the homogeneity of variances. To do this, I will use Levene’s test for homogeneity of variance. The method to conduct this test is stats.levene().
The test is not significant meaning there is homogeneity of variances and we can proceed. If the test were to be significant, a viable alternative would be to conduct a Welch’s t-test. Next to test the assumption of normality. This can be done visually with a histogram and/or as a q-q plot, and by using the Shapiro-Wilk test which is the stats.shaprio() method. First, I will check them visually.
From the looks of the histogram, each variable appears to be fairly normally distributed. Let’s see how it looks on a q-q plot, it’s easier to get a sense of normality visualizing the data as q-q plot. If you are unfamiliar with reading a q-q plot, the data should be on the red line. If there are data points that are far off of it, it’s an indication that there are some deviations from normality.
There is some deviation from normality in the Setosa q-q plot, but it does not appear to be a large violation. In all, the data looks to have normality. To be sure, we can test it statistically using the Shapiro-Wilk test for normality which is the stats.shaprio() method. Unfortunately the output is not labeled. The first value is the W test statistic and the second value is the p-value.
Neither of the tests for normality we significant meaning neither of the variables violates the assumption of normality. We can continue as planned. To conduct the Independent t-test, one needs to use the stats.ttest_ind() method.
The Independent t-test results are significant! Therefore, one can reject the null hypothesis in support of the alternative.
Another component one needs to report the findings is the degrees of freedom (df). This can be calculated by adding the two group Ns and subtracting 2. In our case, df = (50 + 50) – 2 = 98.
Interpretation of Results
The purpose of the current study was to test if there is a significant difference in the sepal width between the floral species Iris-setosa and Iris-versicolor. Iris-setosa’s average sepal width (M= 3.418, SD= 0.381) is wider and has greater variation than Iris-versicolor (M= 2.770, SD= 0.314). Levene’s test for homogeneity of variances indicated equality of variance (F= 0.664, p=0.417); therefore an Independent t-test was used. Results indicate that there is a significant difference in the sepal width between Iris-setosa and Iris-versicolor (t(98)=9.282, p=4.362).


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- Take the quiz on canvas about the Sage workshop (this helps me assess where the class is and also improve the worksheet for next time).
- Read Chapter 5, from beginning to page 136 inclusive. Keep reading if you have time (if so, this will preview our next material).
- Contemplate the question when can you solve a linear congruential equation (i.e. solve ax = b mod N)? Try to rephrase this problem into one just about integers.
- Note, on the Resources page I now list tutors in MARC (and hours) where they know and are willing to teach number theory. Near the bottom.
- IMPORTANT: Thursday’s office hours are 10:30-11:30 instead of 2-3 pm.


Recording the derivation of BackPropagation & Levenberg–Marquardt & Bayesian Regularization Algorithm, to have a deeper understanding of the Neural Networks.
In fact, there are two types of differential methods in neural networks computing: forward-mode differentiation and backward-mode differentiation(Automatic Differentiation).
Consider the computational graph below, we need to compute the gradient of the output with respect to the input, namely , where can be multi-dimensional vectors.
- For forward-mode differentiation:
Each step of the iteration starts from the input cacluate upward, for example we consider the step of , thus we need to calculate derivative by chain rule:


Hi , What a busy week this has been. I hope you're doing well and taking care of yourself. I have been up to something really awesome which I want to tell you about.
Hi , This is the first issue of my weekly newsletter. Are you as excited as I am? I know you are. ProgrammingThis week's programming topic is - Pointers in C. Have you been
An 18 year old brilliant kid, who solved a 350 year old Mathematical problem gracefully and doing so, introduced an entirely new branch of Mathematics that redefined algebra, and changed how we look at nature - how do you think Life treated him


Top maths team represent NE
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The performance of young mathematicians from Gateshead scored them a place representing the region in a new competition open to elite teams from across the UK.
The year ten team from Emmanuel College, comprising Cameron Barker, Frederick Potts, Sophie Farrell and Callie Ferguson, earned a place in the inaugural national finals of the UK Further Maths Support Programme Championship after taking part in a regional heat held at Northumbria University.
In the regional competition, the students were faced with hours of maths challenges including puzzles, a Countdown-themed round, mind-bending algebra, Sudoku and questions on latitude and longitude.
Emmanuel's A team came out on top at the end of the gruelling day, narrowly beating another team from the college of James Knox, Robin Larkin, Ben Heath and Adele Woolsey, who came second.
The A team then went on to compete in the national finals held at York University.
Frederick explained: "After a two and a half hour journey south, the A team was catapulted straight into more manic maths, with extra rounds testing our logic and problem solving skills."
James added: "Despite one member of the team falling ill for a short period, they recovered and remained strong throughout the competition."
The final result put the Emmanuel team in sixth place out of teams from all Britain.
Continuing the college's strong performance in the subject, Olivia Coltman earned a senior challenge certificate and Ishank Arora was in the top 13 of junior entrants in the Newcastle University national maths challenge awards, which attracted 1,200 entries from across England.


These examination papers were kindly sent to me by Pam Cruise and were taken by her Uncle Alfred Edward Audas. The certificates gained by Alfred are shown in another biography on this web site. After graduating he worked as a draughtsman at ICI in Warrington (NW England). I am very grateful to Pam for her generosity.
An uncle to be proud of.
Below are examples of ULCI examination papers taken by Alfred for 1939, and 1940 for English, Practical Drawing, Practical Mathematics and Science. It is interesting and fascinating to note the content, the standard, the wording and the practical bias of the papers.
(A recent report in England showed the dramatic decline in standards in mathematics over the past decades e.g. a grade B currently awarded for GCE ‘A’ level in Mathematics would have gained an E grade 50 years ago.)
Left click to see the image more clearly.
Union of Lancashire and Cheshire Institutes: Preparatory Senior Technical Course 1st Year in 1939 for English, Practical Drawing and Science:
Union of Lancashire and Cheshire Institutes: Preparatory Senior Technical Course 2nd Year in 1940 for Science, Practical Drawing and Practical Mathematics:
Remember to left click to view papers clearly.


It aims to offer the most flexible framework for solving potentially coupled systems of linear and nonlinear partial differential equations with the finite element method. It works in arbitrary dimension and allow to couple 1D, 2D and 3D problems.
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This allows a wide range of experiments. Many examples and demos are provided. It is therefore often necessary to import meshes. An open-source finite element library. A symbolic derivation that allows to automatically obtain the tangent system for nonlinear problems. A compilation of assembly terms into optimized basic instructions.
A model description that gather the variables, data and terms of a problem and some predefined bricks representing classical models : elasticity in small and large deformations, Helmholtz problem, scalar elliptic problem, Dirichlet, contact and Neumann boundary conditions, incompressibility constraint, A complete separation between geometric transformation, finite element method, integration methods and partial differential term description, which allows to easily switch from a method to another.
MATLAB Guide to Finite Elements : P.I. Kattan :
Additionally, short answers to all problems are provided at the end of the book. On balance, this book written in interactive manner can be very useful to students and engineers dealing with applications of finite element method in structural mechanics. The book's style is straightforward and easy to comprehend.
Summing Up: Recommended. Lower- and upper-division undergraduates; professionals. Problems from linear elastic structure mechanics are used throughout the book.
The book is very useful to both students and researchers in engineering. The book is well written and very easy to read by students The author succeeded in providing a valuable tool to help engineering students learn the main steps of finite element analysis using MATLAB. You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.
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- MATLAB Guide to Finite Elements: An Interactive Approach.
Please create a new list with a new name; move some items to a new or existing list; or delete some items. Your request to send this item has been completed. In this edition, I amproviding two email addresses for my readers to contact me pkattan tedata. The old email address that appeared in the first edition wascancelled in Problems will be solved mainly using MATLAB to carry out the tediousand lengthy matrix calculations in addition to some manual manipulations especiallywhen applying the boundary conditions.
In particular the steps of the finite elementmethod are emphasized in this book. Problems from linear elastic structuralmechanics are used throughout the book. The emphasis is not on mass computationor programming, but rather on learning the finite element method computations andunderstanding of the underlying concepts. Each chapterdeals with only one type of element.
Also each chapter starts with a summary of thebasic equations for the element followed by a number of examples demonstratingthe use of the element using the provided MATLAB functions. They should work with other later versions. Each chapteralso ends with a number of problems to be used as practice for students. It is intended as a supplementary text to be used with a main textbook foran introductory course on the finite element method. Since the computations of finiteelements usually involve matrices and matrix manipulations, it is only natural thatstudents use a matrix-based software package like MATLAB to do the calculations.
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The book is divided into fifteen chapters that are well defined ad correlated. It is usedmainly for problems in structural mechanics. A sequence of six steps is outlined in the first chapter for the finite element method. These six steps are then used systematically in each chapter throughout the book. No ready-made subroutines are provided tobe used as black boxes. Answers to the all problems are provided at the end of the book.
It is over pages in length. ThomasDitzinger for their cooperation and assistance during the writing of this book.
Related MATLAB Guide to Finite Elements: An Interactive Approach
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Who Else Wants To Boost Student Interest and Performance In Science, Math, and Engineering?
This competition from the National Science Teachers Association is geared toward sparking an interest in STEM fields among K-12 students. It challenges students to envision and communicate new technology 10+ years in the future through collaborative brainstorming and research of current science and technology.
Initiatives like ExploraVision promote real-world problem solving, design thinking and the collaborative learning of STEM concepts across subject areas. Learn more about how ExploraVision inspires the next generation of scientists, engineers and communicators.


As we continued to become acquainted with each other and our new routines at school we took the opportunity to focus on shapes. We had various play centers (as always housekeeping, blocks, cars & library) plus a few centers dedicated to shapes. I kept the paper in the sensory box (see my post about color) and posted a new shape to search for each day. This was only a hit when I pulled the box into a circle time activity and had everyone find four rectangles - then we couldn't get enough!
A shape sorting center helped connect our color and sorting skills. I found printable shapes at mathsisfun.com, cut them out, and put them on the table with our color mats. I will definitely reuse these shapes throughout the year for various activities.
Our main project for the week was to make a shape book. I created a simple cover on publisher.
Each day we made a new page for our book.
Page 1: Square Rubbing, sandpaper squares and crayons (use tape to prevent the paper from slipping!).
We had mixed results with this activity, my younger 3's didn't quite get the concept.
Page 2: Circle painting, tp rolls and paint
Page 3: Rectangle collage (we did the rectangle search in the sensory box prior to this activity and reviewed how to use glue sticks)
Page 4: Triangle paint, triangle cut sponges & paint
(I use lids from some of my storage containers for paint and a place mat on the table to catch paint - they work great!)
To bind the book I simply punched a hole in the top corner and tied with some cute ribbon - simple and quick.
At the end of the week I pulled out the tp tubes and the triangle sponges and had the students paint again exploring colors and shapes.


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Abacus Tutors and Abacus Tutors of Wokingham has been providing a quality service since 1982 when Jonathan Cledwyn-Davies provided tuition in Physics, Pure Mathematics & Applied Mathematics ( Mechanics ) to GCE Advanced level and Chemistry or General Science to GCE Ordinary level.
By engaging tutors, Abacus Tutors increased the number of subjects available. Having originated in Middlesex, Hertfordshire and Buckinghamshire, Jonathan & Susan Cledwyn-Davies moved to Wokingham to establish Abacus Tutors of Wokingham.
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Jonathan obtained his B.Sc. ( Special Honours ) in Physics from King’s College, University of London and his P.G.C.E. and M.A. in Science Education from the University of London Institute of Education. Jonathan’s Dissertation was titled, “Is there a technology of Artificial Intelligence and if so, how might it affect the teaching of Science ?
Jonathan enjoys Physics and Mathematics and is a Member of the Institute of Physics, a Chartered Physicist and holds an Advanced Certificate in Educational Management from the University of Leicester.


Thousands of London schoolchildren will take time out from their lessons this week 10th-14th June to take part in a series of fun activities designed to dispel maths anxiety.
Around 500 primary and secondary school pupils across key stage 1-3 are involved in Maths Week London, supported by children’s learning platform Sumdog and the Mayor’s Fund for London, and designed to spark curiosity in the subject.
On top of a city-wide online maths competition, activities will focus on day-to-day maths use such as running market stalls, interacting with a “mathmagician” show and challenging parents and teachers in times table quizzes.
The week has been organised in a bid to change perceptions about the subject. A half of all UK adults have been found to have numeracy levels no higher than an 11-year-old, according to charity National Numeracy, and last summer government figures showed one in four pupils did not achieve the lowest pass – a grade 4 – in GCSE maths.
Maths Week London launches against a background of acute shortages in maths teachers across the city. According to the Education Policy Institute, only 80% of placement targets for maths teachers were filled in 2018 and in London only 56% of maths teaching hours were taught by a maths specialist.
Two celebrated TV mathematicians have endorsed London Maths Week and its aims. Veteran children’s TV presenter Johnny Ball, loved by millions of youngsters in the 70s and 80s for shows like Think of a Number and Think Again, said: “We need to inspire children with maths and teach them to apply it to the world around them. Maths teachers are tied by what the national curriculum tells them to teach and can’t use their expertise and love of the subject to show how maths can be fun and engaging. Thanks to government policy, primary age children spend hours on times tables and straight numeracy which are never going to make maths interesting. Small children need more dedicated time to enjoy using numbers. If teachers had more freedom, they could teach what the government wants and then leave time for more creative and engaging activities to spark children’s interest. But the curriculum and continual tests mean that doesn’t happen, even though teachers are keen and children are capable of so much more.
TV presenter and maths teacher Bobby Seagull added: “After people leave school, many adults find that their numeracy skills decline and we are in a situation nationally where nearly half of all adults have the numeracy skills we would expect from an 11 year old. The National Numeracy charity have shown that questions like working out what a 5% increase on a £9 hourly rate would stump 50% of adults. This is a tragic situation but events like Maths Week London can help engage parents, students and adults. Maths is everywhere and a positive mindset towards it can help to change attitudes and outcomes. Particularly in our capital city, adults need competent numerical skills to help them navigate the complexities of life. Maths Week London is hopefully the first step in the right direction for our capital’s approach to numbers.”


To show that I come by my ability to visualize and adapt knitting patterns naturally, I am showing off my mother’s grey improvised sweater.
I gave my mom this wonderful grey linen blend which contains flecks of white since my mother always has room for one more grey item in her wardrobe. One of my uptown knitting buddies had given it to me when she was destashing. It seems that my knitting friends all know that I can envision how to turn some longer cherished stash into something wonderful.
Since there was sufficient yarn for a sweater, my mother decided to adapt a simplified pattern that she had used before. At its core, the pattern consists of two rectangles which are sewn together at the shoulders forming a boat neck. Then stitches are picked up for sleeves which are knit down. This has the great advantage of allowing the knitter to measure the length as she goes which is good because the sweater has a dropped shoulder.
Before she started, my mom knit a swatch and we measured it. The swatch allowed my mom to try out a couple of variations of stitches. Then I took her measurements and applied some easy math to get the basic cast on. And she was off and knitting.
You’ll note that my mom used a variety of ribbed stitches to make the sweater more fitted.
If you’re interested in trying it, follow these easy steps:
1] Knit a swatch of at least 20 stitches using the appropriate needle for the yarn and your gauge.
2] Take your measurements. Add 2 inches to your widest measurement and divide that number by 2.
3] Multiply the number of stitches per inch by half of your measurement to get your cast on number of stitches.
4] Knit 2 rectangles to the length that you want your sweater to be. My mom knit about 24 inches.
5] Sew the shoulders together (Take the measurement from step 2 and subtract 8 inches. Then divide by 2 this is the number of inches that you need to sew on each shoulder.)
6] Pick up stitches at the armhole. My mother used 8 inches * her stitch gauge (with half of the stitches picked up on either side.) She then slowly decreased to her wrist. I usually decrease every 10 rows a couple of times, then 8 rows a couple of times, etc. until I have the appropriate amount for my wrist.


What would be the time dilation in math? The answer is often a fantastic deal greater than you believe. A actual understanding of these ideas will help you determine whether or not they want to know extra in regards to the notion of causality in physics or never ever.
You need to comprehend the significance of time in mathematics to know the concept of time dilation in physics. Time is a thought in mathematics. As with other measures of length and period in math, it is a measure of this passage of time for a thing concerning a distinctive strategy.
Let us commence to study what’s the significance of free-fall in mathematics having a question. What precisely does impulse me-an in math? This could take a although excuse. This bit of this article’s objective is usually to use to present into the reader precisely the which means of your concept of freefall in mathematics.
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So we know what impulse indicates in physics, now let’s appear at what time dilation in physics is all about. https://keisan.uchicago.edu/ Suppose we are offered an object, and we press a button. What does the object do in that case?
Now we have come to understand the concept of time dilation in physics. Time is usually a measure of how long it takes for an object to travel from the point of origin towards the point of effect from the object that press the button. To make use of the example from earlier; Let’s say we’ve got an object like a baseball along with the pitcher throws it a extended way.
So that brings us towards the first part of the definition of what is time dilation in physics. Which is the time it takes for the object to travel extended distances in one particular second. That definition of time dilation in physics is applied to determine if the method that was just accomplished a time dilation action for example that of the baseball player, are going to be in one second.
Another essential part of what’s the meaning of freefall in physics is the fact that time is usually a measure of distance. For example; What does the time it requires for the baseball player to throw the ball be?
The answer to this question would be about three feet. essay-company com Now lets appear in the second a part of the question. What does the which means of time dilation in physics mean for the object?
The a single time dilation the baseball player makes when he throws the ball is one second. As you’ll be able to see, time is relative. If the baseball player has the velocity of a single foot per second, he may have the time dilation of one second.
When you use the word ‘time’ in physics, it should be in reference for the objective time that 1 could perceive by themselves in the point of view of time in the universe. The one time dilation that a baseball player makes in one particular second would be the normal time it takes for the baseball player to fly from the point of origin to the point of effect in the universe. But what would the regular time be when the baseball player flew a lot quicker?
So after you make use of the word ‘time’ in physics, what does it imply? If you’re curious about what is the which means of freefall in physics, comply with the hyperlinks to find out extra.


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By José Natário, Leonor Godinho
In contrast to many different texts on differential geometry, this textbook additionally deals attention-grabbing functions to geometric mechanics and common relativity.
The first half is a concise and self-contained creation to the fundamentals of manifolds, differential types, metrics and curvature. the second one half reports functions to mechanics and relativity together with the proofs of the Hawking and Penrose singularity theorems. it may be independently used for one-semester classes in both of those subjects.
The major rules are illustrated and extra built via a variety of examples and over three hundred routines. particular ideas are supplied for lots of of those routines, making An advent to Riemannian Geometry perfect for self-study.
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You by no means knew theoretical physics may be so easy! during this interesting and important ebook, Andrew Thomas sincerely illustrates the simplicity which lies at the back of nature at its primary point. it really is printed how all unifications in physics were in line with enormously easy ideas.
Using a logical method, it really is defined how the good twentieth century theories of relativity and quantum mechanics percentage a standard base, and the way they are often associated utilizing an idea so basic that any one can comprehend it.
An proposal that is so basic it's been hidden in simple sight.
About the Author
Andrew Thomas studied physics within the James Clerk Maxwell development in Edinburgh collage, and got his doctorate from Swansea college in 1992. he's the writer of the what's fact? web site (www. whatisreality. co. uk), the most renowned web pages facing questions of the basics of physics. it's been known as “The top on-line advent to quantum theory”.
'Albert Einstein's conception of basic relativity describes the impression of gravitation at the form of house and the circulation of time. yet for greater than 4 a long time after its e-book, the speculation remained mostly a interest for scientists; although exact it appeared, Einstein's mathematical code, represented via six interlocking equations, used to be probably the most tough to crack in all of technology.
This creation to the speculation of quantum fields in curved spacetime, meant for mathematicians, arose from a direction taught to graduate scholars and is designed for self-study or complex classes in relativity and quantum box concept. the fashion is casual and a few wisdom of common relativity and differential geometry is believed, but the writer does offer historical past fabric on functionality research and quantum box concept as required.
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- Manuale di Relatività Ristretta: Per la Laurea triennale in Fisica (UNITEXT) (Italian Edition)
Additional info for An Introduction to Riemannian Geometry: With Applications to Mechanics and Relativity (Universitext)
However, the commutator X ◦ Y − Y ◦ X does define a vector field. 2 Given two differentiable vector fields X, Y ∈ X(M) on a smooth manifold M, there exists a unique differentiable vector field Z ∈ X(M) such that Z · f = (X ◦ Y − Y ◦ X ) · f for every differentiable function f ∈ C ∞ (M). Proof Considering a coordinate chart x : W ⊂ M → Rn , we have n X= Xi i=1 ∂ ∂x i n and Y = Yi i=1 ∂ . ∂x i Then, n (X ◦ Y − Y ◦ X ) · f =X· Yi i=1 ∂ fˆ ∂x i n X · Yi = i=1 n −Y · Xi i=1 ∂ fˆ ∂x i ˆ ∂ fˆ i ∂f − Y · X ∂x i ∂x i 28 1 Differentiable Manifolds n + X jYi i, j=1 2 ˆ ∂ 2 fˆ j i ∂ f − Y X ∂x j ∂x i ∂x j ∂x i n = X · Y i − Y · Xi i=1 ∂ ∂x i · f, and so, at each point p ∈ W , one has ((X ◦ Y − Y ◦ X ) · f ) ( p) = Z p · f , where n X · Y i − Y · X i ( p) Zp = i=1 ∂ ∂x i .
9) Let f : M → N be a diffeomorphism between smooth manifolds. Show that f ∗ [X, Y ] = [ f ∗ X, f ∗ Y ] for every X, Y ∈ X(M). Therefore, f ∗ induces a Lie algebra isomorphism between X(M) and X(N ). (10) Let f : M → N be a differentiable map between smooth manifolds and consider two vector fields X ∈ X(M) and Y ∈ X(N ). Show that: (a) if the vector field Y is f -related to X then any integral curve of X is mapped by f into an integral curve of Y ; (b) the vector field Y is f -related to X if and only if the local flows FX and FY satisfy f (FX ( p, t)) = FY ( f ( p), t) for all (t, p) for which both sides are defined.
Bn }. There is a unique linear transformation S : V → V such that bi = S bi for every i = 1, . . , n. We say that the two bases are equivalent if det S > 0. This defines an equivalence relation that divides the set of all ordered bases of V into two equivalence classes. An orientation for V is an assignment of a positive sign to the elements of one equivalence class and a negative sign to the elements of the other. The sign assigned to a basis is called its orientation and the basis is said to be positively oriented or negatively oriented according to its sign.


At the Iffley Academy we promote real life applications in the teaching of mathematics. Mathematics is a vital life skill and at the Iffley Academy we ensure students have the opportunity to focus on mathematical skills they require for life. This can include the importance of understanding, for example, money and telling the time, which are a regular focus each term in our medium term planning.
At The Iffley Academy, students will have access to the full breadth of study at National Curriculum level in Key Stage 2 and 3 before moving on to undertake relevant qualifications in Key Stage 4 and 5. We currently offer Entry Level 1, 2, and 3 Edexcel Functional Skills and Level 1 and 2 qualifications. We focus on personalising our learning for our students and invest in qualifications that meet our students’ needs.
Mathematics teaching is delivered though our curriculum thematic approach, where skills are taught and developed, making links across the curriculum. It is taught using a wide range of ICT based resource such as Ipads, MacBooks, and laptops. We also access a wide range of ICT based software, such as Active Learn, My Maths and TT Rock stars. Students can also access these resources online at home as part of their home learning opportunities.
At the Iffley Academy all students are encouraged to take part on mathematical home learning challenges, which are intended to include the whole family. Home learning opportunities focus on real life scenarios and problem solving, which encourages students to engage with the wider world around them. This can include supermarket price challenges, baking tasks, as well as home DIY measuring opportunities. Many families engage with these opportunities and are keen to share their learning with the rest of the school via our home learning email firstname.lastname@example.org
We ensure mathematical learning is purposeful and practical, encouraging students to use resources to aid their learning. We encourage our students to take risks and challenge themselves, supporting them to develop impendence and skills to enhance learning for life.


and 11 again!
hyper-permutable prime! All the combinations and permutations (with 1 or 2 or 3 figures) are prime! or not?
Are you referring to Hypercentrally embedded subgroup?See reference (google books):http://books.google.ca/books?id=nw9ujImV3pwC&pg=PA393&lpg=PA393&dq=Hypercentrally+embedded+subgroup&source=bl&ots=cGgeazmtWD&sig=iqXlNifog2oBnHADzW7xb2rVRP0&hl=en&ei=RAoqTeahNI_EsAO4vq22CA&sa=X&oi=book_result&ct=result&resnum=3&ved=0CCUQ6AEwAjgK#v=onepage&q=Hypercentrally%20embedded%20subgroup&f=false
Or google: Canadian Mathematical Bulletin Dec 1989, Hypercentrally embedded subgroup


Sports are, at their core, a numbers game.
You keep score to see who wins and loses. You keep track of who has the most points, the most rebounds, the most yards, the most carries, the highest shooting percentage and the fewest number of turnovers.
It comes as no surprise, then, that Doherty High senior Tariq Massenburg, a two-sport standout for the Highlanders, wants to major in accounting in college. But, it’s not for the reason you think.
“I like math because there is always just one right answer,” Massenburg said after dropping a game-high 27 points on Dorchester in Doherty’s 53-46 victory in the regular season finale. “In English and social studies you can argue about what the right answer is. In math there is only one answer. The answer you come up with, it’s either right or it’s wrong.”
Thing have been pretty right – as in all right – this year for Massenburg.
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Senior Data Scientist - Advanced Analytics & Data Science
Suman is a Senior Data Scientist with 10+ years of experience in statistical analysis, predictive modelling and machine learning across various industries such as Technology, E-commerce, and Energy & Utilities.
Suman has expertise in Survey Analytics, Consumer Behaviour Models, Customer Segmentation Models, Simulation & Optimization techniques.
Her areas of interest include causal inference and discovering new approaches in statistics, and machine learning techniques.
She has master’s in statistics (gold medallist).


The STEM Ambassadors programme is an important part of the government’s efforts to increase the supply of people with STEM skills in the economy.
We are proud to be STEM Ambassadors!
STEM Ambassadors have a positive impact on young people’s engagement, interest and enjoyment of STEM subjects. You can make a real difference to a young person’s perception of STEM subjects and careers.
STEM Ambassador impact on young people
The ambassadors play a crucial role in closing the STEM skills gap. They get involved in a range of activities to impact on young people’s learning and enjoyment of STEM subjects. When it comes to the types of activities you can do, the opportunities are endless.
The Stem Ambassador programme works with over 30,000 STEM Ambassadors from more than 2,500 different employers. They volunteer their time, enthusiasm and experiences to encourage and inspire young people to progress further in science, technology, engineering and mathematics (STEM) subjects.
Through a range of activities, including presentations, mentoring and careers talks, STEM Ambassadors play an essential role in inspiring the next generation with the world of STEM subjects and careers. Their support isn’t just limited to the classroom – you can invite a STEM Ambassador into your STEM Club, employer, or youth and community group.
If you work in a STEM industry and want to showcase to the next generation your experience, sign up to be a STEM ambassador!
"It doesn't matter if you are a woman or a man, the important thing is your determination"
-- Milka Duno
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I am a software engineer at Infinite Campus, and a graduate of UW-Madison with a BS in Computer Science, Mathematics, and Philosophy. Previously, I worked in the Solís-Lemus Lab at the Wisconsin Institute for Discovery, developing MiNAA: Microbial Network Alignment Algorithm.
My interests include almost anything related to discrete math, but especially graph theory and cryptography. Outside of academia, I enjoy camping, tea, and mathematical/logic riddles.
My modest blog was inspired by Rishi Banerjee’s Rising Entropy.


I divided the days in a year by the turns in a year to get the days per turns. I got .00734 days per turn. I am super confused, and I hope the math works out to make sense, I love the idea of a moon being the suitable location for life.
Try to calculate it again. I'm not in the mood to do it now (basically - I hate maths), but I calculated it carefully when I made the map. The table and the sun/planet schematics left of it should make it clear.
Breathtaking presentation, and such fine detail! It may seem obvious, but thank you for providing such a high-resolution download for this. I'm pretty sure I'd need to print it all out and mount it somewhere in order to take the map in properly!


Home > Academic > Mathematics
World Scholars Academy offers elite summer courses providing high-level insights into leading disciplines and personalised academic and career guidance to accelerate your future success.
Bringing STEM learning to life. Join us in August 2023 for an educational 1 or 2 week STEM World summer Camp.
Maths Summer Course
Maths revision lessons online for students going into Year 11. One hour long class each day from 22nd - 26th August 2022, plus set independent study. Lessons will focus on the IGCSE course.
Maths Challenge & Maths Olympiad
We run weekly online classes and summer courses in Maths Olympiad. Classes are taught by current and former members of the UK Maths team. For more infor visit https://smsolympiads.com or 07486886686
Summer MATHS IGCSE Course
Online summer maths course for students going into Year 11. Revise and refresh your maths ready for the new school year. August 22nd - 26th.


Equity in STEM Education Science, Technology, Engineering, & Mathematics for the Next Generation
Women and underrepresented minorities make up a disproportionately small fraction of the science, technology, engineering, and mathematics (STEM) workforce. Addressing these inequities ensures that each child can access a future s/he chooses and we further innovation in science and technology.
Teaching for Equity in Mathematics and Science Education (TEMSE), 2009 - 2014 Analyzed a 2.5 year professional development program designed to assist math and science teachers in understanding issues of equity in southern California classrooms.
Learning Sciences Understanding the Contexts and Practices of Learning
The learning sciences bring together interdisciplinary researchers to think rigorously about how people learn in different real-world contexts, and design innovative learning environments. More than looking at educational outcomes, the learning sciences provides a way to investigate the processes of learning with different types of people across schools, homes, and communities.
Kids Engaged in Learning Programming (KELP-CS), 2013 - 2015 Developed a curriculum for 4th-6th grade students to teach computational thinking and to study the deeper question of how young students learn computational thinking, as well as how well the curriculum teaches it.
Gender Equality "The Longest Revolution" - Gloria Steinem
Women across racial and ethnic backgrounds earn less then their male counterparts and continue to assume primary responsibility of home-related work. We still need rigorous research and firm understanding of how gender -- as well as other aspects of identity such as race, ethnicity, class or ability -- impact social justice, access, and equality in education.
The Intersection of Gender, Ethnicity, and Math in the Lives of Math Majors, 2011 - 2014 Interviewed 45 math majors one-on-one and in focus groups about they experiences in math at a public research university with specific focus on women and Latinos/as.


At CSPS, the goal of our numeracy program is to promote the love of maths while simultaneously developing maths skills in a structured and supportive environment. We aim to achieve this by developing each student’s ability to understand and apply reasoning, fluency and critical thinking to everyday experiences. As part of our approach to teaching Mathematics, teachers use diagnostic assessments and teacher observations during small group work to determine individual learning needs which then informs future teaching and planning of mathematical concepts.
Learning in Maths centres around 4 key proficiencies: Understanding, Fluency, Problem Solving and Reasoning, working interchangeably to develop mathematical thinking. The proficiencies are fundamental to the learning process. These 4 proficiencies outlined in the Victorian Curriculum are applied across all three strands Number & Algebra, Measurement & Geometry, and Statistics and Probability.
Research shows us that successful mathematicians engage in all of these skills at any given time, which is why we use open-ended tasks and real-world problems to deepen students’ understanding of maths concepts.
At CSPS, we understand the importance of choice which is why we encourage students to represent and share their thinking using a variety of tools including whiteboards, iPads, unifix, MAB, play and real money and so much more. We encourage students to work independently, in pairs or small groups. Through mixed groupings, students come to realise the value of collaboration and peer learning is strengthened.


Description: The syslog-ng application can store fractions of a second in the timestamps according to the ISO8601 format. The frac-digits() parameter specifies the number of digits stored. The digits storing the fractions are padded by zeros if the original timestamp of the message specifies only seconds. Fractions can always be stored for the time the message was received.
NOTE: The syslog-ng OSE application can add the fractions to non-ISO8601 timestamps as well.
NOTE: As syslog-ng OSE is precise up to the microsecond, when the frac-digits() option is set to a value higher than 6, syslog-ng OSE will truncate the fraction seconds in the timestamps after 6 digits.


- What can be said about a data set with a standard deviation of 0?
- Is it possible for a list of numbers to have a mean of 7 but a standard deviation of 0?
- Why is the mean 0 and the standard deviation 1?
- What does it mean when standard deviation is negative?
- Is standard deviation resistant to unusual values?
- What is the 2 standard deviation rule?
- Can the sample standard deviation be zero?
- How do you interpret the standard deviation?
- Is a standard deviation of 0 good?
- Can standard deviation be greater than mean?
- What does a mean of 0 mean?
- What is 2 standard deviations from the mean?
- Is a standard deviation of 1 high?
- Is the standard deviation always positive?
- What does it mean to have a standard deviation of zero?
- What does a standard deviation of 1 mean?
- Is the sum of deviations always zero?
- What does standard deviation mean in test scores?
- What is Z value?
- Why do z scores have a mean of 0?
What can be said about a data set with a standard deviation of 0?
When the standard deviation is zero, there is no spread; that is, the all the data values are equal to each other.
The standard deviation is small when the data are all concentrated close to the mean, and is larger when the data values show more variation from the mean..
Is it possible for a list of numbers to have a mean of 7 but a standard deviation of 0?
Yes, it is possible for the standard deviation of a list of numbers to equal 0.
Why is the mean 0 and the standard deviation 1?
The mean of 0 and standard deviation of 1 usually applies to the standard normal distribution, often called the bell curve. The most likely value is the mean and it falls off as you get farther away. … The simple answer for z-scores is that they are your scores scaled as if your mean were 0 and standard deviation were 1.
What does it mean when standard deviation is negative?
Why Standard Deviation Can’t Be Negative Mathematically Standard deviation is the square root of variance, which is the average squared deviation from the mean and as such (average of some squared numbers) it can’t be negative.
Is standard deviation resistant to unusual values?
Is standard deviation resistant or nonresistant to extreme observations? … The standard deviation, s, like the mean, is not resistant. Strong skewness or a few outliers can make s very large.
What is the 2 standard deviation rule?
The empirical rule states that 95% of the distribution lies within two standard deviations. Thus, 5% lies outside of two standard deviations; half above 12.8 years and half below 7.2 years.
Can the sample standard deviation be zero?
Explanation: It is possible but (in my opinion) only if a sample consists of the same data. … Every component of this sum is equal to zero because the mean is equal to every element in the data set. Sum of 10 zeros is also zero, and the square root of zero is zero, therefore the deviation σ is also zero.
How do you interpret the standard deviation?
More precisely, it is a measure of the average distance between the values of the data in the set and the mean. A low standard deviation indicates that the data points tend to be very close to the mean; a high standard deviation indicates that the data points are spread out over a large range of values.
Is a standard deviation of 0 good?
This means that every data value is equal to the mean. This result along with the one above allows us to say that the sample standard deviation of a data set is zero if and only if all of its values are identical.
Can standard deviation be greater than mean?
The answer is yes. (1) Both the population or sample MEAN can be negative or non-negative while the SD must be a non-negative real number. A smaller standard deviation indicates that more of the data is clustered about the mean while A larger one indicates the data are more spread out.
What does a mean of 0 mean?
A mean of 0 means that the average value in the distribution is 0. … More precisely, if you added up all the numbers, the total would come out to 0 exactly, because if the mean is zero, the sum is 0/n, in which n is the number of values.
What is 2 standard deviations from the mean?
68% of the data is within 1 standard deviation (σ) of the mean (μ), 95% of the data is within 2 standard deviations (σ) of the mean (μ), and 99.7% of the data is within 3 standard deviations (σ) of the mean (μ).
Is a standard deviation of 1 high?
For an approximate answer, please estimate your coefficient of variation (CV=standard deviation / mean). As a rule of thumb, a CV >= 1 indicates a relatively high variation, while a CV < 1 can be considered low. ... Remember, standard deviations aren't "good" or "bad". They are indicators of how spread out your data is.
Is the standard deviation always positive?
Standard deviation measures how spread out the values in a data set are around the mean. More precisely, it is a measure of the average distance between the values of the data in the set and the mean. … The standard deviation is always a positive number and is always measured in the same units as the original data.
What does it mean to have a standard deviation of zero?
Standard Deviation means deviation of each element from mean value. If standard deviation is zero, it means all the individual values contributing to the mean are identical. … All the data values are identical so that there is no variation for the individual sets…
What does a standard deviation of 1 mean?
A normal distribution with a mean of 0 and a standard deviation of 1 is called a standard normal distribution. Areas of the normal distribution are often represented by tables of the standard normal distribution. … For example, a Z of -2.5 represents a value 2.5 standard deviations below the mean.
Is the sum of deviations always zero?
The sum of the deviations from the mean is zero. This will always be the case as it is a property of the sample mean, i.e., the sum of the deviations below the mean will always equal the sum of the deviations above the mean.
What does standard deviation mean in test scores?
The standard deviation of a set of numbers measures variability. Standard deviation tells you, on average, how far off most people’s scores were from the average (or mean) score. … If the standard deviation of a set of scores is low, that means most students get close to the average score (in this case, 1051).
What is Z value?
The value of the z-score tells you how many standard deviations you are away from the mean. … A positive z-score indicates the raw score is higher than the mean average. For example, if a z-score is equal to +1, it is 1 standard deviation above the mean. A negative z-score reveals the raw score is below the mean average.
Why do z scores have a mean of 0?
A z-score equal to 0 represents an element equal to the mean. A z-score equal to 1 represents an element that is 1 standard deviation greater than the mean; a z-score equal to 2, 2 standard deviations greater than the mean; etc.


Bachelor of Arts in Mathematics or Computer Science
The Department of Mathematics and Computer Science also offers several Bachelor of Arts degrees. These degrees are more general in nature and are often for students who may not require advanced studies. Bachelor of Arts degrees are available in computer science, mathematics, computer graphic design and computer information systems.
Bachelor of Science in Computer Science
Students interested in computer science can pursue their Bachelor of Science in Computer Science. Let NNU prepare you for today's technology-driven workforce. After graduation, you will be ready for careers in programming, database design, networking, web development, bioinformatics research and more.


This calculation is used to calculate flow rate using a choice of algorithms commonly used by distributed control systems (DCS).
Honeywell – Advanced Process Manager Control Functions and Algorithms – AP09-600
Kelton calculation reference C195
FLOCALC calculation reference F052
KIMS calculation reference K195
Select option based on desired flow parameter.
- Linear Value
- % Linear
- % Square root
Select option based on whether the uncompensated flowrate is a linear or square rooted term.
- A: Liquids
- B: Gasses and Vapours
- C: Gasses and Vapours with Specific Gravity
- D: Volumetric Flow of Gasses and Vapours
- E: Steam
Select option based on properties of the measured fluid.
Flow compensation term
The flow compensation term is calculated by:
|A, B, C, D, E||=||Refer to the calculation method for which the formula is employed|
|RG||=||Design Specific gravity|
|RX||=||Design Steam Compressibility|
|Q||=||Steam Quality Factor|
|RQ||=||Design Steam Quality Factor|
Note: If input method is linear square root is not necessary.
Compensated flow rate
The flow rate is calculated by:
|C1||=||1st correction constant|
|C2||=||2nd correction constant|
|F||=||Uncompensated flow input|
|COMPTERM||=||Flow compensation term|


Paper ID sheet UCL-INMA-2017.08
A collection of nonsmooth Riemannian optimization problems
- P.-A. Absil, S. Hosseini
Nonsmooth Riemannian optimization is a still scarcely explored subfield of optimization theory that concerns the general problem of minimizing (or maximizing), over a domain endowed with a manifold structure, a real-valued function that is not everywhere differentiable. The purpose of this paper is to illustrate, by means of nine concrete examples, that nonsmooth Riemannian optimization finds numerous applications in engineering and the sciences.
- Key words
- In: Hosseini S., Mordukhovich B., Uschmajew A. (eds) Nonsmooth Optimization and Its Applications. International Series of Numerical Mathematics, vol 170. Birkhäuser, Cham


Preferred Networks appoints Professor Kenji Fukumizu of the Institute of Statistical Mathematics as a Technical Advisor
On November 22nd, 2018, Preferred Networks, Inc. (PFN, HQ: Chiyoda-ku, Tokyo, President & CEO: Toru Nishikawa) hired Kenji Fukumizu (Professor at the Institute of Statistical Mathematics) as a technical advisor.
Professor Fukumizu is a leading researcher in statistical machine learning. He has achieved notable research accomplishments on singular models, kernel methods, and geometrical analysis of algorithms, including the best paper award at NIPS 2017. His current research interests also include topological data analysis.
In this role as a technical advisor, Professor Fukumizu will jointly advance theoretical research of neural network models with PFN researchers by his technical advice and supervision, in order to deepen our knowledge of deep learning technology and contribute to other research and applications at PFN.
Prof. Kenji Fukumizu
Kenji Fukumizu is a professor in the Department of Statistical Modeling at The Institute of Statistical Mathematics, where he also serves as director of the Research Innovation Center. He received his B.S. from Kyoto University in 1981 and joined the Research and Development Center, Ricoh Co., Ltd. He received his Ph.D. from Kyoto University in 1996. He worked as a researcher at the Institute of Physical and Chemical Research (RIKEN) from 1998 and became an associate professor of The Institute of Statistical Mathematics in 2000. He was a visiting scholar at the Department of Statistics, UC Berkeley in 2002-2003, and a Humboldt fellow at Max Planck Institute for Biological Cybernetics in 2006-2007. He served as Area Chair on the Program Committee of NIPS 2010, 2011, 2015, 2017 and 2018, and Area Chair on the Program Committee of ICML 2009, 2015, 2017, and 2018. He currently serves as an action editor of The Journal of Machine Learning Research.


A Numerical Primer for the Chemical Engineer eBook PDF Free Download
Edited by Edwin Zondervan
Published by CRC Press
About the Book
A Numerical Primer for the Chemical Engineer is edited by Edwin Zondervan. This First Edition textbook of A Numerical Primer for the Chemical Engineer, published by CRC Press Publications, provides information on Numerical Methods for Solving Chemical Engineering Problems.
– Emphasizes the derivation and use of a variety of numerical methods for solving chemical engineering problems.
– Deals with algorithms which are used to solve linear equations, nonlinear equations, ordinary differential equations, and partial differential equations.
– Includes chapters on linear and nonlinear regression, and on optimization.
– Adopts MATLAB as the programming environment throughout the book.
What You will Learn
The Topics Covered in this Textbook are
The role of models in chemical engineering
Errors in computer simulations
Ordinary differential equations
Partial differential equations 1
Partial differential equations 2
Data regression and curve fitting
Basics of MATLAB
Numerical methods in Excel
For Whom is this Book For
A Numerical Primer for the Chemical Engineer, 1st Edition is perfect for Engineering Students. It is the must have reference for Engineers! It acts as Reference Material for those students those who are pursuing their Graduation in Chemical Engineering.
Format of the eBook: PDF Size: 2 MB
If the Download Links of eBook / PDF are Not Working or Broken, then Contact Us Immediately via Broken Links Form.


A worksheet function is represented by a keyword in an Excel formula that performs some action on input and returns output to the calling procedure, either a worksheet cell or another function.
I have 3 ranges of numbers and the answer depends on the range. 75-79=0.255 80-84=0.327 85+ =0.559 I tried to create an equation …excel if-statement worksheet-function
I plan to have a workbook with 24 sheets. The sheet names will be: Jan, Jan item, Feb, Feb item, etc. …excel excel-formula worksheet-function


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How to set the position of a new scale in the chart?
The position of a scale can be set by means of the following methods:
ilog.views.chart.IlvScale.setCrossingValue(double), for a fixed value on the dual axis (the "dual axis" description can be found in the
ilog.views.chart.IlvScale.setCrossing(IlvAxis.Crossing), to compute the
crossing point by a function receiving the dual
ilog.views.chart.IlvAxisas parameter. The default implementations are
When two scales share the same crossing (
IlvAxis.MAX_VALUE), the chart automatically arranges the scales to avoid overlapping.
For example: in a Cartesian chart, setting several scales at the
IlvAxis.MIN_VALUE crossing will have the scales drawn one after another at the left side of the chart.


Worksheet Maker- Create measurement worksheets automatically with over
70 different unit conversions for the 4 main forms of measurement.
unit conversions include:
- ft., cm. - inch, cm. - mm., cm. - meters, cm. - km., cm. - yards,
ft.- inch, ft.- mm., ft.- meters, ft.- km, ft.- yards, inch - mm.,
inch - meters, inch - km., inch - yards, mm. - meters, mm. - km.,
mm. - yards, meters - km., meters - yards, km. - yards