Understanding the House Edge, The basics of casino gambling are very simple. Even though the rules of each game are different, the fundamental principle is basically the same for all of them.
Whether it’s a blackjack hand, round the roulette wheel, dice rolls at the craps table, or rounds on slot machines, DATA SGP players install pegs and bet on casinos (also known as houses).
When the players lost, the house took their bets. When the players win, the house pays their stake.
In principle, it’s almost all you need to know to start playing casino games. Of course, you also need to know the rules for certain games that you want to play, but they are usually quite easy to learn.
However, in our opinion, at least, pay to have a basic understanding of how casino gambling works.
In particular, you must understand how casinos make money and must be familiar with the concept of the percentage of houses and payments.
You also have to understand why players win money even though their opportunities oppose them. We explain all these things on this page.
How casinos make money
Basically, casino games are all coincidental games, which means that a player ultimately depends on luck. There are several games that also involve elements of skills, such as blackjack, but good luck is generally an over-riding factor in determining whether a player wins or not.
However, this does not mean that casinos need to be fortunate to get profit from people playing their games.
Every single casino game provides long-term benefits for home, and this is how they make money.
The benefits that are effectively built into every casino game are known as the edge of the house. This edge means that, over time, the casino will always win money.
The edge of the house is because the casino does not pay the winner’s bet according to the true opportunity of the bet. Thus, they technically make money every time the player bets money.
Even though the house does not win every bet, mathematically, the possibilities always support them. The casino game is known as a negative hope game because of its negative long-term expectations.
Understanding the House Edge
First, we will see the example of American Roulette versus the probability of European Roulette to help give us a better understanding of how the game works, so we can better understand how the end of the house starts to apply:
Probability of betting payments
Opportunity 1: 1 46.37%
Even 1: 1 46.37%
Black 1: 1 46.37%
Red 1: 1 46.37%
1 – 18 1: 1 46.37%
19 – 36 1: 1 46.37%
1 – 12 2: 1 31.58%
13 – 24 2: 1 31.58%
25 – 36 1: 1 31.58%
Single number 35: 1 2.63%
Combination of two numbers 17: 1 5.26%
Combination of three numbers 11: 1 7.89%
Combination of four numbers 8: 1 10.53%
Combination of six numbers 5: 1 15.79%
Combination 1,2,3,0,00 6: 1 13.16%
Examples of Europe.
Probability of betting payments
Opportunity 1: 1 48.6%
Even 1: 1 48.6%
Black 1: 1 48.6%
Red 1: 1 48.6%
1 – 18 1: 1 48.6%
19 – 36 1: 1 48.6%
1 – 12 2: 1 32.4%
13 – 24 2: 1 32.4%
25 – 36 2: 1 32.4%
Single number 35: 1 2.7%
Combination of two numbers 17: 1 5.4%
Combination of three numbers 11: 1 8.1%
Combination of four numbers 8: 1 8.1%
Combination of six numbers 5: 1 5.1%
We will now use an example to show how the edge of the house works in practice. Let’s say we play Roulette and bet $ 1 in one single number for each round. DATA SYDNEY The Roulette wheel has 37 points or 38 points, depending on whether you play American or European style.
Understanding the House Edge, So you have a chance 1 in 37 or 1 in 38 to win your bet. We will use the European version for this example.
Theoretically, you will hope to win your bet once every 37 rounds. In practice, it doesn’t work like that because of the standard deviation and variance, which we explain a little later, but in the long run, each number must rotate about every 37 rounds.
For the sake of this example, we will work based on that every number appears exactly every 37q


Christopher Zeeman presents the second Christmas Lecture from his groundbreaking 1978 series.
As mathematics has developed down the centuries, our concept of "numbers" has grown more sophisticated to include many different types of numbers.
From rational and irrational numbers used for measuring the real world to complex numbers used for solving equations, Zeeman outlines the historical development of maths and explains why it happened.
It's not as complex as it sounds. Through demonstartions and simple proofs, we are introduced to the contributions of Greek mathematicians during the fifth centruy B.C. through to 1799 when Gauss proved the famous theorem that with complex numbers all equations can be solved.
Plus, watch out for the giant calculator!
Sir Christopher Zeeman


Download Profit And Loss Formula In Hindi Pdf
Download free profit and loss formula in hindi pdf. Profit And Loss PDF Download In Hindi: लाभ – हानि नमस्कार दोस्तों, आज हम अपने Students के लिए Profit And Loss PDF लेकर आये हैं, Competitive Exams में अगर कोई किसी भी Section से सबसे ज्यादा Question पूछे जाते हैं तो वो. Profit and Loss Formula Tricks in Hindi PDF Download. Dear students, Today We are sharing Profit and Loss Formula Tricks in Hindi PDF prodecoring.ru PDF contains questions related to profit and loss which will prove beneficial in your preparation for any exam.
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SSC, Railway, Defense, And Competitive Exams में प्रतिशत. Profit and Loss formula is used in mathematics to determine the price of a commodity in the market and understand how profitable a business prodecoring.ru product has a cost price and selling price.
Based on the values of these prices, we can calculate the profit gained or the loss incurred for a particular product. The u/LuckyExam community on Reddit. Reddit gives you the best of the internet in one place. Profit and Loss Aptitude PDF.
In this we have given Profit & Loss Aptitude Notes Pdf for those who are preparing for Competitive Examination. This, we believe shall be useful in preparing and gearing up for taking the exams. Cost Price: The amount paid to purchase an article or the price at which an article is made, is known as its cost price. The cost price is abbreviated as C. P. लाभ और हानि (Profit and Loss) || Math Magic Tricks || Maths Tricks In Hindi क्रय मूल्य (Coast Price): जिस मूल्य पर वस्तु खरीदी गई हैं, वस्तु का क्रय मूल्य कहलाता हैं।.
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We are trying to cover the basic definitions, formulas, solved examples and some tricks. Apart from it, if you want to check Profit And Loss Formulas In Hindi, Profit And Loss Formulas and other facts, scroll down this page as soon as possible or be in touch with us. Formulas For Profit And Loss (Part-1).
This is the aptitude questions and answers section on "Profit and Loss Important Formulas" with explanation for various interview, competitive examination and entrance test. Solved examples with detailed answer description, explanation are given and it would be easy to understand. In this video I discussed important formulas of Profit and Loss.
You can copy this formulas in your note book and also can memorise with me. PROFIT & LOSS |. This course will begin with a basic approach to play with percentage and ratio and after that it will discuss profit and loss problems.
(All necessary questions are covered). Later, profit and loss will be merged with discount. In the last lecture true discount is also included. Abhinay Sir Class Notes Profit and Loss PDF Hindi or English में डाउनलोड कर. SSC CGL, CHSL, SSC GD, Bank, Police, NDA, Airforce, CDS, Bihar Police, MPPolice, Group D, Loco Pilot, RPF and other Competitive Exam की तैयारी कर, रहे Students के लिए आज हम. The percentage of profit or loss is: a) 15% loss b) 15% gain c) /7% loss d) /7% profit.
Q A reduction of 20% in the price of salt enables a purchaser to obtain 4 kg more for Rs The reduced price of salt per kg is: a) Rs 4 b) Rs 5 c) Rs d) Rs Profit and Loss. Q A person sells a table at a profit of 10%. Profit And Loss PDF Notes In Hindi. You are very well informed and the related questions are asked in many exams and you will know this well and many questions come from Profit and Loss in Maths.
Brought them. And you will understand this very well and it. Profit & Loss Pdf Free Download Now: Profit & Loss Question Pdf for Banking, SSC, RRB, FCI, Railway, UPSC, State PCS, Insurance & other Competitive prodecoring.ru & Loss shortcut Tricks Pdf, Profit & Loss MCQ, Profit & Loss Objective Question & Answer Pdf.
“Profit & Loss Questions PDF” In this post we are providing you the Profit & Loss pdf with detailed solution & Short. This is the aptitude questions and answers section on "Profit and Loss" with explanation for various interview, competitive examination and entrance test.
Solved examples with detailed answer description, explanation are given and it would be easy to understand. Download Profit and Loss, Discount formulas PDF for CAT The formulas will make profit and loss, discount topic easier for your CAT exam. Using the shortcuts given in this section, you can solve any word problem on profit and loss easily. To download profit and loss shortcuts as pdf document, Please click here Profit and Loss Shortcuts.
Shortcut 1: Cost price and marked up percentage are given. Cost price = C.P, Profit. Maths Book Pdf Download: Maths Shortcut Tricks Pdf in Hindi & English for competitive exams: I welcome all of you in this new article about Maths book pdf. In this article, I am sharing the best math book for all competitive prodecoring.ru you want to download these books, then.
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When each of the two things is sold at the same price,and a profit of p% is made on the first and a loss of L% is made on the second,then the percentage gain or loss is. If profit percentage and loss percentage are equal, put P=L => %loss = p 2 / This completes this list of Profit and Loss formulas, shortcuts and tricks.
Profit and loss account is commonly known as the account which enlists and shows all the profits and loss of a company have in a special period of time. Profit and loss account format is built in excel and is using the excel formulas to aggregate the total profit or loss of a company even of a small business.
Quantitative Aptitude – Profit & Loss Section | Points to Remember. Profit & Loss is one of the important Quant topic of the Exams like SBI PO. SBI ClerkIBPS RRBIBPS POIBPS Clerk Exam, SSC CGLRRB Railway Recruitment With the right tutor around, it is easy to answer this section.
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Profit and Loss Formulas. Cost Price – It is basically the price at which a commodity or object is bought at.e.g. Shopkeeper buying Sugar from Farmer to sell in his grocery store. In its short form it is denoted as C.P.; Selling Price – The price at which the commodity is sold at. e.g. Shopkeeper selling sugar to his customer.
In its short form is denoted as S.P. यहाँ प्रकाशित किए गए लाभ और हानि प्रश्न और उत्तरों की संख्या 10 (Important Profit and Loss Questions in Hindi) है. Profit and Loss Reasoning Questions and Answers in Hindi Examinations. प्रश्न 1. Profit and loss formula is one of the most important mathematical formulas which are used to calculate many maths problems in our academic and daily life.
These formulas have high usage in small and large businesses, retails and those related to finance apart from the calculations involved in our schools and college life.
Profit Loss Formula In Hindi. Novem by Jerry. 21 Posts Related to Profit Loss Formula In Hindi. Profit Loss Formula. Operating Profit Loss Formula. Profit Loss Formula Maths. Profit And Loss Statement Form Pdf. Profit Loss Statement Form. Simple Profit And Loss Format. Profit and Loss Question and Answers with easy solutions in Aptitude topic are present here.
There are understandable, simple solutions useful for RRB - ALP, Group D and Bank Jobs. Questions are answerd with detailed explanations. Profit and Loss questions are confusing questions for most of the students.
Profit and Loss questions asked generally in SSC, Bank Exam and other competitive exams. So, students should practice these profit and Loss questions and answers to get a good score in their competitive exams. Profit and Loss Questions and Answers in Hindi - हिंदी for RRB NTPC Exams MCQs for RRB NTPC and AP Grama Sachivalayam Exams in hindi are given here.
These are useful to those are preparing for AP Grama sachivalam jobs, RRB NTPC, group II, group - III, panchayat secretary jobs. Profit and Loss: Underneath points make you to understand about profit and loss. Cost price is defined as price at which an article is purchased. Selling price is defined as price at which an article is sold.
When an article is sold out at more price than cost price in that case You will get profit. NCERT Solutions for Class 7 Math Chapter 12 Profit And Loss are provided here with simple step-by-step explanations.
These solutions for Profit And Loss are extremely popular among Class 7 students for Math Profit And Loss Solutions come handy for quickly. Every company prepares a Profit and Loss Account/statement at the end of the year generally, to get the visibility of the income, earning, expenses and loss incurred in a specific range of period.
It is important to prepare Profit and Loss statement because this information helps an organisation to take the right business decision like where should we do the cost-cutting, from where can a.


So: how to insert a numbered equation in Word 2007 and reference it in the text. For the first part, I follow this blog post.
- Insert a 3 column, 1 row table.
- Format the table to fill 100% of the page width, with the column widths in percent as 15:70:15.
- Centre the text in the middle column and remove all table borders. Make the spacing below the table the same as other paragraphs.
- Insert your equation in the middle column. (I use insert>object>M$ equation 3.0 since the new equation package won't work on my machine).
- Insert a number in the right-hand column by insert>multilevel list. You can define your own so that the numbers are formatted like (x).
Here is the nice part (ha ha). Since my "equation gallery" is broken too, I can't save these shenanigans for easy re-use. To insert a new equation later, I simply copy the whole table and paste it elsewhere and change the equation! The numbers automatically sort themselves out (hallelujah).
To reference the numbered equation in the text:
- Highlight the equation number and insert>bookmark. Give it a nice name.
- Put the cursor at the place where you want your reference inserted and insert>cross-reference. Insert a reference of type "bookmark", select the name of your equation and insert the reference to the paragraph number (full context).
There. That was a complete pain, wasn't it? And it took about 40 mouse-clicks! Doesn't your equation look horridly rendered too? Oh, I love LaTeX and I want it back.


News & Features
More than 100 Grade 6 student graduates from Itaas Elementary School Main in Muntinlupa are all set to move up to junior secondary level this school year. Insular Foundation recently celebrated the elementary school graduation of its 121 scholars in a meet and greet event with the InLife employees. InLife employees provided the scholars’ school materials, uniforms, shoes and bags from Grade 1 to Grade 6.Read More
This AY 2023-2024, the Gold Eagle College Scholarship Grant is offered to incoming 1st year college students in Science, Technology, Engineering and Mathematics (STEM) courses offered by Insular Foundation’s 6 partner schools. This scholarship program aims to support intelligent and deserving students who need financial assistance to have access to the best education they need to improve their lives, their home, and the country.


Dia: Dimecres, 21 de juny de 2017
Lloc: Aula T2 (2n pis), Facultat de Matemàtiques i Informàtica, UB.
A càrrec de: Renato Calleja, Departamento de Matemáticas y Mecánica, IIMAS-UNAM
Títol: KAM tori in mechanical systems with friction: the limit of small friction
Resum: Many problems in Physics are described by conformally symplectic systems (e.g. mechanical systems with a friction proportional to the velocity, variational problems with a small discount or thermostated systems.
I will present a study of the limit of small dissipation in conformally symplectic systems. Conformally symplectic systems are characterized by the property that they transform a symplectic form into a multiple of itself. I will present a conjecture about the geometry of the domains and numerical computations that support it. The numerical computations are based on the parameterization method for conformally symplectic systems. This is joint work with Alessandra Celletti, Rafael de la Llave, and Adrián P. Bustamante.
Last updated: Mon Jun 19 08:21:09 2017


Archimedes’ Quadrature of a parabola states that the volume enclosed between a line and a parabola is four-thirds the volume of the largest inscribed triangle that can be drawn in that same region.
What other methods of numerical integration do you know of?
The idea for this post came from my other half, who wanted me to post about numerical integration. Thank you Ces <3
Per usual, graph was generated using WolframAlpha and all of their usage restrictions apply to reposting this content.
This is the NGC 595 it is a gigantic region of ionised hydrogen in the Triangulum Galaxy, about three million light-years away, the nebula was discovered by the German astronomer Heinrich Ludwig d'Arrest on 1 October 1864. ———————————— — PC; NASA / ESA / & M. Durban ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ — i get my wisdom teeth out today let’s hop the process goes as smoothly as everyone tells me


Bobby's Baking Goods Kickstarts Bake-Off Competition
Recently one of our colleagues and supporters sent us these photos of how she used Bobby's Baking Good in her classroom. We thank her so much for the support. This is what we envisioned when we began YGO!
The lesson was introduced with the book "Bobby's Baking Good."
Students applied knowledge of entrepreneurship skills by creating a bakery with their group.
Students also applied knowledge of math skills while collecting money from customers.
The Bake Off competition helped students understand how businesses compete to gain more customers.


In determining the cash deposit required to collateralize a stock borrow position, the general industry convention is for the lender to require a deposit equal to 102% of the prior day's settlement price, rounded up to the nearest whole dollar and then multiplied by the number of shares borrowed. As borrow rates are determined based upon the value of the loan collateral, this convention impacts the cost of maintaining the short position, with the impact being most significant in the case of low-priced and hard-to-borrow shares.
Account holders may view this adjusted price for a given transaction in the "Non-Direct Hard to Borrow Details" section of the daily account statement. An example of this collateral calculation and its impact upon borrow fees is provided below.
Sell short 100,000 shares of ABC at a price of $1.50
Short sale proceeds received = $150,000.00
Assume the price of ABC falls to $0.25 and the stock has a borrow fee rate of 50%
Short stock collateral value calculation
Price = 0.25 x 102% = 0.255; round up to $1.00
Value = 100,000 shares x $1.00 = $100,000.00
Borrow fee = $100,000 x 50% / 360 days in year = $138.89 per day
Assuming the account holder's cash balance does not include proceeds from any other short sale transaction then this borrow fee will not be offset by any credit interest on the short sale proceeds as the balance does not exceed the minimum $100,000 Tier 1 threshold necessary to accrue interest.


Head of Faculty: Will Sheppard
The mathematics program at Campbell High School aims to promote a positive attitude towards mathematics and its relevance to students both personally and in their community. The program gives students the opportunity to develop a sound understanding of mathematics and its processes by following the Australian Curriculum.
The year 7 courses cover the basic skills of mathematics and enable students to be numerate in our society as well as preparing them for further high school mathematics studies.
In years 8 and 9, the course is structured to accommodate the range of students in each cohort. The year 8 and 9 courses cover the basic skills of mathematics and enable students to be numerate in our society as well as preparing them for further mathematical enquiry.
In year 10, all students will study a common core program. This program provides students with the opportunity to study mathematics in different levels of depth. Students can follow a 10 or 10A program of study which cover topics which prepare students for tertiary level mathematics at college. The 10A program leads to a further study of mathematics as needed in heavily mathematics based college courses such as Physics, Chemistry and Mathematical Methods to Specialist Mathematics. High achieving students have an opportunity to be selected for the 10A course.
A formalised mathematics tutorial session is available to all students through the Enrichment program. It is designed to give those students who require extra help in mathematics the opportunity to work through problems with a teacher in a smaller group. The mathematics faculty also offers lunch time support one day per week.
Students at Campbell High School have the opportunity to compete in a number of national mathematics competitions including the Computational and Algorithmic Competition, ICAS Mathematics Competition and the Australian Mathematics Competition. Students who have an interest in the creative understanding of mathematics can also join the mathematics and engineering section of the Tournament of Minds.
Each year, the school purchases the online version of the Pearson Maths textbook. This is a great resource and has numerous features that will help your child master the concepts covered during class time. The resource can be accessed at any time and contains tutorials, quizzes, worked examples and of course heaps of questions to work through. At Campbell we also use the website MyMathsOnline to help further consolidate the learning in the classroom and provide your child with homework activities. These can be set by the teacher or completed independently by your child without being explicitly set by the teacher.
Head of Faculty: Ian Mongan
The languages curriculum at Campbell High School provides students with the opportunity to develop language proficiency through a four-year sequential program. This continuity allows our students to pursue college language studies at intermediate or advanced levels. Our courses are therefore a part of a continuum of language studies that may start in primary school and go through to university. In years 7 and 8 students must study either French or Japanese.
We aim to provide opportunities to travel and learn in Japan, France and/or other French speaking destinations on a rotational basis. Participation in these trips is not essential to student success in language learning as they are in addition to our curriculum. However these trips give students an incentive to study because they can look forward to using the language in context at some stage whilst at Campbell High School. Positions on the trips are sought after and students attending have a rich immersive cultural experience.
Our course is a fun, interactive course designed for high school students. It unfolds in a sequential manner that allows students to build on their acquired knowledge year after year. Students learn vocabulary and grammatical constructions through practical themes appropriate to their level. Teachers design handouts and use online programs to supplement the vocabulary and grammar supplied in textbooks. Songs and short poems are used to teach pronunciation in an entertaining manner. The cultural assignments allow students the chance to "visit" France. They are taught how to organise their research, use the library resources and the internet to obtain current information and to take notes and record bibliographical details. Films provide an insight in the French way of life and sense of humour often establishing a valuable link with historical facts and often establish contexts.
The Japanese course is based on Obento and iiTomo textbooks. Each text is an up to date course specifically designed to appeal to Australian high school students. The hiragana script is taught immediately and students will be able to read and write hiragana within a few months. Supplementary resources such as CDs, videos, computer programs, games and worksheets enhance the learning process. Our students have a lot of fun trying out their language skills and making new friends. Students complete major cultural assignments using extensive online resources. An understanding of Japan and Japanese culture is integral to our classes. The courses ensure progressive development following a familiar pattern and provide a solid basis for higher studies.
The study of Japanese in years 9 and 10 builds on the work completed in earlier years. The four semester units are sequential and students selecting Japanese are expected to study the language for a full year. Students in Year 9 have the opportunity to visit Japan, experiencing school and living with a Japanese family while they are there. Each year in August we receive a visit from our sister school in Japan, we invite Campbell High families to host a student.
Students who come from non-English speaking backgrounds may be eligible for targeted English language lessons. Enrolment into an EAL/D class is dependent upon a series of individual tests in four key areas of language acquisition: reading, writing, speaking and listening. Each of these areas is aligned with the Australian Curriculum, Assessment and Reporting Authority documents related to language acquisition. In addition, length of time in an Australian school determines eligibility. Students, who undertake an EAL/D course to support their understanding and acquisition of Australian English, focus on developing their cross curriculum academic skills suitable for their age group.
Students are placed in classes of combined years 7 & 8 and years 9 & 10 groups. The classes are run on an elective line to support student learning in their core curriculum areas.
Formative assessment tasks and testing as prescribed by the ACT Education and Training Directorate provides an accurate indication of student learning progression. Students are able to graduate from EAL/D classes to choose electives after a parent/carer, teacher and student consultation process.
Students are encouraged and supported to participate in the numerous activities offered at Campbell High School. Opportunities are offered to the students to enable them to gain further understanding of Australian culture and society through excursions to places and events such as The Botanic Gardens, museums and other events as they arise. Students proudly and actively maintain their mother language and culture and put these on display during events such as Harmony Day and NAIDOC week.


There are many tools on the Internet that perform the conversion directly from pounds to kilograms. It is always good to know the explanation of the steps involved in its calculation . One of the simplest methods is to simply divide the number of pounds per 2.2 for an approximate result.
In the USA, England, Australia and other countries the unit weight is still pound (lb).
How is the conversion of pounds to kilograms or kilograms to pounds?
1 pound (pound) = 0, 45 Kg
1 kg = 2.2 lbs (pounds)
So, a person with 70 kg have 154 lbs (pounds).


20/01/2014 - Hans Smellinckx
Yesterday we introduced you to one of our speakers Dr. Richard D. Gill, the professor of mathematics at Leiden University. Well, Dr. Gill got our heads thinking about statistics and numbers which led us to this lesson on TED-Ed from mathematician Jeff Dekofsky based on David Hilbert's Infinite Hotel. The Infinite Hotel, is a thought experiment created by Hilbert in the 1920s about a hotel with an infinite number of rooms. Still with us? Why not take a look at the lesson video below and start to understand more about the concept of infinity as Dekofsky brings Hilbert's Infinite Hotel to life in this quirky animation.
And don't forget to book your tickets for our event in March! (you can find the link on top of this page)
Visit TED-Ed for more lessons worth sharing.


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Math::Algebra::Symbols is a Symbolic Algebra in Pure Perl. SYNOPSIS Example symbols.pl #!perl -w -I.. use Math::Algebra::Symbols hyper=>1; use Test::Simple tests=>5; ($n, $x, $y) = symbols(qw(n x y)); $a += ($x**8 - 1)/($x-1); $b += sin($x)**2 + cos($x)**2; $c += (sin($n*$x) +...
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First Delphi tutorial starts with a simple database created in MS Access. It shows how to create and connect to a database in Delphi. It also shows how to display records in a dbgrid. Essential tutorial, a starting point for understanding next delphi tutorials. Second Delphi tutorial shows how to...
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Custom Actionscript 3 Scrollpane Component with OOP
One of cool things about being a Flash Developer is making your own components. With that being said, one of the things that I’ve wanted to make was my own, custom scrollpane.
After numerous hours, I finally did it.
I thought it would be a lot harder to make one, but it wasn’t that hard. It just involved basic Math and logic. The line that makes the content move the way it does it:
_content.y =-( _handler.y*(_content.height/_track.height));
The “_content” is a movieclip of what you want to move. Since you want that to move vertically, you are going to use the y axis, unless you were going to do a horizontal scrollpane, then you would use the x axis. The “_handler” is slider. The content depends on where that slider is on the scrollbar. Next, you want to get the difference in height between the track and the content. To do that, you divide them both. Then you are going to multiply the y location of the handle to give you a number that the content would use to move up and down.


I recently reached a milestone in my photography printing journey with the realization that, unless I was printing a photo specifically for framing, my prints were really just “test prints.” Mostly I was simply printing the photos to see how they would look on paper; rather than creating a print designed to present the image to the viewer.
The solution to this issue is to print the photo on the page in an aesthetically pleasing manner such that the printed image is surrounded by a suitable border that frames the image on the page and provides some room for the viewer to hold the paper without covering the photo. Of course, this then begs the question of what is a suitable border? Is it some percentage of the short or long side of the image? Is it based on a standard for a certain size of print? And how do I determine this quickly for a particular photo?
A search for the answers to these questions returns diverse opinions on the matter. Many are based on determining the appropriate mat size to fit within standard frame dimensions. Others are based on high level principles of art and how the human eye perceives space and something about Greek columns. Others are very simple-Martin Bailey offers a spreadsheet calculator based on the using a border that is 10% of the length of the short edge of the image (but this percentage must be adjusted as the page size increases).
I fumbled around for a few hours working on an Excel spreadsheet to calculate some type of “optimal” image size and borders for a given image aspect ratio and page size. However, once my calculator was working, I quickly discovered that there is no optimal size to print images on a standard letter-size sheet for anything other than the 2×3 aspect ratio. For all others, the top/bottom and side borders will be different and, therefore, ugly.
Back to the internet and I soon discovered the answer, apparently conceived long ago in 2010 by an American in Spain, which is to base the size of the borders on the Golden Ratio. I printed a photo to try it and realized that I had found perfection.
Golden Ratio Print Borders
If one sets the ratio of the image area to the area of the borders equal to the Golden Ratio, then the border size will be visually pleasing for any size of image. The Golden Ratio, or divine proportion φ (~1.618:1), is found everywhere in nature and is often considered an aesthetic ideal for design and proportions in visual composition. It has been used for centuries to create harmony and balance in art and architecture including DaVinci’s Last Supper, the Sistine Chapel, and the design of the Parthenon.
Robert Reiser has developed an online Golden Ratio Print Borders calculator, and after experimenting with his calculator for several image sizes, I was sold. Robert sums it up nicely:
The real beauty of the golden ratio approach reveals itself if you look at the resulting ratios. The ratio of the paper area to the picture area is φ, as expected. But additionally, the ratio of the picture area to the border area is φ. And if you have chosen to increase the lower border, the ratio of the lower border to the other borders is also φ.Robert Reiser
Robert’s calculator can be used to calculate the size of the image for a given page size or vice-versa, but is too cumbersome to use for my objective since neither the image aspect ratio nor page size can be set as fixed constraints. I needed a calculator to determine the maximize size of the printed image at a particular aspect ratio for a given size of paper, e.g., what is the largest 4×5 image that can be printed on 8.5×11” paper according to the Golden Ratio?
Being an engineer, I created my own Golden Ratio print borders calculator, again in Excel, this time using an iterative technique to find the solution. The calculator allows me to enter the aspect ratio of the photo and the page size, then finds the dimensions of the largest size image that can be printed on that size of paper.
So, what is the largest 4×5 image that can be printed on 8.5×11” paper according to the Golden Ratio? The answer is 7.9″ wide and 6.3″ tall with a border of 0.8″ on the top and sides and 1.33″ on the bottom as shown below. The page will have to be trimmed down on one side after printing, but the finished print will be perfectly balanced.
The optimal image size can be calculated using an equal width for all borders or “optically centering” the image by extending the bottom border. I prefer the optically centered print, and again the Golden Ratio provides a pleasing result with the bottom border being 1.618x larger than the others.
I used my calculator to determine the optimal print dimensions for a number of common image aspect ratios (2:3, 4:5, 5:7, 16:9, 1:1) and paper sizes (letter, A3+, and half sizes of each) for both portrait and landscape orientations. These have been compiled into tables to provide a quick reference for use when printing.
Update (November 2023): After finally getting a quality paper cutter (Dahle 18″ guillotine trimmer) to trim my prints, I went through my stack of prints from the last six months and trimmed every print that could be trimmed so that the top and side borders were uniform with the bottom border larger. I am absolutely astounded at the difference that this step makes for a printed photograph. Photos that were previously just randomly printed on a letter-size page now look like they were intentionally printed with specific dimensions. I really cannot overstate the importance of using appropriate borders around printed images.


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Stationary marked point processes : an intuitive approach / Karl Sigman.
By: Sigman, Karl.Material type: BookSeries: Stochastic modeling. Publisher: New York : Chapman & Hall, c1995Description: xiii, 200 p. : ill. ; 24 cm.ISBN: 9780412984310.Subject(s): Point processesDDC classification: 519.232 Online resources: Publisher description https://www.crcpress.com/Stationary-Marked-Point-Processes-An-Intuitive-Approach/Sigman/p/book/9780412984310
|Item type||Current location||Call number||Copy number||Status||Date due|
|Monograph||Indian Institute of Management Udaipur On Display||519.232 (Browse shelf)||1||Available|
Includes bibliographical references (p. -195) and index.
Marked Point Processes
Random Marked Point Processes
An Interlude: Constructing Stationary Versions
Further Topics on Stationarity
Processes Jointly with Marked Point Processes
Applications to Queues
The Space of Marked Point Processes
Taking an applied point of view, this book provides an accessible introduction to the theory of stationary random marked point processes on the non-negative real line. The reader will be able to gain an intuitive understanding of stationary marked point processes and be able to apply the theory to stochastic modeling. The emphasis is on time averages and asymptotic stationarity. Proofs of the main results are given using shift-coupling methods and measure theory is kept to a minimum. Examples and exercises are given involving explicit construction of time and event stationary versions, using the 'inspection paradox' as an intuitive guide. The Rate Conservation Law is given and used in applications to queueing theory. The prerequisites are a background in probability theory and stochastic processes up to conditional expectation.


9 edition of Recursion on the countable functionals found in the catalog.
|Series||Lecture notes in mathematics ; 811, Lecture notes in mathematics (Springer-Verlag) ;, 811.|
|LC Classifications||QA3 .L28 no. 811, QA9.6 .L28 no. 811|
|The Physical Object|
|Pagination||viii, 190 p. ;|
|Number of Pages||190|
|LC Control Number||80019391|
The factorial of any other number is that number multiplied by the factorial of the number one less than it. Scholz, "Recursion and the Infinitude Claim. The computer keeps function calls on a stack and once too many are called without ending, the program will crash. Why not write a program to see how many times the function is called before the program terminates?
Indices and Enumerations. It can also apply to intransitive verbs, transitive verbs, or ditransitive verbs. Note: this is a brute force approach. Haskell decides which function definition to use by starting at the top and picking the first one that matches.
It takes an extra argument, res, which is used as an accumulating parameter to build up the final result. In the case of the program, a boolean flag "seen" or "visited" should be used. A procedure is a set of steps based on a set of rules, while the running of a procedure involves actually following the rules and performing the steps. This is very similar to an inductive definition of lists of strings; the difference is that this definition specifies how to access the contents of the data structure—namely, via the accessor functions head and tail—and what those contents may be, whereas the inductive definition specifies how to create the structure and what it may be created from.
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Haskell decides which function definition to use by starting at the Recursion on the countable functionals book and picking the first one that matches. And for every possible door you can move through, the computer remembers those what ifs, and for every door after that, and after that, etc, until the end is found.
The base case says that concatenating the empty list with a list ys is the same as ys itself. Creative Sets and Completeness. Recursive functions in the general sense are functions that are defined in a recursive way, like recurrence relations are sequences that are defined in a recursive Recursion on the countable functionals book or recursive data structures are data structures that are defined in a recursive way.
It can also apply to intransitive verbs, transitive verbs, or ditransitive verbs. The answer is we don't but we can let the computer figure it out for us. In all these cases of recursion we have countable many instances and the definition includes one or more base instances and a way to define new instances from existing instances.
Recursion Recursion means "defining a problem in terms of itself". It is not unusual for such books to include a joke entry in their glossary along the lines of: Recursion, see Recursion.
Thus the two words "recursive" and "recursion" have a completely different meaning. This is more naturally framed as corecursion, building up from the initial values, tracking at each step two successive values — see corecursion: examples. Morrison, He's Just a Friend.
The Finite Extension Method. The maximum value in a list is either the first number or the biggest of the remaining numbers. In each case, think what the base case would be, then think what the general case would look like, in terms of everything smaller than it.
So when it comes time to evaluate fib 6we are going to evaluate fib 5 over again, and then evaluate fib 4 even more times. Of course, it must be possible for the "process" to sometimes be completed without the recursive call.
However, you can always translate a loop into an equivalent recursive form by making each loop variable into an argument of a recursive function. Note The factorial function above is best defined in a file, but since it is a small function, it is feasible to write it in GHCi as a one-liner.
Tail recursive algorithms can be directly translated Recursion on the countable functionals book loops. For this reason, recursive definitions are very rare in everyday situations. What if I take the first door, what if I take the second door, what if I take the Recursion on the countable functionals book door, etc.
Chains of three or more functions are possible; for example, function 1 calls function 2, function 2 calls function 3, and function 3 calls function 1 again. The word and, for example, can be construed as a function that can apply to sentence meanings to create new sentences, and likewise for noun phrase meanings, verb phrase meanings, and others.
Note that all of these functions are available in Prelude, so you will want to give them different names when testing your definitions in GHCi. Like This Article? How do we know if a door leads out of the maze?Don't use recursion for factorials or Fibonacci numbers.
One problem with computer-science textbooks is that they present silly examples of recursion. The typical examples are computing a factorial or computing a Fibonacci sequence. Recursion is a powerful tool, and it's really dumb to use it in either of those cases.
In the book  and the series of papers [a, b, c, ] Tucker and Zucker explore several other notions of computability over abstract algebras. Among other topics these works consider versions of μ-recursion, while-programs, semi-computability, flow charts, infinitary quantifier-free definability, and computable functionals.
Recursion is often closer to the underlying mathematics • There is a mechanical means to convert recursion to iteration, used by compilers and algorithm designers. It s complex, and is used to improve efficiency – Overhead of method calls is sometimes noticeable, and converting recursion to iteration can speed up execution.
Exercise 1 •.Many functions pdf use a for statement can be rewritten so they use pdf instead. But does it always make sense to use that approach? No. The example here is not an ideal one, because it causes the program to store all the values 1 through n on the stack, rather than totaling them up directly in a loop.Recursion is often closer to the underlying mathematics • There is download pdf mechanical means to convert recursion to iteration, used by compilers and algorithm designers.
It s complex, and is used to improve efficiency – Overhead of method calls is sometimes noticeable, and converting recursion to iteration can speed up execution. Exercise 1 •.Many functions that use a for statement can ebook rewritten so they use recursion instead.
Ebook does it always make sense to use that approach? No. The example here is not an ideal one, because it causes the program to store all the values 1 through n on the stack, rather than totaling them up directly in a loop.


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By Inder K. Rana
Integration is without doubt one of the cornerstones of research. because the basic paintings of Lebesgue, integration has been interpreted when it comes to degree thought. This introductory textual content begins with the old improvement of the suggestion of the critical and a assessment of the Riemann indispensable. From the following, the reader is of course ended in the distinction of the Lebesgue imperative, the place summary integration is constructed through degree idea. the real simple themes are all lined: the basic Theorem of Calculus, Fubini's Theorem, $L_p$ areas, the Radon-Nikodym Theorem, switch of variables formulation, and so forth. The e-book is written in an off-the-cuff sort to make the subject material simply obtainable. techniques are constructed with the aid of motivating examples, probing questions, and lots of workouts. it'd be appropriate as a textbook for an introductory path at the subject or for self-study. For this variation, extra routines and 4 appendices were additional.
Read Online or Download An introduction to measure and integration PDF
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This booklet is to begin with designed as a textual content for the path often known as "theory of services of a true variable". This path is at this time cus tomarily provided as a primary or moment 12 months graduate path in usa universities, even though there are symptoms that this kind of research will quickly penetrate higher department undergraduate curricula.
Extra info for An introduction to measure and integration
Time to haul out your calculator. ) choices for a and b. What are they? 6: This all in hand, what is the conclusion telling us? ” If we specify to our particular situation (insert our particular f , a, and b) this means . . 7: Is your intuition satisﬁed that x as claimed exists? Can you approximate its value? (“SOLVE” on your calculator might yield x such that f (x) = 0, but x is not in the interval (a, b). As far as the conclusion of the theorem goes, that isn’t of interest. The theorem gives a point in the open interval, so you have to ﬁnd that one (or ones?
And doesn’t attempt to say anything about why the trip was made. But it’s easy to remember and captures the theorem quite precisely. 13: Repeat the work above with f deﬁned by f (x) = ex − xe−x − 2. 2 Also, if trying x3 hinted at of another version of the theorem, hold that (good) thought. 2 43 Why These Hypotheses? We now have some understanding of what the theorem means. However, the examples above don’t make it clear whether the continuity assumption is important. Could we guarantee the same conclusion without assuming continuity of the function on the closed interval (either assuming no continuity, or perhaps only continuity on the open interval (a, b))?
Explore with some more functions. Can you construct an example of a function with a right-hand limit of 5 at the point x = 3? Right-hand limit 5 and left-hand limit 2 at the point 3? Right-hand limit 5 and with no limit? A function with right-hand limit 5 and with no left-hand limit? A function with neither right-hand nor left-hand limit? 22, continued) Armed with the preceding deﬁnitions, we may give the following. 4 We say that f is continuous on [a, b] if f is continuous at each point of (a, b), limx→b− f (x) = f (b), and limx→a+ f (x) = f (a).


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Let’s look at a few techniques for efficiently calculating percentage scores in Excel and learn the basic percentage formulas that will make it a breeze.
A percentage is a fraction of one hundred that is calculated by dividing the numerator by the denominator and multiplying the result by one hundred.
Excel Basic Percentage Formula
In Excel, the basic percentage calculation formula is:
Percentage = Part/Total
In Excel, you don’t need to multiply the factor by 100 because Excel does it for you.
For much more easier ways to calculate your percentage,
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Thank you for your reply.
we haven't used any log.
for the DFA or Linear regression I never have to use log to make the prediction equation. I only use continuous data in my own research so I'm a bit at a loss of how to use the transformed variables and come up with the predictive value.
all the best
Dear RickThis is very useful. I am still confused what she needs to use as values in the prediction equation. It is usual in our field to publish a prediction equation for others to use on their own data. So another scientist will need to use his/her own scores to solve the equation and the value will then be the sex estimate. If I understand it well:So if we take the example from the link you sent, there were originally 4 categories for the REGION - these have now been turned into region 1, region 2, region 3, and the reference "region" (for those from the 4th category)? Region does not have a coefficient because it is the reference so this will never appear in the equation and individuals who were in the reference category will thus always use a value of 0 if region 1,2 or 3 appears in it? REGIONREGION(1) 2.549343REGION(2) 2.019601REGION(3) -.281382So, if the equation has an individual from region 2, then we replace the value of region 2 with value "1" and replace region 1 and 3 with value "0"? In our example this would look like: sex = 75.8 + (-57.296*1) + (-37.333*0) + (-18.504*1) + (-55.213*0) + (38.256*0) + (-57.519*1) + (-1.946*0) We then insert the value of sex (z) into this equation: 1/(1 + EXP(-z)) this should return a value between 1 and 0?Thank you!Isabelle


Blackjack is one of the most popular classic casino games, and players can count on excellent odds. It features a low house edge, and it is one of the most attractive aspects for blackjack players. You can increase your chances of winning thanks to your skills, not only by relying on luck. Therefore, a proper strategy and skills can make a real difference between losing and winning. That is another reason why blackjack is so famous in casinos. The ability to predict the likelihood of receiving a certain card can bring you an advantage over a dealer. In this article, we will deal with the blackjack probability and ways you can increase your chances of winning in an online casino.
- It can help you develop proper strategies
- Calculate the probability of losing streaks
- Estimate how a removed card can affect your odds
- Blackjack probability: The mathematics behind the game
- Probabilities of different-length losing streaks in blackjack
- The house edge for blackjack under review
- How card removal influences blackjack odds and probabilities
- Expected hourly loss and/or win
- The blackjack basic strategy: Does it work online?
- Try It Out in Practice
Blackjack probability: The mathematics behind the game
If you can calculate the chances of getting a “small” or “big” card, it can help you make better decisions. For being successful in the long run, knowing the house edge and the odds is not enough. You should have a reliable plan and establish a proper strategy to get better results. Some players rely on card counting techniques such as speed count, but you can use probability as your weapon.
Probability deals with the likelihood of a particular event, and it is a very popular branch of mathematics. It applies to many industries, and it became inevitable in the casino world for performing casino games analyses. The probability formula is the foundation for determining the outcome of an event, and it is a ratio between the number of paths and possible events.
Thanks to this formula, you can easily determine the probability of getting the ace of spades. Knowing that there is only one card of that kind in the deck and that the standard card deck contains 52 cards, the probability of getting it is 1/52, or 1.92%. The likelihood of any event is between 0% and 100%, and if you know its exact percentage, you can drive your decisions upon it.
Speaking about blackjack, the following two terms will help you understand the game better. The odds you may get under particular circumstances during the game are known as the positive and negative expected win rates. Professional blackjack players also speak of another term – true odds. It is the case when the probability percentage matches the payout of a particular bet.
If you know your chances of winning, you can easily determine the probability of losing the game as well. This can provide you a good insight into a position you are currently in. For example, your chances of losing when having a total of 12, 13, or 14 in hand are 31%, 39%, and 56%, respectively. Of course, when you have 11 or fewer, your chances of losing are equal to zero.
Remember, your ultimate goal in a blackjack game is to beat the dealer by getting a higher total. However, you should pay attention not to go over 21, as you will lose. As you have two options during gameplay, hitting and standing, the probability can help you make a better decision for the next move.
This drives to a conclusion that the chances of busting increase when having a higher total in your hands. Consequently, when you have 19 or 20 in your hands, you will likely lose if hitting another card. Therefore, standing would be a much better option in this case. If you wonder what the probability of getting a blackjack is, we have an answer. The figure stands at 4.77% for the two-decks game, while the chances are slightly higher for a single-deck blackjack game – 4.83%.
Probabilities of different-length losing streaks in blackjack
As blackjack is the game with one of the lowest house edges, your chances of winning each hand are just below 50%. However, that doesn’t mean that winning or losing streaks are impossible. Of course, entering a winning streak is every blackjack player’s goal, but what about having a bad run?
The math says that the majority of streaks last up to three hands. Therefore, losing four times in a row or more is, statistically speaking, less possible. However, it doesn’t mean they cannot happen despite the low probability. Let’s check the blackjack probability table of losing streaks based on the streak length.
|Streak Length||Probability of a Losing Streak|
As we can see, the probability of losing five straight hands is as low as 4%, but it will inevitably happen at some point in your gaming experience. Therefore, it is crucial to handle the losing streaks properly. The first thing you should do is start reducing your stakes, so you can extend your budget. Eventually, it can give you more chances of getting back on the winning track. On the other hand, chasing losses is what you should avoid at all times. This way, you will not damage your bankroll even more and run out of your playing funds quickly.
Taking a break after five lost hands might be a sound choice as well. It can help you collect your thoughts and get back on the winning track. Remember, the ultimate goal is generating profits, so it’s not a shame to walk away from the game.
The house edge for blackjack under review
The concept of a house edge shouldn’t be underestimated when calculating your odds of winning a blackjack game. The house edge represents the built-in advantage that casinos have over players, ensuring they win in the long term. In other words, it is the percentage of each bet that a casino keeps as a profit, indicated in a long period.
The house edge is not the same for different variants of a blackjack game. For example, if the house edge is 1.20%, it means that on every $1000 wagered on that particular game, a casino would theoretically win $12. In other words, a player would lose $1.2 on every $100 wagered.
Other casino games have a considerably higher house edge, like roulette. A double-zero roulette has a 5.26% house edge, meaning that you would lose $5.26 on every $100 wagered. Suppose you spin the wheel 60 times per hour, it means you would lose more than $300 per hour. Of course, this is just a statistical percentage measured in the long run, and it doesn’t imply that every player would lose this amount of money.
How card removal influences blackjack odds and probabilities
Card removals can affect your odds of winning a hand in both directions. Particular card removals can increase the house edge but also boost your chances of winning. Generally speaking, the odds increase in your favor if smaller cards are removed from the deck. On the other hand, your chances of winning decrease when a larger card is dealt. Some people use card counting to estimate better their chances of winning. If you want to try it out, here is a table of the odds movements for each removed card.
|Removed Card||Odds movement|
Expected hourly loss and/or win
Another convenient metric that can help you estimate how much money you can win or lose over a more extended period is the Expected hourly loss/win. Of course, it can only give you insights into the estimated figures, which doesn’t necessarily mean it will happen. Also, the results may hugely vary for a small number of sessions. Let’s see how this works on a practical example.
- You are a perfect basic strategy player in a game with a 0.5% house edge.
- Your stake is $100 per hand, and you’re averaging 40 hands per hour.
- You stake $4,000 per hour
- 0.5% of $4,000 is $20.
- Your expected losses are $20 per hour.
If you are a skilled card counter, the estimation might be different.
- You can get a 1% edge over the casino by counting cards.
- You’re playing the same 40 hands per hour at $100 per hand.
- You stake $4,000 per hour
- 1% of $4,000 is $40.
- In this case, your estimated winnings are $40 per hour.
The blackjack basic strategy: Does it work online?
The Basic Blackjack Strategy is essential if you want to be successful in this game. Back in the ’50s, a group of mathematicians developed the basic strategy to help players optimize their decisions. Again, it relies on the probability and calculates which player’s decision is optimal at a certain point to generate profits. Therefore, it prevents you from making irrational decisions at a blackjack table, which is exactly what an online casino hopes you would do. Thanks to the blackjack probability charts that basic strategy provides, you can easily see what would be your optimal move in a given situation.
Since blackjack is a game of skill and not just a pure game of chance, this strategy works online as well. Of course, this strategy can help you become more successful in your blackjack gaming experience, but it doesn’t guarantee you profits. You should also make sure to use the correct basic strategy developed for specific blackjack rules. Although it cannot guarantee you profits, a basic blackjack strategy can help you lower the house edge.
Try It Out in Practice
As we already stated, understanding how the maths work in the blackjack game can increase your chances of winning. At this point, you should apply everything you learned from this article in practice. Sign up for one of our recommended online casinos, apply your strategy, and start winning at a blackjack table!


Top ten revision tips for a GCSE maths exam
|Date Added: December 01, 2011 04:19:24 PM|
The following tips can be used by anyone studying mathematics at GCSE level, and in particular revising for a maths exam.
1. Schedule your revision time; use a calendar to mark off which days you will be revising maths and allow yourself enough time to revise. Work out how many hours you can spend each day on revision, and set yourself targets for total hours of maths study. Mark off milestones in your revision as you complete them.
2. Break the maths into main topics you need to revise. For example, algebra might be one topic, trigonometry might be another topic, and statistics and probability might be another topic. Check the GCSE maths syllabus and also with your teacher to categorise the main topics you need to revise.
3. Make sure you have a studying and revision environment – a study room with no distractions, no TV, no music, no noise from family or friends. This can be difficult if you’re revising in the house but if you let others know that you’re revising for your maths exam, and that you need to be left alone, this should be easier. Of course an even better option is to use the library to study since you’re guaranteed peace and quiet.
4. Start revising early in the day. Maths revision is very difficult if you are stressed or find yourself rushing to complete targets. It’s also a great idea to start your maths revision ahead of schedule if possible. This gives you some extra slack should you need it later on.
5. Start small then build up. Tackle the basics first. Some parts of the GCSE maths curriculum will come easier to you than others. It’s a good idea to revise these first, give yourself confidence before tackling the more difficult topics. Break the difficult topics into smaller sections and tackle these one by one rather than trying to learn everything at once. Trust your memory. Once you’ve revised a topic thoroughly, move on to the next. Don’t keep testing your memory on the same subject.
6. Make use of maths revision guides and GCSE maths revision books. Check the syllabus to make sure you use the right books. There’s also lots of great information available online in the form of maths revision websites or videos. Highlight essential points to learn, underline key facts and formulas.
7. Use GCSE maths past papers. Ask your maths teacher if you’re unable to get hold of them. These can really help focus your mind on the kinds of questions you might have to tackle in an exam. Near the end of your revision schedule, try to complete one or two of these past papers in the allowed time frame. This will give you an idea of how you’ll handle the exam on the actual day and give you more confidence going into it.
8. Take regular breaks and reward yourself. Nobody can concentrate on any one subject let alone GCSE maths for too long before they burn out. Give yourself time limits and then take a break. Get up and have a snack, do something else, and leave the area of study. It’s better to have a few small breaks than to have one long break (this can make it difficult to start revising again, and refocus on study).
9. Make sure you look after yourself while you’re studying for GCSE maths exams. Get plenty of sleep, this is crucial. Do not attempt to cram hours of study into a day, doing an all-nighter will tire you out for the next day’s revision and won’t make you remember any better. Don’t deny yourself a healthy diet – get plenty to eat and drink during revision. Too much tea, coffee or caffeine drinks can increase your anxiety and are a recipe for insomnia.10. Revise with others. Organise a study or revision group. Sometimes it helps to bounce thoughts and ideas of your peers. Share your worries and concerns with your friends and practice some questions with them. If needed, you might also consider hiring a private maths tutor and this can really help give you more confidence before the exam.


|Size (L x W x H)||14 cm x 1 cm x 20.3 cm|
This product has a maximum quantity of 20
During summer vacation in his second year of high school, math genius Kenji is offered a job by Natsuki, his senpai (and secret crush). That job is to go with her to her great-grandmother's house in the countryside – and pretend to be her fiance?!
After managing to survive the first day of dealing with 27 of Natsuki's relatives, Kenji receives a mysterious e-mail with a math problem. Unable to resist, Kenji replies with the solution to the equation. Little does he know that this will trigger a catastrophe...


Precalculus homework help
Dezember 3, 2017 —
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Simpson’s Rule Calculator
Simpson’s rule calculator’s main application is to find the approximate area under a graph. It can find the closest value of the area of a definite integral.
This tool is a Simpson ⅓ rule calculator due to the fact that it uses quadratic functions to find approximations.
The graph of the function with the labeled divisions is also displayed along with the answer. Moreover, this graph can be zoomed in and out.
How to use this Simpson’s rule calculator?
This calculator is simple to use. You will have to:
- Enter the function in the required area.
- Input the values of a and b i.e start point and endpoint of the curve for the area.
- Put the n value.
- Click calculate.
- The result will appear on the screen in a fraction of a second.
What is Simpson's rule?
Simpson’s Rule is another method to estimate the area of a nonlinear graph like the left and right Riemann’s sum and Midpoints sum.
It is an algorithmic application of the 1-4-1 quadratic approximation which finds the best fitting parabolas instead of rectangles. This approximation can be applied to the signed areas as well.
Derivation of Simpson’s rule: Simpson’s formula
As mentioned before, Simpson's rule originates from the quadratic approximation. So, before heading ahead, let’s review what it means.
Divide a graph into equally spaced sample points at the end and the middle let's say of the half-width h.
Now, this division can help to find the function values or the y-axis values i.e YL, YC and YR required in the formula. When these four values are used then the area under the quadratic curve that passes through these points can be expressed as
= h/3 (yL + 4yC + yR)
This is approximately equal to the area under the curve as well.
Now, the example discussed above is a simple and ideal one. Not every curve is sleek and smooth like this. If we apply it on irregular graphs, it will tell an extremely inaccurate value of the area. For example, see this graph below.
So to find the area under some irregular graph, we cannot apply the quadratic approximation one time. Instead, we divide it into a suitable number of curves so that each curve can give a decent estimation of the parabolic area under it.
For instance, have a look at this graph
Let's say you are interested in finding the definite integral for this curve between point a and point b.
The goal is to use the approximation repeatedly on this function to get the area estimation. Secondly, we will make subdivisions of equal length to ensure that “half widths” are uniform.
Lastly, Subintervals that we denote with n, have to be in even numbers for the application of the 1-4-1 approximation.
Now that we have gone over the fundamentals, it is time to divide this graph. We will assume a general situation without any defined domain.
Start labeling the endpoint from \(x_0,\:x_1\) and so on to \(\) and \(x_n\).
After that, we will let the common half-width be Δx.
Note: In this graph, black lines represent the divisions of the parabolic curves and the orange lines are subdivisions.
Now, is the time to apply the quadratic approximation. For the first pair of subintervals, we have
It is explained as half-width divided by 3 into the sum of the left-hand function value, center function value, and right-hand function value.
For the second pair, our contribution is:
And then the third.
Now if we add all three expressions, the sum will be:
The delta x over 3 is taken as common. One can notice that certain values like f(x2) contribute to each other and make 2f(x2). Moreover, there is a certain pattern of coefficients i.e 1,4,2,4,2,4,1.
So going back to the general case, the summed expression will be:
There are pairs of 4 and 2 all over, internally. The first and last single values make a pair. So only the second last value (n-1) is left alone. It means there are odd numbers of values.
This is Simpson's rule.
To find delta x, minus the endpoint from the starting point of the curve and divide by n.
How to apply Simpson’s rule?
The best way to apply Simpson’s rule is to use an online tool like the calculator above. If you don't have access to any tool then read the steps coming up ahead to learn to apply Simpson's rule manually.
If the graph is given, then
- Analyze the graph to divide it into a fair even number of uniform subdivisions to vaguely cover the whole area between points.
- Name the divisions and apply the pattern of the coefficients.
- Multiply the whole thing by delta x over 3.
If the value of n is given, then
- Find the Δx as taught before.
- Use the Δx to make the subdivision. Must be in an odd number!
- Apply the pattern and multiply with Δx/3 as before.
Apply Simpson's rule on the function below and find the error as well.
n = 6
Step 1: Find Δx.
Step 2: Divide the intervals [1,4] into n=6 subintervals with the length Δx=0.5.
a = 1, 1.5, 2, 2.5, 3, 3.5, 4
Step 3: Evaluate the function at these endpoints.
f(x0) = f(1) = 12 + 4 = 5
4f(x1) = 4f(1.5) = 4(1.52 + 4) = 25
2f(x2) = 2f(2) = 2(22 + 4) = 16
4f(x3) = 4f(2.5) = 4(2.52 + 4) = 41
2f(x4) = 2f(3) = 2(32 + 4) = 26
4f(x5) = 4f(3.5) = 4(3.52 + 4) = 65
f(x6) = f(4) = 42 + 4 = 20
Step 4: Add these values.
= 5 + 25 + 16 + 41 + 26 + 65 + 20
Step 5: Multiply with Δx/3.
= 0.5/3 (198)
Step 6: Find the definite integral.
Step 7: Find the error by subtracting the integral value from the approximation value and also dividing it by the integral value.
= (33 - 33) / 33
This is one of those rare cases where integral value and Simpson's rule value are the same.


Thomas Schwarz is a Jesuit priest and is currently an associate professor in the Department of Mathematical and Statistical Sciences and the Department of Computer Science. Previously, he was an associate professor in the Department of Computer Engineering at Santa Clara University before spending 5 years teaching in Latin America at the Universidad Católica del Uruguay and at the Universidad Centro-Americana in El Salvador.
Schwarz holds two doctorates, one in Mathematics from the Fernuniversität Hagen (1984) and one in Computer Science from the University of California (1994). He has more than 100 publications in mathematics and computer science.
His research interests are in distributed systems and in particular large storage systems. He is very interested in collaboration with Jesuit institutions around the work.


“International Millennium Research Award” in the fields of Pure Mathematics & Theoretical Physics
Pediredla Suhaas is a pure mathematician and theoretical physicist who conducts heavy research in the fields of pure mathematics and theoretical physics. He has authored and published a total of more than 10 international mathematics and physics research papers. At the age of 15, he invented and proved a mathematical paradox, known as the “Suhaas Paradox” (which is named after him as an honor), in 4 sequential research papers published by the publisher Elsevier BV. At the age of 16, he published 3 more papers, in one of which he proposed a complete mathematical proof and solution to the “Riemann Hypothesis” (a 164-year-old unsolved problem, widely considered to be the greatest unsolved mathematical problem in the world and one of the Millennium Problems), while in the other paper, he proposed complete proofs and solutions to all the 7 “Millennium Problems” (the top 7 greatest unsolved mathematical problems in the world, for which the Clay Mathematics Institute pledged a $1 million prize for the first correct solution to each problem) using physics. In his third paper, he proposed a new complete theory on the existence and nature of black holes, white holes, and wormholes, which he invented when he was just 14 years old. At the age of 17, he published a research paper in which he invented and proved 32 new trigonometric theorems. Also, he published a research paper in which he proposed a complete solution to the time travel paradox. After that, he published another research paper in which he invented and proved the most advanced and complex generalizations of the Riemann zeta function, Dirichlet eta function, and Bernoulli numbers. He later published another paper in which he discussed and explained the classical ways of deriving and proving Einstein’s famous equation, E=mc2. He received appreciation and offers from many researchers and publishers for his research. He won the “International Best Researcher Award” at IISTAC 2022 in the fields of pure mathematics and theoretical physics. He was honored with a lifetime membership in the World Research Council. He also won the prestigious “Indian Achievers’ Award” in recognition for his outstanding achievements and contributions toward nation-building. He won the prestigious “Global Kids Achievers Award 2022” (given to the top 100 child prodigies in the world) in the field of intelligence and got his name published in 50+ national and international news media like ANI, The Print, Hindustan Times, Zee5 News, etc. He also won the “Super Talented Kid Award (One in a Million)” and the “Star Kid Award” under the title “Super Genius Kid” for his intelligence and excellence in the field of academics. He received an appreciation letter from the World Book of Records, as they were greatly inspired by his achievements and contributions. He holds 9 world records in the International Book of Records and nearly 300 awards and honors in the fields of mathematics, science, and technology. He scored an IQ of 153 (out of a maximum possible score of 160) in a certified IQ test at the age of 16. He has nearly 48 professional certifications and specializations from top American and international universities like Harvard University, Stanford University, the Massachusetts Institute of Technology (MIT), etc. He represented India and won a total of 15 gold, 8 silver, and 9 bronze medals in international and national mathematics, science, and computer science Olympiads.


[caption id="attachment_226427" align="aligncenter" width="700"]
Children differ substantially in their mathematical abilities. But, some may remain persistently bad at addition or subtraction as a result of abnormalities in the brain areas supporting procedural memory.[/caption]
Children differ substantially in their mathematical abilities. But, some may remain persistently bad at addition or subtraction as a result of abnormalities in the brain areas supporting procedural memory, a study that developed a theory of how developmental "math disability" occurs has revealed.
Procedural memory is a learning and memory system that is crucial for the automatisation of non-conscious skills, such as driving or grammar and depends on a network of brain structures, including the basal ganglia and regions in the frontal and parietal lobes, the study said.
"Various domains, including math, reading, and language, seems to depend on both procedural as well as declarative memory -- where conscious knowledge is learned," said Michael T. Ullman, Professor at the Georgetown University in the US.
"However, for some children with math disability, procedural memory may be dysfunctioned, so math skills may not get automatised," added lead author Tanya M. Evans, postdoctoral student at the Stanford University in the US.
In fact, the aspects of math that tend to be automatised, such as arithmetic, are more problematic in children with math disability.
Evidence suggests that when procedural memory is impaired, children may have math disability, dyslexia, or developmental language disorder, though declarative memory -- where conscious knowledge is learned -- often compensates to some extent," Ullman said.
The researchers said that their theory, called the procedural deficit hypothesis of math disability, "offers a powerful, brain-based approach for understanding the disorder, and could help guide future research."
"We believe that understanding the role of memory systems in these disorders should lead to diagnostic advances and possible targets for interventions," Ullman noted, in the paper published in the journal Frontiers in Psychology.