Prof Patricia Eaton
- I am responsible for all teaching and learning within the College and continue to teach mathematics education at undergraduate level and supervise dissertations up to Master’s level.
External Interests / Community Service
- Fellow of the Leadership Foundation
- Member of Institute of Mathematics and its Applications (and formerly Chair of Irish Branch)
- Fellow of the Higher Education Academy
- Member of the Mathematics Association
- External Examiner in Mathematics education
- Mathematics and mathematics education
- Diversity and inclusion and community relations.
Background & Qualifications
- 1991 B.Sc. Pure Mathematics, First Class Honours, Queen’s University, Belfast
- 1994 Ph.D. Pure Mathematics, Queen’s University, Belfast
- 1995 P.G.C.E. Mathematics with IT (Commendation) Queen’s University, Belfast
- I taught mathematics at post-primary for a number of years before joining the staff of the College.
Research & Scholarship
McMullen, J.D. & Eaton, P. (2020). ‘The Impact of a School-based Life Skills Intervention in Ugandan Secondary Schools: Perspectives of Teachers and Students.’ Pastoral Care in Education,
Hagan, M., and Eaton, P. (2020) ‘Teacher Education in Northern Ireland: Reasons to be Cheerful or a Wicked Problem?’ Teacher Development, DOI: 10.1080/13664530.2020.1751260
Moffett, P. & Eaton, P. (2018) The impact of the Promoting Early Number Talk project on the development of abstract representation in mathematics. European Early Childhood Education Research Journal https://doi.org/10.1080/1350293X.2018.1487166
Moffett, P. & Eaton, P. (2017): The impact of the Promoting Early Number Talk project on classroom mathematics talk, Early Child Development and Care: https://doi.org/10.1080/03004430.2017.1412954
Eaton, P., McKenzie, L., McCracken, O., Richardson N. (2015) Teachers’ Reflections on Community Relations and Diversity: A Northern Irish Perspective The International Journal of Diversity in Education, Volume 16, Issue 1 pp 1-14
Conference proceedings and papers
Eaton, P., Horn, C., Oldham, E. & O’Reilly, M. (2019) ‘Reflections on the Development and Application of an Instrument to Access Mathematical Identity’ Presented at CERME 11 2019, Utrecht, Holland.
Eaton, P., Horn, C., Liston, M., Oldham, E. & O’Reilly, M. (2015) ‘The Collaborative Learning of Student Teachers: An insight from a study of mathematical identity’ Presented at ATEE (Association for Teacher Education in Europe) 2015, Glasgow, UK
Eaton, P., Horn, C., Liston, M., Oldham, E. & O’Reilly, M. (2015) ‘Using Narrative to Access Mathematical Identity: An overview informed by an empirical study in five third level institutions in Ireland British Society for Research into Learning Mathematics (BSRLM),’ Mathematics Education Ireland (MEI) Joint Conference, St. Patrick’s Drumcondra, 27 – 28 February 2015
Eaton, P., Horn, C., Liston, M., Oldham, E., OReilly M. (2014) From learner to teacher: using reflection to develop mathematical teacher identity, Proceedings of ATEE 2014, University of Minho, Braga, Portugal
Eaton, P., McKenzie, L., McCracken, O., Richardson, N. (2014) Teachers’ Reflections on Community Relations and Diversity: A Northern Irish Perspective, Paper presented at Fourteenth International Conference on Diversity in Organizations, Communities, and Nations, Institute for Gender and Diversity in Organizations, Vienna University of Economics and Business, Vienna, Austria
Hagan, M., Eaton, P. (2014) Professionalism’ and the Governance of Teacher Education: a Northern Irish Perspective, Paper presented at UK symposium at ECER 2014, University of Porto, Portugal


The passion of 1 teacher has impacted over 50,000 through STEM education. Imagine how the Passion of 50,000 can impact the world of STEM. Through C-STEM we have discovered 67% of C-STEM students enjoy working on projects that connect art and math, and 73% of C-STEM students enjoy working on projects that connect art and science. That is why C-STEM is so important to America’s classrooms. Every child deserves to go to school and experience STEM (science, technology, engineering, and mathematics) through hands on exploration and discovery. Don’t just imagine a brighter STEM future for children. Be the change you want to see..


- How do you calculate the average between two numbers in Excel?
- How do you find a number from a range in Excel?
- What is difference between Countif and Countifs?
- What is the formula of discount?
- How do you reverse a percentage formula?
- How do you find a number between two numbers in Excel?
- How do I find the median?
- How do you find the percentage of an area?
- How do I find the percentage of two numbers in Excel?
- How do I calculate a percentage between two numbers?
- What is percentage formula?
- What is the formula to calculate percentage?
- What percent is 2 out of 48?
- How do you create an IF formula in Excel?
- What is the formula for average?
- How do I find the percentage of two numbers without a calculator?
- How do I do a percentage formula in Excel?
How do you calculate the average between two numbers in Excel?
AutoSum lets you find the average in a column or row of numbers where there are no blank cells.Click a cell below the column or to the right of the row of the numbers for which you want to find the average.On the HOME tab, click the arrow next to AutoSum > Average, and then press Enter..
How do you find a number from a range in Excel?
Enter formula =IF(COUNTIF(A1:E8,”new”),”Yes”,”No”) into the Formula Bar, and then press the Enter key. Notes: 1. In the formula, A1:E8 is the range you want to find certain number or value inside.
What is difference between Countif and Countifs?
The difference is that COUNTIF is designed for counting cells with a single condition in one range, whereas COUNTIFS can evaluate different criteria in the same or in different ranges.
What is the formula of discount?
The first step of the primary method is to use the formula S = p – rp, where S = sale price, r = discount percentage rate, and p = the original price. Using the alternative method, you look at the remaining percent of the price you’d be paying; for example, 90% is left if 10% is taken off.
How do you reverse a percentage formula?
Reverse percentagesEither add/subtract the percentage given in the problem from 100% to determine what percentage we have.Find 1% by dividing by percentage found in previous step.Find 100% (original amount) by multiplying your answer in step 2 by 100.
How do you find a number between two numbers in Excel?
IF statement between two numbers=IF(AND(C6>=C8,C6<=C9),C11,C12)Step 1: Put the number you want to test in cell C6 (150).Step 2: Put the criteria in cells C8 and C9 (100 and 999).Step 3: Put the results if true or false in cells C11 and C12 (100 and 0).Step 4: Type the formula =IF(AND(C6>=C8,C6<=C9),C11,C12).
How do I find the median?
MedianArrange your numbers in numerical order.Count how many numbers you have.If you have an odd number, divide by 2 and round up to get the position of the median number.If you have an even number, divide by 2. Go to the number in that position and average it with the number in the next higher position to get the median.
How do you find the percentage of an area?
Find the percentage of a portion of an object by dividing the area of the portion by the area of the whole original object. Multiply the length times the width of the original piece to calculate its area in square inches, feet or centimeters.
How do I find the percentage of two numbers in Excel?
Enter the formula =C2/B2 in cell D2, and copy it down to as many rows as you need. Click the Percent Style button (Home tab > Number group) to display the resulting decimal fractions as percentages. Remember to increase the number of decimal places if needed, as explained in Percentage tips. Done! : )
How do I calculate a percentage between two numbers?
Percentage Change | Increase and DecreaseFirst: work out the difference (increase) between the two numbers you are comparing.Increase = New Number – Original Number.Then: divide the increase by the original number and multiply the answer by 100.% increase = Increase ÷ Original Number × 100.More items…
What is percentage formula?
Formula to Calculate Percentage The Percentage Formula is given as, Percentage = (Value ⁄ Total Value) × 100.
What is the formula to calculate percentage?
Finding the percentage For this type of problem, you can simply divide the number that you want to turn into a percentage by the whole. So, using this example, you would divide 2 by 5. This equation would give you 0.4. You would then multiply 0.4 by 100 to get 40, or 40%.
What percent is 2 out of 48?
4.166666666667%Convert fraction (ratio) 2 / 48 Answer: 4.166666666667%
How do you create an IF formula in Excel?
To enter your IF Function Arguments,Click the spreadsheet cell where you wish to use the Excel formula.From the Formulas tab, click Insert function…In the Insert Function dialog text box, type “if“.Make sure your cursor is in the Logical_test text box.Click the spreadsheet cell you wish to evaluate.More items…
What is the formula for average?
Average, which is the arithmetic mean, and is calculated by adding a group of numbers and then dividing by the count of those numbers. For example, the average of 2, 3, 3, 5, 7, and 10 is 30 divided by 6, which is 5.
How do I find the percentage of two numbers without a calculator?
If you need to find a percentage of a number, here’s what you do – for example, to find 35% of 240: Divide the number by 10 to find 10%. In this case, 10% is 24. Multiply this number by how many tens are in the percentage you’re looking for – in this case, that’s 3, so you work out 30% to be 24 x 3 = 72.
How do I do a percentage formula in Excel?
To get around this, you can calculate your numbers as percentages first. For example, if you type the formula =10/100 in cell A2, Excel will display the result as 0.1. If you then format that decimal as a percentage, the number will be displayed as 10%, as you ‘d expect.


The app takes complex mathematical problems and breaks them down into simpler components, which users can use to figure out the answer. It works by scanning each part of the problem and providing instant results for each part. The app also gives you hints when you get stuck on difficult math problems.
• Step-by-step explanations for every solution .
The Photomath app shows step-by-step explanations for every solution. The explanations can be viewed at any time and don’t require the user to solve problems again in order to understand how they work.
• Quiz mode: test your knowledge with fun math quizzes!
Play against the Photomath app to test your knowledge of math. The quiz mode includes a wide variety of different types of questions, from basic addition and subtraction problems to more advanced ones such as multiplication and division.
Download Now here:
• Solve advanced equations .
In addition to the simpler calculations, Photomath also offers users the ability to solve equations that require more complex calculations.
• Save your favorite math problems .
Photomath lets you save your favorite solutions for later use. This is especially useful when you are trying to remember a problem and don’t want to spend time searching through hundreds of previously saved answers .
• More than 400,000 math problems
Photomath is able to store over 400,000 different types of math problems. The app is constantly updated with new questions that are added by users all around the world.
An answer isn’t all you’ll get from this free app:
When a problem is selected, the app will display a step-by-step explanation of how to solve it. The explanations can be viewed at any time and don’t require the user to solve problems again in order to understand how they work.
Photpmath can help you with all math topics:
Photomath can also help you with advanced topics: Algebra, arithmetic, Statistics, Calculus/Differential Linear Equations, Advanced Calculus and Probability. Photomath is the only math app that lets you test your knowledge of math against other users. Play a quiz with Photomath and get a score on how well you did!More than 400,000 different types of problems are available in the Photomath database. The questions are always being updated with new questions that are added by users all around the world.
Photomath is a great app for anyone who wants to learn math. It’s easy to use and fun to play with. Photomath is available for free on the App Store and Google Play. Photomath is developed by a team of developers who are passionate about math. This passion shows in the app’s accuracy and flexibility, as well as its ease of use.


When I was going through grade school, we learned how to subtract by borrowing. We learned how to add by counting. It was ok to use your fingers to count when we started, and I still use them occasionally today.
Flash forward a few years and it seems like schools are teaching a whole new language. Is this the math I learned? Drawing counters? What makes this easier? Sure, I get that most people learn how to round to ten first before adding, and it definitely makes things easier and faster, but trying to teach that right from the get-go?
If I, someone who knows and excels in math, have trouble understanding these lessons, then how do the kids handle it? These seem to be such convoluted methods to get to the same answer! Take, for instance, this math paper from a Boing Boing employee’s daughter. Sure, I understand what they’re trying to do here, and it’s a trick we all learn. But starting out with this? Why?
My own children bring home math papers that use the oddest methods for adding and subtracting. My son brought home a math paper about subtraction and had trouble completing it. I tried to explain borrowing to him and he looked at me like I had two heads. Apparently borrowing is no longer taught, instead they use regrouping. They draw pictures to get the answer rather than using mathematics.
Yeah, yeah. In the end, they do subtract, but why the need to draw pictures? Do we not have enough fingers? Can we not use them to figure out every subtraction problem? Regrouping is basically borrowing, but the concept seems so much more convoluted and difficult to explain.
To make matters worse, I tried to explain why he needed to borrow/regroup. “You see, the top number is smaller than the bottom number, so if you subtract them, you’ll get a negative number.” He floored me by asking what a negative number was. Seriously? I tried explaining the number line and while he understood, he explained that the teacher never taught such things.
I fear for our youth’s future. These are simple concepts. What happens when they get to the difficult stuff? Will they start relying on calculators and computers to multiply and divide because it’s “difficult” and they’d have to draw really big pictures?
What is our education system coming to?


Copyright © 2014 by Princeton University Press
Published by Princeton University Press, 41 William Street,
Princeton, New Jersey 08540
In the United Kingdom: Princeton University Press,
6 Oxford Street, Woodstock, Oxfordshire, OX20 1TW
All Rights Reserved
Library of Congress Cataloging-in-Publication Data
Chartier, Timothy P., 1969–
Math bytes : Google bombs, chocolate-covered pi, and other cool bits in
computing / Timothy P. Chartier.
Includes bibliographical references and index.
ISBN 978-0-691-16060-3 (acid-free paper) 1. Mathematics–Popular works.
2. Mathematics–Data processing–Popular works.
3. Computer science–Popular works. I. Title.
British Library Cataloging-in-Publication Data is available
This book has been composed in Minion Pro
Printed on acid-free paper ∞
Typeset by S R Nova Pvt Ltd, Bangalore, India
Printed in the United States of America
1 3 5 7 9 10 8 6 4 2
To Noah and Mikayla,
snuggle up close,
I have math-nificent stories to share
before this day ends,
and then may your dreams lead you
to explore what you learn in new ways.
I await your stories. …
Your First Byte
Two by Two
Plot the Course
Doodling into a Labyrinth
Painting with M&Ms
A Pretty Mathematical Face
Ranking a Googol of Bits
A Byte to Go
Up to the Challenge
“WHY STUDY MATH?” can be a common question about
mathematics. While a variety of answers are possible, seeing
applications of math and how it relates to the world can be
inspiring, motivating, and eye opening. This book discusses
mathematical techniques that can recognize a disguised celebrity
and rank web pages with the roll of a pair of dice. Math also
helps us understand our world. How can poor reviews on Twitter
impact a big budget film’s poor showing on opening weekend?
How are fonts created by computers?
Mathematics has many applications, too many for any book.
The purpose here is to cover and introduce mathematical ideas
that use computing. Some of the ideas were developed by others,
like Google’s PageRank algorithm. Other ideas were developed
specifically for this book, like how to create mazes from
mathematical images created with TSP Art. The goal is to give
the reader a good taste for computing and mathematics (thus a
byte). Still, many ideas are not presented in their full depth with
the mathematical theory or most complex (and robust) approach
(thus a bit of math and computing).
This book is intended for broad audiences. It was developed in
this way. For example, Chapter 6 begins with math and doodling,
which is adapted from content taught to non-majors at Davidson
College. Later in the chapter, the content on the Traveling
Salesman Problem and TSP Art was developed from lectures to
math majors at Davidson College and the University of
Washington. The chapter concludes with the creation of mazes,
which is an application of these ideas developed specifically for
this book. Other chapters have been adapted from ideas
developed in my seminars with the Charlotte Teachers Institute.
As such, teachers should find ideas that align with their curricular
Some sections of this book have been used in my public
presentations in which audiences range from children to adults.
Other sections, like the later portions of Chapter 12 on the theory
of PageRank, tend to appeal to mathematicians. This multileveled
approach is intentional. Given the eclectic collection of ideas, I
imagine a reader can delve into what’s interesting and skim
sections of less interest. Throughout the development of this
book, readers have ranged from self-proclaimed “math haters” to
professors of mathematics. Wherever you, as a reader, fall in this
range, may you enjoy these applications of mathematics and
Throughout the book, you’ll find hands-on activities from using
chocolate to estimating π to computing a trajectory of flight in
Angry Birds. I expect such explorations to be a tasty byte of math
and computing for many readers. If you enjoy these
investigations, I encourage you to view the supplemental
resources for this book at the Princeton University Press website;
My hope is that this book will broaden a reader’s perspective
of how math can be used. So, when someone turns to you and
asks for a reason to study math, you’ll at least have one, if not
several, reasons. Math is used every day. Such applications can
be enjoyed and appreciated even if you simply consider a bit and
a byte of it.
Acknowledgments. First and foremost, I thank Tanya Chartier
who walks this journey with me and affirms choices that lead to
roads less travelled and sometimes possibly even untrodden.
Tanya encouraged me to write the first draft of this book when it
was clearest in my mind during my sabbatical at the University of
Washington in Seattle. Thank you, Tanya, for such wise counsel.
I’m grateful to Melody Chartier for being my first reader as her
input supplied great momentum and the ever-present goal of
reaching a broad audience. I also thank Ron Taylor, Brian McGue,
and Daniel Orr for their readings of the book. I enjoyed
developing the Jay Limo story and chocolate Calculus with Austin
Totty. I’m grateful for the various lunch conversations with Anne
Greenbaum that largely led to our coauthored text  but also
inspired a variety of ideas for this book. I appreciate Davidson
College’s Alan Michael Parker for encouraging me, when I thought
I was done with an earlier draft, to write “my book” with “my
voice.” Having studied mime with Marcel Marceau while I pursued
my doctorate in Applied Mathematics, it seems almost natural to
have written a book that computes π with chocolate, finds math
in a popular video game, and explores math in sports. As such, I
believe this book reflects my journey as a mathematician and
artist. I thank my parents who taught me to apply my learning
beyond preset boundaries and to look for connections in
unexpected areas. Finally, I appreciate the many ways Vickie
Kearn has supported me in this writing process and her guidance,
friendship, and encouragement. It is difficult, if not impossible, to
thank everyone who played a part in this book. To colleagues,
students, and friends, may you see your encouragement and the
results of conversations in these pages.
Your First Byte
MATHEMATICS HELPS CREATE THE LANDSCAPES
on distant planets in the
movies. The web pages listed by a search engine are possible
through mathematical computation. The fonts we use in word
processors result from graphs of functions. These applications use
a computer although each is possible to perform by hand, at least
theoretically. Modern computers have allowed applications of
math to become a seamless part of everyday life.
Before the advent of the digital computer, the only computer
we had to rely on was a person’s mind. Few people possessed the
skill to perform complex computations quickly. Johan Zacharias
Dase (1824–1861) was noted for such skill and could mentally
in 54 seconds, two 20-digit numbers in six minutes, two 40-digit
numbers in 40 minutes, and two 100-digit numbers in 8 hours and
45 minutes. As another example, Leonhard Euler, the most
prolific mathematical writer of all time with over 800 published
papers, was renowned for his phenomenal memory. Such ability
became important during the productive last two decades of his
life, when he was totally blind. He once performed a calculation in
his head to settle an argument between students whose
computations differed in the fiftieth decimal place.
Multiprocessors, in a certain sense, also existed. Gaspard
Riche de Prony calculated massive logarithmic and trigonometric
tables by employing systematic division of mental labor. In one
step of the process, mathematically untrained hairdressers
unemployed after the French Revolution performed only additions
and subtractions. De Prony’s process of calculation inspired
Charles Babbage in the design of his difference engine, which was
an automatic, mechanical calculator operated by the turn of a
crank. The advent of computational machinery added a level of
certainty in comparison to hand calculations. Computing machines
could benefit from parallel calculations, seen in Figure 1.1, much
like de Prony’s calculations did from his team of hairdressers.
Algorithmic advances play a key role in the efficiency of
modern mathematical computing. Consider simulating a galaxy.
Prior to the 1970s, a computer simulating a cluster of 1,000 stars
would compute the attraction of each pair of stars on each other
resulting in 999,000 computations. The motion of a star is
determined by summing the 999 forces tugging on it by other
stars. If a computer calculates this for all 1,000 stars for many
instances in time, the motion of the cluster emerges and we see
how that galaxy evolves over time.
Figure 1.1. Early parallel computing? At least 30 workers at the
Computing Division, Veterans Bureau, in Washington, DC in the
early 1920s used Burroughs electric adding machines to compute
bonuses for World War I veterans.
In the 1970s, a cheaper computation was discovered. The
process begins by pairing each star with its nearest neighbor,
then grouping each pair with its closest pair, and subsequently
clustering each superpair with its nearest neighbor until a single
group remains. The forces are then computed for the groupings on
each level. For our galaxy of 1,000 stars this results in a
simulation that involves 10,000 computations at each step in
SUPERCOMPUTING AND LINEAR SYSTEMS
The U. S. national laboratories house many of the world’s
fastest high performance computers. Such computers enable
sometimes involving billions of variables. One of the fastest
computers in the world (in fact the fastest in June 2010) is
Jaguar (pictured above) housed at Oak Ridge National
Laboratory that can perform 2.3 quadrillion floating-point
operations per second (flops). A flop is a measure of computer
calculations performed per second, similar to the older, simpler
instructions per second.
Algorithmic improvements increase the speed of computation.
Improvements in processor speed make things even faster.
Before 1970, computers performed less than 1 million instructions
per second (MIPS). Today, laptops easily perform over 1,000
times as fast. The Intel®Core i7-990X chip, released in 2011,
operates at 3.46 GHz and reaches 159,000 MIPS. This means
what can be done in a second or less on a computer today would
have taken over 16 minutes by that 1975 mainframe. However,
this assumes we run the same algorithm on both computers.
Suppose we run our modern algorithm (which involves 1/100 as
many computations) and its slower counterpart on the older
mainframe. Now a simulation that takes 6 seconds of
computation on today’s computer would have taken over 2
months of constant computation on the 1975 mainframe.
These types of advances have led to the integral role of
computing in our world, from ATMs to digital watches to home
computers with internet browsers and word processing. In this
book, we’ll apply mathematics to a variety of topics. Computing
will play an important role, sometimes making the application
possible. In reading this book, you should get a taste of how
math and computing influences our world and culture.
enough. In fact, that is
largely what a computer does, and a computer only adds 1s and
0s. Yet, even this most foundational mathematical operation can
be tricky and require attention.
AND SUBTRACTION CAN SEEM EASY
Homer Simpson’s Method
In the 7th season of The Simpsons, Homer has a nightmare in
which he travels into 3D space. In this episode entitled
“Treehouse of Horror VI” as Homer struggles with this newfound
reality, an equation flies past 3D Homer that reads:
Simple enough, unless you happen to remember some fateful
words written in 1637.
It may have been a dark and dreary night in 1637 as Pierre de
Fermat delved deeply into the work Arithmetica written by
Diophantus some 2,000 years prior. Mathematical ideas swirled in
Fermat’s mind until suddenly the numbers fell into an
unmistakable, miraculous pattern. Quickly, he scratched into the
margin of his copy of the ancient work the statement that would
be forever linked with his name:
It is impossible to write a cube as a sum of two cubes, a
fourth power as a sum of two fourth powers, and, in general,
any power beyond the second as a sum of two similar powers.
For this, I have discovered a truly wondrous proof, but … the
margin is too small to contain it.
Let’s look at this statement carefully as it will help us understand
the humor and ingenuity of the equation in Homer’s 3D world. For
any two positive integers, if we take the first number raised to
the third power, then add it to the second number raised to the
third power it will never equal a positive integer raised to the
third power. Written mathematically:
but the cube root of 35 is about 3.27, which isn’t an integer.
Fermat’s statement became known as his Last Theorem and is
stated mathematically as:
Fermat’s Last Theorem For n ≥ 3, there do not exist any
natural numbers x, y and z that satisfy the equation
What did Fermat actually “prove”? He was notorious for making
mathematical claims with little or no justification or proof. By the
1800s, all of Fermat’s statements had been resolved except the
last one written on that fateful night.
On another night in 1994 in New Jersey, Princeton University
professor Andrew Wiles discovered a proof of Fermat’s Last
Theorem. What kind of proof? It called on mathematics that had
not yet been discovered in Fermat’s time. He didn’t write it in the
margin … it took 130 pages.
Many brilliant minds worked on this problem and many
mathematical advances took place even with the failed attempts.
As more mathematicians failed to prove and disprove Fermat’s
statement, the “theorem” grew in its prestige. It turns out the
initial proof even had an error in it—that was corrected. It took
357 years, but Fermat’s Last Theorem was finally indeed proven
to be a theorem. The accomplishment was even headline news,
which is particularly newsworthy when the topic is mathematical.
Now, back to Homer’s dream. Did Homer dream up a counterexample to Fermat’s Last Theorem? Again, his world proposed
Will there be new headlines regarding Homer’s disproving Wiles’
accomplishment? Let’s wait a moment and look carefully at this
equation. Do you notice anything odd about it? Indeed, there is.
The left-hand side of the equation is the sum of an even number
(178212) and an odd number (184112), which will be an odd
number, whatever it happens to be. What about the right-hand
side of the equation? It will be even since it is an even number
raised to a power. Even Homer (hopefully) would recognize that a
number cannot be even and odd at the same time.
So, why include the equation? The humor is evident if you try
testing the equation on some calculators, especially those
available at the time the show originally aired. You can test the
equation by noting if 178212 + 184112 = 192212 then
So, what do you get? On many calculators and even some
computers that use mathematical software, you will find that
results in an answer of 1922.0000000.
What happened? It becomes clearer if you can print out an
additional digit which uncovers that
1921.99999996. Many calculators of the time would have
indicated the equality we just saw.
Pretty clever! Where is all this math coming from in The
Simpsons? It turns out that many of the writers have a
mathematical background. David S. Cohen (a.k.a. David X.
Cohen), writer for The Simpsons and head writer and executive
producer of Futurama, graduated magna cum laude with a
bachelor’s degree in physics from Harvard University and a
master’s degree in computer science from UC Berkeley. Watch
The Simpsons carefully and you’ll see bits of math appearing.
Futurama has even more references to mathematics. To read
about math appearing in these shows, visit .
Now, it is your turn with a challenge problem. They are posed
throughout the book with answers in the back. See how you do. If
Author Tim Chartier Isbn 9780691160603 File size 5MB Year 2014 Pages 152 Language English File format PDF Category Mathematics Book Description: FacebookTwitterGoogle+TumblrDiggMySpaceShare This book provides a fun, hands-on approach to learning how mathematics and computing relate to the world around us and help us to better understand it. How can reposting on Twitter kill a movie’s opening weekend? How can you use mathematics to find your celebrity look-alike? What is Homer Simpson’s method for disproving Fermat’s Last Theorem? Each topic in this refreshingly inviting book illustrates a famous mathematical algorithm or result–such as Google’s PageRank and the traveling salesman problem–and the applications grow more challenging as you progress through the chapters. But don’t worry, helpful solutions are provided each step of the way. Math Bytes shows you how to do calculus using a bag of chocolate chips, and how to prove the Euler characteristic simply by doodling. Generously illustrated in color throughout, this lively and entertaining book also explains how to create fractal landscapes with a roll of the dice, pick a competitive bracket for March Madness, decipher the math that makes it possible to resize a computer font or launch an Angry Bird–and much, much more. All of the applications are presented in an accessible and engaging way, enabling beginners and advanced readers alike to learn and explore at their own pace–a bit and a byte at a time. Download (5MB) Fractal Music, Hypercards and More A Java Library Of Graph Algorithms And Optimization Math Lab for Kids Cakes, Custard And Category Theory 50 Mathematics Ideas You Really Need To Know Load more posts


Understanding Teaspoons and Fluid Ounces
Before we dive into the answer to this question, let’s first understand what teaspoons and fluid ounces are. Teaspoons, as the name suggests, are a unit of measurement typically used for measuring small quantities of ingredients, such as spices, sugar, or salt. On the other hand, fluid ounces are used to measure liquids and are commonly used in recipes and cooking.
The Conversion Factor
To convert teaspoons to fluid ounces, we need to know the conversion factor. One fluid ounce is equal to 0.2 teaspoons. This means that if we want to convert 2 fluid ounces to teaspoons, we simply need to multiply 2 by 0.2, which gives us 0.4 teaspoons.
Why Knowing the Conversion is Important
Knowing how to convert teaspoons to fluid ounces (and vice versa) is important, especially if you’re into cooking or baking. Recipes often call for specific measurements, and if you’re not familiar with the measurement system, you might end up using the wrong amount of ingredients, which can affect the taste and texture of your dish.
Let’s take a look at some examples to help us understand the conversion better. Example 1: If a recipe calls for 3 teaspoons of sugar, how many fluid ounces do you need? To answer this question, we need to use the conversion factor. 1 fluid ounce is equal to 0.2 teaspoons, so we need to divide 3 by 0.2, which gives us 15 fluid ounces. Example 2: If a recipe calls for 2 fluid ounces of lemon juice, how many teaspoons do you need? Again, we need to use the conversion factor. 1 fluid ounce is equal to 0.2 teaspoons, so we need to multiply 2 by 0.2, which gives us 0.4 teaspoons.
In conclusion, there are 0.4 teaspoons in 2 fluid ounces. Knowing how to convert between teaspoons and fluid ounces is important if you want to ensure that your recipes turn out perfectly. It’s a simple equation that can make all the difference in your cooking and baking. So, the next time you come across a recipe that calls for teaspoons or fluid ounces, you’ll know exactly how to measure it out!


After looking at pretty math charts, the email then shifts to a rambling bit about giving 100% and perhaps a little more, then goes into the value of numbers. It shows that when letters are translated into numbers (a=1, b=2...y=25, z=26) and the numbers are added up, words/phrases like "knowledge" and "hard work" get you 96(%) and 98(%), respectively, and "attitude" will get you 100(%), "love of God" will get you 101%, which, the email claims, proves with mathematical certainty that "While Hard Work and Knowledge will get you close, and Attitude will get you there, It's the Love of God that will put you over the top!"
Such infallible logic led me to do more research. I did some calculations, and it turns out "disinterested Jew" puts me at 199%, nearly twice what love of God will get me. In fact, my combined knowledge, attitude, and apathetic Judaism puts me at 395%, a number love of God can only aspire to.
Aren't numbers fun? Of course, I always thought numerology was a form of divination, which Christians try to avoid (Satan and all). But I guess I was wrong. Numerology is a sign of God's Divine Providence, so long as we use carefully selected words in God's official language, English.
GWW X update when I find the energy.


Math Olympiad Top Ten 2018-19
The 5th grade Bath Math Olympiad team has wrapped up their competition season. Congratulations to Nicky Ghiorgie for finishing in first place with a top score of 22 points!
With scores of 21 points, are Rohan Dasanoor and Hank Gretter in a very close second place finish. In 3rd place with 20 points each are Tessa Milicia, Will Sibbald, and Vincent Willits. Tied for 4th place with 19 points each are Ben Boots and Kyle Molter. In 5th place with 18 points is Gabi Iler. And wrapping up the Top Ten with a 17-point finish is Ashley Gardner.
Congratulations to the entire Math Olympiad team. We have a team score of 197 out of a possible 250 points. We will have to wait until the end of the school year to find out if we earned enough points be in the top ten percent of competing schools internationally to receive an award plaque.


I excitedly informed Yo-Yo Boy and Miss Becca Boo that I had ordered some math books for them and they should come in the mail in several days. Yo-Yo Boy said, “What’s math?” I suppose I should’ve been scandalized and embarrassed, but instead I busted out laughing. I guess it’s high time we do some figuring, eh?
Saxon Math 2, and all the stuff that goes with it (I already have the teacher’s book).
what math books did you get?


Welcome to Class 6
Teacher: Mrs Edwards
The topic for this half term is Ancient Maya For further details please visit: Class 6 Curriculum Page where you will find the relevant knowledge organiser, knowledge notes and vocabulary lists.
Writing to Inform
Independent explanation of the Circulatory System.
Link to Science
High Quality Text link: Knowledge Encyclopedia Human Body!
Writing to Entertain
Link to History (Ancient Maya)
High Quality Text: Rain Player by David Wisniewski
For maths we follow White Rose Maths units of work. We will be completing the following units:
- Number: Place Value For the unit knowledge organiser, follow this link.
- Number: Addition, Subtraction, Multiplication and Division For the unit knowledge organiser, follow this link.
For further details please visit: Class 6 Curriculum Page where you will find the relevant knowledge organiser, knowledge notes and vocabulary lists.
Art & Design
Art will be linked to our topic on Ancient Maya. We will be completing some printing work.
This half term we will be learning about 'school'
We will be completing a unit on 'Happy'. For more detailed information click here
Things to remember!
PE-is on a Monday morning with Mrs Bryant and a Tuesday afternoon with Mrs Edwards
For this half term, the children will change for PE and will need full PE kits in school (warmer clothing for outdoor PE ).


What Exactly Are Dimensions in R?
If you have questions concerning which exactly are dimensions inside math, then you are not alone. Once we are all aware, as it should measurements are required to work, to ensure it is feasible for the calculators to help calculate precisely the answers which we want and desire. rankmywriter.com Not just this, however measurements really are crucial in different fields of math also.
For example, in mathematics, probably the measurement in physics would be period. In other words, the duration of the specific thing at a particular time. But, there are also other dimensions, such as burden, space, volume, energy, and momentum, that might be demanded as it should to successfully both work.
Which are measurements in mathematics? http://sps.northwestern.edu/program-areas/summer/high-school-programs/college-preparation-program/ Dimensions in mathematics would be an object’s span, width, and elevation. These measurements are used in many different methods, so be sure to have a look at what they are able to perform to youpersonally.
Length and depth are traditionally employed in physics, including at specifying the rate of light and the rate of sound. Just like other dimensions, these are expected for that functioning of many matters within physics. In other words, Regardless of What occurs, you will know also the length, as well as the width, of objects since the equation for all these may be composed like that, that you examine:
To convert in 1 dimension into the next, we just need to make use of”x”x ray” (no sign) to indicate the first dimension, and the term”length”x ray” (minus sign) to mark the next measurement. This really is the formulation for converting from 1 dimension to another:
Therefore we’ve essay writing service review got x ray and”x ray” (minus sign) to indicate the very first measurement. And the 2nd dimension is decided by”x”. So the criteria for switching from 1 measurement to the next is”x”x ray” (minus sign) -“x” (minus sign) -“x ray” (minus sign).
In physics, the speed of light is loosely understood to be the time for a single object to go to the next upon the universe in one place it can take. It quantified with regard to several referred to as the time-distance distance or can be described in relation to the circumference or distance of the given thing. Let’s look at these 2 measurements relate solely with eachother.
The speed of light will be measured in terms of that time period that it can take for the light traveling from 1 area into the next. And it is measured from 1 area to the other.
Time has to complete with all the distance before it reaches its destination, that light has ever traveled. Quite simply, the traveling period, which is corresponding to the speed of light squared is measured by time.
By comparing the rate of lighting with the speed of light emitting, we can ascertain that the time it takes for light to travel in one spot to the next is time = time * sqrt(x ray ). Put simply, it’s measured in terms of the speed of light emitting.
Width and height may be altered between measurements from the formula x 5 – z. What is the dimension? X, this dimension , is your measurement, therefore we have x = x + y – z, that will be what we desire.


Popular Series By George Lenchner. MOEMS Contest Problems. 4 books in this series. Math Olympiad Contest Problems Volume 2. from: $ George Lenchner, a nationally prominent mathematics educator whose work gave rise to interscholastic math leagues throughout the country. George Lenchner is the author of Math Olympiad Contest Problems for Elementary and Middle Schools ( avg rating, 61 ratings, 4 reviews, published
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Among his honors are: Mathematical Olympiads; 2nd edition Language: Retrieved from ” https: Unsourced material may be challenged and removed. AmazonGlobal Ship Orders Internationally.
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Competition Math for Middle School. A Handbook of Math Strategies.
Today it serves over students a year. ComiXology Thousands of Digital Comics. Cannot find better one Nice price, nice book,best value Verified purchase: Amazon Drive Cloud storage from Amazon.
Mathematical Olympiads for Elementary and Middle Schools – Wikipedia
Shopbop Designer Fashion Brands. Please try again later. Read more Read less. ComiXology Thousands of Digital Comics. Show More Show Less. In he became Director of Mathematics for the Valley Stream Central School District, working with elementary schools for the first time. Becoming a Problem Solving Genius: Any Condition Any Condition.
Mathematical Olympiads for Elementary and Middle Schools
Packaging should be the same as what is found in a retail store, unless the item is handmade or was packaged by the manufacturer in non-retail packaging, such as an unprinted box or plastic bag. Amazon Inspire Digital Educational Resources. This item doesn’t belong on this page.
Alexa Actionable Analytics for the Web. About 24 hours gerge, he passed away at the age of 88, with his wife Edna, and his sons Eric and David at his side. Top Reviews Most recent Top Reviews.
Returning to civilian life, he earned a Masters degree in music in from New York University. Discover Prime Book Box for Kids.
Math Contests For Grades 4, 5, and 6: He was a member of a championship high school math team in the georeg and was All-America in Lacrosse at the City College of New York. Amazon Drive Cloud storage from Amazon. Jong Pil Lee’s request to help design several more projects to improve mathematics teaching on Long Island, several gelrge which still flourish.
Five years after its final printing, it still sells thousands of copies a year.
Are you an author? Cards that had problems divided into such skills as draw a picture, make a chart or graph, but Turns out this book is the granddaddy of all that and is the main book to get your class started on a year long problem solving challenge. Lenchner was seriously wounded on Omaha Beach D-day while leading the second wave and spent over a year in hospitals. Amazon Second Chance Pass it on, trade it in, give it a second life. There’s a problem loading this menu right now.
Amazon Rapids Fun stories for kids on the go. This page was last edited on 22 Februaryat Schools, home schools and institutions may participate in the contest.
It also has seven foreign subsidiaries, serving additional schools in 21 other countries. It’s very challenging for the 4th graders but moving along with hints and solutions, we learn a lot. I use this book as georgf for our fifth grade math olympiad team.
So glad I bought it.
Skip to main content. I had seen a list of problem solving skills in several math texts and a spotty attempt to incorporate them into the curriculum, then I bought a set of edupress. Provide feedback about this page. This article needs additional citations for verification.


Pure and Impure Methods
Pure functions :
Pure functions are functions which will give exact result when the same arguments are passed.
For example the mathematical function sin (0) always results 0. This means that every time you call the function with the same arguments, you will always get the same result. A function can be a pure function provided it should not have any external variable which will alter the behaviour of that variable.
let square x
return: x * x
The variables used inside the function may cause side effects though the functions which are not passed with any arguments. In such cases the function is called impure function. When a function depends on variables or functions outside of its definition block, you can never be sure that the function will behave the same every time it’s called. For example the mathematical function random() will give different outputs for the same function call.
let Random number
let a := random()
if a > 10 then
Here the function Random is impure as it is not sure what will be the result when we call the function.


NW1 Maths Hub
NW1 Maths Hub Impact Case Studies
NW1 Maths Hub’s mission is to improve system leadership by providing accessible and meaningful school to school support in all our communities to meet their mathematical education needs. With over 500 participating schools in Bury, Manchester, Oldham, Rochdale and Stockport, the impact has been quite dramatic in improving our children and young people’s mathematical skills and understanding and also their social mobility. NW1 works closely with the local authorities, school improvement teams, teaching schools and GMLP.
Please click here to read more about our work in this area and the impact it has had.


When both my boys were in pre-school, they were given a good foundation for future academics. I remember our three-year-old church pre-school introducing age appropriate math and other curriculum. At the end of the year, the average three year was to collect and count out loud using three teddy bear shaped pieces. What the teacher was expecting was each child would see several bears on the table and collect them one by one and hand them to the teacher while counting as they did so. “One bear. Two, Three.” They were counting their own age.
When it was my eldest’s turn at this instruction to see if he was capable of showing what three meant, he collected three at one time and handed them over to his teacher. When it was my baby’s turn, eight years later, he grabbed five and subtracted two. Our pre-school teacher, having taught both of my boys, told me that she always thought our first child was smart with his adding the bears before giving her the answer, but when the youngest had his turn she was astonished that at three he was subtracting.
It was then I knew their aptitude for math should make it easy for them. Our eldest did well throughout his years in school. Our youngest performed the same until the NEW MATH was introduced in his 9th grade year. That year, the Common Core standards offered a new approach to math that emphasized more conceptual forms of understanding and “…if states and districts implemented the reform well, the instruction will give students deeper math skills. Common Core math also has the potential to better prepare students for a career.”
I get this lofty idea. But the state didn’t start this new math just in elementary school but as soon as possible, which meant, those who had learned one way of deciphering math problems were jerked into something totally new, without preparation, to begin how to understand math. My youngest was in 9th grade and it was one of the worst times of his life. Not only him, but about 75% had to take even another math class at the same time to repair and supplement whatever they were behind on with the new regular, but foreign, math class. It was like being thrown into the deep end with hopes you will just survive.
These supplemental classes also took away from a time slot for learning something else besides math. His father, an accountant, couldn’t help. He was schooled in old math. I was just a math dummy.
This is how word-problems in math looked to me:
1. If you purchase two of the books, MATH FOR DUMMIES, each costing $16.99, when the clerk adds the total and it comes to $50.00, is he incorrect?
2. If the teacher says, “You have ten chocolate cakes and someone asks for two, how many do you have left?” And if the student answers, “Ten” and the teacher continues, “Okay, well what if somebody forcibly takes two of the cakes, how many would you have left?” and the student answers, “Ten AND a dead body”, is the student incorrect?
3. Is this restaurant sign correct? “Today’s special – Buy one Fish & Chips for the price of two and receive a second Fish & Chips absolutely free!”
4. If the teacher loudly comments, “Don’t worry, I’m not actually saying anything important up here, in the front of the room, about your lesson” what percentage of the class of students will answer with, “So, if I just do my homework, my grade will improve?”
5. On the first day of face to face instruction at school, students are required to bring 30 pencils, 64 crayons, 20 pens, 12 rulers, and 10 notebooks. How many of these items will be left after a month of instruction? Answer: ONE pencil found on the ground, or classroom, or hallway.
And it will probably be missing an eraser and no lead at the point.
Hope 2021 improves for teachers and parents!


I remember when I was in elementary; I always had stomachache when it was time for my arithmetic class. I had butterflies in my stomach when my teacher asked me to show him how to divide. My parents said it was psychological but the pain and nausea I felt were real, so they had to transfer me to another class. My recollection of that event is not so clear. I can't remember how I was able to pass the subject.
Later in high school, Algebra was a subject I was anxious about because of my previous experience in Math during elementary. I dreaded the subject! I was contemplating on having a pre-algebra tutorial. But serendipity stepped in before I could act. During the first day of school, I met the gentlest teacher I have ever known, and his subject was Algebra.
I learned very quickly about notations and algebraic expressions so easily, I got perfect scores in my exams. That was a pleasant surprise for me because I have been thinking that I was a "dumbo" in math or anything that has something to do with numbers. My Algebra teacher knew how to motivate me to excel and conquer my fears.
Nowadays, students are luckier. They have all the learning tools they can use right in their fingertips; all they have to do is click the mouse. They can easily solve Algebra equations through legitimate and reliable online companies. This awesome company offers an unlimited 24/7 tutorials with an affordable fee. They even offer a free demo for interested persons who would like to use the product.


Takt Time Calculator
Try our Takt Time Calculator, and you'll receive your time to beat for your analysis.
How This Takt Time Calculator Works
When you use this Takt Time Calculator, you'll determine what your limit that a product can be produced to satisfy your customer's demand.
By filling out the above calculator, you'll learn what your Takt Time is by seconds, minutes, and hours.
The first question is "What are your working shifts per day", Enter the amount of shifts your company currently performs.
The second question asks "How many hours are there per shift", Enter the hours that a worker performs during their shift. They may clock in for 8 hours.
The third question asks about the total downtime a worker may experience. This includes scheduled and unscheduled maintenance, set-up times, breaks, lunch, etc. This all needs to be added together for an accurate result.
The final question is "How many units need to be delivered per day", this question is asking how much demand is coming from the customer.
Based on your answers, the Takt Time Calculator will provide you your takt time which can then be used in tools such as a Yamazumi Board.
Takt Time Calculation
In order to use the Takt Time Calculator, you will need two numbers. The first number that is required is D, or the average customer demand for that item per day. The second number is W, or the total available production time in seconds per day. To find "T", you would divide W by D. This will give you the Takt time.
T = W / D in seconds = Takt time.
There are some rules that need to be followed for this calculation. You need to define the day in the light of production, as opposed to demand or the actual consumption. If your processing is only performed 5 days a week, then your daily demand will only be 1/5 of the week. While customers are "consuming" the item 7 days a week, it is only being made 5 days out of the week.
There may be a situation where you produce the item more frequently than the customer uses it. Even in this case, the rule still applies. The customer may only use your product 4 days a week, but if you are manufacturing the product 7 days a week, your daily demand will still be 1/7th of the weekly demand.
An Example of the Takt Time Calculator
An example of the rule is given for when production and manufacturing runs in shifts. If you are running your factory for 2 shifts for 5 days every week, and a single shift on one day each weekend, you will run a simple calculation of (2 x 5) for the first five days, and then a 2nd calculation of 1/5 for the weekend day. Add the two numbers together, and you have 2.2 shifts per days through your "week".
You will calculate your available working time as the number of shifts per day (2.2 in the previous case) times the number of seconds per shift. Subtract any time that is not being used for production, such as rest breaks, meals, or meetings, set-up, maintenance time, and any unscheduled down time. The result will be your number of seconds that is required to run all of your production areas.
Let's say that your plant runs for 18 hours per day Monday - Friday and 9 hours on Saturday. You have 2 hours of downtime for breaks, meetings, lunches, or other downtime Monday - Friday and 1 hour of downtime on Saturday. This gives you 2.2 shifts per day. Multiply that by the number of seconds per shift. In this case, each shift is 9 hours, so 32,400 seconds x 2.2 is 71,280 seconds. Subtract the number of seconds not used in production, which in this case is 1 hour per shift, or 3,600 seconds. The result is 67,680 seconds. If customer demand is for 100,000 items, you would divide the number of seconds by the number of items. This would provide the number of seconds required to run your production for this specific customer's demand.


I obtainedmy PhD in Computer science from School of Computer Science and Communication
, KTH Royal institute of Technology (Supervisor: Lars Arvestad
). Before my PhD I earned a bachelor's degree in mathematics (my Bachelor thesis
on theoretcal properties of splines) and a master's degree in mathematical statistics (my Master thesis
on convergence and burn-in estimation of MCMC output) from Stockholm University, Sweden. I'm currently a postdoctoral researcher (started October 2015) at Penn State University in Paul Medvedev's
I use mathematics, modeling, algorithms and simulations to understand problems in biology. My main focus has been on developing algorithms to analyze DNA and RNA sequencing data for problems related to genome assembly, structural variation detection, and transcriptome analysis. Recent reasearch involves transcript reconstruction, isoform detection, and SNV calling in long-read sequencing data (paperd
), and long-read clustering techniques (manuscript
). I have also worked a lot with genomic (short) read sequencing for genome assembly, e.g., for scaffolding
and structural variation detection
. I'm looking into aproaches integrating both long and short as well as genomic and transcriptomic datasets for, e.g., intron and UTR variation detection, isoform specific expression analysis.
Motivation and interests
I'm interested in applications of statistical and mathematical methods and algorithms to analyze data. I'm also strongly motivated by developing sustainable and easily accesibele open source software --- all my code can be found on GitHub.


There are 425 games in this collection. The BGG average rating for this collection is 6.38. Your average rating for this collection is 6.92.
On average you have played each of these games 6.75 times. Your Friendless Metric is 1 (88 games played 10+ times, 48 games never played.) Your Continuous Friendless Metric is 3.28 which corresponds to an average utilisation of 53.04%.


Diploma in Civil Engineering
Faculty of Built Environment
Graduates from this programme may venture into careers such as Project Supervisor, Project Executive, Technical Officer, Technical Specialist, Technical Assistant, Draughtsman, Field Engineer, Construction Sales Executive, Assistant Engineer, etc.
- SPM / SPMV / O-Level / Equivalent: Pass with minimum 3 credits / grade-C including Mathematics and 1 relevant science / technical / vocational subject and pass in English; or
- UEC: Pass with minimum Grade B in any 3 subjects including Mathematics and 1 relevant science /technical/vocational subject and pass in English in SPM; or
- Community College Certificate: Pass with Level 3 MQF in relevant field with minimum Grade C and credit in Mathematics in SPM; or
- STPM / A-Level: Pass with minimum Grade-C in any 1 subject with credit in Mathematics in SPM/equivalent; or
- STAM: Pass with Maqbul Grade with credit in Mathematics in SPM; or
- A recognised certificate in Engineering/ Engineering Technology or its equivalent; or
- A recognised vocational and technology/skills certificate or its equivalent with 1 year of relevant work experience or a minimum of 1 semester of a bridging programme.
- Other equivalent qualification recognised by the Malaysian Government
*(Candidates without a credit in Mathematics in SPM/equivalent may be considered for admission into this programme if the certificate programme contains subjects that are equivalent to SPM Mathematics)
International students must pass
- IELTS minimum Band 5.0; or
- TOEFL with a score of 500
- MUET Band 3
This programme develops the knowledge needed to succeed in civil engineering, incorporating the necessary analytical, industrial, laboratory and Fieldwork skills. It offers good employment prospects in and out of Malaysia. Graduates may either choose to further their studies at degree level or seek employment as engineering supervisors working for contractors, architects or local authorities, or in the fields of construction, property management or consultancy.


Odds of getting a poker hand
10 Dec 2018 ... While the vast majority of you seem to understand the probability of being dealt certain poker hands as well as the probability of completing ...
If you flop an open-ended straight draw this gives you eight outs (eight possible cards that will complete the hand), so you'll hit your hand by the river 31.5% of the time. Just make sure you're getting pot odds (the value of the pot versus the value of your bet) to see the next card. Poker Odds Calculator | Odds of Winning w/ Any Poker Hand How to Use the Poker Odds Calculator. Pick the poker variation you're playing in the top drop-down menu and the number of players in the hand (you can add in up to five players). Odds are available for: Texas Holdem, Omaha, Omaha Hi-Lo, 7-Card Stud, 7-Card Stud Hi-Lo and Razz. To enter each player's hand,... Texas Hold'em Poker Odds Calculator - Card Player Poker odds calculate the chances of you holding a winning hand. The poker odds calculators on CardPlayer.com let you run any scenario that you see at the poker table, see your odds and outs, and ... Poker Odds for Dummies - #1 Beginner's Guide to Poker Odds Some common poker hand odds are open-ended straight draws at 4.8:1, four to a flush at 4.1:1, inside straight (belly buster) at 10.5:1, one pair drawing to two pairs or trips at 8.2:1, overcards on a ragged board on the turn at 6.7:1, drawing to a set at 22:1, and drawing to X outs at (46-X) / X:1.
Poker Odds Calculator - How these software work
game of poker, players attempt to assemble the best five-card hand ..... By virtue of having the best hand the probability of Player 3 winning is simply the. Seven Card Stud Odds - 7 Card Stud Odds of Being ... - Online Poker
Common to all is the fact that players get - one way or another - hands of five cards each. ... Thus the probability of getting a royal flush is 4/2598960 = 1/ 649740.
6-Card Poker Hands There are a few 6-card poker games so it is worth looking at probabilities for winning with certain kinds of hands. One chooses the highest ranked 5-card poker hand among the 6 cards and values the hand based on the 5-card hand. Pre-Flop Poker Probability Statistics - Chances Dealt AA Aces The answer here is 169 unique hands. Pre-Flop Poker Probability - 169 Distinct Starting Hands. Now we are getting somewhere. Next we can use the numbers above to work out what the probability of being dealt AA, KK (or in fact any pair) is. This is a case of taking the total number of possible hands and then seeing how many of these are your pair.
Poker Calculator – Texas Holdem Poker Odds Calculator - 888 Poker
Odds of getting a king in a five card poker hand Each Poker players gets 5 cards.They then bet on the strength of their hand and its potential strength, as the hand progresses. Once initial bets are done, players canA Royal Flush is the highest possible hand in poker and the odds are 649,739 : 1The above is true for 5 card poker, but not true for Holdem.
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Free online Card games are distinguishable in many ways from the rest of the casino offerings. This is because the odds of the game preset due to the subsequent hands. For successful bettings, mathematics is also involved in curating the best strategy. Understanding the probability of the odds determining the combination leads to easy decisions and guaranteed success.
Card Games and Maths
Typically, casinos aim to make profits from every bet offered in free card games. The player will try to beat the edge and crack the best in every way possible. To do this, a bettor must first make a few crucial decisions.
- Decision on the card game: Deciding which game will be played is essential. This is because each game offers additional variations and has a different user interface. All the choices made by the player lead to the motive of reduction of losses. This is where mathematics can be put to use.
- Research on the subject: A player who has done enough research on the subject will have a basic understanding of the same. Mathematics will lead the bettor to make profits and survive the game financially. There are many situations where casino customers are awarded high advantages through offers to generate a win.
- However, one must also understand that players must have in-depth knowledge to successfully play card games online.
This is the most basic concept that is related to gambling. Any game’s mathematical expectation is calculated by multiplying the possible gains by the likelihood of each.
This can change quickly if the pay-offs are changed. If such a thing happens, the expectation of profits is also increased. However, each bettor must remember that there are different expectations of profits when the betting amounts are different. With this change, the percentage of the amount bet remains constant.
This concept of the expectation from individual bets is the same as the mathematical expectation from the series of bets. This is essential for the customers. The so-called “staking systems” do not seem to work because of negative expectation bets. The previous concept applies to both positive and negative stakes.
Repetition of Trials
As explained, the expectation is the average amount a betting player will win or lose when people play cards online. When it comes to repeated trials, the concept of action should be integrated. The player understands the concept of the “law of averages” through the repetition of trials. This law states that T/A will be approximately equal to E/A in profit and loss cases. Here A stands for action, and (T) represents the total profit or loss over a betting session. However, this law is misunderstood by most bettors who equate expected profit and loss (E) with the total profit or loss (T).
Casino customers can mint huge amounts of money if they strategise their gameplay. Mathematics helps increase the probability of wins and should be used extensively. Along with all other determining factors, this will help the bettors to maximise profits.


By Alfredo M. Ozorio de Almeida
This advent to the idea of Hamiltonian chaos outlines the most ends up in the sphere, and is going directly to ponder implications for quantum mechanics. The examine of nonlinear dynamics, and specifically of chaotic structures, is likely one of the quickest transforming into and best components in physics and utilized arithmetic. In its first six chapters, this well timed publication introduces the speculation of classical Hamiltonian structures. the purpose isn't to be entire yet, particularly, to supply a mathematical trunk from which the reader might be in a position to department out. the focus is on periodic orbits and their neighbourhood, as this method is mainly compatible as an creation to the consequences of the speculation of chaos in quantum mechanics, that are mentioned within the final 3 chapters.
Read Online or Download Hamiltonian systems: chaos and quantization PDF
Best quantum theory books
Examining Bohr: Physics and Philosophy bargains a brand new viewpoint on Niels Bohr's interpretation of quantum mechanics as complementarity, and at the relationships among physics and philosophy in Bohr's paintings, which has had momentous importance for our figuring out of quantum thought and of the character of data regularly.
Physics has lengthy been considered as a wellspring of mathematical difficulties. Mathematical tools in Physics is a self-contained presentation, pushed via historical motivations, very good examples, particular proofs, and a spotlight on these elements of arithmetic which are wanted in additional formidable classes on quantum mechanics and classical and quantum box conception.
The superb accuracy in verifying quantum results experimentally has lately renewed curiosity in quantum mechanical size concept. during this ebook the authors provide in the Hilbert area formula of quantum mechanics a scientific exposition of the quantum conception of size. Their procedure contains the thoughts of unsharp objectification and of nonunitary variations wanted for a unifying description of varied specified investigations.
A latest creation to physics,captivating, basic, with many color photos, animations and flicks, riddles and demanding situations. It covers mechanics, thermodynamics, relativity, quantum physics and glossy makes an attempt at unification.
- Quantum Mechanics on the Macintosh ®
- Vorlesungen über Atommechanik
- A quantum mechanics primer: An Elementary Introduction to the Formal Theory of Non-relativistic Quantum Mechanics
- Anderson Localization and Its Ramifications: Disorder, Phase Coherence and Electron Correlations
- Nonperturbative Quantum Field Theory and the Structure of Matter (Fundamental Theories of Physics)
Extra resources for Hamiltonian systems: chaos and quantization
23d) which substituting Eq. 23e) s in agreement with Eq. 23a). 24a) and the corresponding trace dynamics equation of motion of Eq. 15b). Thus, for Weyl-ordered Hamiltonians formed with c-number coefficients, we conclude that the trace dynamics equations of motion generated by H agree with the Heisenberg picture equations of motion generated by H , on an initial time slice on which the phase space variables are canonical. It is also evident that on this time slice [H, i] = 0. 24b) But since Eq. 24b) guarantees that the Heisenberg picture equations of motion preserve the canonical algebra on the next time slice, integrating forward in time step by step then implies that trace dynamics agrees with Heisenberg picture dynamics at all subsequent times, and therefore can be extended to a unitary dynamics in this case.
The example of Eq. 20c) required the use of two pairs of canonical variables q1,2 , p1,2 ; using our Weyl-ordering result, we shall now show that any trace dynamics for a single 36 Trace dynamics pair of bosonic variables q, p, when extended to the canonical algebra [q, p] = i, always can be represented as a unitary Heisenberg evolution. We shall proceed by induction, and assume that the result has been proved for any trace dynamics generated by a trace Hamiltonian H = TrH of degree n or less in p and q.
We conclude that as of this writing the localization model is favored, both because the assumptions needed to derive it within our framework are more robust, and because there are unresolved problems with the mechanisms that have been proposed to explain reduction in the energy-driven model. Finally, in Chapter 7 we indicate how our proposal for an emergent quantum theory addresses the motivational questions raised above in Section 3, and discuss some of the issues that will be relevant for future developments.


When he was small, his mother found his naughtiness too much to handle. She devised a way out — she simply gave him sums to do. And the kid got hooked to the subject. In fact, Mahan Maharaj, a monk of the Ramakrishna Mission (RKM) order, went on to bag this year’s Shanti Swarup Bhatnagar Award for mathematics, the country’s highest academic award.
Since the day the award was announced, the RKM headquarters at Vivekananda University opposite Belurmath in Howrah has been flooded with phone calls and visitors. Everyone wants to meet this brilliant, 45-year old mathematician who has been working with hyperbolic geometry and topology for nearly two decades. However, the shy Maharaj has been completely elusive, denying interviews sternly.
So one day, this reporter simply landed at the university unannounced and walked into his cubicle, catching him off guard. He was rattled initially and it took some convincing to calm him down. Finally, he laughed out aloud and threw his hands up in exasperation. “How can I tell you within the span of an interview what I have done to receive this award? I have worked at certain mathematical problems for nearly 18 years and it is not possible to sum it up in layman’s language,” he says when asked about his work.
This mathematician, equally at ease with English, Hindi and Bengali, was born Mahan Mitra. He went to St Xavier’s Collegiate School, Kolkata, before he entered IIT-Kanpur where he started with electrical engineering.
Soon, Maharaj realised he was in the wrong field. He switched to mathematics. After completing his MSc, he went to the University of California, Berkeley. But then, he returned to the city and decided to renounce the world, becoming a monk. He joined the RKM order in 1998 as a brahmachari and graduated to monkhood in 2008. “The award is incidental. There’s so much to be done. I will be able to learn only a small fraction of mathematics in my lifetime,” he says sagely. Though lovingly called Mahan Maharaj by his fellow monks at RKM and students at Vivekananda University, he is officially called Vidyanathananda in the order. He’s now dean of research and coordinator of the school of mathematics in the university.
Why did Maharaj choose to be a monk? “Perhaps because I wanted to find the peace to work,” he says, laughing. “I enjoy being a monk as much I enjoy my math.” He travels all over the world collaborating with mathematicians and lecturing students. His aim is to instill the love of numbers in students. “The biggest mathematical problems have their roots in simple logic and that’s what I want my students to know. I want them to use mathematics for the betterment of mankind.”
The V-C of the university, Swami Atmapriyananda, says, “Maharaj is the perfect synthesis of religion and scientific quest, a breed that Swami Vivekananda wanted to establish.” Such stars, say those who know the man, blaze forth but once in a lifetime.


Data Science is an interdisciplinary field that involves the use of statistical and computational methods to extract insights and knowledge from data. It combines aspects of statistics, mathematics, computer science, and domain-specific knowledge to process, analyze, and interpret data to solve real-world problems.
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We use AI computations and data mining techniques to create data structures and information architecture that are diverse, resilient, and scalable for your company needs. Our approaches enable the development of AI pipelines in programming and online applications.
Data Science Technologies
Methods We Use
- Descriptive statistics
- Bayesian inference, etc.
- Decision trees, linear regression, logistic regression, and support vector machines are examples of supervised learning algorithms.
- Unsupervised learning methods such as K-means clustering and hierarchical clustering are examples of unsupervised learning algorithms.
- Q-learning, SARSA, and temporal differences approaches are examples of reinforcement learning methods.
- Recurrent and convolutional neural networks (including LSTM and GRU)
- Adversarial networks that generate (GANs)
- Q-network in depth (DQN)
- Deep Bayesian learning


Abraham S. Fischler College of Education and School of Criminal Justice
Department of Education
With a doctoral degree in mathematics education, Trotman previously worked in the Caribbean as a mathematics educator and assistant high school principal. During that time, she worked with a regional learning group to harmonize the mathematics curriculum for the Organization of Eastern Caribbean States, resulting in the co-authoring of text books and teacher guides for the Caribbean Primary Mathematics series. Trotman joined NSU in 2002. She works with students at the undergraduate to doctoral levels, serving as field and internship supervisor, counselor to the Kappa Delta Pi chapter, dissertation chair, and Honors student advisor and mentor. Trotman is a lead program reviewer for the National Council of Teachers of Mathematics/Council for the Accreditation of Educator Preparation (CAEP).


Union of Assassins
Pascal's Triangle (or Yanghui's Triangle)
When I was creating the actual game play, I found that probability is key to a successful game. If things are too random, chaos ensues. If things are not random enough, then the game play can become boring.
I used Pascal's Triangle to help calculate probability. (Yanghui, a Chinese mathematician, discovered the triangle 500 years before Pascal did.)
For you math/crypto people out there see if you can find Fibonacci Numbers when you play the game...


Monthly Recurring Revenue (MRR) is your predictable monthly revenue based on the number of subscribers for each subscription plan. MRR calculations take into consideration subscribers from dissimilar subscription plans offered at different price points and aligns them to provide a single, recurring revenue figure.
We take the latest invoice amount of each customer with active subscription access (which consists of those end-users with statuses of active and pending cancellation who still have access to their subscription until the end of the billing cycle) then we divide by amount of days in their subscription period.
From there, we multiply daily recurring revenue on the average amount of days in the month during the year (30.42 days).
MRR is designed to align subscribers based on the amount of revenue each month and is the most accurate way to predict recurring revenue when there are subscribers paying different rates.
MRR is helpful for reporting growth, analyzing trends, and planning for the future.


Tip for today: Percent Made Easy.
What :: X Is :: = Of :: ( )
Example: What is a 20% tip for $60 check?
X = .20 (60)
What is your total if you pay a 6% tax and a 20% tip on $60?
X = 1.26 ($60)
What is the total if you wish to pay the tip after tax?
X = (60) (1.06) (1.20)
Now, how about product pricing?
Assume a merchant buys a product for $70; marks sit up 60%; then offers a 30% discount for Christmas?
1.. The Sale price is ($70) (1.60) (.70)
Think about it !! :)
Being a slow reader, did not hurt him in math class because reading slowly, he could "think between the lines" as he read a math problem. Because of his math skills and his natural people skill, Mr. A was hird at 18 as the industrial engineer in training, with responsibility for all the piece-work salaries for a small lingerie company in his home town. Later during 4 years of college, while earning a BS in Math and Physics, he worked full time for the Marshal Space Flight Center in Huntsville, Alabama. Leaving NASA for th computer industry in 1965, he developed operating systems and managed software development teams. In 1975 he founded his own computer systems company, led it to one of the top providers of turnkey systems for health care automation, and sold it in 1985. In 2003, Mr. A left the computer industry and began teaching math in middle and high schools in Florida and Mississippi. Today, at 81, he teaches and tutors for fun and donates most of his salary. Mr. A challenges his students to think beyond he obvious and perform above expections. His style of teaching is that of Escalante in the movie: Stand and Deliver. He believes students can perform beyond current expectations - if they have desire!
One-on-one or small groups, Mr. A teaches simplification for complex processes. He believes that students need to transition from Elementary Math to Algbraic thinking before 8th grade.
For tutoring or parental counseling,
Mr. A can be reached at (601) 325-3811.
Mr. A Says: Seventh grade is a good time to make the transition from Elementary Math to Algebraic thinking.


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The most gripping book I've read so far on my two week holiday is Marcus du Sautoy's Music of the Primes. These types of books are destined to be described as a 'fascinating journey'. It was, how shall I put it? A fascinating journey through the drama and personalities of the search for an explanation of prime numbers.
One of the sad things about it all is that there's a belief among mathematicians that your mathematical abilities decline after you're 30. Kind of depressing. Having said that, Euler and Erdos were apparently mathematically active to a ripe old age.


On this Christmas morning, let’s spread the holiday cheer by reliving some of the best pitching performances in Mets history. For this week’s Mind Boggler, we’re asking you to name every pitcher in team history to post a game score of at least 95.
Every pitcher in Mets history with a game score of at least 95
Game score is a nice little stat that tries to boil down a single-game pitching performance into one number. To calculate game score, you simply start with 50 points and add one point for each out recorded, one point for each strikeout, and two points for each inning completed after the fourth. You then subtract one point for each walk allowed, two points for each hit allowed, two points for each unearned run allowed, and four points for each earned run allowed.
Fifty points is considered an average game score. Scores that get closer zero represent poorly pitched games, while scores near 100 signify gems.
You’ll have two minutes for this quiz. Good luck, and remember to post your time and score in the comments!


The Wobbly Table Problem
Note: I’ve written an essay about why I got interested in this problem
The Wobbly Table Problem: Given a continuous function , is it always possible to place a square table of fixed side length on the graph so that the the bottoms of each table leg are simultaneously in contact with the graph?
In other words, if you sit down at a table in a restaurant, and the table wobbles, can you always pick up the table and rearrange it so that it doesn’t wobble? The graph of the function represents the curvy floor on which the table is supposed to stand.
There are multiple ways to interpret this problem, so we’d better fix an interpretation before continuing. For example, do we want to insist that the table be level, in addition to being stable? What if the table is very short, so that the floor would poke through the tabletop unless we made the table taller? If the table isn’t level, the floor might poke through the table legs as well, do we want to allow that?
So let’s fix the following interpretation: First we don’t insist that the table be level. If our function were (for example) , then our table wouldn’t have a chance of resting level, and it can be made stable (non-wobbly) by placing the four legs at an incline along the -axis. So to make the problem interesting we shouldn’t require that the table be level.
Second, let’s actually make the table legs and table top permeable, and only pay attention to the bottoms of the table legs. Now we don’t need to consider whether the floor is so lumpy as to poke through other parts of the table, and we can focus our attention only the configuration on disembodied 4-tuples of points in the configuration of a square.
A proof that doesn’t work
There’s a seductive proof strategy which is actually very difficult to make work. Here’s the rough idea:
- Place the table on the surface so that a pair of diagonal legs both touch the surface. At first, the other pair of legs will generally not be touching the surface. Maybe one will and the other won’t, or maybe they’re both hovering over the surface, or maybe one is hovering and the other is piercing below the surface.
- Fix the two diagonal legs which are in contact with the table, and rotate the table while keeping those legs fixed so that the other pair of legs are equally above or equally below the table. So for example if they’re equally above the table, you could take two wedges of equal thickness and fit them under the off legs and then have the table be stable. Let’s assume they’re above the table — the proof strategy when they’re below is basically the same. Call this Configuration A.
- Perform the following maneuver: push the table straight down, so that the two legs in contact with the surface pierce through, and the two legs which are above the surface (by equal amounts) exactly touch the surface. Call this Configuration B.
- We’ve described one way to get from Configuration A to Configuration B: push the table down. Now we’ll describe a different way to get from A to B: Rotate the table clockwise around its center by 90 degrees, all the while making sure to (1) keep the pair of diagonal legs in contact with the surface, and (2) making sure to keep the other pair of diagonal legs an equal distance above or below the surface.
- Since we start with the off-pair of legs equally above, and end with them equally below, and all the while they’re an equal distance above/below, then at some intermediate point they must be exactly on the surface. Since the first pair of diagonal legs always remains on the surface, there must be some point at which all the legs are in contact with the surface. Hooray!
The problem is in step 4: it’s not clear that it’s possible to rotate the table around its center while keeping the opposite legs in contact with the surface. And if it were possible, it might be that there’s more than one configuration like that, so which one do you pick? And even then, it’s not clear that it’s possible to ensure that the two other legs are equally above/below the surface during this process.
Anyone who objects “yes but it should be possible as long as the surface isn’t too wobbly” should be prepared to explain what “too wobbly” means, and how to make the rotation argument precise using their hypothesis of “not too wobbly”.
To drive the point home here’s an example of a surface where this strategy fails. One table leg is on the top of the short mountain at left, and the diagonally opposite leg is on the taller mountain-within-a-valley at right:
One successful attempt at making this proof strategy watertight is due to Bill Baritompa, Burkard Polster, and Marty Ross. Their proof has the advantage of also working for rectangular tables, and takes into account more realistic tables whose tops and legs are not permeable to the ground. The main downside (to my taste) is that restricts attention to surfaces which are not too steep — which locally do not rise by more than about 35 degrees. (Happily, most floors found in restaurants should be covered by their theorem.)
A theorem of Dyson
In 1951 Freeman Dyson proved the following theorem:
Let be a continuous function from the 2-sphere to the real numbers. Then there are two orthogonal diameters of the sphere whose endpoints and all take the same value of .
In other words, for any continuous function on the sphere, there are four points forming the vertices of a square on some great circle of the sphere, so that the function takes equal values on those vertices. It’s not immediately clear that it relates to tables, but it was noticed at least as early as 1970 by Roger Fenn that it implies the wobbly table problem. In fact George Livesay generalized this theorem to non-orthogonal diameters which Fenn notes resolves the wobbly table problem for rectangular tables as well as squares.
How does Dyson’s theorem resolve the wobbly table problem? Well, given the graph of a function representing the ground, take a function , where is defined on the standard 2-sphere embedded in 3-space. Now apply Dyson’s theorem to this function , and we find a square in 3-space whose vertices all have the same value of , or in other words all lie the same distance above or below the ground. Simply slide them up or down without moving the center side to side, and we’ve found a stable place for our table.
How, then, do we prove Dyson’s theorem? Dyson’s original proof is fairly short, just a few pages, but I found it unsatisfying because it makes use of unusual objects called -sets: sets which separate the origin in Euclidean space from infinity along any ray. The feeling I get is that he would have liked to use a more standard tool but was unable to get it to work. (Of course my feeling is only an opinion, not rooted in any specific knowledge about Dyson’s choices.)
To me, the flavor of Dyson’s theorem is very reminiscent of the famous Borsuk–Ulam theorem (the classic illustration of this theorem is that, at any given moment, there are a pair of antipodal points on the Earth’s surface with the same temperature and pressure). I sought — and found — a proof along the lines of the standard proofs of the Borsuk–Ulam theorem.
In part 2, I’ll explain my proof of Dyson’s theorem.


Math-Drills' worksheets are easy to tailor to specific classroom, lesson or student needs. Students read the word form of a number and then find and color the flower that matches each answer. The problems are multiple choice to help with test taking skills. Helpful idea: The two versions have the same questions, but in slightly different order and the pictures have been altered. The worksheets on this page are of a hard level of difficulty. Answer, Find, and Shade Time Review - Level 1 This art worksheet reviews time. Student misunderstanding: Even though a part of an expression or equation is surrounded by parenthesis, it can still be pulled apart using the Distributive Property.
Each student chooses their own colors to create a unique art project. The layout only allows for a maximum of 17 words. The midpoint formula is actually the same as finding the average of two numbers. Students use their prior knowledge to determine the unknown sides and volume of specific shapes. Students answer the word problems, find the answers in the grid, and then shade the squares that match the answers. It also covers estimation and diameter of a circle. Introduction - Pythagorean Theorem All Levels This one page worksheet introduces the Pythagorean Theorem.
Key concept: Using formulas is a problem-solving strategy that can help students solve math problems and real-world situations. Version 1 Version 2 Answer, Find, and Shade - Level 1 Squares and Square Roots This one page art worksheet reviews squares and square roots. Key concept: Students should know what each term means and how to find the solution. Students are given a chart and must fill in the empty spaces. Answer, Find, and Shade Basic Arithmetic using Estimation Level 1 This free art worksheet reviews basic arithmetic add, subtract, multiply, and divide and estimation. Students color certain objects to recognize their place in a set. Questions are different but the picture is the same.
Key concept: Students should be able to count, read, and write whole numbers up to 100,000, and identify the place value of specific digits in numbers. Level 1 Level 2 Level 3 Multiplying and Dividing by Multiples of 10 Level 2 This one page worksheet reviews multiplying and dividing by multiples of 10. Drawing Circuit Diagrams Worksheet Answers Wiring Diagram Us Series. The picture is symmetrical and students choose their own colors to create a unique art project. Stained Glass - Level 2 Comparing Fractions and Decimals This one page art worksheet covers comparing fractions and decimals. Answer, Find, and Color Subtraction These one page art worksheets review multi-digit subtraction.
Each student chooses their own colors to create a unique art project. Print out the worksheets and cut out each square. This is great practice for estimating two digit division. Level 1 Level 2 Level 3 Answer, Find, and Shade The Three Basic Properties Level 2 These one page worksheets have students use the distributive, associative, and commutative properties to simplify expressions. Level one and two include equations to help students, but the level 3 worksheet makes students research or use prior knowledge. Students write the correct number for each place value and then color the object with the corresponding letter. Sign up for a student account.
It explains what the theorem is and how it can be used. Just like the original game, kids try and sink each other's ships by calling out coordinates. Here you will find a range of fun math riddles that will entertain and occupy your child. Prior knowledge: Students should already know how to find the area and circumference of a circle. Students use long division to solve the problems.
This website provides fewer worksheet options, but the customization makes it a worthwhile resource from which to pull. Using riddles is a really good way to explore mathematical ideas and concepts in a fun way! Answer, Find, and Shade Basic Operations with Decimals Level 2 This art worksheet reviews the basic operations add, subtract, multiply, and divide with decimals. So the first number is the x-axis number going across. Answer, Find, and Shade Multiplication These one page art worksheets review multi-digit multiplication. What's more, correction worksheets give students more practice identifying common grammar, spelling, and punctuation errors.
Key concept: Students need to be able to compare fractions and decimals and be able to visualize the size of a number. Answer, Find, and Shade Solving Proportions These one page, art worksheets review proportions. The puzzles can also be used as a template for the children to write their own clues for a partner to guess. It uses the simple process of drawing squares in the figures and counting them. If that happens, make the puzzle bigger by entering higher values for down and across.
This is helpful, but many students then think that multiplication comes before division and addition comes before subtraction. Math is one of the initial subjects that kids are taught and there is a particular reason for that. Some of the worksheets displayed are Area perimeter work, Answer key area and perimeter, 11 circumference and area of circles, Area, 3 parallel lines and transversals, Greatest common factor es1, Volume and surface area work, Answer key. Student misunderstanding: Count how many digits are to the right of the decimal in all the numbers before multiplying. Quadratic Equation Worksheets Printable Pdf Download. Each riddle is a mathematical problem that will hopefully prove both stimulating and interesting.


I’m a Data Science Degree Apprentice at Santander UK, where I rotate across various teams within the bank whilst obtaining an undergraduate degree in Data Science.
I’ve worked on a variety of projects ranging from chatbots, churn models and credit risk projects using a wide range of technologies but primarily Python, SQL and SAS.
BSc (Hons) in Data Science, 2021 - 2024
Nottingham Trent University
Computing (D*), Media (A), Maths (C)
Reigate Sixth Form College
Soft Skills/Business Skills
Rotational degree apprenticeship program with a specialism in Data Science across the corporate and retail bank.
Rotations within Core Data Science, Corporate Financial Crime Analytics and Quantitative Risk
Projects involved in include:
Managing the development of the Suneeta London website www.suneetalondon.co.uk and the respective CBD website www.suneetacbd.co.uk, whilst ensuring that we complied with legislation for the CBD website.
Attending a variety of events and acting on the companies behalf, most notable collaboration was being invited to the HQ of ASOS.


|Deep Learning with R|
Deep Learning with R is meant for statisticians, analysts, engineers, and students with a reasonable amount of R experience but no significant knowledge of machine learning and deep learning. You’ll learn from more than 30 code examples that include detailed commentary and practical recommendations. You don’t need previous experience with machine learning or deep learning: this book covers from scratch all the necessary basics. You don’t need an advanced mathematics background, either—high school level mathematics should suffice in order to follow along.
An introduction to a broad range of topics in deep learning. The text offers mathematical and conceptual background, covering relevant concepts in linear algebra, probability theory and information theory, numerical computation, and machine learning. It describes deep learning techniques used by practitioners in industry, including deep feedforward networks, regularization, optimization algorithms, convolutional networks, sequence modeling, and practical methodology.
|Deep Learning with Keras Cheatsheet|
A quick reference guide to the concepts and available functions in the R interface to Keras. Covers the various types of Keras layers, data preprocessing, training workflow, and pre-trained models.
In-depth examples of using TensorFlow with R, including detailed explanatory narrative as well as coverage of ancillary tasks like data preprocessing and visualization. A great resource for taking the next step after you’ve learned the basics.
Introductory examples of using TensorFlow with R. These examples cover the basics of training models with the keras and tensorflow packages.