WHY MATHS IS IMPORTANT
Maths is an essential skill that enables us to live an independent life. It teaches us how to make sense of the world around us, whether it be: calculating the total amount of money we need to purchase items, knowing what time to meet a connecting train or weighing precise amounts of ingredients when following a recipe. Maths helps us to develop problem solving and reasoning skills that allow us to solve a variety of problems in our every day lives.
NATIONAL CURRICULUM PURPOSE OF STUDY
Mathematics is a creative and highly inter-connected discipline that has been developed over centuries, providing the solution to some of history’s most intriguing problems. It is essential to everyday life, critical to science, technology and engineering, and necessary for financial literacy and most forms of employment. A high-quality mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject.
WHAT MATHS LOOKS LIKE AT PBRATTON PRIMARY SCHOOL – WHITE ROSE MATHS
Our main aims at Bratton Primary are to make our children fluent in solving calculations involving the four mathematical operations and to equip them with the tools to solve a variety of problems. We follow the White Rose Maths scheme of work. The units of work are, by necessity, organised into distinct areas, but pupils will make rich connections across mathematical ideas. Developing problem solving and reasoning skills is a thread that runs through all our Maths lessons. Children are constantly challenged to explain why, to prove how they know, to convince that they are correct or to find all possible outcomes. They have the opportunity to use a wide range of resources to support their learning such as hundred squares, number lines, Numicon, cubes, place value cards and other small apparatus as we follow a CPA approach in our delivery. Mathematical skills are developed across the curriculum in subjects such as Science, Design and Technology and PE. Vocabulary is explicitly taught at the beginning of every lesson and in order to facilitate children to know more and remember more key concepts run through the whole of our curriculum and opportunities to revisit previous learning are planned into every lesson.
Ultimately our Maths Curriculum is designed to:
– Embed those Maths skills that are vital throughout life. Research from the Institute of Education has shown: children who develop these skills early in life and who become confident with maths are more likely to: Stay in education longer; be in work as adults; earn more throughout their lives. – Ensure a good understanding of everyday maths which will help all children establish skills transferrable into all learning, such as: making more evidenced based decisions, problem solving, reasoning, rationalising and more clearly interpreting and understanding information. We also want children to see that maths will help them develop essential lifelong skills. – Challenge our children to make rich connections across mathematical concepts and to use their strong factual and procedural knowledge to help solve problems.
Maths at Bratton Primary:
- Maths ethos and advice at Bratton Primary
- BPS KIRFs
- KIRFs Zebra Class (Terms 1-6)


2007 EMET Prize Laureate – Exact Sciences
Prof. Micha Sharir is awarded the EMET Prize for his pioneering work in computational geometry and its applications and for his fundamental contributions in the fields of Algorithmic Motion Planning in Robotics and Discrete Geometry.
Prof. Micha Sharir was born in Tel-Aviv in 1950. As a high-school student he won first prizes in the Mathematics Youth Olympics of the Weizmann Institute and in the Technion’s Grossman Contest in Mathematics. In 1970 he completed his B.Sc. in Mathematics at the Tel-Aviv University. He later served in the Intelligence Corps where he was part of a research team that won The Security of Israel Award. During his military service he completed his M.Sc. and PhD (1976) in Pure Mathematics at the Tel-Aviv University.
Following his military service he decided to specialize in computer science and received his training at the New-York University. In 1980 he joined the staff of the School of Computer Science at the Tel-Aviv University as senior lecturer, and in 1985 he was appointed full professor. In the early 1980s, together with Prof. Jacob Schwartz who was his supervisor in New-York, he laid the foundations for a new research field – Algorithmic Motion Planning in Robotics. The theory was introduced in a series of articles about the “Piano Movers”. He served as deputy director of the Robotics Lab in New York for four years. As a result of this research he started the study of Computational Geometry – a field that was then in its infancy. It combines theoretical research of the mathematical elements of algorithms in solving problems of a geometric nature and of geometric structures, with the application of these algorithms to a variety of fields such as robotics, bioinformatics and computer graphics. Over the years he has gained a reputation as one of the leading scientists in the field. His studies have yielded basic results and many breakthroughs that have shaped the field and promoted knowledge of it.
He holds the The Isaias Nizri Chair in Computational Geometry and Robotics, and served two terms as Head of the School of Computer Science and Head of the School of Mathematical Sciences. He was also a member in many committees, and has been editing some of the leading journals in the field. Over the years he has published ca. 275 articles in scientific journals, and in 1995 a book was published in which his research is summarized. He has supervised almost 20 PhD students and a similar number of M.Sc. students. Most of his former students now hold academic posts, both in Israel and abroad.
His studies won him many prizes, including the Max Planck Research Award (1992), and an honorary doctorate by the Utrecht University (1996). In 1997 he was elected as fellow of the Association for Computing Machinery (ACM) and received the Feher Prize in Computer Science (1999) and the Landau Prize for Science and Research (2002).


Sudoku puzzles are classified according to their difficulty. My old newspaper, the LA Times, did so as Gentle, Moderate, Tough, and Diabolical. Sites like Daily Sudoku have basically the same division, though the names are different (hard and very hard instead of tough and diabolical). Difficulty is determined by the techniques needed to solve the Sudoku. Simple elimination techniques, naked twins, and indirect inferences come up in Gentle and Moderate. Tough and Diabolical additionally require more advanced stuff.
Hidden twins is an advanced technique I've already talked about, where candidates are eliminated based on a twin that isn't readily apparent. This is a bit tricky, since you're actually adding a candidate to a triplet that isn't there so that it matches two other squares. With practice, though, hidden twins are easy to spot.
However, we need to go beyond those techniques to solve a very hard puzzle like the following that I got from Daily Sudoku:
Using a combination of box, row, and column searches, twins, and indirect inferences, we can get to this point with the puzzle (I've put in all pencil marks):
To see how I got this, see the end of this post. You can convince yourself that the puzzle cannot be solved further using any basic techniques.
The first thing I notice is that the first row has hidden twin in 1 2. See how squares two and four of that row are the only squares with those numbers? Thus, we can remove the candidate 4 from Box 2 square 1.
This lets us solve for the 4 in Box 2, and eliminate a few other candidates. Here is the puzzle as it stands:
Not much progress. However, I think of a Sudoku like this as a delicately balanced thing. If the puzzle wasn't just so, it would collapse. Solving for even one more square could lead to many solutions. Finding that is the key to finishing tough puzzles like this.
What I'm looking at is squares that contain a cycle of three digits that can "see" each other. So, for instance, the 3 7 in Box 1 can see the 1 7 in Box 3. The common digit is 7. So the question is, can either of these squares see the other pair, 1 3? It just so happens that the 1 7 can see the 1 3:
How does this help us? If the leftmost highlighted square were 7 then the lower square must be 3. If the leftmost square is 3, then the lower square is also 3. Thus, the lower highlighted square is 3.
We actually got a little bit lucky. Under other circumstances, this would only have allowed us to eliminate 3 as a possible in Box 3 square 5. That itself would have led to a number of solves, though. Like I said, it's a fragile structure.
Because the structure of the highlighted box vaguely resembles a Y, this tends to be called a Y-wing elimination. I think it's kind of a silly term, and rather like to think of it as a cycle rule. In this case it was 3 7 sees 1 7 sees 1 3. The cycle is complete. You start with a square with two possibles, and look around for any square with a pair that has one number in common. If you find one, see if that square sees any squares with the complementary pair. If so, you have found a Y-wing. Then just use basic logic to determine what candidates can be removed.
With just this one technique, the puzzle is solved very quickly. The finished puzzle is below, along with the solution to get to the second step.
Solution to get to step one: The labeling scheme is box,square, where numbering runs from left to right.
5,6 = 8
4,1 = 1 (indirect from box 5)
6,2 = 6
7,4 = 9 (column)
9,9 = 9
8,1 = 9
5,3 = 9
6,6 = 3
2,9 = 5 (enumeration)
9,1 = 4
9,2 = 2
7,3 = 5
7,8 = 6
4,3 = 2
6,1 = 5
6,4 = 2
8,9 = 7
9,7 = 8
9,8 = 5
6,7 = 7
6,9 = 8


Education / Training
Other Education, Training, and Library Occupations
Grade Levels: High School
Subjects: English language arts, Math, Science, Foreign language, Other
Benefits not specified

Crescent City Tutoring Services, LLC provides high-quality tutoring and academic support for students ages 7 and up. Crescent City Tutoring Services provides tutoring in English, mathematics and the sciences.

To learn more about the employer visit their profile.
New Orleans, LA, 70125


How to Calculate 35 Days From Today
When you want to know how many days will pass until a specific date, you might need to know how many days are left until that date. The tool below can help you calculate how many days are left until that day, or from any other date. The calendar days in this calculator include Saturdays and Sundays, and you can also find out how many business days are left after that date. By using the calculator below, you’ll have accurate information at your fingertips.
Calculate 35 days from today
You may be wondering how to calculate 35 days from today. Basically, it is the number of days that will fall on a specific date in the future. This includes all business and calendar days, as well as Saturdays and Sundays. When you enter the date, it will display all of the days in the following order. You can also use this calculator to figure out how many days are in between today and a specific date.
The next step in using a days from today calculator is to input the start date you wish to find. It will then use a calendar to make it easier to input the date. After that, you will have to enter the time value. Alternatively, you can also add or subtract a number of days. The calculator will display the final date and facts about the date. In this way, you can determine how long it will take you to complete a task, or when to plan your next vacation.
If you need to calculate the date of a specific date in a different time zone, you can use the calculator for that format. You can also use multiple day month year formats. The calculator is provided as a service and is not responsible for any damages. You are using it at your own risk. An incorrect calculation can put you or a loved one in danger. So, make sure you use it correctly! This date calculator will give you a precise date of when you will get your next paycheck.
The next time you want to calculate the date of a birthday, anniversary, or wedding, try putting it on a calendar. You can also find out how many days will pass between today and the birthday you are celebrating. If you want to calculate the date of a pending birthday, you will need to use calendar days and computer timezone. It will take you a little more time, but it’s a great way to see what your birthday will look like.
Calculate 35 days from a specific date
Do you want to know how many days are left until a specific date? This simple date calculator will help you figure out the exact number of days to the specific date. All you need to enter is the start and end day, and your desired date. In addition, the calculator also shows the day of the week, which makes it easy to determine a day’s duration. The results of this simple date calculator will be displayed in a list with the number of days to the specific date.
The formula to calculate 35 days from a specific date is simple. To start, you can use today’s date as your reference. This would be a Sunday. Next day would be Monday, and so forth. Thus, to calculate 35 days from today, you would have to count 49 days in total, which would equal to July 17, 2022. Then, you would simply divide 49 by the number of weeks.
The calculator can also be used with year and month formats. Be aware that we don’t take responsibility for inaccurate calculations, and you should use it at your own risk. It is possible for the calculation to be incorrect and lead to serious harm, even death. So, always use a calculator with caution. It is best to avoid using such a tool if you’re not sure how to use it properly.


28 SAT Math Lessons to Improve Your Score in One Month
Hate SAT Math? Get 28 SAT Math Lessons to Improve Your Score in One Month
28 SAT Math Lessons to Improve Your Score in One Month workbook is designed by Dr. Steve Warner to help students get a Perfect Score on the SAT Subject Test and how to prepare for your SAT Math in the most effective way while investing the minimum amount of time. 28 SAT Math Lessons to Improve Your Score in One Month emphasize that any difficult math question can completely be solved with a solid understanding of basic concepts. As the old proverb says, “Where there is a will, there is a way.”It is Dr. Warner’s great wish that all students who work on these books can reach their ultimate goals and enter the college of their dreams. There are three main components to SAT Math preparation, first learning strategies, practicing problems, taking practice test. All of these were collaborated in the book by SAT Math exam experts which can help you ace your test. Through your hard-work, perseverance, and practicing tests in 28 SAT Math Lessons to Improve Your Score in One Month your door towards acing your SAT Subject Test would be wide open.
28 SAT Math Lessons to Improve Your Score in One Month
Put your first-choice college well within your reach with 28 SAT Math Lessons to Improve Your Score in One Month. The lessons in this series of books have been created by a Ph.D. in mathematics with more than a decade of SAT math tutoring experience. Each lesson has been carefully constructed to provide you with clever and efficient ways of solving problems while ensuring that you spend less time on each question.
The books in this series contain beginner, intermediate and advanced courses. The beginner course is designed for students scoring below 500 in SAT math and the intermediate course is specifically designed for students that are currently scoring between a 500 and 600 in SAT math on official College Board practice SATs and want to get a higher score. The advanced course is designed for students that are scoring above 600 in SAT math and want to get an 800 score. The targeted nature of these courses will ensure that not a single moment of time is wasted during your SAT math prep. Simply complete each lesson in the order given, and the results will follow.
The main part of each book consists of 28 lessons that teach precisely the concepts, strategies, and SAT math problems necessary to take you to the next score level. Additional optional material is also included for students that find themselves progressing at an accelerated rate.
The Material in 28 SAT Math Lessons to Improve Your Score in One Month
The material in 28 SAT Math Lessons to Improve Your Score in One Month includes 32 of the most effective SAT math strategies ever published, 115 problems with solutions showing how to use each strategy properly and several different solutions for most solved problems.
“I am a tutor in Atlanta, and I’ve taught SAT Math for years. This book (28 SAT Math Strategies To Improve Your Score In One Month) is extraordinary.
There’s something about this book that’s drastically different about the others. Other books usually have the layout of 20 sample questions (like they would in the SAT), and you work through them, and check your answers. This book breaks down the types of questions seen in the SAT. Geometry, Algebra, Statistics. And you work through one problem at a time. The book offers multiple methods to approach any given problem. And the thing is that every student tackles math questions differently. By offering multiple angles to the problem, he allows the student to pick the method easiest to him/her.
I’ve used several books such as Kaplan, Princeton Review, Barrons, but honestly there’s nothing different among all those books. I used to teach with those books, but slowly I’ve transitioned all my students to using this book. They have the same layout, but this brings something new and refreshing to the table. I’m happy to see SAT tools like this out on the market!!” Alex Ahn, Atlanta, Georgia
“I just love this book (28 SAT Math Strategies To Improve Your Score In One Month). It is written by an Associate Professor of Mathematics who has also been tutoring SAT Math students over the past decade, so the book is filled with years of experience and knowledge in what students need to know to maximise their marks. I think it is very clearly explained with plenty of good, relevant, practice questions and solutions. The shortcuts and strategies that are taught to help speed up answering the questions are simple and easy to follow, and I like the way the solutions to the problems show both the shortcut strategies, plus the more formal methods that are used at school, to give the student a good comparison between the two methods. The extra tips, optional information and further questions are good too for extra practice.
I think this book would really help those students who are working at an intermediate level to improve their SAT score, and it should really boost their confidence. It is a great self-study book, but would be really helpful for tutors as well. For students studying alone, I think the amount of work in this book is perfect to be covered in a one month period. To be able to improve your SAT score with just one month of good practice makes this book real value for money. Of all the SAT Math books you could choose from, I think this one is the best.” Kathi Wyldeck, Tutor, Australia, FunFitnessLearning.com


Singapore Math® students earn #1 ranking on 2015 TIMSS and PISA international achievement tests after consistently using education publisher Marshall Cavendish’s curriculum
TARRYTOWN, NY, Jan. 24, 2017 – Marshall Cavendish Education, publisher of Singapore Math® textbooks Math In Focus® and Primary Mathematics, proudly announced that its math and science students in the Republic of Singapore scored first internationally again on the 2015 Trends in International Math and Science Study (TIMSS). These students have topped the world in math and science for 20 years now. Marshall Cavendish Education (MCE) dominates the Singapore school market, with all of the primary schools using only its science curriculum and 75% exclusively using its math curriculum. The same curriculum and teacher training that propelled Singapore Math® students to the #1 ranking on both the 2015 TIMSS and the Program for International Student Assessment (PISA) achievement tests is also helping to turn around American school districts and improve students’ performance in math on state assessments.
While many factors contribute to students’ success, a common thread in this story is MCE’s collaborative role with Singapore’s Ministry of Education in the development of Singapore Math® curriculum and teacher professional development courses. As a result, Singapore students have consistently performed the best out of 60 countries studied by the TIMSS. Singapore students scored 100 points higher in math than students in the USA, which scored below the top 10 out of 60 countries. These results have been consistent over a 20-year period.
The Singapore Math® pedagogy emphasizes teaching students to think and persevere when solving problems. In addition to demonstrating math content mastery, Singapore Math® students are able to apply their knowledge and conceptual understanding to solve problems. These important competencies provide a strong foundation for higher education and continuing learning throughout their lives.
MCE’s holistic approach to learning and teaching is fundamentally changing math education in the United States by providing teachers with the same pedagogy, curriculum, supplemental materials and digital resources that have put its Singapore students at the top of all global math performance studies. The company has been successfully helping American students at many K-8 schools to get on the right track and measurably improve their performance in math on state assessments. MCE offers adapted and aligned to Common Core State Standards core math curriculum and textbooks for the USA as Singapore Math® Math In Focus® and Primary Mathematics, as well as 16 customized In-School Professional Development courses for teachers, each containing six hours of mathematics content woven with Singapore Math® pedagogy that equips teachers with strategies and best practices to provide great teaching for every child.
Eight two-year comparisons between 2013 and 2015 of state test scores at different school districts using Singapore Math® in New York, New Jersey and Nebraska with at least 400 and as many as 6,400 students showed significant improvement. The comparisons were done during the year students began using Singapore Math® textbooks and the year before. They show improvements in student’s math achievement at every set of participating primary grades 3-5 or middle grades 6-8. Every grade level of participating students at each school district gained at least 3 percentage points and most gained 9 or more percentage points after implementing the curriculum. Third graders at Southern Valley School District in Oxford, NE made the greatest improvement out of all the comparisons, with a whopping 37-percentage-point climb to 89% of those students scoring at levels 2 (meets) and 3 (exceeds) on their state assessment. The average gain among all participating grades in Southern Valley was 23%.
According to Paul Castiglione, Vice-Principal of Middle School at North Haven, CT, his public school district’s students in grades 3 to 8 scored well above the state average by as much as 21 percentage points in math on the 2015/16 state SBAC test after using Singapore Math® textbooks. Every grade level improved their 2014/15 math scores by 14 to 31 percentage points in 2015/16.
“Singapore Math® pedagogy changed the way teachers planned and delivered instruction from a classroom,” said Castiglione. “What was once a teacher-led classroom where the teacher did the vast majority of talking and explanations, turned into a student-led classroom. Over the last seven years, we have been able to see that both teachers and students have a better understanding of the meaning behind the math by using the conceptual understanding of concrete, pictorial and abstract approach.”
“Our district adopted the Singapore Math® series as the primary instructional resource for K-5 mathematics approximately five years ago,” said Dr. Corrine Edwards, Director of Learning, Curriculum, Instruction and Assessment for Saginaw Township Community Schools in MI. “Since that time, we have experienced the value in expanding its uses throughout grade 8 and coupling the use of this resource with job-embedded and sustained intensive teacher professional learning and training. All of which has resulted in a district-aligned K-8 math curriculum and model for Tier I instructional practices and approaches to teaching and learning that puts and keeps each and every one of our students at the center of our work. Our student achievement scores provide evidence of the ongoing benefits of these efforts.”
Hoover Herrera, Professional Development Manager, International, at MCE, trains teachers in the USA, Latin America and around the world. All MCE professional development staff are trained directly in Singapore for authenticity and consistency.
“What is different in Singapore Math® classrooms, is that we are interested in finding answers to math problems, but our higher goal is to get students to think deeply when faced with a problem,” said Herrera. “Sometimes we give the answer, but want students to give different ways to solve the problem. There is lots of talking and dialogue among students. It is not teacher-focused. We use ‘model drawing’, using bar models that work great for visualizing problems. We give students tools and strategies to problem-solve. Math is an excellent vehicle for a person to develop their problem-solving abilities!”
Math In Focus and Primary Mathematics
Singapore Math® Primary Mathematics textbook series for grades K-6 is the adapted version of the internationally respected mathematics materials MCE created in collaboration with the Singapore Ministry of Education. It follows the five key learning models integrated in the Singapore Math® Approach: Concrete-Pictorial-Abstract approach, model drawing, teaching-to-mastery, metacognition and spiral progression. Primary Mathematics curricula also include a digital courseware that engages students for differentiated learning and gives teachers easy-to-use tracking and management features.
Singapore Math® Math In Focus for grades K-8 is adapted from Singapore’s My Pals Are Here math series. This series aims to ensure that students strengthen critical thinking and reach mastery of concepts, computational skills and problem-solving and its applications to real-life situations. Math In Focus combines research-based print components with online resources that make math engaging and accessible to students. Content is developed using the Concrete-Pictorial-Abstract Approach, which allows students to master math concepts, develop critical thinking and strengthen problem-solving skills. The series includes eBooks, interactive whiteboard activities, online activities, both concrete and virtual manipulatives, and a Bar Modeling app that provide students with hands-on experiences that lead to positive attitudes towards math and increased confidence as they grow in the subject.
Singapore Math® Primary Mathematics and Math in Focus textbook series are available in print format with digital components. Math In Focus is sold through Houghton Mifflin Harcourt. Primary Mathematics is available only through Singapore Math, Inc. Singapore Math® In-School Professional Development courses may be scheduled through MCE. For information, visit http://www.mceducation.us/professional-development/, call (800) 821-9881, or email firstname.lastname@example.org.
Marshall Cavendish Education
Marshall Cavendish Education (www.mceducation.us) is the authentic provider of Singapore Math® educational solutions. For nearly 40 years, Marshall Cavendish Education has been a leading academic publisher of K-12 math textbooks, workbooks, and digital curricula, as well as a respected provider of professional development for educators. With headquarters in Singapore and US offices in Tarrytown, NY, Marshall Cavendish Education has been on a mission to revitalize math instruction in classrooms worldwide. The company’s products have been adopted by educators and embraced by students in over 50 countries.
# # # #
Julie Gates for Marshall Cavendish
562-429-5972 or email@example.com


Recently, research on the geometric properties of value functions and attempts to apply these properties to various fields of Reinforcement Learning (RL) have been actively conducted. This post is an introduction to Value Function Geometry including an introduction of the paper "The Value Function Polytope in Reinforcement Learning" by Dadashi et al 1.
This post aims to explain the basic concepts of value function linear approximation and representation learning. Also, the paper 1 establishes the geometric shape of value function space in finite state-action Markov decision processes: a general polytope. By reimplementing the paper myself, I was able to check the surprising theorems and geometric properties. I have attached some results that I checked directly in the post.
Figure 1: Mapping between policies and value functions 1
We usually consider an environment with a Markov Decision Process(MDP) in Reinforcement Learning 2. Markov Decision Process
A stationary policy
The state-value function
The action-value function
In particular, the state-value function is an expectation over the action-value functions under a policy
In the case, we take an action by following an argmax policy
Figure 2: Geometric View of Value Function 3
Figure 2 represents the geometric relationship between the state-value function and the action-value function, when following an argmax policy. Each line corresponds to the action-value function and the bold line corresponds to the state-value function. It can be seen that the maximum action-value selected for each state is the state-value function. In Figure 2, it can also be checked that
Figure 3: Value Functions for the mountain car problem using DQN
Figure 3 is an example of value functions that I obtained for the mountain car problem. Both used DQN (Deep Q-Networks) to train the agent. Figure 3(a) is based on 2000 runs of mountain car without changing the reward, and Figure 3(b) is based on 500 runs of mountain car with adding a heuristic reward. I gave a bonus reward of 15 times the velocity of the next state. By giving a heuristic reward to the agent, the mountain car was able to learn and train faster.
3. Value Function Linear Approximations
A value function for a policy
For a given representation
Figure 4: A deep reinforcement learning architecture viewed as a two-part approximation 4
Assume a finite state space:
Let's start by introducing some vector and matrix notation to make it more convenient.
It is well known that the state-value function
Given a policy
In the case, we do not know the entire model completely, we cannot calculate
Projection operator is a widely used operator in Statistics for Multiple Linear Regression Models and Least Squares Estimation.
Projector operator satifies the normal equations:
Back to the value function approximation, let's assume a finite state space
We consider the approximation minimizing the squared error:
4. Value Function Polytope in Reinforcement Learning
Definition 1 : Polytope
Definition 2 : Polyhedron
The Space of Value Functions
The main contribution of Dadashi et al 1 is the characterization of the space of value functions. The space of value functions is the set of all value functions obtained from all possible policies.
Dadashi et al 1 show that
Figure 5: Space of Value Functions for 2-state MDPs
Figure 5 depicts the value function space
Figure 5: Left
Figure 5: Right
I used the following convention to express
To easily check the shape of the polytope, I checked with the value function spaces from 2-state MDPs, which is convenient to visualize. The policy space
In fact, if you look closely at the right of Figure 5, you'll find something a little odd. You may think it's not a perfect polytope because the upper left hand is a little empty. To double-check if the policy was sampled uniformly from the policy space, I visualized the mapping between policy samples and value function samples.
Figure 6: Mapping between sample policies and sample value functions. The red points are the value functions of deterministic policies
To easily visualize the policy space and value function space, 2-state 2-action MDP was used for Figure 6. It includes 50,000 pairs of policy and value function samples. The specific details of MDP presented in this figure are as follows.
The left of Figure 6 definitely shows that the policy has been sampled uniformly. Despite the uniformly selected policies, you can still see the sparse empty space in the upper left corner of the value function space. Also, to confirm the existence of the polytope's vertex, I took the value functions of deterministic policies and confirmed that they become the vertex. In conclusion, we can know that the sparse empty space in the figure is simply due to the lack of sample numbers. It can also be seen that the polytope of the value function space does not consist of equal density.
Definition 3 : Policy Agreement
For a given policy
Definition 4 : Policy Determinism
-deterministic for if .
- semi-deterministic if it is
-deterministic for at least one .
- deterministic if it is
-deterministic for all states .
We denote by
Value Functions and Policy Agreement
Now, I will introduce one of the most amazing theorem of this paper, line theorem. It characterizes the subsets of value function space that are generated by the policies which agree on all but one state. Surprisingly, it describes a line segment within the value function polytope and this line segment is monotone.
Theorem 1 : Line Theorem
Furthermore, the image of
Furthermore, the image of
Theorem 1 implies that we can generate
Figure 7: Illustration of Theorem 1 Line Theorem.
Figure 7 actually illustrates the value function space drawn by the interpolated policies between
Figure 7: Left
Figure 7: Right
For both figures in Figure 7, the following
Figure 8: Value functions of mixtures of two policies in the general case.
The red points in Figure 8 are the value functions of mixtures of two policies. You can see that the red points are curved, not straight. It can be seen that the condition, the policies should agree on all but one state, is a necessary condition.
By visualizing the policy space, we can easily recognize that the two policies do not agree on any states. In the case of
Corollary 1.* *For any set of states
Corollary 1 can be proved by mathematical induction on the number of states
Figure 9: Visual representation of Corollary 1. The red dots are the value functions of deterministic policies.
As you can see in Figure 9, the space of value functions is included in the convex hull of value functions of deterministic policies. Also, you can check the relationship between the vertices of
Figure 10: Visual representation of Corollary 1. The value functions of deterministic policies are not identical to the vertices of V.
The Boundary of
Theorem 2 and Corollary 3 show that the boundary of value function space is described by semi-deterministic policies.
Let's start with first defining the affine vector space before we mention Theorem 2. Consider a policy
Consider the ensemble of policies
Corollary 3.* *Consider a policy
Figure 11: Visual representation of Corollary 3. The orange points are the value functions of semi-deterministic policies.
The Polytope of Value Functions
Consider a policy


7:00 – 10:00, 10:30 – 5:30 ASRC
- Tenure review meeting at 10:00? Show up and see, I guess
- Continuing Opinion Dynamics With Decaying Confidence: Application to Community Detection in Graphs. Details here.
- We prove, under some conditions, the existence of a solution to the system dynamics, convergence to clusters, and a non-trivial lower bound on the
distance between clusters. Huh. So bubbles must exist at a certain minimum information distance from each other??
- Inverse matrices are needed because we can’t divide by a matrix but we can multiply by its reciprocal.
- Lemma – a subsidiary or intermediate theorem in an argument or proof.
- (From Wikipedia) In measure theory, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of n-dimensional Euclidean space. For n = 1, 2, or 3, it coincides with the standard measure of length, area, or volume. In general, it is also called n-dimensional volume, n-volume, or simply volume. It is used throughout real analysis, in particular to define Lebesgue integration. Sets that can be assigned a Lebesgue measure are called Lebesgue measurable; the measure of the Lebesgue measurable set A is denoted by λ(A).
- The backward slash is kind of the set theory equivalent of subtracting, i.e.,
- Group doc on how to fix fake news
- Back to working through NMF.
- Looks like we’ll watch videos tomorrow morning


Kumon of Scott Township
Kumon Math and Reading Center offers individualized and personal instruction. For more than 50 years its after-school enrichment program has helped children achieve knowledge and independence. Friendly instructors not only teach your child math and reading, they motivate all "students to perform at their highest potential," and their goal is to instill a love of learning.
Kumon of Scott Township is part of the world's largest after-school math & reading program, helping children of all ages become self-learners.
- Hours: Tue 3pm-7pm, Fri 3pm-7pm


Statistics about how kids are doing with STEM in our schools.
Modelling by PwC shows that shifting just 1 per cent of the workforce into STEM roles would add $57.4 billion to GDP (net present value over 20 years).
The mathematical literacy levels of Australian 15 year olds have declined significantly since at least the turn of the century. The top 10% of Australian students now perform at about the same level as the top 40-50% of students in Singapore, South Korea and Chinese Taipei.
Year 12 participation in STEM subjects is declining. Over the twenty-year period from 1992 to 2012 there was a fall in participation of 11% for intermediate mathematics,10% for biology, 5% for chemistry and 7% for physics.
In the most recent round of Year 4 TIMSS (Trends in International Mathematics and Science Study) Australia came 18th out of 50 countries in mathematics and 25th out of 50 in science. We have fallen behind Canada, Ireland and many of our Asian neighbours.
In 2012 in the highly innovative manufacturing nation of Singapore, 52% of university graduates were from a STEM-related course. In Australia the proportion was just 16%.
According to the Chief Scientist, less than 3% of total primary school teaching time is devoted to science instruction. By contrast, in Western Europe the average is 9% of total teaching time. (PwC, 2016)
Engaging children in science before the ages of 11 to 14 is critical to generating long-term interest in the discipline. However, Australian primary school teachers are required to spend only 1.5-2.5 hours on science and technology in the 30 hour school week.
Participation in STEM subjects in Australian schools is declining, with enrolment in some elective subjects at a 20 year low.


When inputted into a BAII+ calculator, the \(PY\) automatically copies across to the compounding frequency (\(CY\)). Unless your \(CY\) also changed to the same frequency, this means that you must scroll down to the CY window and re-enter the correct value for this variable, even if it didn’t change. Similarly, the formula for calculating the present value of an annuity due takes into account the fact that payments are made at the beginning rather than the end of each period. Average annual growth rate is the average increase in the value of an investment, portfolio, asset, or cash stream over a period of time. All else being equal, the future value of an annuity due will be greater than the future value of an ordinary annuity because it has had an extra period to accumulate compounded interest. In this example, the future value of the annuity due is $58,666 more than that of the ordinary annuity. The future value of an annuity is a way of calculating how much money a series of payments will be worth at a certain point in the future.
In the previous section you learned to recognize the fundamental characteristics of annuities, so now you can start to solve any annuity for any unknown variable. This section covers the first two, which calculate future values for both ordinary annuities and annuities due. These formulas accommodate both simple and general annuities.
For example, if the $1,000 was invested on January 1 rather than January 31 it would have an additional month to grow. An annuity due, you may recall, differs from an ordinary annuity in that the annuity due’s payments are made at the beginning, rather than the end, of each period. You can calculate the present or future value for an ordinary annuity or an annuity due using the following formulas. There are several ways to measure the cost of making such payments or what they’re ultimately worth. Here’s what you need to know about calculating the present value or future value of an annuity. Perpetuity, in finance, is a constant stream of identical cash flows with no end, such as an annuity. In an ordinary annuity, payments are made at the end of each agreed-upon period.
The future value of an annuity is the total value of payments at a specific point in time. In ordinary annuities, payments are made at the end of each period. With annuities due, they’re made at the beginning of the period. An annuity table is a tool for determining the present value of an annuity or other structured future value of annuity series of payments. When he was 23 years old while attending the University of Utah he was hurt in a construction accident. Over the next 12 months he had several surgeries, stem cell injections and learned how to walk again. During this time he studied and mastered how to make money work for you, not against you.
Future Value Of Annuity:
The PV of an annuity can be found by calculating the PV of each individual payment and then summing them up. Generally speaking, annuities and perpetuities will have consistent payments over time. However, it is also an option to scale payments up or down, for various reasons. Annuity – A fixed sum of money paid to someone – typically each year – and usually for the rest of their life. If the last argument is not supplied, the annuity is assumed to be an ordinary annuity.
So, for example, an immediate annuity or when that being payouts in five years is worth more than an annuity that will make distributions in twenty years. All of this information can be found in your annuity contract. And, once you have it in hand, it only takes a couple of minutes for the calculator to generate a quote that will indicate interest rates, market value, and the impact of time. In this scenario, you could take a lump sum or $300,000, with a 5% discount rate. To learn more about or do calculations on present value instead, feel free to pop on over to our Present Value Calculator.
Present Value Of Annuity Calculation
To find the FV, you need to know the payment amount, the interest rate of the account the payments are deposited in, the number of periods per year, and the time frame in years. The six potential variables included in an annuity calculation are the present value, the future value, interest, time , payment amount, and payment growth . Annuities are basically loans that are paid back over a set period of time at a set interest rate with consistent payments each period. Payment/Withdrawal Amount – This is the total of all payments received or made receives on the annuity.
- In the examples in this article, a person invested $4,000 per year for 8 years and deposited $500 per quarter for 10 years.
- The PV of an annuity can be found by calculating the PV of each individual payment and then summing them up.
- Calculate the future value of an annuity, with case A being an ordinary annuity and case B being…
- First, divide the discount rate by the number of payments per year to find the rate of interest paid each month.
You can find derivations of future value formulas with our future value calculator. Ordinary annuities are more common, but an annuity due will result in a higher future value, all else being equal. Julia Kagan has written about personal finance for more than 25 years and for Investopedia since 2014. The former editor of Consumer Reports, she is an expert in credit and debt, retirement planning, home ownership, employment issues, and insurance.
An annuity is basically a financial contract that a person signs with an insurance company. You purchase the contract through either a lump sum payment or a series of payments, and then receive monthly payments in retirement. There are both fixed and variable annuities, with different levels of risk and reward. Before explaining how to find the present value of an annuity, we should first define the present value of an annuity. In simplest terms, this is the cash value of all your future annuity payments. Included in the calculator is the discount rate or rate of return. That’s important to be aware of since the discount rate can rescue an annuity’s future payments.
The first and last payments of an annuity due both occur one period before they would in an ordinary annuity, so they have different values in the future. The Present Value of an annuity can be found by calculating the PV of each individual payment and then summing them up. As in the case of finding the Future Value of an annuity, it is important to note when each payment occurs.
- The future value of an annuity is the total value of payments at a specific point in time.
- Additionally, you can use a spreadsheet application such as Excel and its built-in financial formulas.
- We will also assume that amounts paid out are negative and amounts received are positive.
- For example, in the RRSP illustration above, the statement “you have not started an RRSP previously and have no opening balance” could be omitted.
At the top of the list would be that annuities aren’t liquid. They also come with high fees and penalties, misleading high yield rates. And, overall, annuities are more complex https://www.bookstime.com/ than most other retirement vehicles. FV (along with PV, I/Y, N, and PMT) is an important element in the time value of money, which forms the backbone of finance.
When Is The Present Value Of An Annuity Calculated?
An annuity creates a guaranteed income for your retirement. While it is unlikely to be your sole source of cash during retirement, it can effectively supplement yourIRAor401.
- Your annuity’s discount rate also has a high impact on its present value.
- The first payment is received at the start of the first period and, thereafter, at the start of each subsequent period.
- Since you do not have the yearly $100 annuity, or $300 in your hand today, you can’t earn interest on it, giving it a discounted value today of $272.32.
- You can use the FV function to get the future value of an investment assuming periodic, constant payments with a constant interest rate.
- Because the annuity payments are made quarterly, we need to look at the fortieth period row until we find the factor .
- Since you added 1 to perform the compounding, mathematically you now need to remove the 1.
- So, let’s assume that you invest $1,000 every year for the next five years, at 5% interest.
Present value calculations are influenced by when annuity payments are disbursed — either at the beginning or the end of a period. Companies that purchase annuities use the present value formula — along with other variables — to calculate the worth of future payments in today’s dollars. The payments are at the end of the payment intervals, and the compounding period and payment intervals are different. The formula for the future value of an ordinary annuity is indeed easier and faster than performing a series of future value calculations for each of the payments.
Calculator Symbol Key
You can use the PV function to get the value in today’s dollars of a series of future payments, assuming periodic, constant payments and a constant… The Excel FV function is a financial function that returns the future value of an investment. The PV function is a financial function that returns the present value of an investment. You can use the PV function to get the value in today’s dollars of a series of future payments, assuming periodic, constant payments and a constant interest… Additionally, many business investments consist of both cash inflows and cash outflows. When a business wants to make an investment, one of the main factors in determining whether the investment should be made is to consider its return on investment. Commonly, not only will cash flows be uneven, but some of the cash flows will be received and some will be paid out.
Learn the formula used to calculate an annuity’s value, and understand the importance of labeling specific numbers to calculate an output over time. This means to multiply the factor shown in the table for a given number of periods and interest rate by the periodic investment amount. In other words, find the factor in the table, look at the column for the interest rate you are using, and multiply that factor by your periodic payment. The future value of an annuity is the sum of all the periodic payments plus theinterest that has accumulated on them. An annuity is a series of equal payments made at specified intervals. Annuities are often called rents because they are like the payment of monthly rentals.
Representatives may utilize an autodialer and standard cellular rates apply. If a present value (\(PV\)) is involved, by formula you need to do two calculations using Formula 9.3 and Formula 11.2. If you input values for both \(PV\) and \(PMT\), the calculator does these calculations simultaneously, requiring only one sequence to solve. The P/Y is no longer automatically set to the same value as C/Y. If the values are the same, as in the case of simple annuities, then taking advantage of the “Copy” feature on your calculator let’s you avoid having to key the value in twice. Use this calculator to find the future value of annuities due, ordinary regular annuities and growing annuities. Roger Wohlner is a financial advisor with 20 years of experience in the industry.
The present value of an annuity is based on a concept called the time value of money. For the uninformed, this is a widely accepted theory that it’s better to accept a lump sum of money today than waiting for an identical sum in the future. The reason being that future payments aren’t as valuable because of uncertain economic conditions.
The future value of an annuity is the sum of the future values of all of the payments in the annuity. It is possible to take the FV of all cash flows and add them together, but this isn’t really pragmatic if there are more than a couple of payments. Payment/Withdrawal Frequency – The payment/deposit frequency you want the present value annuity calculator to use for the present value calculations. The interval can be monthly, quarterly, semi-annually or annually.
Calculating The Present Value Of An Ordinary Annuity
While you can make money via interest and other return mechanisms, that rate of return you may get in five or ten years won’t be as much as the initial investment. In other words, that $10,000 today is worth more money than what you’re promised in the future. An individual is paid biweekly and decides to save one of his paychecks per year for retirement. One of his paychecks is $2,000 for the first year and he expects to earn a 5% raise on his net pay each year thereafter. After finishing this calculation, we find his amount after the 5th cash flow would be $11,700.75.


Number and Counting Rhymes and Jingles: A number and counting book for junior classes. It is photocopiable.
MakeSure Maths: A series of 8 learning workbooks covering the whole of the primary mathematics curriculum. Three assessment pages included. Answers are in removable centre section.
Maths Zone: a series of 8 textbooks for the pupil learning maths with the help of the Resource Teacher or Learning Support Teacher.
Maths Together: a series of 6 manuals from Junior/Senior Infants to 6th Class level.
Number Facts: a series of 3 books on Multiplication, Division, and Addition & Subtraction.
Tangrams: a hands-on book with lots of mathematical activity in shape and space.
Dictionary of Primary Maths: all the terms encountered at primary level.
Spelling Progress: a series of four spelling workbooks.
All of the above books were written by primary school teacher Florence Gavin MA(Ed).
Mental Health in Children and Adolescents: A Guide for Teachers.
All the books are published and printed in the Republic of Ireland
Metric Wooden Rulers: 25cm and 30cm school rulers.
You will find the prices of all items on the ORDER page.
Why not browse the site to see if we meet your needs? If you are a teacher you can place an order directly from this site and it will be dispatched within a couple of days. If you prefer, post your order or order by phone by calling us at 041-9831908 (9 a.m. to 6 p.m.).
Our email address is firstname.lastname@example.org
Mulberry Publications, Drogheda,


Math is recognized as a hard subject making students fear mathematics leading to low scores. Math exams are conducted over the grades. Pressure of having good marks in test creates math anxiety in students. All students need assistance outdoors the classroom to maintain the mathematics class and also to gain confidence. If they do not get the assistance they require, studying math turns into a frustrating and uncomfortable experience.
Students missing a powerful math foundation, find math very hard within the greater grades. So, parents must take a hands-on method of their child’s math education right from the start itself. They ought to make certain their child gets all of the help he/she must set up a strong math foundation.
Employing an Math tutor is a great fix for your problem. Since the teaching of Math ought to be child centered, an individual tutor could be a great resource. An individual tutor won’t gauge the aptitude and degree of students and may devise learning strategies accordingly. Every student has different needs with no two students have a similar learning style. Inside a large classroom setting, it’s impossible for that instructor to consider proper care of the training requirements of each and every individual.
Math tutors could be located by requesting recommendations from family and buddies. You may also look for a math tutor online. You will find a lot of websites that provide sites. A number of them offer online for free math tutors. You are able to make contact with an online tutor, and may request a demo session. If you want his/her teaching, you are able to go for further sessions.
Best results in tough subjects like mathematics can be achieved by way of choosing the right kind of math tutor who is able to lend a helping hand and expert support for almost any queries or clarifications that one may have.


For Entry Level Certificate (ELC) Mathematics at Edith Kay School, we follow the AQA specification. This qualification is helpful for our students to prepare for GCSE. The component-based structure of the qualification provides our students with the opportunity to work in short programmes. There are eight components:
This qualification is linear, where students submit all the eight components that form the assessment at the end of this course.
At Edith Kay School ELC lessons are interactive, challenging and fun – with all students fully engaged. There are plenty of maths resources available for our students to help picture abstract maths concepts in the real world, including:
Each student will complete a portfolio containing all of the eight components of work made up of between four and eight external assignments. Any remaining components will be made up of internally set classwork.
All components are internally assessed by the teacher and then moderated by AQA. Each component is marked out of 30, giving a total mark out of 240 for the whole portfolio. The outcomes are awarded from level 1 to level 3.


By Martin J. Erickson
Praise for the First Edition
“This first-class textual content may still turn out an invaluable accoutrement for any constructing arithmetic application . . . it’s brief, it’s candy, it’s fantastically written.” —The Mathematical Intelligencer
“Erickson has ready an exemplary paintings . . . strongly advised for inclusion in undergraduate-level library collections.” —Choice
Featuring a contemporary technique, Introduction to Combinatorics, moment Edition illustrates the applicability of combinatorial tools and discusses themes that aren't normally addressed in literature, corresponding to Alcuin’s series, Rook paths, and Leech’s lattice. The ebook additionally provides basic effects, discusses interconnection and problem-solving recommendations, and collects and disseminates open difficulties that elevate questions and observations.
Many very important combinatorial equipment are revisited and repeated a number of occasions during the publication in workouts, examples, theorems, and proofs alike, permitting readers to construct self assurance and make stronger their realizing of advanced fabric. moreover, the writer effectively courses readers step by step via 3 significant achievements of combinatorics: Van der Waerden’s theorem on mathematics progressions, Pólya’s graph enumeration formulation, and Leech’s 24-dimensional lattice. Along with up-to-date tables and references that replicate fresh advances in a number of components, equivalent to error-correcting codes and combinatorial designs, the Second Edition additionally features:
- Many new routines to assist readers comprehend and follow combinatorial thoughts and ideas
- A deeper, investigative examine of combinatorics via workouts requiring using machine programs
- Over fifty new examples, ranging in point from regimen to complicated, that illustrate very important combinatorial concepts
- Basic ideas and theories in combinatorics in addition to new and leading edge leads to the field
Introduction to Combinatorics, moment Edition is a perfect textbook for a one- or two-semester series in combinatorics, graph concept, and discrete arithmetic on the upper-undergraduate point. The booklet can be a good reference for an individual drawn to some of the purposes of basic combinatorics.
By Ian Stewart
By Janet Beissinger
Join the Cryptokids as they follow easy arithmetic to make and holiday mystery codes. This booklet has many hands-on actions which have been established in either study rooms and casual settings. vintage coding equipment are mentioned, akin to Caesar, substitution, Vigenère, and multiplicative ciphers in addition to the fashionable RSA. Math subject matters coated comprise: - Addition and Subtraction with, adverse numbers, decimals, and probabilities - Factorization - Modular mathematics - Exponentiation - major Numbers - Frequency Analysis.
The accompanying workbook, The Cryptoclub Workbook: utilizing arithmetic to Make and holiday mystery Codes provides scholars with difficulties relating to each one part to aid them grasp the strategies brought through the ebook. A PDF model of the workbook is out there at no cost at the obtain tab, a published workbook is out there for $19.95 (K00701). the trainer guide might be asked from the writer through contacting the educational revenues supervisor, Susie Carlisle
Written through an expert with nice functional and educating event within the box, this booklet addresses a few themes in computational quantity conception. Chapters one via 5 shape a homogenous material appropriate for a six-month or year-long path in computational quantity thought. the following chapters care for extra miscellaneous subjects.
By James W. Anderson
The geometry of the hyperbolic airplane has been an energetic and interesting box of mathematical inquiry for many of the previous centuries. This e-book offers a self-contained creation to the topic, appropriate for 3rd or fourth 12 months undergraduates. the elemental method taken is to outline hyperbolic strains and boost a average workforce of adjustments keeping hyperbolic traces, after which research hyperbolic geometry as these amounts invariant below this team of transformations.
Topics lined contain the higher half-plane version of the hyperbolic airplane, Möbius alterations, the final Möbius team, and their subgroups keeping the higher half-plane, hyperbolic arc-length and distance as amounts invariant lower than those subgroups, the Poincaré disc version, convex subsets of the hyperbolic airplane, hyperbolic quarter, the Gauss-Bonnet formulation and its applications.
This up to date moment variation additionally features:
an accelerated dialogue of planar versions of the hyperbolic airplane bobbing up from advanced analysis;
the hyperboloid version of the hyperbolic plane;
brief dialogue of generalizations to raised dimensions;
many new exercises.
The kind and point of the ebook, which assumes few mathematical necessities, make it an incredible creation to this topic and gives the reader with a company seize of the options and methods of this gorgeous a part of the mathematical panorama.
By Hosam M. Mahmoud
A state of the art examine the rising distributional idea of sorting
examine on distributions linked to sorting algorithms has grown dramatically over the past few many years, spawning many targeted and restricting distributions of complexity measures for plenty of sorting algorithms. but a lot of this data has been scattered in disparate and hugely really expert assets through the literature. In Sorting: A Distribution thought, major authority Hosam Mahmoud compiles, consolidates, and clarifies the massive quantity of obtainable learn, supplying a much-needed, entire therapy of the whole rising distributional thought of sorting.
Mahmoud rigorously constructs a logical framework for the research of all typical sorting algorithms, targeting the improvement of the likelihood distributions linked to the algorithms, in addition to different matters in chance concept reminiscent of measures of focus and premiums of convergence. With an emphasis on narrative instead of technical factors, this awfully well-written booklet makes new effects simply available to a wide spectrum of readers, together with computing device pros, scientists, mathematicians, and engineers. Sorting: A Distribution Theory:
* includes introductory fabric on entire and partial sorting
* Explains insertion variety, quickly type, and merge variety, between different methods
* deals verbal descriptions of the mechanics of the algorithms in addition to the required code
* Illustrates the distribution idea of sorting utilizing a wide array of either classical and sleek techniques
* encompasses a number of end-of-chapter routines
By Ingmar Lehmann
An cutting edge and attractive method for the layperson to improve math skills--while truly having fun with it
Most humans agree that math is necessary, yet few might say it is enjoyable. This booklet will convey you that the topic you realized to hate in highschool will be as wonderful as a witty comment, as engrossing because the secret novel you cannot positioned down--in brief, enjoyable! As veteran math educators Posamentier and Lehmann show, for those who observe that doing math may be relaxing, you open a door right into a international of unforeseen insights whereas studying an immense skill.
The authors illustrate the purpose with many simply comprehensible examples. the sort of is what mathematicians name the "Ruth-Aaron pair" (714 and 715), named after the respective profession domestic runs of Babe Ruth and Hank Aaron. those consecutive integers comprise a number of fascinating positive factors, one in all that's that their best elements whilst additional jointly have an identical sum.
The authors additionally discover the weird elements of such numbers as eleven and 18, that have fascinating houses frequently missed through average math curriculums. And to make you a greater all-around challenge solver, a number of difficulties is gifted that seem uncomplicated yet have unusually shrewdpermanent solutions.
If math has pissed off you through the years, this pleasant procedure will educate you several belongings you idea have been past your achieve, whereas conveying the foremost message that math can and will be something yet dull.
By Richard Rusczyk
This can be the ideas handbook simply to The paintings of challenge fixing, quantity 1. The artwork of challenge fixing, quantity 1, is the vintage challenge fixing textbook utilized by many profitable MATHCOUNTS courses, and feature been a major development block for college kids who, just like the authors, played good sufficient at the American arithmetic Contest sequence to qualify for the mathematics Olympiad summer time application which trains scholars for the USA overseas Math Olympiad staff. quantity 1 is acceptable for college students simply starting in math contests. MATHCOUNTS and amateur highschool scholars quite have chanced on it worthwhile. even though the paintings of challenge fixing is ordinary through scholars getting ready for arithmetic competitions, the booklet is not only a set of tips. The emphasis on studying and knowing equipment instead of memorizing formulation permits scholars to unravel huge periods of difficulties past these awarded within the ebook. conversing of difficulties, the paintings of challenge fixing, quantity 1, includes over 500 examples and workouts culled from such contests as MATHCOUNTS, the Mandelbrot pageant, the AMC exams, and ARML. complete options (not simply answers!) can be found for all of the difficulties within the resolution handbook.


Middle School Fellow
I graduated from the University of Virginia in 1994 with a Masters of Education and have been teaching ever since! I started as a Mathematics teacher at the National Cathedral School for Girls and taught my first computer science course there. Since then, I've bounced between mathematics and computer science and currently teach at the Peabody School in Charlottesville, VA. As the Director of Educational Technology, I'm constantly looking for new ways to inspire my students. Currently, I'm working to implement an Engineering 1 course in our Middle School, and am anxiously awaiting the opening of our school's Makerspace in the spring of 2020.
Why did you become a NASEF Scholastic Fellow?
I want to explore eSports as an addition to my school's curriculum and to motivate both girls and boys to create the future of eSports.


This example shows how to invert a non sparse matrix of 500x500
elements of type VpFCartesian (complex number in Cartesian
co-ordinates with fields of type real.
The WFC matrix is initialized with the values of the Fourier transformation and its inverse is compared to the known result placed in WFCI.
The distance between the inverse and the known result is displayed.
The $PrintM statement is commented out in order to show its syntax in
case it is needed, but not to produce over 250,000 lines of output given that
the matrix has 500x500 elements.
Note: This example runs only on Linux and Solaris platforms, using FinSim version 10_0_0 or any subsequent version.
`define mod(val, n) (val - (val/n)*n)
parameter SIZE = 500;
VpFCartesian WFC[SIZE-1:0][SIZE-1:0], WFCI[SIZE-1:0][SIZE-1:0];
real phi0, distance;
integer i, j, mone;
mone = -1;
phi0 = 2*$Pi/SIZE;
$display("phi0 = %e\n", phi0);
$InitM(WFC, $VpCos(phi0*`mod($I1*$I2, SIZE)),
$InitM(WFCI, $VpCos(phi0*`mod($I1*$I2, SIZE))/SIZE,
WFC = WFC**(mone);
/* $PrintM(WFC, "%e");*/
distance = $VpDistAbsMax(WFC, WFCI);
$display("distance = %e\n", distance);


Draft version, Sep 4, 2022
The provided data are extracted from CD proofs as basis for experiments with other systems and techniques, for example, machine learning or computing tree edit distance measures. A particular working thesis to be investigated with such techniques is formulated at the end of this outline, after the necessary concepts have been introduced.
We call the format of the provided data FragSeq, suggesting sequences of proof fragments.
The considered data are composed of pieces that are extracted individually from proofs. Hence we outline their content in the following from the perspective of a single given proof, that is, a D-term that proves a given goal from given axioms. As a particular example we consider a proof of problem LCL044-1. Its axioms are, in Prolog notation:
Its goal is:
We generalize D-terms to permit, in addition to leaf nodes representing an axiom, also leaf nodes considered as open, which we label by 0.
We ascribe to the proof a sequence of construction steps that lead from a one-node tree consisting of a single open leaf to the proof, where in each step an open leaf is replaced either by an axiom leaf or by an inner node with two open children. We call the D-terms appearing in this sequence, where all but the last have at least one open leaf, proof fragments, or briefly frags.
We assume a specific sequence of construction steps, characterized by the replaced node in each step the leaf that appears first in depth-first left-to-right order. (There is actually a vast number of ways to ascribe a sequence of construction steps to a proof tree. For an example tree of size 7 more than 2 million such sequences are possible, such that we defer the consideration of sequences characterized in alternate ways to future work).
The following image shows the D-terms of the proof sequence for the considered proof of LCL044-1, which appears as last member, step 8, in the sequence.
The IPT (in-place theorem) of a node of a D-term with respect to a goal and axioms is its conclusion formula under the most general substitution that takes account of the goal instantiation at the root of the D-term, of copies of axioms at leaves that are not open, and of the relationships induced by detachment.
The frontier of a proof fragment is the sequence of IPTs at its open leafs (in order as these appear depth-first left-to-right) with respect to the overall proof goal and the given axioms.
The following table shows for each proof fragment in the sequence the operation that was applied to close the first open leaf of its predecessor and the resulting frontier. The operations are as follows: d for replacement by an inner node with two open successors; axiom(N) for replacement by a leaf representing axiom N; or the special value init for the first member of the sequence.
|3||d||[i(B,i(A,i(a,n(n(a))))), B, A]|
|5||d||[i(D,i(C,i(a,n(n(a))))), D, i(n(C),i(a,n(n(a))))]|
The construction steps can also be viewed as operations that are directly performed on frontiers. For example, viewed in this way, the frontier of step 3 in the above sequence is obtained from that of 2 by replacing the first member with i(B,Y) and B, where B is a fresh variable and Y is bound to the replaced first member. The frontier of step 4 is obtained from that of 3 by applying the MGU of its first member with a fresh copy of axiom 5 and then removing this first member.
The scope of variables occurring in the formulas associated with a D-term cover the whole D-term (for tableaux, such variables are known as rigid). Hence, a variable may occur in different members of a frontier, expressing constraints between these.
In addition, although different frontiers represent different stages of the proof construction, we use here global variable names to display them, which facilitates to track the changes from one stage to the next.
Our data sets do not just represent the sequence of frontiers that leads to the proof, but also negative examples, data for steps that do not lead to the proof. We represent these as a special kind of partial proofs, which we call nonfrags, and also provide their frontiers. A nonfrag is obtained from a frag, an actual partial proof in the sequence of frags that leads to the full proof, by a single step with an operation other than that used to obtain the successor of the frag in the sequence. An additional prerequisite for the nonfrags is that they have a defined most general theorem with respect to the overall goal, and thus have a defined frontier. As an example, consider step 3 of our example. Its successor, step 4 is obtained from 3 by the axiom(5) operation. Hence, the "other" possible steps would be d, axiom(1), axiom(2), axiom(3), axiom(4). For each of these other steps, the data set contains a nonfrag with the frag of 3 as parent. Their respective frontiers are:
|[i(C,i(B,i(A,i(a,n(n(a)))))), C, B, A]|
A particular working thesis to be addressed with the data is the conjecture that there are general characteristics of and relationships between frontiers and also the axioms that help to distinguish between the step that leads from a proof fragment to its proper successor and the misdirected steps leading to a "nonfrag". If such a distinction is possible, it may be applied to guide a theorem prover.


Calculate the volume of cube, surface area of cube and diagonal of cube for given values:
The Cube is regular hexahedron having six faces which are all squares, the each face has four equal sides and all four interior angles are right angles. The cube has 12 edges and 8 vertices.
On putting the value a for the length, width and height into the formulas for volume and surface area of a rectangular solid.
See Volume and Surface Area of a Cube, below:
Volume of cube : a x a x a = a3
Surface Area of Cube: [ 6a² ]
Diagonal of Cube: [ √3 a ]
Diagonal of Cube ?
The diagonal of a cube is a line segment that joins two vertices of a cube. It is shown with red line in figure.
Properties of a Cube
A cube is a three-dimensional solid object having different diagonals of a cube as the face diagonals and the body diagonal. It has the equal length, width, and height and each of its faces is a square:
The cube has 12 edges, 6 faces, and 8 vertices.
All the faces of a cube are having square shaped, therefore the length, breadth and height are the same.
Each of the faces in a cube meets the other four faces.
The opposite faces or planes in a cube are parallel to each other.
The opposite edges in a cube are parallel to each other.
The angles between any two faces or surfaces are 90°.
Each of the vertices in a cube meets the three faces and three edges.


Nous accueillons Antoine Deza qui est depuis peu professeur à Orsay.
On the polynomial Hirsch conjecture and its continuous analogue
The simplex and primal-dual interior point methods are the most computationally successful algorithms for linear optimization. While simplex methods follow an edge path, interior point methods follow the central path. Within this framework, the curvature of a polytope, defined as the largest possible total curvature of the associated central path, can be regarded as the continuous analogue of its diameter. In this talk, we highlight links between the edge and central paths, and between the diameter and the curvature of a polytope. We recall continuous results of Dedieu, Malajovich, and Shub, and discrete results of Holt and Klee and of Klee and Walkup, as well as related conjectures such as the Hirsch conjecture that was disproved by Santos. We also present analogous results dealing with average and worst-case behaviour of the curvature and diameter of polytopes, including a result of Allamigeon, Benchimol, Gaubert, and Joswig who constructed a counterexample to the continuous analogue of the polynomial Hirsch conjecture. Based on joint work with Tam ́as Terlaky (Lehigh), Feng Xie(Microsoft), and Yuriy Zinchenko (Calgary).


Book Title: 3D Interactive Plots for Multivariate Calculus
Download this book
Book Description: An open textbook created to improve both teaching and learning vital concepts and techniques in multivariable calculus, one of the fundamental courses across the undergraduate curriculum in science and engineering. The goals of this resource are to help learners develop their geometric intuition about abstract and complex mathematical concepts (e.g., partial derivatives, multiple integrals, vector fields), and train them to make connections between concepts visually (e.g., connecting “vectors” in mathematics with “magnitude” and “direction” in physics) in order to more fully understand engineering, physics and mathematical problems (e.g., differential equations) in their subsequent STEM coursework.
3D Interactive Plots for Multivariate Calculus by Dr. Na Yu, Ryerson University is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.


Design a PLL
Design for determining the Free running frequency,Lock range and Capture range of a PLL
In the earlier post about Phase Locked Loop IC we had discussed about the free-running frequency (fOUT), lock range (fL) and capture range (fc) equations. Here let us discuss about the appropriate values that can be given for fOUT, fL, and fc.
Given below is the circuit of an NE/SE 565 IC or the PLL IC.
We assume values for each parameter.
+V = 12 Volt
-V = -12 Volt
R1 = 15 Kilo Ohms
C1 = 0.01 Micro Farads
C2 = 10 Micro Farads
Free-running Frequency = 1.2 / 4R1 C1= 1.2 / (4*15*103* 0.01* 10-6) = 2 Kilo Hertz
Lock Range, fL = ± 8fOUT / V Hertz = 8*2*103/ +12 –(-12) = ±2/3 Kilo Hertz
Capture Range, fC = ± [fL / 2∏ (3.6) (10)3 C2]1/2 = [fL / 2∏*3.6*103*C2]1/2 = ±54.29 Hertz
From the above calculations, the relationship between free-running frequency, lock range and capture range are illustrated in the figure given below.


This course covers, in more depth, basic algebraic concepts introduced in Elementary Algebra. Topics of study include: linear equations and inequalities; quadratic equations; polynomial and rational expressions; radicals and complex numbers; exponential expressions (negative and rational exponents) and logarithmic expressions; linear systems of equations; introduction to conic sections; introduction to functions. Graphing of functions will be done by hand. Real world applications of algebra will be addressed throughout the course.
Intermediate Algebra (QS)
RDG 0900; within the last year, MATH 0990 w/C grade or better, or appropriate Accuplacer score.
Contact Program Manager/Coordinator for upcoming sections.


compound angle formula 中文
Compound angle formulae A-Level Mathematics revision (AS and A2) section looking at compound angle formulae and double angle formulae. This section covers compound angle formulae and double angle formulae. sin(A + B) DOES NOT equal sinA + sinB. equal sinA + sinB.
compound interest formula的中文翻译，compound interest formula是什么意思，怎么用汉语翻译compound interest formula，compound interest formula的中文意思，compound interest formula的中文，compound interest formula in Chinese，compound interest formula的中文，compound interest formula怎么读，发音，例句，用法和解释由查查在线词典提供
double angle formula的中文翻譯，double angle formula是什麼意思，怎麽用漢語翻譯double angle formula，double angle formula的中文意思，double angle formula的中文，double angle formula in Chinese，double angle formula怎麼讀，发音，例句，用法和解釋由查查在綫詞典提供，版權所有違者必
cagr 中文, annual control 中文, annual pharmacotherapy 中文, current annual 中文, annual maintenance 中文, annual median 中文, annual traffic 中文, annual program 中文, annual outlet 中文, compound angle formula 中文, compound animal 中文,
Duplication formula for trigonometrie function are widely used in mathematics field, but generally the material only involves two-fold and three-fold duplication formula. 三角函数的倍角公式在实际中有着广泛的应用 ,而教材中一般只给出了二倍角与三倍角的公式。
Formula for compound angle cosine (+) Despite lacking the dexterity of our modern trigonometric notation, it should be clear from the above corollaries that in Ptolemy’s theorem (or more simply the Second Theorem) the ancient world had at its disposal an
Double-Angle and Half-Angle formulas are very useful. For example, rational functions of sine and cosine wil be very hard to integrate without these formulas. They are as follow Example. Check the identities Answer. We will check the first one. the second one is
Hi there’ There is a formula in penstock standard which can calculate the rolled bend angle from vertical and horizontal projection angle. In one of our case study, two tie in points are connected to each other by having two rolled bends. So, horizontal ( top or plat plan
· PDF 檔案
數學科常用英漢辭彙 2019年4月9日版 angle between two planes 兩平面的交角，兩平面的相交角 angle bisection 角平分 angle bisector 角平分線，分角線 angle of depression 俯角 angle of elevation 仰角 angle of greatest slope 最大斜率的角 angle of inclination （傾
The skeletal formula, also called line-angle formula or shorthand formula, of an organic compound is a type of molecular structural formula that serves as a shorthand representation of a molecule’s bonding and some details of its molecular geometry. A skeletal formula shows the skeletal structure or skeleton of a molecule, which is composed of
The skeleton ·
3. Double-Angle Formulas by M. Bourne The double-angle formulas can be quite useful when we need to simplify complicated trigonometric expressions later. With these formulas, it is better to remember where they come from, rather than trying to remember the
Creating Compound Angles and ISOGEN Output in Tube and Pipe Hello all, I’m new to the Tube and Pipe in Inventor having been used to using AutoCAD to create pipe runs. In an attempt to see what sort of an output the ISOGEN.pcl files produce I drew up a
Math for Machine Technology: Compound Angles study guide by injones79 includes 13 questions covering vocabulary, terms and more. Quizlet flashcards, activities and games help you improve your grades. 1. Rotate the part to the angle of rotation (care must be
Formulas For Arcs and Sectors of Circles
Compound interest, or ‘interest on interest’, is calculated with the compound interest formula. Multiply the principal amount by one plus the annual interest rate to the power of the number of compound periods to get a combined figure for principal and compound
Learn double angle formula with free interactive flashcards. Choose from 500 different sets of double angle formula flashcards on Quizlet. Double and compound angle formula cos2x cos2x cos2x sin2x 2cos^2x-1 cos^2x-sin^2x 1-2sin^2x 2sinxcosx cos2x
8/10/2015 · This video provides the lewis dot structure of AlCl3. It also discusses the geometry, bond angle, and hybridization of AlCl3.
作者: The Organic Chemistry Tutor
Compound definition, composed of two or more parts, elements, or ingredients: Soap is a compound substance. See more. The English verb compound, first appearing in Middle English in the late 14th century as compounen, compownen, comes from Old French compondre, compundre “to direct, arrange,” from Latin compōnere “to put together, add together, match, match up.”
chemical formula definition: the way of representing a substance using the symbols of its elements: . Learn more. These examples are from the Cambridge English Corpus and from sources on the web. Any opinions in the examples do not represent the opinion of
Trigonometry helps us find angles and distances, and is used a lot in science, engineering, video games, and more! Right-Angled Triangle The triangle of most interest is the right-angled triangle.The right angle is shown by the little box in the corner: Another angle is
Know orthocenter formula to find orthocentre of triangle in coordinate geometry along with distance and circumcentre formula only @byjus.com The orthocenter is the intersecting point for all the altitudes of the triangle. The point where the altitudes of a triangle meet
27/7/2009 · 38.angle bisector 39. perpendicutar bisector 40.x-coordinate 41.y-axis 42. orgin 43. polar coordinate system 44.discrete data 45. continuous data 46. frequency distribution table 47. broken- line graph 48.compound bar chart 49. stem-and-leaf diagram 50. back-to
Representing structures of organic molecules using line (or line-angle) diagrams. The one thing that probably causes some of the most pain in chemistry, and in organic chemistry, in particular, is just the notation and the nomenclature or the naming that we use.
Let’s review the basics of chemical bonds including dot structures, hybridization, bond-line structures, electronegativity, and polarity. We will also discuss how bonding and intermolecular forces relate to physical properties such as boiling point.
12/10/2017 · This trigonometry video tutorial provides a basic introduction into reference angles. It explains how to find the reference angle in radians and degrees. New
作者: The Organic Chemistry Tutor
A condensed formula in chemistry, unlike a molecular formula, indicates the bonds between the atoms in a molecule. The condensed formula of a molecule is the formula where the symbols of atoms are listed in order as they appear in the molecule’s structure with bond dashes omitted or limited. dashes omitted or limited.
Polypropylene, a popular synthetic resin built up by the polymerization of propylene. Isotactic polypropylene is produced at low temperatures and pressures, using Ziegler-Natta catalysts.The polymer shares some of the properties of polyethylene, but it is stronger, stiffer, and harder, and it softens at higher temperatures.
Compound Interest: Periodic Compounding Annuities Making Money Introduction to Investing What To Do With Your Money Personal Budget Pay (Wages, Salary) Present Value Net Present Value Internal Rate of Return Investment Graph Numbers Index
Compound definition is – to put together (parts) so as to form a whole : combine. How to use compound in a sentence. History and Etymology for compound Verb Middle English compounen, from Anglo-French *cumpundre, from Latin componere, from com-+ ponere to put — more at position
Find the cutting tool for your specific task andget instant cutting data recommendations.Go to CoroPlus® ToolGuide This section covers threading formulas and definitions for how to calculate cutting speed, feed rate or any other parameter for your thread turning, thread milling or tapping
Based on the comparison of calculation accuracy between compound trapezoid formula,variable step-size trapezoid formula and Romberg formula,the article comes up with some specific selection methods,which contribute to high calculation accuracy and a lower computation complexity.
· PDF 檔案
Helix Angle = arc tan ì. í ì ì ì”/ î. í ñ î ì” or 2.66053 deg [2 deg, 39 min, 38 sec) NOTE: Helix Angle has to be calculated if you are going to grind threads. The reason is that if the grinding wheel head is not rotated to the same as the lead angle the thread will have either a
As, in an inquiry into every other subject, it is necessary to separate the different parts of which it is compounded, till we arrive at their first elements, which are the most minute parts thereof; so by the same proceeding we shall acquire a knowledge of the primary parts of a city and see wherein they differ from each other, and whether the rules of art will give us any assistance in
Engineering Metals and Materials Table of Contents Engineering Calculators Engineering Analysis Menu The following links are to calculators which will calculate the Section Area Moment of Inertia Properties of common shapes. The links will open a new browser
Buy Diamond 提供高質素，價格優惠的美鑽，網上知名，配合手機應用，戒指鑽飾，一應俱全，無論求婚或愛鑽之人，均能輕鬆購買價廉物美之鑽石。 本公司主要出售GIA 認證鑽石，於尖沙咀自設千呎陳列
No compound of gallium(II) is known; any such compound would have an unpaired electron and would behave as a free radical and be destroyed rapidly. The only compounds in which gallium has a formal oxidation state of +2 are dimeric compounds, such as [Ga 2 Cl 6 ] 2− , which contain a Ga -Ga bond formed from the unpaired electron on each Ga atom.
Formula definition is – a set form of words for use in a ceremony or ritual. How to use formula in a sentence. Noun His investment strategy is based on a simple formula. This has proven to be a winning formula. The product is made using a secret formula that the company refuses to reveal.
自动控制原理专业词汇中英文对照 中文 自动控制 自动控制系统 自动控制理论 经典控制理论 现代控制理论 智能控制理论 开环控制 闭环控制 输入量 输出量 给定环节 比较环节 放大环节 执行环节 控制环节 被控对象 反馈环节 控制器 扰动/干扰 前向通道 反馈通道 恒值控制系统 随动控制系统 程序
Mortgages Here you can learn about different types of mortgages and use our free calculators to find monthly payments, interest rates, compare options and terms, and much more. We have a standard mortgage calculator for fixed mortgages, a simple loan calculator, and many others., and many others.
Free financial calculators from mortgage and car loans to credit cards, debt management, investing, and retirement calculators. Investment Calculators Compound Interest Calculator Use for periodic investments, for example when you’ll add money every month.
探索資源 精神堡壘 button 圓柱曲面 仿澳洲迪肯大学毕业 证扣薇374936141办澳洲毕业 证/使馆认证&留信网认证 仿澳洲西澳大学毕业 证扣薇374936141办澳洲毕业 证/使馆认证&留
Symbolab: equation search and math solver – solves algebra, trigonometry and calculus problems step by step
θ = Angle formed by S. Manning’s n Coefficients To calculation The Manning’s n coefficients were compiled from the references listed under Discussion and References and in the references at the bottom of this web page (note the footnotes
Acetic acid has been prepared on an industrial scale by air oxidation of acetaldehyde, by oxidation of ethanol (ethyl alcohol), and by oxidation of butane and butene.Today acetic acid is manufactured by a process developed by the chemical company Monsanto in the 1960s; it involves a rhodium-iodine catalyzed carbonylation of methanol (methyl alcohol).
Free Right Angled Triangle Area & Perimeter Calculator – Calculate area, perimeter of a right-angled triangle step-by-step Math notebooks have been around for hundreds of years. You write down problems, solutions and notes to go back
Condensed structure formulas are also an efficient way to identify a chemical compound. Instead of drawing it out, the structure utilizes the elemental symbols to indicate the number of carbons and the bonded molecules. CH₃CH₂OH is a condensed organic formula.
Taper Degree Calculator Taper Degree is the central angle of the taper measured in degrees. It can be calculated from the taper % or it can be calculated with the number of the different type of tapers. For instance, a #2 morse taper has an angle of 2.86133 degrees.
ASTM International is an open forum for the development of high-quality, market-relevant technical standards for materials, products, systems, and services used around the globe.


READ ‘ABOUT PACIOLI’ AND THE ORIGINS OF ACCOUNTING
Five hundred years ago, Luca Pacioli, a Franciscan Friar, wrote a book on mathematics in which he included a section on the double entry system, “because it would be useful for merchants.” He provided a set of rules for them to follow, but written in a form that the clerks could apply without having to understand his use of a simple equation.
When we return to Pacioli’s simple use of that equation, the whole subject becomes clear and easy to use.
It is as easy as 1 = 1. That’s why it forms the framework on which ‘Understand Accounting’ is built.


What is the common number for Shilong Teer? Find the most recent Shillong Teer Common Number Today, ShillongTeer’s official normal number, here. The Shillong Teer Common Number Today would be built on the performance and goals of previous tests. A mathematical formula will serve as the foundation for the Shillong Teer Common Number. Continue to stay up to date with the latest current Shillong Teer Common Number Today on this page.
Shillong Teer Hit Numbers: What is it?
Shillong Teer Common Number Today which was anticipated from the preceding result number is known as ShillongTeer Hit Numbers. You may also determine ShillongTeer Hit Numbers for your next game using the specific formula for Teer. To provide you with ShillongTeer Hit Numbers, we update them every day.
What are the prevalent numbers in Shillong Khanapara?
In Khanapara, Assam, Khanapara is one of the most popular games. KhanaparaTeer Target is therefore required daily in order to win the game. Every day at 11:00 A.M., we deliver khanaparateer regular figures or objectives. We calculate the Khanapara Hit Numbers using the Khanapara Previous List that we have stored in our database for the current Khanapara game. from the recovered historical khanaparateer outcomes.
Additionally, you may find the daily KhanaparaTeer house, finishing, and hit numbers on the website above, in addition to the KhanaparaTeer direct numbers. Similar to the Guwahati teer game and the Khanapara game.
Teer Common Number: What is it?
Shillong Teer Common Number and Teer Common Number are the same. You are on the correct page if you’re looking for a common number. You may find a total of three common numbers here, all of which are verified. These figures were generated using a unique formula. Shillong Teer Common Numbers are often asked about in the following ways
What mathematical equation is used to determine Shillong Teer Common Numbers?
Shillong Teer Common Numbers Today is calculated using a unique formula. Shillong Teer Common Numbers are calculated using this formula by Teer specialists. Shillong Teer Common Numbers are calculated using the previous results numbers as a source of data.
What is a Shillong Teer Common Numbers formula?
- Shillong Teer Common Numbers may be calculated using a particular formula. Shillong Teer Common Numbers may be calculated using data from past outcomes.
- What is the current Shillong Teer Common Number?
- The current Shillongteer common number is Shillongteer common number. This page publishes the standard Shillong Telephone number.
- What was the common number yesterday in Shillong?
- Shillong Teer’s common number yesterday is the common number for yesterday. On this website, you may also check the Shillong Teer common numbers from yesterday.
Teer Common Number: What is it?
Shillong’steer common number is referred to as “the common number.” Shillong’steer common number and the Teer common number are the same.
What number is most popular today?
Teer common number and Shillong Teer Common Number Today are the same nowadays. Instead of using the teer popular number today, you may use this page’s version.
What are the frequent ShillongKhanaparaTeer numbers?
Since Shillong and KhanparaTeer are the same, Shillong and KhanparaShillong Teer Common Number Today are also identical.
What is the 100% common number in Shillong?
The Shillongteer 100% common number is one of the Shillongteer common numbers that has a 100% probability of appearing in your next draw. You may find a 100% verified common number on this website.
What is the 99% frequent number in Shillong?
The Shillongteer 99% frequent numbers are those that have a 99% probability of appearing in your next draw. You may find a 100% verified common number on this website.
What is the official common number for ShillongTeer?
The Shillong Teer Common Number Today, which is issued by the Shillong Teer association, is the recognized common number. On the shillongteer’s official website, you may get the official common numbers.


Cute numbers is a new concept for me. As I googled the term, I discovered that 4 and 10 are cute numbers. The use of diagram help me to understand the concept better.
There is a large square divided into 4 quarters. Two of these quarters are subdivided into eight smaller squares. These 8 smaller squares together with the last two bigger quadrants make up 10 squares.
Richard Skemp (1978)'s theory on the continuum from relational understanding to instrumental is also new to me. Children need to understand concepts, conventions and procedures.


Sitting down this week and having a look at army lists for tournaments in 2024 and was trying to work out "what is the best unit to use?" and "which unit is most cost effective?" As such I started looking at probabilities and math to try and assist in squad selection. Fortunately, someone has already done some of the hard work so I didn't need to tax my A level math too much!
This article on Goonhammer is appropriate across the board for wargamers, so when planning your gaming have a read and I hope it helps: https://www.goonhammer.com/getting-better-at-warhammer-40000-understanding-probability/


Finds the prime factors of positive integers, solves triangles and circles problems, manipulates complex numbers, does base conversions. Results can be saved or printed. Includes a help file with instructions, example and methodology.
Math Miscellanea is a free software application from the Mathematics subcategory, part of the Education category.
The app is currently available in English and it was last updated on 2002-12-28. The program can be installed on Win98, WinME, WinNT 4.x, Windows2000, WinXP.
Math Miscellanea (version 1.00) has a file size of 2.00 MB and is available for download from our website.
Just click the green Download button above to start. Until now the program was downloaded 115 times.
We already checked that the download link to be safe, however for your own protection we recommend that you scan the downloaded software with your antivirus.


A New Test for correlation on Bivariate Non-Normal Distribution
College of Arts and Sciences
Master of Science in Mathematical Sciences (MS)
Mathematics & Statistics
The sampling distribution of the sample correlation coefficient is unstable, even when the population is bivariate normally distributed. It is the main reason why a reasonably good test for the correlation is difficult to obtain, not to mention that most of the populations in the real world are not normally distributed. This thesis proposes a new method to conduct a right-tailed test for the correlation on bivariate non-normal distributions. The test unitizes the inverse Edgeworth expansion on the standardized form of the sample correlation. A comparative simulation study shows that the new test controls the type I error rates very well for all the distributions considered. An investigation of the power performance of the new test is also provided.
Wang, Ping, "A New Test for correlation on Bivariate Non-Normal Distribution" (2009). UNF Graduate Theses and Dissertations. 1054.