Maths can feel like a tricky subject for some kids, but it doesn’t have to be a chore. In reality, children often avoid these sorts of exercises because they know how difficult they can be for them. If avoided for long enough, maths can fall by the wayside and cause a lot of learning difficulties, issues and mental health problems later on down the line.
All schools will have the facilities to help children with their maths studies, just like at this private school in Cheshire. There will also be ways teachers can help support parents as well, by providing tips to use when teaching your child at home.
Talk About Maths All The Time:
Maths is a subject that some of us just struggle with, so if you keep the conversation going then you can normalise what is interesting and important about learning maths. There are other ways to use maths that your child can incorporate into their learning skills. For example, baking or cooking requires measuring out ingredients, counting out vegetables, and weighing out flour or sugar.
Praise Your Child For Their Efforts:
Keep praising your child where you can. They are going to need that help and direction where they need it, so continue to praise them as best as you can. It’s not about the performance your child does each week, it’s also about how well your child can handle under pressure. Show them that you are proud of their work each week and that will help your child further in their confidence. This doesn’t just apply to Maths either, it can be helpful for a lot of other subjects as well.
Be Positive About Maths:
Having positive thoughts and feelings about maths in front of your child will help reassure them that they can overcome problems they might be facing. Having open conversations that talk about your potentially poor experience with maths back in school won’t do them any favours. While you can talk about maths in a negative way, it’s important to be realistic as well. Your child will have to learn about this subject up until they reach GCSE age, so it’s important to talk more about the positive aspects where possible.
Maths is something every child will go through with many ups and downs, but there’s a lot we can support our children with, including hiring an online maths tutors. Ensuring your child is enjoying school as much as possible should be your aim, so making maths (and other subjects, if applicable) exciting can give them more of a reason to enjoy those days.
This post complies with my Disclosure PolicyFound this useful wondering how you can show me your appreciation? Well, there are some ways you can say thanks and support my website: ➡


I am going to start solving all of the Project Euler problems on my blog. This will take an incredibly long time, but I believe that it's a great warm up for coding. So that being said, there's no better place to begin than with number 1.
Project Euler #1
If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6, and 9. The sum of these multiples is 23.
Find the sum of all the multiples of 3 or 5 below 1000. Project Euler #1
After reading the problem, I have a basic understanding of what I need to do. I need to first find all of the multiples or either 3 or 5 that are less than 1000. Once I have those multiples, I need to add them all together to get my solution.
Collecting the Multiples
First I need to find all of the multiples under 1000. In order to do that I have to know what makes a number a multiple or 3 or 5. A great way to tell is if the number in question divided by either 3 or 5 results in a whole number with no remainder. If this is true, the number is evenly divisible by either 3 or 5 and a multiple. I know that Ruby has a great function for checking for remainders called modulo.
This code will return
true if the
number_in_question is a multiple of 3 or 5. However, we stil have no way of finding the
The problem gives us a hint at where to start for this part. The problem is asking for all multiples that are below 1000. Therefore, we need to check all numbers below 1000. That suggests that we need to use an exclusive range. So to collect all of the numbers below 1000 in an array we can do the following:
However, this will collect all of the numbers below 1000, and we only want the numbers that are multiples of 3 or 5. To do this, we can use the select method.
This will only select numbers that are less than 1000 but a multiple of either 3 or 5 and store them in an array. Let's turn it into a function, so that it is easily accessible for our next step.
1 2 3
Adding the Multiples Together
Now that we have access to an array of all the multiples we want, all we have to do is add them together. Luckily, Ruby has a great function to help us out. The
reduce function will allow us to perform an operation on all of the items in an array. So to find the sum of the multiples this is all we have to do:
Arriving at a Solution
We've done all the coding necessary to find the solution! Now I don't want to give it away, so I'm not going to post it here, but if you're unsure if your code works or not, look at the example in the problem. Use 10 as your limit and try to get 23 as a result. When you think you have a solution, you can sign up for a Project Euler account and submit it here. Here's some proof that this code works:
And if you want to see all the code in one place:
1 2 3 4 5
In the terminal, running
ruby file_name_here.rb with whatever you named the file that you are coding in, will display the soluton to the terminal screen.
If you feel that you have a better solution, post a gist to it in the comments!


Published July 30, 2002 by Hodder Murray .
Written in EnglishRead online
|The Physical Object|
|Number of Pages||336|
Download Hodder Mathematics Foundation (Hodder Mathematics)
Mathematics Discover exam board approved/endorsed Maths textbooks and a range of supporting resources, including revision, exam practice and the new digital question generator for. Hodder Gibson Hodder Gibson overview Parent Hub; Support for schools during coronavirus; Supporting schools, parents and teachers during Coronavirus.
Visit our Home Learning pages. Home Learn more. Foundation Practice Book Answers. CCEA GCSE Mathematics Foundation Student Book Learn more. Foundation Student Book Answers. CCEA GCSE. hodder mathematics gcse in a year Download hodder mathematics gcse in a year or read online books in PDF, EPUB, Tuebl, and Mobi Format.
Click Download or Read Online button to get hodder mathematics gcse in a year book now. This site is like a library, Use search box in. This Student's Book provides ideal preparation for the new WJEC GCSE in Mathematics specification at the Foundation tier. It offers comprehensive guidance and practice for tackling problem-solving questions and the functional elements of mathematics - how maths is applied in everyday life.
Fully supported by a Teacher's Resource and Homework Book, learners are encouraged. Description: Hodder Mathematics (second edition) is a carefully planned, clearly structured course specially written for OCR's GCSE Mathematics Specification B (MEI; ).
For students there are two text books (i.e. one for each of Years 10 and 11 in schools) for each examination tier (Foundation, Intermediate and Higher). "Hodder Mathematics" (Second Edition) is a carefully planned, clearly structured course specially written for OCR's GCSE Mathematics Specification B (MEI; ).
For students, there are two text books (i.e. one for each of Years 10 and 11 in schools) for each examination tier. Hodder Mathematics Foundation 1 (Bk. 1) 2nd Edition by Catherine Berry (Author), Pat Bryden (Author) ISBN ISBN X. Why is ISBN important. ISBN.
This bar-code number lets you verify that you're getting exactly the right version or edition of a book. Author: Elizabeth A. McClure, Catherine Berry, Dave Faulkner, Geoff Rigby, Hodder Mathematics Foundation book Spencer, Pat Bryden, Diana C.
Hodder Mathematics Gcse in a Year (Hodder GCSE Mathematics) 2nd Edition by Dave Faulkner (Author) out of 5 stars 3 ratings. ISBN ISBN Why is ISBN important. ISBN. This bar-code number lets you verify that you're getting exactly the right version or /5(3).
COVID Resources. Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus.
Hodder Education Singapore acquired select titles from the Pearson Singapore Schools’ list, with a clear mission: to improve the range of resources available to support schools throughout Singapore.
Online shopping from a great selection at Books Store. FREE Delivery on orders over £10 for books or over £20 for other categories shipped by Amazon. Exam Board: Edexcel Level: GCSE Subject: Mathematics First Teaching: September First Exam: Summer Provide structured support and extra practice with differentiated questions that focus on reasoning and problem-solving building Hodder Mathematics Foundation book exam skills needed to succeed in the new GCSE specifications;developed by a team of expert authors with examining experience.
Foundation WJEC GCSE Mathematics. Answers to the Students Book exercises Foundation WJEC GCSE MathematicsHodder Education 5 a). Not /5. Retrouvez WJEC GCSE Mathematics Foundation Student's Book 2nd Welsh Edition. This website contains online information and resources to support Hodder Education and Philip Allan Updates.
Key Stage 3 Please select Fast Forward Levels Stacks of Stories Hodder Literature Hodder Northern Ireland Hodder Reading Project Hodder Tests Journeys – Religious Education for Key Stage 3 NI Michel Thomas for Schools Seada: An. Buy Hodder Maths 2ED Foundation Teacher's Resource: Foundation Level (Hodder GCSE Mathematics) 2nd Revised edition by Faulkner, Dave, Berry, Catherine, Thomas, Julian, Spencer, John, Cowey, Diana (ISBN: ) from Amazon's Book Store.
Everyday low prices and free delivery on eligible : Dave Faulkner, Catherine Berry, Julian Thomas. HigHER gCSE MATHEMATiCS FOR CCEA PRACTiCE BOOK Chapter 1 1 a 18, 24, 60 b 25, 60 c 24, 60 d 24 e 60 2 a 4, 12 b 35 c 12, 21 d 17 3 a 2, 18 b 1, 2, 5 c 15, 18 d 2, 5, 17 4 a 36 b 1 c d 25 e f 64 g 1 h 1 i j 8 5 a 7 b 3 c 9 d 10 e 6 f 1 g 10 h 1 i 32 j 6 a 28 b 65 c d 7 a 43 b 74 c 39 d 69 e 72 f 2 4 × 53 g 2 3 × Checkpoint Maths is the first series to be written specifically for students who are preparing for the University of Cambridge International Examinations Checkpoint test and IGCSE exam.
The series is fully endorsed by CIE and is included in their Checkpoint Mathematics Resources List. Find many great new & used options and get the best deals for Hodder Mathematics Foundation Level Bk 1 Hodder Porkess Roger at the best online prices at eBay.
Free shipping for many products. Cambridge Igcse International Mathematics 2nd Edition. Welcome,you are looking at books for reading, the Cambridge Igcse International Mathematics 2nd Edition, you will able to read or download in Pdf or ePub books and notice some of author may have lock the live reading for some of ore it need a FREE signup process to obtain the book.
Teacher's Resource. Author: Ric Pimentel,Terry Wall; Publisher: Hodder Education ISBN: Category: Education Page: View: DOWNLOAD NOW» This Teacher's Resource Book will ensure you can deliver the Cambridge. Take a look inside Hodder Cambridge Primary Mathematics Learners Books to see how you can use them with your class.
Hodder & Stoughton published their first original Biggles book in with Biggles Sweeps the Desert around September/October of that year (they had previously published a reprint of Biggles Flies East in May ) and the Brockhampton Press published Johns' Gimlet books from FromBrockhampton Press would also publish Biggles books Parent company: Hachette.
Hodder Education ; Hodder Gibson ; Philip Allan 75; Galore Park 1; Subjects. Nonfiction ; Study Aids & Workbooks ; Science 53; History 32; Literary Criticism 16.
Cambridge O Level Mathematics Hodder - Free download Ebook, Handbook, Textbook, User Guide PDF files on the internet quickly and easily.
The Hodder Cambridge Primary Maths series is written by experienced authors and primary practitioners to reflect the mastery approach. It provides complete coverage of the Cambridge Primary Mathematics curriculum framework for Stages 1 to 6 and includes the following components at each of the six stages.
Hodderscape. Hodderscape puts the ‘odd’ in Hodder. For science fiction, fantasy and horror lovers. Find out more; Bookends. Bookends is a vibrant reading community to help you ensure you’re never without a. Hodder Cambridge Primary Maths Story Book A Foundation Stage by Paul Broadbent,available at Book Depository with free delivery worldwide.
About this Item: HODDER EDUCATION, United Kingdom, Paperback. Condition: New. UK ed. Language: English. Brand new Book. Exam Board: OCRLevel: GCSESubject: MathematicsFirst Teaching: September First Exam: Summer Provide structured support and extra practice with differentiated questions that focus on reasoning and problem-solving building the exam skills needed.
Mathematics syllabus. The original ME. author team for Pure Mathematics comprised Catherine Berry, Bob Francis, Val Hanrahan, Terry Heard, David Martin, Jean Matthews, Bernard Murphy, Roger Porkess and Peter Seeker.
©ME!, First published in by Hodder Education, a Hachette UK company, Euston Road London NW. 3BH. Mathematics for the IB MYP 1 Irene Amlin £ £ Add to basket% Mathematics for the IB MYP 4 & 5 Rita Bateson £ £ Add to basket% Spanish B for the IB Diploma Teacher’s Resource Book Mike Thacker £ £ Read more% Chemistry for the IB Diploma Study and Revision Guide Christopher Talbot £ £.
Hodder Cambridge Primary Maths Activity Book B Foundation Stage by Paul Broadbent,available at Book Depository with free delivery worldwide. Explore, support and consolidate Early Years Mathematics with a colourful, simple story for agescontaining key mathematical concepts and practice opportunities.
Support learners with a brightly illustrated story and simple text, linked to the topics covered in Activity Book A. Welcome to Mrs. Hodder’s Mathematics Website The purpose of this website is to provide information, resources, and communications that support the mathematics standards and educational goals of Pinnacle High School.
Hodder Education Group has bought the TeeJay Publishers’ list of 90 titles for the Scottish mathematics market. The acquisition follows TeeJay founders Tom. ♥ Book Title: Hodder Cambridge Primary Mathematics Workbook 6 ♣ Name Author: Chris Baker ∞ Launching: Info ISBN Link: ⊗ Detail ISBN code: ⊕ Number Pages: Total 80 sheet ♮ News id: 6lkCkAEACAAJ Download File Start Reading ☯ Full Synopsis: "Endorsed by Cambridge International Examinations to support the full curriculum framework from GCSE Hodder Mathematics Textbooks.
Title and link to Amazon: Image: ISBN: The Student's Book, used in conjunction with the workbook and teachers' book, provides engaging activities that support students in developing a true understanding of representing, analysing and interpreting data.
The titles in the series tackle individual topics and. Thanks to Sarah Minty, Commissioning Editor for SEN at RS Assessment from Hodder Education, for the following article. Following a government consultation on the Rochford Review, the pre-key stage standards, which have been in place for /, are now final, after a review by teachers and other educational experts.
Edexcel A level Economics A Book 1 (Hodder) ISBN: Design and Technology: (Pearson) ISBN (or Foundation ISBN ) German: Stimmt AQA GCSE German Higher (Pearson) ISBN (or Foundation ISBN ) Foundation: CGP Mathematics for GCSE (CGP) ISBN: Edexcel GCSE File Size: KB.
Cambridge International AS & A Level Mathematics (Hodder) Take mathematical understanding to the next level with a course written by experienced authors, examiners and teachers. Improve confidence with clear explanations, worked examples, diverse activities and engaging discussion points.
AQA A Level Further Mathematics Statistics John Du Feu £ £ Add to basket% AQA A Level Mathematics Year 1 (AS) Sophie Goldie £ £ Add to basket% AQA A Level Mathematics Year 2 Sophie Goldie £ £ Add to basket% AQA A Level Physics Student Book 1 Nick England £ £ Add to basket% AQA.
GCSE Exam Revision: Mathematics for OCR (Foundation, Intermediate, Higher) Foundation Tier. Answers to pages (68kb) Answers to pages (54kb) Answers to all pages (97kb) Intermediate Tier. Answers to pages (76kb) Answers to pages (73kb) Answers to .CCEA GCSE Mathematics Foundation Practice Book Learn more.
Foundation Practice Book Answers Edexcel A level Economics A Dynamic Learning: Hodder Education. Edexcel A level Economics A Book 1 Whiteboard eTextbook Develop your students' knowledge of the economic themes of the Edexcel A specifications and help them put theory into context, with.Hodder Cambridge Primary Maths Learner's Book 2 (PDF ebook) By Casey, Catherine Endorsed by Cambridge Assessment International Education to support the full curriculum framework from Develop learners' mathematical fluency, problem solving and reasoning skills using the mastery approach, with this series of Learner's Books.


Matrix Reference Manual
Go to: Introduction, Notation, Index
Iff A is hermitian positive definite there exists a non-singular upper triangular U with UHU=A . This is the Cholesky decomposition of A.
[A,B:n#n, hermitian] If A is positive definite there exists X such that XHAX=I and XHBX=DIAG(k) where k contains the eigenvalues of A-1B.
Every matrix A:m#n can be expressed as A=BCP where B:m#m is non-singular, P:n#n is a permutation matrix and C:m#n is of the form [I D;0] for some D. The matrix C is the row-echelon or Hermite-normal form of A.
For any A:n#n, there exists X such that A=X-1BX where B is of the following form:
Finding the Jordan form of a defective or nearly defective matrix is numerically illconditioned.
Every non-singular square matrix A can be expressed as A=PLDU where P is a permutation matrix, L is unit lower triangular, D is diagonal and U is unit upper triangular.
Every square matrix A can be expressed as A=PLU where P is a permutation matrix, L is a unit lower triangular matrix and U is upper triangular.
This decomposition is the standard way of solving the simultaneous equations Ax = b.
Every A[n#n] can be expressed as A=UH=KV with U, V unitary and H, K positive semidefinite hermitian. H and K are unique; U and V are unique iff A is nonsingular. If A is real then H and K are real and U and V may be taken to be real.
For any A:m*n with m>=n, A=QR for Q:m*m unitary and R:m*n upper triangular.
Every square matrix A is unitarily similar to an upper triangular matrix T: A=UHTU.
Every square real matrix A is orthogonally similar to an upper block triangular matrix T: A=QTTQ where each block of T is either a 1#1 matrix or a 2#2 matrix having complex conjugate eigenvalues.
If A and B are square matrices, then there exist unitary U and V and upper triangular S and T such that A=UHSV and A=UHTV.
If A and B are real square matrices, then there exist orthogonal U and V and upper block triangular S and T such that A=UTSV and A=UTTV where each block of S and T is either a 1#1 matrix or a 2#2 matrix having complex conjugate eigenvalues.
Every matrix A:m#n can be expressed as A=UDVH where U:m#m and Vn#n are unitary and D:m#n is diagonal with real positive diagonal elements arranged in non-increasing order (i.e. if j>i then d(j,j) >= d(i,i)). The diagonal elements of D are the singular values of A.


We analyse statistical arbitrage with pairs trading assuming that the spread of two assets follows a mean-reverting Ornstein-Uhlenbeck process around a long-term equilibrium level.
Mazo, Lafuente, Gimeno: We carry out a study to evaluate and compare the relative performance of the distance and mixed copula pairs trading strategies. Instead, we observe that the underlying convergence properties are less reliable - there is an increased probability that a pair of close substitutes over the past 12 months are no longer forex kursy walut on line substitutes in the subsequent half year.
Pairs Trading with Copulas http: Furthermore, we critically evaluate the power of the traditionally applied pair selection procedure. Second, we decompose the pair-wise stock return correlations into those that can be explained by common factors such as size, book-to-market, and accruals and those that cannot.
This fragility in the Law of One Price dynamics reflects increased fundamental risks, or uncertainty in market perception of relative values of the paired securities. In addition, we perform an out-of-sample analysis to cross-validate our results in different subperiods. However, contrary to popular belief, we find that the rise in hedge fund activity is not a plausible explanation for the decline.
Again these results imply that the strategy benefits from increased volatility or a drop in liquidity. Adopting the false discovery rate work at home health coach jobs to control for data snooping bias and exercising 18, technical trading rules, we find evidence of significant predictability and excess profitability, especially for commodity spreads, in which the best performing strategy generates an annualized mean excess return of This paper applies cointegration tests to identify stocks to be used in pairs trading strategies.
Pairs Trading with Stocks
Within this framework, we prove the existence of statistical arbitrage tjana lite pengar pa sidan derive optimality conditions for trading the spread portfolio.
A Statistical Arbitrage Strategy http: An optimal double stopping problem is formulated to analyze the timing to start and subsequently liquidate the position subject to transaction costs. A metric of closeness constructed from the cointegrating relation strongly predicts both convergence probability and profitability in cointegration-based pairs trading.
Chen, Chen, Li: Mean Reversion vs Momentum https: The overall empirical results have verified that the proposed strategy can generate higher profits compared with the conventional distance method. Finally, consistent with the adaptive market efficiency theory, the return to this simple pairs trading strategy has diminished over time. While liquidity factor is negatively correlated to all strategies' returns, we find no evidence of their correlation to market excess pairs trading strategy pdf.
First, we find that this return is not driven work at home sms jobs by the short-term reversal of returns.
To evaluate the effect of market frictions on the strategy we use several estimates of transaction costs. Our results show that pairs trading portfolios typically have little exposure to known equity risk factors such as market, size, value, momentum and reversal. Pairs Trading Strategy and Idiosyncratic Risk.
Rad, Yew Low, Faff: Caldeira, Moura: Pairs Trading: Algorithmic Trading of Co-Integrated Assets http: Incorporating different assumptions about bid ask spreads leads to reductions in performance estimates. Selection of a Portfolio of Pairs Based on Cointegration: In other words, if a pair of equities is found to be cointegrated in one period, is it likely that it will be found to be cointegrated in the subsequent period?
Moreover we report a positive risk-return relationship between the strategy and market volatility, which best option trading indicators enhanced during the bear market. Xie, Liew, Wu, Zou: Modeling the price spread by an Ornstein-Uhlenbeck process, we apply a probabilistic methodology and rigorously derive the optimal price intervals for market entry and exit. Our findings are robust to liquidity issues, bid-ask spread, and limits of arbitrage.
Our insights explain why pairs trading profitability varies across markets, industries, macroeconomic circumstances, and firm characteristics. Motivated by the industry practice of pairs trading, we study the optimal timing strategies for trading a mean-reverting price spread. Psaradellis, Laws, Pantelous, Sermpinis: We show that an equity pairs trading strategy generates large and significant abnormal returns.
Our results remain valid when pairs trading strategy pdf the strategy to European index data.
pairs trading, equity long short, arbitrage
The relative value arbitrage rule best option trading indicators trading" is a well-established speculative investment strategy on financial markets, dating back to the s. For instance, the average one-month return on long-short US stock pairs that open on high distraction days is about twice as high as the return on pairs that open on low distraction days.
On the Determinants of Pairs Trading Profitability http: Jacobs, Weber: We also provide some evidence on the performance of the strategies over different market states. Bowen, Hutchinson: We perform a large-scale empirical analysis of pairs trading, a popular relative-value arbitrage approach.
Source Paper http: The proposed framework provides a new filtering technique for identifying best pairs in the market. A simple trading rule yields average annualized excess returns of up to 11 percent for selffinancing portfolios pairs trading strategy pdf pairs. In addition to estimating long-term equilibrium and to model the resulting residuals, we select stock pairs to compose a pairs trading portfolio based on an indicator of profitability evaluated in-sample.
It investigates if the profitability of pairs opening after an above average volume day in one of the assets are distinct in returns characteristics and if the introduction of a limit on the days the pair is open can improve the strategy returns.
However, the asymptotic probability of loss can be bounded as a function of the standard error of the model parameters.


Our Christmas Performance
Twinkle Twinkle Christmas Star
Numicon Stay and Play 29.11.16
A fantastic hour of mathematical learning took place this morning in Nursery when we were joined by our parents to learn all about number. The children explored a variety of activities that supported them in developing number concepts. Parents also had a chance to see some of the approaches that we use to help the children learn, including Numicon. There was also an opportunity to buy Numicon sets that could be taken home to practice with. Parents said:
Lots of great activities and ideas to help assist at home with learning.
Thank you again for another lovely session. It was well planned and executed. It is great to be involved with our child’s learning.
Had lots of fun at Stay and Play. Lots of fun activities. Great to see what my child is learning at nursery!
Number Stay and Play – 3.11.15
We had lots of fun in Nursery singing number songs and using the Numicon with our families.
Comments form the morning included
“Had a fun time, especially the number hunt.”
“Had a great time really enjoyed that they are learning as well as playing.”
“A great way to spend a morning.”
Maths is fun this document is an explanation of what Numicon is and how it can be used at home with your EYFS child.


Practical life exercises include important tasks of needed in daily life, such as washing dishes, flower arranging, and learning to button and snap. Other exercises are specifically intended to foster “grace and courtesy, ” through which children develop understanding of themselves in relation to others. Through the Practical Life exercises, children establish their ability to concentrate, coordinate their movements, and achieve self-confidence by experiencing the joy of “I did it myself.”
Sensorial materials involve training and developing children’s sense of touch, sight, hearing, smell, and taste. By practicing, children sharpen their ability to differentiate between various shapes, sounds, smells, colors, textures, and tastes. The result is a heightened awareness of the physical environment and deepened powers of observation that are highly useful for future academic explorations.
Montessori builds on children’s remarkable natural capacity for language development. Students are exposed to rich language in all areas of the classroom. This phonetic approach leads to reading words, phrases and sentences, and ultimately to reading books. The language materials appeal to all styles of learners: auditory, visual, and kinesthetic. Children are also exposed to the mechanics of both manuscript and cursive writing, parts of speech, and grammatical concepts.
Cultural subjects, such as geography, history, biology, botany, zoology, art, and music are an important part of the Montessori classroom. Children use the Montessori materials to gain understanding and appreciation of the world around them. Throughout the school year, the seven continents are introduced through hands-on artifacts cultural celebrations, and culinary traditions.
The Montessori math program ranges from simply learning to count and recognize numerals to hands-on work with the decimal system and place value (units, tens, hundreds, thousands, etc.). By working with these lessons, children also learn the process of each mathematical operation: addition, subtraction, multiplication, and division. Concrete materials help children develop a deep level of understanding of mathematical concepts.


This Set includes:
Math Game: Formulate equations on the tile stands with the numbers & math symbol tiles. The more equations you make, the higher your score will be. The player with the highest score wins. Children will learn to recognize numbers, learn addition, subtraction, multiplication & division with this game. This game will help children's math knowledge.
Fraction Puzzle Game: This game helps children understand the meaning and concepts of fractions. They will learn how fraction parts make up a whole as well as how a whole is made up of different fractions. It will help enhance your child's math ability and develop logical thinking.
|Minimum Age||Ages 3 +|
|Age Range||Ages 3-5, Ages 6-8|


KAMI GRAPH SHEET A4 60G 20CM X 24CM - 30S SKOT6030
Product Code : SKOT6030
Product Name : KAMI Graph Sheet A4 60g 20cm x 24cm - 30S
Brand : KAMI
- Kami brand graph sheet
- Size: 60gsm 200mm x 240mm.
- Specifications: printed with fine lines making up a regular grid.
- The lines are often used as guides for plotting graphs of functions or experimental data and drawing curves.
- Measured graph/grid paper for use in a variety of math learning situations.


The R Book by
Publication Date: 2007-06-19
The high-level language of R is recognized as one of the most powerful and flexible statistical software environments, and is rapidly becoming the standard setting for quantitative analysis, statistics and graphics. R provides free access to unrivalled coverage and cutting-edge applications, enabling the user to apply numerous statistical methods ranging from simple regression to time series or multivariate analysis. Building on the success of the author's bestselling Statistics: An Introduction using R, The R Book is packed with worked examples, providing an all inclusive guide to R, ideal for novice and more accomplished users alike. The book assumes no background in statistics or computing and introduces the advantages of the R environment, detailing its applications in a wide range of disciplines. Provides the first comprehensive reference manual for the R language, including practical guidance and full coverage of the graphics facilities. Introduces all the statistical models covered by R, beginning with simple classical tests such as chi-square and t-test. Proceeds to examine more advance methods, from regression and analysis of variance, through to generalized linear models, generalized mixed models, time series, spatial statistics, multivariate statistics and much more. The R Book is aimed at undergraduates, postgraduates and professionals in science, engineering and medicine. It is also ideal for students and professionals in statistics, economics, geography and the social sciences.


Daniel Traian Pele graduated Mathematics at University of Bucharest (2000) and got his Ph.D. in Statistics (2007) at Bucharest University of Economic Studies. He currently serves as an Associate Professor at Department of Statistics and Econometrics, Bucharest University of Economic Studies, Romania, teaching Statistics of Financial Markets and Time Series. He is an author of more than 20 scientific publications in internationally refereed journals. The corresponding research profile is that of a data scientist, focused on statistical modelling of financial markets. He was a postdoctoral researcher at ICMA Centre, Reading University, United Kingdom (2011) and a Guest Researcher at Research Data Center from Department of Statistics, Humboldt University from Berlin (2014). He is the co-founder of SAS Centre of Excellence in Bucharest University of Economic Studies (2009), aiming to use SAS as a platform for analytics with applications in economy and finance. He was also a World Bank consultant in Romania and he taught courses of Statistics, Econometrics and SAS for the employees of the Romanian National Bank (BNR), National Statistical Institute (INS) and other financial institutions.


When playing a standard deck of 52 cards, the probability of getting a 10 or a jack depends on the number of cards in the deck and the number of 10s and jacks available. Let’s calculate the probability with some simple math.
A standard deck of cards has 4 suits (hearts, diamonds, clubs, and spades), and each suit has one 10 and one jack. Therefore, there are a total of 8 cards that are either a 10 or a jack in a deck.
To calculate the probability, we divide the number of favorable outcomes (getting a 10 or a jack) by the total number of possible outcomes (drawing any card from the deck).
The total number of possible outcomes is 52 since there are 52 cards in a deck.
The number of favorable outcomes is 8 since there are 8 cards that are either a 10 or a jack.
Therefore, the probability of getting a 10 or a jack is 8/52, which simplifies to 2/13.
So, the probability of drawing a 10 or a jack from a standard deck of cards is approximately 0.154 or 15.4%.
Keep in mind that this probability assumes that the deck is well-shuffled and each card has an equal chance of being drawn.
Remember to gamble responsibly and don’t rely solely on probabilities when making decisions during a game. Good luck!


The set of indices that correspond to the positive entries of a sequence of numbers is called its positivity set. In this paper, we study how dense is the positivity set of a given linear recurrence sequence. We show that one can compute this density to arbitrary precision, as well as decide whether it is equal to zero (or one). If the sequence is diagonalisable, we prove that its positivity set is finite if and only if its density is zero. Lastly, arithmetic properties of densities are treated, in particular we prove that it is decidable whether the density is a rational number, given that the recurrence sequence has at most one pair of dominant complex roots.


Numbers? This isn't a website about mathematics! No, but this subject is worth considering in terms of the Universe. The cosmos we inhabit is a great environment for exploring the biggest and smallest integers - and even going way beyond that.
When we casually say that the Universe contains "billions and billions of galaxies", how many are there, exactly? What about how many atoms of hydrogen exist? All extremely large numbers, as I think you'll agree.
At the other end of the scale, what is the smallest possible distance? It's far smaller than the diameter of an electron. We'll explore all this - and more.
Here, we'll explore all the numerical superlatives the Universe has to offer, plus others that go way beyond that.
How small is it possible to go? What dimensions are involved when we reach the ultimate units from which the Universe is made?


Given the temporal density of the data we collect (viz. EMA and passive sensing smartphone metrics), we often employ statistical methods to enhance inference of repeated assessment within people over time. These methods include Multilevel Modeling (MLM; e.g., Fulford, Johnson, Llabre, et al., 2010), Structural Equation Modeling (SEM; e.g., Fulford, Piskulic, et al., 2018), and other robust approaches to analyzing longitudinal data (e.g., Generalized Estimating Equations; Fulford, Treadway, & Woolley, 2018).
We are also excited to employ new and evolving statistical methods in our work. Current projects involve the use of Exploratory Structural Equation Modeling (ESEM) for survey development, multilevel vector autoregressive network analyses for time series data, and machine learning approaches to improve inference of clinical classification.


♦ Metal Wall Sculpture
♦ Bespoke Copper Décor
♦ Geometric Paintings
♦Residential ♦Corporate ♦Hospitality
Acid Patina… Transmuting Metal into Art!
Geometric Painting ‘The Multiverse’
‘The Multiverse’ abstract geometric art
Inspiration and Design of ‘The Multiverse’
The initial inspiration for this complex and highly detailed work came from the mathematical problem known as ‘perfect square dissection’ or ‘squaring the square’. The solution to this math problem presents an interesting graphic that is exquisitely fine-tuned but also appears to be random and arbitrary.
The universe we experience appears to be fine-tuned to allow life to develop; sometimes referred to as the ‘just right Goldilocks universe’. There is much debate as to the possible explanations for this apparent fine-tuning among philosophers, cosmologists and theologians. Various multiverse hypotheses have been proposed by some cosmologists to explain this phenomena; essentially, we just happen to inhabit a universe, among countless others, that is fine-tuned for us to thrive.
The overall rationale of the painting was to convey the enormity of the Universe, its apparent mathematical structure, and our fundamental connection back to the source of our creation; even a multiverse does not eliminate the concept of a point of creation.
Theories encompassing fractal cosmology, the multiverse, brane cosmology, and the holographic universe were referenced during the conceptual drawings.
Description of ‘The Multiverse’
A large square has been divided into the ‘perfect square dissection’. Over this, squares of torn canvas have been laid-up in a random, overlapping pattern, hinting at the multi-dimensional nature of the Universe.
This canvas mosaic is painted with a free-flowing blend of indigo, ultramarine and iridescent blues that merge and fuse to provide a richly-coloured backdrop, evoking feelings of the infinity of space.
In each square region of space, a universe-like constellation is shown, trapped within a fine 2-dimensional net-like membrane. Above this floats a higher-dimensional plane; represented as a golden checkerboard. Contained within lay more net-like membranes and universes. Fractal-like in their nature, each universe contains a smaller universe, repeating ad infinitum. Each new universe has had recursive and rotational operations applied to ensure each is ‘fine-tuned’ and different.
Gold microwaves connect all of the universes back to the small gold square near the painting’s centre. This square is the unique 1×1 square in the ‘perfect square dissection’. It is the foundation point of the painting. The source of creation.
Fine artist grade acrylic paints on canvas squares bonded onto wood board. Finished edges, no frame required.
Approx. 800 x 800 x 18mm. (31½ x 31½ x ¾”).
Repaints and custom variations available.


I am a native Slapoutian and a third generation graduate of Holtville High School. I am married to Casey Antley who is also a graduate of Holtville High School. We have a daughter, Scarlett, and three large fur babies. My husband and I both take a lot of pride in our school and our community.
I graduated from Holtville in 2009 and went on to AUM where I graduated in 2014 with my degree in Secondary Education - Mathematics. Recently, I returned to AUM where I completed my Masters in Math Education. After college, I spent a year teaching 7th grade math at Eclectic Middle School before returning "home" to HHS in 2016. I have been teaching math here at HHS ever since. I love math and I hope to pass on my love for the subject to my students.
Please feel free to contact me at anytime if there is anything I can do to help your student succeed!


Monday (Day 4-Gym)
-complete Math fact and homework sheets for Lesson 35
-complete the Spelling “Trace and Write” worksheet
-practice Key Word cards for “Animal Park”
Tuesday (Day 5-Library/Book Exchange-please send Library books to school on every Day 5)
- practice the Key Word cards and read the story “Animal Park.”
Wednesday (Day 1-Music)
- practice the Key Word cards and read the story “Animal Park”
-complete Math fact and homework sheets for Lesson 36
Thursday (Day 2-Art)
-complete Math fact and homework sheets for Lesson 37
-complete Spelling Practice book pg. 21, write each word twice
No school for students, Teacher In-service!
-I returned the top of the report card to parents that sent them in! We only need the bottom signed and cut off.
-We will have the Personal Body Safety program on Thursday morning.
-Please sign and return all papers in the red Test Folder weekly.
-We will have snack every afternoon. Please send your child a snack daily or you can send a box of snacks with your child’s name on it and I will distribute the snacks daily.
Have a nice week!!


Hello! I’m a multi-talented artist and sign all of my works with my pen name: Ilia. The works on display here are Digital Art. I create the foundation as one or more *fractals. Then I use graphic programs to combine, subtract, add and adjust until I get the artwork as I want it. The final touch to the art that I do is working on the colors, shading and highlighting to get the image to take on 3-dimensional properties.
*Fractal – a fractal is a self-similar shape that, when you look at a small part of it, has a similar (but not necessarily identical) appearance to the full shape. The shapes are found in nature as well as in mathematical equations. Computer generated fractals are mathematical equations.


Interesting talks at the CUMC 2011
June 22, 2011 1 Comment
In June, Université Laval held the CUMC 2011. The CUMC is one of North America’s largest undergraduate conferences. Undergraduate students across Canada come to exchange on mathematics and to learn on different interesting fields. There is usually 8 Keynote Speekers and a lot of different talks given by the students. This year, I have learned on subjects that I had no idea of their existence. I also learned on different activities and student organizations that exist in Canada.
Here are the talks that I really enjoyed for different reasons.
Before I begin, I just want to write about Bruno Joyal’s talk: Universality across mathematics. I did not see his talk, but he put a paper of his talk on his blog that I found interesting.
First, let’s begin with the Keynote speakers.
- I really enjoyed Pamela Gorkin‘s talk: Not an ellipse? Not my problem. She talked about “Blaschke Products and several seemingly unrelated results in which ellipses make an unexpected appearance.” The talk was really clear and surprising!
- Frederick Rickey was also a great speaker. His talk, The fundamental Theorem of Calculus: History, Intuition, Pedagogy, Proof, was dynamic. I really enjoyed to hear him talking about how it was to teach in a military school.
- Ana Iorgulescu : Why Mathematicians Will Never be Out of a Job: Gödel’s First Incompletness Theorem. The talk was about a simplified proof of the FIrst Incompleteness Theorem, which was given by George Boolos. I did not know about this simplified proof and found the concepts involved interesting. It is based on the paradox that the least integer not nameable in fewer than 19 syllables is in fact nameable in 18 syllables.
- John Yang : A Painless Introduction to Complex Dynamics. This talk was about Complex Dynamics. John Yang made an introduction to Julia Sets, Normal families, invariance lemma and iteration lemma. These concepts really kept my attention and I will certainly read on this in the future.
- Jean- Sébastien Turcotte : Une généralisation de l’intégrale de Riemann. This talk was about the Henstock-Kurzweil integral. This is a really nice concept, which is more general then the Riemann and the Lebesgue’s integral. For instance, the set of Henstock-Kurzweil integral functions contain the set of Riemann integral functions and Lebesgue integral functions.
- Eric Naslund : Pretentious Number Theory. This talk was about a new branch of analytic number theory. It tries to give elementary proofs to important theorems of analytic number theory, that is, without using the Riemann Zeta function and its zeros. This theory has been mainly developed by Granville and Soundararajan.


Dudley Weldon Woodard
Dudley Woodard was a gifted teacher in mathematics. Always the scholar, Weldon earned numerous degrees and was the second African American to receive a PHD in mathematics. Woodard taught as such prestigious schools as the Tuskegee Institute, Howard University, and the University of Chicago. He attained he PHD from Penn in 1928. Dudley Woodard devoted his entire professional life to the promotion of excellence in mathematics through the advancement of his students, teaching and research.
Dudley Weldon Woodard was born October 3, 1881, in Galveston, Texas,
where his father worked for the U. S. Postal Service. Woodard was a
smart child whose curiosity was supported by his family. After finishing
his primary education in his home state, Woodard attended Wilberforce
College in Ohio, receiving a bachelor degree in mathematics in 1903, and
an M. S. degree in mathematics at the University of Chicago in 1907.
From 1907 to 1914, Woodard taught mathematics at Tuskegee Institute and
then moved to join the Wilberforce faculty from 1914-1920.
In the early 1920s Dudley Woodard began taking advanced mathematics
courses in the summer sessions at Columbia University. It then became clear
that he was among the gifted mathematicians in the nation. Columbia's loss
was Penn's gain when in 1927 Woodard took scholarly leave from Howard and
spent a year at Penn, working under the direction of John R. Kline, one of
the best and brightest of Penn's mathematics faculty. On Wednesday, June 28,
1928, Woodard became the 38th person to receive a Ph.D. in Mathematics from
Penn. More significantly, Woodard was only the second African American in
the nation to receive that degree.
When he retired in 1947 as chairman of the department, he had led Howard's mathematics faculty through a quarter century of steady advancement. In an age of discrimination, Dudley Weldon Woodard had competed and triumphed in the face of overwhelming odds. Penn is proud to claim him among its most distinguished alumni.
Janet Emerson Bashen
Miriam E. Benjamin
Andrew Jackson Beard
Bessie Blount Charles Brooks George Washington Carver George Carruthers Benjamin S. Carson Emmett W. Chappelle David Crosthwait Ronald Demon Dr. Charles R, Drew Thomas Elkins Philip Emeagwali Thomas Jennings Frederick Jones Percy Julian Dr. Ernest Everett Just Roscoe Koontz Lewis H. Latimer Jan Ernst Matzeliger Elijah McCoy Alexander Miles Garrett Morgan Derrick Pitts Norbert Rillieux Louis Roberts Cordell Reed Henry Sampson Valerie Thomas
Neil deGrasse Tyson Madame Walker James Edward West Doctor Daniel Hale Williams Joseph Winters
Dudley Weldon Woodard Granville T. Woods
Contact Us Advertise
Alaskan Nature | |Floridian Nature | Free Holiday Ideas | Reflections | Michael Arnold Art


Math Phonics Multiplication & Division Quick Tips and Alternative Techniques for Math Mastery Marilyn B Hein - 3-6 Teaching & Learning Company Reproduction Book Series
Product Code: TLC10346-Z
Buy Now: $12.88 US
List Price: $12.95
You Save: $0.07
Seen It Online for Less?
We will beat it right now! See your new price here in seconds.
Free shipping in the USA (lower 48) when your order is over $89 (excluding gift certificates and sales tax, if applicable).
A specially designed program using rules, patterns and memory techniques similar to those found in language arts to teach difficult math concepts to children. This bonus book contains 10 all new lesson plans, including worksheets, take-home pages, assessment pages and a variety of support materials to teach multiplication and division. Return Policy Exception: This product can not be returned. But it can be exchanged if defective, for the exact same title. Here is a listing of related products.


Counting cards in blackjack is not an overnight culture change to your gaming habits. It takes studying, learning and and endless amount of practice for it to become second nature. Even to those who’ve made it a regular part of their game, though, there can be questions that arise from time to time on how to handle something out of the ordinary.
Which brings me to the question of the day – how do you handle conversion of the running count to the true count if the fraction doesn’t work to an even number?
First, let’s quickly review. Running count is what the current count of the hand is, while true count is dividing this number over the estimated number of decks remaining in the shoe. So if the running count is 8, and there are an estimated 4 decks remaining in the hand, that makes for a nice, clean true count of +2.
Most expert and regular card-counters will tell you to do the basic math in your hand, and then just round up or down. If it’s at .5 or higher, you round up. Then, keep in mind where the actual true count number is on close plays and make a judgment call accordingly.
Some players do their math in reverse, meaning they’ve trained their minds to count how many decks have been used, and arrive at the fraction by doing subtraction from the whole. A bit of a roundabout way of doing things, but as in all walks of life, if that’s the process that works best for you, there’s no reason to change – so long as you can keep up with the count changes.
Another related question on this topic has to do with whether you count the cards after the cut but still remaining in the shoe as part of the equation for determining the true count, and the answer to this is a resounding “yes.” The cards exist, and even though they won’t be part of this particular hand, you definitely use them in your calculations.
This is a great question that has bearing on every card counter from beginning up through expert. You have to be able to train yourself to handle quick changes in numbers, and practicing messy division is all part of the game. It’ll pay off when you’re sitting at the table trying to work out a running count of 11 over 3.5 remaining decks. Go ahead, I’ll wait.


Because of our non-public school status, we have the flexibility to choose from available curriculums in each subject area according to what we believe best fits our students’ needs. Because of our size, we are able to integrate curriculum throughout the grade levels. That means that students will experience the smoothest transition possible as they progress through the system.
To learn more about a particular aspect of our curriculum, browse the resources below. For additional information, contact our Director of Curriculum and Learning.
- Math Standards At-A-Glance (K-12)
- Math Standards and Benchmarks (K-8)
- Math Standards and Benchmarks (9-12)
- Traditional Vs Reformed Math
- Science Standards At-A-Glance
- Science Standards and Benchmarks (6-8)
- Science Standards and Benchmarks (9-12)
- Science and our Catholic Faith (Faith and Knowledge)
- Social Studies Standards At-A-Glance (6-11)
- United States History
- World History
A, 93% or better


Place your order now for a similar assignment and have exceptional work written by our team of experts, At affordable rates
Review and summarize the key terms of statistics; descriiptive and inferential statistics, scales of measurement, types of variable, population and sample, population parameters and sample statistics.
Define descriiptive and inferential statistics. Focus on the difference between the two types of approach.
Define population and sample. List typical parameters from population and sample statistics.
Refer to Table 1.6 (textbook) and indicate the types of variable and the scale of measurement for each variable.
Refer to Table 1.6 (textbook) and Indicate how you can summarize the information in each variable.


A discontinuous Petrov-Galerkin method with Lagrangian multipliers for second order elliptic problems
Wednesday 7th May 2003
Causin, Paola; Sacco, Riccardo
We present a discontinuous Petrov-Galerkin method (DPG) for finite element discretization scheme of second order elliptic boundary value problems. The novel approach emanates from a one-element weak formulation of the differential problem (that is typical of Discontinuous Galerkin methods (DG)) which is based on introducing variables defined in the interior and on the boundary of the element. The interface variables are suitable Lagrangian multipliers that enforce interelement continuity of the solution and of its normal derivate, thus providing the proper connection between neighboring elements. The internal variables can be eliminated in favor of the interface variables using static condensation to end up with a system of reduced size having as unknowns the Lagrangian multipliers. A stability and convergence analysis of the novel formulation is carried out and its connection with mixed-hybrid and DG method is explored. Numerical tests on several benchmark problems are included to validate the convergence perfomance and the flux-conservation properties of the DPG method.


Date Math Gotcha
We can sometimes get unexpected results, and this applies to several different programming languages and Query Date Math.
A month can contain 28 29 30 or 31 days.
A year can contain 365 or 366 days.
- Start with date 2005-03-31
- add one month
- this gets date 2005-04-30
- subtract one month
- this gets date 2005-03-30
In this example we learn that if the math would produce an invalid date 2005-04-31, it lowers the result to the previous valid date, but there is no "memory" of this "rounding".
- subtract 2005-03-31
- from 2005-04-30
- the result is ZERO months
- because it sees that 30 is less than 31 and not recognize that these are last days of months


KS2 Year 6 SATs
On this area of the site you’ll find all the information you need for KS2 Year 6 SATs Papers including all the papers to download for free.
We have free information on how to best prepare for the Year 6 KS2 SATs test, as well as very detailed information on the contents of the English and Maths papers.
Please read: To increase your child’s preparation and chances of success, we have produced preparation guides and book recommendations for the whole of KS2. After analysing the range of products available we wholeheartedly believe that these materials give the best chance of success. Please follow this link for more information.
We have an extensive list of past KS2 SATs Papers going back many years that you can download for free with no annoying adverts or registration. You can find them on our KS2 SATs Papers page. There are English Reading, SPaG and Maths papers from 2000 to 2017.
- KS2 Year 6 SATs Papers
- KS2 Year 6 SATs Preparation
- Contents of KS2 English SATs Test
- Contents of KS2 Maths SATs Papers
- KS2 Maths Free Worksheets
- KS2 English Free Worksheets
KS2 year six SATS Papers and Worksheets are free to download no registration needed
We often get questions about the Multiplication Tables Check which is being introduced in 2020 for children in Year 4. To find out more information about the new check, click here.


Pomeroy and Betty Perry Smith Professor in Engineering, Emertius.
Professor of Chemical and Biological Engineering and Applied and Computational Mathematics, Emeritus. Senior Scholar.
A319 Engineering Quad
Ph.D., Chemical Engineering, University of Minnesota, 1986
M.A., Mathematics, University of Minnesota, 1986
Dipl., Chemical Engineering, National Technical University Athens, 1982
- Applied and Computational Mathematics
- Environmental and Energy Science and Technology
- Process Engineering and Science


Why is my percentage calculation failing?
hope this fix your issue Based on what you are saying you expect... It seems as though you are looking for what percent item(1) is of the total.For example if Item1 = $10 and the totalCost = $100 Then the percent you are looking for is 10%?
November 01 2020, 11:01 PM ,
How do I convert a hexadecimal number in IEEE 754 double precision (64bit) format to a decimal number?
should help you out Going from https://en.wikipedia.org/wiki/Double-precision_floating-point_format,
November 01 2020, 01:04 PM ,
Find all natural number solutions in Prolog program
it should still fix some issue You can use the Constraint Logic Programming library over Finite Domains (clpfd) for that:
October 18 2020, 03:08 PM ,
What would be a good mathematical notation for image warping given an image I and transformation T?
I wish this help you I would like to express image transformation (warping) in a mathematical form. For example, image transformation T may be an affine, homography, and so on. , Possibly
October 15 2020, 01:08 AM ,


The Salt Lake Tribune reports
For all those John Hollinger fans, Miller told me he uses his own statistical system to assess a player’s value and contribution.
It’s pretty simple: Add up points, rebounds, steals, blocks and assists. Subtract fouls, turnovers and shots taken. Then divide by minutes played. This gives you what Miller calls a player’s batting average, to borrow from baseball.
Miller can figure it out approximately in his head after every game. When we talked, he was excited that Andrei Kirilenko’s batting average for the Jazz’s first preseason game (10 points, eight rebounds, four blocks) was .583. He’s now at .490.
A player with a batting average of .300 usually approaches All-Star status, Miller said. A player with a .400 average is definitely an All-Star and a player with a .500 average is a likely MVP candidate. Karl Malone’s career average, which Miller cited, was .457.
Appearantly, it’s a very effective measuring tool
What’s remarkable, Miller said, is how accurate he believes the formula to be. That’s part of the reason the Jazz calculate it at the end of every season for every player in the NBA, then cross-check it against a couple of other statistical ratings.
Over the years, it regularly spit out John Stockton as the NBA’s top point guard, Michael Jordan as the top shooting guard, Larry Bird as the top small forward, Malone as the top power forward and Shaquille O’Neal as the top center, Miller said.
Update: A year forward, Dave Berri compares his WoW stat versus Miller’s – link – which appearantly produces very similar results to Berri’s stat.


Algebra 2 - Chapter 10: Exponential and Logarithmic Functions
Students will learn to simplify exponential and logarithmic expressions, solve exponential and logarithmic equations and inequalities, and solve problems involving exponential growth and decay.
|Glencoe Lesson Title||Link to Online Manipulative||Use||Worksheet|
|10.4 Common Logarithms||Logarithmic Functions – Activity A|
|10.4 Common Logarithms||Logarithmic Functions – Activity B|
|10.5 Base e and Natural Logarithms||The number e|
|10.6 Exponential Growth and Decay||
Exponential Growth and Decay - A
Exponential Growth and Decay - B
|10.6 Exponential Growth and Decay||Grapher||Launch or Explore||The Tractor Problem (Decay)
The Restaurant Problem (Growth)
If you would like to contribute an alignment or activity worksheet to complement any Glencoe Algebra 2 lesson, please email the SELECT Math team.
Back to Algebra 2 Alignments


Dr. Sc. Masato WAKAYAMA
November, 1955 (Date of Birth)
Executive Vice President
Institute of Mathematics for Industry, Kyushu University
Graduate School of Mathematics, Kyushu University
Research & Education Projects
|2006-2011.3||Program Leader, Challenge to Open Problems in Mathematics and Mathematical Sciences, "The Kyushu University Research Superstar Program (SSP), 2006, Special Coordination Funds for Promoting Science and Technology, MEXT".|
|2007-2010.3(Expiration)||Program Leader, GP Program "Training Program of Ph.D. and new Master's in Mathematics as Required by Industry", MEXT.|
|2008-2013.3||Program Leader, Global COE Program "Education and Research Hub for Mathematics-for-Industry", MEXT.|
|2009||Program Leader, Investigation project commissioned by MEXT in 2009:“Investigation and estimation of promotion of cooperation of mathematics and mathematical science with other fields --- For examination of the fourth governmental science & technology master plan”|
|2010-2015||Program Leader, Graduate School of Mathematics “Special Project Fund of Graduate Education for Mathematics”|
|2014-2019||Member of a research project JST CREST, Mathematical Modelling for Next-Generation Cyptography|
Grant-in-Aid for Scientific Research (Supported by MEXT & JSPS) and JST/CREST
|2016-2018.3 Grant-in-Aid for Scientific Research(C), MEXT, Japan||Development and Deepening of Number Theory and Representation Theory through Mathematical Analysis of Quantum Interaction Models|
|2014.10-2020.3 CREST(Core Research of Evolutional Science & Technology), JST, Japan||Mathematical Modelling for Next-Generation Cryptography|
|2013.4-2017.3, Challenging Exploratory Research, MEXT, Japann||A new development of studies on stochastic process, statistical distributions and representation theory|
|2010.10-2016.3, CREST(Core Research of Evolutional Science & Technology), JST, Japan||Mathematics for Expressive Image Synthesis|
|2009-2014.3,Grant-in-Aid for Scientific Research(B), MEXT, Japan||Mathematics for Non-commutative Harmonic Oscillators and Representation Theory of α-determinants|
|2006-2009.3, Grant-in-Aid for Exploratory Research, MEXT, Japan||Invariant Theory of α-determinants and Zeta Functions for Matrix Variable|
|2003-2007.3, Grant-in-Aid for Scientific Research(B), MEXT, Japan||Study of Zeta Functions and Duality --- “Infinite Sum = Infinite Product” Based on the Trace Formulas Viewpoint|
|2001-2004.3, Grant-in-Aid for Exploratory Research, MEXT, Japan|| Study of Casimir Effects --- from Casimir Elements and Prime Geodesic Theorems
|1999-2003.3, Grant-in-Aid for Scientific Research(B), MEXT, Japan||Duality Based on Trace Formulas --- Applications of "Infinite Product=Infinite Sum" Type Formulas and Representation Theory|
|1997-1999.3, Grant-in-Aid for Scientific Research(B), MEXT, Japan||Duality Based on Trace Formulas --- Study on "Infinite Product=Infinite Sum" Type Formulas|
|1996-1997.3, Grant-in-Aid for Scientific Research(B), MEXT, Japan||Study on "Infinite Product=Infinite Sum" Type Formulas, Based on Evaluation of Determinants|
Doctor of Science (Hiroshima University, 1985)
Automorphic forms and zeta functions
・ Casimir effects, Prime Geodesic Theorems
・ Invariant theory of classical and quantum groups
・ Minor summation formula of Paffians and its aplications to combinatrics and representation theory
・ Spectrum of Non-commutative harmonic oscillators and related arithmetic study (elliptic curves and automorphic forms)
・ Zeta regularized determinants and their applications to number theory
・ Representation and Invariant theory of α-determinants
・ Harmonic analysis on symmetric spaces and orthogonal polynomials
Lectures in the past
"Quantum Rabi's model and non-commutative harmonic oscillators-between number theory and physics", Colloquium, Department of Mathematics , University of Hawaii at Manoa, September 5, 2014.
"An introduction and application of Lie theory-a theme from spherical harmonics", Seminar for undergraduates, Department of Mathematics , University of Hawaii at Manoa, September 3, 2014.
"Non-commutative harmonic oscillators and the Rabi model", RIMS Workshop, RIMS, Kyoto University, June 24-28, 2014.
"Activities of Mathematics for Industry", University Montpellier 2, Feb. 26, 2014.
"An application of Lie theory to computer graphics via spherical harmonics", Berliner Colloquium fur wissenschaftliche Visualisierung, Zuse-Institut Berlin (ZIB), Germany, Feb. 28, 2014.
"Activities of Mathematics for Industry", Zuse-Institut Berlin (ZIB), Germany, Mar. 1, 2014.
"Spectrum of non-commutative harmonic oscillators - Modular forms, representation theory and the Rabi model", Mathematical Institute, Leiden University, November 29, 2013.
"Plans for cooperation in the Pacific region - Activities of Mathematics for Industry ", EU-MATHS-IN, the Centre for Mathematics and Computer Science (CWI), Science Park 123, Amsterdam, November 27, 2013.
"Residual modular forms and curves, the quantum Rabi model, and discrete series representations from the study of spectral zeta functions of the NcHO.", Masato Wakayama, Geometric zeta functions and related topics, Saga University, October 30 to 31, 2013. (my talk is scheduled on October 31, 2013)
"A Lie theoretic proposal on algorithms for spherical harmonic lighting.", Masato Wakayama, Symposium: Mathematical Progress in Expressive Image Synthesis, Centennial Hall Kyushu University School of Medicine, October 21 to 23, 2013. (my talk is scheduled on October 22, 2013)
"Quantum Interaction Models and Number Theory.", Masato Wakayama, Zeta Functions in OKINAWA 2013, 沖縄コンベンションセンター, October 19 to 22, 2013. (my talk is scheduled on October 19, 2013)
"Aiming at New Industrial Mathematics", Masato Wakayama, The Japan Society for Industrial and Applied Mathematics 2013, ACROS Fukuoka, September 9 to 11, 2013. (my talk is scheduled on September 10, 2013)
"Hankel actions, holomorphic discrete series and Meixner-Pollaczek polynomials.", Masato Wakayama, JSPS-NWO Seminar "Analysis, Geometry and Group Representations for Homogeneous Spaces", Graduate School of Mathematics, Nagoya University, August 26 to 30, 2013. (my talk is scheduled on August 28, 2013)
April 22-26, 2013
"Analysis and Number Theory for Non-commutative Harmonic Oscillators"
i) Spectral problem of non-commutative harmonic oscillators
ii) The spectral zeta function of NcHO and modular forms
iii) Residual modular forms and related cohomology groups
Distinguished Lecture Series, Department of Mathematics, Indiana University, Bloomington
March 01, 2013
"Introduction to Mathematics for Industry" Seminar in Grenoble, Univ. Joseph Fourier
March 01, 2013
Basque Center of Applied Mathematics BCAM Seminar, "Analysis and arithmetic of non-commutative harmonic oscillators", Speaker:Masato WAKAYAMA, Director of Institute of Mathematics for Industry, Kyushu University, Japan
November 27, 2012
Masato Wakayama, Kyushu IMI, "Eichler cohomology groups for spectrum of NcHO's", Spectral analysis of non-commutative harmonic oscillators and quantum devices, Kyushu University
"Remarks on parity of eigenfunctions of NcHO via Heun DE", Zetas and Limit Laws in OKINAWA 2012, Festone, Ginowan, OKINAWA, November 18, 2012
"Multivariate Meixner-Pollaczek polynomials and an application"(Jun 22, 2012, Research Institute for Mathematical Sciences, Kyoto University)
"Multivariate Meixner-Pollaczek Polynomials", Sala de Seminarios (Jun 6, 2012, Centro de Modelamiento Matematico, Chile)
"Long-term-internship for PhD students in Mathematics in Japan -status and procedure in the course-curriculum, joint research activities " (Jun 6, 2012, Centro de Modelamiento Matematico, Chile)
"Higher regularizations for zeros of cuspidal automorphic L-functions of GL(d)", Mathematical Society of Japan 2012 (March 29, 2012, Tokyo University of Science) (M. Wakayama, Y. Yamasaki)
"Γ(2)-modularity appealing at the special values of spectral zeta function for the NcHO", Mathematical Society of Japan 2012 (March 28, 2012, Tokyo University of Science (K. Kimoto, M. Wakayama)
"Remarks on geodesics for multivariate normal models", Mathematical Society of Japan 2012 (March 28, 2012, Tokyo University of Science)(T. Imai, A.Takaesu, M.Wakayama)
"Hermitian symmetric spaces of tube type and multivariate Meixner Pollaczek polynomials", Mathematical Society of Japan 2012 (March 28, 2012, Tokyo University of Science)(J. Faraut, M. Wakayama)
"Number theoretical approach to spectrum for non-commutative harmonic oscillators"( March 7-9, 2012, Workshop on "Avoided ? Crossing of Eigenvalue Curves" -- Non-commutative Harmonic Oscillator, Special Functions and Number Theory- , Inamori Center, Ito Campus, Kyushu University)
"Residual modular forms, Eichler cohomology and spectrum of non-commutative harmonic oscillators(February 27-28, 2012, "New Zealand Institute for Advanced Study + NZIAS.)
"Educational & Research with Mathematics-for-Industry in Japan", Mathematics and Statistics-in-Industry Study Group 2012 (February 6, 2012, RMIT University, Australia)
"Long-term-internship for PhD students in Mathematics in Japan ?status and procedure in the course-curriculum, joint research activities ", IDTC Research Methodology Workshop (February 3, 2012, RMIT University, Australia)
"Remarks on geodesics for multivariate normal models" , WIAS+MATHON joint seminar(January 9, 2012, WIAS+MATHON, Berlin)
"Non Commutative Harmonic Oscillators and Modular Forms" (January 6, 2012, Bologna University)
"Spectrum of Non-commutative Harmonic Oscillators and Modular Forms", Spectral and Scatteing Theory and Related Topics, (December 15, 2011, RIMS, Kyoto University)
"Negative Weight Modular Forms", Zetas and Limit Laws in OKINAWA 2011, (November 27, 2011, Festone, Okinawa)
"Non-commutative harmonic oscillators and Number theory.", Industrial mathematics Institute Johannes Kepler University Linz (February 18-19, 2011, Linz)
"On Mathematics-for-Industry", mathematics in the real world 2(December 17-18, 2010, TMU)
"Hermitian symmetric spaces of tube type and multivariate Meixner-Pollaczek polynomials", Analysis, Geometry and Group Representations for Homogeneous Spaces (November 22-26, 2010, Lorentz Center, Leiden University)
"Non commutative Harmonic Oscillators and Number Theory", Non Commutative Geometry and Number Theory RIMS Special Year on Non Commutative Geometry (November 25-26, 2010, Department of Mathematics, Kyoto University)
"Number theory for Non commutative harmonic oscillators", 2010 Annual Symposium of Representation Theory (November 9-12, 2010, Izu, Shizuoka)
"Ramanujan's Delta and zeta regularizations",Zeta conference in Okinawa (November 6-9, 2010, Okinawa Convention Center)
"A Trial for PhD Education & Research in Mathematics for Industrial Technology ","Educational Interfaces between Mathematics and Industry (EIMI-study)"Lisbon, October 11-15, 2010
"Over the zeta regularized numeration", RIMS, Kyoto University, October 4-8, 2010
"A study on zeta regularized products", Representation theory; a link of Number theory-Analysis-Combinatorics, Ehime University, August 23-26
“Prime numbers can produce (elusive) Vacuum energy” The 5th Seminar on Algebra・Analysis・Geometry, Department of Mathematics, Kagoshima University, February 16, 2010
”Wreath type Group Determinants” Various problems and their perspectives in mathematical analysis−in memory of Professor Tetsuro Miyakawa −, Kanzawa University, February 20, 2010
"Representation Theory of α-determinants" Department of Mathematics, National University of Singapore,January 29, 2010
"Representation theory for α-determinants" Mathematical Sciences Colloquium, RIKEN, 6 July 2009
"Geodesics on a multivariate normal distribution- from Representation theoretic points of view", Workshop on Deeping and Expansion of Statisical Mechanical Informatics, Informatics on log P, Nishijin Plaza, Kyushu University, 16 June 2009.
Arithmetics on Non-commutative harmonic oscillators, International workshop on verified computations and related topics, University of Karlsruhe (TH), Germany, March 7-10, 2009.
Harmonic analysis on Hermitian symmetric spaces of tube type and multivariate Meixner-Pollaczek polynomials, Zetas and Limit Laws in OKINAWA 2008, Okinawa Convention Center, November 22-25, 2008.
Special values of the spectral zeta functions for the non-commutative harmonic oscillator and elliptic curves, “International Conference on Arithmetic Geometry" Euler International Mathematical Institute, Saint Petersburg, June 2007.
Zeta Functions for the Spectrum of the Non-Commutative Harmonic Oscillators, "Conference on L-function" Nishijin Plaza, Kyushu University, February 2006.
|1986.9 - 1989.3||Full-Time Lecturer, Faculty of Engineering, Fukuyama University|
|1989.4 - 1994.3||Associate Professor, General Education, Tottori University|
|1994.4 - 1997.6|| Associate Professor, Faculty of Science, Kyusyu University
(1994.6- Graduate School of Mathematics)
|1997.9 -|| Professor, Graduate School of Mathematics, Kyusyu University
(2000.4- Facuty of Mathematics)
|2006.7 - 2010.7||Dean, Faculty of Mathematics, Graduate School of Mathematics, Kyushu Univetsity|
|2009.5-||Distinguished Professor, Faculty of Mathematics, Graduate School of Mathematics, Kyushu Univetsity|
|2010.4- 2011.3||Director, Mathematical Research Center for Industrial Technology, Kyushu Univetsity|
|2010.10- 2014.9|| Vice-President, Kyushu Univetsity
|2010.10- 2011.9||Director, Center for Research and Advancement in Higher Education, Kyushu University|
|2011.4- 2014.9||Director, Institute of Mathematics for Industry, Kyushu University|
|2011.10- 2014.9||Executive Vice Dean, Faculty of Arts and Science, Kyushu University|
|2014.10-||Executive Vice President, Kyushu University|
|1995.9 - 1996.8||Visiting Fellow, Department of Mathematics, Princeton Univeisity|
1999.3 - 4,
2000.3 - 5,
2006.4 - 5
|Guest Professor, University of Bologna|
|2007.12||Nice-Step-Researcher Award 2007（by MEXT)|


You Could Drink, Or…
Social Worker: Do you drink?
Social Worker: How much a day?
Man: Three six packs.
Social Worker: How much is a six pack?
Man: about $10.00.
Social Worker: And how long have you been drinking that much?
Man: Fifteen years.
Social Worker: So one six pack costs you $10.00, and you have three
six-packs a day, which puts your spending each month at about $900. In
one year, it would be $10,800. Correct?
Man: Yeah, that math works out. Sure.
Social Worker: If in one year you spend $10,800, not accounting for
inflation, the past 15 years puts your spending at around $162,000,
Social Worker: Do you know that if you hadn’t drank all that beer,
that money could have been put in a step-up interest savings account
and, after accounting for compound interest for the past 15 years, you
could have now bought a brand new Ferrari?
Man: Do you drink?
Social Worker: No.
Man: Then why the hell are you driving a Chevy?
For a frequent joke fix ,follow me on your Kindle.


A prominent mathematician, an engineer, a physicist.
Was born on 21st August, 1909.
He spent his childhood (1911-1913) in Nizhyn, where his father worked as a teacher of religion in Nizhyn historical and philological Institute. His father, Mykola Boholiubov, was a philosopher and a theologian (1872-1934).
A doctor of physical and mathematical sciences (1930), a professor (1946), an academician of the USSR (1948). A honorable member of a lot of AS and scientific communities. An honoured scientist of the USSR (1970). He founded scientific schools of nonlinear mechanics, statistical physics and quantum field theory. He worked as director of Theoretical Physics Institute, as director of the Mathematical Institute of the USSR, as director of Joint Institute for Nuclear Research in Dubno. For his outstanding achievements in the development of mathematics, mechanics and theoretical physics he was awarded twice the Hero of Socialist Labor (1969, 1979), the winner of Lenin (1958) and three USSR State Prizes (1947, 1953, 1984).


A novel algorithm called Isometric Method (IM) for solving smooth real-valued non-linear inverse problems has been developed. Model and data spaces are represented by using m+1 corresponding vectors at a time (m is the dimension of model space). Relations among vectors in the data space are set up and then transferred into the model space thus generating a new model. If the problem is truly linear, this new model is the exact solution of the inverse problem. If the problem is non-linear, the whole procedure has to be repeated iteratively. The basic underlying idea of IM is to postulate the distance in the model space in such a way that the model and data spaces are isometric, i.e. distances in both spaces have the same measure. As all model-data vector pairs are used many times in successive iterations, the number of the forward problem computations is minimized. There is no necessity to deal with derivatives. The requirement for the computer memory is low. IM is suitable especially for solving smooth medium non-linear problems when forward modelling is time-consuming and minimizing the number of function evaluations is topical.
The code on this page is available in MATLAB. Please, do not hesitate to contact us for more information: malek [at] irsm.cas.cz.
Program for 3D seismic refraction data processing using the modified time-term method.
download current version 0.2 |
source code |
article Valenta and Dohnal (2007)
Matlab code for dispersive waveform calculation of the surface wave. Calculation is based on summation the particular frequency components with the introduction of phase shifts, corresponding to velocity dispersion and given distance from a seismic source.
A program for surface waves analysis, dispersion curves determination and inversion and their forward modeling.
A program designed for surface wave phase velocity estimation using the two-station method.
A program for estimation of expected uncertainties of relative location in a network of seismic stations.
Matlab code for visualization of outputs from program LocErr.
MouseTrap: Python/ObsPy module for automated detection of long-period disturbances in seismic records.
ISOLA-ObsPy: Python/ObsPy module for automated moment tensor inversion.


Arriving in Banff, Alberta Sunday, February 12 and departing Friday February 17, 2017
- Leonid Chindelevitch (Simon Fraser University)
- Caroline Colijn (Imperial College London)
- Amaury Lambert (University Pierre and Marie Curie, Paris)
- Marta Luksza (Institute of Advanced Study, Princeton University)
- Vincent Moulton (University of East Anglia)
- Tandy Warnow (University of Illinois)
The objectives of the workshop are to bring mathematicians working in three key areas together to make progress in these problems. We will also invite several biologists who are keen to engage with mathematicians on the challenges posed by new data on evolutionary processes. Key challenges in the field at the moment are focused around the following emerging inter-related areas, each of which is raising mathematically interesting problems:
1. Inference with evolutionary trees and networks: Ultimately it is necessary not just to obtain evolutionary trees from data using standard methods, but to infer aspects of an underlying biological process. This requires understanding the likelihood of an evolutionary tree or network, or at least some of its informative features, using some stochastic process as the underlying ecological model. In principle, this approach allows simultaneous inference of both evolutionary trees and parameters of the ecological model. Coalescent theory has made considerable progress, for example, in obtaining tree likelihoods for sparsely sampled populations with geographical structure or with known past demographics (see for just one example ). In some simplified cases, epidemiological inference methods can estimate transmission trees , branching rates through time  and other aspects of epidemic spread . However, none of these approaches is currently applicable if there is non-tree-like evolution, or where datasets are large. Furthermore, the range of models for which we can write down a tree likelihood is very limited. This raising nice new problems in probability, statistical inference and ecological modelling. Recently, more general processes (e.g. Lambda-coalescents, which allow multiple rather than strictly pairwise coalescent events) are beginning to be used to model populations with large offspring variance, or even to model selection in a non-parametric fashion . This is potentially a powerful tool particularly for bacteria, which may acquire resistance to antibiotics and spread rapidly as a consequence, yielding both highly variable effective offspring numbers and a need to model selection carefully.
2. Understanding spaces of evolutionary trees: There are a large number of possible labelled, rooted binary trees for a given set of nn tips (ie for a given set of sequence data): (2n−3)!!=(2n−3)(2n−5)...(3)(1)(2n−3)!!=(2n−3)(2n−5)...(3)(1). This works out to 1018410184 trees on 100 tips; in contrast, current datasets for evolving bacteria contain thousands of tips. Not even the tools of Bayesian inference, the natural approach in such situations, can systematically explore spaces this big. This motivates the development of mathematical approaches for the exploration of tree space. These include new approaches to continuous tree spaces, including those from tropical geometry , and the use of tree metrics . These in turn can lead to tools for averaging trees , and for navigating tree space in efficient ways  -- with profound applications in statistical inference from sequence data. Generalizing metrics to the case of evolutionary networks (for example tree-based networks) is another natural and important question.
3. Summarising trees and networks using combinatorial tools: Uncovering shape features, spectral features and other ways to describe trees using quantities that are mathematically tractable will be of considerable interest . As one example, where likelihoods are truly intractable, rapid tools for likelihood-free inference can be used to infer evolutionary processes from sequence data, but only where there are informative ways to summarize key features of the data. Trees are natural combinatorial structures with connections to data; for example, a binary tree is a sequence of partitions of the set of tips (sequences in a dataset), where each partition is one block smaller than the previous one, moving back through time from the partition with each tip on its own to the partition with all tips in one block as we move from the tips of the tree to the root. If the tree is not binary (ie it allows multifurcations), more than two blocks can combine at a branching event. Because of the natural link to partitions, the study of tree shapes links to the enumeration of partitions and to lattice path combinatorics. These in turn allow the characterization and enumeration of possible tree shapes. Meanwhile the study of motifs in other biological networks has been fruitful, and could be extended to tree and evolutionary network shapes. Trees and evolutionary networks are of course also graphs (with an added time dimension); the tools of algebraic graph theory are now finding application in this area of mathematical biology.
The community's response to the idea for this workshop has been very positive. A * beside a participant's name indicates that they have expressed enthusiasm for the workshop, and plan to attend.
References  Louis J Billera, Susan P Holmes, and Karen Vogtmann. Geometry of the space of phylogenetic trees. Adv. Appl. Math., 27(4):733–767, November 2001.  Xavier Didelot, Jennifer Gardy, and Caroline Colijn. Bayesian inference of infectious disease transmission from whole-genome sequence data. Mol. Biol. Evol., 31(7):1869–1879, July 2014.  Alison M Etheridge, Robert C Griffiths, and Jesse E Taylor. A coalescent dual process in a moran model with genic selection, and the lambda coalescent limit. Theor. Popul. Biol., 78(2):77–92, September 2010.  Fanny Gascuel, Regis Ferriere, Robin Aguilee, and Amaury Lambert. How ecology and landscape dynamics shape phylogenetic trees. Syst. Biol., 64(4):590–607, July 2015.  Amaury Lambert and Tanja Stadler. Birth–death models and coalescent point processes: The shape and probability of reconstructed phylogenies. Theor. Popul. Biol., 90(0):113–128, December 2013.  Tom M W Nye. An algorithm for constructing principal geodesics in phylogenetic treespace. IEEE/ACM Trans. Comput. Biol. Bioinform., 11(2):304–315, March 2014.  David A Rasmussen, Erik M Volz, and Katia Koelle. Phylodynamic inference for structured epidemiological models. PLoS Comput. Biol., 10(4):e1003570, April 2014. 2  David Speyer and Bernd Sturmfels. The tropical grassmannian. Adv. Geom., 4(3):389–411, 2004.


(Text by Jenneke Krüger)
Karen Uhlenbeck (1942, Cleveland, Ohio, USA) is the eldest of four children; her mother, Carolyn Windeler Keskulla, was an artist and schoolteacher and her father, Arnold Keskulla, was an engineer. The family lived in a rural community; Karen liked (and likes) to spend time outdoors, but she also liked reading very much. In her own words: “I used to read under the desk in school. … I was particularly interested in reading about science.”
She enrolled at Michigan University to study physics; however, she discovered that she enjoyed mathematics much more than physics, so she decided to switch to mathematics. An added advantage in Karen’s mind was that in mathematics she could work on her own; at the time she didn’t like very much being involved with other people. That attitude changed gradually when she met more people with whom she could share her ideas on mathematics. She got her BSc in 1964, continued her studies at the Courant Institute in New York, married the biophysicist Olke Uhlenbeck and went with him to Boston, where she was awarded her MSc at Brandeis University in 1966. She remained at Brandeis for her PhD research, with Richard Palais as her adviser. Her doctoral thesis was titled The Calculus of Variations and Global Analysis (1968).
After finishing her PhD, Karen Uhlenbeck did not straight away see herself as a professional mathematician. She and her husband had temporary positions at MIT and the University of California in Berkeley, where she also took courses in general relativity and Lorentz-geometry (the geometry of space-time). In those years Karen Uhlenbeck realized that however good she was in mathematics, many universities did not want to hire women; in the early seventies the place of a woman was still seen as primarily at home. Her husband would be able to get a position at universities such as Princeton, MIT and Stanford, but these top ranking institutions would not hire her as well. When both she and her husband were offered a position at the University of Illinois, in Champaign-Urbana, they decided to accept and started working there in 1971.
However, Karen felt unhappy about the mathematics and the social environment. She travelled a lot thanks to a fellowship she received, and met and worked with other mathematicians such as Lesley Sibner and Jonathan Sachs. In 1976 Karen moved to Chicago, where she taught at the University of Illinois and from 1982 at the University of Chicago. She published many important papers on a variety of subjects, both on her own and with other mathematicians, such as J. Sachs, R. Schoen and S.-T. Yau.
Around that time she also became a strong advocate for greater gender diversity in mathematics and sciences. In 1987 she became a mathematics professor at the University of Texas, Austin. In 1990 she was the second woman who gave a plenary lecture at the International Congress of Mathematicians; the first woman was Emmy Noether, in 1932. She remained at the University of Texas until her retirement. She is still an active member of academia in the University of Texas at Austin and the Institute for Advanced Study in Princeton.
Karen Uhlenbeck made it to headlines worldwide in early 2019 when it was announced that she had been awarded the Abel prize –the equivalent of the Nobel prize in mathematics. Even though the Abel prize has been awarded yearly since 2003, Uhlenbeck was the first woman to receive this honour. Congratulations to her and let’s hope that many more will come!
Jim Al-Khalili (2019). A biography of Karen Uhlenbeck. www.abelprize.no


My girlfriend surprised me with the most incredible gift last night.
Some time ago, we were talking about our favorite books as kids. Mine was an illustrated account of the Earth's ecology long after human extinction. It belonged to my best friend, and we'd pass it around at school. I couldn't remember the title or author, but I'd tried a number of times to find it.
She found my "rosebud."
I found this program, CLOUDMIR.BAS, on a diskette of my first programs. In QBasic, it's a vague pattern of plump white pixels on a black screen. Porting it to Processing, I got some amazing output:
This is an iterated function system, where functions are repeatedly applied to a set of numbers and the result is plotted at each step. Its only by chance that the output looks 3D.
This algorithm for the left image goes like this:
x = x * cos(n) + c
y = y * sin(n) + c
n += c
c += 0.001
At each step, there is a little bit of error in the calculation from the computer's limited precision. Accumulating through millions of loops, rounding errors are likely reponsible for most of the chaos happening in the output.


I am a recent graduate of the Mechanical Engineering program at the University of Victoria. I have experience tutoring math, physics, statistics and engineering courses. I have worked with students at the following schools: - University of Victoria - University of Okanogan - Camosun College - South Island Distance Education School (SIDES) - High Schools in Canada and Australia I like to go through many practice problems in our sessions that will prepare you for assignments, midterms, and final exams. All sessions are done online at 45 $/hr. I offer a free session for new students so that you can try out my services free of risk. For students booking 8 weeks of tutoring, I offer a 10% discount. Please reach out if you have any questions.


Mix and match the pieces of a ladybug (or "ladybird") toy to develop mathematical thinking skills.
|Hints for uses in your library||This write-up is based on Snap-N-Learn Number Bugs from Learning Resources, but the activity can be adapted for a variety of mathematical toys or even paper or felt objects. The toys are very engaging, but older siblings or adults will need to prompt young children to complete the three challenges described in the write-up.|
|Related Links||Snap-N-Learn Number Bugs|
|Originating Source||Courtesy of Dr Francesca Iezzi, Mathematics Engagement Officer, University of Edinburgh|
|Related Books||Suggest a book|


The study of Mathematics is a unique and important discipline which encompasses so much more than the numeracy skills which most people remember from their school days. How to construct a logical argument or how to systematically tackle a new problem are important skills in their own right but the manipulation of data and numbers also underpins any financial, technical or scientific activity. An understanding of mathematics is essential for success in the modern world.
We are fortunate at this school that so many of our students already arrive with a love of mathematics and very high levels of numeracy. Our aim is to continue their enthusiasm for mathematics while supporting the development of their mathematical skills through some very tricky concepts. We ensure that they gain the mathematics they need to be successful in all subjects while also ensuring that they have access to every level of mathematics available at school level and beyond. It is a balance of developing numerical skills alongside skills in evidence based argument and interpretation of data.
In principle maintaining an enthusiasm for mathematics should be relatively straightforward as this subject is a creative and highly interconnected subject that has been refined over several thousand years. Some of the most intriguing problems in history have been mathematical and the Clay institute is still offering a million dollars for the solution of 6 important mathematical problems. We should remember that people use logic to solve sudoku problems for fun! However we do need to acknowledge that while the importance of the subject is clear, school will largely be a time for gaining and consolidating mathematical knowledge distilled from two thousand years of human endeavour. This is important to support success in other subjects and it is vital in preparing for examining the cutting edge of mathematics at graduate levels of study. What is equally important though is the simultaneous development of competence in applying the skills .
The study of mathematics at this school should allow all of our students to become accomplished mathematicians who are able to reason mathematically and interpret data across a wide range of topics. We try and do this while maintaining a sense of enjoyment and curiosity about this beautiful and powerful subject.
Information on how Mathematics is taught across the Key Stages can be found below


Find out the value of pips for the currency pair you are trading
Never enter a trade of the wrong size again!
Manage your risk per trade with our FXTM pip-size calculator. Use our simple yet powerful tool to work out your exact pip risk-to-reward ratio for each trade.
Pip calculators explained
'Pip' stands for 'point in percentage' and measures the movement in the exchange rate between the two currencies.
So, how do I find a pip? Here's how...
In most forex currency pairs, one pip is on the 4th decimal place of the Forex pair (0.0001), meaning it's equivalent to 1/100 of 1%. For JPY pairs, one pip is on the 2nd decimal place of the Forex pair, so the second digit after the decimal point is the pip.
Using these small units to measure price movement can also protect inexperienced traders from big losses. A fractional pip or 'pipette' is 1/10th of the value of a standard pip and can give you tighter spreads and a better understanding of a currency's price movements.
For pairs without JPY, one pipette is on the 5th decimal place of the Forex pair.
For JPY pairs, one pip is on the 2nd decimal place of the Forex pair.
What is a pip’s worth?
Still not sure what the true value of a pip is? Learn more by watching this short video.


Test and Interview
Admissions to Grades 1 to 9 and Grade 11 are finalized based on the performance in the written admission test conducted in the month of April / May.
All students appearing for the written test are tested on their previous years' portions.
|STD I - II STD||English , Maths , II Language (ORAL)|
|III STD – VI STD||English , Maths , II Language|
|VII STD - IX STD||English , Maths, Science, II Language|


CSC 4170: Theory of Computation
Finite automata and regular expressions; push down automata and context-free grammars; Turing machines; Church's thesis; computability; NP-completeness.
- Demonstrate an understanding of the Chomsky hierarchy of grammars and languages.
- Demonstrate understanding of fundamental concepts of theoretical computer science, such as decidability, undecidability, recognizability, etc.
- Demonstrate an understanding of basic complexity theory and NP-completeness.
- Develop skills in generating mathematically rigorous definitions and proofs.


How can we discover novel and interesting things from data?
How can we explore the data, and not our assumptions?
That's what we develop theory and algorithms for.
Last summer, Polina Rozenshtein did an internship in our group, and will present the resulting paper `Reconstructing an Epidemic over Time' at ACM SIGKDD 2016. Together with B. Aditya Prakash and Aris Gionis we studied the problem of finding the seed nodes of an epidemic, if we are given an interaction graph, and a sparse and noisy sample of node states over time. We propose the CulT (Culprits in Time) algorithm, that reliably, efficiently, and without making any assumptions on the viral process can recover both the number and location of the original seed nodes. We give a short explanation, with kittens, on YouTube here.
During the summer of 2014 Roel Bertens did an internship in our group, and he will present the outcome `Keeping it Short and Simple: Summarising Complex Event Sequences with Multivariate Patterns' at ACM SIGKDD 2016. In this paper we propose the Ditto algorithm, an efficient heuristic for finding succinct summaries of complex event sequences with patterns that can span over multiple attributes and may include gaps. You can find the paper and implementation here, and for a short introduction, see our YouTube video here.
Kailash Budhathoki has been invited to attend the 4th Heidelberg Laureate Forum. During the 18th and 23rd of September 2016, he will get to meet laureates of the most prestiguous awards in Mathematics and Computer Science, such as Turing Award winners Manuel Blum, Vinton Cerf, Richard Karp, and John Hopcroft, as well as 199 other highly talented young scientists.