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We know that 1 liter 1.06 quarts, and 1 quart 32 ounces, so: 1 liter 1.06 32 33.92 ounces We want to divide a 2-liter container of soda into 20-ounce containers. 2 liters 2 33.92 67.84 ouncesWelcome to Knowledge on the Go™ for Grade 4.Below you will find free video lessons across math, science, and English language arts. Our team of teachers and teacher–writers are recording consistent and coherent daily lessons to provide support for teachers and students nationwide. Spotlight on Math A Story of Units has several key mathematical “models” that will be used throughout a student’s elementary years. Students began in earlier grades to build arrays, showing multiplication and division as a series of rows and columns. In 4th grade, they learn to show these types of problems as an area model. 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He was born on 03 August 1989 in Aghdam.
In 2010 he graduated from the department of applied mathematics at Baku State University. In 2013 he attended preparatory language courses at St. Petersburg State University of Telecommunications, and in 2015 graduated with master’s degree in information systems and technologies.
He has been employed at Azerbaijan University of Technology since 2015. In 2018 he was appointed an adviser to the rector.


Prof. David Keyes
Extreme Computing Research Center
King Abdullah University of Science and Technology, Saudi Arabia
"Efficient Computation through Tuned Approximation"
Wednesday, November 2, 5 pm - 6 pm, Arabic Standard Time (AST)
7 am PDT / 10 am EDT / 2 pm UTC / 3 pm CET / 5 pm AST / 11 pm JST
Supercomputing Spotlights is a new webinar series, presented by the SIAM Activity Group on Supercomputing (SIAG/SC, https://siag-sc.org) as part of new initiatives that focus on raising awareness of high-performance computing (HPC) opportunities and growing the community. The webinars feature short TED-style presentations that highlight the impact and successes of HPC throughout our world. Presentations, emphasizing achievements and opportunities in HPC, are intended for the broad international community, especially students and newcomers to the field. Join us!
Abstract: Numerical linear algebra software is being reinvented to provide opportunities to tune dynamically the accuracy of computation to the requirements of the application, resulting in savings of memory, time, and energy. Floating point computation in science and engineering has a history of “oversolving” relative to expectations for many models. So often are real datatypes defaulted to double precision that GPUs did not gain wide acceptance until they provided in hardware operations not required in their original domain of graphics. Indeed, the condition number of discretizations of the Laplacian reaches the reciprocal of unit roundoff for single precision with just a thousand uniformly spaced points per dimension. However, many operations considered at a blockwise level allow for lower precision and many blocks can be approximated with low rank near equivalents. This leads to smaller memory footprint, which implies higher residency on memory hierarchies, leading in turn to less time and energy spent on data copying, which may even dwarf the savings from fewer and cheaper flops. We provide examples from several application domains, including a preview of a 2022 Gordon Bell finalist computation that benefits from both blockwise lower precisions and lower ranks.
Bio: David Keyes is a professor of applied mathematics, computer science, and mechanical engineering at the King Abdullah University of Science and Technology (KAUST), where he directs the Extreme Computing Research Center, and where he was founding Dean in 2009. He is also Adjunct Professor of applied mathematics at Columbia and an affiliate of several US national labs. He earned a BSE in aerospace and mechanical sciences from Princeton in 1978 and a PhD in applied mathematics from Harvard in 1984. He works at the interfaces between parallel computing and the numerical analysis of PDEs and spatial statistics, with a focus on scalable implicit solvers and exploiting data sparsity. He helped develop and popularize the Newton-Krylov-Schwarz (NKS) and Additive Schwarz Preconditioned Inexact Newton (ASPIN) methods. He has been awarded the ACM Gordon Bell Prize and the IEEE Sidney Fernbach Prize and is a fellow of the SIAM, AMS, and AAAS.


Teaching your kids some fundamental math concepts at a young age is never too early. Kids may learn the proper sequence of numerals and how to recognize numbers by using a number painting kit to help them identify numbers, make patterns, and identify patterns. As a result, they can better connect the dots between concrete objects and abstract ideas. With the help of these kits, young kids may learn how to read numbers, recognize numerals, and count items. These kits are crucial in preschool and primary education.
The most outstanding selection of beginner painting kits includes stencils, paints, brushes, a paint palette, and other equipment that may improve your child’s hand-eye coordination and motor abilities while they are having fun. Even some kits for number painting include soothing poetry or rhymes that may make learning the numbers and having fun with them more enjoyable for your youngster. These number painting kits teach kids how to count numbers while allowing them to express themselves via painting, drawing, or sculpture.
Here are the seven best number painting kits for kids:
Table of Contents
1. Fuzzy Wuzzy Number Painting Kit
For kids to learn their numbers and how to count them, use this number painting kit. It comes with everything your youngster needs to begin writing and counting the numbers on the wall. The convenient double-sided chalkboard paint included in this 5-panel set allows your youngster to draw patterns and designs on the wall. It is more entertaining when they try to count the numbers since the panels have inset faces that appear to be peeling away. Additionally, there is a vibrant, poop-scented fizz that your youngster will enjoy anytime they hear him crow.
2. Simple Start Number Painting Kit
Use the Simple Start Number Painting Kit with your kids to help them practice writing numbers and counting. This number painting kit includes all the supplies you will need for painting, writing, drawing, and counting. So that your child may choose the color of the numbers, it comes with eight stencils and a paint palette loaded with a choice of colors. It is easy to put the stencils on the wall and utilize them. Dashes, dots, and dots on either side of each number are among the several numerals included in this number painting set.
3. Up & Down Number Painting Kit
Your youngster can learn the numbers and how to count them while having fun with the Up & Down Number Painting Kit. This number painting kit is composed of sturdy cardboard, so it won’t be at risk of breaking or quickly becoming ruined. You may write, draw, and paint numerals using the materials in the kit. The stencils are simple to use since all your youngster needs is to rip them off the backing paper, put them on the cardboard panel, and hang them on the wall. The number painting set includes both capital and lowercase letters to make writing the numbers more enjoyable and simple.
4. Jumbo Number Painting Kit
It is excellent for teaching your kid numbers and counting. Everything you need to paint and write numbers on the wall is included. This package includes stencils, a paint palette, a brush, a needle, and a cutting mat so your youngster can practice counting while getting their hands dirty. While counting the numbers, students may also utilize this set to exercise their imaginations by writing relatable words. The collection also includes scissors for your youngster to cut the stencils and paper. Visit this site and learn more about the number painting kits.
5. 4 In 1 Number Painting Kit
Using the Kit, your child may practice counting while also learning to count. The kit has everything you’ll need to paint, write, carve, and draw numbers on the wall. Detailed stencils and the majority of the required trade tools are included in the bundle. Without any problems, your child may place the stencils in any order they like on the cardboard panels before adhering them to the wall. This number painting set also includes a helpful towel, ensuring that your youngster always has something to use while painting and writing numbers on the wall.
6. Cloud Colored Number Painting Kit
Your child may learn to count and recognize different numbers with the help of the Cloud Colored Kit. With this, they may have fun and learn the numbers while developing their hand-eye coordination. Your child will get everything they need to cut, write, draw, and paint the numbers on the wall included with it. Due to its robust cardboard construction, this kit will not easily shatter or become damaged.
Water-soluble stencils and colors are included in this box, which your youngster is free to use as frequently as they like without any problems. Additionally, if your youngster needs additional help getting started, it includes an instructional handbook to help them.
7. No Mess Painting Kit
The No Mess Painting Kit is a fantastic tool for teaching your child numbers while having fun. This set includes the tools required for your youngster to write, draw, and paint numbers on the wall. It has a different palette for your youngster to draw those lines without creating a giant mess or painting everything else. Since no ties hold the stencils together, your youngster may take them off the backing paper and stick them on the background board.
Using number painting kits is fun and engaging for kids to learn their numbers. They may be used to assist a youngster in comprehending the idea of counting, writing, reading, and drawing numbers independently. These number painting kits come with equipment that is inexpensive, easy to use, and clean to use. These can help you as a parent simplify the task of teaching your kid to count, expand their vocabulary, and develop the most incredible coordination possible as they paint various designs on the wall.


If you’re serious about forex trading, you need to understand how charts and chart analysis tools can help you identify trades that maximize your potential earnings while minimizing risk.
Standard chart patterns are easy to identify just by glancing at a chart and spotting certain movements, but advanced patterns, also known as harmonic patterns, require additional tools and information to identify trade opportunities and monitor price movements.
These harmonic patterns offer incredible value to traders who use them to inform their trading plan, and all of the tools you need to spot and track these patterns are available on online platforms such as MetaTrader 5. In general, the key characteristic of any harmonic pattern is the way the chart movement corresponds to the famous Fibonacci levels.
The History Behind Fibonacci Levels
Fibonacci levels are named after the Italian mathematician Fibonacci, who played a significant role in the rising popularity of mathematics in Europe in the 12th and 13th centuries. His most significant contribution was the development of a “golden ratio” and a number sequence that now bears his name as the Fibonacci levels used in investment trading.
The logic behind these levels has to do with the ratios created between this string of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.
This series of numbers goes on indefinitely, and the next number is determined by adding together the two numbers that precede it. In this example, 89 + 144 = 233, which is the next number in the sequence.
Ratios can be used to measure the relationship between all of these numbers. Dividing one number by the number following it, for example, yields a %age of 61.8. Divide that same number by the second number to the right, and the %age is 38.2. These numbers form the framework for Fibonacci ratios, which the mathematician claimed bore a relationship with the natural order of the world.
The most common figures used are 11.4 %, 23.6 %, 38 %, 61.8 %, 70.7 %, 76.4 %, 88.6 %, and 100 %. Although it’s not technically a Fibonacci number, 50 % is also regularly used in Fibonacci-based trading.
Here’s a look at how Fibonacci levels are displayed on a EUR/USD chart:
Today, investors use these numbers because they tend to reflect the price movements taking place in forex and other markets. By turning these ratios into levels reflecting the extensions and retracements of a currency pair’s price, traders can estimate when price shifts will occur, and they can time their trades to maximize profits when a currency pair’s movements align with these ratios.
The Importance of Fibonacci Levels
Harmonic patterns are named after measurements known as Fibonacci levels, which are mathematical markers, expressed as ratios, that are used to indicate potential lines of support and resistance with a given asset.
Harmonic patterns develop when an asset’s price movements reach certain Fibonacci markers, moving both up and down in retracements and extensions that can foreshadow price breakouts. Although there are exceptions, most harmonic patterns feature four price movements from a starting point, X.
By studying these retracement levels and using them to time your trades in forex, you can reduce your risk. The graphic below shows the lines of retracement and range of risk associated with an asset that has fallen into a harmonic pattern:
The pattern that has developed indicates a future price breakout. An overeager trader might try to open a position quickly after the fifth point is established, in fear of missing out on the breakout if they wait too long. But the guidance provided by the Fibonacci levels, and the prevailing strategy used when analyzing harmonic patterns, suggests that traders are better off waiting until the price moves closer to the 61.8% retracement level.
This patience minimizes the potential risk if your prediction is wrong and the price dips to the stop area, and it increases your range of potential profit if your prediction is right.
Advantages and Disadvantages of Fibonacci-Level Trading
Fibonacci levels are a popular tool for forex trading for a few reasons. The first reason is their relative ease of use: Levels are easily displayed on a forex chart, and even amateur traders can monitor price movements in relation to these levels, which can be useful in developing an eye for identifying trades.
Fibonacci levels are also useful for traders embracing a trend-trading strategy, largely because the Fibonacci numbers themselves are designed to identify and predict trending movements. Traders can use levels of resistance, as well as extensions beyond those levels, to identify a strong trading opportunity.
The biggest challenge is that Fibonacci levels are inherently subjective and can be interpreted in different ways based on who is reviewing the chart. Results from using Fibonacci levels can vary widely.
Whereas some traders are passionate supporters of this strategy, detractors argue that the Fibonacci levels themselves aren’t connected to any concrete financial or economic theory. The most reliable aspect of using these ratios is that, when many other traders are also tracking movements along these levels, the ratios can become self-fulfilling prophecies: Enough traders anticipate the influence of these levels that Fibonacci ratios end up being relevant to the price movements on the forex market.
Although these ratios were developed by a renowned mathematician, the theory behind them does not have any proven logic behind it. The lack of mathematical validity to these ratios can be off-putting to traders who are looking for a more data-driven approach.
Understanding the Gartley Pattern
One of the most famous patterns in history, and the most important harmonic pattern to understand in forex trading, is the Gartley pattern. This pattern has been modified over time since it was first conceived by H.M. Gartley in 1932, and many other harmonic patterns—including butterfly, bat, crab, and cypher patterns—all exist as variations of the Gartley pattern, with different Fibonacci ratios used to define their shape. If you understand the Gartley pattern, it’s easier to apply these other harmonic patterns to your forex evaluations.
To identify a Gartley pattern, you first need a plain chart with no indicators present other than the Fibonacci lines. Any chart being analyzed for harmonic patterns needs to have four price movements that switch directions each time, with points X, A, B, C, and D. In this sequence, point C needs to have a 61.8% or 78.6& retracement from point B. At the same time, the movement of lines AB and CD must match, and point D should be a 78.6% retracement of point X.
If these parameters are all met, you’ve got a Gartley pattern. Points A and C will tell you whether the price setup suggests a positive or negative breakout: If A and C are the highest points on the chart, you can likely expect a price decline. If A and C are lower than X, B, and D, plan for a price breakout. The chart below illustrates a bullish Gartley pattern that has developed on a GBP/USD chart:
Taking a Profit
Because you’re using Fibonacci lines to identify patterns and time your trades, you can also use them to decide when to take a profit. Consider two profit goals, depending on your own evaluation of a forex asset’s potential price movement. One goal comes at a 38.2% retracement, at which point you can safely close your position and claim a profit. Or, if you’re feeling confident in the price, you can consider waiting until a 61.8% retracement, capturing a nice return from your harmonic pattern analysis.
Harmonic patterns may be more complicated to analyze than standard patterns, but they offer clear rules when you’re making trades. Incorporate this analysis strategy into your trading plan to improve your risk management and your ability to time your trades.
The information provided herein is for general informational and educational purposes only. It is not intended and should not be construed to constitute advice. If such information is acted upon by you then this should be solely at your discretion and Valutrades will not be held accountable in any way.


Sebastian Ceria is Chief Executive Officer of Axioma and founded the company in 1998. Prior to Axioma, Sebastian was an Associate Professor of Decision, Risk and Operations at Columbia Business School from 1993 to 1998.
Sebastian has worked extensively in the area of robust optimization and its application to portfolio management. He is the author of many articles in publications including Management Science, Mathematical Programming, Optima and Operations Research. He has co-authored numerous papers on the topic, including, "Incorporating Estimation Errors into Portfolio Selection: Robust Portfolio Construction," published in the Journal of Asset Management, “To Optimize or Not to Optimize: Is That the Question?” published in the Oxford Handbook of Quantitative Management, and “Factor Alignment Problems and Quantitative Portfolio Management,” published in the Journal of Portfolio Management. He is a recipient of the Career Award for Operations Research from the National Science Foundation.
Sebastian completed his PhD in Operations Research at Carnegie Mellon University's Tepper School of Business, and his undergraduate degree in Applied Math at the University of Buenos Aires, Argentina.Close bio >


The Pythagoras Puzzle
In mathematics, the Pythagorean theorem, also known as Pythagoras's theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the "Pythagorean equation":
where c represents the length of the hypotenuse and a and b the lengths of the triangle's other two sides.
The theorem has been given numerous proofs – possibly the most for any mathematical theorem. This puzzle is a way for the students to verify the Pythagorean theorem themselves.
1. Have the student work in groups.
2. Distribute the copying material and scissors to the groups.
3. Instruct them to put the four triangles in the square to somehow form the area a2.
4. After they have managed to form the area c2 they should rearrange the triangles to try to form the areas a2 and b2.
5. Instruct them to discuss if this verifies the theorem. And encourage them to draw their own right-angled triangles to try to verify if this is true for all right angled triangles.
Note 1: Before the introduction to this puzzle it is recommended to talk a little about the history of the Pythagorean theorem and Pythagoras himself.
Note 2: The students can use a spreadsheet application to further examine if the theorem is true for different values of a and b.
|The Pythagoras Puzzle_copying material_ENG 421 KB|
|The Pythagoras Puzzle_teachers manual_ENG 424 KB|
Open the form


Category: 3 – SHELF it (All Categories are 1 – Read ASAP!, 2 – BUY it!, 3 – SHELF it, 4 – SOMEDAY it)
Comments: This is a Statistics textbook. So, it definitely isn’t for everyone. However, if you are interested in Statistics, it is an awesome book. Lays out concepts with a ton of clarity.
Top 3 Learnings:
1. Let’s say you are tossing a coin.
The law of averages says nothing about an increased likelihood of a tail after 4 rows of heads. Instead, it says that – as you keep increasing the number of tosses, the chance error as a percentage of tosses keeps going down.
2. Regressions ONLY deal with associations or correlations. An increase in x is associated with an increase in y.
3. A test of significance gets at the question of whether an observed difference is real (alternative hypothesis) or just a chance variation (null hypothesis). The observed significance level is the chance of getting a test statistic as extreme or more extreme than the observed one. The chance is computed on the basis that the null hypothesis is right. Small values of p are evidence against the null hypothesis – i.e. the observed difference is real.


It is time again for Mystery Monday, brought to you by Professor Layton and the Curious Village. A glass jar holds a single germ. After one minute, the germ splits into two germs. One minute after that the two germs each split again, forming a total of four germs. Continuing at this rate, a single germ can multiply to fill a whole jar in exactly one hour. Knowing this, how long in minutes would it take to fill the jar if you had started with two germs?


- Saturdays 9:30AM – 2:00PM
- Location: P.S. 1 at 8 Henry Street
- Lunch is Provided
Elementary School (Grades 1 – 5)
Students in Grades 1 – 5 in our Saturday Program will be at Lighthouse Development Center, while students in Pre-K and Kindergarten will be at Lighthouse Preschool for class.
Our Saturday Program for Grades 1 – 5 are focused on educational reinforcement at our student’s pace. Different students learn at different paces, and our teachers customize their curriculum to make sure all our students are able to stay on track. Every few weeks, Progress Reports are handed out to the students’ parents/guardians explaining your children’s progress.
Students here focus much more on academic gain and reinforcement than the younger students do. Students will be given lots of practice in the new Common Core testing system for New York State.
We also provide individual tutoring for students from Grade 6 to 12.
Junior High School (Grades 6 – 8)
Junior High School students will be focusing primarily on the SHSAT, and is designed to bolster students’ abilities in public school as well as prepare them for the exams.
Students in Grade 6 will start by learning the fundamentals pertaining to the Verbal and Mathematics section of the SHSAT. These provide a more in-depth look into the English language, logical reasoning, and mathematics taught in school.
Students in Grade 7 will be learning the more advanced concepts and techniques that appear on the SHSAT as well as beginning 8th Grade material once 7th Grade concepts are finished.
Students in Grade 8 will be focusing on the 8th Grade NY State Exams: English, Math, Science, and Social Studies, as well as any Regents the students are required to take at the end of the year.
High School and College Prep (Grades 9 – 12)
High School Students may be tutored in PSAT/SAT Prep or Regents exams from a choice of: English, Trigonometry, Algebra, Geometry, Biology, Chemistry, and Physics. Each tutoring session lasts 2 hours, the first from 9:00AM – 11:00AM, and the second from 12:00PM – 2:00PM.
High School Students attending PSAT/SAT Prep Classes will be tutored from 9:00AM – 2:00PM. This section will include rigorous biweekly full timed exams (with first day diagnostic), weekly vocabulary quizzes, practice of timed essay writing, and practical applications of mathematical rules/tricks.


Gifted and High Ability STEAM Magnet
Bancroft Middle School is proud to offer the STE[a]M (Science, Technology, Engineering, art, and a Mathematics) Magnet, one of only 54 STEAM schools in LAUSD. This is a criteria magnet for gifted and high achieving students who are interested in pursuing an in depth education in the fields of mathematics, science, engineering, and technology. Students learn through an array of thematic International Baccalaureate units, emphasizing depth, complexity, acceleration, and novelty to address the learning needs of GATE children. Students in our STEAM Magnet take the following 8 classes and an Intervention or Enrichment class:
Honors English, Honors Math, Honors History, Honors Science, Project Lead the Way Engineering Elective, Visual Art & Design, PE and Mandarin Language (Chinese).
Bancroft STE[+a]M Program Mission:
Bancroft STE[+a]M Magnet empowers innovative thinkers to use the design process within science and technology to strategically and creatively incentivize global change.


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Born to a poor Lutheran pastor in what is today the Federal Republic of Germany, Bernhard Riemann (1826-1866) was a child math prodigy who began studying for a degree in theology before formally committing to mathematics in 1846, at the age of 20. Though he would live for only another 20 years (he died of pleurisy during a trip to Italy), his seminal work in a number of key areas—several of which now bear his name—had a decisive impact on the shape of mathematics in the succeeding century and a half.
In Simply Riemann, author Jeremy Gray provides a comprehensive and intellectually stimulating introduction to Riemann’s life and paradigm-defining work. Beginning with his early influences—in particular, his relationship with his renowned predecessor Carl Friedrich Gauss—Gray goes on to explore Riemann’s specific contributions to geometry, functions of a complex variable, prime numbers, and functions of a real variable, which opened the way to discovering the limits of the calculus. He shows how without Riemannian geometry, cosmology after Einstein would be unthinkable, and he illuminates the famous Riemann hypothesis, which many regard as the most important unsolved problem in mathematics today.
With admirable concision and clarity, Simply Riemann opens the door on one of the most profound and original thinkers of the 19th century—a man who pioneered the concept of a multidimensional reality and who always saw his work as another way to serve God.
About the author
Jeremy Gray is Professor Emeritus at the Open University in the U.K. and an Honorary Professor in the Department of Mathematics at the University of Warwick. A specialist in the history of mathematics in the 19th and early 20th centuries, he is the author of Henri Poincaré: a Scientific Biography, Princeton University Press (2012); (with Umberto Bottazzini, Milan) Hidden Harmony—Geometric Fantasies: The Rise of Complex Function Theory, Springer (2013); and A History of Abstract Algebra, Springer (2018), among other titles. Professor Gray is a fellow of the American Mathematical Society and received the Albert Leon Whiteman Memorial Prize in 2009 for his work on the history of mathematics.


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The Making of a Math Movement
Transforming mathematics education at community colleges, 4-year colleges, and research universities
College math has often been "sink or swim" for students. But instead of sitting by while students struggle with algebra and calculus and their career paths narrow, a group of high-level mathematicians have joined together to “fix” math. In June, many of those big thinkers were convened by Carnegie Corporation of New York to present their ideas to representatives of foundations and education nonprofits sharing an interest in addressing mathematical problems that cannot be solved on any blackboard.
The challenge put to the meeting participants was how to transform the discipline of mathematics, at all levels, in order to tackle the barriers that block a large number of students from completing college, and ultimately embarking on a rewarding career. “To give money is easy,” said Vartan Gregorian, president of Carnegie Corporation. "To build ideas is difficult.”
Leading the charge is Transforming Post-Secondary Education in Mathematics (TPSE Math), a partnership that launched in 2013 with support from Carnegie Corporation of New York and the Alfred P. Sloan Foundation.
At the meeting, a series of grim statistics demonstrated the urgent need for mathematics reform across the post-secondary landscape. For example, 60% of students attending the nation’s 1,200 community colleges were put into remedial math classes in 2012—for no credit. Staggeringly, 80% of those students would eventually fail their remedial math classes or a subsequent regular math course. At the university level, 40% of all engineering students and 60% of computer science students drop out of their programs or end up switching fields. Such rates of attrition are not healthy for the country, especially at a time when the demand for graduates with strong mathematics skills is expanding in most fields. “We are failing our kids,” said LaVerne Srinivasan, vice president of Carnegie Corporation's National Program. “We are failing our country by not preparing students adequately for higher education and careers in STEM.”
Phillip Griffiths, professor emeritus of mathematics at the Institute for Advanced Study and chair of TPSE Math's Board of Governors, said that experiments are taking place at the local level throughout the mathematics community. He told the gathering that “TPSE Math will identify innovative practices where they exist and advocate for innovation where they do not, and work with and through partners to implement and scale effective practices.”
William “Brit” Kirwan, a mathematician and chancellor emeritus of the University System of Maryland and executive director of TPSE Math, mapped out the movement’s strategy: 1) Make math relevant by broadening the curriculum, meeting the needs of students at all levels and from a range of disciplines. 2) Train educators in more effective teaching methods, redesign courses, and don’t be afraid to experiment in the classroom. 3) Develop partnerships with people both inside and outside the mathematics department, while reaching out to leaders in government, nongovernmental organizations, and foundations.
Participants at the meeting recommended programs to investigate and offered their support. Some voiced constructive concerns. Muriel Howard, president of the American Association of State Colleges and Universities, encouraged TPSE Math to get other academic disciplines on board as well. “It’s a heavy lift when you are talking to a faculty senate and trying to implement a new direction for curriculum.”
Kirwan reminded the group that university administrators are very concerned about college completion rates, and they see mathematics as the primary obstacle for many students. And that’s where, he pointed out, the power of partnerships come in. “You can bring the presidents and provosts together, we can bring the mathematicians together. That combination is our best hope making systemic change.”
TPSE Math is working to build a movement that addresses more than just mathematics. There is a broadly diverse group of students entering college today, including returning veterans, former stay-at-home moms, and young men and women from underserved communities. “Can we really tell them," asked Daniel Goroff, vice president and program director at the Sloan Foundation, "that we are doing the best that we can to make sure that these courses work for them?" He assured the group that "if we work together on this, the answer will be yes.”
Vartan Gregorian agreed, observing that "we need to provide true equality, and not organized inequality.” He reminded people that Abraham Lincoln launched the first public university in the middle of the Civil War, making the workforce of America ready for the coming Industrial Revolution. For today’s students, Gregorian concluded, the goal is nothing less than “to bring coherence and logic to the teaching of mathematics and rescue democracy’s future.”


By discounting the cash flows from future dollars into today’s dollars, this method takes into consideration the time value of money. The time value of money says that $1 today is worth more than $1 a year from now.
Discounted cash flows are used in formulas such as net present value that consider the value of projects over several years.
The discount rate used in discounted cash flows is also used in capital budgeting and other valuation methods. This makes discounted cash flows a very good baseline to begin valuing investments and projects. Continue reading


From Coursera, State Estimation and Localization for Self-Driving Cars by University of Toronto
- The edges is defined by the segments of the road that connect each sample point according to the rules of the road.
- the edges of the graph are directed
- When the graph is unweighted, a good candidate algorithm is the Breadth-First Search or BFS.
- At a high level, BFS can be thought of as iterating through all of the vertices in the graph but doing so in a manner such that all adjacent vertices are evaluated first before proceeding deeper into the graph.
Algorithm Dijkstra's (G,s,t)
- a search heuristic is an estimate of the remaining cost to reach the destination vertex from any given vertex in the graph.
- in this case, a useful estimate on the cost or length between any two vertices is the straight line or Euclidean distance between them
- Exploits structure of the problem
- Fast to calculate
- Straight-line distance between two vertices is a useful estimate of true distance along the graph
$$h(v) = |t-v|$$
Extensions to Other Factors
- Traffic, speed limits, and weather affect mission planning
- Time rather than distance is better at capturing these factors
- Replace distance edge weights with time estimates


Embodied Mathematical Imagination & Cognition (EMIC)
Embodied cognition is growing in theoretical importance and as a driving set of design principles for curriculum activities and technology innovations for mathematics education. The central aim of EMIC (Embodied Mathematical Imagination and Cognition) is to attract engaged and inspired colleagues into a growing community of discourse around theoretical, technological, and methodological developments for advancing the study of embodied cognition for mathematics education. We, as a thriving, informed, and interconnected community of scholars organized around embodied mathematical cognition, seek to broaden the range of activities, practices, and emerging technologies that count as mathematical.
EMIC Conference Proceedings
Nathan et al. (2017) - Psychology of Mathematics Education - North American chapter (PME-NA) proceedings.
Williams-Pierce et al. (2017) - International Conference on Computer-Supported Collaborative Learning (CSCL) proceedings.
Nathan et al. (2016) - Psychology of Mathematics Education - North American chapter (PME-NA) proceedings.


A compass (or pair of compasses) is a drawing tool that can be used to draw circles or arcs, parts of circles. They can also be used to measure distances, in particular on maps. Compasses can be used for mathematics, drafting, navigation, and more.
Who invented the compass drawing tool?
The geometric and military compass of Galileo belonged to this class of instruments. Invented in Padua in 1597, the instrument is also linked to Galileo’s activity (fig.7) in the Accademia Delia (fig.8), founded in Padua to provide mathematical instruction for young noblemen training for a military career.
What is the definition of a compass in geometry?
A pair of compasses, also known simply as a bow compass, is a technical drawing instrument that can be used for inscribing circles or arcs. As dividers, they can also be used as tools to measure distances, in particular on maps. Compasses can be used for mathematics, drafting, navigation and other purposes.
Which way is west?
The four cardinal directions or cardinal points are the directions north, east, south, and west, commonly denoted by their initials N, E, S, and W. East and west are at right angles to north and south, with east being in the clockwise direction of rotation from north and west being directly opposite east.


Science Activities in Metric Measurement
- This project requires various items such as paper clips, coins, marbles, washers and rocks plus enough scales or triple-beam balances for several groups. Explain the units of mass in the metric system to your students (grams, kilograms, etc.) and split them into groups. Have them estimate how many grams certain items or combinations of items weigh. Make it a game, with the group that gets the closest estimates winning prizes.
- Have each student create a chart called a body ruler that essentially turns a body into a measuring device. The students mark down measurements of their bodies in metric terms: their height; the length of their hands, arms and feet; and their mass. Using these standards, they can estimate the length and mass of various objects in the room in the metric system. For instance, they can see that the length of a book is twice the length of their hands, which they now know. They can check their estimates with a tape measure.
Mini Metric Olympics
- Dividing your classroom into teams and creating a game out of your metric activity will help students solidify the concepts. Create various stations around the room, each with a challenging metric activity for the teams to participate in: the Paper Plate Discus, the Cotton Ball Shot Put and the Right-Handed Marble Grab, for example. Rules to these various games can be found on the University of Arkansas web site (Reference 3). Students will enjoy themselves and learn about the metric system in the process.
- Create a list of real-life comparisons for your students and help them to generate as many additional comparisons as they can. For example, 8 kilometers equals about 5 miles and 1 gram equals the mass of a jellybean. Go through a list of easy ways to think about the metric system and have them create comparisons for volume, length and mass. If each student creates an accurate chart for comparisons, this will generate a large number of examples that your students can use and that you can use for future classes.


Decision Tree for Regression Models in Machine Learning
A sport hosting company would like to decide to host a cricket match between India and South Africa based on whether data. Weather data that is available has attributes like outlook, temperature, humidity and wind. And has a decision variable how many hours were played. We need to build a decision tree model to predict based on weather data how many hours will be played?
The ID3 algorithm can be used to construct a decision tree for regression type problems by replacing Information Gain with Standard Deviation Reduction — SDR
A decision tree is built top down from a root node and involves partitioning the data into subsets that contain instances with similar values mean homogeneous data.
Here, standard deviation is used to calculate the homogeneity of a numerical sample (target variable). If the numerical sample (more specific target variable) is completely homogeneous with respect to independent variable (we check for each independent variable separately), then its standard deviation is zero.
Will use the same concept of standard deviation and will check on each split how much reduction in standard deviation is there, and the node (independent variable) which has more reduction in standard deviation that will be declared as a decision node. (In first iteration this node will be called as root node). If not clear at this point, no worries, follow the complete article and I am sure it will be clear.
Reduction in Variance or Standard Deviation Reduction (SDR):
Variance tells us the average distance of all data points from the mean point. Standard deviation is just the square root of the variance. As variance is calculated in squared unit and hence to come up a value having unit equal to the data points, we take square root of the variance and it is called as Standard Deviation.
So, what is standard deviation reduction. So basically, first we calculate the standard deviation of the target variable. And then calculate the weighted standard deviation of target with respect to each independent variable. Then take a difference. And this is known as reduction in standard deviation.
Step 1: First will calculate the total standard deviation with respect to target variable:
Coefficient of variation is ratio of standard deviation divide by the average value and take the percentage of it. This will be used as the stopping criteria for further split. Will discuss this point at the time of using it so it will be clearer there.
Step 2: will calculate SDR with respect to independent variables and decide on root node, decision nodes and leaf nodes. Deciding the root node
SDR for Outlook:
SDR for Temperature: (use same formulas as mentioned above)
SDR for Humidity:
SDR for Windy:
- SDR (Hours, Outlook) = 1.66
- SDR (Hours, Temperature) = 0.39
- SDR (Hours, Humidity) = 0.09
- SDR (Hours, Windy) = 0.39
Outlook has most reduction in standard deviation hence outlook will be the root node.
For the next node we need some termination criteria like when to stop splitting. Hence, we consider coefficient of variance as one of the termination criteria and for example can set CV = 10% as a threshold. So, if we have CV > 10% then further splitting is required else will stop there. Or we can also set threshold on number of data points (rows) if less than or equal to 3 then no split required.
And the prediction at leaf node will be the average of that branch. Here Sunny and Rainy nodes need further splitting as both have CV > 10% however Overcast does not need splitting as CV for overcast <= 10%.
Average value of overcast branch = 46.25 will be the prediction at overcast leaf.
Now will repeat the same SDR check for data filtered for Sunny and Rainy to get other decision nodes and subsequent leaf nodes.
SDR check for Sunny data rows:
SDR check for Rainy Data rows:
Decision Tree Interpretation:
- If outlook condition is sunny and temperature is mild then prediction on number of hours match can be played is 41.5 hours irrespective of other conditions.
- If outlook is overcast then irrespective of other conditions, prediction is 46.25 hours.
- If outlook is rainy then if it is windy then prediction is 26.5 hours and if it is not windy then prediction is 47.6 hours.
If you have any doubts, then feel free to get in touch with me:


This is a blog for undergraduates grappling with stats! Last week I was having a chat with an undegraduate student who was due to analyse some data. She was double-checking how to determine the statistical significance of her analysis. I mentioned that she could either use SPSS (which would provide the value directly), or obtain … Continue reading Statistics Tables: Where do the Numbers Come From?
I read a blog this morning introducing a new R package that allows users to include emojis into their ggplot2 plots. As it is the 1st of December, I thought I would try this new package out with a winter-themed plot. Enjoy! R Code


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In this paper we propose a novel method to construct hierarchical $hp$-adaptive Signed Distance Fields (SDFs). We discretize the signed distance function of an input mesh using piecewise polynomials on an axis-aligned hexahedral grid. Besides spatial refinement based on octree subdivision to refine the cell size (h), we hierarchically increase each cell's polynomial degree (p) in order to construct a very accurate but memory-efficient representation. Presenting a novel criterion to decide whether to apply h- or p-refinement, we demonstrate that our method is able to construct more accurate SDFs at significantly lower memory consumption than previous approaches. Finally, we demonstrate the usage of our representation as collision detector for geometrically highly complex solid objects in the application area of physically-based simulation.


A friend sent me a thread on quick divide routines for the AVR microcontroller. While the article is interesting, it is also a very poor solution.
The problem was to provide a fast result for divide by '5' in the range 0..255 (or even 0..100).
The solution was a fixed-point cludge, what was suggested was using the high byte result from: x * 51 + 1.
Unfortunately this gives the wrong result. The original concept can be made to give the correct results from 0..100 by modifying this to: x * 51 + 20
However, an even better solution is simply: (x+1)*51, which gives correct results all the way to 255.
A similar answer is possible for division by 3: (x +1)*81.
(Note: If you want to use this on the PC, don't forget to shift right by 8, eg: y = ((x+1)*81) >> 8
There are many more wonderful bithacks documented online.
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Accuracy and consistency achieve the most genuine outcome.
The above example was done with intuitive scores and works well for decisions of lower importance. For decisions of high importance, accuracy is needed, so the concepts of Percentage and Ratio have to be applied to the anlysis.
The percentage aspect is the reason slider markings are based on scores up to 100.
Here's how to do an accurate analysis starting with the Percentage aspect.
In the example above at Step 6 where there are 3 choices, the added up scores for all three F1 sliders should end up as 100 in order to represent 100 percent. The same applies for all three F2 sliders, and also for the F3 sliders.
If this had been a five choice decision, there would be 5 sliders for F1 and the added up scores for all five F1 sliders would also need to reach 100. E.g. 5 scores of 20 each would give 100 - meaning 100 percent.
Reaching totals of 100 ensures the scoring is consistently balanced, which results in good accuracy.
Unfortunately, it is very unlikely that intuitive scores will naturally add up to 100 unless by chance, so it becomes necessary to put the scores in proportion too. Proportioning is done by finding their ratios to eah other. Here's how to apply Ratios to the chosen scores.
When setting the scores, it should be done in relation to the other values. For example, if there were five different factors with a score of 20 each, it would make the ratios equal and would therefore be an easy assessment of ratios. However, it would mean they all have exactly the same level of appeal which is unlikely to happen with real decisions.
In reality, there might be one you really like, a couple you don't like, and the last couple where you have a neutral opinion, so you might score them as 40, 9, 11, 20, and 20 respectively. Notice that 40 + 9 + 11 + 20 + 20 = 100. Also notice that with 5 choices, a score of 20 represents a neutral score. There is a numeric example below to demonstrate this explanation and shows how to calculate ratios.
Imagine there are 4 choices, C1 to C4, which relate to a time duration. Let's assume
- F1-C1 slider shows 33 hours of effort,
- F1-C2 slider shows 36 hours,
- F1-C3 slider shows 42 hours, and
- F1-C4 slider shows 39 hours.
Adding up the 4 slider values gives 150 (i.e. 33 + 36 + 42 + 39 = 150).
Three points should become apparent to you. Firstly, when there are 4 choices, the neutral score will be 150/4 giving a neutral score level at 37.5 each. Second, when set as a percentage ratio score of 100, the neautral score will be 100/4 giving a neatral score level of 25. Thirdly, when in their current form of hours, two scores are below the neutral score, and 2 are above.
To set the ratio as a percentage, each value needs to be adjusted to become 1.5 times smaller because 150 / 100 = 1.5
Reducing each value by 1.5 (150 / 100) gives the following:-
- F1-C1=22, (since 33/1.5 = 22)
- F1-C2=24, (since 36/1.5 = 24)
- F1-C3=28, (since 42/1.5 = 28) and
- F1-C4=26. (since 39/1.5 = 26)
Each value has the same ratio as before but now the values total 100 (i.e. 22 + 24 + 28 + 26 = 100).
Setting values as a ratio to each other gives extremely accurate results from this decision analysis tool.
For the highest accuracy of all, take actual values wherever possible such as price information and ratio them to each other to give a total added up value of 100. Do the same with the importance level scores where the ratio values add up to a total of 10.


PhD position in Computational Neurosciences in Lyon
physics, mathematics, neuroscience
DETAILS OF THE OFFER
PhD position is open in computational neurosciences at the Neurobiology of Executive Function lab at the Stem Brain Research Institute in Lyon (https://www.sbri.fr/).The project aims at understanding the cellular and circuit mechanisms responsible for cognitive functions, with a focus on the complexity of collective oscillations measured with large scale recordings.primary research focus is on retinal development.
The project combines computational and theoretical aspects of neural modeling as well as data analyses.


COMPUTER CONTROLLED PRECISION PIANO TUNER
FFT BIN INTERPOLATION
When using FFTs for frequency measurement, greater resolution requires longer sample windows. For example, if the sample window is one second long, the FFT bin center frequencies* are spaced at 1 Hz intervals. To get bin center frequencies at 1/2 Hz intervals, the sample window must be 2 seconds long. For the piano tuner, it is necessary to measure frequency with precision finer than 1/6 Hz, but with sample windows much shorter than six seconds. Therefore, some method for interpolating frequency measurements between FFT bins must be used.
When calculating an FFT on a long sequence of data points (longer than the length of the FFT), the sequence must be windowed with a multiplying function that is only non-zero within the scope of the FFT. For example, a pure sine wave extends from - ¥ =< to =< ¥, as shown in Figure 1.
An FFT covers a finite number of points, so multiply the sine wave (Fig. 1.) by the window, as in the example windows shown in Figures 2a and 2b.
*Bin center frequency is the frequency at each point in an FFT. For example, if a 512 point FFT is performed on a band width of 5 KHz, the bin center frequencies will be separated by 5000 / 512 = 9.766 Hz = fbin. The bin frequencies will be 0, fbin, 2fbin, 3fbin, 4fbin, ... .
|Figure A1. Continuous Sine
|Figures 2a & 2b: Two examples
Figure 2c shows the windowed output from a rectangular window.
Figure 2d is the output from a raised
|Recall that multiplication in the time domain is equivalent to convolution in the frequency domain. Therefore, the nice pure spectrum of the sine wave in Figure 3a has been blurred by the spectrum of the window, Figure 3b, to give the result in Figure 3c.|
Figure 3b Spectrum of the window
Figure 3c Blurred signal
|The rectangular window is
the simplest one to implement since it consists of just truncating the
infinitely long input sequence to the number of points in the FFT operation;
and the signal samples require no multiplication operations. Therefore,
we will use the rectangular window function for this application.
We know that the blurring function of the rectangular window (Fig. 3b) is:
sin(k2p/N • N/2) = sin kp = 0
Therefore, we can conclude that a sine wave with a frequency that is exactly on a bin center frequency of an N-point FFT will produce an FFT that has no leakage into other bins, since that is where the zeroes of the blurring curve lie.
The bin centers fs - 2p/N, fs, fs + 2p/N would correspond to -2p/N, 0, 2p/N in the "blurring function" above.
We know, too, that fs is somewhere between the two bins with the greatest energy in them. This seems obvious from a graphical inspection, until you ask, "what if fs is very near bin M, so bin M+1 has a very low value. Couldn't bin M-1 have more than M+1 (assume fs > M)?" The answer is no. The numerators, sin (w N/2), where w = fs-(M-1), fs-(M+1), would be equal in magnitude by the symmetry of the sine function, but the denominator, sin(w /2), would be smaller the closer you are to fs; therefore bin M+1 has a greater value.
However, what happens when the input frequency, fs, does not exactly match a bin center frequency? Essentially, the FFT is sampling the frequency response (or spectrum) of the signal, so we look at it as in Figure 4.
Figure A4. Frequency Response when Input Frequency does not match FFT Bin Center Frequency
The response in any given
bin is a function of the distance from the input frequency to the bin center.
where M, M+1, are multiples of 2p/N, fs is (M + 0.D) 2p/N.
So, the numerators above become:
sin((0.D) (2p/N) (N/2)) and sin((0.D - 1) (2p/N) (N/2))
which reduce to:
which, by symmetry of the sine wave, have equal magnitudes. Therefore, the ratio of the bin values is equal to the ratio of the denominators:
by magnitude symmetry of sine wave
However, sin x
» x when x is small, with
the worst case deviation occurring where 0.D
or 1 - 0.D
is near 1. If N is large, x is automatically very small. For
example, if N = 128, how good an approximation is
Therefore, knowing the magnitudes of the two largest FFT bin results, we can solve for 0.D and therefore, fs. This procedure would work perfectly for a pure complex sinusoid. Any other signals present would also contribute some side lobe energy to the bins of interest - thereby corrupting the calculations. Even a real sinusoid has both a "positive" and "negative" frequency component. If the input signal is known to be, or can be filtered to be, a "clean" sine wave, the side lobe energy from the "negative" frequency component can be made negligible by making it be "far away", which is optimized when
fs = (fsamp)/4
Also, increasing N will minimize the "other" side lobe energy.
This ratio, then, is a satisfyingly simple approach to interpolating frequency measurements between FFT bins for signals having the restrictions noted above regarding other frequencies present.
In the context of the piano tuner, this procedure may be used to provide fast, precise frequency measurements of either the fundamental or second harmonic of the struck note. For optimum performance, the only other digital signal processing required is to bandpass filter (allowing only signals in the region around the frequency of interest to pass through) and decimate the filter result so that the sampling frequency is approximately four times the frequency of interest.
Barry D. Kulp


A lot of times I find myself looking for my calculator and forgetting that there’s a perfectly good one right on my PC already!
It’s practically impossible to lose this one!. Just go to Start, All Programs, Accessories and choose Calculator, or just type in “calc” into your search bar in Windows Vista and choose it above. A little calc will pop up and you just use your mouse to punch in the numbers that you need.
This calculator has quite a few of the functions of a dekstop version. The plus (+), minus (-), multiply (x), division (/) and percent (%) signs are off to the right and it even has a fraction (1/x) and squareroot (sqrt) button in case you need those. There’s also a Backspace button for when you accidentally type in the wrong thing. You can even use your number pad, if clicking about with the mouse doesn’t suit you!
By clicking the View menu, you can switch it over to a scientific calculator if you have more advanced number crunching to do. That one comes with a bunch of other features as well, all located under the View menu. If you need any Help working the calculator, just go to the Help menu and check out the Help Topics. It’s just a really easy way to use a calculator when you’re doing your online banking, etc.
It all adds up!


This is unquestionably a million dollar question. Incalculable endeavors have been made to concoct a triumphant lottery equation. Many have attempted, yet, obviously, have fizzled and surrendered their quest for a triumphant lottery framework. Some have succeeded, however. One of such individuals is Brad Duke, a Powerball champ, who a couple of years back prevailed upon well 200 million greenbacks, taking more than 80 million dollars in a singular amount.
Here is what Mr. Duke needed to state for Fortune, a well known monetary magazine:
“I just began playing number games with myself about how to catch the most different numbers. At that point I took a gander at the latest Powerball numbers throughout the most recent a half year and took the arrangement of 15 numbers that were most generally coming up. My Powerball numbers would have been those 15. So I began messing around with it, and my number games got somewhat more unpredictable and somewhat greater. I was beginning to win littler sums like $150 and $500.”
What he isn’t stating is whether he was spending more than he was winning. While a hundred bucks or even multiple times that sounds decent, in the event that he was spending more than he was winning, his framework was not a triumphant one by any means. Luckily, regardless of whether it were the situation, all misfortunes were in the long run secured by one immense win, so the bet was for sure justified, despite all the trouble.
His framework dependent on looking for a most various pool of numbers appears as though a positive development contrasted with frameworks that expect that all arrangements of numbers are similarly great. 동행복권파워볼 To see this, let us think about the accompanying arrangement of five numbers: 1,2,3,4,5. This is a lot of continuous numbers and there are just a couple many such sets which can be framed from the entire numbers extending from 1 to 39 or to 56 or to whatever the top number in a given lottery happens to be. Let us remind the peruser that in a standard lottery, without a super number, 5 or 6 numbers are drawn from the universe of entire numbers going from 1 to some top number that is generally around 50. On the off chance that you analyze this (a couple handfuls) to a huge number of five number mixes that you can draw, you rapidly understand that it bodes well to wager on the arrangements of non-continuous numbers all things considered sets are factually bound to come up. Also, the more you play, the more evident this becomes. This is the thing that Brad Duke would most likely mean by a progressively differing pool of numbers.
That is decent, then again, actually this contention isn’t right. Furthermore, here is the reason: every single number mix are similarly likely and keeping in mind that there are more blends that don’t comprise sequential numbers, the wager isn’t on the property (successive or non-continuous), however on an exact mix and it is this specific mix that successes and not its scientific property.
So why that Mr. Duke won? Indeed, his framework made things simpler for him. By picking just 15 numbers and concentrating on those rather than, state, 50, he rearranged things and, inevitably, lucked out. He may have lucked out, yet in some other drawing, with some other arrangement of numbers, not simply those 15 that he picked in light of the fact that they appeared to be most generally coming up. It is not yet clear if his arrangement of numbers was all the more measurably legitimate in their supposed higher recurrence than some other set. I to some degree question it.
Does that imply that this methodology has no legitimacy? Not in the slightest degree. In actuality, it’s the best if not by any means the only reasonable methodology you can use in such a case, a methodology that is regularly utilized by researchers to land at an inexact arrangement if a careful one is difficult to make sense of. Utilizing 15 “probably up-and-comers” as Mr. Duke did to win his millions or just a littler example is a case of a guess to an increasingly mind boggling issue which can’t be dealt with precisely in a practical, cost proficient way because of its huge size. Some of the time an inexact arrangement, on the off chance that we are sufficiently fortunate, may go out to the accurate one similar to the case for Brad Duke a couple of years back.