String theory notwithstanding, we live in three-dimensional space. But physics in reduced dimensionality need not be a purely theoretical exercise. Atomically thin materials such as graphene are well described as 2D systems, and polymers and quantum wires have many 1D characteristics.
What if the number of dimensions could be tuned continuously between 1 and 2? A century ago mathematician Felix Hausdorff developed a new way of measuring dimensionality that could take fractional values. For most familiar shapes—points, lines, planes, and so on—the Hausdorff dimension is equal to the usual topological dimension. But fractals, due to their infinite complexity, have noninteger Hausdorff dimension.
Now Ingmar Swart, Cristiane Morais Smith, and colleagues at Utrecht University in the Netherlands have taken a step toward experimentally studying quantum physics in a fractional-dimensional system. On a (111) surface of copper they placed carbon monoxide molecules (black indentations in the figure) to corral the surface electrons into a simplified Sierpinski triangle.
The full Sierpinski triangle, a fractal made up of infinitely many nested smaller triangles, has a Hausdorff dimension of 1.58. If drawn from line segments, it has infinite length, and if carved from a solid triangle, it has zero area, so intuitively, it’s neither 1D nor 2D but something in between. The Cu(111) surface-electron density inside the triangle is an approximation of the fractal, just as a graphene sheet is an approximation of an infinitely thin plane. But like graphene, the surface-electron system inherits the dimensional properties of its mathematical idealization.
Probing the interesting questions of fractal quantum mechanics will require a more intricate experiment. In particular, ensembles of interacting fermions behave in qualitatively different ways in 1D and 2D (see Physics Today, September 1996, page 19). Their behavior in 1.58 dimensions is an open question—but the surface electrons of Cu(111) interact only weakly. Surfaces of other materials, however, might allow the researchers to study interactions in fractal geometry. (S. N. Kempkes et al., Nat. Phys., 2018, doi:10.1038/s41567-018-0328-0.)


8-Piece Stencil Set
Great for use by students, pros and artists!
Stock #: 060713
- Pack of 8
- Material: plastic
- Color: White
- Multi-shape geometric template (circular, hexagon, square, triangle)
- Ruler Measurement Range 0-23 cm
- Helps you draft shapes of circle, triangle, square, heart, moon, star, oval, polygon etc
- Great help for office, school, drafting, art etc
- Brand new product!


A few days ago, I was in an airplane flying at an altitude of over 32,000 feet or 10,000 meters. It was a 13-hour flight. To make this journey a little more comfortable, I did some stretching and, with flight attendants' approval, took a tiny corner to do push-ups. It seems to be easier to do push-ups in this high flying airplane. I did 66 without too much effort, almost tying my record set on ground 20+ years ago.
I'm curious to see how much easier to do this exercise at this altitude. So here's my calculation. If I simplify the calculation by assuming all the mass of the earth to be at the center of the earth (as opposed to integrating the mass along the 6371 km radius), Newtonian universal gravitation between me and the earth is reduced by about 3 thousandths at 10000 meters altitude:
F0 = G (mmemearth)/(6371000)^2 F10k = G (mmemearth)/(6371000+10000)^2
where F0 is the force between me and the earth when I'm at sea level, and F10k the force when I'm at 10,000 meters altitude. Calculation of the percent change can omit the constant G and both masses m's:
1/(6371000)^2 - 1/(6371000+10000)^2 ----------------------------------- = .00313189770433034782 i.e. 0.313% 1/(6371000)^2
For a person weighing 70 kg or 154 pounds, that translates to 0.22 kg or about half a pound.
What's more, since the plane travels at the speed of 900 km (560 miles) per hour on this inter-continental flight, the centrifugal force [note] additionally reduces a 70 kg person by 686 newtons or 700 grams:
Fc10k = 70000 * (900000/3600)^2/(6371000+10000) = 685.62921172230057984641 newtons or 700 grams or 1.54 pounds
So in total, the body weight is effectively reduced by about 0.5 + 1.5 = 2 pounds in the plane traveling at 900 km/hour at 10000 meters altitude.
[note] Centrifugal force is imaginary in Newtonian mechanics and is used as a convenient expedient. A physicist may choose to do calculation in Lagrangian mechanics.


My name is Wilson Lin and welcome to my website!
On this website you’ll find articles about statistics and some older articles that I’ve written.
In addition to these articles, I have created several interactive apps using R Shiny.
- Conjugate – Bayesian conjugate distributions
- Distribution explorer – simulates what different probability distributions look like (based on those in-built in R)
- Outlier – this app tries to identify outliers in time series
- Test – basic hypothesis test based on Binomial proportion or t-test
- Difference – hypothesis tests for difference between means
- Bayes – investigate the use of Bayes Theorem for looking into the intentionality behind unusual events
- NBA Mock Draft Simulator – input in a list and figure out whether you should trade your picks in a H2H points-based fantasy sports league (not limited to the NBA)
- Socks – an app that uses Approximate Bayesian Computation to try to estimate the solution to Karl Broman’s “Sock Problem”
Note: All apps on this page are made for educational purposes only.


Advanced Level Further Mathematics (Edexcel, OCR, MEI, AQA, Cambridge)
Further Mathematics A level is now a completely separate subject from Mathematics A Level. Grades awarded based on 4 examinations at the end of the two year course. Two of the papers cover pure maths and two of the papers cover applied maths. While everyone sit the same pure maths papers, students can choose the their two applied options, although in many cases, schools choose which options to teach. Further Maths continues to grow in popularity as an A level, which is good news for grade boundaries, as not that long ago only a few elite mathematicians in the country would study the subject. It is a pre-requisite for undergraduate degrees in mathematics at most UK universities, but many students are surprised that it is a pre-requisite for some Economics, Science and engineering degrees as well. The maths in the course is challenging; beyond college level calculus, and including college level mechanics, statistics and linear algebra.
Pure topics usually covered include (everyone studies these topics):
- Proof: inductive, algebraic, contradiction, exhaustion, geometric
- Complex numbers: Argand, conjugates, De Moivre, Modulus-Argument, roots of unity
- Matrices: calculations, transformations in 2-d and 3-d, inverse of 3×3 by hand, solving systems of equations, geometric interpretations in 3-d
- Algebra: roots of polynomials, method of differences, manipulate sums of series, Mclaurin series
- Vectors: scalar product, cross product, equations of lines and planes, intersections, distances between lines and planes
- Integration: volumes, mean of function, undefined limits, inverse trig functions, selecting trig substitutions
- Polar co-ordinates: converting between Cartesian and polar, curve sketching, areas
- Hyperbolic functions: manipulate, calculus, derive logarithmic form, use for integration
- Differential Equations: 1st and 2nd order, general and particular solutions, auxiliary equations, complementary functions, Euler’s method, separation of variables, integrating factors, simple harmonic motion including damped oscillations, systems of differential equations
- Further Pure Mathematics 1
- Further Pure Mathematics 2
- Further Statistics 1
- Further Statistics 2
- Further Mechanics 1
- Further Mechanics 2
- Further Decision Mathematics 1
- Further Decision Mathematics 2
Typical problem areas include:
- Application of vector geometry in real life contexts
- Defining and linking variables to solve problems involving connected rates of change
- Selecting the appropriate technique to solve a differential equations, especially if it is not presented in the standard form
- Sketching polar graphs
- Getting lost part-way through a proof by induction
How a tutor can help:
This is a very challenging course, comprised almost exclusively of college level mathematics. It is usually taken as one of four A Levels, so students who select forfeit most of their free periods. Time is also an issue in these exams; there just isn’t time to approach problems in different ways. To do well, you need to be able to immediately spot what you need to do. The maths in this course is above the comfort level of most maths teachers, and it is not uncommon for teachers to be ‘a page ahead’ of their classes. Our tutors are highly experienced teachers who know exactly what students find difficult in this course and have developed succinct and clear explanations and examples to help you understand the material. They have impeccable records with their own classes and are experts in preparing students for these exams. Furthermore, the syllabus changed in 2018 to encourage students to make full use of their calculators. Understandably, it is taking schools a little longer to catch up with these changes, and you may find that you are not benefiting from the full capability of your calculator. A tutor can show you how to use your calculator to solve equations, calculate definite integrals and even find equations of tangents and normal.
Another way our tutors have helped students with Further maths is by supporting them to learn a different option than their school might offer. Most schools decide the two options they will teach, and students learn this content (typically Statistics 1 and Mechanics 1). If you find that Mechanics has always made sense to you, but Statistics never has, a tutor could help you to prepare for the Mechanics 2 option. Similarly, the Decision modules are especially interesting for anyone hoping to study computing at university, and a tutor could support you to learn this content. Any students applying to study maths at Cambridge must have knowledge of at least the Pure Mathematics 1 option for their STEP exam.
Warp Drive Tutors, Inc. has been developed independently from and is not endorsed by Cambridge Assessment International Education. A-Level, GCSE and iGCSE are registered trademarks owned by Cambridge Assessment International Education.


Children uncover more arithmetic secrets with this toy. As they open away the screens based on the rows and columns, they learn to count and add values. Planting the trees in the slots, helps them learn multiplication while counting. The toy also exposes them to the numerous multiplication combinations that can be created and helps build logical reasoning.
Set includes a wooden box with slots that can be unraveled by opening the puzzle pieces and the wooden tray, a lid with dials for setting the multiplication problem, 100 wooden trees, chalk pieces, and a detailed instruction manual


I remember dreading writing out my multiplication tables in a square grid against the stop watch each morning in primary school and I don’t want my future students to have that same pit in their stomach because they are struggling with their multiplication tables.
After all, the daily multiplication square and stop watch approach wasn’t even a successful approach for me.
Learning needs to be fun and students should be engaged. Using different approaches allows all students to learn as their learning style is taken into account.
Here are some ideas I have come up with and have seen work well in classes to help students learn their multiplication tables in a fun manner:
1. Identify the patterns in a hundred chart.
2. Skip counting as a class.
3. Create a rap song or poem as part of a homework activity or class activity about a multiplication table.
4. Sing the multiplication table together as a class.
5. Create a game show as a class where the teacher acts as a host and there are rotating pairs of students with a buzzer to answer a multiplication sum.
6. Multiplication bingo.
7. Have the students line up in pairs and choose one student to stand at the front of the line (provide them with an answer sheet). The student at the front calls out a multiplication sum and the first of the pair to state the correct answer returns to the back of the line and the other student sits out and watches. This continues until there is one students left.
8. Students work in pairs to test each other.
9. Focus on particular multiplication sums each week. For example 6×3 = 18, 6×5=30 and 6×6=36 and make it a challenge that the students remember those three. The teacher may ask a student at random one of those multiplication sums.
10. Focus on a multiplication table for a specified amount of weeks within the school year. All maths warm ups and homework activities would pertain to that specific multiplication table. For example, weeks 1-3 of term 1 may be decicated to the multiplication table of 3.
11. Dedicate a part of the classroom to the multiplication table that is being focussed on.
12. Ask the students to create a powerpoint slide of the multiplication table including images and voice recording.
13. The students may create a poster for the multiplication table which can be displayed in the classroom.
14. Include the multiplication table in their homework each week.
15. Use a fun multiplication CD and have the students sing along.
16. Record your voice reading the multiplication tables on your class blog or on a CD for students to listen to as part of their homework.
17. Have the students record themselves onto a CD.
Be creative and make learning fun!
What strategies do you use to teach multiplication tables?
digitalart / FreeDigitalPhotos.net


Platonic Solids Paper Balloons
Polyhedron, or Platonic solids, are 3D shapes consisting of identical regular polygons with the same number of faces meeting at each vertex.
This is a set of five paper balloons of the five possible polyhedron platonic solid shapes: tetrahedron, cube, octahedron, dodecahedron and icosahedron.
Each 3D shape is just large enough to fit inside a 10cm diameter sphere, and these are for you to assemble yourself so have a glue stick ready and enjoy building each polyhedron! (each polyhedron is packaged in its own plastic and cardboard paper and the five sheets are put together as one)
Package Size: W215×H364mm
Made in Japan


Meet the Year Group Team
|Head of Year||Class Teachers||PTP Support|
|Miss C Wyers||Miss C Wyers||Mrs N Arnold|
|Miss P Light||Miss R Minte (maternity leave)|
|Mrs M Toobe|
Summer 1 Topics
“Are beasts always dangerous?”
This half term is an exciting topic – Dragons! The children will be given a chance to show off what they have learned about different forms of writing so far.
The children will explore poetry by Jackie Morris – “Tell Me a Dragon”. They will have a go at writing about their own dragon based on the book.
This year, we have practised our persuasive techniques. The children will write a letter of application to apply for the job of a dragon tamer.
Using the book “The Clockwork Dragon” by Jonathan Emmett, the children will write their own instructions about how to trap a dragon.
Finally, the children will write a short story based on the painting “Saint George and the Dragon” by Paolo Uccello.
This half term we will be revising rules that have already been taught this year such as:
- plural nouns of words ending in “o”
- unstressed vowels
We will revisit reading times of both digital (12 hour and 24 hour) and analogue clocks. The children will also practise problem solving from time tables and completing test style questions.
Multiplication and Division
The children have been working very hard on their multiplication and division facts at home. This half term, we will be looking at multiplication and division methods, to help the children when working with larger numbers.
It is time to revisit rounding whole numbers to the nearest 10,100 and 1000, as well as rounding decimals to the nearest whole number and 1 decimal place.
The children will recap units of measure, and apply their understanding in problems including data and graphs.
To link in with our Dragon topic, the children will study the artist Paolo Uccello.
Then, they will have a go at drawing and painting parts of his pictures in their own way.
Finally, the children will create a dragon batik, and evaluate their end product.
Telling Stories through Digital Media - eBook creation
All the learning in this unit is focused around one song: Blackbird by The Beatles - a song about civil rights.
The scheme of work shows how games, the dimensions of music (pulse, rhythm, pitch etc), singing and playing instruments are all linked.
This half term, the children will have a close look at road safety, and why it is important to be safe on the roads.
Devotion in Hinduism
We will learn about how the concept of devotion is shown in the Hindu faith
PE - on a Monday
Athletics (Running and Jumping), Striking and Fielding Softball, Rounders lead to competition and Swimming
Homework Routines are:
- Monday to Monday spellings
- Reading and times tables expected at least 4 times a week. (please have their profiles filled in and signed)
- Maths will be set Monday to Monday and be based on the previous week’s learning


Languages and the creative arts are falling out of favour among GCSE and A-level students. Provisional figures for the number of entries for GCSE and A-level qualifications in England this summer have been published.
Here’s what we know
Boost for Maths and Computing
Rishi Sunak has a reason to celebrate, as entries for maths subjects are on the rise. Although his plan to make maths education compulsory until age 18 has yet to be implemented, Statistics entries at GCSE level have increased by 18.4% since last summer. Meanwhile, Maths entries have risen by 5%.
Also, computing A-level entries rose up to almost 15% from 15,210 last year to 17,420 this year.
Languages in trouble
According to these figures for England, exam entries for German have dropped by 17% for A-level students and 6% for GCSE studies. Meanwhile, Spanish and French entries have fallen by 13% at A-level. However, there has been a 5% increase in Spanish GCSEs and French entries have remained at a similar level.
Classical subjects are getting popular but creative subjects decline
Not only maths and tech subjects are enjoying a burst in popularity. Entries to classical subjects at GCSE rose by almost 25%, while at A-level entries increased by 20 %.
However, art and design entries are down by 3% at GCSE level, music entries fell by 12%, drama entries declined by 7%, and performing arts entries dropped quite significantly – by 16%.
We wish good luck to all our students taking their last exams!
If you are looking for a tutor for your child (or yourself), we will be happy to help. Please contact us for professional advice.
Email: [email protected]
Tel. +44 79307 32407
Elena Colquhoun, MSc, PGCE, ACIL
Director of Best Start Education, qualified teacher and examiner


Reliability analysis for 0.5-month lead forecasts of global precipitation. Forecast data for all seasons are used during 1997–2013. The green curve pertains to forecast probabilities for above-normal precipitation, the orange curve forecast probabilities for below-normal precipitation, and the gray curve for near-normal precipitation. For above and below normal, least squares regression lines are shown, weighted by the sample sizes represented by each point. Points representing probability intervals that are forecast in a relatively greater proportion of the time are shown using larger symbols. The diagonal y = x line represents perfect reliability. The colored marks on the axes show the overall means of the forecast probabilities (x-axis) or observed relative frequencies (y-axis). The lower panel shows the frequency with which each interval of probability was forecast, where interval widths are 0.05 (e.g., 0.175–0.225 is labeled as 0.20), except that the climatological (0.333) probability is also explicitly shown.


It's your time to discover
The mission of the Mathematics Department at Aquinas College is directly linked to the mission of the College in that it provides a program for all students that is an essential part of a liberal arts education. It promotes the study of mathematics in depth in preparation for graduate school or an immediate career, supports the mathematical needs of other disciplines, and supplies a curriculum for all students to enhance their understanding of mathematical thought.
Explore mathematics at AQ
Career Preparation based on leadership
Upon completing a major in mathematics, a student will be able to:
- approach complex problems with creativity and persistence.
- give an insightful statement about how mathematics fits into a liberal arts curriculum.
- verbally explain and discuss mathematics using precise language and an audience-appropriate delivery.
- produce mathematical writing that uses proper terminology, notation, and proof techniques.
- provide several specific examples of connections among various branches of mathematics, such as calculus, linear algebra, and abstract algebra.
- effectively use technology to support mathematical inquiry.
The Juan Olivarez STEM Scholars Program
Build the Skills, Confidence and Connections you need to succeedGet settled into Aquinas College before traditional orientation and join a cohort of STEM students, faculty, and professionals with the STEM Scholars ProgramLearn More


Vedic Mathematics Syllabus For Beginners:
- Find addition of consecutive number
- Easy tricks of addition
- Finding the Square of a Two-Digit Number That Ends with Five
- Subtraction Trick (Use -1 concept)
- Multiplication by 11
- Find Doubling of Given number
- Find Halving of given number
- Special Subtraction trick of reversible number
- Multiplication by 9
- Divisibility test (4,8,7)
This course has 12 sessions, each of 1 hour duration.
This course is conducted online 1-on-1 between student and teacher via Zoom.
Student and teacher have to together decide the sessions schedule as per their availability.
Student can first confirm the schedule by discussing with us in email and then purchase this course.
We understand that sometimes the schedule can change due to circumstances of student or teacher.
Student must take all 12 sessions within 3 months of registration.
Human brain can calculate faster than a calculator!
This course is for both kids and adults.
Certificate of Attendance will be provided to the student.
Important benefits of learning Vedic Mathematics:
• Increases speed and Accuracy
• Boosts mental ability
• Increases self confidence
• Cultivates interests for numbers
• Improves performance in Olympiads and Exams


GSO-2011: Chrystopher Nehaniv
Hierarchical Coordinate Systems on Symmetry Structures and Automata
Discrete dynamical systems and computational structures can be mathematically understood, decomposed manipulated, and synthesized with the help of algebraic automata theory. Symmetries lead to hierarchical coordinate systems, invariants, and conservation laws. In the realm of reversible computation, we illustrate how every symmetry structure (permutation group) can be decomposed in the iterated wreath product (feedforward cascade) of simple permutation components, and how to compute with the resulting "Frobenius-Lagrange" coordinate system. (For example, for the Rubik's cube permutation puzzle, solving strategies appear to correspond to the use of such coordinate systems in which one can solve the cube via successive approximation in coordinate-form according to a given subgroup chain.)
More generally, any discrete dynamical system can similarly be decomposed using the iterated wreath product permutation groups and identity-reset automata. In the finite case, this is a Krohn-Rhodes decomposition that allows us to find the fundamental building blocks of the system and how they can be put to together to achieve its behaviour. These hierarchical coordinate systems allow one to manipulate the dynamical system via coarse-level to successively finer-level, convergent approximations. [These results, original formulated for finitary deterministic systems, generalize in various ways to non-deterministic or probabilistic and to infinite systems.]
Applications include understanding the dynamics of numerous physical and geometric systems, biological networks (e.g. biochemical and genetic regulatory systems), permutation puzzles, and von Neumann games. The methods also give rise to a natural complexity theory for finitary computation. Open-source computer algebraic software to carry out these decompositions has been developed at the University of Hertfordshire together with Attila Egri-Nagy.
John Rhodes (2009). Applications of Automata Theory and Algebra via the Mathematical Theory of Complexity to Finite-State Physics, Biology, Philosophy, and Games. Edited by C. L. Nehaniv, Foreword by M. W. Hirsch. Singapore: World Scientific Publishing Company.
Attila Egri-Nagy, Chrystopher L. Nehaniv(2008) "Hierarchical Coordinate Systems for Understanding Complexity and its Evolution with Applications to Genetic Regulatory Networks". Artificial Life (Massachusetts Institute of Technology) 14 (3): 299тАУ312. doi:10.1162/artl.2008.14.3.14305. ISSN 1064-5462.
Attila Egri-Nagy, Chrystopher L. Nehaniv, "SgpDec - Hierarchical Composition and Decomposition of Permutation Groups and Transformation Semigroups", Open Source Package for the GAP computer algebra system. http://sgpdec.sourceforge.net/
Attila Egri-Nagy, Chrystopher L. Nehaniv, (2009) "Subgroup Chains and Lagrange Coordinatizations of Finite Permutation Groups", arXiv:0911.5433v1 [math.GR] http://arxiv.org/abs/0911.5433


KhanAcademy.org – fun education !
If you know anyone struggling with their algebra, chemistry or many other subjects, offer them to check out Khan Academy.
It has lessons on: algebra, chemistry, biology, calculus, CST, economics, finance, linear algebra, statistics, probability, trigonometry and many others.
Khan Academy was chosen to be one of top 5 ideas chosen by Google to receive 2 million $ in funding as one of the most promising free education technologies.
Check it out at:
They also have an iPhone/iPod app for it as well, read more about it here:
Admiring the hard work you put into your blog and in depth information
you offer. It’s nice to come across a blog every once in a while that isn’t the same old rehashed information.
Fantastic read! I’ve bookmarked your site and I’m adding your RSS feeds to my Google account.


Calculating antilogs, or antilogarithms, is a mathematical operation that involves finding the inverse of a logarithm. While it may sound complex, especially if you’re not a mathematician, it’s a relatively straightforward process once you understand the basics. In this article, we will explore what antilogs are, why they are useful, and how to calculate them with ease using an antilog calculator.
Before we dive into calculating antilogs, it’s important to have a basic understanding of logarithms. Logarithms are mathematical functions that represent the exponent to which a fixed number (called the base) must be raised to obtain a given number. In simple terms, a logarithm tells you “what power” you need to raise a number to get another number.
The antilogarithm, often abbreviated as “antilog,” is the inverse operation of a logarithm. It helps you find the original number when you know the base and the logarithmic result. In other words, if you have the logarithm of a number, you can use the antilog to find the actual number.
Why Antilogs Are Useful
Antilogs are essential in various fields, including mathematics, engineering, physics, and finance. Here are a few reasons why they are useful:
- Exponential Growth and Decay: Antilogs are used to reverse the effects of exponential growth or decay. For example, in finance, if you want to calculate the future value of an investment, you may need to find the antilog of the logarithmically transformed values.
- Scientific Notation: Antilogs are used to convert numbers from scientific notation (exponential form) to standard notation. This is particularly important in scientific and engineering calculations.
- Signal Processing: In signal processing, antilogs help in converting logarithmic signal measurements back to their original values.
To calculate an antilog, you’ll need two pieces of information: the base of the logarithm (usually denoted as “b”) and the logarithmic result (usually denoted as “log_b(x)”). Here’s the formula for finding the antilog:
Antilog(x) = b^log_b(x)
In this formula:
- “x” is the logarithmic result.
- “b” is the base of the logarithm.
Now, let’s break down the steps to calculate an antilog:
- Input the Values: You’ll need to know the base “b” and the logarithmic result “x.”
- Apply the Formula: Use the formula mentioned above to calculate the antilog.
- Solve: Raise the base “b” to the power of the logarithmic result “x” to find the antilog.
- Obtain the Result: The result is the antilog of the given logarithmic value.
Using an Antilog Calculator
Calculating antilogs manually can be tedious, especially for complex values. Fortunately, there are many online antilog calculators available that make the process quick and easy. Here’s how to use one:
- Open an Antilog Calculator: Search for an antilog calculator online. You’ll find various options.
- Enter the Values: Input the base “b” and the logarithmic result “x” into the calculator.
- Calculate: Click the “Calculate” or “Find Antilog” button. The calculator will instantly provide you with the antilogarithmic result.
Using an antilog calculator can save you time and ensure accuracy in your calculations, especially when dealing with logarithms with non-integer values or complex bases.
Antilogs are a fundamental mathematical concept used in various fields to reverse the effects of logarithmic transformations. Understanding how to calculate antilogs manually is essential, but using an antilog calculator can simplify the process, especially for complex values. Whether you’re working on scientific research, engineering projects, or financial calculations, antilogs play a crucial role in helping you find the original values hidden within logarithmic data.


It can be tempting to manually calculate the amount of VAT by taking a price including VAT and multiplying it by 0.25, or 0.12, or 0.06 or whatever the VAT rate is. This is wrong - remember that VAT is a surcharge on the price excluding VAT. Here is the formula to calculate a price including VAT, in this example it is a 25% VAT rate.
500 kr (excl VAT) * 1,25 = 625 kr (incl VAT)
This is because you take 25% of the price excluding VAT and add this as a surcharge. 25% of 500 is 125 kr which is our VAT amount.
And to calculate the non-VAT price, you can take the formula and run it backwards.
625 kr (incl VAT) / 1,25 = 500 kr (excl VAT)


Through years of careful research and complex calculations, I have developed a formula to determine whether or not a student/person is exhibiting "good" behavior. The formula is as follows:
Number of desired behaviors (δ) - (Number of undesired behaviors (µ ) / Total possible undesired behaviors (τ))* Behavioral coefficient (β) = Behavioral Quotient (BQ)
or δ * β * (µ * τ) = BQ where β = 3.779
So, for example, if a student performed 5 desired behaviors, and only 3 undesired behaviors, and the total possible undesired behaviors is 7, then:
(5 - ( 3/10 )) * 3.779 = 17.3
This is an average score. The grading scale is as follows:
< 10 = evil
11 - 15 = poor
16 - 20 = average
21 - 25 = good
> 26 = saint
I hope this proves to be helpful to whomever uses it.
That is all.


Engaging students in effective classroom talk begins by creating a discourse-rich classroom culture. Participants were secondary mathematics teachers (n = 57) and their students (n = 875) in U.S. schools. Math discussions are important when learning math. Analisamos, assim, como tal produção discursiva se propõe a, em meio a distinções, At times, this can take the form of professional development schools (PDSs) in which mathematics teacher educators and practicing teachers collaborate to prepare pre-service teachers. mathematics classroom. This article illustrates how research about mathematical discourse can be translated into practice. Herbel-Eisenmann (2009) noted the two main functions of talk and distinguished between discourse for content-learning purposes and discourse for social purposes. Teachers can engage students in mathematical discourse by posing questions that encourage discussion and debate. analysis of one senior prospective teacher who is educated about mathematical The important thing is that we create environments in our classrooms where students are active and valued members of the discourse community. All mathematics teachers navigate between curriculum and the real, relatable world when teaching their students. Findings indicate that PTs with higher levels of mathematics teaching efficacy taught lessons characterised by tasks of higher cognitive demand, extended student explanations, student-to-student discourse, and explicit connections between representations. To build a math-talk learning community and to analyze the effectiveness of content-related comics in eliciting student participation, I employed the combined theoretical frameworks consisting of a Hufferd-Ackles’ et al. The study was designed as phenomenological study. Underlying the use of discourse in the mathematics classroom is the idea that mathematics is primarily about reasoning not memorization. Specifically, our study examined how TWI teachers in three schools defined academic language and how they integrated language development into their practice through the use of language objectives. Choppin, 2007; ResearchGate has not been able to resolve any references for this publication. However, to achieve a high level of discussion with everyone participating is difficult to accomplish. A Proposed Pedagogical Approach for Preparing Teacher Candidates to Incorporate Academic Language in Mathematics Classrooms, Mainstream Teachers in Two-Way Immersion Programs: Becoming Content and Language Teachers, A Qualitative Study of the Use of Content-Related Comics to Promote Student Participation in Mathematical Discourse in a Math I Support Class, Characterization of mathematics instructional practises for prospective elementary teachers with varying levels of self-efficacy in classroom management and mathematics teaching, Identifying and Tracking Emotional and Cognitive Mathematical Processes of Middle School Students in an Online Discussion Group, An Integral Part of Facilitating Mathematical Discussions: Follow-up Questioning, Case Study of Participants in a Site-Based Secondary Mathematics Methods Course and Internship: Three Teachers in Transition, Primary teachers notice the impact of language on children’s mathematical reasoning, The Changes of Teachers' Verbal Feedback in Mathematics Classroom within Chinese Context during Ten Years, Participation of Students in Content-Learning Classroom Discourse, Developing learning environments which support early algebraic reasoning: a case from a New Zealand primary classroom. mathematical communication and teaching experience on mathematical discourse Talking about mathematical concepts allows students to reflect on their own understanding while making sense of and critiquing the ideas of others.


SBE PhD candidate awarded 2012 Philips Mathematics Prize17 April 2012
Ruben van der Zwaan, a PhD candidate from the School of Business and Economics (SBE) at Maastricht University, was awarded the Philips Mathematics Prize for PhD Students. The prize was presented during the 2012 Dutch Mathematics Conference held on 12 April at the TU Eindhoven.
Twelve PhD candidates from twelve Dutch mathematics institutions competed for the prize this year. Van der Zwaan won for his lecture entitled ‘Intentions Matter’ about optimising the organisation of search engine results. The award consisted of a challenge trophy and cash prize.
All lectures were aimed at an audience with a general understanding of mathematics. An important award criterion was that the lectures could not exceed 12 minutes in length and must be easily understandable for non-specialists.


Scientific Principles |
|Part D:||Physiology and Anesthesia|
|Chapter 21:||Research Design and Statistics in Anesthesia|
One- and Two-Sample t-Tests
The most widely used, and misused, statistical test is Students t-test, a group of statistical tests designed for analysis of a single group or comparison of two groups. The name of this test refers to a pseudonym used by W.L. Gosset. Gossets employer, the Guinness Brewing Company, did not permit its employees to publish their research under their own names; however, because of the importance of this work, Gosset was permitted to publish under the name Student. 43 Gossets contribution was to develop the t distribution. The Z distribution (Z scores) described earlier is based on an infinite sample size. Gosset recognized that with smaller sample sizes (e.g., less than 30), the distributions differed from the exact bell-shape of the gaussian distribution. In particular, the presence of an extreme value (i.e., one far from the mean) was more likely to occur in a small sample. Gosset examined a variety of distributions of small samples and determined the frequency with which the more extreme values occurred.
Earlier we observed that in an infinitely large, normally distributed sample, 95 percent of all observations fell within 1.96 SD of the mean. Gosset found that with a sample size of 20, a slightly larger range, 2.09 SD, was necessary to include the same 95 percent of the observations. As the sample size decreased to 10, 2.26 SD were necessary; with a sample size of 5, an even larger range, 2.78 SD, was necessary to include 95 percent of all observations. These values (e.g., t = 2.09 for a = 0.05 and N = 20) comprise the t distribution. Every value in the t distribution is associated with a sample size and a value for a. As the sample size becomes large (e.g., >30), the values for the t distribution approach those for the Z distribution; with an infinite sample size, they are identical. Gossets observations were then used to define three statistical tests: the one-sample, the two-sample, and paired-sample t-tests.
If an investigator measures a variable in a single group of subjects, he or she may be interested in determining whether the mean for this sample differs from zero (or alternatively, from some other specific value). This analysis can be performed using the one-sample t-test. To examine the association between diuretic drugs and acid-base status, we might identify a group of patients taking diuretic drugs, obtain arterial blood samples, and determine base excess. A hypothetic set of values is shown in Table 21–7. The mean of these values is 3.0, a fact that might suggest an association between diuretic drugs and alkalosis. However, two of the subjects have negative values and two have zero values. Because a quick and informal appraisal of the data (the eye test) cannot determine whether 3.0 differs significantly from zero, we must use statistical analysisin this case, the one-sample t-test. If we assume that this sample represents the population and that the distribution of these values is normal, we can state with 95 percent confidence that the population mean lies between [mean ( t × SE)] and [mean + ( t × SE)]. This statement is similar to an earlier one that the population mean lies between [mean (1.96 × SE)] and [mean + (1.96 × SE)]. However, the value 1.96 (the Z value to include 95 percent of the population) must now be replaced by the value of t appropriate for the sample size, that is, 2.20. This value can be found on a table of t distribution by locating the row corresponding to the appropriate df (in this case, the value for df is one less than the sample size) and the desired value of a (typically, 0.05). Sample values for t distribution are shown in Table 21–3; a complete listing can be found in any statistical textbook. In this case, the 95 percent confidence limits for the mean are 0.47 and 5.53; these limits do not include the value zero. To determine the 99 percent confidence limits, we use the t value for a = 0.01 and 11 df, 3.11. This results in 99 percent confidence limits of 0.57 and 6.57, a range that does include zero. We can conclude with 95 percent, but not 99 percent, confidence that the use of diuretic drugs is associated with alkalosis. Note that our conclusion is limited to making an association between diuretic drugs and alkalosis rather than implying causality. Statistics does not prove causality, only the likelihood of an association.
TABLE 21–7. Hypothetic Set of Values for Base Excess for Subjects Given Diuretic Drugs
TABLE 21–3. Critical Values of the t Distribution (Two-Tailed)
An alternate approach to this problem, more familiar to some readers, is shown in Table 21–8. The division of the mean value by the SE produces a value for t. This value is compared with a value for t appropriate for the desired level of significance (usually, a = 0.05 or 5%) for the appropriate degrees of freedom. If the value for t exceeds the value from the table (known as the critical value), the null hypothesis is rejected, and we would conclude that a difference exists (at the a level) between zero and the mean value for this population. In this instance, the value for t is 2.6. The critical value for t for a = 0.05 and 11 df is 2.20; the value for t for a = 0.01 and 11 df is 3.11. The value for t exceeds the critical value for a of 0.05, but not for a of 0.01. This fact also leads us to conclude (as we did earlier) that the mean for this sample differs from zero and that the likelihood is between 95 and 99 percent.
TABLE 21–8. One-Sample Students t-Test Applied to Hypothetic Data from Table 217
The one-sample t-test can also be applied to populations for which mean values are expected to be other than zero. For example, if we were interested in whether 90 mm Hg was the mean PaO2 of smokers, we would determine the difference between 90 mm Hg and the mean value for the sample population, divide this value by the SE of the sample to determine the t statistic, and then compare the resulting value with the critical value for t.
More commonly, we make measurements on two groups of subjects and compare the responses. Such a comparison requires use of the two-sample t-test. In this form of t-testing, two independent samples are being compared, that is, an individual datum in one sample is not associated with another datum in the second sample. For example, we might want to compare blood pressure in normovolemic and hypovolemic individuals. Hypothetic values are provided in Table 21–9. In this instance, an informal appraisal of the data would establish that a significant difference exists between the mean values. This difference can be confirmed by using the two-sample t-test to evaluate the null hypothesis that there is no difference between these two samples; that is, they come from the same population.
TABLE 21–9. Application of the One-Tailed Two-Sample Students t-Test to Hypothetic Sets of Mean Blood Pressure Values for Normovolemic and Hypovolemic Subjects
Computation of the t statistic for the two-sample test is slightly more complicated than for the one-sample test. In the one-sample test, we divided the mean by its SE. With two samples, each sample has its own SE; we then determine the SE of the difference between the means. Although the derivation of the SE between the means is beyond the scope of this chapter, 44 the denominator of the equation is similar to that for the one-sample test:
Alternate methods are available to calculate the SE of the difference between means, one of which uses a pooled variance instead of the separate variances of equation (15). 44 Despite the different methods for calculation, the SE are similar.
Next, the difference between groups is divided by this SE; this process produces the now familiar t statistic, which is then compared with the critical value from the tables. If the value for t exceeds the critical value, the null hypothesis is rejected; if t is less than the critical value, the null hypothesis cannot be rejected. An instinctive approach to the comparison between the calculated value for t and the critical value is as follows: the numerator is the difference between the mean values, an estimate of the distance between the central location of the two samples. The denominator, shown in equation 15, is the SE of the difference between means, an estimate of the variability within the samples. The ratio of these values estimates how much of the difference between means can be explained by the variability within the samples. If the variability within each of the samples is small, only a small difference between mean values should be sufficient to suggest that a difference exists between the samples. In contrast, if the variability within one or both of the samples is great, the difference between the means of the samples must be larger if the investigator is to have confidence that a difference exists between groups.
Before using a table of t values to determine the critical value for this example, we should consider one special aspect. In our hypothetic situation, we have been comparing blood pressure in normovolemic and hypovolemic individuals. Our a priori assumption is that blood pressure will be lower, rather than higher, in the hypovolemic group. Therefore, rather than perform a two-tailed comparison that would permit us to assess all possible relationships among the data, it would be appropriate to perform a one-tailed test. Because the critical value for t (a = 0.05, df = 14) is lower for a one-tailed comparison (1.76) than for a two-tailed comparison (2.14), we have increased our chances of detecting a statistically significant difference by using the former.
In this example, the t statistic is markedly greater than the critical value; we conclude that it is unlikely ( P < .05) that these two samples were selected from the same population. Therefore, the mean value for blood pressure is lower for these hypovolemic individuals than for normovolemic individuals. Because the t statistic is markedly greater than the critical value for a = 0.05, we can refer to the table to determine the critical values for higher levels of significance. With 14 df, the one-tailed t is 2.62 when a = 0.01 and 2.98 when a = 0.005. Because the t statistic exceeds both these values, we can conclude that the likelihood of these samples being from the same population is extremely small, less than 0.005 or 1 in 200.
On occasion, an investigator obtains measurements before and after an intervention and then studies whether this intervention produced a significant effect. Under these circumstances, when the two samples being compared are paired, a paired-sample t- test, more commonly called a paired t -test, is used. For example, measuring cardiac output before and after the administration of pancuronium might produce the values shown in Table 21–10. In this instance, an informal appraisal of the data suggests a strong difference between the before and after values, because five of six subjects had an increase in cardiac output. The paired t-test is used to confirm this observation. A new sample is created whose members are equal to the difference between the before and after values for each subject. This new sample is then analyzed by the one-sample t-test. The mean value for this sample is 0.80 L/min, and the SE is 0.30 L/min. Therefore, the t statistic is 2.69, a value that exceeds the critical value of 2.01 (again, we can use a one-tailed test because we assume that pancuronium will increase, not decrease, cardiac output). We would conclude that the before and after measurements are unlikely to be from the same population. This conclusion suggests that pancuronium increases cardiac output.
TABLE 21–10. Application of the Paired t-Test to Hypothetic Values for Cardiac Output Before and After Administration of Pancuronium
An alternate statistical approach to this hypothetic situation would be to use the two-sample t-test (Table 21–11). This test produces a value for t of 1.69, which is less than the critical value of 1.81. Despite the greater degrees of freedom for the two-sample test (10) than for the one-sample test (5), the unpaired test does not support our belief that a difference exists between the before and after values. This lack of confirmation results because of the variability of the before and after values. The two-sample test assumes that the investigator obtained the before measurements in one group of subjects and the after measurements in another group. The paired test is more sensitive to small changes because it assumes that the before and after values were measured in the same subject. For example, a change in cardiac output from 4 to 6 L/min in one subject means something entirely different than would the measurement of 4 L/min in one subject before pancuronium and the measurement of 6 L/min in a different subject after pancuronium.
TABLE 21–11. Inappropriate Application of the Two-Sample t-Test to the Hypothetic Analysis of Data of Table 2110
Nonparametric t-Tests: the Mann-Whitney U-Test
Data on an ordinal scale require special treatment, because determining means and variances for this kind of data is usually inappropriate. In order to make statistical comparisons on ordinal data, nonparametric tests, which assess the relative ranks rather than the magnitude of the data, are applied. Most parametric tests have a corresponding nonparametric test.
Nonparametric tests are also valuable for analyzing samples that deviate strongly from the normal distribution. Although parametric tests are based on the assumption that distribution is normal, they are sufficiently powerful (statisticians use the term robust) to detect differences even when samples are not distributed normally. However, as the samples stray significantly from a normal distribution, parametric tests lose their ability to detect differences. Because nonparametric tests analyze only the ranks rather than the individual values, they may detect differences not detected by parametric tests.
The nonparametric test corresponding to the two-sample t-test is the Mann-Whitney U-test. With this test, the values in each of the two groups are assigned ranks. The smallest (or largest) value is assigned the rank of 1; the next smallest (or next largest), the rank of 2. This process continues until the largest (or smallest) value has been assigned the rank equal to the sum of the two sample sizes. If values are tied in rank, they are assigned a value equal to the average of the corresponding ranks. For example, if two samples are tied for ranks 4 and 5, both are assigned the rank of 4.5. The statistics R1 and R2 are equal to the sum of the ranks for groups 1 and 2, respectively. The test statistic, U, is determined by the following equation:
where n1 and n2 are the sizes of the first and second groups, respectively. The value for U is then compared with critical values for U obtained from a table. The data comparing the blood pressures of normovolemic and hypovolemic subjects (see Table 21–9) can be analyzed using the Mann-Whitney U-test, as shown in Table 21–12. As with the two-sample t-test, the results of the Mann-Whitney U-test suggest a difference between the two groups ( P < .05). Nonparametric tests such as the Mann-Whitney U-test rarely appeared in the anesthesia literature until recent years; however, with increased sophistication in research, these tests are being used more frequently. The nonparametric version of the paired t-test is the Wilcoxon paired-sample test.
TABLE 21–12. Nonparametric Comparison of Hypothetic Data from Table 219 Using the Mann-Whitney U-Test
Comparing Three or More Groups
The critical values for t are calculated with the assumption that comparisons are being made between only two groups. If the investigator collected data on three groups of subjects, three comparisons would be possible: A versus B, A versus C, and B versus C. If each of these comparisons was made using the two sample t-test and a = 0.05, we would be accepting a 5 percent risk of committing a type I error for each comparison. For three comparisons, the chance of committing a type I error increases to approximately 3 × 5 percent, or 15 percent (actually closer to 14 percent*), a level that is usually considered unacceptable. As the number of groups increases, the number of possible comparisons increases such that, with enough groups, the investigator will eventually uncover a nonexistent difference.
Thus, the t-test is properly used for comparing two groups (or a single group to a predetermined value). When more than two groups are being compared, other tests, particularly analysis of variance, are more appropriate. If the investigator chooses to use the t-test to compare more than two groups, a correction must be made to prevent type I errors. When one such correction, the Bonferroni inequality (or Bonferroni correction), is applied, the a level for each comparison is divided by the number of comparisons to be performed. For example, if the investigator chooses a value of 0.05 for a and three comparisons are possible, a value of 0.05/3 or 0.0167 for a should be used for each of the comparisons. Then, the investigator is able to state that, overall, the chance of committing a type I error is less than 5 percent.
If the Bonferroni inequality is used, the investigator must decide in advance which of the comparisons will be made. For example, if there are four groups, the investigator may choose to compare group I with each of the other groups (e.g., if subjects in group I were given the placebo and subjects in groups II to IV were given one of three different drugs). In this case, only three of the six possible comparisons will be made. However, it is inappropriate to examine the data and then decide a posteriori which comparisons to make.
* For each comparison in which the investigator permits a type I error of a, he or she is (1 a) confident that no error exists. For n comparisons, he or she is (1 a) n confident that no error exists; conversely, the probability of a type I error is [1 (1 a) n].
Copyright © 2000, 1995, 1990, 1985, 1979 by Churchill Livingstone


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The second revised edition of the modern tensor analysis lecture on physical and engineering science. The author gives detailed definitions of a differentiable manifold, a vector and a tensor and explains why a vector does not belong to space at points of which it is defined. The subjects discussed include the Lie derivative and its relations to symmetries and conservation laws, relative tensors and finding geodesic lines, as well as the representation of the geodesic deviation equation in the form of a system of equations for Jacobi scalars. Apart from the main text, the publication includes examples and tasks. The last chapter is a monograph on tensor analysis applications for investigating the curvature and symmetry of a Riemann space and space-time.
Keywords: Riemann space, geodesic, differential manifold, vectors, tensors.
- The articles by Polish and German researchers documenting the current state of studies on memory from a linguistic perspective. The papers show the diversity of theoretical and methodological approaches and thus they are an attempt to provide answers
- A book about the history of the Białystok pogrom in 1906, and simultaneously an important voice in the field of the theory and methodology of research on pogroms


A group of Swiss researchers claims that their high-performance computer has added 12.8 trillion new digits to the number Pi, resulting in a total calculation of 62.8 trillion figures.
The high-performance computer, housed at the University of Applied Sciences of the Grisons’ center for data analytics, visualization, and simulation (DAViS), completed the Pi calculation with a precision of exactly 62,831,853,071,796 digits, smashing Timothy Mullican’s previous record of 50 trillion digits set last year.
Prior to Mullican, the trophy was held by Google, whose team discovered over 31.4 trillion digits for Pi in 2018.
The Swiss team achieved the result in just over 108 days, which is three and a half times faster than Mullican’s previous record of 303 days, and it is now awaiting verification before being entered into the Guinness World Records. The entire number will not be made public until then, but the researchers teased that the last ten known digits of Pi are now: 7817924264.
For most people, the number Pi conjures up images of math class, where it was defined as the ratio of a circle’s circumference to its diameter and frequently shortened to its first few digits: 3.1415.
Mathematicians have been attempting to calculate the digits of Pi with as much accuracy as possible for centuries – in fact, as far back as the ancient Babylonians. However, because Pi is an irrational number, which means it can never be represented with absolute precision, the point isn’t to find practical applications; rather, the calculation has become an unofficial benchmark for high-performance computing, as well as an opportunity for scientists to compete against one another.
The DAViS researchers used a well-known algorithm known as the Chudnovsky formula, which was developed in 1988 and is widely regarded as the most efficient method of calculating the number Pi. The Chudnovsky algorithm was also used by Google’s team and Mullican.
The algorithm was executed using y-cruncher, a popular computer software program created in 2009 by American developer Alexander Lee specifically to compute Pi.
According to the Swiss team, one of the most difficult challenges was the amount of memory required to perform such a large calculation. DAViS’s high-performance computer was outfitted with two AMD Epyc 7542 processors and 1TB of RAM, which was insufficient to hold all of the digits they hoped to generate. As a result, the y-cruncher program was used to swap out the digits to an additional 38 hard disk drives (HDD) with a total storage space of 16TB, saving a large portion of the RAM on the HDDs.
The computer and disks could reach temperatures of up to 80°C during operation, so the system was housed in a server rack with constant air cooling to avoid overheating. This contributed more than half of the total 1,700 watts of power estimated by the scientists to be required for the full calculation, putting the system in 153rd place on the Green500 list.
The Chudnovsky formula, for example, is well-known for its complexity: when scientists implement the algorithm, they discover that the time and resources required to calculate the digits grow faster than the digits themselves, while it becomes more difficult to survive hardware outages as the computation grows.
The new achievement, according to the Swiss researchers, reflects the capabilities of high-performance computing systems and their potential for other research areas. “The calculation demonstrated that we are prepared for data and computing power-intensive use in research and development,” said Thomas Keller, project manager at the Grisons University of Applied Sciences. “The calculation also made us aware of infrastructure flaws, such as insufficient backup capacity.”
DAViS encourages the use of high-performance computing in machine learning, such as in the Translaturia project, which is developing a computer-aided tool to translate from the Romansh language, which is spoken primarily in the Swiss canton of Grisons and is on the verge of extinction.
The computing center is also investigating the use of DNA sequence analysis in allergy and asthma research, which necessitates the use of high-performance computing systems. The new record contributes to laying the groundwork for future practical applications.


Reading GPS coordinates can seem a bit difficult for the untrained do to all those crazy numbers on display.
Learn How to Read GPS Coordinates
To really understand how to read GPS coordinates, you first need an introduction to the system of latitudes and longitudes. Don’t worry, it’s actually easier than it looks!
Imagine looking at the earth in the typical way, with the North Pole at the top and the South Pole at the bottom. The lines of latitude are the lines that go from east to west. The main latitude line is the equator in the middle, and it’s designated as 0 degrees (0°) latitude.
At the topmost is the North Pole, and it marks the point known as 90 degrees latitude. So you can just imagine 90 lines of latitude from the equator to the North Pole, and each line will denote an increase of 1 degree latitude.
Since this goes up to the North Pole, this is marked as 1 degree N. You can be in a city that’s located 15 degrees N, or 30 degrees N, and so on.
The same goes south of the equator all the way to the South Pole. This time, you mark the first degree of latitude from the equator as 1 degree S. The further south you go the larger the number gets.
So you can be at 15 degrees S, and when you go further south you can get to 30 degrees S, and so on up to the South Pole.
This time the lines are vertical, stretching from the North Pole to the South Pole. The Main Line of longitude is the Prime Meridian, which is basically the vertical line that goes through London.
When this line was drawn in the late 1880s, Great Britain was the most powerful nation in the world, so they decided that their capital would denote the Prime Meridian.
Since a circle is 360 degrees, you can go up to the other side going east in degrees up to 180 degrees (180°). As you go east, you can denote your location as 15°E, 30°E, and so on up to 180 degrees.
You can go west and mark your location from the Prime meridian the same way, except this time you denote the location as 15°W, 30°W, and so forth.
With the two lines of latitude and longitude, you can find the intersection that denotes your location on the world map. So you can be 15°N and 1°E, and that’s basically the country of Niger in Africa.
The problem is that if you want to be exact, you need to denote the spaces between the basic lines of latitude and longitude. Many specific locations and cities aren’t found in these basic degree lines, so you need to use fractions.
This stands for degrees, minutes, and seconds. From 1° to 2°, you divide the space into 60 minutes. Then every minute you divide it into 60 seconds
New York City in this format is located at GPS coordinates 40° 43′ 50.1960” N and 73° 56′ 6.8712” W. You read that out loud as 40 degrees, 43 minutes, 50.1960 seconds north, and 73 degrees, 56 minutes, and 6.8172 seconds west.
This time, instead of degrees, minutes, and seconds you get degrees and minutes only, with the minutes expressed in decimal terms. So in this case for NYC, you get 40° 43.8366′ N and 73° 56.11452′ W. That’s 40 degrees and 43.8366 minutes north, 73 degrees and 56.11452 minutes west.
In some cases, instead of using north, south, east, and west, the coordinates use positive numbers for north and east and negative numbers for south and west. So for NYC, that can also read as 40° 43.8366′, -73° 56.11452′.
Though this seems simpler, this system isn’t really all that popular. Either people use the traditional DMS, or they simplify everything through the DD (decimal degrees) system.
The decimal degrees system don’t use minutes and seconds, as those figures can make coordinates overly complicated. With this system, everything is just a matter of degrees expressed in decimals. In the case of New York City, you then get the simpler 40.730610° latitude and -73.935242° longitude. In fact, in some cases it’s just presented as 40.730610, -73.935242.
The first number always denotes the latitude (north or south) while the second number is the longitude (east or west). The positive numbers again denote north and east, with the negatives denoting south and west. So in the case of NYC it’s located 40.730610 degrees north and 73.935242 west.
Of course, just getting the numbers won’t really help us ordinary folks who don’t have a mental map in our heads to make sense of these coordinates. These GPS coordinates make a lot more sense when you superimpose them on a map.
With decimal systems for the seconds or for the degrees, you can specify the location of not just a city, but a neighborhood or even a single shop. If you are interested in more of the history and technical data behind GPS Coordinates there is a great Wikipedia article that goes over the global positioning system in depth.


the time is f.8.3
this clock operates in base16 time, where each digit is represented as 0-f. the time is divided into three of these digits. the first digit divides the day into 16 equal parts, the second digit divides those parts into 16 equal parts each, and so on for the third digit.
with this system, there are exactly 4096 distinct times in a day, with the day starting at 0.0.0 (which is set to be equal to 6:00 AM on standard clocks).
- 0.0.0 is dawn
- 4.0.0 is noon
- 8.0.0 is dusk
- c.0.0 is midnight
due to the changing of the seasons, and the presence of daylight savings time (which may affect this clock's time depending on where you live), this clock provides only a rough estimation of the lighting conditions outside. however, it is designed to be constant and predictable, so such a concession must be made.


These components involve various calculations and ratios, which will be broken down in more detail in this guide. Every student has access to the enormous database of essay samples and examples of different academic paper formats with EduRaven. The information we provide is solely to be utilized for research and study. If you want to use any of the provided resources, make sure you cite them properly. CFI is the global institution behind the financial modeling and valuation analyst FMVA® Designation.
- The equation above demonstrates 100 percent of income ($100) minus $60 from variable costs equals $40 contribution margin.
- Businesses use CVP analysis to play out “what-if” scenarios, plugging projected sales numbers into the CVP equation to see how it affects the business’s bottom line.
- If you want to use any of the provided resources, make sure you cite them properly.
- It is quite common for companies to want to estimate how their net income will change with changes in sales behavior.
CVP analysis can assess whether your target selling price gives you the profits you desire. You might return to this step many times before arriving at a selling price that works for your business. If operating income equals zero, then the breakeven point in units has been reached. If the operating income is positive, the business firm makes a profit.
Calculate the variable cost per unit
Manufacturers of unique goods, like furniture and other bespoke items, can’t apply consistent selling prices and variable costs to entire product lines. For accrual method businesses, depreciation and amortization count as fixed costs because they don’t change with the number of units your company sells. Since they’re non-cash expenses that don’t affect your business’s cash profits, you might choose to leave depreciation and amortization off your CVP calculation. Cost volume profit (CVP) analysis reveals how many units of a product you need to sell to cover your costs or meet a profit target. It’s a type of break-even analysis that shows business owners how changes in costs and sales affect business profits.
Complete the CVP analysis
Mary Willis is the advertising manager for Bargain shoe Store. Her ideas include the installation of a new lighting system and… He employs four barbers and pays each a base rate of $1,250 per month. One of the barbers serves as the manager and receives an extra $500 per month. In addition to the base rate, each barber also receives a commission of $4.50 per haircut.
Video Illustration 2: Using the contribution margin income statement to forecast changes in profit from an increase in sales
To recap, cost behavior is classified as variable, fixed, or mixed. In this decision-making scenario, companies can easily use the numbers from the CVP analysis to determine the best answer. You most commonly see CVP analyses explained through graphs like the one below. While fixed costs remain constant at $33,050, total costs increase in proportion to units. Once sales and total costs intersect at the break-even point, all you see is profit. The result should be between 0 and 1, which is the percentage of your selling price that goes toward paying fixed costs.
This can be answered by finding the number of units sold or the sales dollar amount. The formula to compute net operating income, sometimes referred to as net income or net profit, is the organization’s revenues less its expenses. CM ratios and variable expense ratios are numbers that companies generally want to see to get an idea of how significant variable costs are. You can save yourself one surprise by estimating your profit margins with a cost volume profit analysis.
Cost behavior must be considered to estimate how profits are affected by changes in sales prices, sales volume, unit variable costs, total fixed costs, and the mix of products sold. The contribution margin income statement classifies costs on the basis of cost behavior. For this reason, it is an essential tool for cost volume profit analysis. The contribution margin income statement is covered in detail in Chapter 1. In this chapter, cost volume profit analysis using the contribution margin income statement is introduced. Cost volume profit analysis can be used to analyze the effect on net operating income from changes in sales price.
Cost-volume-profit analysis is used to determine whether there is an economic justification for a product to be manufactured. The decision maker could then compare the product’s sales projections to the target sales volume to see if it is worth manufacturing. CVP analysis is only reliable if costs are fixed within a specified production level. All units produced are assumed to be sold, and all fixed costs must be stable in CVP analysis.
Essential features of a cost-volume-profit income statement
The graph above shows the relationship between total revenue and total costs. The area between the two lines below the break-even point represents losses and the area above the breake-even point shows the volume of total profit. This graph can be used to identify profit at different output levels. To find each pajama set’s variable cost per unit, investigate how much direct material, direct labor, and variable manufacturing overhead is required. You’ll want the variable cost on a per-unit basis for the CVP analysis.
The contribution margin ratio with the unit variable cost increase is 40%. The additional $5 per unit in the variable cost lowers https://accounting-services.net/ the contribution margin ratio 20%. Each of these three examples could be illustrated with a change in the opposite direction.
Marty Moser wants Moser Company to use CVP analysis to study the effects of changes in costs and volume on the company. It shows that break-even point can be calculated by dividing fixed cost by the contribution margin per unit. The most critical input in CVP analysis is the relationship between different costs and volume i.e. the categorization of costs into fixed and variable categories. If you’re using CVP analysis to price your product, this step is iterative.
For example, if your contribution margin is $40,000 and you have $100,000 in sales, your contribution margin ratio is 40%. This means that for every dollar increase in sales, there will be a 40-cent increase in the contribution margin to cover fixed costs. The break-even point is reached when total costs and total revenues are equal, generating no gain or loss (Operating Income of $0). Business operators use the calculation to determine how many product units they need to sell at a given price point to break even or to produce the first dollar of profit. Assume that Kinsley’s Koncepts wants to earn a target profit of $10,000.
The equation above demonstrates 100 percent of income ($100) minus $60 from variable costs equals $40 contribution margin. The equation below demonstrates revenues doubling to $200 and deducting fixed costs of $120, that results cvp income statement in $80 contribution margin. The contribution margin ratio is calculated as Contribution Margin divided by Sales. It represents the percentage of margin you can make or lose as the number of units sold increases or decreases.


Estimating Yarn Quantities (1)
When you're designing your own patterns,
one of the most difficult tasks is working out
just how much yarn you'll need
to complete the project.
One shortcut you can use is to take the quantities
from a similar pattern, knitted in the same
yarn, and make some allowances for any
different design features.
But often, this method is just not possible, so how
can you make your estimates?
Here's one solution:
in your chosen yarn
and in the same stitch structure that
you intend to use for your project.
The larger the swatch, the more accurate
your yarn estimate will be.
For ease of calculation, the best size
to knit is a piece 100 stitches wide by
100 rows long.
This yarn won't be wasted.
always unravel it and use it again when
Weigh your knitted swatch and make a
note of the weight in gms.
Say, for example, the swatch weighs 70 gms.
Calculate the total number of stitches
in the swatch
by multiplying the stitches
by the number of rows knitted.
If you knitted 100 stitches by 100 rows
then multiply 100 by 100 giving
you a total of 10,000 stitches.
Calculate the number of stitches in the
actual garment to be knitted.
If the back and front are almost the
same, work with the back section
and take the highest and widest numbers.
In the example shown on the right, the
largest number of stitches
for the back is 150 and
the total number of rows is 260.
Multiply these two numbers together to
calculate the stitches:
150 x 260 = 39,000 stitches
Make the same calculation for the sleeve:
110 x 240 = 26,400 stitches
Add up the stitches for each piece:
Divide the number of stitches in the
garment by the number of stitches
in your swatch.
In this example, divide 130,800 by 10,000.
This gives a result of 13.08
Multiply this result by the
weight of your tension swatch from Step 2.
Using the example weight:
13.08 x 70 gms = 915.6 gms
If your yarn is sold in 100 gm balls, then
you would need 10 balls.
If your yarn is sold on 400 gm cones, then
you would need 3 cones.
(Stitches and Rows)


Inspired by both the traditional kilim, often constructed from horizontal and diagonal lines, and by the current graphic trend for multiplying geometric forms (stripes, polka-dots, squares, hexagons, etc.), Bertjan Pot’s Hex Hex rug brings together a wealth of small multicoloured triangles coloured in seemingly random fashion. Their combinations and permutations offer a multitude of levels on which it can be ‘read’ geometrically: one finds triangular groupings of smaller triangles, diamond shapes, trapezoids, hexagons and chevrons.
The richness of their geometric construction, their coloration and their decoration makes these rugs so lively that they seem almost animated, offering a multiplicity of angles from which they may be ‘read’, much like the op art pieces of the 1960s.
Hand-woven kilim rug in 75 % wool / 15 % silk / 10 % other natural materials (cactus vegetable fibre).


DOWNLOAD>> Pre-K to K Math Task Cards (Set 1 Printables)
Math Task Cards are to be used in your classroom for personal use only!
The packet contains the following:
24 Math Vocabulary Cards (little, big, colors, size, match, shapes, order, classify, count, number, before, after, sort, first, same, last, different, set, greater than, more than, less than, equal, same, fewer.)
I Can Cards (Count, Match sets of objects with a numeral 1 - 5, Match objects that are alike, Sort by (1) characteristic, Choose how to sort, Communicate reasons for sorting, Match objects that are the same.)
23 Task Cards Targets Counting Objects (1-5), Sorting
Task 1:Making Buildings ( Geometry, spatial, and counting skills.)
Task 2:Memory Match Dot Cards (1 to 5)
Task 3:Counting Color Bears (1 to 5)
Task 4:1-5 Bear Counting Mat
Task 6:1-5 Dot Counting Mat
Task 7:Counting Towers
Task 8:Blank 5 Frames
Task 9:Blank Counting Mat
Task 10:Pattern Block Mats (1 to 5)
Task 11:Sort by Colors Mat
Task 12:Sort by Shapes Mat
Task 13:Sort Shapes by Size Mat
Task 14:Sort Letters by Holes/No Holes
Task 15:Sort Letters by Straight/Slanted Lines
Task 16:Sort Letters by Upper/Lowercase Mat
Task 17:Sort Letters by Tails/No Tails Mat
Task 18:Sort Letters by Tunnels/No Tunnels Mat
Task 19:Sort Letters by Tall/Short Mat
Task 20:Sort Letters by In My Name/Not in My Name Mat
Task 21: Sort Letters by Long/Short Stick Mat
Task 22: Sort Letters by Same Upper/Lowercase Mat
Task 23: Alike Mat
• It is suggested to print all pieces on card stock and laminate for durability.
• Perfect for making math tubs for morning work and independent work.
Georgia Early Learning and Development Standards:
Approaches to Play
APL2.4a Demonstrates eagerness to learn about and discuss new topics, ideas and tasks.
APL1.4a Takes initiative to learn new concepts and try new experiences. Initiates and completes new tasks by himself/herself.
Language and Literacy
CLL7.4a With prompting and support, recognizes and names some upper/lowercase letters of the alphabet.
CD-MA4.4b Sorts and classifies objects using one or more attributes or relationships.
CD-MA4.4c Creates and extends simple, repeating patterns.
CD-MA2.4b Counts at least 10 objects using one-to-one correspondence.
CD-CP3.4b Uses both familiar and new strategies to solve a problem.
CD-CP3.4c With adult guidance and questioning determines and evaluates solutions prior to attempting to solve a problem.
If you have any suggestions and/or comments to make this learning packet better, please feel free to email me at: email@example.com
If you find a mistake or typo in the packet, please email me at:firstname.lastname@example.org so I can fix the error and send you a revised packet.


Capacity of a Pen drive/External Drive shown on sales pack or on product brochure is differ/less from the storage shown on the computer.
Let us understand mathematics of the bytes in the below chart
1KB is not equal to 1000 Bytes but 1024 Bytes so
1 KB = 1024 Bytes
1 MB = 1024 * 1024 = 1048576 Bytes
1 GB = 1024 * 1024 * 1024 = 1073741824
1 TB = 1024 * 1024 * 1024 *1024 = 1099511627776
But at the time of manufacturing a Pen Drive/External Drive the manufacturer assumes 1kb equals to 1000 Bytes and so on which results in the shortage of space i.e. 1TB to 931 GB. Let us understand with an example.
Suppose a manufacturer made a External Device which have 1,000,000,000,000 Bytes & labeled it with 1 TB .
Simultaneously the computer calculates or sees 1 KB equals to 1024 Bytes but not 1000 Bytes and the actual storage space will be smaller than advertise.
According to the Manufacturer 1 TB = 1000,000,000,000 Bytes
And as we can see above as per computer –
1 GB = 1024 MB
1 MB = 1024 KB
1 KB = 1024 B
So, if we do reverse calculation as per Computer then
1000,000,000,000 bytes Equals to 1000,000,000,000/1024 KB which equals to 976562500 KB.
Similarly, 976562500 KB Equals to 976562500/1024 MB Equals to 953674.32 MB.
And finally, 953674 MB Equals to 953674.32/1024 GB Equals to 931.32 GB.
Hence 1 TB External drive shows the actual storage capacity of 931 GB.


Mrs. J. Schellin
Welcome to the 2021-2022 school year! We are going to have a great year!
Mrs. Schellin’s Schedule
1st Period - 8th Grade Math Resource in room 803
2nd period -7th grade Math in room 712
3rd Period -8th grade Math in room 814
4th Period - 7th Grade Math Resource in room 803
5th Period - Conference
6th Period - 7th Grade Math in room 714
7th Period - 7th Grade Math Resource in room 803
Julie Schellin- Room 803
Please log into the following URL to fill out a parent survey.
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Every student. Every day.
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As part of the course, the question came up about why anyone would use Double when Decimal has better precision. We talked through it in class, but I thought it would be illustrative to actually run a benchmark on sample code and show the differences. So, I ran up a quick benchmark test and proved that addition and multiplication of Decimals are around 10 times more costly than equivalent Double operations. My laptop results for addition were:
The results for multiplication were:
It was strange for me to see that multiplication was faster than addition, but the magnitudes were not surprising.
As the capstone for the course we had to do a project using C#, so I decided to expand on the idea of benchmarking the different operations by running the tests on different architectures. Another peer is writing a series of blog posts on running Kubernetes on a Raspberry Pi cluster and I happened to have a Pi 3 A+ that I am using for another project so it was an obvious first choice. The results were similar, but somewhat less consistent. The decimal operations cost about 10 times that of the others, but the byte multiplication operations are almost twice as fast as the long integer multiplication operations. There were also a greater difference between the multiplication operations and the addition operations. Here are the addition results:
And here are the results for multiplication:
I have an older Dell PowerEdge R710 that I picked up from TechMikeNY last year to play with some Cloud Foundry stuff so I decided to see what the Xeon processors looked like running the same code. This is more like what would be expected to be seen in a production environment. The addition results look like:
And the multiplication results were:
Wow! Those results looked significantly different than the previous ones. For one thing, these are the first results that I had seen with the MultiModalDistribution warnings, so I ran them again to make sure the results were consistent. The results were similar, but not the same. They were more similar to each other than to the other architectures. Here are the results for the addition tests:
I went on to do tests on a couple of different Azure VMs, but I am going to save that is for a different article. :-) I also have plans to dig into these differences a little more and see if I can't track down the underlying causes for the displayed differences.


Andersen C1 Coffee table | coloured Laminate
The stylish C1 coffee table by Andersen Furniture is inspired by natures mathematics. At the University of St. Petersburg the Russian professor Georgy Voronoi worked with natural, recurring patterns which were transferred to the design of the table. With the soft, organic shapes and minimalist design, it fits perfectly in any living room.
The C1 coffee table by Andersen is available with a base in oak (white pigmented), walnut or black. At the table top, you can select from many different colored laminate surfaces.
The table is also optionally available with an additional shelf. Please contact us and receive an offer for this.
|Product Weight in kg||30|
|Material||oak, laminate, walnut, walnut|
|Colour||dark brown, oak, multicolour, natural, walnut, black|
|Color Note||Please note that the colors may be different on your display device from the original colors.|
|Size (h x w x d) in cm||45 x 140 x 83 cm|


Words like "good" have been replaced with "fantastic" and "bad" with "disastrous". Every kid's a prodigy. "Look at my Mikey!!!! Isn't he great??" Even I'm buying in with mulitple exclamation and quesiton marks, as if adding more than one makes it louder or more "questiony".
The world has gone deaf to this type of bravado. In fact, when I coached, kids would come to me and tell me they'd give me 110%. I'm sure they saw it on a T-Shirt somewhere.
Sometimes I asked them what that meant and they said they would give me everything they had. I would respond, "so I'm going to get 100% of you?" "YES!!!", they would reply. I would tell them if I could get 88%, that would be good, no fantastic! So, here's to 88%, a real number that would get winning results.
A friend of mine, Nancy, recently sent this to me as sort of a measuring stick to percentage of effort. It rings pretty true.
What Makes 100%? What does it mean to give MORE than 100%? Ever wonder about those people who say they are giving more than 100%? We have all been to those meetings where someone wants you to give over 100%. How about achieving 103%? What makes up 100% in life?
Here's a little mathematical formula that might help you answer these questions:
If A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
is represented as 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26,
then H-A -R -D-W-O -R -K, 8+1+18+4+23+15+18+11 = 98%.
And K-N-O-W-L-E-D-G-E, 11+14+15+23+12+5+4+7+5 = 96%.
But , A-T-T-I-T-U-D-E, 1+20+20+9+20+21+4+5 = 100%.
And, B-U-L-L-S-H-I-T, 2+21+12+12+19+8+9+20=103%.
AND, look how far ass kissing will take you.
A-S -S -K -I -S-S -I -N-G, 1+19+19+11+9+19+19+9+14+7=118%
So, one can conclude with mathematical certainty, that While Hard work and Knowledge will get you close, and Attitude will get you there, its the Bullshit and Ass kissing that will put you over the top.
-Thank you Nancy


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Teaching Interests: Professor Carter's teaching
interest includes Differential Equations, Calculus, and courses with
significant applied mathematics content.
Interests: Working with a team of outstanding undergraduates and
colleagues from around the world, Dr. Carter studies how waves propagate in the
deep ocean and how tsunamis evolve as they approach a coastline. This area is
especially exciting right now due to the immense current interest generated by
the recent tsunamis.
J.D. Carter. Plane wave solutions of a dissipative generalization of the
vector nonlinear Schrodinger equation. Mathematics and
Computers in Simulation, 82:1038-1046, 2012. J.D. Carter. A Review of Mathematica: A
Problem-Centered Approach. SIAM Review, 53: 583-585, 2011. J.D. Carter and R.
Cienfuegos. The kinematics and stability of solitary and cnoidal wave
solutions of the Serre equations. European Journal of Mechanics B:
Fluids, 30: 259-268, 2011. D.M. Henderson, H. Segur and J.D.
Carter. Experimental evidence of stable wave patterns on deep water.
Journal of Fluid Mechanics, 658, 247-278, 2010. J.D.
Carter and C.C. Contreras. Stability of plane-wave solutions of a dissipative
generalization of the nonlinear Schrodinger equation. Physica D, 237:
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Updated 2020-2021 Decatur City Schools Calendar. Please click on the link to see the full 2020-2021 school calendar.
Click above to access the infosnap link
Students entering 6th-12th grades are asked to complete summer assignments for math and language arts. These assignments were designed by DCS teachers to help students refresh skills they learned last year. Students should complete assignments for the math and language arts classes they have registered to take for the 2020-2021 school year.
Please click on a link below to access the school supply lists.
DCS Students and Teachers can access CLEVER here.
Resources, communication, and support for parents and students of Decatur City Schools


For For Those Who Are Poker Fanatics, Poker Odds.
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In particular, the card poker odds are discussed to be the likelihoods of being drawn or dealing to different poker hands. It is then considered that due to its being the first essential poker chances, the card poker odds are then reviewed in many resources about poker. To even more provide ideas about this kind of poker odds, one of the likelihoods to discuss this specific thing is to understand that there are 2,598,960 different poker hands in a 52-card deck. So is a poker player is handled 100,000 poker hands in his life time, that poker player will never ever hold on his first 5 poker cards more than 4 percent of all the possible poker hands. With Just what Is The Absolute Best On The Internet Texas Hold'em Site?
, the card odds will then reveal a sort of interesting info.
It is just then necessary to note that the investment poker chances are approximated based on the this formula: the prospective size of the pot by dollar being increased by the probability of winning the pot, over the possible loss by dollar is equivalent to the investment poker chances. With adequate poker experience, you will later on recognize that the accurate computations of the financial investment poker chances are not best attained by mathematical problem resolving but by the proper thinking methods.
Together with Precisely what Is The Very Best Web-based Gambling Website?
about the financial investment poker odds, it is also noted that the financial investment poker chances are important for making playing choices and correct wagering. However, lots of poker players forget this considering that most of them rely on card poker chances which frequently result in incorrect decisions. This is for the factor that sometimes the financial investment poker odds prefer drawing to a within straight and often favor folding 3 aces prior to the draw.
The edge poker chances are then poker chances that operate to suggest the relative efficiency of a gamer in a poker game. With that, the best poker gamer is therefore able to maintain edge poker chances from 25% to 65%, depending on the game and the capabilities of the other poker gamers.
It is a typical understanding that some of the poker gamers today are familiar with the card poker odds, and most of them even base their playing and betting choices on those card poker chances. It is then thought about that due to its being the initially crucial poker odds, the card poker odds are then reviewed in most resources about poker. Is a poker player is dealt with 100,000 poker hands in his life time, that poker player will never hold on his very first 5 poker cards more than 4 percent of all the possible poker hands. The edge poker odds are then poker odds that function to indicate the relative performance of a player in a poker video game.


Filipino students' poor performance in a global assessment in fourth-grade math and science shows a "major crisis" in Philippine basic education, Senator Sherwin Gatchalian said Friday.
Grade 4 Filipino learners scored the lowest among their peers from 57 other countries in math and science in the 2019 Trends in International Mathematics and Science Study (TIMSS).
Their scores of 297 in math and 249 in science were also lower than the country's score of 358 in math and 332 in science from the last time the Philippines joined the study in 2003.
Gatchalian, chairperson of the Senate education committee, said this follows "dismal results" for the Philippines in the 2019 Southeast Asia Primary Learning Metrics and the 2018 Programme for International Student Assessment.
“This is a major crisis. The country has been participating in global assessments as an additional tool to measure the effectiveness of the basic education curriculum. The dismal result for the third time is so depressing and should serve as a wake-up call,” Gatchalian said in a statement.
According to the study, only 1 percent of Filipino students reached the high benchmark in math, which refers to an ability to “apply conceptual understanding to solve problems.”
Similarly, only 1 percent got a high score in science. The high benchmark means students “communicate and apply knowledge of life, physical, and Earth sciences.”
The top-performing students came from the Philippines’ neighbors Singapore, Taiwan, Korea, Japan, and Hong Kong. Singaporeans scored 625 in math and 595 in science.
Gatchalian said a failure to implement reforms will worsen the learning crisis.
He reiterated the need to “decongest” the K to 12 curriculum with focus on boosting learners' basic competencies in reading, writing, math, and science.
At the same time, teachers should be capable of teaching the K to 12 curriculum, he said. The senator, who chairs the Senate committee on basic education, arts, and culture, has filed a bill seeking to reform teacher education and training.
“Kailangan nating ituring na nasa ilalim na ng isang malawakang krisis ang ating sistema ng edukasyon. Hindi na natin kailangang patagalin pa ang pagsulong sa mga reporma dahil kung hindi, patuloy na mahuhuli at mapag-iiwanan ang ating mga mag-aaral,” Gatchalian said.
Pasig Representative Roman Romulo, who chairs the House basic education and culture committee, said "We have to act now."
He suggested that first to third graders focus on good manners and right conduct, reading, writing, and basic math, with basic science being introduced in the second quarter of Grade 2.
He also urged a review of the use of the mother tongue as the medium of instruction in Grades 1 to 3.
In addition, he said the Department of the Education and the Commission on Higher Education have to closely coordinate for the education curriculum at the tertiary level.
He added that the DepEd must be a part of the screening and review of questions in the Licensure Examination for Teachers.
"I trust DepEd knows what has to be done," Romulo told GMA News Online. — Nicole-Anne C. Lagrimas/RSJ, GMA News