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Computational statistics and data analysis (csda), an official publication of the network computational and methodological statistics (cmstatistics) and of the international association for statistical computing (iasc), is an international journal dedicated to the dissemination of methodological research and applications in the areas of computational statistics and data analysis. A statistics t-test is one of the many analyses i can provide as a statistical consultant for your analysis statistical methods & tests statistics. Learn the five most important data analysis methods you need in order to interpret your data correctly (and what pitfalls to avoid in the process.


this crystal ball will amaze you - it can read your mind! just follow the instructions below.
choose any two digit number, add both digits together and then subtract the total from your original number.
for example, lets say you choose 33:
add the two digits together: 3 + 3 = 6
subtract the product from the original number: 33 - 6
when you have the final number, look it up on the chart and find the relevant symbol. concentrate on the symbol and once you
have it clearly in your mind, click on the crystal ball and it will mysteriously reveal the symbol you were thinking of...


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Darko Odic’s research examines how children acquire abstract cognitive and perceptual representations, including those of number, confidence, and mathematical thought. By examining individual and developmental differences in, for example, how children’s earliest intuitions about number inform their formal math abilities, he seeks to understand why children sometimes learn complex ideas with ease, and sometimes struggle.
My plans for the fellowship period
To learn, we must make mistakes. But mistakes are only useful when they are noticed, evaluated, and corrected. When learning mathematics, a topic particularly challenging for many children around the world, “error monitoring” is especially important: math problems often require one answer in a sea of (literally) infinite possibilities. Unlike learning about gravity through building blocks, math problems do not physically fall down when a mistake is made; unlike learning social skills, math problems don’t flash with moments of anger or joy; unlike reading, math mistakes do not lead to meaningless strings of words.
During the Fellowship period, I will be investigating one potential mechanism for how children catch errors in mathematics: by using their intuitive (but approximate) sense of number. We hypothesize that young children use their intuitive number system to arrive at a probabilistic prediction of the likely answer for a simple equation and therefore catch when they are likely to have made a mistake. We have recently shown that differences in children’s number sense correlate with detecting math mistakes made by others. Over the next 2-4 years my lab plans to: (1) use pupillometric measures to measure the degree of surprise children experience when catching mistakes in mathematics; (2) temporarily enhance or impair children’s intuitive number sense and observe the effects this has on their error monitoring; and (3) train children to actively make predictions about the outcomes of math problems to increase the chance of catching and learning from mistakes. I aim to provide both a mechanistic understanding of how core cognition contributes to formal concepts and to characterize why some children are more successful at learning about math compared to others.
How will my work change children’s and youth’s lives?
My research focuses on children’s early mathematical abilities, which have consistently been shown to predict later school and job success, income level, happiness, and personal health. It will help identify mechanisms that allow children to be more independent, effective, and self-efficacious learners, ultimately informing educators on how children can learn complex topics with minimal external feedback. The current proposal, therefore, helps identify the conditions and skills that children should ideally maximize to deepen their development and ability to contribute to society. And, because the intuitive number sense is present in every child from birth, this work also has important universal implications, and seems to promote education initiatives across traditional cultural and economic divides.


To do that we need to define dimensions for the different moments (defined on the pureGrowth tutorial as: [0 -3 0 0 0 0 0], [0 -2 0 0 0 0 0],[0 -1 0 0 0 0 0] ... My question is what is the criteria for it?
Also, a similar vector is used in different instances like the growthModel properties:
minAbscissa minAbscissa [0 -2 0 0 0 0 0] 0.0;
maxAbscissa maxAbscissa [0 -2 0 0 0 0 0] 1.0;
Cg Cg [0 3 -1 0 0 0 0 ] 1.0;
What is the reason for using those particular values? Where can I find an explanation for that?
Post by Alberto Passalacqua on Aug 9, 2017 9:36:52 GMT -6
The unit of the moments become more clear if you consider the unit of the internal coordinate of your population balance. For example, if you use length as internal coordinate, then the unit should be meters, which would lead to [0 1 0 0 0 0 0] for the abscissa. Moments are calculated based on the quadrature as:
m_k = sum_i (weight_i * abscissa_i^k)
where k is the order of the moment, and weight_i is the number of particles per cubic meter (or some other way to express the number density: the code will work as long as units are consistent).
For the constant growth model example, the choice made in the tutorial is to consider Cg as the volumetric growth rate, which led to the units you see.
However, it is not clear to me how the different moments are set up. Is there a physical interpretation for them? How to decide how many moments to use?
Yes, moments have a physical meaning. Remember they are statistics of a number density function (or equivalent distribution). For example, if your number density is based on the particle length: n(L), then:
m0 = integral of the number density with respect to size = number of particles m1 = integral of (L * n(L)) dL = mean length ...
The number of moments you need to have accurate results depends on what information you need. For population balance problems, typically 3 to 4 primary quadrature nodes is the recommended setting, which corresponds to 6 - 8 moments for QMOM and 7 - 9 moments for EQMOM. Note that with EQMOM you are likely to need less moments than with QMOM. You may need more nodes if your number density has a particularly complex shape, or if you are interested in higher-order statistics. For example, if you need to know d43, you will need at least m4. If you use QMOM ("basic" quadrature in OpenQBMM), then m4 will be exactly preserved with 2 nodes.
To avoid an extended answer, a reference to where I can find these answers is also welcomed.
A good introduction and a lot of details of the methods we implement in OpenQBMM are in: D.L. Marchisio, R.O. Fox, Computational models for polydisperse particulate and multiphase systems, Cambridge University Press, Cambridge, 2013.
The implementation is however done differently (See references in header files).
Thanks again for the clear explanation regarding the moment interpretation.
Regarding the choice of how many moments to use for each method, is it really as you stated(?):
Note that with EQMOM you are likely to need less moments than with QMOM
It seems from the book chapter that it is rather # EQMOM moments > # QMOM moments:
6 - 8 moments for QMOM and 7 - 9 moments for EQMOM
More than that, I am having troubles testing the available tutorials (pbeFoam/aggregationBreakup). I focused on that in order to, later on, set-up simple a 1-D phase PBE-EQMOM using length as internal coordinate, perhaps using more than 4 nodes.
At this point, I can run the tutorial, but I do not find how to change the initial conditions (number of particles and respective size, especially when a population with different sizes is present) If I understood correctly, the output is saved on postProcessing folder for each moment and time point.
Again, to avoid an extensive answer, pointing to a tutorial explanation (if exists) will be equally welcomed.
Post by Alberto Passalacqua on Sept 9, 2017 19:33:37 GMT -6
You are comparing QMOM and EQMOM with a given number of primary quadrature nodes. Since EQMOM preserves more moments by definition, you may be good with a lower number of moments (= less primary nodes). It all depends on how many moments you really need to preserve for your problem.
In order to change the initial conditions, you need to set the moments of the number density function at time zero. The number of particles will be your m0, the mean size your m1/m0, and so on. This is all explained in the theory of moment methods, which is summarized in the first chapters of Marchisio and Fox (2013).
P.S. Sorry for the late reply. For some reason the forum did not notify me of your post.


We are a financial literacy and numeracy education company.
On the subject of the need financial education in schools, the Money Editor for the Sunday Times shares his own experience with Maths as a subject. He gives the readers a maths question to calculate.
This question was shared with my close friends and generated a big discussion as to what the answer should be. Why not take a look at the article here:
In the meantime, here is an excerpt from the mention:’On a lighter note, an educational game called bMoneywize aims to introduce children and their parents to complex concepts in a simple way. Its inventor, Arinola Araba, said the idea for the project had hit her when she was out of work and her teenage daughter would bring friends home from school to cook them jollof rice, an African delicacy. Their conversation made it obvious they knew little about money: “Clearly I had to do something that would answer the question: how can we teach children to manage money in a fun and interactive way?”
Were you able to work out the sums?


A fun, visually-engaging counting journey from 1 to 10 and more!
Welcome to our farm! It is a place to learn about farm life and animals on a farm, and to celebrate family, especially grandparents.
Children will love counting their way through Granddad’s farm. Pigs and chickens, cows and horses, apples, tomatoes, and plums-so many things to see and count on the farm.
Learn to Count: Count up to 10. Count the farm animals, tractors, apples, flowers, and anything that can be counted. Read it again! Count down to 1.
Count to Learn: Find and count the number of animals on each page, count how many animals there are all together, ask how many would be left if some were taken away, and talk about more and less.
Count in the Real World: Explore your home, neighborhood, and school. Count everyday objects forward up to any number and backward from any number.
Have fun counting from 1 to 10 and back again as you learn about farm life, farm animals, and family!


Four Cards is a popular Chinese card game that is often played as a competition, and to help students develop basic math skills. The objective of the game is to construct an equation that totals 24 using the four cards you have been dealt, and a combination of the three math operators. The numbered cards are equal to their face value, with A=1, J=11, Q=12, and K=13. The math operators available to you are: Add, subtract, multiply and Divide. Each card can only be used once but the math operators can be repeated. Only whole numbers, zero or greater can be calculated.
To play, you need to place the four cards you are dealt in the four slots, and place the three math operators between them in such a way that the resulting equation equals to 24. You can either drag the cards and operators to the desired slot or simply tap on them. Tapping a card or operator places it in the next open slot from left to right. To remove the card, or an operator from the slot simply tap it again. Four cards, has an intuitive clean interface, and full range of options. It’s a mathematical brain teaser that will test your math skills to the limit.
Let’s say for example, you are dealt the 7, 8, 8 and 2 cards. First place 7 and 8 in the first two slots and place the multiplication operator in between them. This will equal to 56. Next place the second 8 card in the third slot and place a subtraction operator between them. The equation so far equals 48. Now place the final 2 card in the last slot and place the division operator in the third slot making the final equation now equal 24. In the normal mode, you will only dealt cards from Ace to 10. The advanced mode includes face cards 11 through 13 as well, which makes it tougher to solve the equation. Four cards is a classic puzzler game that will both challenge and entertain you.
* Construct an equation equaling 24 using the face value of four cards
* Mathematical brain teaser that will test your Math skills to the limit
* Intuitive clean interface


Another Breakthrough using Modern Mathematics to Understand Music
In October of 2008, a math professor at Dalhousie University in Nova Scotia revealed an astonishing discovery: He had used math to understand the music of the Beatles!
The specific song that this professor of mathematics and statistics (and musical enthusiast) Jason Brown had decided to analyze was the classic tune, “A Hard Day’s Night.” Even more specifically, Brown had sought to understand the exact musical composition of just a single chord: the song’s bizarre opening sound, which had puzzled musicians for years.
Solving the Musical Puzzle
Brown, with his unique skill set, was able to recognize where previous musicians had failed in their attempts to recreate this difficult sound – they had been working with the wrong tools. Generally, a musician with a good ear and a talent for recognizing various sounds has the ability to recreate most traditional musical pieces, but there is a point at which this breaks down. When sounds are compiled using layered sounds and a variety of instruments, it can often be difficult (or even impossible) to fully recreate them using standard instruments.
Brown saw that this was the case with that opening chord of “A Hard Day’s Night,” and so decided that he would use his mathematical abilities to help him solve the puzzle.
To begin with, Brown turned to modern technology to help him break the chord down into its various frequencies. Using a computer, he was able to determine the exact combination of harmonic frequencies which George Harrison had implemented (perhaps unknowingly) into the sound. From here, the construction of the chord merely consisted of finding a combination of tones which would create this same pattern – a mathematical puzzle.
An Answer After 40 Years
So what did Jason Brown finally discover after his long search for the truth?
Nothing quite as remarkable as many people had hoped, but an answer which garnered international attention. Brown found that the chord in question could not be explained by merely George Harrison’s 12-string guitar, John Lennon’s 6-string and Paul McCartney’s Bass. There was a sound containing a frequency which could not have been played on any of these instruments, which made it impossible for the sound to be truly recreated in a traditional sense.
While it may seem simple, and rather trivial, for such a journey to be undertaken in the first place, the journey of one mathematician to solve a generation-old Beatles riddle demonstrates still another important aspect of mathematics – its ability to transcend disciplines and sciences and to be made useful in even the most bizarre places.


Sneak Peek: Worried if calculus course is coming to your way in the next semester. The calculations, formulas, homework assignment and most importantly the calculus exam make you overwhelmed? The struggle is real; we know calculus is tough but preparing for the calculus readiness exam beforehand might help! So in this article so let’s find out!
Calculus is rigorous, demanding, and challenging course. Whether you take it in college or university, your business, engineering, mathematics, physics studies would require you to most opt for it for once during entire undergraduate or graduate programs.
Calculus is not a theory-based subject rather the core purpose of this course is to enhance students’ understanding regarding application and methods. Thus, most calculus professors expect you to define the outcomes and concepts geometrically, verbally, analytically, and numerically.
The technicality of this course does not require you to have knowledge about calculus behind every question or problem. Rather represent your research, findings, or outcomes in a logical and clearly structured manner.
So every time you are struck with a calculus exam, be prepared that it is coming your way in a far more difficult manner than your expected. It would not resemble your ordinary exam paper but require putting your critical, analytical and creative thinking skills at work.
If you do find yourself comfortable in a calculus course, get a professional to Take My Online Exam with flying grades as per their expertise and years of experience. However, if you wish to improve, be prepared and take your calculus readiness exam on your own. Check out our professional tips on how and what possible targets would a calculus readiness exam contain for you to answer.
Possible Targeted Outcomes of Calculus Readiness Exam
The main resources to prepare for the calculus readiness exam may include your instructor’s lectures or textbooks. The instructor or textbooks guidance makes you more efficient and accurate, polishing your ability to carry out simplified to complex calculus computational tasks.
However, the course itself may require you to fulfill some predefined targets to achieve flying colors in the test. It may challenge students’ learning and skills by demanding to solve some predefined targets such as simplifying algebraic equations and expressions, representing domain and range, and becoming familiar with notations. Moreover, find relationships between various functions such as linear, polynomial, rational, logarithmic, exponential.


Modified givens rotations for inverse updating in qr decomposition
A systolic array is a matrix of individual signal processing cells, where overall operation of the systolic array depends upon functions of the individual signal processing cells and the interconnection scheme of such signal processing cells.A clock signal is conventionally applied to a systolic array to control data flow therethrough.However, Gentleman and Kung's matrix triangularization and least squares solution is predicated on processing matrices with only real numbers.For a matrix with one or more complex numbers, namely a “complex matrix,” heretofore, a complex-to-real data reduction was performed to convert each individual cell in the complex matrix to a real number before performing a Givens rotation by factoring out the phase before Givens rotations and applying such phase at a later stage.\[\begin\kappa_S(M, p) & = \left\Vert \left\vert M \right\vert \left\vert M^ \right\vert \right\Vert_p \ \kappa_S(M, x, p) & = \left\Vert \left\vert M \right\vert \left\vert M^ \right\vert \left\vert x \right\vert \right\Vert_p\end\]Konstantinos Konstantinides and Kung Yao, “Statistical analysis of effective singular values in matrix rank determination”, IEEE Transactions on Acoustics, Speech and Signal Processing, 36(5), 1988, 757-763. Since this API is not user-facing, there is no commitment to support/deprecate this specific set of functions in future releases. A complex matrix and a modified Givens rotation matrix are obtained for multiplication by a processing unit, such as a systolic array or a CPU, for example, for the nulling of the cell to provide a modified form of the complex matrix.
Additionally, others have proposed various forms of phase factoring for complex-to-real data reduction. is a block diagram of a prior art internal cell 710 of a systolic array for processing complex numbers.298, Real-Time Signal Processing IV (1981) at pages 19-26 (hereinafter “Gentleman and Kung”).


The topic is prompted by a new US Census report on the Characteristics of New Single Family Houses Completed, which shows that in 2016 most new homes had 3 or 4 bedrooms and 2 or 2.5 baths; and that just over half ranged from 1,400 to 2,399 sq. ft. The median size of a new home built in 2016 was 2,422 sq. ft.
Answer (1 of 5): There are a number of factors which can determine the amount of asphalt needed to cover a certain area. These factors can include the temperature of the asphalt and the surface it is set on, the size and amount of stones within the asphalt, and the size and weight of the roller. On average, one ton of asphalt can cover between 80 to 100sq feet.
May 25, 2020 The force will be around 0.0012 x ((88/60) x (110))^2. The 88/60 converts from mph to fps, and the answer is around 31 pounds per square feet. If we add the height of the dome, it is 55 + 6 = 61' tall, and 12' wide, so the area is 12 x 61 = 732 square feet. Total force acting on the tower is about 732 x 31 = 22,692 pounds, over ten tons.
A beam of 145 pounds per square inch (Psi) when converted, is equivalent to other units as follows : 0.9997 Newtons per millimeter squared (N/mm 2) 0.9997 Megapascal (MPa) 999.775 Kilopascal (KPa) 0.145 Thousands of pounds per square inch (Ksi)
Answer – 1.3 gpm/sq ft 4. What is the detention time in hours through a sedimentation basin measuring 40 feet wide, 60 feet long and 20 feet deep if the daily flow is 950,000 gal/day? Answer – 9 hr 5. How many pounds of chlorine gas would be used each day if the flow of 2,300,000 gallons per day were
Aug 07, 2020 The rates on this Schedule of Equipment Rates are for applicant-owned equipment in good mechanical condition, complete with all required attachments. Each rate covers all costs eligible under the Robert T. Stafford Disaster Relief and Emergency Assistance Act, 42 U.S.C. 5121, et seq., for ownership and operation of equipment, including depreciation, overhead, all maintenance, field …
Surface Area = 624 in2/144 in2/ft2 Surface Area = 4.33 ft2 Volume = Surface Area x Length x (2 ea.) Volume = 4.33 ft2 x 125 ft x 2 Volume = 1083.3 ft3/27 Volume= 40.1 CY 45 CY SECTION 6.0 MACHINE SHOP FOUNDATION Objective: Calculate the estimated volume of C&D debris material that will result from the demolition of the Machine Shop foundation.
3″ to 5″ thick - Approx. 35-40 sq. ft. per ton. Per Ton of Stone. 3 bags of mortar and yd. of sand. Bricks. BRICK SIZES & SQUARE FOOTAGE INFO. Bags of Mortar per 1000 Brick. Approx. 7 bags (143 bricks per bag) yd. of Sand per 1000 bricks. Approx. 1 yd.
A ton of asphalt millings typically covers about 80 square feet at 3 to 4 inches thick. How Much Asphalt Milling is Needed for a Driveway? The average residential driveway is 608 square feet or 16 feet wide by 38 feet long. To cover that area with 3 to 4 inches of asphalt millings, homeowners will need to purchase 7.6 tons of recycled asphalt.
The first step to calculate the mulch needed is figuring out the how many square feet the potential bed covers. Simply multiply the length by the width if the bed is rectangular or square, or for a round bed, multiply the square of the radius (distance from the center of the bed to its edge in a …
Acre. Definition: An acre (symbol: ac) is a unit of land area used in the imperial and US customary systems. It is defined as the area of 1 chain (66 feet) by 1 furlong (660 feet), which is exactly equal to 1/640 of a square mile, 43,560 square feet, or exactly 4046.8564224 square meters.
Start with the depth of the material in the left column. Once at the depth, match the square footage with the depth. The number of yards at the top of the column is the amount of material you will need. For Example: With a depth of 2″ Covering 160 Sq. Ft. you will need 1 Cu. Yd of Material.
Aug 21, 2006 If length and width are in feet and thickness in inches, that product is ft in then multiplying by 1 ft/12 in x 150 lb/ft x 1 ton/2000 lb results in tons Combining the three numerical factors is equivalent to dividing by 160 (or multiplying by 0.00625) 150 lb/ft is 2.025 ton/yd as 1 yd = 27 ft and 1 ton …
Jul 29, 2019 The most popular 747-400 has a wingspan of 211 feet 5 inches (64.4 m) and wing area of 5,650 square feet (525 square meters). The 747-8 has the largest wingspan of all the variants, measuring 224 feet 7 inches (68.4 meters). That also results in it having – at 5,960 square feet (554 square meters) – the largest wing area of all the 747s.
It takes more than 20 full-grown Douglas Fir trees to build every 1,000 square feet of structure. To find out how many trees would it take to build your house, go to Zillow.com, enter your address and add the square footage, (plus any garage footage) for the total. Then divide the total square footage by 20.33 to arrive at the number of trees ...
Use this million to thousand converter to convert values from millions to thousands where 1 million is equal to 1000 thousands. Enter the value to find how many thousands in millions. See conversion chart and formula for reference.
Details about cubic foot and ton (freight) units: Convert Cubic foot to other unit: cubic foot. Definition of cubic foot unit: ≡ 1 ft 1 ft 1 ft. ≡ 0.3048 = 0.028316846592 m ...
Metric conversion for length, area, volume, weight, angle and SI units converter tool. List of conversion tables and unit converter calculators.
Measuring cubic feet. Width in feet multiplied by length in feet multiplied by depth of grain in feet equals cubic feet in square or rectangular enclosures. 10 ft. width x 14 ft. length x 9 ft. grain depth = 1,260 cu. ft. In circular bins, the formula is: pi (3.14) multiplied by the radius squared, multiplied by the depth of grain = cubic feet.
Mar 08, 2008 For normal loads in residential or office spaces you'd typically size the cooling system at about 400 sq ft per ton. One shop I'm familiar with has 20 tons on 5000 sq ft, with 6 turning centers, 3 4020 VMc's, and one 400mm HMC in that space, plus a few manual machines that are used now and then. Works out to 250 sq ft per ton.
To convert square feet to square meters, multiply the square feet value by 0.09290304 or divide by 10.763910417. For example, to find out how many square meters there are in 1000 square feet, multiply 1000 by 0.09290304, that makes 92.90304 sqm in 1000 sqft. sq feet to sq meters formula. sq meter = sq feet * 0.09290304.
The weight of drywall, sheetrock and plaster can be calculated using the square footage of debris and the thickness of the material. A single sheet of 4 foot by 8 foot, -inch thick drywall weighs close to 50 pounds. Use our drywall weight calculator below to estimate the weight of your drywall and determine the right size dumpster for your job.
Size ranges offered by California Steel and Tube range from ” to 3-3/4 round, from ” sq. through a 4” x 2” rectangle, and from 20 ga. through 10 ga., and up to 40” in length. California Steel and Tube serves customers in the Seven Western States, Western Canada, and Mexico.
This is a conversion chart for cubic ton of timber (Lumber measure). To switch the unit simply find the one you want on the page and click it. You can also go to the universal conversion page. 2: Enter the value you want to convert (cubic ton of timber). Then click the Convert Me button. Your value gets instantly converted to all other units on ...


CBSE had announced that class 10 students in the batch ending in March 2020 will be able to opt between two levels of mathematics in their board exams. The move was aimed to make board exams less stressful and to optimize the assessment as per the future endeavors of the student, that is their desire to pursue mathematics as a subject after secondary school.
The move was welcomed by many for it’s student-centric approach but also caused a lot of confusion. One of the confusions that immediately arose was whether the students be made to appear in two levels of mathematics exam instead of one.
CBSE, in its circular, clearly states that there will not be ‘two’ examinations. The two levels will be ‘Mathematics-Basic’ and ‘Mathematics-Standard’ and students will have the option to choose any ‘one’.
The difficulty level of the Mathematics-Standard exam will be the same as the existing exam and the Mathematics-Basic question paper will be easier in comparison.
The idea behind introducing the two levels or two question papers of varying difficulty levels is that several students do not study Mathematics after class 10 and hence do not need to be tested for the same skills as those who would pursue mathematics on higher levels.


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The new odds were released one day after astronomers with NASA’s NEO office at the Jet Propulsion Laboratory (JPL) in Pasadena, Calif., lowered 2007 WD5’s chances of striking Mars from 3.6 percent to 2.5 percent, or about a 1-in-40 chance, on Tuesday. After analyzing results from a new round of observations between Jan. 5 and Jan. 8, scientists now estimate the asteroid will make its closest pass by Mars at a maximum distance of about 16,155 miles (26,000 km).
JPL researchers said that they are 99.7 percent confident that 2007 WD5 will pass no closer than 2,485 miles (4,000 km) from the martian surface.
What you’ve just read was their confidence interval, a statistical concept. The effect of inaccurate measurements on the predicted path of 2007 WD5 has been drastically reduced by taking a few more measurements. So much so, that they can emphatically declare based on current evidence, that no impact will occur. Before these measurements were taken, the range of trajectories was so broad that hitting Mars was a real (albeit small) possibility. Now the range has been so drastically narrowed that it would take a statistical ‘miracle’ to make it happen.
A confidence interval is pretty simple. It is a range of values (such as heights of pine seedlings) that you come up with after you make a series of measurements – after you collect your data. That range of values usually follows a bellcurve, with the most values right in the middle, with fewer and fewer values the farther away from the average you get. But as a proper statistical study is based on randomly selected samples, there’s a possibility that the numbers you have collected are themselves completely random and can lead you to a false conclusion. Maybe the average height of pine seedlings at X days of age is Y centimeters in height, but you happened to pick 20 really tall ones and came up with a much higher average, Z. The chance of picking so many tall ones rather than a mix of tall, medium, and short is exceedingly small, but there’s still a chance. So you can’t ever, using statistics, say that the average height of pine seedlings is exactly Y. It could be wrong by some tiny (or large) amount.
So instead, scientists calculate a confidence interval. This is a range of values on either side of the mean, or average, that you are confidence the True value is inside of. And your level of confidence is expressed in a percentage. “Confidence,” in the statistical sense, reflects the chance that you are correct – not how gung-ho you may feel when you get up in the morning.
Your typical, run-of-the-mill confidence interval is 95% – this means that the true mean has a 95% chance of being within the range that you calculated. (Say, 10 to 12 centimeters in height) This also means that you have a 5% chance of being wrong. A 99% confidence interval is larger, which makes sense, intuitively – by including more values, you have a greater chance of having the true value in your interval. (Say, 9 to 13 cm) But you can easily see that having a larger interval isn’t necessarily a good thing – where exactly is the average height of pine seedlings when your interval is 4 cm across?
The goal, then, is to get a confidence interval that is as high as you can get, (95…99…99.999…%) while being as narrow as you can get. If you collect more data on pine seedlings, you could maybe get a 99% confidence interval of 10.8-11.2 – which would be awesome. Without that new data, you might have only been 25% confident that the true mean would be in the 10.8-11.2 range. That doesn’t sound good at all, and if you put that in your research paper, you’d get it back from the peer reviewers with a post-it note saying “A little early for April Fools, isn’t it?” But it might be enough to get a grant to collect more data.
In statistics, you learn how to figure out how many observations you need to be able to detect a difference of X amount between one group and another, or one group and a chosen value. So a little data here and there can help you pin down the required sample size – which translates to how much money you require to do your research.
In the case of the asteroid, we’re not trying to impress a grant committee, but trying to get enough observations to be able to tell the difference between the position of the planet Mars on January 30 and the position of 2007 WD5. If there’s no difference in their positions, then we’re due for a cool show. But given the small amount of fuzzy data we started with, we couldn’t be sure that the asteroid would or would not hit Mars because the range of possible trajectories was wide, yet encompassed the red planet. As observations increased, the range was narrowed and it made it possible to rule out the possibility of an impact. Paradoxically, it seemed, the chance of impact increased, but this was an artifact of the way the statistics worked out.
To illustrate what I’m talking about, I’ve made a rough sketch of the asteroid’s likely orbit.
The horizontal black line represents the orbit of Mars, and the small image of Mars represents where the planet will be on the the 30th of January. The Blue spot is the asteroid, and the small blue dots trailing behind it are past observations. At first discovery, there was a wide range of possibilities, and the red area under the bell curve represents the cumulative chance of hitting any part of Mars.
As the observations increased, we became more certain of the position and trajectory of the asteroid. This narrowed the Bell curve, at first increasing the chance that it could hit Mars (late December). Mars was starting the get a little more off-center, but because the bell curve was narrowed, the estimated chance of an impact increased – the space occupied by Mars was a bigger fraction of range.
In Early January, however, many more observations narrowed the bell curve so that Mars was realistically no longer in it. There’s still some uncertainty as to where the asteroid will cross the orbit of Mars, however, we are 99.7% certain that 2007 WD5 will pass Mars greater than 4 thousand kilometers from the planet. To put it in perspective, 4,000 km is about half the width of the Earth, or just over one Mars diameter.
So there you have it, no impact, but still the startling realization that impacts are possible. And now, when scientists talk about confidence and statistical chance – you should be 99.7% certain that you know what they mean!


What Kind of Math Do You Need to Know to Be a Medical Assistant?
Medical assistants do not use math on a daily basis because they focus on administrative and clinical duties. … How Do Doctors… How Is Algebra Used in Nursing? Do You Need to Be Certified as a Medical Assistant? What Kind of Math Skills Do You Need for Nursing?
Medical assistants do not use math on a daily basis because… | eHow
What Technology Is Used in Medical Assisting? What Kind of Software Do Medical Assistants Use? Health & Medical Careers; Medical Assistant Careers; Careers in the Medical Field That Require Math; X. … How is Math Used by…
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What Kind of Math Do Pediatricians Use? By Michael Larkin. eHow Contributor. An understanding of fundamental math and basic algebra are required of those wishing to become a medical assistant.
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How Do Landscapers Use Math?. When you think about what a landscaper does every day, you probably picture physical labor: planting trees, laying patio bricks and trimming bushes. What Kind of Math Do You Need to Know to Be a Medical Assistant?
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While not all doctors have to use math as directly and frequently as engineers do, all of them must understand the complex mathematical equations that inform different medical treatments in order to administer treatments correctly.
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NOTE: Federation is disabled on this instance!You can test federation between the following instances:
A simple, 2-player number guessing game in Python 3.
The Impossible Grid is a Python implementation of a game in which one player chooses a secret number between 1 and 16 and the other player must cover that number on a 4x4 grid, given 3 chances to cover rows of numbers in the grid and a further 3 chances to cover columns. It is designed to appear very simple for the player covering the numbers to secure an easy victory but, in reality, this is impossible as the game cheats upon any attempt to cover the first player’s number.
The Impossible Grid is available under the Apache License 2.0.
Copyright © 2018 UltrasonicMadness.


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As part of the drive to improve the capacities of mathematics teachers, the School of Mathematics of the Tecnológico de Costa Rica (TEC), through the “Renova project”, will be giving a series of virtual workshops for primary education teachers.
Searching for triangles at home, magic to teach mathematics or how to make your own online games, are part of the workshops that the project will be teaching, which aims to provide training and updating in mathematics, didactics and technology to teachers who teach math lessons in schools across the country.
Through the online platform, that is enabled, those interested may select one or several workshops according to their availability at the established times. However, they may participate in a maximum of two workshops, which will be confirmed to each participant via email.
The workshops are completely free, lasting 60 minutes each. They are taught through platforms such as Zoom or Teams, so you must have an active microphone and camera. In addition, some workshops require specific materials at the time of their execution. Space for each workshop is limited, so registration will close once the limit of participants is completed.
Renova is an outreach initiative led by a group of researchers from the School of Mathematics, approved by the Vice-Rector’s Office for Research and Extension and supported by students from the “Teaching of Mathematics within Technological Environments” career, that reinforces content and methodologies proposed in the curricular programs of the Ministry of Public Education (MEP).
For additional questions or doubts, you can write to the email: [email protected].


Click the link below to download a sample Excel spreadsheet I created that can develop sales forecast using a Monte Carlo simulation:
(If you haven’t already, see my post “Why most sales forecasts suck…and how Monte Carlo simulations can make them better” for some background.)
Here’s a breakdown on how it works:
The first sheet illustrates a simplified version of how retail sales forecasts are traditionally developed. Basically, it looks at a couple of historical data sets (sales for the same week the prior year and previous iterations of the promotion we plan to run this week) and develops a forecast as follows:
- Start with base sales from the same time period last year
- Apply the current sales trend (which will be determined in this case by average of the previous 10 week comps). This method may vary from retailer to retailer, but this is the general principle.
- Add the average of the incremental results of previous iterations of the promotion
- Voilà! This is the sales forecast.
Of course, this number is impossibly precise and the analysts who generate it usually know that. However, those on the receiving end tend to assume it is absolutely accurate and the probability of hitting the forecast is close to 100%.
Which is pretty much impossible.
It would be far more accurate to forecast a range of sales with accompanying probabilities. And that’s where the Monte Carlo simulation comes in.
The second sheet in the file deals with the Base Business.
On left side of the sheet are the inputs to the Monte Carlo simulation. Fields highlighted in yellow can be changed to modify the structure of the model. (NOTE: Please don’t change fields not highlighted in yellow as these fields all contain calculations.)
In this simple model, there are three input variables: Traffic, Conversion and Average Order Size. You’ll want to estimate the values and the probabilities of those values for each variable based on what you know about your business.
For example, we might look at five iterations of a particular promotion and determine that we got about 75,000 new visitors three time, 100,000 visitors once and 50,000 visitors once. Traditionally, we would average those and assume we’ll always get 75,000 new visitors. But those variances in this variable combined with variances in other variables, such as average ticket and conversion rate, can lead to wildly different sales. Instead, we can say we have a 60% probability of getting 75,000 new visitors, a 20% probability of 50,000 new visitors and a 20% probability of 100,000 new visitors. We’ll do something similar for average ticket and conversion rate.
Important: make sure your probabilities add up to 100%.
Once you get familiar with how the model works, feel free to add more input variables as suits your business. Email me if you have questions about how to do this.
As you enter your input variable probabilities, you’ll be able to see the results in the charts and the columns to the right.
The pie chart is a simple binary chart to quickly show the overall probability that this week’s base business will be positive or negative compared to the same week’s base business the prior year. In this case, it looks like there’s about a 73% chance our base business will comp negatively to last year (which is probably really an indication that we hit on the high end of the scale last year).
While pie chart is useful as a quick look, it’s not really enough to base a decision on. The line charts show the probabilities at various comp percentage increments and dollar increments to give us a better sense of where the base business will fall, with about a 35% chance of being around 2% down and another 13% chance of being down 10%. The columns on the right under the Probabilities heading give all the breakdowns.
You’ll note there are yellow highlighted fields in the output section. Those fields won’t change the model, but changing them allows for showing probabilities in different ranges as might be appropriate for your business.
At the top right, you’ll see a section entitled “Probability Weighted Expected Value.” This is a single number that is the sum of possible sales numbers multiplied by their respective probabilities. It should be used with caution. It can be useful for comparing different options and for trending of multiple periods, but it should not be used as a specific forecast for a specific time period.
The actual Monte Carlo simulation, with its 10,000 iterations, can be seen below the charts. See below for details on how it works, if you’re interested.
Now that we’ve determined probabilities for where our base business might fall, we can layer in a promotion we might run to increase our odds of growing sales year over year.
The third sheet in the spreadsheet, entitled “Incremental Promo” uses a second Monte Carlo simulation and set up inputs to determine our complete forecast.
This sheet works pretty much like the Base Business sheet, but now we’re feeding a simulation that incorporates the variables for the base business and anything we input here that is generated incrementally from the promotion.
Because we’ve likely only run any given promotion a relatively small number of times previously, we have to be really careful about the estimates we make as a small sample size can yield unpredictable results. We should allow for the fact that the promotion could actually cause at least some of our variables to decrement rather than increment. (I read that one of the problems that occurred in our recent economic meltdown was that many analysts built models that had no allowances for housing prices to go down. Let’s not make the same mistake with our models.) You’ll see in the example data that I’ve allowed for the possibility of both conversion and average order size to be lower than any possibility in the Base Business worksheet.
All of the inputs are now combined with the base business variables to create a new simulation, which can be seen on its own worksheet called “Simulation.”
In the pie chart, we can see that the incremental promotion will increase our probability of generating a positive comp for the week, but we’re still slightly more likely to have a negative comp. Basically, though, it’s a coin toss. We can see with the line charts the various probabilities at different increments of where we’re likely to end up based on what we know. And now that we have a better understanding of our risks and potential rewards, we can make a better decision.
How the model works
The model relies on the RAND() and VLOOKUP functions of Excel. The RAND() function randomly generates a decimal between 0 and 1. We feed that random number into the VLOOKUP function, which references the appropriate “Engine Bins” to determine the variable value it uses. VLOOKUP references the first column of a range (range: Two or more cells on a sheet. The cells in a range can be adjacent or nonadjacent.) of cells (Engine Bins, in our example), and then returns the value from the value column on that row. If an exact match is not found in the Engine Bin, the next largest value that is less than random number lookup_value is returned.
So, in our Base Business example, if the RAND() function returns 0.62467547 for one of the traffic iteration variables the VLOOKUP function will reference the Engine Bins for Traffic, see it doesn’t have an exact match and then reference the Engine Bin with the next largest value that is less than 0.62467547. In this case, it chooses the Engine Bin “0” and returns a traffic variable of 300,000. Because the Engine Bin ranges are based on our input probabilities, we will select the 300,000 about 70% of the time, 275,000 about 15% of the time and 325,000 about 15% of the time. You can see how this plays out in the simulation.
In this particular model, we then determine sales by multiplying traffic by conversion rate by average ticket.
The simulation then runs the calculations 10,000 times in order to give us a very statistically valid sample size. There’s no real magic to 10,000, but it’s a large enough data set to give us a reliable result without being so large that it takes a long time to calculate.
We use this data set to generate our probabilities.
- The mode is definitely dependent on the quality of the inputs, but those are generally easier to estimate than the outputs
- Using the RAND() function will cause the entire spreadsheet to recalculate each time you load the spreadsheet, enter a new value or hit F9. This means all the probability outputs will change slightly each time. But they won’t change much. This really illustrates how we can tame the uncertainty of the future with ranges and probabilities, but it also shows how impossible it is to be extremely precise. All that said, I wanted the model to work for you as you enter new values, so I left the RAND() functions in. In actual practice, you might want to cut and paste the values after into another sheet after you’ve run the calculation just so you don’t have to deal with slightly fluid numbers.
- It could take a few iterations of learning to get the inputs right
- Running Monte Carlo forecasts in parallel with the current method can help to refine the inputs


After students have mastered the concepts of more and less and bigger and smaller, they can begin to assign numerical symbols to collections of objects. Most students come to school already knowing the numerals 1-9. The pages in these bundles help students practice matching numerals with collections of objects. Please see below for a selection of Leveled Lessons for Below Level (basic), and/or On Level (median), and/or Above Level (competent) readers.
Identifying Numerals Up to 10 - Grade K


|Friday, 11 September 2015, 15:48 JST|
TOKYO, Sept 11, 2015 - (JCN Newswire) - Sony Global Education announces that it will host the 2nd iteration of its Global Math Challenge on Sunday, September 27th. Math lovers both young and old can participate in this online math competition anywhere through a computer or mobile device, and test their skills against other math fans worldwide. This competition enables participants to engage their true mathematical creativity. The 2nd Global Math Challenge will be offered online simultaneously in Japanese, English, and Chinese, and with more than 500,000 pre-registrants already, it is primed to become the largest math competition in the world.
Global Math Challenge features carefully selected questions devised by the Japan Prime Math Olympic Committee, an organization with a strong track record in math contests geared towards children. The questions will test participants' creativity and will allow them to discover their true math sense. Global Math Challenge will be offered in 9 different grades of difficulty to best suit the education levels of test takers, from the 1st grade in elementary school through middle school and all the way up to the adult level.
While individual participation was the only registration option publicly available for the 1st Global Math Challenge, this 2nd iteration also officially offers a plan for group participation: Global Math Challenge for Schools. With this plan, schools, learning centers, and other participating organizations will enjoy a number of benefits designed to meet their needs as institutions of learning. When a teacher registers an account for the competition, IDs and passwords are issued for all of his or her students. Furthermore, as a benefit only available to groups, each organization will be able to select the test day of its choice, anytime during the two weeks leading up to the worldwide September 27th date. Score results and global rankings will also be provided both individually and for the group as a whole, illuminating the degree to which each test taker was comfortable with the material as well as how each group fared as a whole.
In China, 17zuoye are delivering the challenge to thousands of young learners across the country, while in the USA, Sony Global Education has partnered with Edmodo, the world's leading global education network, to make Global Math Challenge available to their 54 million members worldwide.
Two plans are available for Global Math Challenge, the free Trial Plan and the paid Standard Plan. With the Trial Plan, participants will now be able to receive not only their score, but their global ranking as well, shortly after the test. And with the Standard Plan, under which up to 4 people can take part using one shared account, participants will also be provided with step-by-step, beautifully illustrated explanations for every question, analysis of their critical thinking strengths, and - for the first time - an extra set of bonus questions.
Global Math Challenge is one of Sony Global Education's initiatives through which it strives to enhance literacy in the STEM (Science, Technology, Engineering, Mathematics) fields among people of all ages. Going forward, Sony Global Education will hold this competition twice a year in order to reach more schools, organizations, and individuals in more countries across the globe, and to contribute to the world of education on a global level. For more information about Global Math Challenge, please visit Global Math Challenge.
Topic: Press release summary
From the Asia Corporate News Network
Copyright © 2023 ACN Newswire. All rights reserved. A division of Asia Corporate News Network.


[Đăng ngày: 09/05/2011]
The Department of Mathematics & Economic Statistics established according to the Decision No.100/QD-DHKTL-HCHC, is the unit for training and technological science activities. We are responsible for the content, quality and progress of teaching and learning Advanced Maths (C1, C2), Theory of Mathemetic Probability and Statistics, Statistical Mathematics, Statistical Theory, Econometrics, and economic forecast.
It is also in charge of developing and improving the content, programs, textbooks and reference materials related to the allotted subjects mentioned.
Additionally, the Department seeks to conduct scientific research, and technological development; and provide services of science and technology under the plans of the School.


Jason M. Howard (jhoward@WPI.EDU)
Sun, 18 Mar 2001 02:41:25 -0500 (EST)
It was interesting to read your email. Is your school also a member of the
national consortium of math and science schools (that really long acronym)?
I was also wondering, are you thinking of attending SVS after high school
(or have you applied to any colleges)?
This archive was generated by hypermail 2.0b3 on Thu Mar 29 2001 - 11:17:06 EST


If I wanted to generate all of that electricity using solar PV panels instead of by saving it through conservation, what would that look like?
If you assume 2.5 kW is the average installation size and you can get 8 hours/day of power at that peak level. To generate 231 TWh of energy would take ~31.6 million buildings.
According to the US Census and Dept of Energy, there are about 124 million residential + commercial buildings in the US. That means you'd need an average installation of solar panels on ~26% of all buildings in the US.
That's 1 in 4.
That's a lot.
If you estimate the average install cost at ~$21.4k (assuming Jan 2010 prices and 50% of total installed cost is the module), then that is ~$676 billion.
That's a lot too.


The Governor Patrick/ Lt. Governor Murray administration announces a $1.6 million STEM grant to UMass Lowell:
Wednesday, December 14, 2011 – The Patrick-Murray Administration today announced a $1.6 million grant to the University of Massachusetts Lowell for the creation of a science, technology, engineering, and mathematics (STEM) teacher preparation program in Massachusetts.
This initiative, outlined in the Commonwealth’s successful Race to the Top plan, will bolster the Administration’s efforts to increase the number of highly qualified STEM teachers in Massachusetts. UMass Lowell will administer the program in partnership with UTeach, a university-based secondary STEM teacher preparation program at the University of Texas at Austin.
“In our knowledge-based economy, it is critical that we get our young people engaged in the STEM fields,” said Governor Deval Patrick. “This program will help us attract highly-qualified teachers who are passionate about STEM education and can help expose students to new skills that will prepare them for success.”
“Raising awareness about STEM education is a major part of our Administration’s efforts to prepare students for careers in STEM related fields,” said Lieutenant Governor Timothy Murray, Chair of the Governor’s STEM Advisory Council. “By partnering with UMass Lowell and UTeach, Massachusetts will deliver highly qualified professionals who will not only teach STEM, but also help ignite students with a spark to pursue opportunities in science, technology, engineering, and math and participate Massachusetts’s future workforce.”
Read the full release here:http://www.mass.gov/edu/2-million-awarded-to-prepare-stem-teachers.html


I was working on some prototypes which required me to animate properties which were not supported by UIKit animators. So I was left with no choice but to build my own animator.
No worthy animator exists without springs. And I knew nothing about springs beyond "they are bouncy!". I had a lot to learn.
I remember looking at those properties of a spring (mass, stiffness, damping, velocity) and had very little idea of what they meant. Creating a spring was more of a guessing game inputting numbers randomly until I got something that worked.
Well let me tell you, it took a LOT of googling to understand these damn, I mean awesome, things! Most articles were super advanced and assumed a greater understanding of math than I currently have. So I wanted to try to write my own post, targeted at designers and developers who like me might not have prior understanding of these principles.
I’m going to try to get as basic as possible, which at times may be too basic for some of you.
I’m also going to explain why stiffness and mass don’t need to be manually set, but it helps to understand springs in order to understand why that is.
Hooke’s Law / Harmonic Oscillators
First of all, let’s forget about the spring in the real world. The springs we know have a size, a thickness and often have something attached at the end of them.
But in mathematical terms I spring is what’s called a Harmonic Oscillator. Basically an infinite wavy curve like this.
To “draw” this curve with math you obviously need to plot the position over time.
So let’s break that down.
If we're drawing a wavy line, it means there a change in velocity going on - acceleration and deceleration. And if there’s acceleration then there’s gotta be a force making it go faster and slower.
A resting spring has no force, so you need to “activate” it by pulling it. How far you pull is called our displacement.
Now that it’s pulled, there’s a force pulling it back to its original position. There’s a special formula to get the force of a spring based on Hooke’s Law.
F = -kx
k is a stiffness coefficient
x is the displacement value (how far the object moved from previous value)
Force = Negative Stiffness Value * Displacement value
Notice that mass is not a part of this force. All we need to define a spring’s force is how stiff it is.
We have the force, so we can calculate the acceleration.
The formula for acceleration is:
a = F / m
Acceleration = Force / Mass
The mass will be a constant, say 1, since we’re assuming our object is not changing weights.
That means our acceleration is:
a = (-kx) / m
Acceleration = (Negative Stiffness × Displacement) / Mass
Now we know the acceleration, we can calculate the velocity of our object at any given time.
To accelerate velocity you need to add the acceleration rate to the previous velocity.
v1 = v0 + a × t
New Velocity = Previous Velocity + (Acceleration × Time Interval)
The time interval when it comes to computers is normally set in frames per second (hertz).
60 frames per second = 1/60 = 0.016666 seconds
Finally, you can calculate the new position.
p1 = p0 + v × t
New Position = Old Position + New Velocity × Time Interval
Do you see how that never-ending wave is formed? The displacement (x) affects our force since F = -kx. So that means that the force will change based on how far it’s displaced, and if the force changes the acceleration changes too, and if the acceleration changes the velocity changes and the displacement changes, which affects the force… 🤯
All it means is that this will go on forever making the oscillator curve with nothing to stop it. Which is obviously not what we want in an animation.
And that’s where damping comes in.
In nature, no spring is perfect like that. There are forces at play like friction and heat. So the springs we are familiar with always stop at some point. That stopping force is called damping.
The damping force formula is:
F = -dv
Force = Negative Damping coefficient × Velocity
In UI animation terms this force is often represented as a number between 0 and 1.
And depending on the value, they even get some fancy names.
- Critically damped Damping = 1 (The most common in Apple UI)
- Over Damped Damping > 1 (Not a good look, not often use in UI animation)
- Under Damped Damping < 1 (The smaller the number the bouncier it gets and the more likes you get on Dribbble.)
Now you just add this dampening force (which will be a negative value) to your spring force, and your spring will stop.
With the new damped force, our acceleration formula looks like this.
a = (-kx) + (-dv) / m
And so you get a spring that looks more like this:
Notice that time is not a variable that we’re setting, and normally when you’re animating something you want to tell it how long it’s going to animate for.
Well, I’m sorry to tell you that springs don’t really care about time. They’ll just take however long it takes them to come to a stop. And that’s a problem for me because I find it more intuitive and feel more in control when I can specify how long my animations will last.
Luckily, math is on our side. Your mass, stiffness, and damping all influence the time it’ll take for the spring to rest.
That means you can technically control the mass / stiffness / damping to match the exact time you want.
The damping coefficient determines how springy your animation is, so you don’t want to mess with that. So you can either change mass or stiffness to control the final time.
So how do we calculate the mass or stiffness to match our time?
To make things simple, you can set one of them to a constant, so I’ll pick stiffness and set it to 5. I want our damping coefficient to be 0.9, and our animation to last 1 second.
That leaves us with one value to calculate, our mass.
But first, in order to reverse engineer the mass value, we need to know how to calculate the duration for the spring animation to come to a rest - called relaxation time.
The formula for relaxation time is
T = 2/𝜻
Relaxation Time = 2 / Damping Ratio
But not so easy, damping ratio is not the same as the damping coefficient we’ve been setting.
The formula for damping ratio is:
𝜻 = damping coefficient / (2 × square root of(mass × stiffness))
Ok, so now we can calculate time, through some complicated math (or Wolfram Alpha), we can calculate that the formula for mass given a relaxation time of 1 second.
Mass =((time)² × damping²) / (16 × stiffness)
So our final values are:
Stiffness = 5
Damping Coefficient = 0.9
Mass = 0.162
And that spring will rest is approximately 1 second. DONE!
I’ve been doing all this in swift and made a little git gist with the formulas.
Note that this is not the actual code or formula used by Apple for UIViewPropertyAnimator(duration: TimeInterval, dampingRatio: CGFloat) method. They do some complicated secret sauce and calculate not only the mass and stiffness but also recalculate the damping value you just set.
So if you apply the formulas above and make an animator and play alongside an UIViewPropertyAnimation you’ll see slightly different results.


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The BrainX Online Learning System was originally fitted with content created by the Orange County Department of Education in direct alignment with state standards for the California High School Exit Exam (CAHSEE). Today, the standards can be easily aligned to any state to meet the requirements of its math and English exit exams.
The system offers several courses in: academic vocabulary, English language arts, and mathematics. Before beginning any of the courses, students take a pre-assessment which generates a report, so they can see what they know and what they still need to study.
The pre-assessment can be used in two ways:
- As students study, they are notified when they master one of the standards that they missed in the pre-assessment.
- Teachers can see the standards that are missed most by students, so they can modify their lesson plans to cover those standards.
This gives students a global view of what they are missing and notifies them each time they overcome one of their gaps for motivation. By providing teachers with standard by standard data for their entire class, they can identify those standards that are least known without having to rely on students to ask for elaboration.
After the global pre-assessments, students take a pre-test for each of the courses. These pre-tests prescribe specific state standard course work that is tailored to each student’s learning needs.
Exit Exams Nation Wide
BrainX has a math and English Language Arts content library that covers standards required for exit exams in every state. BrainX can align its existing content to any state’s exit exam upon purchase.
The BrainX Online Learning System covers all state standards for the California High School Exit Exam (CAHSEE). All of the math and ELA content was created by the Orange County Department of Education in direct alignment with state standards covered on the CAHSEE.
New Mexico- ELA and Math Exit Exam
BrainX has recently been aligned to New Mexico state standards for the English and math portions of its exit exam.


Life is full of uncertainties. So is any real-life mission. Suppose, you are given responsibility of a mission module. How would you systematically evaluate the uncertainties involved in your module? One scientific approach is as follows. First, the events, that might be of your concern, need to be identified. Then they need to be kept under observation for a reasonable period of time. It would produce a data matrix where (i, j)th cell contains required information about occurrence of the ith event at the jth time point. From this data, the uncertainties can be quantified using probabilistic and linear algebraic tools.
Probability Topics - Basic: Combinatorial analysis, Axioms of probability, Conditional probability, Independence, Distributions (discrete and continuous); Advanced: Random variables, Expectation, Law of large numbers, Limit theorems, Random walk, Markov chains.
Linear Algebra Topics - System of linear equations, Vector space, Linear transformation, Inner product, Determinants, Eigenvalues and eigenvectors, Matrix decomposition, Norms.
Class Location and Time Calendar
Location: Room 2204 (at Core 2, 2nd Floor)
- Monday  9 - 9:55 AM
- Tuesday  10 - 10:55 AM
- Wednesday  11 - 11:55 PM
- 5-6 Assignments: 15%
- 5-6 Quizzes: 25% (Best 5 will be considered)
- Mid Semester: 25%
- End Semester: 35%
Syllabus and References
Background reading material will be made available before the respective lecture, if required.


Space Club: Math Adventure (1:00 pm to 1:30 pm)
Let’s put on our spacesuits and travel into outer space with our fellow Astronaut, Elise. We’ll zoom past planets and satellites in our imaginary spaceship as we complete missions and tasks by solving different math problems. Once we get to the end of the journey, we’ll uncover some amazing facts and tidbits about our final destination.
This course will not only enhance the learners’ mathematical awareness and understanding but also equip them with solid problem-solving skills and collaboration skills.
Duration: 6th September, 2021 to 30th September, 2021
Schedule: Tuesdays and Thursdays
Time: 1:00 pm to 1:30 pm (for the 3:00 pm class, please click here)
For Ages: 3 to 6 years old
Class Size: 2 to 6 learners
Supply List: None
Guidance: Adult supervision advised, but not necessary


Prior to the early 1980s, all running events were run in yards. Since running event records exist in both meters and yards it is necessary to convert these earlier performances.
The basic procedure is that of interpolation, taking the following steps (I've also given an example below):
Suppose a person runs the 100 yard dash in 12.1 seconds. Since the time is only in seconds, we can skip step one above. The yard conversion factor from the table below is 91.44. Dividing 12.1 by 91.44, we obtain an answer of 0.1323272. Multiplying this answer by the race distance of 100 meters, and then rounding to the nearest tenth of a second, the final time becomes 13.2. Running a 100 yard dash in 12.1 is equivalent to running a 100 meter dash in 13.2.
Calculating the yard conversion factor
The yard conversion factor is simply the result of converting the distance in yards into its equivalent distance in meters. For example, take the distance of 100 yards. 100 yards is the same as 300 feet, which is the same as 3600 inches. Since 1 inch equals .0254 meters, 3600 inches equals 91.44 meters. That is, 100 yards is equal to 91.44 meters (making 91.44 the conversion factor for 100 yards).
The table below lists the yard conversion factors for each race.
(equivalent meter distance)
|100 yards||91.44 meters|
|110 yards||100.584 meters|
|220 yards||201.168 meters|
|330 yards||301.752 meters|
|440 yards||402.336 meters|
|880 yards||804.672 meters|
|1760 yards (1 mile)||1609.344 meters|
|3520 yards (2 mile)||3218.688 meters|