Come and relive your childhood with this classic silly game that really is just as easy as it seems. Practice comparing number values with this mud hoppin' game. To get started, try choosing a game that reviews a subject they've already learned to give them some extra practice. Sight Word Bingo. Help kids learn to identify these features with this silly newspaper article. Kids must use subtraction skills to craft perfect pizzas in this game. This quiz-style game is great to waste time and just have some layback entertainment. 1. Whether your child is just starting their educational journey in preschool or taking the leap into 5th grade, our collection of games will help your child … Kids practice borrowing in this three-digit subtraction mountain-themed game. Kids must help Cuz-Cuz and Birdee read bar graphs in this colorful data game. With our diverse range of learning games, your child will have a blast building essential skills in math, reading, writing, digital literacy, and more. Math is a crucial subject to learning success, which students will continue through each grade of their school journey. These activities have proven to be great suggestions for parents of children with RAD (reactive attachment disorder). Mice or mouses? Try these 10 fun active learning games to help your child learn sight words and more! Switch the game by using one verb as the starter word. Kids create compound words to feed Roly in this matching game. Kids practice putting apostrophes in irregular and commonly misspelled nouns in this sea-themed game. Text features highlight important facts in sources of information. In most of our keyboarding games it's possible to choose which keys are practiced during the game session. Text with Teens The actions must be selected so that at least one will be impossible for each child and they will need a substitute. They ask the child to illustrate what this fast-moving looks like. Copyright © 2020 Education.com, Inc, a division of IXL Learning • All Rights Reserved. In addition, simply putting a tune to an activity can be a fun game that … Take advantage of our wide array of options by letting your child explore outside their grade level too. Once their minds are warmed up and their basic skills sharpened, challenge them to take the plunge into learning a new skill. Forget dull and dry lessons that you have to convince reluctant students to complete. With adventures in every skill from counting to algebra, calculations to fractions, and much more, these interactive math games will have your students growing their knowledge while they play to win and beat their high scores. You can configure our games to use only home row keys and we also have a few games in a special homerow category. Whether your little learner is just starting to recognize numbers, count, and solve simple addition and subtraction problems, or they're diving into beginning algebra, geometry, and numbers with fractions and decimals, Education.com has a game to challenge your child's skills wherever they are on the math journey. Help this little robot make new friends -- literally -- in this game that works on beginning sounds. In my Kindergarten classroom we do the “colour game” where when my child presses any colour on his AAC device we all have to run around and touch something of that colour. Kids must move quickly to catch eggs for Farmer Brown, organizing and displaying the data using bar graphs in this silly game. Your child will love playing to earn points, win the games, and set high scores, and you will love seeing their knowledge grow as they set off on the path to becoming lifelong learners. Older students will enjoy more advanced challenges, like solving equations with fractions and mastering the keyboard. They'll have so much fun racing that they'll forget how much they're learning. Kids practice finding products using arrays in this delicious math game. Yum! The child must then create a sentence that makes sense, including a verb, capital letter and punctuation. This technique can be applied to help the child learn about self-control. Play hide and seek. Ditch the dry lessons and let learning games transform study time into an adventure students will want to go on again and again! Paint each other’s faces withRead More It begins with the therapist explaining what self-control is and describing how it is sometimes difficult to maintain our self-control if we are moving very fast. With activities suited for preschool through 5th grade, your students will build foundational skills in everything from counting to reading comprehension, fractions to basic coding, and much more. Cuz-Cuz needs your help! Songs. Quick Games = Better Learning. The Command Card game, used in Montessori schools to help teach young learners how to follow simple instructions, is another easy and entertaining game for fostering recollection skills 1. Kids sort 2D and 3D shapes in this engaging geometry game. Kids practice identifying numbers 11 to 20 in this demolition game. Kids build blending and spelling skills to help get the gang to school in time. Kids must sort short and long vowel words at the toy store. The Command Card game, used in Montessori schools to help teach young learners how to follow simple instructions, is another easy and entertaining game for fostering recollection skills 1. Introduce your younger learners to important concepts in an accessible way, such as letter recognition to build writing skills. Also Read: 15 Easy & Fun Christmas Party Games For Kids With hundreds of cheerfully animated and professionally designed games, your child will be asking to play one more round again and again, while you watch their math skills and confidence grow. Get your students excited about learning with our collection of teacher-designed educational games. Aside from harnessing their musical abilities, songs also help children learn new words. For example, use the words "dog" and "brown" and have the child complete the sentence. Kids use shapes to create mosaic designs. Guide him through the mud by identifying sight words in this colorful, interactive game with audio support for early readers. Have clear rules and enforce them … Active learning will not only help your child retain the sight words, but will also develop skills such as critical thinking, communication, collaboration, creativity, innovation, self-regulation, and working memory. With our diverse range of learning games, your child will have a blast building essential skills in math, reading, writing, digital literacy, and more. The activities in these boxes can help improve your child’s eye-hand coordination, sense of direction, vocabulary, and other soft skills at the right age. Yum! Give your child a head start for more advanced math practice by showing them that they can actually enjoy solving equations!


INTRODUCTION TO BOOST GEOMETRY LIBRARY
Boost Geometry is a general purpose library written in C++ providing concepts, components and algorithms developed for solving computational geometry problems. Boost Geometry is a generic library implemented using modern and portable C++ generic programming techniques and built upon foundation of C++ Standard Library and Boost C++ Libraries.
Generic and modular design of the Boost Geometry library kernel as well as agnostic approach achieved for coordinate dimensions and coordinate systems of geometry objects promises degree of scalability and extensibility. Rich set of geometry models delivered already by Boost Geometry can be easily complemented through adaption of user-defined geometry types according to concepts defined by Boost Geometry. Users can also extend existing set of algorithms.
Boost Geometry project introduced and adapted a concept of extensions. Extensions are dedicated mainly for developing domain-specific tools based on Boost Geometry kernel.
Originally, the library was developed by Barend Gehrels and Bruno Lalande and published in 2008 as Generic Geometry Library (GGL). Mateusz Loskot joined the project in 2009. In October 2009, the library was submitted to Boost project with request for formal review. In November 2009, Boost Community accepted the Generic Geometry Library to the Boost collection under the name of Boost Geometry. The library is available under the terms of Boost License.
The presentation is supposed to give accessible introduction to design and applications of the Boost Geometry library.
Mateusz Loskot - Cadcorp Ltd.


By R. Adams and C. Essex
Read Online or Download Student Solutions Manual for Calculus: a Complete Course PDF
Best calculus books
This CBMS lecture sequence, held in Albany, big apple in June 1994, aimed to introduce the viewers to the literature on complicated dynamics in larger measurement. the various lectures are up-to-date types of previous lectures given together with Nessim Sibony in Montreal 1993. The author's motive during this ebook is to provide a diffusion of the Montreal lectures, basing complicated dynamics in larger size systematically on pluripotential thought.
- A Basic Course in Probability Theory
- Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling
- Calculus. Introductory Theory and Applications in Physical and Life Science
- The collected mathematical papers of Arthur Cayley
- Calculus and Analysis in Euclidean Space
Additional resources for Student Solutions Manual for Calculus: a Complete Course
Equation Solution Indicial Equ. x ( ; 1) = 0 2 2 = y = Jn (ix) = In (x) n2 y00 + x1 y0 ; 1 + nx2 y = 0 6 00 3 ; 2 2 y ; x2 y = 0 y = C1 x + C2 x ; =6 00 3 y ; 6y=x = 0 essential singularity x = 0 ;6a0 = 0 2 2 = a2 y00 + x1 y0 ; xa2 y = 0 y = C1 xa + C2 x;a +2 0 3 c = ; ( + )(2+ +2 1 (2 ; 1) = 0 y00 + x2+1 x y + 2x y = 0 ;1) c ;1 2 c ;2 y00 ; 21x y0 + x2x+12 y = 0 c = ; ( + )(2 +2 2 ( ; 1)( ; 2) = 0 ;3)+1 c xy ; 3 2 00 0 y + 3x y + 3 = 0 c = ; ( + )(3 +3 ;1) 3 (3 ; 1) = 0 (n; )c = 0 1 ::: =0 y00 ; xy0 + ny = 0 c +2 = (;+1)( +2) Due to the recurrence formulae one has c +2 =c !
12) This term describes the work done by the external forces when the points on the plate are displaced by the displacement u. 16) This is the plate equation for weakly varying thickness h(x y). 11), a consequence of Hooke's law, comes from. There are people believing that these fundamental laws are preexistent in nature (or have been originated by a creator). Modern natural philosophy tends to another view. So mathematicians know that di erential equations are invariant under special transformations of coordinates.
2003 byCRC Press LLC Problems 1. Using y(x) = z (x) + b transforms the inhomogeneous boundary value problem y00 (x)+y0 (x)+y(x) = a y(0) = 0 y( ) = 0 into an homogeneous equation for z with two inhomogeneous boundary conditions. (a b are constant parameters, it will turn out b = a). 2. Now use inhomogeneous boundary conditions y(0) = 2 y( ) = 1 and try to homogenize both for b 6= 0. (z 00 + z 0 + z + b = a z (0) = 0 b = 2 but z ( ) = ;1. 3. DSolve[y00 [x]-y[x]-1==0,y[x],x] y x] ! 16) and then an homogeneous boundary condition.
Student Solutions Manual for Calculus: a Complete Course by R. Adams and C. Essex


Calculate maximum 3d-print speed
The problemThe slowest link in 3D printing is the hot end, which cannot melt enough filament from a speed x. Therefore we have to calculate the maximum flow rate of your hot end based on the maximum melting rate mm³ / s. Once we know this, we can calculate how fast you can print with your 3D printer without having to struggle with extrusion.
Determine maximum print speedIf we know the maximum flow rate of the hot end, we can use this formula: Recommended maximum speed = maximum flow rate / (layer height * extrusion width) to calculate the maximum printing speed. Let's assume that we have a maximum flow rate of 13.86 mm³ and we want to print with a layer height of 0.2 mm and a layer width of 0.48 mm. Now we can use this calculation 13.86 / (0.2 * 0.48) to calculate the max speed, in this example we can then print at a maximum of 144 mm / s.
Increase print speedSometimes things can't go fast enough and you want to print faster. However, this requires the hotend e.g. To modify E3D-V6 to this hot end there is the extension Volcano or Super Volcano due to the larger melting zone the printing speed can be increased considerably


Calculating heart rate from ekg strip
Measure and Calculate Heart Rate on a 12-lead ECG
The second method can be used with an irregular rhythm to estimate the rate. Count the number of R waves in a 6 second strip and multiply by 10. For example, if there are 7 R waves in a 6 second strip, the heart rate is 70 (7x1070).
How Do You Calculate a Six-Second Rhythm Strip on an EKG
A heart rate can be calculated from a sixsecond segment of an EKG strip by counting the number of R waves in the section and multiplying by 10, according to RnCeus. com. Each small square on an EKG strip's horizontal axis represents 0. 04 seconds, so a sixsecond segment is 150 squares long.
How to Calculate Heart Rate on an EKG
Jun 02, 2018 From the length of a heart beat on the ECG trace, you will be able to calculate the heart rate. A normal heart beat contains a P wave, a QRS complex, and an ST segment. The one you will want to pay particular attention to is the QRS complex, as this is the easiest one to use to calculate heart rate.


My recent visions have been showing complex combinations of etheric cubes, and how the cubes align with each other to form different resonances or different vibrational energy signatures. The cubes come in from different angles, and then rotate (move) into different alignments. It seems the main combinations being shown are the constructs of 9d, 19d and 27d worlds.
We know from observing the etheric energy around people that there is an etheric cube surrounding them that is an aspect of their higher self. It is their personal energy signature. We’ve also observed how energy travels between people through the form of etheric tubes. When several people are nearby each other, you can see it quite clearly how the etheric cubes also intersect each other, which is like standing inside of each other’s energy field. At other times, you can see how the tubes connects the cubes together from a distance.
The following image is something that I drew up that’s one of the main combinations I’ve been seeing. It seems to me to be showing the complexities of the 9d Mirror World…. This image is a very basic representation, because the way it really looks isn’t a two or three dimensional drawing, the real thing’s a multidimensional rotating energy field. Energy is always moving within it.
Each cube represents a person… but also represents a specific resonance or inner-dimensional world. I believe each cube is actually a 6d or 9d form, or each cube represents 6 resonances within a 9d form. So, the overall image could represent a group of 9 people, or could be 9 aspects within one person. Both are possible. But what I find amazing is that the math always seems to point back to a 9-dimensional reality.
If you look at each cube as a 6d form:
6 x 9 = 54
5 + 4 = 9
If you look at each cube as a 9d form:
9 x 9 = 81
8 + 1 = 9
Even if you look at it as each cube being only a 3d form:
3 x 9 = 27
2 + 7 = 9
Hypercubes have been drawn before by mathematicians as a representation of the 4th dimension…
But even if you look at each cube as being a 4d form, you still get 9d.
4 x 9 = 36
3 + 6 = 9
Now, if you look at it as being 6 resonances (6 sides) within each cube, and each cube representing a 9d form, and you have 9 cubes connected… you get:
6 x 9 x 9 = 486
4 + 8 + 6 = 18
1 + 8 = 9
A person could stop at 54 and add 1 to represent the overall whole, which would be 55 (another number we know of). Or, a person could stop at 27 and add 1 for the overall whole, which would be 28.
5 + 5 = 10
1 + 0 = 1
27 + 1 = 28
2 + 8 = 10
1 + 0 = 1
It’s enough to fry your noodle, but we’ve been shown many things about the cubes and how they compose reality. It seems to me the vision of this 9d hypercube is explaining the rotations through a 9d hyperspace, which eventually lead to a 27-dimensional hyperspace reality, or a single unified field, much like quantum physicists theorize.
© 2009 Khris Krepcik
All Rights Reserved


If you are here, you must be aware of technical analysis. Anyway, to brush up on the concepts, you can visit the first part of this blog series on technical analysis here. This is the second part, where we will be walking you through the concepts that facilitate technical analysis.
What are technical indicators?
The opening and closing prices of a stock are not just any random events. They represent the behaviour of the market participant and the price trend. Traders perform mathematical calculations using this price data to come up with insights about stocks.
Although you will always see technical indicators being used in a candlestick chart, you should remember that technical indicators do NOT depend on any particular chart. Yes, candlestick charts make technical indicators more useful, but these indicators can function independently of the chart.
What is the moving average, and what is its importance?
The underlying concept of moving average is similar to that of the basic average taught in schools. However, it gets slightly complex as it is used in technical trend analysis. Nevertheless, the moving average is widely used because of its effectiveness and ease of understanding.
Here, the closing prices of a stock, over a certain period, are added. The sum is then divided by the number of closing prices taken into consideration. This gives the average of the closing prices corresponding to the specific period. Since the average is continuously updated as time or day passes, we call it a ‘moving’ average.
Moving averages are used by market participants to estimate the support and resistance of a security by examining the movements in its price. The moving average is also known as a lagging indicator. This technical indicator reveals the earlier price movement of an asset. Such data helps traders and investors decipher the probable directions of the security price.
What are the different types of moving averages?
There are four types of moving averages-simple moving averages, and exponential moving averages.
1. Simple moving average: A simple moving average just takes the closing prices of a stock over a fixed number (usually 20) of minutes, hours, weeks, days, or months (or even years) and then calculates the average of those prices. The average is recalculated every passing minute, hour, week or month. So, the Simple Moving Average forms a trend line over the specified period.
This is what an SMA looks like –
Disclaimer: The trademark TradingView belongs to the company
2. As you can see, the ups and downs in the SMA are in line with the ups and downs in the price of the stock.SMA helps you to identify a downward or upward trend in the stock price movement. However, the Simple Moving Average is not very effective in identifying such a trend before it becomes apparent. This is where Exponential Moving Average comes in.
3. Exponential moving average: The Simple Moving Average gives the same weightage to all the price points. What if we give more weightage to the recent price points? The curvature of such a moving average will be more pronounced. This is what an Exponential Moving Average does.Look at this –
As you can see in the circled part, EMA is more sensitive than SMA. When the SMA was still moving up, EMA displayed a reversal.
To calculate EMA, you need to use this formula:
EMA = (Closing price – Previous EMA) * Multiplier + Previous EMA
Here, the multiplier is the one that determines how much weightage should be given to the recent price points. Usually, it is taken as 2/11. In case the previous EMA is not available, use SMA.
4. Weighted moving average: In the case of the weighted moving average, weights are assigned to each data point depending on its age. The most recent ones get more importance. Unlike a simple moving average, the weighted moving average is more sensitive to price changes.
5. Hull moving average: Preferred by many traders, the hull moving average is a directional trend indicator. It is a combination of all weighted moving averages. Similar to WMAs, it also focuses on recent price points rather than historical ones. Its developer, Alan Hull, claimed that HMA eliminates lag and gives a dynamic moving average that helps identify dominating market trends.
Different applications of moving average:
- The primary purpose of a moving average is to identify price trends before they become apparent.
- Once the price trend is identified, the moving averages help traders make informed buying or selling decisions.
- Specialised moving averages can be used to identify the direction of a trend.
What is a moving average crossover?
In the moving average crossover system, a trader combines two moving averages, and this system is known as smoothening. A common example is combining a 50-day EMA with a 100-day EMA, where the shorter moving average is referred to as the faster-moving average, and the longer one is called the slower moving average. It helps traders to lower the number of trades in a sideways market.
|Moving averages are the building blocks of many other technical indicators. This is why we focused on them in such a detailed way.|
Other Common Technical Indicators and Their Applications:
1. Relative Strength Index (RSI): RSI is technically known as the ‘momentum indicator,’ However, it is used to identify whether a stock is in an overbought zone or oversold zone. To calculate RSI, you first need to find out the average of up closes and the average of down closes. Then, you need to divide the first result with the second one. An RSI of 70 indicates that the stock is in an overbought zone, while an RSI of 30 indicates that the stock is in an oversold zone.
2. Elder Force Index: You can also identify oversold or overbought conditions by examining the volume of trades. The Elder Force Index does this. The EFI is calculated by dividing the volume of up closes by the volume of down closes and then multiplying the result by 100. An EFI of 70 indicates a strong buying pressure, while an EFI of less than 30 indicates a strong selling pressure.
3. Bollinger Bands: One of the overlay technical indicators is the Bollinger Bands, developed by technical trader John Bollinger. It is a technical analysis tool represented by a set of trendlines. This tool helps traders when an asset is oversold or overbought. Three lines are plotted, where the upper and the lower bands are two standard deviations, positive and negative, respectively. The middle band is the simple moving average. Based on the security price’s vicinity towards the upper or lower line, traders determine if the market is overbought or oversold.
4. Volume-weighted Average Price (VWAP): It is a measure of a security’s average price over a trading period. VWAP is used on intraday charts that reset every day when the market opens. Mostly useful in short-term trading, this single-line indicator gives insights into the trend and value of a security’s price.
There are several tools that facilitate technical analysis. However, developing a thorough understanding of each of these indicators is important before diving deep into the market. From portfolio risk management to identifying trend changes, you can find all the help you need in the Dayco app.
Hope you found the article useful!
If you have a question, share it in the comments below or DM us or call us – +91 9051052222. We’ll be happy to answer it.


The fundamental unit of electric energy consumption per unit time is the watt, in which we express the power rating of an electric appliance. For example: your color TV set might use 200 watts; a kitchen can opener, maybe 180 watts; the frost-free refrigerator, perhaps 400 watts; your dishwasher-1,300 watts; and, that deluxe, super hair dryer, the one your daughter dims the room lights with, can use a whopping 2,000 watts.
A kilowatt (kW) is 1000 watts, so that monster hair dryer consumes power at the rate of 2 kW.Power is simply the rate of consumption. Think of your car. If your velocity is 60 mph, this is your rate of travel. Keep that rate of travel up for one hour and you will have traveled 60 miles. Run that dryer continuously for 1 hour and you will have consumed 2 kWh of energy. Energy is power summed over time. Run your TV set for 1 hour and you end up using 0.200 kWh of energy.
Here is a little simple math to help you understand:
Let’s do some math.
Run your TV set for 6 hours a day for an entire month, and your energy bill for that usage will be:
In this example, we assume our cost for electricity is an average value of a dime a kWh, which is not a bad approximation for a residential customer. Certainly with higher electricity costs, higher operating costs result; the same with greater hours of usage.
Now for the super hair dryer-
Let’s say your daughter uses it for 15 minutes every day for one month, so 30 days times 0.25 hours per day is 7.5 hours of usage for the month. Here we go….
As you can see, just because an appliance uses more power, it does not mean it will use more energy, unless you know how long the appliance operates. The TV costs more to operate, yet it is ten times less in power consumption than the super hair dryer; but the TV set is on many hours more than the hair dryer.


Adult Height Predictor
The BoneXpert adult height prediction (AHP) method is founded in the classical Bayley-Pinneau method from 1952, but it includes various improvements in the math and the underlying clinical data, and it adds various features, including some from the more recent Tanner-Whitehouse-3 method.
From gender, age, height and bone age, it predicts the adult height. Optionally, one can enter parental height, which improves the accuracy.
The uncertainties of the predictions of adult height are given as a standard deviation (±SD), i.e. the true values will be within the indicated range with 68% probability.
The predictor is intended to be used with Greulich-Pyle (GP) bone age determined by BoneXpert; however, it can also be used with manual GP bone age, but the uncertainties of the predictions are then considerably larger than indicated, due to the rater variability.
Enter the Adult Height Predictor here:
The tool gives four different adult height predictions
They all depend on population height.
The most accurate of these predictions is highlighted in green and shown on the growth chart:
- AHP(x-ray) is the prediction based on age, bone age and height
- AHP (parental) is the prediction based solely on the parents’ heights. This is similar, but not identical, to the conventional “target height” (which is mid-parental height ± 6.5 cm), but it is more accurate, because it includes a drawing towards the population height
- AHP(x+p) is the prediction based on age, bone age, height and parental height
- AHP(x+m) is the prediction based on age, bone age, height and height at menarche
- A large discrepancy between AHP(x-ray) and AHP(parental) indicates that the child grows differently from what is expected from its parental heritage, i.e. it could be a sign of disorder. The evaluating of this is the task of a pediatric endocrinologist – the tool implements the most accurate statistical model, but is not in itself a diagnostic tool.
The Age of Peak Height Velocity (APHV) and the growth path
For Caucasian children, the tool also predicts the APHV, and based on that it draws the most likely growth path from the current height to the predicted adult height in a growth chart.
The nine population groups
The AHP depends on the ethnicity, and within each ethnicity it depends on the assumed population height. One can choose among nine population groups. There are five Caucasian populations with different population heights.
For the Asian Chinese and Asian American populations, the tool uses a preliminary AHP model presented at ESPE 2012. For Hispanic and African-American ethnicities, the Caucasian AHP model is used, which renders it only approximately correct.
The choice of population also affects the computation of standard deviation scores (SDS).


Lissajous curves (http://en.wikipedia.org/wiki/Lissajous_curve) are two dimensional figures where the points (x,y) are defined by sine functions with different coefficients:
x = sin(t)
y = sin(at+b)
By modifying a and b over the period t, a wide variety of fascinating curves can be drawn, some of which look almost 3D!
For example, if y is a sine wave that is exactly 90 degrees offset (“out of phase”) from x, the plot is a perfect circle:
x = sin(t)
y = sin(t+pi/2)
In the lab, an oscilloscope is the ideal instrument for plotting x and y coordinates. Typically, an oscilloscope will plot the voltage of an primary input on the y axis vs. time on the x- axis.
However, most oscilloscope will allow you to supply an external input that will allow you to directly control the x axis. We can connect a function generator to both the x and y axis and begin to draw Lissajous patterns.
By shifting the frequency and phase of the signals, you can get different shapes. However, even at the office we don’t yet have two (working) function generators which can be phase locked. In the picture above, you can see that we’re using a HP33120A and a HP 200AB. The 33120A has a trigger input, but no such luck for the old-school 200AB. With some fiddling, they can be brought into phase, but it’s much easier and more fun to build our own frequency generators. That’s where the DAC Shields and an Arduino come in.
The DAC Shield has inputs for positive and negative power and an output for the signal. For this exercise, we’ll be using two bench power supplies (Mastech HYB3003 and Mastech HYB3003), but you could also use two batteries.
The output of one shield is connected to the X-axis input of the ‘scope the other is connected to the Y-axis. On the Tektronix 2246 shown here, channel 1 can be set to drive the X-axis.
The trick to initially plotting a circle is to make sure that the amplitude of both axis move the cursor equal amounts, so make sure to set both “volts/div” settings the same.
To start with a circle we simply write a program that generates a sine wave at a given frequency on channel 1 and then creates a second sine wave on channel two which is 90 degrees out of phase.
While this pseudo code is close, some considerations have to be made due to the discrete nature of the DAC. For instance, the resolution of the DAC will determine the value of the minimum output, zero and the maximum output. In this case we have a 12bit DAC with positive and negative supply rails at 10 V and -10V, respectively. Writing a “0″ to the DAC will result in an output of -10V. Similarly, writing “2048″ will output 0V and “4096″ will output 10V.
Thus, we need to scale our original pseudo equations:
write (channel1, (sin(t) * 2048 + 2047))
Where t = 0 would be 2047, t=pi/2 is 4096 and ….
Another consideration is the base frequency for the sine wave; this will depend on how fast you can write to the DAC and how many cycles it takes to compute the sine wave. Inserting different delays between samples of the wave generates different frequencies. For example if you the second channel is doubled in frequency from the first you will generate the following shape.
Also by increasing the phase of one the the sine wave though every iteration of the loop the figure can be animated as seen here on a Rigol MSO4050 in which we are evaluating.
Example source code and schematic for the DAC shield can be found on Github here, Also the Power DAC Shield can be purchased from Tindie.


Caption for Sandoval Robotics Picture: (front left) Brittney Meyer, Cherokee Ray, Tori Koehler, Alicia Tarlton, (back left) William Pennington, Edwin Kingston, Caralina Guidish, Mickayla Schulte. Submitted Photo.
Sandoval High School Starts Robotics Program
Math teacher Rose Brandmeyer says they were looking for ways to improve the STEM (Science, Technology, Engineering, Math) program at the school and came up with the program after attending a robotics seminar. "We knew the kids would get into it. Plus it involves computer programming in which I did some of that as well. So it's just a way to get something that the kids would be interested in doing that would increase their math and science skills", said Brandmeyer.
During 4th hour Study Block, a group of sophomore, junior, and senior students meet to build and program their robots. The students use LEGO Mindstorm sets that were purchased through the School Improvement Grant as well as other building materials. While working, the students are confronted with problems that require them to integrate math, science, and STEM technology in order to find solutions. Students also learn cooperation, teamwork, compromise, and responsibility.
Brandmeyer says they are hoping to compete in robotics competitions in Carbondale and Edwardsville later this year. She says right now the kids are just building robots. "The goal is after Christmas that they'll probably be given a task and they'll have to build a robot to do that task. This will help them start thinking creatively how to solve problems to hopefully build their thinking skills and that their thinking skills will become sharper", said Brandmeyer.
The program is asking for donations of LEGOs so they can build more robots. Anyone interested in donating can call 618-247-3361.
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Before you order your sod, you must first calculate how many square feet of sod you will need for your site.
To begin your calculations, sketch your site onto a piece of paper, and mark off areas into geographical shapes (front yard, back yard, side yard 1, side yard 2, etc). Then, with a tape measure or wheel, measure the dimensions (length, width, diameter, etc.) of each shape, and record those on your sketch. Next, enter the dimensions in our measuring tool below to calculate total square feet.


If you missed our 13th Annual International Women’s Day Forum, hosted in partnership with the U.S. Department of State, fear not – we are sharing key moments and takeaways here.
Let’s start by examining closely our workforce today and why we don’t have an inclusive and diverse tech workforce:
As the demand for Science, Technology, Engineering and Math (STEM) jobs continues to grow, companies need to focus on sustainably building equity into such opportunities. Discovery Education strategically partners with like-minded organizations, such as the Caterpillar Foundation, to deliver engaging learning experiences every single day to classrooms in the U.S. and across the world to foster more pathways for STEM careers.
There’s no denying that the world has undergone major changes in the past year that have affected individuals, families, communities, the workforce and the economy as a whole.
Digitally driven careers are for everyone.
Shaping the future – and diversity – of the science, technology, engineering and math (STEM) workforce starts with education today.
Research shows that young girls like STEM subjects, but as they get older, something changes. They start feeling like STEM isn’t for them based on outdated stereotypes about the fields of science, technology, engineering and math.


The debate in Washington over the U.S. debt ceiling. The euro zone's struggles with Greece (and vice versa). The Arab spring. Investor's views of News Corp's value following revelations of phone hacking by journalists at one of its newspapers.
Perhaps less easy to understand is why it's important to understand mathematics in order to master economics.
Incoming students who have been taking the SAIS Online Math Tutorial this summer, with the help of seven DVDs covering 86 modules, may be asking themselves that question. As might prospective applicants.
I asked Prof. Erik Jones about this relationship between mathematics and economics. Here is what he told me:
If you're tempted to wager that the connection between mathematics and economics is relatively recent, think twice. The use of math in economics dates back at least to the 17th century before hitting its stride in the 19th.


If the "resistors" are real resistors, than you can use U = RxI to determine what voltage will be applied...but if you don't have the resisotrs value (it is often around 56 Ohms), that won't help
Actually, you don't need to know the resistance, you only need to know the ratios. In this case, one resistor gives 7V across the fan and 5V across itself. Two resistors therefore gives (7/(7 + 5 + 5)) * 12 ~= 5V across the fan.
That's assuming the resistors are in series. If they are in parallel then it will be (7/(7 + (5/2))) * 12 ~= 9V


On Monday, May 24, 2010, the ONCE organization launched a new lottery called Super Once Ya (now called Super 11). It was the version of a very common game in casinos, called Keno.
The Super 11 (Super Once) is a product of the active game modality, formed by a matrix of 85 numbers (80 numbers until October 01, 2023), numbered from 1 to 85, in which we must choose between 5 and 11 numbers from the matrix, being their order indifferent.
A draw gives a Winning Combination formed by 20 numbers out of the 85. There are 7 types of bets depending on the amount of numbers chosen: 11, 10, 9, 8, 7, 6 or 5. With these elements you can opt for the corresponding prizes, depending on the type of bet, the amount in euros bet and the number of successes obtained.
The price per bet is €1 per draw, regardless of the number of numbers played. The highest prize that we can obtain is 1.000.000 euros although we have the possibility of playing up to 10 euros per combination with which, a winning combination of 11 numbers and 10 euros bet, would make us win a whopping 10.000.000 euros. The more numbers chosen, the higher the prize to be won!
There are different prize categories depending on the type of bet you wish to participate and the number of correct guesses of the Winning Combination of 20 numbers. In this table you can see the corresponding prizes according to the amount of numbers played and the number of hits. It should be noted that if we do not match any of the chosen numbers, we will be entitled to a refund of the amount played, except in the categories of 11, 10 and 9 numbers where the prize is 2€.
|Number of Hits||Numbers Played|
We discover with mathematical formulas, the combinations and options of winning in this game, as well as comparing it with others.
Get all the information on the output of numbers, broken down by Months and Years, since this Game started in 2010.
Results of all Super 11 (Super Once) Drawings since 2010 with relevant information of each Drawing, sorted by Drawing and day.
Check your favorite combination among all the ones that have come out and find out if it has already come out and how many times.
We will address the predictive analysis of this game with computer programs, in order to establish a winning strategy.
Shortly, we will open a Super 11 (Super Once) pool to be able to play with more combinations and more probabilities.


0 = ∞ ?
- Project team: Hrvoje Čop, Miro Roman, Luka Vlahović
- Year: 09/2004
- Location: space
- Area: 250 m²
- Type: research
One's perception of thier surroundings is relative to their own position. Human beings are able to understand four dimensions (length,width, height and time), and perceive those dimensions through their senses. It is possible to calculate more of them mathematically, but not to comprehend nor feel more than those four.
Extremes have the same effect on humans. The examples of effects of two opposite elements, like the ones given above, suggest that the same rule could be applied in the following situation:
Following this assumption, and considering the fact that humans cannot understand more than four dimensions, IF ONE COULD DESIGN A HOUSE OF ZERO DIMENSIONS, IT WOULD CREATE AN ILLUSION OF A HOUSE WITH AN INFINITE NUMBER OF DIMENSIONS.
The house is designed in such a way to negate the four comprehensible dimensions, and thus becoming, in effect, a house of zero dimensions.
The house has the shape of an icosahedron. It is the result of combining a sphere with a system of opposing mirrors. Its surface is 250 m2. Its radius is 4.9 m. It is positioned in universe, where weightlessness works with the mirrors to make impossible for one to understand the space within, nor to determine their position and time in the space. Because one does not have a sense of volume, they are disoriented. They see themselves simultaneously reflected from an infinite number of angles. Since time is always perceived in relation to some fixed event, their existence being the only absolute thing, there is nothing else they could use as a reference point for determining time.
Space is defined by three dimensions. Those dimensions are reflected and multiplied an infinite number of times within the icosahedron. With every reflection being slightly different than the previous one, we achieve a fractal space of infinite variety - a house of infinite dimensions.


SAT vs. ACT: Which one should you take?
Most colleges accept scores from either. Both exams measure your verbal and math abilities, but the ACT also tests you on the natural sciences, and it has a smaller math portion...
Most colleges accept scores from either.
Both exams measure your verbal and math abilities, but the ACT also tests you on the natural sciences, and it has a smaller math portion.
You can try taking practice tests of both to see which works better for you (see www.gocollege.com).
Beginning this spring, both tests will have a writing component. The SAT will require a timed essay in March, but the old version of the test will be offered until January. That means this year's junior class has the opportunity to try both. Some colleges will only accept results from the new exam, while others will take your single best section scores from either the current or new test.
ACT will begin offering a writing test in February but it's optional. Some colleges will require the results, so be sure to check with the schools where you're applying before deciding whether to take it.
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|Haga clic aquí para ver enlaces a sitios en español.
Here's our collection of useful web sites!
Disclaimer: MathNerds is not responsible for the content of sites
other than our own. We believe the sites mentioned here contain reliable information, but
you should use your own judgment. Don't believe everything you read, especially on the
Our Photo Gallery includes pictures from recent MathNerds activities!
MathNerds Mentoring Network
The MathNerds Mentoring Network is an exciting new project for linking school district
classes to university classes to support local school districts and better prepare future teachers.
Top 5 Web Sites
These are the web sites that we refer people to most often; one of them probably already had the explanation you are looking for.
Covers all aspects of high-school algebra in detail.
Fractions, number bases, polynomials, matrices, solving, tips on word problems.
Dr. Math FAQ Answers nearly all Frequently Asked Questions in math. Some examples include: compound interest, names of big numbers, names of polygons, how to get started on a word problem, how to organize a two-column geometry proof, a vast table of geometric formulas (areas, volumes, etc.), N to the zeroth power, division by zero, why negative times negative is positive, and why study math.
MathWorld An online math encyclopedia, it answers nearly any question that asks "What is ...?"
Math Forum A great site for teachers. It includes lesson plans, activities, science fair projects, discussions of teaching methods and Problem of the Week.
Cut The Knot! A more advanced site that shows how to solve many classic and challenging problems. Things you will find here : 38 proofs of the Pythagorean Theorem (including President Garfield's), the 12 coins (or 12 bags of gold) problem, constructions with ruler and straightedge (and why some angles cannot be trisected).
Maybe your question has already been answered! Check out these archives of answered
The MathNerds own archives Contains all the questions
that have been answered by the MathNerds. Often the same question gets asked several
times; see if your question is already answered in the archives!
Cardano's formula for the cubic One of our most popular
requests: what's the formula for the roots of a cubic equation?
Why is m used
for slope? Another popular request: why do we use the letter "m" for the
slope of a straight line?
Ask Dr. Math A very large archive and good search
engine. The Dr. Math FAQs are especially good.
Cut The Knot! This site focuses on
problem-solving techniques, and includes solutions to a number of intricate problems.
About 500 articles in all areas of mathematics, covering intermediate and advanced topics.
A help site for all kinds of science questions except mathematics; includes FAQ and searchable archive.
Find answers to your Physics and Computer Science questions here!
Nick's Mathematical Puzzles
A site with many interesting and challenging mathematical problems. Each entry
has hint, answer, and complete solution.
Automated Answering, Online Calculators
All the MathNerds are human, but there are some clever computers out there that can
work (some) math problems too, and give you an instant answer.
QuickMath An automated service that
uses Mathematica to give immediate answers to
various kinds of algebraic and symbolic problems.
Yahoo! financial calculator links There are an
enormous number of financial calculators online (for example, mortgage, amortization). Go
to Yahoo! and search for the desired kind of calculator, for example, mortgage calculator.
MathServ - Mathematica Web Server
Site that uses an online version of the Mathematica program to do various symbolic and
WebMath Automated answers in many categories up
through calculus. Includes compound interest. Interesting site because the automated
answer not only gives you the answer but shows step by step how to get it.
Cryptarithmetic Puzzle Solver
Cryptarithms are puzzles like SEND + MORE = MONEY where each letter stands for a single
digit and you are asked to find the meaning of each letter. This site solves addition
cryptarithms for you.
All Kinds A collection of on-line calculators
for every purpose: scientific uses, currency conversion, time, unit conversion, and lots
Derivatives Anyone?An automated site that helps you
with long multiplication,long division, and derivatives. Integrals coming soon!
Financial Calculators, including a College Savings Calculator
Handy to show to your folks to see if they are saving enough to send you to college!
Math Words and Definitions
math encyclopedia. An excellent resource for looking up words and concepts; often goes
into a great deal of detail on the math involved. Try this one first!
AltaVista search engine Mathematics is very well
represented on the Web, and often you can find definitions and explanations simply by
searching with a general-purpose search engine like AltaVista.
Google search engine Another good general-purpose
Extensive descriptions of all areas of mathematics, indexed in several ways including by the
Mathematical Subject Classification (MSC) used by
Mathematical Reviews and Zentralblatt für Mathematik.
A collaborative online encyclopedia, it has very good coverage of mathematics topics (and much else).
Math History and Biography
Online Math Books
Good Math Software
MathGV Free function graphing program for Windows.
Plotting Software Free downloadable
software for differential equations, statistics, geometry (2 and 3-D), plotting, voting
methods, network analysis, games, linear algebra and more!
Number Sense Computerized Software for sale that helps with number sense and UIL competition preparation, written (and used for many years) by Larry White, friend of MathNerds.
The MathNerds use a method called Discovery or Inquiry-Based Learning, where we try to
lead you to discover the answer for yourself. Read more about this method here.
Academy of Inquiry-Based Learning an
association of professors, instructors, teachers and non-teaching supporters (such as retired professors or teachers
having IBL experience, administrators, foundation personnel) who are committed to developing and disseminating
inquiry-based learning (IBL) techniques.
Creative Teaching: The Heritage of R. L.
Moore A book-length biography and study of R. L. Moore and the "Moore
method" of discovery learning. Originally published as a print book by the University
of Houston in 1972, now available online in several digital formats.
Discovery Learning Project Two sites in
one! The Discovery Learning Project tracks various projects that use and encourage the use
of discovery methods. The Legacy of R. L. Moore site traces the influence of Robert Lee
Moore (1882-1974), a famous proponent and practitioner of discovery methods of teaching.
Personal experiences with
discovery learning methods Everyone who teaches by discovery or inquiry-based methods
does it a little differently. This page (part of the Legacy of R. L. Moore site) contains
about 30 short notes online and references to about 30 more. Teachers give their
experiences using these methods and their impressions of their own teachers who used the
R. L. Moore: Mathematician & Teacher (Amazon.com listing)
A new (2004) biography of R. L. Moore, by John Parker.
Exercises and Drills
SOS Math Lots of good explanations, examples, and
drills. Especially good on fractions and polynomials. Covers algebra, trigonometry,
calculus, and several advanced math areas.
Worksheets Generates worksheets with algebra problems. (No answers though, so you'll
have to check your work yourself.)
A+ Math Mostly arithmetic. Has flashcards,
FreeMathHelp.com The name says it all; help in various categories including flashcards, worksheets, mini-lectures, and more.
MathStories.com Hundreds of story problems
with answers. Elementary school level. This site is not free, it requires a subscription.
Based Problems in Calculus These problems have a higher level of complexity than
traditional text book problems and foster use of a computer algebra system. Each problem
set includes discussions of related teaching issues and solutions worked in Mathematica.
Multiflyer A nice site that uses a game to teach basic multiplication.
Aunty Math Challenging problems for K-5 students; a new problem every two weeks.
Math Forum Problem of the Week New problems each week in many categories, aimed at grades 3 - 12.
For true reference resources, universities often have excellent information.
For Parents and Teachers
(Also see Discovery/Inquiry Learning above).
Math Forum A very large site with lots of good
information for teachers (also useful for parents). Lesson plans. Internet resources.
Problem of the week.
Mudd Math Fun Facts A collection of over
100 fascinating math tidbits that lead into broader areas of mathematics.
Merlot A site with links to an assortment of sites,
including mathematical sites. Includes a reviewing system so you can see if other people
liked the sites before you go.
Learning Disabilities Online - Math Skills
A collection of articles on math learning disabilities.
Dyscalculia is another name for math learning disabilities. This site has a variety of resources,
including diagnosis methods and ideas for treatment.
NCTM Illuminations Project
Several hundred classroom projects for grades K-12, tied to the NCTM
(National Council of Teachers of Mathematics) standards.
CRAFTY and Curriculum Foundations
CF is a project to find out from other disciplines what they expect their students to be
taught in math. This site contains all the reports, by discipline.
Single-purpose sites and specialized references.
On-Line Encyclopedia of
Integer Sequences Search engine and database of sequences; tell it your sequence and
it will attempt to identify it.
Tablas Mathemáticas de David
Explicaciones y diccionario en español.
MathDork Interactive math lessons with multimedia
razzle-dazzle. Has some free samples, but most of the material requires you to subscribe
and pay by the month.
Search MAA journals via Harvey Mudd
Search Site Index and abstracts for Mathematics Magazine and College Mathematics
Jen's Stem-and-Leaf Plot Instructions and
Jen's Box-and-Whisker Plot Instructions and
Jen's Line Plot Instructions
Simple, clear instructions on how to draw these statistical charts.
Statistics at Square One
An online statistics textbook; includes data display (including all kinds of statistical charts),
descriptive statistics, hypothesis testing, correlation and regression, study design.
Emphasizes biomedical applications.
Covers all aspects of high-school algebra in detail.
Massachusetts Institute of Technology is gradually placing all their course materials online.
Metric System Unit Conversions
(see the links at the bottom left of this Dr. Math page) All about the metric system and how to convert units.
Dr. Math lists all kinds of formulas for two- and three-dimensional figures: area, perimeter, volume, much more.
Print Free Graph Paper Many styles of free, printable graph paper perfect for homework, tests, sketches, craft projects and more.
How to Type Math on a Computer
A thorough description of the conventions to use when typing math.
MathBits Devoted to offering free
teacher/student worksheets, including stuff on Geometer's Sketchpad,
Math and the Movies, Graphing Calculator, algebra and geometry.
Fun Math Stuff
Mudd Math Fun Facts Fun Mathematics
Problems from Harvey Mudd College. Ask for a random Fun Fact and see if you can answer it
The Mathematics Quotation
Server Consists of a large collection of information on both contemporary and past
mathematicians (and some non-mathematicians).
ZomeTool Really cool mathematical building toys - think mathematical Legos.
Fun Nerd Stuff


N.B. all benchmarks were measured on a Surface Pro 6, with an i7-8650U CPU at 2.1GHz, 4 physical cores and 16GB RAM.
Our open source library, barretenberg (https://github.com/AZTECProtocol/barretenberg), contains an implementation of TurboPLONK over the BN254 curve. This variant implements Pedersen hashes using our fixed-base scalar multiplication gate. We benchmarked barretenberg against the current fastest Groth16 prover that also supports the BN254 curve, Bellman. TurboPLONK is approximately five times faster than the Groth16 implementation.
When comparing raw constraint counts, TurboPLONK requires 5 times fewer constraints than an equivalent R1CS-base SNARK
It should be noted that a TurboPLONK constraint requires approximately twice as much prover 'work' than a Groth16 constraint. 20% of the Groth16 constraints are also bit decompositions; these binary gates are approximately 4 times as expensive for the prover in TurboPLONK than Groth16. (Since PLONK doesn't have the property that the scalars in prover computation are actually equal to the witness.)
Under this model, the TurboPLONK prover should be approximately 2.25 times faster than Groth16.
The remaining speed advantage between the TurboPLONK prover and the Groth16 prover can be explained by considering the relative speeds of the two libraries when computing multi-scalar-multiplications in G1, where the bulk of prover time is spent
Using original techniques for performing this algorithm, Barretenberg can compute over 1 million scalar multiplications in < 1 second on average consumer-grade hardware.
Pippenger's multi-exponentiation algorithm is the fastest known method to compute a multiple scalar-multiplication over different bases. Our new contribution is the observation that, when computing multi-products, using the affine point addition formula requires substantially fewer field multiplications than formulae for projective and jacobian coordinates.
When evaluating affine point addition, the formula is:
Computing requires a modular inverse, which is orders of magnitude more expensive than a field multiplication.
However, the Pippenger multi-products can be arranged to produce sequences of independent point additions. That is, the outputs of additions in the sequence are not inputs to any additions in the sequence.
This allows for the use of Montgomery's trick to compute batch modular inverses
Assuming a sufficiently large , the cost of a batched modular inverse is 3 field multiplications per inverse. This produces a cost of 6 field multiplications to compute a point addition. For short Weierstrass curves, the traditional mixed-addition (projective) formula requires 11 field multiplications.


Download Citation on ResearchGate | Foundations of differentiable manifolds and Lie groups / Frank W. Warner | Incluye bibliografía e índice }. S. A. ROBERTSON. FOUNDATIONS OF DIFFERENTIABLE MANIFOLDS AND LIE GROUPS. (Graduate Texts in Mathematics, 94). By FRANK W. WARNER. Foundations of differentiable manifolds and Lie groups. Front Cover. Frank Wilson Warner. Scott, Foresman, Frank W. Warner Limited preview –
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Introduction to Linear Ahd Gilbert Strang. Learn more about Amazon Giveaway. Most recent customer reviews. Read more Read less. Linear Algebra Georgi E. Write a customer review. Differential Geometry for Physicists and Mathematicians: Graduate Texts in Mathematics Book 94 Hardcover: Foundations of Differentiable Manifolds and Lie Groups.
To learn more about Amazon Sponsored Products, warner foundations of differentiable manifolds and lie groups here. In fact, the organization of Chapter 5 is more suitable for self-study than for being taught in class lots of theory developed first, with all applications delayed until the end. Differential Geometry of Curves and Surfaces: In particular, the section on cochain complexes could have been incorporated in the rather short de Rham Cohomology Chapter 4, so that MV could have been proved and used to compute the cohomology of spheres beyond the circle.
Foundations of differentiable manifolds and Lie groups Frank W. Warner
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ComiXology Thousands of Digital Comics. Spivak and Lee are quite wordy and do not have the same breadth. Fiundations mention is made of Mayer-Vietoris or Kunneth formula, even though the former follows easily from the section on cochain complexes in Chapter 5 and the latter with some effort from Chapter 6.
Topology and Geometry Graduate Texts in Mathematics. Description Foundations of Differentiable Manifolds and Lie Groups gives a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups.
Foundations of differentiable manifolds and Lie groups
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Foundations of Differentiable Manifolds and Lie Groups
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Everytime I see this picture posted, I become angry. Especially when it is tagged #education. Can you imagine something similar being posted by teachers about reading? Why do teachers and adults think it is okay to perpetuate the idea that it’s okay to be bad at math? It’s not. And we need to stop the excuses and become better teachers. If you teach math, and you’re not a good math teacher, get better. Stop making excuses.
I definitely feel the need to reblog this. Something that has really been bothering me lately is when people (especially professors) say, “I’m just not a math person.” I hope that when I start teaching math, I am able to convince students that they aren’t “not math people”. Everyone can get something out of math, especially if it’s taught in a way that makes it accessible to students who don’t necessarily thrive in an environment of computations and procedures.
[Too relevant to queue]
Numeracy, like literacy, is a crucial aspect of every single subject area you could possibly think of. It’s not ok for someone to teach with the philosophy, “I’m not a kid person”, yet just as our jobs require we deal with children constantly (and draw positive outcomes from each and every interaction), every lesson we teach children will be imbued with some aspect of numeracy (assumed, or explicit) that will be necessary to succeed.
Oh, and in a sort-of-side-point-but-not-really: If, as a teacher, you can read and interpret your paycheque; you have mathematical ability. If you can do your groceries, and estimate before reaching the register how much you are likely to owe, and whether you will be able to afford that into your budget, you have mathematical ability. Not only that, but you almost certainly have a greater level of ability (not to mention experience) in these matters than many of your students. If you can impart some of this mathematical expertise, skills and values on to your students, you will be doing them a valuable (and necessary) service for their later lives.
Here’s the thing, additionally:
We know that if we tell our students consistently that they are good at something, they will have more confidence, and thus approach the subject differently than if we tell them they are poor at it. Positive feedback gives positive results; negative feedback gives negative results.
It’s similar with ourselves. And if someone thinks their students will never KNOW that they feel this way about math just because they never say it aloud, they are kidding themselves. Their attitude about the subject will permeate the way they approach the subject — their tone, the amount of time and effort with which they approach it, the emphasis they put on the subject’s importance in general for their students.


Ernst Lindelöf presented in 1908 a
conjecture known as Lindelöf hypothesis which concerns
the order of the Riemann zeta function on the
“critical line” . Up to now (2015), this
hypothesis has not been proved. It is weaker than the Riemann hypothesis such that this latter implies it but not conversely.
Lindelöf hypothesis. for every when .
Here is the Landau big ordo notation.
- 1 Ernst Lindelöf: “Quelques remarques sur la croissance de la fonction ”. –Bull. Sci. Math. 32 (1908).


This number tracing book is great for children who are just starting to learn how to count, or to improve kids’ penmanship skills using a dot-to-dot tracing method. We’ve included helpful directional arrows to make it easier for children to learn how to properly write their numbers. With multiple lines of dot-to-dot letters on each page, kids are sure to grasp the concept of writing each number from zero to twenty in no time.
What to expect in this activity book:
- Learn to write the numbers from zero to twenty.
- Trace and color illustrations that match the corresponding number.
- Fun activities that include more tracing, counting, and coloring.


In 12th century Italy, a man known as “Fibonacci” developed a simple mathematical system, derived from ancient Indian teachings, to explain the complex algorithms, sequences and equations that make up the spiral pattern, one of the oldest and most enigmatic sacred images known to man.
If you look closely at things, you’ll find Fibonacci spirals everywhere: tree branches, sea shells, flower petals, pine cones, romanesco, galaxies, human DNA; it’s mind boggling how prevalent spirals are in nature.
While at the beach the other day, we created a Fibonacci spiral of our own, using a square piece of paper to create a grid structure in the sand, and stones to build the actual curve. If you get the chance, please watch the video above. We didn’t make it ourselves, but it’s a visually stunning, crafty and informative video. It directly inspired this to-do of ours.


Price: £95 (NON OASA Students)
Price £75 (Existing OASA Students)
Please choose the correct option on payment.
For some years our students have said they have found the maths in GCSE Astronomy a challenge. Although we do not regard it as rocket science, we thought we could knock up a course which not only helped tackle the demons of the maths involved. But also provide the student with some introduction to the GCSE Astronomy itself and the process, like the Observational Tasks. The aim of the course is to not only prepare the student for the maths involved but also so they know what is expected when the move on to take their course with us.
Topics covered include
Kepler’s Laws of Planetary Motion
Measuring Circumference of the Earth
Distance to the Stars
The equation of Time
Depending on the learner it can take up to 3- 6 months to complete.
Please note the price is £95 for non OASA students. If you are an existing student please contact us before enrolling.
There is an end of course quiz with a certificate at the end


Most of us are familiar with the work of Dutch graphic artist and mathematician M.C.Escher. He is most famous for his so-called impossible structures such as; Ascending and Descending (see above), Relativity, his Transformation Prints, such as Metamorphosis I, Metamorphosis II and Metamorphosis III, Sky and Water I or Reptiles.
In this short film Spanish filmmaker Cristóbal Vila has made a three minute work inspired by Escher, a piece that imagines how Eschers workplace might have been like;
what things would surround an artist like him, so deeply interested in science in general and mathematics in particular
277 total views, 1 today


Maths Long Term Plans
Take a lesson with Professor Von Hans!
Written multiplication! Click here!
Through our mathematics curriculum we enable children to:
- become fluent in the fundamentals of mathematics. For example knowing number facts and times tables off by heart.
- reason mathematically. This involves our pupils explaining their thinking and testing out theories.
- solve problems. Our pupils participate in regular problem solving activitiy to enable them to apply mathematics in a range of situations.
These documents show the core teaching for each year group over the course of a year.


GeoGebra 3D 6.0.726.0 Final Lifetime Version Crack 2022 Download
Everything available in GeoGebra is interwoven to become a powerful and enjoyable tool for understanding and solving any problem about geometry. Through a combination of direct teaching tools and online educational material, geometry offers an enormous potential to become a pivotal and successful educational tool for students, parents and teachers. By combining all the relevant contents in one intuitive geometric environment, GeoGebra allows users to navigate and tackle even the hardest of problems in mathematics. It can improve collaboration between students, teachers, parents and all those who are interested in mathematics.
As part of BYJUS, we are really enjoying the integration of GeoGebra into our learning material and app. But what really grabbed us were the toolset and the wide variety of resources. The only thing we missed was a better, more flexible math program.
GeoGebra comes with various tools, such as programs to simulate and analyse geometric structures, like cylinders, cones, planes, spheres, and cylinders. GeoGebra comes with a variety of amazing tools, which allow for the construction of 3D geometric models using any of the previously mentioned shapes. For example, one can easily create a prism, a cone, and a hemisphere.
Furthermore, GeoGebra makes it possible to view and compare properties and surfaces in 3D, including areas, volumes, and moments. These are only a few of the amazing capabilities of this stunning mathematics program.
GeoGebra offers a seamless integration with our online and offline editing of forms, models, graphics, and equations . It is simple, secure, powerful and above all FREE. You can use it on your computer, online or even on the go. With GeoGebra you can create and collaborate on multiple forms, models, graphics, equations and other content in the cloud. You can transfer forms over a network, you can access it anywhere and you can share it easily through social media.
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Geometric (box, line, rectangle, angle, triangle, circle, ellipse), numeric (number, %, currency), and text.Each chart is treated as an independent sheet, allowing you to create a detailed, interactive flowchart of your data. You can use as many sheets as needed, as well as a custom format or simple text, as well as edit the values in the cells or append a new one. For example, you can use this application to draw various signs, thermometers, and other things. The user can add text, tables, and graphs.
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GeoGebra Crack is a useful and powerful graphing software. You can create mathematical constructions in this program. You can use an input device to define parameters. Thus, you can quickly solve problems. Furthermore, GeoGebra can be an interactive with others to plot functions, work with sliders to investigate parameters, find symbolic derivatives, and use powerful commands like Root or Sequence.
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Cactus Hands Is a fun way to tell time by counting fingers, IF your fingers were made of cactus and were growing in pots!
You can tell time by counting the fingers on each cactus. Of course, with only five fingers per hand, it can get a little tough to count to 8! So sometimes there will be two hands per digit.
Designed by @hollowheadart in Portland, Oregon, a town nearby to Plaid’s hometown of Boring. More of @hollowheadart’s work can be seen in other Clockinator faces, and on his website at http://hollowheadstudio.com.


Hint: look and say sequence!!!
II. បង្ហាញថា 1+1=3
I. As I said it is look and say sequence…the next numbers are gonna be like this:
The first number is 1. If you were to describe this number to
someone who was writing it down digit by digit, you would say:
Write down a single one – that is, one one.
Put them together: one one:11
and repeat the steps you will have the next number: two one: 21
one two one one:1211……keep repeating!!
II. Let me say first of all that there is no real proof for the statement
1 + 1 = 3. You cannot use correct mathematics to prove an incorrect
let . then
Now we know that 1 = 1, so add the following three equations together:
1 = 0
1 = 1
1 = 1
On the right is 1+1, and on the left is 3 ones, and 3 ones make 3.
Ref: Dr. Math


Two of the biggest obstacles to learning Data Science are for most people. The first is that we must learn how to code and the second is mathematics. Maths has been a bully in our school days so we might be more hesitant to learn it. We will be tackling that bully by learning why maths is important and what it can do for us. It isn’t difficult to learn.
There is a story. There was once a wild horse. Anyone who attempted to mount it would be thrown off. It scared everyone. It was so fearful that many people didn’t even attempt to control it. Alexander was born. Alexander soon learned to ride the horse with his wits, and soon became one the most skilled riders in Macedonia.
Later, he died from malaria -Alexander, and not the horse.
What does this have to do with Mathematics?
Most people don’t bother trying because they have heard it’s difficult.
It is easy to master if you have a little humor.
Mathematics is your ticket to success.
An analogy such as the one above can be used to motivate (for the first 30 minutes of starting), but it is not enough to motivate the effort towards learning Mathematics.
It is a requirement to become a Data Scientist.
The following is a long answer if you aren’t convinced to learn mathematics. First, maths are necessary for modeling and measurement. It is simple to measure. Dairy milk starts from 10 Rs and Mt Everest measures 8848m in height (a little more than Maria Sharapova). The modeling is what can scare you. Imagine Tony being three times taller that Moni (Tony = 3-Moni). This was not alarming. However, I would say that the equation for height is just as under-estimating.
This is how a mathematical model might look. It is important that you can read it in plain English. It states that y depends on both number x and number z. It is the sum of three times the value x squared, three times the log of x with base 2 and three times the constant e raised up to the power z (negative means invert this and use the fraction), as well as the rate of change for y with x at that point.
This equation is infinitely easier if we know that x = 16, z = 1, and that the rate of change for y is 13. You only need a calculator to find your value for y.
What is our ultimate goal? Is it to solve this equation, or write similar ones? Answer- Neither. This is the job for the machine. Your job is two-pronged.
To help your clients understand that y depends on x, a bit on z and none on a variable called t.
This equation will have many solutions. The machine will solve it, not you. Take a look at these solutions and decide which one you want for your goal.
Second, you must be able to compare two things when learning mathematics. Let’s say that you want to find out how much each product is selling. You are told that Toffee and Chocolates are very popular. This information is crucial. Can you make a decision? Maths can help you understand the situation by rephrasing it. For example, Toffees have an annual demand of 3,000,000 units and Chocolates have an annual demand of 19,000,000 units. Toffees and Chocolates are strongly correlated. Therefore, supplying 10,000,000 units of Chocolates will result a decrease in demand for product A to 2.6 millions units.
We can also raise the price of Toffees 10 percent. This will result in a decrease in total sales by 3 percent. However, the price to the company will drop by 17 percent. This will increase our total profit by 9 per cent. (Isn’t that common sense? Sales may decrease if manufacturing costs have decreased. In this case, total profit may actually rise. It is important to find the sweet spot where the universe conspires to make you and/or your company rich. Data Science and math can help you do this.
Maths are also available


This page is about numbers in Welsh. Including the cardinal (counting) and ordinal (order) numbers. Each of which is used in a different situation.
|Thirteen: tri ar ddeg
|Fourteen: pedwar ar ddeg
|Sixteen: un ar bymtheg
|Seventeen: dau ar bymtheg
|Nineteen: pedwar ar bymtheg
|Thirty three: trideg tri
|One hundred: cant
|Three hundred and sixty: tri chant chwedeg
|One thousand: mil
Here are some examples in Welsh for the cardinal numbers above.
|Two thousand and fourteen: dwy fil a pedwar ar ddeg
|One million: miliwn
|I'm thirty years old: Rwy'n drideg mlwydd oed
|I have 2 sisters and one brother: Mae gen i dwy chwaer ac un brawd
Now we move on to the ordinal numbers, which helps us organize things by order or rank.
|Eleventh: unfed ar ddeg
|Thirteenth: trydydd ar ddeg
|Fourteenth: pedwaredd ar ddeg
|Sixteenth: unfed ar bymtheg
|Seventeenth: ail ar bymtheg
|Nineteenth: pedwaredd ar bymtheg
And here are a couple sentences related to the ordinal numbers above.
|English is my first language: Saesneg yw fy iaith cyntaf
|Her second language is Spanish: Sbaeneg yw ei ail iaith
After this lesson about the numbers in Welsh, which included cardinal and ordinal numbers, now we move on to the next subject below. You can also choose your own topic from the menu above.


- Revise the curriculum to provide a calculus pathway, a statistics pathway, and a quantitative thinking pathway. Many students who would have previously taken college algebra would now take one of two courses: social and behavioral science majors would take statistics, and arts and humanities majors would take a course in quantitative reasoning.
- Improve college advising through the creation of "meta-majors" with similar core and math requirements, and use multiple measures (beyond a sole placement score) to determine a student's readiness for college-level mathematics.
- Support and develop instructors to teach pathway courses, especially the increased number of introductory statistics courses that will be needed.
- Use multiple venues to improve communications about the pathways and their recommended use.
Lieutenant Governor Joe Garcia led off the conference with comments about Colorado's successes in preparing undergraduates and our continued need to prepare more. Reflecting on a particular reform effort during his time leading Pikes Peak Community College, Garcia remembered a proposal to shift from three to four remedial courses prior to a gateway math course. When he looked at the data, he learned that fewer than 10% of students enrolled in remedial courses were actually making it to the gateway course. At Pikes Peak and elsewhere in Colorado, there has traditionally been more focus on enrollment and revenue generation than actually getting students through their programs. For an unfortunate number of students, they find themselves able to complete everything in their program except their mathematics requirement, and that is why the work of the Math Pathways Task Force is so important.
Dean Allison, the math department head at UNC, discussed the growing need for graduates to interpret and analyze data. For this reason, he and the task force want to join a national trend that moves away from college algebra as the default math course and towards courses in statistics and quantitative reasoning. This will require a lot of effort on the part of departments, advisors, and instructors.
The task force has been working with the Dana Center at the University of Texas at Austin, a national leader in mathematics education who has been working with multiple states on math pathway revisions. Uri Treisman keynoted the conference to describe some of the efforts, trends, and findings he's seen across the country. He said that math was currently under two different spotlights: the first, a harsh spotlight, that shows a lack of completion and high failure rates, and a second, a positive spotlight, where students with skills in mathematics are more successful negotiating rough job markets and becoming upwardly mobile in society.
Treisman continually stressed that the reality of today is different than the reality of 10 or 20 years ago. Right now, three times as many students take calculus in high school (almost 25% of all high schoolers) than in higher education, and those students tend to succeed at high rates in college. Studies of transcripts reveal that those succeeding in college calculus almost certainly took calculus in high school. Only about 1% of students going beyond college calculus to a higher level course (like differential equations) started college in college algebra. We've been placing students in college algebra to start them on a path towards math-intensive majors, but almost no students are actually following this path to get there. It's not that we haven't been trying to make this path work, either. At a meeting of community college leaders in Ohio, Treisman had the group list all the various initiatives for improvement that they've tried. They managed to list a total of 81 initiatives, most of which lasted 2-3 years, and zero of them were sustained long-term. People work hard, but too often people vital to the effort move elsewhere, money dries up, or 4-year institutions don't cooperate.
|Uri Treisman and Amy Getz, comparing the success rates of a co-requisite support model vs. a pre-requisite support model.|
Treisman recommended four coordinated innovations needed in new pathways:
- Relevance: Too often college advisors accept students' wishes when it comes to course placement, rather than really trying to align the student's interests with the mathematical skills required of various majors. Placement tests haven't helped this, either. Said Treisman, "No longer should a placement test ensure a student is misplaced into a course, supported by a criminal enterprise of testing companies."
- Acceleration: We've been trying to help students catch up by slowing them down in remedial courses, but we've learned that about two-thirds of students can succeed in regular courses when they're given proper support. There was a belief that these supports would ensure success for all students — a belief that was "polished by hope and unfettered by data" — but we now recognize that to see success for this other third of students it will take a national, Manhattan-type project to figure it out.
- Narrow the gap between support and instruction: At Northwest Vista Community College in Texas, an advising "SWAT Team" crashes classes to confront students about why they're enrolled in the class they're in. About a quarter say it's because it fit their schedule, not because it's the class they need. They also aggressively supply support to students in the first three weeks of a course, before students slip behind or think there's a stigma about asking for help.
- Introduce evidence-based strategies into instruction: Treisman says this may very well be the hardest part, yet it's less important relative to the structural improvements needed and described above.
Amy Getz, also working with the Dana Center, spoke passionately about needed shifts in our thinking. We need to think beyond the classroom and past our old ways of unnecessary prerequisites, predictable outcomes, inconsistent course alignments, and a lack of clear messaging about math requirements.
The rest of the day was structured around breakout sessions and whole-group debriefs of those sessions. In the morning, the breakouts were organized around each of the quantitative reasoning, statistics, and calculus pathways. In the "StatsPath" breakout, I learned that the CU-Boulder math department is preparing to drop college algebra altogether, knowing that the easiest way to get advisors to stop recommending it would be to eliminate it. The discussion moved towards the details of the content of a prerequisite course students might take before statistics, but Uri redirected the conversation back to structural elements, which led to good conversations about transfer credits, the need for leadership, and developing the capacity to offer new courses. People in the quantitative reasoning breakout talked about how to work with partner disciplines, while the calculus path group reported on various ways to provide student support.
Afternoon breakouts centered on issues of advising, degrees with designation, and on-ramps for under-prepared students. With advising, we talked about the need to coordinate higher ed and high school advising, and to see if the meta-major model really helps advisors and students make decisions about the math courses that align with student interests. The degrees with designation group talked more about working with partner disciplines to determine the learning outcomes they want and why, and putting people in positions to advocate and create change in the system. The on-ramps group focused on issues of communication, including things like email lists, websites, blogs, virtual open houses, and coordinating with organizations like the Colorado Mathematics Association of Two Year Colleges (ColoMATYC), the Colorado Association for Developmental Education (CoADE), the Rocky Mountain Section of the MAA, and CCTM.


Teaching Math to a classroom with students with developmental disabilities can be a challenging task. The cognitive functioning level most often varies from student to student.
I wrote this subtraction song in hopes that the lowest functioning students would grasp the concept of subtraction by the fact that subtraction means "take away". This can be taught in numerous ways. Real visuals are most helpful and the student can be taught to "take away" something from a box or bin.
All students enjoy playing subtraction with some sort of reward (subtracting with skittles, m&m's, crackers,etc), and each student takes a turning "taking away" a snack from a bowl. This makes the basic lesson of "taking away" (aka subtraction), fun and motivating. Later, students can be assigned certain numbers of things to "take away", and the teacher can facilitate counting what's left.
Stay tuned for more songs to help teach Math!


More than once I’ve seen people ask questions like “In A/B Testing, how long should you wait before knowing which option is the best?”.
I’ve found that the best solution is to avoid a binary question of whether or not to use a variation. Instead, randomly select the variation to present to a user in proportion to the probability that this variation is the best based on the data (if any) you have so-far.
How? The key is the beta distribution. Let’s say you have a variation with 30 impressions, and 5 conversions. A beta distribution with (alpha=5, beta=30-5) describes the probability distribution for the actual conversion rate. It looks like this:
This shows that while the most likely conversion rate is about 1 in 6 (approx 0.16), the curve is relatively broad indicating that there is still a lot of uncertainty about what the conversion rate will be.
Let’s try the same for 50 conversions and 300 impressions (alpha=50, beta=300-50)”):
You’ll see that while the curve’s peak remains the same, the curve gets a lot narrower, meaning that we’ve got a lot more certainty about what the actual conversion rate is – as you would expect given 10X the data.
Let’s say we have 5 variations, each with various numbers of impressions and conversions. A new user arrives at our website, and we want to decide which variation we show them.
To do this we employ a random number generator, which will pick random numbers according to a beta distribution we provide to it. You can find open source implementations of such a random number generator in most programming languages, here is one for Java.
So we go through each of our variations, and pick a random number within the beta distribution we’ve calculated for that variation. Whichever variation gets the highest random number is the one we show.
The beauty of this approach is that it achieves a really nice, perhaps optimal compromise between sending traffic to new variations to test them, and sending traffic to variations that we know to be good. If a variation doesn’t perform well this algorithm will gradually give it less and less traffic, until eventually it’s getting none. Then we can remove it secure in the knowledge that we aren’t removing it prematurely, no need to set arbitrary significance thresholds.
This approach is easily extended to situations where rather than a simple impression-conversion funnel, we have funnels with multiple steps.
One question is, before you’ve collected any data about a particular variation, what should you “initialize” the beta distribution with. The default answer is (1, 1), since you can’t start with (0, 0). This effectively starts with a “prior expectation” of a 50% conversion rate, but as you collect data this will rapidly converge on reality.
Nonetheless, we can do better. Let’s say that we know that variations tend to have a 1% conversion rate, so you could start with (1,99).
If you really want to take this to an extreme (which is what we do in our software!), let’s say you have an idea of the normal distribution of the conversion rates, let’s say its 1% with a standard deviation of 0.5%.
Note that starting points of (1,99), or (2,198), or (3,297) will all give you a starting mean of 1%, but the higher the numbers, the longer they’ll take to converge away from the mean. If you plug these into Wolfram Alpha (“beta distribution (3,297)”) it will show you the standard deviation for each of them. (1,99) is 0.0099, (2,198) is 0.007, (3, 297) is 0.00574, (4, 396) is 0.005 and so on.
So, since we expect the standard deviation of the actual conversion rates to be 0.5% or 0.005, we know that starting with (4, 396) is about right.
You could find a smart way to find the starting beta parameters with the desired standard deviation, but it’s easier and effective to just do it experimentally as I did.
Note that while I discovered this technique independently, I later learned that it is known as “Thompson sampling” and was originally developed in the 1930s (although to my knowledge this is the first time it has been applied to A/B testing).


The 3D Measurement Tools allow you to measure 3D models including measuring edges, radius and diameter, measuring the angle between faces and points, point to point measurements, and measuring the distance between any combination of faces, edges, and circle centres. The 3D Measurement Tools are found on the 3D toolbar:
You can click and drag measurements to adjust the measurement’s location in the Viewer. You can also suppress the X, Y, and/or Z measurements for the Measure Point to Point and Measure Distance tools. To suppress a measurement, click the absolute measurement and X, Y, and Z icons should appear next to the absolute measurement.
Click the axis measurements you want to suppress.
The CoLab Viewer relies on Boundary Representation (BREP) data for measurement tools. For file formats that do not have BREP data, the measurement tools that rely on BREP data will be hidden.


Dear Granger Jr. High Students,
Welcome to the Marvelous World of Math!
If you love math already, I promise to continue to fuel the flame of your math excitement and help you reach your highest potential! You will not be bored and you will become an expert problem solver! You will enjoy fun challenges that help you grow as a math scholar!
And if you are thinking, “Math is Marvelous?!?! - she must be crazy!", hang in there, because I have a promise for you, also! I promise to help you reach your highest potential in a fun, safe, and exciting class! You will see your math-confidence build this year! You will start to make connections and your math skills will grow! And in the end, you may still think I am a little crazy, but you will begin to love math!
I’m looking forward to a GREAT 2019-2020 school year!
SCHOOL SUPPLIES NEEDED FOR EACH OF MRS. C's MATH CLASSES:
8th grade math students are expected to have their school assigned calculator in math class each day!
MRS. C's WISH LIST OF ITEMS MOST NEEDED IN CLASS:
Dry-Erase markers (thin and regular), post-it notes, highlighters