The air pollutants are represented in either volume fraction/total volume or weight/volume. The former one may be of several types. For example, moles of pollutant/ total moles of air (mole fraction) in specific volume, number of molecules of pollutant/total number of molecules in the specific volume, etc. Overall, the concentration has quantity but no units. For example, 400 ppmv of CO2 is a representation by 400 moles of CO2 / 1000000 moles of air in a given volume. Therefore, it just a number. Another way of expressing the gas concentration is the weight of pollutant/volume (g/m3 or mg/m3 or μg/m3).
The conversion of ppmv, ppbv to mg/m3 or μg/m3 respectively will depend on the molecular weight of the pollutant, and atmospheric temperature and pressure as follows.
(PPM/1000000)*(1000mg/1g)*(MW g/1 mole)*(1 mole/22.4L)*(1000L/1m3) at STP
Canceling out the numerators and denominators will yield the following equation.
=> PPM*MW/22.4 mg/m3 at STP. This equation clearly shows that molecular weight is very important to convert. However, atmospheric properties change dramatically. Therefore, by using the equation of state, we can calculate the volume occupied by 1 mole of gas as follows.
PV= nRT, where P is atmospheric pressure in hPa, V in Liters, n is a number of moles, T temperature in Kelvin and the R is gas constant of 83.144 L hPa/K mole.
V= RT/P because n is 1 mole. Substituting this at 22.4 L in the above equation will give the full controlled equation of MW, P, T that can be used to convert the pollutants into weights/volume.
Concentration in mg/m3 = ppm*WM*P/83.144*T
In the same way,
(PPB/1,000,000,000)*(1000,000 μg/1g)*(MW g/1 mole)*(1 mole/22.4L)*(1000L/1m3) at STP
Cancelling out the numerators and denominators will yield the following equation.
Therefore, the concentration in μg/m3 = ppb*MW*P/83.144*T
What is the concentration of CO2 in mg/m3 when it has 400 ppmv and the atmospheric temperature and pressure are 298K and 1010 hPa, respectively?
Concentration of CO2 = 400*44*1010/83.144*298 mg/m3
= 717.44 mg/m3
What is the concentration of Ozone in μg/m3 when it has 80 ppbv, and the atmospheric temperature and pressure are 298K and 1010 hPa, respectively? The molecular weight of O3 is 48.
Concentration of O3 = 80*48*1010/83.144*298 μg/m3
= 156.5 μg/m3


t’s always good to have a little knowledge of mathematics on hand. It can come in handy for solving problems that arise in your everyday life, and it just might impress your friends enough for them to want to study math too! Â
Posted: September 26th, 2022
It’s always good to have a little knowledge of mathematics on hand. It can come in handy for solving problems that arise in your everyday life, and it just might impress your friends enough for them to want to study math too!
1) If you’re cooking, measure the ingredients with cups or spoons. You’ll be able to tell if something is too salty or not spicy enough by using ratios from arithmetic. This way, you’ll make sure you get the exact flavours that you want in your food.
2) If you need help finding a solution because both sides of an equation look-alike it, remember that “anything times anything equals anything.” This means that if one side has a plus sign and the other doesn’t, the answer will also have a plus sign.
3) Help your kids with their homework! Parents can check if their children are adding the right numbers when they come up with a sum. Or, parents might want to get involved in the problem-solving process themselves by writing out an equation. Helping your child get started on doing math at home is very important.
4) Check expiration dates on medicine to ensure that you’re taking it while it’s still effective. You’ll need to use division skills for this one. Just multiply the number of days left by the dosage per day and make sure it works out correctly according to the instructions on the bottle or box.
5) Forgot how many hours are in a half-day? Good thing you took that math class years ago. You can figure it out by multiplying the number of hours in a day by the fractional number of days you’re looking for.
6) Help your kids practice their time’s tables! Helping your children learn and memorize times tables is one of the most important things you can do to help them with mathematics and school success.
7) Scientists, engineers, and doctors all use math every day; we wouldn’t have cars or medicines without them! If these professionals need to provide an estimate on something they might not be able to count exactly like when looking at stars or living cells under a microscope, they’ll still want to use as much math as possible even if those aren’t perfectly accurate.
8) Help your kids practice their fractions with baking! Learning about fractions is an extremely important mathematical concept that most students struggle with. Help them learn by cooking or baking together!
9) Help your kids find the right path to take when trying to decide what direction they’d like to go in their lives. Ask them how many different ways they can think of using their chosen subject once they graduate college? Helping children narrow down a life path is an essential part of being a parent/advisor.
10) Help protect yourself from getting ripped off when shopping for higher-price items at the store! If something costs over $100, you probably want to check out several stores before buying what you are looking for. This is a good way to make sure you’re getting the best deal possible before buying something.
Mathematics is an important part of our everyday life. It’s difficult to imagine a day without math calculations for things like driving, cooking, and doing the laundry. However, some people may not realize that they use mathematical knowledge all the time in their daily lives even if it’s just basic arithmetic. As you can see from this list we compiled of top 10 ways you can put your mathematics skills into practice every day, there are many different avenues where we could apply these principles so let us know what other examples you have! We would love to hear them and share them with everyone else who reads this blog post as well! What do you think? Do you agree or disagree with any of these ideas? Let us know by checking out www.9paragraphs.com 🙂
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This calculator is for educational purposes only and can help you estimate the number of milligrams of THC and or CBD in your recipe, provided you input accurate information into the input fields. Always use tested Cannabis when making your own butter or oil. Ask the dispensary or cultivator that you are procuring your Cannabis from for test. This easy and mobile-friendly calculator will calculate a 1% increase from any number. Just type into the box and your calculation will happen automatically. This easy and mobile-friendly calculator will calculate a 1.5% increase from any number. Just type into the box and your calculation will happen automatically. Our calculator will divide your conversions into this number in order to get your conversion rate. 3 Reap the benefits of your new-found conversion rate! Your conversion rate is expressed as a percentage and as soon as you click "solve" on our conversion rate calculator, you'll have an immediate result. Learn more about your conversion rate below!. Fat Mass and Lean Mass Calculator After obtaining a client’s body fat percentage, it is often helpful to calculate his or her body composition in terms of fat weight and lean weight. This is crucial for re-assessment when you want to compare the loss of fat and the maintenance or gain of lean weight to the client’s original baseline values. Input your age, select your gender and race/ethnicity, input (optionally) your observed calcium score and click "Calculate". Observed Agatston Calcium Score (optional): Race/Ethnicity: Gender: female male black chinese hispanic white Age (45-84): Out of Range Out of Range Please Input Age Back to MESA CAC. We strive to create simple and easy to use online calculators, ... We strive to create simple and easy to use online calculators, converters, utilities, and other online tools to make your life easier. ... Percent Off Calculator. Small Text Generator ⁽ᶜᵒᵖʸ ⁿ. Guide how to enter data into the percent calculator. You can input only integer numbers, decimals or fractions in this online calculator (3, -2.4, 5/7, ...). More in-depth information read at these rules. Additional features of percent calculator. Use and on keyboard to move to previous or next field. Rules. B is what percentage of A?. Percentage calculator (%) - calculate percentage with steps shown free online. About this percentage calculator. This new percentage calculator has been designed to be the best user-friendly online tool for working out various percentage calculations.. It was built in 2018 with speed and ease of use in mind — born out of the frustration from using many existing online percentage calculators and finding them all to be too slow, clunky, cluttered with ads and each. Check your answer using the percentage increase calculator. Working out the problem by hand we get: [(1,445 - 1,250)/1,250] * 100; 0.156 * 100; 15.6 percent increase. The percentage growth calculator is a great tool to check simple problems. It can even be used to solve more complex problems that involve percent increase. Determine your body fat percentage with our body fat calculator. Use a tape measure to determine your waist, wrist, hip and forearm circumference. Then input your gender and measurements below to receive a body fat index based on average values. The body fat index is not an indicator of fitness level since the calculation is made with no regard. This is one of the most accurate methods for determining fat percentage out of body measurements. Jackson and Pollock devised two more formulas, one for 4 site calculation and another for 7 skinfold testing. Similarly, there is the Durnin and Womersley 4 site calculator. According to the formula we calculate (15/100)*160 = 0.15*160 = 24. 2. Adding or subtracting a percentage. This calculation answers the question: add P percent to V or subtract P percent of V. First we deal with how we can add percentages. Add P percent to the value V. To add percentages the formula is: V + (P/100*V). How to calculate CGPA? The Central Board of Secondary Education has a curriculum where 5 subjects are compulsary and one is optional. • TO CALCULATE AVERAGE CGPA Assume the grade points of the 5 subjects as: S1,S2,S3,S4,S5 Grade point(GP)=S1+S2+S3+S4+S5 CGPA=GP/5 EXAMPLE: Subject 1 Grades= 10 Subject 2 Grades=9 Subject 3 Grades=10 Subject 4.
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Enter starting value and final value to find percentage increase. How to Calculate Percentage Increase Subtract final value minus starting value Divide that amount by the absolute value of the starting value Multiply by 100 to get percent increase If the percentage is negative, it means there was a decrease and not an increase.
Welcome to How to Calculate Percent (with a calculator) with Mr. J! Need help with finding a percentage? You're in the right place!Whether you're just starti...
Calculation. Example: 30 is what percentage of 125. Equation ( 30 ÷ 125 ) * 100 = 24%. Equation Breakdown. 30 ÷ 125 = 0.24 ( divide 30 by 125 to calculate the percentage as a decimal ) 0.24 * 100 = 24% ( multiple the result by 100 to get a nicely formatted percentage )
Welcome to the LOTRO Ratings Calculator! 1) calculate rating to percentage: number columns 1 & 2. enter rating in 1 and percentage shows in 2. 2) calculate percentage to rating: number columns 3 & 4. enter percentage in 3 and rating shows in 4. 3) shows a graph of the rating to percentage formula for visual information with cap percentage and ...
Most popular Calculator Percentage Function apps. Calculator Percentage Function found at Orange Calculator, Za-Calculator.


Edushape Letters & Numbers - 36 Foam Playtiles
Edushape Letters & Numbers
Edutiles Letters and Numbers are a set of 36, thick, 30 x 30 cm Edu-foam interlocking tiles, perfect for providing a safe play area for children. Features pop-out letter and number shapes which can encourage the development of counting skills letter recognition. Contains 26 alphabet tiles A-Z (upper case) and 10 number tiles 0 - 9.
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Q: What size tablecloth do you need for your table?
A: It is easy to calculate the proper size of a tablecloth:
· For a square or oblong table:
o Measure the length and width of the table.
o Decide on the length of the drop you prefer. The drop is the amount of fabric that hangs down from the top of the table. A typical drop ranges between 10 to 12”. If you want your tablecloth to go to the floor, then the drop would usually be 30” (a typical table height), but measure just in case.
o Add the amount of the drop multiplied by two to both the length and the width of the table.
o For example: If the table measures 42” wide x 84" long and you want a 12” drop, then the oblong tablecloth should measure 66” (42” width + 24” total drop) x 108” (84” length + 24” total drop).
· For a round table:
o Measure the diameter of your table.
o Decide on the length of the drop.
o Add the amount of the drop multiplied by two to the diameter of the table.
o For example: If the table measures 60” in diameter and you want it to go to the floor with a 30” drop, then the round tablecloth should measure 120” (60” diameter + 60” total drop).


Acoustical Porous Material Recipes
Scheme representation of the motion of an object (the falling apple) following various variational approaches.
Alternatives to the Newtonian approach [New87] for describing the motion of objects or systems exist. The Lagrangian approach is one of those, based on energy to describe the motion of systems instead of forces.
Lagrange approach [Lag88] may appear as an overcomplicating mathematical tool compared to Newton's one for simple systems. However, Lagrange approach allows the use of generalized coordinates compared to Newton's approach which can greatly simplify the resolution of a problem depending on its symmetries or on the geometry.
Hamilton's functional approach [Ham35] is the formulation of the principle of stationary action based on the Lagrangian approach.
From the Physics point of view, its advantage compared to Lagrange approach is the fact that it allows to identify the "natural" boundary conditions during calculation in elastodynamics.
Hamilton's functional approach is not the only functional formalism used in elastodynamics. While Hamilton’s functional only depends on the displacement field (and its derivatives), The Reissner’s functional [Rei50] depends on two variable fields: the displacement one and the stress one.


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posted by qtjoel on 11.08.10 at 8:59 pm
If you want to know how to win those “guess the number of M&Ms in this jar” contests, you should watch this video. In it, Adam Micolich – a physics lecturer at the University of New South Wales – explains how to scientifically calculate the number of the M&Ms in a jar. Skip to the 3:30 mark for the fun stuff.
Andrew Hicks, a mathematician at Drexel University, used some of his math skills to make a mirror that reflects an image without reversing it.
It’s called a non-reversing mirror and the effect can be recreated pretty easily. Just take two mirrors and put them 90degrees to each other and look directly at them.
Hick’s mirror is slightly more complex because its all on one mirror. I think he uses some sorta parabolic math mumbo jumbo to make his. Either way, its pretty cool.


Cancer Control Research5R01CA081345-07
Eisen, Ellen A.
DOSE RESPONSE MODELING IN EPIDEMIOLOGIC COHORT STUDIES
DESCRIPTION (provided by applicant): This revised proposal builds on my current work applying semiparametric statistical methods to model nonlinear exposure-response curves with smooth functions of exposure in occupational cohort studies (R01 CA81345). In the course of adapting penalized splines for survival analysis, we have identified two issues that need further development: criteria for choosing the optimal amount of smoothness and diagnostic statistics to identify influential observations and measure their influence on the fitted values of the curve. These issues will be examined in the presence of right skewed distributions typical of workplace exposures. We propose to compare the goodness of fit and resistance of penalized splines to that of two other common smoothers: restricted cubic splines, and a locally weighted regression smoother called loess. In this revised application, we propose to compare the three smoothing methods by evaluating model fit in a series of simulation studies. Data will be generated under linear, cubic polynomial, and threshold (broken stick) exposure-response models, assuming exposure has a lognormal distribution. We will identify the technique with the best fit to the true data, after calibrating the amount of smoothness across the three methods. We also now propose to develop statistical methods to quantify influence and identify points with high leverage in semiparametric models, with particular attention to values at the high end of the skewed exposure distribution. We will compute Cook's distance for parametric and nonparametric components and develop rules for assessing statistical significance as well as diagnostics for determining the sensitivity of the smoothing parameter to subject deletion. The new diagnostics will be developed for penalized splines and then extended to restricted cubic splines and loess. The models will be applied to the re-analyses of two cancer mortality studies; larynx, lung, prostate and rectal cancer in autoworkers exposed to metalworking fluids (MWF) and lung cancer in workers in California's diatomaceous earth industry exposed to crystalline silica. We plan to focus our methodologic investigations on MWF and silica because we believe that clarifying the shapes of their exposure-response curves can make a substantial contribution to current controversies over their control in the workplace.


Imaginary-time matrix product state impurity solver for dynamical mean-field theory
Phys. Rev. X, 5 (4), 041032, (2015)
We present a new impurity solver for dynamical mean-field theory based on imaginary-time evolution of matrix product states. This converges the self-consistency loop on the imaginary-frequency axis and obtains real-frequency information in a final real-time evolution. Relative to computations on the real-frequency axis, required bath sizes are much smaller and less entanglement is generated, so much larger systems can be studied. The power of the method is demonstrated by solutions of a three band model in the single and two-site dynamical mean-field approximation. Technical issues are discussed, including details of the method, efficiency as compared to other matrix product state based impurity solvers, bath construction and its relation to real-frequency computations and the analytic continuation problem of quantum Monte Carlo, the choice of basis in dynamical cluster approximation, and perspectives for off-diagonal hybridization functions.


The essence of the Fibonacci Strategy for soccer betting – published in by Fragiskos Archontakis and Evan Osborne - is simple: bet on a draw, and if you. Football Betting Systems. We investigate the Martingale system, Labouchere System & The Kelly Criterion. A martingale is any of a class of betting strategies that originated from and were popular in 18th century France. The simplest of these strategies was designed.
Betting system Video
Strategy: Short Odds Treble Football Betting It follows that N is finite with probability 1; therefore with probability 1, the coin will eventually show heads and the bettor will realize a net gain of 1 unit. Like the Fibonacci sequence itself, betting system Fibonacci betting strategy is best appreciated as a mathematical concept. In a casino, the expected value is negativedue to the house's edge. In order to prove this point I created a program that simulated two systems, the Martingale and flat betting, and applied each by betting on the pass line in craps which has a In other words, all betting systems brauche ganz schnell geld equally worthless. Let one round be defined as a sequence of consecutive losses followed by either a win, or bankruptcy of the gambler. However, in the long run no betting system can withstand the test of time. I have said all I have to say on the topic here and in my Gambling FAQ. The graph below shows the results: This article needs additional citations for verification. Mere money management strategies like staking systems, or progression systems, Betfair Predicts Football Stats Live Sport on TV Betfair Apps Customer Support Betfair Casino What's New on Betfair? Eventually he either goes bust or reaches his target. Betting strategies 1 Betting strategies 2. The anti-martingale approach instead increases bets after wins, while reducing them after a loss. Text is available under the Creative Commons Attribution-ShareAlike License ; additional terms may apply. Following are the results of all four tests. Can a betting system beat a game with a house edge this small and a 1, bet spread? Betting systems constitute one of the oldest delusions of gambling history. The only real difference is the actual staking sequence. Gaming mathematics Mathematics of bookmaking Poker probability. The Fibonacci sequence are numbers in the following sequence:. Articles lacking sources from October All articles lacking sources. Not without cheating anyway. By definition, the first two numbers in the Fibonacci sequence are either 1 and 1, or 0 and 1, depending on the chosen starting point of the sequence, and each subsequent number is the sum of the previous two. The Fibonacci sequence is one of the most widely known numeric sequences in mathematics, characterised by its simple formula:. Sports Betting Casino Live Casino eSports Betting Resources Mobile. Specials Two weeks ago. With this method, your bet should be your edge divided by the odds.


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Some are financial calculators, some are scientific calculators, and some are mixed use or what I called multi-purpose calculators. It also looks and calculates a lot better than the Windows 7 version. The simplest mode provided by this app is the Standard one, which displays all the numbers and the corresponding figures for the basic operations: addition, subtraction, multiplication and division. I see that the window edges cannot be dragged to enlarge them. Basic functions include add, substract, multiply, divide, potential, square root and absolute value. I would suggest you to provide some information to help you better.Next
Matrix Calculator Pro is a tool designed to handle complex mathematical operations, especially the calculation of matrices. It is designed for the researchers who need to execute a fast test and to determine if the difference between two percentages is statistically significant. From the web site: Moffsoft FreeCalc is a great replacement for your existing Windows® calculator. Color schemes - Select a color combination or use your Windows color settings. Switching is not a huge deal, but it's very annoying when I just want a quick calculation and try to enter them and suddenly the period doesn't work.Next
It's quite advanced, but doesn't do common arithmetic. Mini Calculator is a simple pocket calculator equipped with all the basic functions addition, multiplication, subtraction, division, etc. Pattern-Making Calculator is a program that has the particularity to convert the decimal into fraction. Have they stopped producing it? I can't use a decimal point, for example, when I leave it on programmer. Click on the below link to check how to create new user account in Windows 10 Microsoft Support link: Note:Install all the pending updates after logging in to Microsoft account and check. It was a very capable product, able to solve equations, draw graphs, do calculus, and much more.
This application allows you to complete many different types of conversions; it also includes all the mathematical functions offered in Microsoft Calculator. This is one of the few times I have not found what I needed on Gizmo- thanks for this great site and all the help with software. The standard default option calculator gives the answer of 5 which is wrong while the scientific option gives the correct answer of -15. You can read my previous post on. It can also save a list of variables for use in expression.Next
The Microsoft Download Manager solves these potential problems. But its critical in your build. Oh well, I'll leave it in case someone else wants it. Next to the keyboard, it offers a virtual paper tape. The idiots at Microsoft have once again decided that they think they know what the users want better than the users and have eliminated the calculator plus program and converted it into an massive, useless app that takes up more than half of your screen.Next
If you upgraded from Windows 7 or Windows 8 to Windows 10, that could also be the cause. The loan calculator makes calculating S. Looking for more functionality in your calculator software? I went with SpeQ Mathematics as well. They've merely stopped selling it, and are now giving it away! I graduated from Emory University with a degree in Computer Science and Mathematics. With an administrator rights Explorer window, you should now be able to copy and paste the calc. With Microsoft Mathematics, students can learn to solve equations step-by-step while gaining a better understanding of fundamental concepts in pre-algebra, algebra, trigonometry, physics, chemistry, and calculus.Next
It also includes a calculator, meant to assist in solving simple math operations. Strange, I have no idea why since it looks the same but includes mathematical and conversion functions. Standard Calculator Scientific Calculator Programmer Calculator Statistics Calculator Microsoft Calculator Plus The Winaero. Now make sure to check the Calculator box. You should confirm all information before relying on it. Unit conversions of the following types are supported: length, mass, time, velocity, and temperature. You can also click on View and choose Standard to remove the conversion options on the left and just have the old standard calculator.Next
It probably isn't possible, certainly isn't supported and may well be in violation of the license agreement for Windows although you may want to have that reviewed by a lawyer to be sure. It starts itself and keeps forming multiple tabs of the app its really irritating and the problem is I cannot uninstall this app. What has Microsoft done to the windows 10 calculator? Luckily, there are a couple of alternatives. It easy-to-use and provides fast calculation. If you have any further queries, feel free to contact us. Otherwise, standard scientific functions are available to you here. It also offers the possibility of working with user functions: g x and function var , where the user sets the apropriate operation to accomplish.Next


— Albert Einstein
Mathematics can be defined as the scientific study of quantities, including their relationships, operations and measurements expressed by numbers and symbols. In simple words, mathematics deals with study of numbers and their various calculations. The most important skills in mathematics are analysis and reasoning.
A mathematician is a person whose primary area of study or research is mathematics. Mathematicians are concerned with particular problems related to logic, space, transformations, numbers and more general ideas which encompass these concepts. They do research, come up with problems and solutions, etc.
Mathematicians solve problems in diverse fields such as medicine, management, economics, banking, government, insurance, computer science, physics, psychology, engineering, bio-mathematics, bio-informatics and weather forecasting.
Mathematics can be pursued with other allied subjects and various careers can be pursued. After BSc Mathematics with B Ed and higher education like MSc Mathematics one can become a teacher. After BSc mathematics followed by MSc stats/ MSc Operations Research one can become a statistician. One can become an economist or Actuary after BSc Mathematics with Economics and higher studies. One can also become a Physical Sciences Observer/Scientist after BSc Mathematics, MSc Physics. A career in life sciences can be pursued with BSc Mathematics combined biology.
Are your Aptitudes and Personality suitable for becoming a good Mathematician?
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Go math assessment guide grade 6 paperback 2011 by author 38 out of 5 stars 5 customer reviews see all 5 formats and editions hide other formats and editions houghton mifflin harcourt 32 out of 5 stars 22 755 go math student interactive worktext grade 6 2014 paperback holt mcdougal 50 out of 5 stars 10 2325. Harcourt math assessment guide grade 6 1st edition by harcourt school publishers author be the first to review this item isbn 13 978 0153365423 isbn 10 0153365420 why is isbn important isbn this bar code number lets you verify that youre getting exactly the right version or edition of a book . Harcourt math teacher assessment guide grade 2 by harcourt school publishers 1550 buy it now 740 0 bids harcourt math teacher assessment guide grade 2 by harcourt school publishers condition is very good could be considered like new but it has property of stamped inside front cover math expressions volume 2 houghton mifflin harcourt. Houghton mifflin harcourt go math assessment guide grade 6 by houghton mifflin harcourt prepared for publication by starting at 3050 houghton mifflin harcourt go math assessment guide grade 6 has 1 available editions to buy at alibris. Harcourt math assessment guide grade 3 includes answer key 999 buy it now 24d 11h see details harcourt math assessment guide grade 3 2002 397 buy it now 6d 10h see details new harcourt math assessment guide grade 5 1270 buy it now 16d 17h see details harcourt k 2 literacy assessment teachers guide
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Tube curvature radius
Curvature of a curve. The curvature of the plane curve is a tangent to the curve of a certain point on the tangent of the angle of the arc length of the rotation rate, the definition of the differential to show the extent of the curve deviate from the line.
When the K=lim| / alpha Delta Delta s| Delta s tends to 0, K is the definition of curvature.
The reciprocal of curvature is the radius of curvature.
Radius of curvature is used to describe the curve of a certain extent of the curve of the curve of the extent of the special, such as: a circle radius of curvature of a circle is exactly equal to the radius of the circle, may be able to understand: that is, that a section of the curve as possible differential, until the end of a circular arc, the radius of this circle, personal understanding
Application problems of curvature and curvature radius
A plane along a parabolic path y= (x^2) /10000 (Y axis vertical, the unit is m) for diving flight, in
The speed of the aircraft at the origin of O is v=200m/s. Pilot weight G=70kg. Find the plane dive to the most
Low that is the origin of the O at the time of the seat to the pilot's reaction.
Requires the aircraft to dive to the origin of the O seat to the pilot's anti force, so that x=0, then:
Into the formula of curvature radius P =1/k=[(1+y''^2) ^ (3/2), y, =5000 M / "
So the centripetal force of F=mv^2/ P =70*200^2/5000=560 pilots by cattle
To dive to the origin of the aircraft to the O position of the pilot's anti force


This BBC documentary on Infinity is blowing me away. As I relayed a few quotes re: large numbers to my wife I started to tear up. It was like a fuller appreciation of the concept of infinity really was putting me in contact with the Infinite.
“On January 22, 1886, Georg Cantor, who had discovered the existence of an infinite number of infinities, wrote a letter to Cardinal Johannes Franzen of the Vatican Council, defending his ideas against a possible charge of blasphemy. A devout believer, the mathematician considered himself a friend of the Church. God, he believed, had used his preoccupation with numbers to reveal a further aspect of His infinite nature.” (p255 Thinking in Numbers)
Cantor was right. Here are the quotes (direct and paraphrased) I was sharing with Fran;
“A googol [is a number that starts with 1 and] has a 100 zeroes, but a googolplex (10Googol ) has so many zeroes that there’s is not enough space in the entire observable universe just to write the number down; even if you could write each zero on a single atom.”
And yeah, of course there’s an even bigger number. It’s called Graham’s number. What the number 10 is to a googolplex, a googolplex is to a Graham’s number!
We don’t know how many digits are in Graham’s number (not even Graham himself knows, but it ends with a ‘7’)… it’s a mystery (as the documentary makes these points a celestial soundtrack plays in the background).
Then Graham himself says these words, “Graham’s number is not really any closer to infinity than the number one.” My jaw dropped at the thought and it felt like God was in the room.
Can’t wait for Sunday.


Question: I know the maximum elevation figures (MEF) depicted on a sectional chart show the highest terrain and/or obstacles within a quadrant, but can you tell me how the MEF is calculated?
Answer: For man-made obstacles taller than 200 feet, the MEF is calculated by determining the elevation of the top of the obstacle above mean sea level (msl). Then, additional height is added according to a cartography formula to cover a possible vertical error. Finally, the figure is rounded up to the next highest 100-foot increment. For example, if the highest man-made obstacle within a sector is 2,250 feet msl, 100 feet would be added to cover a possible vertical error (2,350 feet). This figure would then be rounded up to the nearest 100 feet and be charted as a 2,400-foot MEF for that sector. A similar process is used for calculating the MEF for terrain or natural obstacles, except that an additional 200 feet is added just in case there is a man-made obstacle on that terrain that wasn't charted because it is less than 200 feet tall. Learn more in the AOPA Air Safety Foundation's Safety Hot Spot,NACO Aeronautical Chart User's Guide.


Funded PhD Studentships in the Mathematics of Information by CCIMI
The CCIMI invites applications for fully funded PhD studentships in Mathematics of Information. We held an Open Day on Thursday 15th November where prospective students came along and discovered more about our Cambridge Mathematics of Information (CMI) PhD program. Further information is available on our.
CCIMI Fully Funded PhD Studentships in the Mathematics
The advance of data science and the solution of big data questions heavily relies on fundamental mathematical techniques and in particular, their intra-disciplinary engagement.
This is at the heart of the center for the Mathematics of Information which involves mathematical expertise ranging from statistics, applied & computational analysis, to topology and discrete geometry – all with the common goal of advancing data science questions.
Alongside this, specific questions which feed into fundamental methodology development arise naturally in applications we focus on in interdisciplinary engagements.
For instance, economists and social scientists on questions about financial markets and the internet, with physicists and engineers on software and hardware development questions in the context of security, imaging, and structured data processing, as well as biomedical scientists on data science in healthcare and biology.
More info – CCIMI invitation on Funded PhD Studentships
Both this general advancement of data science, and its applications to specific questions is realized by key mathematical expertise represented in the institute including:
- inverse problems,
- convex analysis,
- sparse optimization
- stochastic analysis
- compressed sensing
- sampling theory
- approximation theory
- random matrices
- harmonic analysis
- partial differential equations
- functional analysis
- quantum computation
- discrete geometry
- graph theory.
We welcome applications for studentships relating to projects and subject areas covering all aspects of the broad field of mathematics of information. Further information on some of the projects currently being investigated by students and faculty can be found on our website, linked here.
The Cantab Capital Institute for the Mathematics of Information is hosted within the Faculty of Mathematics of the University of Cambridge and is a collaboration between DAMTP and DPMMS.
It accommodates research activity on fundamental mathematical problems and methodology for understanding, analyzing, processing and simulating data. Data science research performed in the Institute is on the highest international level, aiming to extract the relevant information from large- and high-dimensional data
Eligibility (Funded PhD Studentships)
The academic requirements for entry to this PhD are a first-class honors degree, awarded after a four-year course in mathematics or related subject, or a three-year degree with a one-year postgraduate course on advanced mathematics or related subject. For further details on how to apply for this program see the relevant entry on the website.
- The scheme is open to applicants from all countries.
Applicants must meet the following criteria:
- The academic requirements for entry to this PhD are a first-class honours degree, awarded after a four-year course in mathematics or related subject, or a three-year degree with a one-year postgraduate course on advanced mathematics or related subject.
- The usual minimum entry requirement is a first-class honours degree, awarded after a four-year course in mathematics or mathematics-related subject, or a three-year degree together with a one-year postgraduate course on advanced mathematics or a mathematics-related subject. Part III (MMath/MASt) of the Mathematical Tripos provides such a course. Note, however, that entry is competitive and a higher level of preparation may be required.
English Language Requirements:
- Applicants whose first language is not English are usually required to provide evidence of proficiency in English at the higher level required by the University.
Funding (Funded PhD Studentships)
Fully funded PhD Studentships do include University Composition Fees and maintenance for the duration of your course to match the RCUK minimum level. The scheme is open to applicants from all countries.
- Applications Deadline: Jan three, 2022
- Course Level: Studentships area unit out there to pursue Doctor of Philosophy program.
- Study Subject: Studentships area unit awarded in fields of arithmetic of data.
- Scholarship Award: office offers:
- Fully funded Doctor of Philosophy Studentships does embody University Composition Fees and maintenance for the length of your course to match the RCUK minimum level.
- The theme is hospitable candidates from all countries.
- Nationality: The theme is hospitable candidates from all countries.
- Number of Scholarships: ranges not given
- Scholarship may be taking within Britain.
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Route for application (Funded PhD Studentships)
Apply using the standard PhD application procedure via the University’s Graduate Admissions website.
It is very strongly encouraging that applications are receive(d) by 3rd January 2023.
Shortlisted candidates will be interview(ed) – the date for interviews will be communicated once shortlisting has taken place.
Please contact email@example.com in the first instance for any inquiries about the applications process, and for any inquiries regarding the PPh.D.programme.
How to Apply:
- Apply using the standard PhD application procedure via the University’s Graduate Admissions website (https://www.graduate.study.cam.ac.uk/courses/directory/mapmpdmal); and
- Send an expression of interest letter to cmi-at-maths.cam.ac.uk which explains why you are interested in this course.


At the Henslow School we aim to transform our students into adept mathematicians by ensuring that all lessons are fun, have practical elements and real-life application. Many of our students come to us with negative experiences in Mathematics and it is our aim to develop student confidence, perseverance and resilience. This is aided by individualised plans for student progression, which allows them to make progress at their own rate and fulfil their potential.
Using Nrich’s (Cambridge University Mathematics) definition of what makes a mathematician, our starter activities focus on one area per week, ensuring students develop the skills of exploring, questioning, working systematically, visualising, conjecturing, explaining, generalising, justifying and proving their reasoning. At the Henslow School we believe that we learn better when we are curious, resourceful, resilient and collaborative. All groups use these activities to develop team work and to give a class focus before students continue on their individual plans.
When students leave the Henslow School it is our intention that they will have the mathematical qualifications they need to help them with their lives. Alongside an understanding that Mathematics is a life skill that helps to make things easier and will support their future career.


People think that mathematics is complicated. Mathematics is the simple bit, it’s the stuff we CAN understand. It’s cats that are complicated. – John Conway 1937-2020
John Conway Interests me because of his work in a variety of math subjects. He studied the theory of finite groups, knot theory, number theory, combinatorial game theory, and coding theory. He moved between subjects always learning and making new things, like the doomsday rule or the game of life. Personally, I tend to jump from new ideas to new ideas trying to learn as much as I can as fast as I can, so I feel that we have some connection. He inspires me to want to have a career in mathematics when I grow up. I also enjoy math and have an analytical mind and I enjoy challenges. I aspire to be more open to learning and understanding new things like john Conway. I also aspire to be better at communicating with other people like him. Some challenges I could have with connecting with John Conway is that he worked with very complex math, so it could be hard to get in his headspace and that he was an adult, and I am still a kid. And because I am still a kid, I have never held a job but, he was known for his career. Even though I am still a kid I could research, learn, and study what he taught in order to have a better understanding of his work and who he was. When I grow up, I think that I will get a stronger connection when I start my career. He contributed to society and the field of mathematics by working on the theory of finite groups, knot theory, number theory, combinatorial game theory, and coding theory. He left a ding in the universe by teaching mathematics at Princeton. I don’t think that he’s someone who will become more famous in 50 to 100 years as time goes by than he because he did not win a lot of awards and also because generally, mathematicians are not as famous as celebrities. He is worth researching because he was an inspiration to his students and peers alike. He moved through math making discoveries and teaching the public in a way that kept their interest. He wasn’t called “the world’s most charismatic mathematician” for nothing. I picked him over other mathematicians because he did not settle down and work in one field, he moved between them and shared his genius with the entirety of the math world. One of my takeaways so far from studying John Conway is that you don’t need to stay in one element. This is true not just for math but is also true for all areas of life.


I’m working on data having two columns (one categorical (type), one numerical(amount)). If I want to make a plot showing the fraction of each category and the mean value of numerical variable corresponding to each category, how can I do it?
Which plot to be used?
I thought of a pie chart. But I’m not sure how I can include mean of amount column corresponding to each category .
df[categorical_col].value_couts() / len(df) - will help you get fractions of categorical columns
df.groupby(categorical_col).mean() - will help you get mean amount for each category.
You can use a bar plot to visualize both together.
You can draw boxplot per each category to gain even more insights.
Refer to the documentation here https://seaborn.pydata.org/generated/seaborn.boxplot.html, the chart I am talking about is the second one.


Yes I do! I use some very complicated, developed pieces of software that can do thousands of calculations every second and help to make my job so much easier. However there are sometimes that, for whatever reason, there is a simple measurement that it can’t show me. Often this means that I need to use pencil, paper and a calculator to work out a certain angle or distance.
This is good though, because it does mean that I get to use the equations that I learned at school such as pythagoras’ theorum. I’m happy that I have a reason for learning it all those years ago!


Head of the Department of Information Computer Technologies and Mathematics, doctor of physical and mathematical sciences, professor O.P. Nechuiviter took September 27, 2022 participation in the work of the first seminar "Quantum Computing", which was held at the base V. M. Hlushkov Institute of Cybernetics of the National Academy of Sciences of Ukraine. The participants of the seminar were greeted by the deputy director of the institute for scientific work, Academician of the National Academy of Sciences of Ukraine, Doctor of Physical and Mathematical Sciences, Professor O.M. Chemist The leader of the seminar is an academician of the National Academy of Sciences of Ukraine, a doctor of physical and mathematical sciences, a professor V.K. In his report, Zadiraka highlighted the tasks and work plan of the workshop.
The audience was very interested in the report "Quantum computer from the point of view physics", made by an employee of the Physical and Technical Institute of Low Temperatures named after B.I. Verkin of the National Academy of Sciences of Ukraine, Doctor of Physical and Mathematical Sciences S.M. Shevchenko. IN the report analyzed the current state of the problem related to the creation quantum computer as a real working device.
In addition, the speaker allocated special attention to areas of possible use of quantum computers: from cryptography to the modeling of large-scale systems, description and prediction of the course of ultra-complex systems processes, etc. The report discussed the basic concepts of quantum computing, such as logical operations and examples of modern studies of physical implementations are given quantum bits - qubits.


Maths and science were not my strong points when I was at school, and it really wasn’t for a lack of trying. In fact I know exactly why I grappled with these subjects; I never had a solid foundation, the fundamental principles were lost on me which meant that anything that I tried to learn never really made complete sense to me. Now I’m not saying that I missed my calling as a mathematician or engineer, but I do know that having a firm foundation in these subjects would have made my life a lot easier… I may have even enjoyed them!Science, technology, engineering and mathematics are barely represented by females, and this needs to change, and quickly, if we want our girls to truly be able to be anything that they want. Some quick global stats that you might not know about when it comes to girls and STEM: • Girl’s self confidence in the ability to excel in STEM drops 3.5 times faster from primary to high school than boys. • As a result of girls feeling less and less confident when it comes to STEM, only 23% of STEM jobs are held by women, and even more frightening; only 3% of start-ups pioneered by women get funding. • Research also shows that in South Africa specifically, the male to female graduate ratio is completely out of proportion with less females being represented in both maths and statistics (3:4) and engineering and construction (1:4) Because of how much I struggled at school and after reading these statistics, I know how important it is to introduce my girls to science, technology, engineering and mathematics as early as possible. The trick though is making it fun and something that they want to get involved in. And this is why I was so happy to discover the Girltivity subscription box. The boxes were born from a desire to get girls excited about STEM, and to make the process fun for all age groups. Girltivity curates boxes for ages 3-12 which I was thrilled about; the younger that we can get our girls excited about these subjects, the sooner they will get the basics right, the less likely they are to struggle in school later on. Each box contains 10-15 activities to encourage science, technology, engineering and mathematics and they are all age appropriate. The mascot, GT holds personality traits that all girls can aspire to; bravery, fearlessness and the belief that she can do anything she sets her mind to. This is such an amazing message for our girls to see, because even now, in 2019, they are told that they can’t do certain things “because you’re a girl”. I don’t know about you, but I want my girls to grow up knowing that the can achieve their wildest dreams! The pure convenience of Girltivity is something that appeals to me as well – everything comes to your door once a month. All the gizmos and gadgets are in the box (as well as instructions) so you don’t need to run around like a headless chicken trying to put everything together.


22.214.171.124. Multiple regression models
While comparing exposure prevalence in sub-groups of a population may have benefits in elucidating exposures that have pronounced effects on disease, often, several factors may contribute to disease outcomes. In these cases, multivariate regression analysis can be conducted to highlight exposure factors that differ between groups. If the outcome is at the individual level, a multivariate logit or probit may be appropriate. If the outcome is at a group level, a multivariate logistic regression may be preferred, although if most ratios or percentages range between 0.3 and 0.7, a linear regression can often give a good fit. Standard statistical packages (SAS, R, etc.) permit fairly straightforward disease modelling for datasets that are complete, that is have all the needed exposure measures present for each "diseased" and "non-diseased" epidemiological unit. However, frequently, cross sectional studies have incomplete data.


Guidelines for mathematics papers start early choose the topic with both the assignment and the audience in mind if the paper is a course assignment, the audience is usually the students. Wikipedia:manual of style/mathematics today many research papers or even (incorrect—typeset from 2sin x) when operator (function) names do not. Print paper that is designed for working math problems - coordinate grid notebook, graph paper, number line paper, and math problem papers. How much math do you need to win your march madness scientific american maintains a strict policy of editorial independence in reporting developments in science. Lists of mathematics topics of research papers and expository articles to list subject codes from the mathematics subject classification in their papers.
Basic arithmetic practice : how many can you do timed addition, subtraction, multiplication, and division problems for basic math practice. Welcome to ixl's 1st grade math page practice math online with unlimited questions in more than 200 first-grade math skills. Writing a research paper in mathematics gerver, r, writing math research papers: a guide for students and instructors, key curriculum press, 2007. Use of mathematics in the medical field research papers examine the use of mathematics for mri's or any other statistically intense medical procedures. I asked a similar question previously, though this is more specific and directed in the writing of mathematics research papers, when is information cited, such as definitions.
Advice for amateur mathematicians on writing and publishing papers there's no reason why amateurs can't make worthwhile research contributions in mathematics. Some of our faculty have listed ideas for undergraduate research work meant to introduce you to advanced but well-established topics in graduate level math. Essays, term papers, book reports, research papers on mathematics free papers and essays on pythagorean theorem we provide free model essays on mathematics, pythagorean theorem reports.
Kerravala research paper, marketing coursework help, do math homework for me i need to get used to writing essays again didn't really do them in maastricht :/ psych terms are awesome. These questions relate both to ensuring that such machines do not harm humans and other morally relevant beings machine intelligence research institute. Welcome to ixl's 2nd grade math page practice math online with unlimited questions in more than 200 second-grade math skills. So you need to do a math project math project assistance from the what is the purpose of doing a math research paper to top.
On this page you ca get sample pages of a research paper research paper topics pertaining to algebra research paper topics pertaining to geometry research paper topics on calculus how we can. Mathematics journal so i guess that i know how to do it i have never or three good papers and work through them in detail. Where to order custom research papers take a look here, the best research papers writing site will do your assignment from scratch on time. 10 good college research paper topics in math math is immensely present everywhere we go so much so, that finding a good college research topic in math should be a fun and adventurous.
We can do your homework for you any class: math from history and economics to sociology and law, you can expect thoroughly researched papers on any subject 0.
Cambridge international as and a level mathematics cambridge international as and a level mathematics you can download one or more papers for a previous session. Writing a research paper in mathematics ashley if you do mathematics purely for the selection of notation is a critical part of writing a research paper. Yes and no but basically no in more detail, i didn’t have to write any papers as a math major, where “paper” means something that you might find in a humanities class: here is a topic, now. Math 115 elementary statistics research paper proposal note: the there only to give you an outline as to how to write your final paper name. Motivation-sorensen 2 motivating middle school mathematics students abstract in this action research study i examined the relationship between the teacher, the.


Mathematics to me as a young child was a subject that I studied for and practiced doing problem sums because I was told to do so. I was told by my parents that it is a subject that I must concentrate on because it is important for me to do well in it. As time passed and I grew, I really did not like the subject very much mainly because I found it difficult, tricky and the most boring part of it was that there was always only one right answer to a question! That was how, I drifted away from liking Mathematics.
Of course, when I became a pre school teacher, I realized how fun and interesting Mathematics could be! After reading through Chapter 1 and digesting the National Council of Teachers of Mathematics (NCTM)'s Principles and Standard for School Mathematics, I feel so relieved. The six principles sums up a high quality mathematics education that is so promising. One particular quote from the NCTM that I totally support is:
"Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well". (NCTM, 2000, p.16)
I totally support this because I believe that every child has a different learning phase and technique and therefore, the teacher should be able to understand that before challenging them further. I do not believe that any child is not capable of doing Mathematics, it is just how a teacher changes the situaton for the child to learn. Teaching Mathematics in this era would involve learning through concepts and tapping on their capabilities and that is how the children are able to learn. Becoming a good mathematics teacher would also mean that one has to have a positive attitude, have persistence and she must be ready for changes. I believe that with a positive attitude, a teacher can bring her students to new heights of learning. Teachers should also be ready for changes as it makes the subject more "relaxed" and not too "structured". As there can only be one answer to a question in Mathematics, I do not believe that there can only be one method to go about solving it. When children are open to solutions to an answer, they are willing to try. If they are told to be rigid, they may withdraw.
Therefore I believe that loving Mathematics is not only about following the curriculum and teaching standards, it is also about the teacher and if she wants to make a change in her classroom.
How is Mathematics best learnt?
In Chapter 2, it is stated that there can be a setting for doing Mathematics. I believe that a productive classroom can benefit the children very well. As stated in the classic book Making Sense (Hiebert et al.,1997), the author described four features of a productive classroom from where children can learn from one another:
1. Ideas are the currency of classroom
2. Students have autonomy with respect to the methods used to solve problems
3. The classroom culture exhibits an appreciation for mistakes as an opportunity to learn
4. The authority for reasonability and correctness lies in the logic and structure of the subject, rather than in the social status of the participants.
These four features best describes my feelings towards a good classroom environment for Mathematics to take place.
What Does It Mean to Learn Mathematics?
Fig 2.8 on pg 20 shows a model that best describes how does one learn Mathematics. I totally agree that by using ideas that we already have to construct new ideas, we are acutually developing a connection between the ideas. The more we do so, the better we are understanding. This should be understood ny all teachers so that there is a common understanding ground that we are all standing on.
Conclusion of my understanding
Mathematics is a subject full of ideas and concepts. What we teachers can do is to ensure that we adopt some startegies that best fits into our classroom and implement it. We should ensure that all children learn something out of Mathematics and have a love for this subject because it is indeed a beautiful subject. I really hope to learn and share more in class.


Write in scientific notation calculator
Demonstrates how to convert between regular formatting and scientific notation writing a number in scientific notation is by using a calculator. Homecalculatorsmath calculators scientific notation calculator scientific notation converter write how to improve this page. Scientific notation teacher notes scientific notation on a calculator powers provide a way of writing numbers in an equivalent form. Kids these days don't know how to use a calculator to do scientific notation this lesson shows how. Quickly convert exponential notation to and from decimals with this free online scientific notation calculator will convert a scientific notation write the.
Scientific notation (also referred to as scientific form or standard index form, or standard form in the uk) is a way of expressing numbers that are too big or too. A way to remember how to write numbers in scientific notation is to think about moving the decimal point in the original if you have a scientific calculator. Calculator to multiply, divide and convert numbers written in scientific notation calculator will generate a step by step expalnation for each operation.
To write this out not-in-scientific-notation, write 167 and then move the using scientific notation on your calculator if you all scientific. Calculator to convert numbers written in standard format to scientific notation explantion also available. Scientific notation is a standard way of writing very large and very small numbers so that they’re easier to both compare and use in computations to write in. 7 our last task is to interpret how the calculator denotes scientific notation instead of writing 24∗106, the calculator writes 24e6 if you want to enter a. What is scientific notation write this number in scientific notation by following the steps below calculator (21 x 108) x.
Webmath is designed to help you solve your math problems composed of forms to fill-in and then returns analysis of a problem and, when possible, provides a step-by. Examples write 782,000 in scientific notation move the decimal point 5 places to the left 782000 since the decimal point is moved 5 places to the left, multiply by 105. Powers of ten or exponential notation on a scientific calculator in science, we deal with numbers that are sometimes extremely large or extremely small. How to do calculations: on your scientific calculator: make sure that the number in scientific notation is put into your calculator correctly. Scientific notation is a way of writing very large or very small numbers a number is written in scientific notation when a number between 1 and 10 is multiplied by a.
Using the calculator to compute with scientific notation. Scientific notation refers power of 10 notation this method is use to write very big and small numbers scientific notation calculator is an online tool to convert. Integer exponents and scientific notation in this section, we will introduce another symbol for a fraction of the form and then we will use this symbol to write.
Convert numbers to scientific notation calculator for conversion of numbers into scientific notation and e notation converts to proper scientific notation format. Preparation for bioscience academy math assessment test math problems in this booklet without a calculator rules for writing numbers in scientific notation. Scientific notation on the graphing calculator (if a problem asks for the answer to be in expressed in scientific notation a scientist would write.


The finished product
|Steps required||27 main steps + 7 primer|
|Tool set||Compasses and straightedge|
|Index number||No. 6.12.01$006|
|View Template Page|
- Create points A and B. You know the drill.
- Create circle AB.
- Create line AB.
- Create perpendicular of AB passing through A.
- The antipode of B is C.
- Halve AC, midpoint D.
- Where the perpendicular crosses circle AB mark F. F is above A.
- Create circle, center F, radius AD.
- Where this new circle crosses AF, mark G. F is in segment AG.
- Create line parallel to AB passing through G.
- Create line parallel to AG passing through B.
- Where circle AB and FG cross mark H, where ABHF is a convex quadrilateral.
- Create line parallel to AG passing through H.
- Where the line from step 10 and 11 cross mark I.
- Where GI and the line two steps ago cross mark J.
- Create circle IJ.
- Where this circle crosses segment IB mark K.
- Trisect* IJ, making two new points. Order: J V W I.
- Create circles IJ and JI.
- Where these circles cross mark L and O. L is above IJ; O is below IJ.
- Create circle LJ.
- Create rays JL and IL.
- Where these rays cross circle LJ mark M and N, respectively.
- Create segments MO and NO.
- Where these new segments cross IJ mark V and W. JV = VW = WI.
- Trisect* IK, making two new points. Order: I T U K.
- Create circle KI.
- Where circle IK and KI cross mark P and S. P is to the right of IK; S is to the left of IK.
- Create circle PI.
- Create rays IP and KP.
- Where these rays cross circle PI mark Q and R, respectively.
- Create segments QS and RS.
- Where these new segments cross IK mark U and T. IT = TU = UK.
- Create line parallel to IJ passing through T.
- Create line parallel to IB crossing through V.
- Where these lines cross mark Z.
- Create line parallel to IJ passing through U.
- Create line parallel to IB passing through W.
- Where this new line crosses ZT mark X.
- Where WX crosses the line in step 23 mark Y.
- GVZXYUBA is a capchalogue card!


Counting On: Learning Math at Home
Math. It has always been my kryptonite. I love history, fly through Shakespeare, and diagram Dr. Seuss in my sleep. But, I still have no idea who Pythagoras is, in fact what is a theorem anyway? And, if two trains are traveling at the same speed and leave at two different times, I’m more worried about the crash that’s going to occur when they meet than the time. I guess you’ve figured it out: math is not my forte.
When we began homeschooling about four years ago, I thought “piece of cake, I can teach a five year old math.” Have you ever sat with a five year old and tried to explain to them that 4+2=6? It goes a little like this:
“No, it’s 6. So, what’s 4+2?”
“No, really it’s 6. So, what is 4+2?”
“I know!!!” (Hope springs.) “…623.” Face palm.
You see, I’m an adult. Clearly I can add and subtract and multiply- and if I can’t well there’s an app for that. The thing is, teaching and doing are two completely different things. Success at homeschooling is not measured by how well you aced those geometry tests in school but how well you translate that into teaching someone else. Some of us (me) need a little (or a lot) of help.
After several years of tears and frustration (from me), I realized I needed a solid math curriculum. That’s when I found Math-U-See. We went from daily tears over math lessons to excitement to flip to a new chapter and watch the instructional DVD. The thing we both love about Math-U-See is the outside instruction. Though I can’t imagine why anyone wouldn’t want to listen to me drone on day in and day out, sometimes hearing someone else say it is just what you need. Anyone can write a textbook, send it out, and leave mothers to struggle to remember the exact numerical value of pie (3.14 something right?).
But, that’s not what Math-U-See does. Thank you Professor Steve Demme. Between the instructional DVD, the easy to use workbook, and the manipulatives (counting rods that my younger children like to design pizzas out of), math has gone from a struggle to a piece of cake, or should I say pie?
Math-U-See: c/o Demme Learning
**We received this years’ curriculum as part of a collaboration but have been using them for three years now. I love Math-U-See and so do the littles. Less crying over math and more time to play. All opinions herein are my own and the result of several years of experience (and two children) with the curriculum. I don’t recommend Math-U-See because I got it for free. But, I do recommend it to end the tears over math lessons and I mean yours.**
I like your post! I plan on homeschooling when my children are older. Great ideas here.
Visualization is huge! I taught high school math, and this looks awesome.
Straight A Style
Love this post. I plan on homeschooling my daughter so reading about anything that has to do with homeschooling interests me. Thanks for sharing!
You already know how much I admire you for homeschooling. Seriously, you’re such a rockstar, Jamie! This curriculum sounds like it’s the right fit for your family. If I ever decide to homeschool, it definitely sounds like it would be an option for us as well!
this is such a good idea, i can see it being a lot of fun for kids, with the huge bonus that it encourages learning too. learning can be fun!
Loved this post! I’m thinking of possibly home schooling my children in the future so it was great to learn how to teach math at home. Thank you!
LOL! It’s “pi” not “pie.” But hey, I’d rather eat pie any day than figure out pi to the hundredth place.
I am a dummy in math to so I will problably purchase Math-u-see for myself before I could proudly teach my daughter it!? Just so I dont need to tell her “Go and ask your dad” all the time…
Haha love it. I am the same way. I still call my dad and ask him what I’m doing wrong when we’re stuck on something.
Looks like a great math curriculum. Thanks for sharing
Homeschooling is something we have thought about doing with our son, it really all comes down to where we are living when it’s time to start school. I suck at Math so I will have to keep this in mind if we do home school.
What a great concept. I am more logic driven but my husband is more conceptual. It will be interesting to see how our 15 month old learns. I will have to remember Math – U – See.
We homeschool and so I can totally appreciate this post. My little ones love math. Thanks for sharing.
Thank you for this post! I am considering home school for my Little and I know I will need a strong math curriculum when the time comes. I’ve bookmarked this one!
I love this post. My son is a visual learner so it seems this would be perfect for him
Thank you for sharing excellent information and resources,
Thanks for sharing. These would come in real handy for me. I’ve just started homeschooling since September.
Oh my what a fun way to learn! Totally checking these out.. My Son is too little right now but I have been looking into homeschooling and this would be perfect!
Comments are closed.


Below is a list of great websites and video tutorials that explain the math standards, and skills your child are being taught (K-5):
- http://www.cgcs.org/Page/244 – The Council of the Great City Schools’ parent roadmaps in mathematics provide guidance to parents about what their children will be learning and how they can support that learning in grades K-8. These parent roadmaps for each grade level also provide three-year snapshots showing how selected standards progress from year to year so that students will be college and career ready upon their graduation from high school.
- https://www-k6.thinkcentral.com – ThinkCentral is an online portal that gives you access to Math Expressions. Math Expressions is the math series our district has chosen for mathematics instruction. Click the hyperlink to view instructions on how to access ThinkCentral from home. ThinkCentral
- https://www.khanacademy.org/math – Khan Academy has great video tutorials that explain math skills.
- Discovery Education – Videos and tutorials explain basic operations and help with the mastery of math skills in addition, subtraction, multiplication and division.
- https://medium.com/i-math- A blog that offers various math tutorials
Below are some great websites students can access to practice and enhance their math skills:


1000 Java Tips ebook
Free "1000 Java Tips" eBook is here! It is huge collection of big and small Java
programming articles and tips. Please take your copy here.
Take your copy of free "Java Technology Screensaver"!.
Java: Random numbers - intro
JavaFAQ Home » Java Notes by Fred Swartz
When to use random numbers
There are many types of programs that use random numbers.
Game programs use them to create situations that are
not always the same every time a player is in the same situation,
or maybe you want to program to shuffle a deck of cards.
Simulations usually use random numbers.
You might want to use random numbers to change the
appearance of something -- screensavers are an
example of use. There are many other uses also.
Type, Range, and Distribution
When you generate random numbers, you need to decide
which type you need (eg, int or double), what range
you need (minimum to maximum), and how they are
distributed. There are two common types of distributions:
uniform and normal (equivalent to Gaussian).
In a uniform distribution all numbers in the range are
equally likely to be produced.
How can a computer generate a random number?
Computers are deterministic -- they do the same thing whenever
they have the same input. Therefore, in some way it is
impossible for a computer to compute a truly random number.
But the methods that are used generate sequences of numbers
that meet the statistical requirements of randomness.
Because the numbers are not truly random, they are
sometimes referred to as pseudorandom numbers.
These random number generates will produce exactly the same
sequence of pseudorandom numbers if they start with the
same initial value. This initial value is called the seed.
If we start a program with the same random seed, we
will get the same sequence of numbers.
The default seed is the current time in milliseconds since 1970.
This works very well, but there are two issues.
- You may want to set the seed so that the sequence
can be reproduced when you are testing your program.
- If you want more than one random sequence, you should
use only one random generater because, if two
random generators are created during initialization,
it is very likely that they are created in the same
millisecond, which means they have the same seed,
and will produce the same sequence of "random" values.
Math.random uses only one seed, so it
is safe for this even if it has less convenient
methods than the
Excursion 1: Random Thoughts by Joshua Bloch, author of Effective Java.
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Using an MPC to control a system: Discretizing the state-space equation system
Last time we discussed what controllers are and some examples where they are used. We also defined a system to control and deduced two important equations that allow us to model it:
In this post we are proceeding with some more manipulations and then we are going to discretize the model since computers don’t work in a continuous fashion. Finally we deduce the algebraic form for the predictions within a certain horizon of samples.
But why more manipulations? Currently the equations still don’t fit into the canonical form of a State-Space Equation System (SSES). This system is going to be quickly explained at the end of its deduction. Let’s see how we can shape them to the correct form.
State-Space Equation System
What we’ll do first is the following change:
This is a simple change that gives the first equation the shape it needs. Note that both temperatures can be separated into two different terms in the equation, which makes the transformation into algebraic form more complicated and can be avoided by aggregating both temperatures.
But what’s the implication? Whilst the reference for T_o is 0 °C, the reference for T is T_i. So if T_i is 10 °C, meaning the solution is entering in the vessel at that temperature, and we want it to heat up to 80 °C, we set our reference point to 70 because it is a difference of 70 °C from 10 to 80 °C. That’s it!
For the second equation we face the same problem. We need to have our control input be multiplied by a constant. If we unfold the pressures we get one term too many.
A new variable θ will be our control input and will cover the pressure ranges that p can take by creating a linear relationship between the lowest and greatest value. We set p_o to be 1 atm and p_i to be the greatest pressure value, 1.2 atm for instance. We can see that p will be 0.8 atm when θ is -1 and 1.2 atm when θ is 1.
The system equations are now in the desired form. We have two states: V dot and T and a control input θ. These are the variables of our system. It is time to transform the equations into algebraic form.
For simplicity’s sake, let’s turn the parameters into the letters a, b and c. Can you unfold the algebraic system of equations to match the two equations we had before?
You may see it more clearly now that the purpose of these equations is to understand how the system changes in time based on the current states by calculating their variation w.r.t. time.
Also, it sould be mentioned that this system of equations does not need to take this form. What I mean is that both equations may be more complex and contain all states and control input in them like the following examples:
Consider these systems. K, J and R are some random states and ξ a random control input. You can see that all states have their dotted counterparts and that the matrices of parameters may be more or less sparse. Instead of only one control input, there might be various other variables that help control the system.
For instance, in the system we are working with, we may increase the steam’s flowrate but we could also decrease the solution’s fowrate. This would allow the same mass of solution to recieve energy from the steam for a longer time and heat up more.
Now we need only add one more equation. A very simple one that will isolate T since it is the variable that we are controlling for and we’ll need it to calculate the error later on.
Let’s join both systems together and make some changes for the sake of ease of visualisation.
We have finally derived our State-Space Equation System (SSES), in which the first equation describes how our system behaves and the second isolates the controlled state. The transformation of θ into a vector containing its value is just to represent the SSES in a more general way to be applicable to systems with two or more control inputs.
Discretizing the SSES and the Forward Euler method
The SSES as we have it now is function of a continuous time variable. However, machines work in a discrete fashion and instead of dealing with time, we have to deal with samples that are a discrete snapshot in time of the value of the states. So, instead of calculating how the state changes w.r.t. time, we are calculating its value one sample of time later.
To calculate the states one sampleof time later, we are using the Forward Euler method. This method says that in an infinitesimally small variation, the system variation can be linearly approximated.
If we make our time samples (t_s) small enough they could fit the method well. The subscript K stands for the sample number. Let’s substitute it in our system equation.
I is the identity matrix of the same shape of vector X_K. By changing the notation we can make this expression closer to what we had before. We can also represent the second equation of our SSES in a discrete form even though nothing changed.
Great! We have discretized our system. We can now calculate the value of the states a time sample later. How can we extend it to make an horizon of time samples greater than the first?
Horizon of predictions
Before we go into the calculation of the horizon of predictions let’s get the difference between iterations and predictions clear. First, in each iteration there is an actual variation in our system. Each prediction is the how the model predicts the system to change with the following iterations that haven’t happened yet.
Let’s discuss this further with an example of a rocket doing a vertical landing.
At every iteration (three are shown with different colours and represented by the first subscript), our controller calculates an horizon of seven predictions (represented by the second subscript), using seven control inputs and the states at the instant zero (where the rocket is).
We take the first control input (θ_1,0) to produce the predicted change for the next iteration and discard the remaining predictions.
Because models aren’t perfect, if we actually had a real world system, we would see a difference between the measured height by a sensor attached to the rocket and what the model had predicted. So X_1,1 isn’t really equal to X_2,0.
However, since we are not making real world measurements, we assume we have a good enough model so that X_1,1 is equal to X_2,0. Well, at least for now.
So, at the new iteration, after we used θ_1,0 to calculate X_2,0, we repeat the process. We calculate a new set of control inputs that the model believes to be the new best and use the first value to calculate the states for the next iteration.
Now that we understand how the variables are intertwined, let’s see it in an algebraic form.
To extend the horizon of predictions we need only take the prediction for the sample number K+1 and use it to calculate sample K+2. Same for the sample K+3 and so on. If we have an horizon of three samples, we’ll have the following:
We want to calculate the predictions based only on the current iteration (K). This is important because the way the MPC works is that for every iteration, a new set of predictions is calculated like it was discussed with the rocket example.
Can you see a pattern? The generalization for the (K+N)th time sample would be:
And the generalization of all N time samples of the horizon is:
These are the calculations for the predictions, not the change in iteration. Now we need to pick θ_0 from this iteration and apply it to our real world system to create the changes of the states that our model tells us would be best in order to decrease the error. After these changes are applied, we enter a new iteration, calculate a new vector of control inputs and, along with the new states, the predictions. Then we take our new θ_0, apply it to our real world system and make changes to our states. And now it’s rinse and repeat.
And there you have it. We went from giving the system equations the proper form, creating the SSES, discretizing it and to being able to predict values of the states for a certain horizon of time samples.
Next time we are going to make slight changes to the control input so that it makes more sense in the perspective of the real world and we are going to close the loop by solving an objective funtion that deals with the error to calculate the vector of control inputs. Finally we’ll see how we apply the control input to integrate our OLS and change states.
I hope the explanations are clear enough. I know it is alot of theory to take in. Read as many times as you want and don’t be affraid to ask questions if you need to!
Thanks for reading and stay tuned!


Hi Juan,Juan Conejero said:On a side note, combining linear L and RGB is possible in PixInsight. However you must perform a YRGB combination instead of LRGB.
In this case, instead of the CIE L*a*b* space, the CIE XYZ space must be used. CIE XYZ is a linear color space; however, the underlying RGB working space must also be linear in order to preserve linearity in the combined image. The basic procedure would be as follows:
- Define a linear RGB working space. With the RGBWorkingSpace tool, set gamma = 1.0 (disable sRGB gamma function). In addition, I would define a uniform RGB working space in the same operation. So the steps with RGBWorkingSpace are:
* Set the three luminance coefficients = 1.
* Define a uniform energy illuminant by setting the six chromaticity coordinates = 0.333333.
* Disable the sRGB gamma function and set gamma = 1.
* Apply to both the RGB and L images.
- Use the ChannelCombination tool to perform a YRGB combination. Select the CIE XYZ space, disable the X and Z components, and select the L image for the Y slot. Apply to the RGB image and you're done.
- To process the linear luminance of the combined YRGB image, you must select "Linear luminance" in the applied tools, when applicable (for example, Deconvolution and ATrousWaveletTransform allow you to select it).
- After the initial nonlinear stretch with HistogramTransformation, you may want to apply the default RGBWorkingSpace parameters, as a linear uniform space no longer will describe the image appropriately.
This should work
I've tried this method just for curiosity, but when I try to use RGBWorkingSpace with all six chromaticity set to 0.333333 I get the error:
Instance Validation Failed
Reason: Singular Matrix in RGB working color space inizialization


Paper by Martin L. Demaine
- Erik D. Demaine, Martin L. Demaine, and Ryuhei Uehara, “Any Monotone Boolean Function Can Be Realized by Interlocked Polygons”, Algorithms, volume 5, number 1, March 2012, pages 148–157.
Suppose there is a collection of n simple polygons in the plane, none of
which overlap each other. The polygons are interlocked if no subset can
be separated arbitrarily far from the rest. It is natural to ask the
characterization of the subsets that makes the set of interlocked polygons
free (not interlocked). This abstracts the essence of a kind of sliding block
puzzle. We show that any monotone Boolean function f on n variables can be
described by m = O(n) interlocked polygons. We also show that the decision
problem that asks if given polygons are interlocked is PSPACE-complete.
- This paper is also available from MDPI (open access).
- The paper is 10 pages.
- The paper is available in PDF (2189k).
- See information on file formats.
- [Google Scholar search]
- Related papers:
- InterlockedPolygons_CCCG2010 (Any Monotone Boolean Function Can Be Realized by Interlocked Polygons)
- Related webpages:
- Interlocked Polygons
See also other papers by Martin Demaine.
These pages are generated automagically from a
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Is there a way to avoid all that extra dough in between the cookies? (Photo: Christmas Tree Cookie Cutter from Bigstock)
It should come as no surprise that food, chemistry and mathematics meet in baking. For once I will leave the chemistry aside for a while and turn to the mathematical aspects of baking. More precisely I will delve into geometrical problems encountered in baking. When cutting cookies from a rolled out dough or placing cookies on a sheet for baking you actually attempt to solve a mathematical problem known as a packing problem. The purpose is to maximize the distance between the cookies and maximize the size of the cookies, paying attention that the cookies should not touch. Many will perhaps start with a square packing (see below), but soon figure out that a hexagonal packing will fit even more cookies onto the rolled out dough or onto the baking sheet (especially when the dough/sheet is large compared to the cookies). The optimum way of placing 2-17 circles in a square are shown below (and the solution for up to 10.000 circles is also available).
My challenge for you however is a different one as I’m interested in eliminating the leftover dough when cutting cookies. To achieve this the cookies cannot be circular. Using a square cookie cutter (or simply a knife) would be the easiest way to leave no gaps, but how cool are square cookies? What I’m really looking for are cookie tessallations which are aesthetically pleasing, and at the same time transferable to a baking sheet. Oh yeah: a tessallation “is the process of creating a two-dimensional plane using the repetition of a geometric shape with no overlaps and no gap” according to Wikipedia. So – no gaps – no leftover cookie dough! (more…)


For high rise buildings, if the stiffness distribution is unsuitable, whipping phenomenon can occur at the top, and the upper part will be subject to extreme shaking. On account of this, the section of the upper part is limited not from required strength considerations but by appropriate stiffness distribution. In the case of structural planning of a pure frame building, if the story and span numbers are fixed, column / beam sections of lower stories can be established by long term axial force limitation and base shear coefficient. Then the shear stiffness for lower stories is decided. After establishing a suitable shear stiffness distribution, dimensions of members can be decided.
This paper describes the examination of shear and bending deformation for reinforced concrete frame buildings, and the appropriate stiffness distribution to avoid whipping phenomenon. Finally, the method of deciding the member section is shown.
The bending stiffness EI of a frame building of height H and span m (building width B = ml) as shown in figure 1, is given by equation (1), in which the column section is square and section area is Ac.
The story shear stiffness GA is given by equation (2) by the Muto's D method when the story height is h and stiffness coefficients obtained from stiffness ratio of columns to beams are all "a".
With a model of the bending-shear system fixed at base with height H
, constant bending stiffness EI and shear stiffness GA, the bending deformation and the shear deformation at the top are obtained by equation (3) where x is the distance from base.
The deformation at the top (x = H) is given by equation (4).
EI and GA obtained from equations (1) and (2) are substituted into this expression. When the stiffness ratio of column / beam is equal, the coefficient "a" becomes 0.5. Usually it comes within the range 0.2-0.4 because beam span is longer than height and the section of a column is greater than the section of a beam for a building designed by the beam yielding method. is known as the column ratio and it is about 0.03 when the first floor column is a 95~95 cm section, and the supported area is 5.5~5.5 m. The ratio of deformation of bending and shear deformation at the top is given by equation (5).
On the other hand, for the bending-shear model in which shear stiffness GA varies linearly to zero toward the top, it is given by the following equation.
at the top,
It becomes double that of the model with uniform shear stiffness. The ratio of bending and shear deformation is given by equation (8).
The ratio is between equation (5) and (8) for a real building, and would be 0.02(n/m)^2 . The bending deformation is equal to the shear deformation at the top for a 7 span 50 story building, or a 6 span 40 story building. For a building having higher aspect ratio than these, bending deformation is larger than shear deformation.
From equation (1), bending stiffness is proportional to column cross-sectional area, and shear stiffness is in proportional to the square of column cross-sectional area according to equation (2). Therefore, bending stiffness reduction is proportional to the square root of shear stiffness reduction by decreasing cross-sectional area of the column. The effect of stiffness distribution on eigen mode was examined using this relation in the study.
These eigen modes and story drift modes are shown in figure 2. For the first mode, the story drift is large at the lower part when the bending deformation rate is small, and is greatest at the top part when there is considerable bending deformation. The greater the rate of bending deformation, the larger the story drift in the higher part.
When there are few bending deformation, the change of eigen mode with stiffness reduction is considerable. The shape becomes susceptible to whip with stiffness reduction. The change in eigen mode with stiffness reduction with a large bending deformation rate is small. If shear stiffness at the top is more than 0.5 times that at the base and the bending deformation is smaller than the shear deformation at the top, the first mode shape of story drift never become large at the upper part. When the bending deformation is larger than the shear deformation at the top, the story drift is large in the upper part even for the uniform system. The tendency increases with decreasing the shear stiffness.
For the case where the shear stiffness decreases to 0.2 at the top, the story drift mode becomes considerable at the upper part, and will lead to whipping phenomenon by a combination with response spectrum. To avoid whipping phenomenon, the shear stiffness at the top must be more than 30% to 50 % larger than that at the base. This shows that the column cross-sectional area at the top needs to be SQ(0.5)ą0.7 times that at the top, and column dimensions needs to be SQ(0.7)ą0.85 times those at the base when the top shear stiffness is larger than 50% of the bottom stiffness.
In reinforced concrete column members, limit deformation and relation of axial force ratio are suggested from meaning of ductility considerations (Inai et al., 1997). The following equation is given for a column with constant axial force.
Here,Å is the axial force ratio for core cross-sectional area and R is the drift limitation. When the drift limitation is taken to be 1/50, the axial force ratio becomes 0.36. Because core cross-sectional area is assumed to be 0.75 times that of the total section in the literature, it becomes around 0.27 at the axial force ratio limitation for total sections.
As the horizontal load is equivalent to weight of 4 story (Shimazaki et al., 1994), regardless of building height, column section is fixed only by the axial force limit for high rise buildings. Based on the assumption of a 0.25Fc axial force limit, 0.03 column rate and 1.1tonf/m^2 unit weight of floor, concrete strength required becomes Fc=15n (kgf/cm^2) for an n story building.
First, the sections of the lower story are set. Column sections are established from the long term axial force limit of 0.25Fc. Beam moment is calculated from base shear required, and section / reinforcing arrangement of the beam is established. Column strength at the base is made double the beam strength for yielding column at the base after beam yielding. If reinforcing bar can not be arranged in the column section, the section is changed. The calculation procedure and the section calculated are shown in table 1.
Next, section setting for each story is performed as follows:
Comparison with the estimated reinforcing arrangement of the lower story shown in table 1, the reinforcing arrangement amount becomes large for the 25 story building, because the first period is short and weight increases. For the 60 story building, because the section is less than that of general structures due to the use of high strength materials, and the period is longer than the abbreviated expression, the required shear force becomes small, and the reinforcing arrangement also becomes small.
The eigen periods agree well. There is almost no difference in both total eigen mode and drift mode. It can therefore be said that the eigen period and eigen mode shape obtained by this abbreviated algorithm have sufficient precision.
Calculated results are shown in figure 7. The response values by frame analysis are less than the estimated values and the distribution of drift for every ground motion is similar. Thus it can be said that if the section for a building is set by the proposed method, the building has the earthquake resistance intended by a design method such as drift limitation.
Shimazaki, K. (1992). Seismic coefficient distribution of high-rise reinforced concrete buildings. Proc. 10th WCEE, 4281-4286, Madrid, Spain
Inai, E. and H. Hiraishi (1997). Structural design charts and equations of deformation capacity of reinforced concrete columns after flexural yielding. Proc. 11th WCEE (will be published), Mexico
Shimazaki, K. and A. Wada (1994). Design base shear coefficients for high-rise reinforced concrete buildings. Journal of structural and construction engineering, AIJ, No. 458, 99-108, Tokyo, Japan


Thursday, September 26 @ 15:00
Quantum mechanics is the branch of physics that studies how the universe works at the smallest scales. It has given us technologies like semiconductors, lasers, LEDs, and electron microscopes, and promises even more exciting applications like quantum computing.
The quantum world is notoriously difficult to understand, since few of our intuitions about physics apply at the subatomic scale. But not so for functional programmers! Many of the mathematical ideas that we use to understand the quantum world, like Hilbert space, operators, tensors, and group representations, can all be understood in terms of functions. In this talk, I'll use familiar concepts like composition, partial application, and currying to make the foundations of the subject clear and show how to solve some basic problems in F#. At the end, I'll show how these techniques can be used to model a simple quantum computer.
I'm the co-founder and CEO of a company called Tachyus, where we build enterprise software for the energy industry using the F# programming language. I am also passionate about scientific and mathematical programming, particularly in F# and other functional languages. I did a lot of work in my graduate degree on solving mathematical problems in quantum and particle physics using F#. I also have a forthcoming book called "Math for Programmers" teaching professional software developers calculus, linear algebra, and applications.