Factors affecting an American County’s Politics: A Statistical Approach
I always enjoyed looking at election results by county (a geographic subdivision) and the factors that affect it (like education, race, population density). While I could do simple calculations that could compare one variable to another, I always wanted to compare multiple variables and see how they would combine together. This would be much more interesting than just one variable.
Journey of reaching the data:
This is data that I combined from an online source for election results and the US Census’ Bureau’s data on demographics. From here, I managed to put all the necessary variables into R (a statistical programming language) to do a multivariable regression. I then took the constants from the linear regression, which I could then use to create an estimate for how a county would vote, based on the demographics of the county.
The variables I took for the regression were the share of population in a county that is non-Hispanic White, African-American, Asian and Hisapnic, along with the common (base 10) logarithm of the population density and the education levels (the share of residents that are aged 25 or above and that have a Bachelor’s Degree or higher). I had studied these variables earlier and found that these had an effect on the county’s politics on their own.
Visual depiction :
Here is roughly what you get when you try to estimate how the counties vote just by using their demographics and the regression constants. The Bluer the dot, the more Biden (the Democrat) should have won it by. This is not too far from the actual results.
This map measures the difference between what the regression estimates and the actual results. The Bluer it is, the more Democrats beat the regression estimates by, while the Redder it is, the more the Republicans beat the regression estimates. You can see some patterns here, of certain areas generally being more Democratic or more Republican than the regression model expects.
The linear regression gives a “line of best fit” based on the values you already have, which can then be used to estimate an output value with multiple inputs, even if you do not have the actual output for those inputs.
This regression works rather well, with the expected values having a strong relationship with the actual values. It is much more reliable than using a few variables on their own. However, its accuracy has limits because it uses the education level of a county too heavily in it’s analysis. Education is a large factor in a county’s results, but the model often makes errors in more-educated Republican counties and less-educated Democratic ones. This leads to many suburbs around big cities being underestimated for Republicans while many working-class areas are underestimated for Democrats, which includes much of the rural Midwest, New England and working-class areas in cities with many minorities. Still, it is a useful tool to estimate how a place will vote, just given its demographics.


By Vincenzo Capasso, David Bakstein
This concisely written booklet is a rigorous and self-contained advent to the speculation of continuous-time stochastic methods. A stability of conception and functions, the paintings positive aspects concrete examples of modeling real-world difficulties from biology, drugs, commercial functions, finance, and coverage utilizing stochastic equipment. No past wisdom of stochastic techniques is required.
Key issues lined include:
* Interacting debris and agent-based types: from polymers to ants
* inhabitants dynamics: from beginning and demise methods to epidemics
* monetary industry versions: the non-arbitrage precept
* Contingent declare valuation versions: the risk-neutral valuation thought
* probability research in coverage
An creation to Continuous-Time Stochastic Processes could be of curiosity to a large viewers of scholars, natural and utilized mathematicians, and researchers or practitioners in mathematical finance, biomathematics, biotechnology, and engineering. appropriate as a textbook for graduate or complicated undergraduate classes, the paintings can also be used for self-study or as a reference. necessities contain wisdom of calculus and a few research; publicity to likelihood will be beneficial yet no longer required because the worthy basics of degree and integration are provided.
Read Online or Download An Introduction to Continuous-Time Stochastic Processes: Theory, Models, and Applications to Finance, Biology, and Medicine PDF
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With its many easy-to-follow mathematical examples, this publication takes the reader on a virtually chronological journey throughout the interesting and outstanding legislation of probability, omnipresent within the wildlife and in our day-by-day lives. alongside the course many desirable issues are mentioned, equivalent to: hard chance paradoxes; "paranormal" coincidences; video game odds; motives and results; interpretation of opinion polls; profitable percentages as a video game proceeds; the character of randomness; entropy and randomness; randomness in lifestyles; algorithmic complexity and the undecidability of randomness; chances and obstacles of studying the legislation of a Universe immersed in likelihood occasions.
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Extra info for An Introduction to Continuous-Time Stochastic Processes: Theory, Models, and Applications to Finance, Biology, and Medicine
The triplet (a, σ 2 , λL ) is called the generating triplet of the inﬁnitely divisible characteristic function φ. 11. A distribution is inﬁnitely divisible if and only if it is the weak limit of a sequence of distributions, each of which is compound Poisson (the reader may refer to Breiman (1968)). 12. We will say that two distribution functions F and G on R are of the same type if there exist two constants a ∈ R∗+ and b ∈ R such that F (ax + b) = G(x) for any x ∈ R. It is easy to see that this is an equivalence relation.
0, n i=1 f (yi ), if y1 < y2 < · · · < yn , otherwise. 18. Let X and (Yn )n∈N be random variables such that X ∼ E(1), Yn (ω) = n, if X(ω) ≤ n1 , 0, otherwise. Give, if it exists, the limit lim Yn : n→∞ • • • • in distribution, in probability, almost surely, in mean of order p ≥ 1. 19. Let (Xn )n∈N be a sequence of uncorrelated random variables with common expected value E[Xi ] = μ and such that sup V ar[Xi ] < +∞. Xi n Show that i=1 converges to μ in mean of order p = 2. 20. Give an example of random variables X, X1 , X2 , .
S. Proof: Let G ∈ G; then, by independence, Y dP = IG Y dP = E[IG Y ] = E[IG ]E[Y ] = P (G)E[Y ] = G E[Y ]dP, G from which the proposition follows. 122. Both the monotone and dominated convergence theorems extend in an analogous way to expectations conditional on σ-algebras. 123. A family of random variables (Yn )n∈N is uniformly integrable if lim sup m→∞ n |Yn |≥m |Yn |dP = 0. 124. Let (Yn )n∈N be a family of random variables in L1 . Then the following two statements are equivalent: 1. (Yn )n∈N is uniformly integrable, 2.
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|LITIGATION GRAPHICS - COMPUTER ANIMATION - TECHNICAL ILLUSTRATION - CAD DRAFTING - AUTOLISP PROGRAMMING
Copyright 2019 - Pixel Graphics, Inc. All rights reserved.
AutoLisp Program: Intersection of a Line and a Plane
Overview of the Autolisp Program LinePlaneInt.lsp
This Autolisp program draws a point at the 3D intersection of a line and a plane. The user first picks the
three points on the plane, then picks two points on the line in AutoCAD. The point is plotted whether or not
the line actually passes inside the perimeter of the defining points.
After loading the program into AutoCAD ( Tools -> Load Application...-> then selecting the file, simply type
LinePlaneInt at the AutoCAD command prompt to run the command.
Below is a screen shot showing the results of a test case.
Jeff Winship - Computer Graphics Consultant May 3, 2008
AutoCAD Screen Shot using LinePlaneInt.lsp
Copyright Info & Downloading the Program
If you copy and use the function, please respect my work and the time I've put into it by keeping my
copyright info with the function, and giving me credit where it's appropriate. A link from your site would be
appreciated as well. If you don't have a website, please help promote my site by passing along a link to my
site to other fellow Autolisp programmer(s) via e-mail. Thanks.
If you have any comments or questions regarding Autolisp program, or even find a bug, feel free to e-mail
The Autolisp program for LinePlaneInt.lsp is solved using vector calculus and contains the following
Calculates and returns the determinate of a 3 x 3 matrixMatrix_Inverse3
Calculates and returns the matrix inverse of a 3 x 3 matrixLine_Plane_Int
Calculates and returns the intersection point of the line and the plane. It also returns a T value if the intersection
point lies within the boundaries of the plane, nil otherwise.
There is one known bug in this program: it will return a "divide by zero" error if the line and plane are parallel.
Since they don't intersect, this isn't so much of a bug as it is an error handling issue.
*Revised 3-13-2009: Fixed a bug where the "POINT" command would not execute properly in non-English
versions of AutoCAD. Thanks for the fix Lukas.


Sum Calculator: A Handy Tool for Quick and Accurate Calculations
Have you ever found yourself in a situation where you need to add up a long list of numbers? Maybe you’re working on a budget, or you’re trying to balance your checkbook. Whatever the reason, adding up a long list of numbers can be time-consuming and prone to errors. But with the help of a sum calculator, you can quickly and accurately calculate the sum of any list of numbers. In this article, we’ll take a closer look at what a sum calculator is, how it works, and how you can use it to simplify your calculations. Check Our More Online TOOL’s
What is a Sum Calculator?
A sum calculator, also known as an addition calculator, is a tool that allows you to add up a list of numbers quickly and accurately. With a sum calculator, you can simply input a list of numbers, and the calculator will do the rest. The result will be the sum of all the numbers you entered.
How Does a Sum Calculator Work?
A sum calculator works by using a simple algorithm to add up a list of numbers. When you enter a list of numbers into the calculator, it first checks to make sure that all the numbers are valid. Once it has verified that all the numbers are valid, it then adds them up using a simple addition algorithm. The result is then displayed on the calculator’s screen.
Why Use a Sum Calculator?
There are several reasons why you might want to use a sum calculator. Here are a few:
- Saves Time: Adding up a long list of numbers can be time-consuming, especially if you’re doing it manually. With a sum calculator, you can quickly get the sum of any list of numbers in just a few seconds.
- Accurate Results: When you add up a long list of numbers manually, it’s easy to make mistakes. With a sum calculator, you can be sure that the result is accurate.
- Easy to Use: Sum calculators are typically very easy to use. All you need to do is enter the numbers you want to add up, and the calculator will do the rest.
How to Use a Sum Calculator?
Using a sum calculator is very easy. Here’s a step-by-step guide:
- Open the Sum Calculator: You can use an online sum calculator, or you can download an app on your phone or computer.
- Enter the Numbers: Once you have the sum calculator open, enter the list of numbers you want to add up.
- Click the Calculate Button: After you’ve entered all the numbers, click the “Calculate” button.
- View the Result: The result of your calculation will be displayed on the calculator’s screen.
Tips for Using a Sum Calculator
Here are a few tips to help you get the most out of your sum calculator:
- Double-Check Your Numbers: Even though sum calculators are very accurate, it’s always a good idea to double-check your numbers before you hit the calculate button.
- Use Parentheses: If you’re working with a long list of numbers, it can be helpful to use parentheses to group them together. This will make it easier to keep track of which numbers you’ve already added together.
- Save Your Results: If you need to refer to your results later, be sure to save them somewhere. You can take a screenshot of the calculator’s screen or copy the result to a spreadsheet or document.
In conclusion, a sum calculator is a handy tool that can save you time and help you avoid errors when adding up a long list of numbers. With a sum calculator, you can quickly and accurately calculate the sum of any list of numbers. Whether you’re working on a budget, balancing your checkbook, or just need to add up a list of numbers,
- Is a sum calculator accurate? Yes, sum calculators are very accurate as long as you enter the correct numbers.
- Can I use a sum calculator for multiplication or division? Yes, many sum calculators can perform other mathematical functions like multiplication and division.
- Are sum calculators easy to use? Yes, sum calculators are typically very easy to use. All you need to do is enter the numbers you want to add up and click the calculate button.
- Can I use a sum calculator for complex calculations? It depends on the calculator. Some sum calculators can handle more complex functions, while others are better suited for basic calculations.
- Are there any limitations to using a sum calculator? Yes, there are some limitations to using a sum calculator. For example, some calculators may not be able to handle very large numbers or decimals. Additionally, if you’re working with very complex calculations, you may need to use a more advanced calculator or consult a professional.


The breadth of knowledge and expertise required of individuals working in Science, Technology, Engineering, and Mathematics (STEM) is increasing as the skills and problem solving strategies necessary to address the world’s challenges become more interdisciplinary and complex. Today, elementary school, middle school and high school students all must learn both the concepts and content that are typically addressed in core disciplines such as biology, physics, mathematics, and computer science, while also understanding deeply how these disciplines influence one another. King’s PreKindergarten-Grade 12 STEM program encourages the depth of interdisciplinary preparation necessary for college and for success in the 21st century.
All King students are deeply immersed in the study of STEM. Students passionate about STEM can elect to graduate with a Certificate of Distinction in STEM. These STEM scholars pursue challenging courses, club activities, project development and/or research opportunities, culminating with a Capstone Project. Students learn first-hand the real-world skills used by today’s researchers and innovators, such as literature review, experimentation or project design, modeling, data analysis, and information presentation.
Our students learn to think like scientists. Students experience hands-on applications of key ideas that span multiple scientific disciplines, such as energy, matter, weather, space, and changes in nature.
At King, technology includes the study of computers and computational systems that enhance our students’ critical thinking skills – and we also teach students to use technology as a creative tool.
At King, engineering is the application of mathematics, science, technology and practical knowledge to solving societal issues. It brings together research, innovation, design, and construction of structures, machines, tools, systems, components, materials, and processes.
King helps students develop a passion for mathematics, in terms of recognizing both the inherent beauty of the discipline as well as its crucial importance to other fields of knowledge.


How to add fractions which have different denominators. Add fractions using the following steps.
Correct answers include 10 12 15 18 20 24 25 30 and 30 36 10 12 15 18 20 24 25 30 and 30 36.
How to add algebraic fractions with different denominators. Add or subtract fractions with different denominators. Whether adding mixed numbers solving word problems or comparing fractions everyone can find value from these lesson. Write equivalent fractions making sure that each equivalent fraction contains the least common denominator LCM 3.
When applied to fractions this number is called the lowest common denominatorLCD of the fractions. Add the equivalent fractions that you wrote in step 2. Find the LCD of 2 2 3 3.
Find the lowest common multiple of the denominators. Identify the least common denominator by finding the least common multiple for the denominators. Steps for Adding Fractions with Unlike Denominators.
Different denominators — The LCM. Multiply the two terms on the bottom to get the same denominator. Applying the four operations to algebraic fractions.
Get a common denominator if the denominators are different. The Lowest Common Multiple LCM of a series of terms is the smallest product that contains every factor of each term. To convert fractions into decimals divide the denominator into 100 then multiply the answer by the numerator and finally add the decimal point i guess.
To get the denominator just multiply all the. Add fractions the easy way. 1 2 1 3 1 2 1 3.
Do the same with the second fraction and add this value to the first. Ideal for GCSE or C1C2Practice Questions. Simplify the numerators to obtain the numerator of the answer.
Do the same with the remaining fraction s. Change into equivalent fractions with the LCD 6 6. The numerator is 3 and 02 x 3 06.
Simplify the numerators and denominators. The first step in adding fractions with different denominators consists of finding the Least Common Denominator LCD. 1 Find two fractions equivalent to 5 6 5 6.
Teach addition and subtraction of fractions with the lesson plans on this page. 2 x-2-3 x21 x-2 x2. For example 35 is equal to 06 because 5 going into 100 is 20 which would make the decimal 02.
In order to make the denominators same you need to take LCM. Add and Subtract Fractions with Different Denominators Once we have converted two fractions to equivalent forms with common denominators we can add or subtract them by adding or subtracting the numerators. The denominators should now be the same.
There is nothing to factor in the first two so that leaves the third one. Here are the steps. 3 6 2 6 3 6 2 6.
Start out by multiplying the numerator of the first fraction by the denominators of all the other fractions. Express all fractions in terms of the lowest common denominator. I hope this helped.
Click the Calculate button to solve the equation and show the work. The first part is to make the denominators same. Convert each fraction to an equivalent fraction that has the LCD as its denominator.
To add fractions with different denominators we must learn how to construct the Lowest Common Multiple of a series of terms. For more math v. For example consider this series of three terms.
This video shows how to add or subtract algebraic fractions by putting both fractions over a common denominator. Adding or subtracting algebraic fractions with different denominators might be little bit tricky. To add or subtract algebraic fractions.
13 23 12 32 1 3 2 3 1 2 3 2. Select the number of fractions in your equation and then input numerators and denominators in the available fields. Do note that making denominators same is important otherwise you cant add or substract numerators.
In order to be able to do that we must have all denominators factored. You can add and subtract 3 fractions 4 fractions 5 fractions and up to 9 fractions at a. Find the lowest common multipleof the denominators.
These adding and subtracting fractions with unlike denominators lesson plans are great for teaching kids strategies for dealing with fractions. This video is provided by the Learning Assistance Center of Howard Community College.


8. Blaise Pascal
(June 1623 – 19 August 1662)
Blaise Pascal was born in Clermont-Ferrand, France. His father was a talented mathematician and a tax collector. He being a child prodigy was educated by his father.
Pascal was naturally very drawn towards mathematics. In 1642, while he was still a teenager, he started working on calculating machines. After three years of hard work, he was finally able to invent the mechanical calculator. He initially created a wooden box that had 16 separate dials.
Addition and subtraction was done by the turning of each dial. Pascal did what other has been trying to do and failed. Leonardo di vinci also tried to make a machine that was similar to the one made by Pascal. Who can deny that this invention is among the great inventions that have so far remained relevant?


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The xtractis® robot benefits from the most recent advances in Fuzzy Logic coupled with Machine Learning. Using its unique mathematical approach and proprietary algorithms, xtractis® analyzes your multidimensional databases and automatically discovers decision-support systems, able to predict the process under study in the most reliable way.
The use of gradual and intelligible “If … Then” rules allows the domain expert to better understand the behavior of his/her process.
Thanks to its robust learning strategies, xtractis® “does not learn off by heart”: it builds and selects the decision-making models that have the best generalization capacity. xtractis® models hence have a better predictive power: they are effective even in unknown situations. They enable you to model and gain more insights into Real-World complexity without any simplification.
xtractis® is fully autonomous thanks to an infinite number of robust learning strategies: it uses all the available data without any a priori knowledge.
All its functionalities are fully automated: launch xtractis® immediately by simple mouse click, without any need for programming or special knowledge of mathematics .
xtractis® is able to model expert decision-strategies, positive or malicious human behaviors, technical or socioeconomic processes or natural phenomena…
It identifies steady relationships between structured datasets of various types: qualitative and quantitative data, hedonic evaluations, liking, expert opinions, sensory/instrumental data, signals, images, socioeconomic data, formulations, product characteristics, genome sequences…
xtractis® helps you to predict the value of a numerical variable (regression), to identify to which set a new observation belongs (classification), to predict the risk of occurrence of a studied event (scoring), or to identify stable clusters in your data (clustering).
Some criteria may appear irrelevant when taken individually. The xtractis® approach is holistic: it highlights the existing synergies between these criteria and other parameters, to build the predictive model.
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LAMBDA CALCULUS på tyska - OrdbokPro.se engelska-tyska
Lambda Calculus : Encodings
If you want these things, you must encode them using functions. No state or side effects. It is purely functional. Lambda calculus is a model of computation, invented by Church in the early 1930's.
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Köp boken The Lambda Calculus. Its Syntax and Semantics av Henk Barendregt (ISBN 9781848900660) Pris: 825 kr. inbunden, 2013. Skickas inom 5-16 vardagar. Köp boken Lambda Calculus with Types av Henk Barendregt (ISBN 9780521766142) hos Adlibris. The Lambda Calculus, treated in this book mainly in its untyped version, consists of a collection of expressions, called lambda terms, together with ways how to The lambda calculus forms a prototype universal programming language, which in its untyped version is related to Lisp, and was treated in the first author's av D Lidell · 2020 · Citerat av 1 — Other Titles: Formalizing domain models of the typed and the untyped lambda calculus in Agda.
Lambda Calculus Playground – Appar på Google Play
As mentioned, the evaluation order is irrelevant in the lambda calculus. 2013-06-04 · Lambda calculus and lambda math may seem daunting. But for developers who want to take full advantage of Lambdas in their programming language of choice, or for those who want to pursue functional programming, it's a worthwhile endeavor. Lambda calculus All functional programming languages have their roots in lambda calculus.
Lambda Calculus : Encodings
lambda calculus In 1937, Turing proved that the two models were equivalent, i.e., that they deﬁne the same class of computable functions. Modern processors are just overblown Turing machines. Functional languages are just the lambda calculus with a more palatable syntax. 2021-02-06 · The lambda calculus is a formal mathematical system for expressing the notion of computation. Most functional programming languages are based upon the lambda calculus.
Conventions: the body e of
We develop the operational semantics of an untyped probabilistic λ-calculus with continuous distributions, and both hard and soft constraints,as a foundation for
Introduction to Lambda Calculus. Reduction and functional programming. A functional program consists of an expression E (representing both the al-. The lambda-calculus is a minimal programming language. Though it contains forms only for function applications, variable references and anonymous functions,
25 Oct 2014 Well, lambda calculus is basically a simple notation for functions and applications in mathematics and computer science. It has a significant
24 Aug 2014 The Lambda Calculus for Absolute Dummies (like myself) http://palmstroem.
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This is a formal description of a small functional language (that looks a bit like Elixir). We will build it from the ground up, starting with the basic data structures and then define how expressions are evaluated. 2021-02-24 · Lambda calculus is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. It is a universal model of computation that can be used to simulate any Turing machine.
In Python, you can use a lambda
Jan 19, 2016 Lambda calculus (also written as λ-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction
Download scientific diagram | Grammar and type system for the simply-typed lambda calculus used in the example derivation. from publication: Making Random
1.1k votes, 44 comments. 376k members in the EngineeringStudents community. This is a place for engineering students of any discipline to discuss …
We define a simply typed, non-deterministic lambda-calculus where isomorphic types are equated.
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Why the Lambda Calculus is not really equivalent to the Universal
Lambda calculus is a model of computation, invented by Church in the early 1930's. Lambda calculus and Turing machines are equivalent, in the sense that any function that can be defined using one can be defined using the other. Here are some points of comparison: Functional programming languages began with John McCarthy’s invention of Lisp, which showed computer scientists the importance of lambda calculus. Without Lisp, would we still be stuck with Turing machines for the theory of computation?


Essen, September 17 - 21, 2018
Mini-courses by Fabrizio Andreatta, Ana Caraiani and Eugen Hellmann,
plus a couple of research talks.
University of Duisburg-Essen
45127 Essen, Germany
(located south-east of the university campus, see the map in the useful information sheet (pdf) --- this is not the math building!)
Further local information for download: useful information sheet (pdf)


Dating calculator days
Please see the full disclaimer for more information.
Formula fetched from the book Poor Sucker Syndrome by Mitch Vandell.As an alternative, you could try the birthday calculator, which will show you all sorts of fun facts about your birthday, including the day on which you were born. It will not only calculate the chances for you and another person to make it in the future, but also calculate how long you have been dating, when (or if) you will break up, and if so, why you will break up. If the calculation did not give you the result you expected, please write which values you used and what you expected the calculation to do.The months of April, June, September, and November have 30 days, while the rest have 31 days except for February, which has 28 days in a standard year, and 29 in a leap year.The Gregorian calendar is a reformed version of the Julian calendar, which was itself a modification of the ancient Roman calendar.In order to accomplish this, Caesar inserted an additional 10 days to the Republican calendar, making the total number of days in a year 365.
He also added the intercalation of a leap day every fourth year, all in an attempt to further synchronize the Roman calendar with the solar year.
This calendar allowed summer and winter months to become completely misplaced, leading to the adoption of more accurate calendars.
The Republican calendar later used by Rome followed Greek calendars in its assumptions of 29.5 days in a lunar cycle, and 12.5 synodic months in a solar year, which align every fourth year upon the addition of the intercalary months of January and February.
The Gregorian calendar is the most prevalently used calendar today.
Within this calendar, a standard year consists of 365 days with a leap day being introduced to the month of February during a leap year.
You can find pregnancy and baby apps and tools in the NHS apps library.


There are 10 wooden numbers and 100 wooden sticks in the package. Children can learn 1-10 numbers and learn counting through the wooden stick. By practicing putting the wooden numbers on the corresponding card, children can learn numbers and counting better. It makes learning fun, enriches the child imagination, stimulates children's logical thinking, improves children hand eye coordination and learning ability. There are 30 math calculation cards, children can use the wooden numbers to indicate the answer, or use a pen to write the answer on the card to learn basic math. Math games make it easy for children to learn simple math calculations. It is suitable for home preschools and kindergarten.


I developed an Android solution to identify if a vehicle is stopped with the engine turned off, or stopped with engine turned on or if it is moving.
Instead of working with all three axis separately I decided to calculate the magnitude of the vector using the formula:
magnitude = sqrt(x^2 + y^2 + z^2);
This way if the device is stopped in the right position (Z axis is aligned to gravity force) the magnitude will be “9,8…”. This is exactly the value of gravity force.
I retrieved 1000 samples with the device stopped on the floor and when plotting a histogram I noticed that the magnitude values are concentrated in discretes positions (9,82.. 9,86.. 9,78.. 9,85.. etc). Also I noticed these positions may vary slightly from device to device, but it always will concentrate in 4 or 5 positions.
Then I decided to add up all occurrences of each individual magnitude from these 1000 samples (it is like creating a vector that represents the histogram). Now I could to identify all 4 more frequent magnitudes.
If the device is in movement the magnitude values for these 1000 samples will be distributed almost equally, but yet at least 4 or 5 magnitudes will surpass all the others. If I add up these four more frequent magnitudes I could to classify the type of vibration.


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Let’s face it, there are always going to be some students who complain that math is boring. Luckily, there are plenty of opportunities to put aside the worksheets and make it more exciting. Math board games are a fun way for kids to practice their math skills. They may not even realize they’re learning since they’ll be having such a good time playing. There are options for toddlers up to teens, and some games can even be customized to the players’ ages and ability levels. Whether your students are swatting flies, traveling through space, or making their way through a swamp, they will be practicing math concepts along the way with these great math board games!
1. Math Swatters!
We love how versatile this game is since there are a number of different ways to play including head-to-head or solo. Little friends will love getting their hands on one of the four bright-colored “swatters” and whacking the flies.
Buy it: Math Swatters! at Amazon
2. Sums in Space
Since a lot of kids love outer space, we think this game will hold their attention. The Even Stevens Twins and Captain Odd Duck help early elementary–age students work on basic addition and subtraction skills while also teaching greater-than/less-than, as well as even and odd numbers.
Buy it: Sums in Space at Amazon
3. Clumsy Thief
In this multi-award-winning game, students race to see how quickly they can find two money cards that equal $100 while also stealing from their friends. This game is probably best suited for first through third grades since students will need to have a good handle on basic addition before playing.
Buy it: Clumsy Thief: The Crazy, Fast-Paced Money Game at Amazon
We love how versatile this game is since the rules can be adjusted based on age, skill level, and number of players. We also love that it can be played by older kids since it can include multiplication, division, and even square roots.
Buy it: Proof! at Amazon
5. The Genius Square
Perhaps more of a puzzle than a math game, though we think the same skill set is definitely required. Players roll the dice, place blockers in those corresponding coordinates, then race to complete the rest of the puzzle.
Buy it: The Genius Square at Amazon
This game is best suited for students ages 8 to 12 and includes star rankings on each card to indicate difficulty level. Since working in math workbooks can get stale fast, this game provides a fun alternative that allows kids to learn while having lots of fun too.
Buy it: Adsumudi at Amazon
7. Fraction War
The best math board games have straightforward instructions that make them easy to learn and fast to play. Just split the deck, play your cards, and the larger fraction collects.
Buy it: Fraction War at Amazon
8. Jump 1
With two levels of difficulty, this game will be perfect for preschoolers while also keeping elementary-age students entertained. Math board games that have eye-popping colors and fun illustrations like this one will be sure to keep kids’ attention.
Buy it: Jump 1 at Amazon
9. Tiny Polka Dot
Deal all the cards face up, then take turns matching pairs from different suits with the same numbers. This game is especially versatile since there are a whopping 16 different games included in one small box!
Buy it: Tiny Polka Dot at Amazon
Think Scrabble but with numbers instead of letters! Players take turns making crossword-style equations and then adding up their totals based on their tiles played.
Buy it: Smath at Amazon
11. Little Bud Kids Counting Pegs
Made of nontoxic, solid wood, this Montessori-style game will stand the test of time. Toddlers will love using the pegs to work on counting and number recognition while slightly older kids can use the boards for beginning math.
Buy it: Counting Pegs at Amazon
12. Sum Swamp
Players must race through the swamp while completing math challenges and meeting swamp creatures along the way. We think kids will love this game, but don’t just take our word for it: There are over 5,000 five-star reviews on Amazon!
Buy it: Sum Swamp at Amazon
13. Prime Climb
This game has won numerous awards and has been included on several best-of lists. We love that the game will prove challenging even for teens since strategies can range from simple to complex.
Buy it: Prime Climb at Amazon
14. Exact Change Card Game
This game is perfect for upper elementary or even middle school since younger students may struggle with the concept of making exact change. We love that it teaches a real-life skill while also enforcing basic math concepts.
Buy it: Exact Change Card Game at Amazon
Unlike some math games, this one can be customized based on the skill level of the players, making it perfect for any age. You will definitely see your students’ math scores improve after playing this game!
Buy it: Target at Amazon
What are your favorite math board games? Come and share in our WeAreTeachers HELPLINE group on Facebook.
Plus, check out the best board games for preschool.
Source by s18670.pcdn.co


See Fraction Puzzle Worksheets, Printable Multiplication Times Table Games & Printable Fraction Board GamesSee 5 Best Images of Multiplication Fraction Printable Games. Inspiring Multiplication Fraction Printable Games printable images. Fraction Puzzle Worksheets Free Printable Fraction Bingo Cards Printable Multiplication Times Table Games Multiplication Game Boards Printable Fraction Board Games
Fraction Puzzle Worksheets via
Free Printable Fraction Bingo Cards via
Printable Multiplication Times Table Games via
Multiplication Game Boards via
Printable Fraction Board Games via
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Quantitative Literacy & Mathematics
Quantitative Literacy Requirement (QL)
Quantitative Literacy (QL) is a "habit of mind," competency, and comfort in working with numerical data. Courses in this area will develop your ability to reason and solve quantitative problems from a wide array of authentic contexts and everyday life situations. QL courses help develop the skills necessary to understand and create sophisticated arguments supported by quantitative evidence, and to clearly communicate those arguments in a variety of formats (using words, tables, graphs, mathematical equations, etc., as appropriate).
See the current KCA and Quantitative Literacy Options.
Competency in Basic Mathematics
**Please note**: All students are also required to demonstrate basic mathematic competency in one of the following ways before they are able to take a QL course.
- Pass the College’s mathematics competency exam administered by the Office of Academic Advising numerous times during the year
- Successfully complete MATH 101 or a higher level mathematics course at Simmons College
- Achieve a sufficiently high score on the mathematics section of the SAT, the mathematics achievement test, or an Advanced Placement exam in Math
- Present evidence of satisfactory completion at another accredited college of a mathematics course at the level of MATH 101, or above, to the Registrar’s office
You must satisfy the math competency requirement during your first year at Simmons. Students who do not pass the mathematics competency exam during orientation, or who do not meet the math competency requirement in one of the other ways described above, may choose to take MATH 101 in their first semester or to retake the test in November. If they do not pass the November test, they will enroll in MATH 101 in the spring semester. Students who matriculate in January who do not pass the mathematics competency exam, or do not meet the requirements in one of the ways described above, may take MATH 101 during their first semester or retake the exam in March. If they fail the test in March, they will enroll in Math 101 in the following fall semester.


Please enter the subject title and grade average and any comments you wish in the fields to the right, click the “SUBMIT” button when finished. Please fill this form out for each student.
Note: To calculate the grade averages: Add all the scores from the lessons of the particular subject you are working on, then divide that total by the amount of lessons scored.
Sample formula: Grade 1 + Grade 2 + Grade 3 + Grade 4 + Grade 5 ÷ 5 = Grade Average
Example: 95% + 89% + 92% + 87% + 96% = 459 ÷ 5 = 91.8% Grade Average
Click here to download a sample grade book in Microsoft Excel format.
Important, the following information is required to receive credit for these subjects.


This is the first post in a three part series on Raycasting in Unity. The follow up posts are:
Find the code on GitHub
Raycasting is the process of pointing (“casting”) a line (“ray”) in a direction and seeing what it hits.
This guide will walk through some of the foundational concepts, and then build some basic examples in Unity.
Intro to Vectors
Most of the heavy maths is done for us by Unity, but there are some concepts which will be helpful for us to have a solid grasp on going forward. If you’re confident using vectors in Unity, skip to the next section.
There are a few way to think about vectors, depending on who you are. This guide will give the briefest overview of vectors from a graphics perspective. It is my intention to provide just enough of an intuition that we can start experimenting meningfully. If you’re interested in diving deeper into the world of vectors I can’t recommend threeblueonebrown more highly.
A vector is a line with a direction.
This line could represent either a specific position, or a general direction.
“Magnitude” is the fancy term for the length of the line. In high school they’d tell you that to find the magnitude you need to take the square root of the sum of the squares of the length of each axis, but Unity does this for us. Conceptually, all you need to know is that the magnitude of the vector is the length of the line it represents.
A normalised (normalized for Americans) vector is a vector whose magnitude is 1. To normalise a vector is to squish it down (or strech it out) so that it still points the same way, but its length is 1. This is useful for getting a ‘pure’ direction vector without any stretching.
Separate to normalising, a Normal is a vector that points perpendicular to a surface. In the case of 2D vectors (such as the image below), the Normal points perpenducular to a line.
Now that we have a sense of Vectors, let’s apply them! Head to Foundations of Raycasting to continue this guide


Dorry Segev and Sommer Gentry are two of the smartest people I know. Dorry is a transplant surgeon at Johns Hopkins University and Sommer is a math professor at the United States Naval Academy. Individually that's admirable, but together they are a force to be reckoned with.
Dorry and Sommer are doing remarkable work combining their individual pursuits to create new systems to allocate the distribution of organs between donors and patients around the US. Check out this fantastic video about these two and the mathematical systems are developing that can save thousands of lives.
Directed by Andrew Rozario.
More about Dorry and Sommer at this great profile in the Baltimore Sun.


Hui Wang (王辉)
I am an associate professor at the School of Information Science and Technology of Shijiazhuang Tiedao University (STDU).
I obtained my Ph.D. degree in the School of Mathematical Sciences, Dalian University of Technology (DLUT), China, under the supervision of Prof. Zhixun Su. From Sep. 2011 to Sep. 2012, I visited the GrUVi Lab, School of Computing Science, Simon Fraser University (SFU), Canada, under the supervision of Prof. Hao (Richard) Zhang supported by China Scholarship Council (CSC). From Feb. 2017 to Aug. 2017, I visited Visual Computing Research Center (VCC) in Shenzhen University under the supervision of Prof. Hui Huang.
Digital geometry processing; Shape analysis; Image processing


Zhifang joined Bryden Wood Singapore in July 2016 as a mathematical modeller and data analyst. She graduated from National University of Singapore (NUS) with a master degree in Industrial & Systems Engineering in February 2016. With a solid engineering background, she has obtained good knowledge and experience in various quantitative modelling techniques (including discrete-event modelling, inventory optimization and statistical forecasting etc.). In addition, her internship experience in a decision analysis consultancy firm allowed her to develop proficiency in a large number of data analytics tools (including Advanced Excel, VBA, R, MatLab etc.) and gained profound understanding in applying modelling techniques to solve complex real-life problems.
Zhifang is currently working on her first FE project Chittagong, with 2 components Project Tropical and Project Potent. The project objective is to identify the best phased investment strategy and plant layout to deliver key capacity and quality related projects at the Chittagong Site whilst maintaining supply. In this project, Zhifang has deeply involved herself in various stages of quantitative modelling, including data source determination, data collection, modelling strategy development, model design and validation, output analysis, assessment of data uncertainty, identification of the optimal solution and reporting.


Caterpillar Number Match is a fun and easy early math activity for preschoolers. A great way to practice counting with your toddler or preschooler. This makes a great spring math activity or a fun activity to do anytime of the year!
Supplies for Caterpillar Cup Number Match for Preschoolers
(This post and list contains affiliate links for your convenience. If you make a purchase using one of these links, I may earn a commission. Please visit my disclosure policy for more information.)
- Construction paper
- Paper Cups
- Small Black Pom Poms
- Googley eyes
Looking for more spring or caterpillar activities and crafts? Check out these great ideas!
How to Make Caterpillar Cup Number Match for Preschoolers
Grab your supplies. Cut out a circle from green construction paper, glue on googley eyes and draw a smile. Glue the head on to the another larger sheet of paper. Draw antenna and glue on two small black Pom Poms at the end.
Take a paper cup and draw 9 circles to make the caterpillar body. Draw little feet under each circle.
Draw dots to represent numbers 1 to 9. Write the corresponding number on the bottom of 9 paper cups.
Invite your little one to match the cups to the numbers.
Extending Caterpillar Cup Number Match for Preschoolers
Here are some ways to extend this caterpillar number match activity:
- Invite your little one to count and glue the corresponding Pom Poms into each circles.
- Invite your little one to use a Pom Pom to paint the corresponding number of dots in each circle. (messy)
- Invite your little one to use dot stickers and stick the corresponding number of dots in each circle.
This activity is good for kids 3 years and up. My kids are 4, 4, and 7 year old.
Exciting Sensory Bins for Curious Kids
Boring afternoons are made exciting with awesome animal-based bins, like Salty Shark Bay or Yarn Farm. Pretend play bins like Birthday Cake Sensory Play or Bubble Tea Party encourage creativity and imagination. And your kids will have so much fun they won’t even know they’re getting smarter with STEAM (science, technology, engineering, art and math) activities like Sink or Float Soup, Magnetic Letter Hunt or Ice Cream Scoop and Count.
STEAM Activity Book
Looking for a fun activity book for your preschooler or kindergartner? Check out my new book Super STEAM Activity Book: Launch Learning with Fun Mazes, Dot-to-Dots, Search-the-Page Puzzles, and More! ! Click here to learn more or order it now!


MPHS's math department offers Foundations of Math 1, Math 1-4 regular and honors, Honors Pre-Calculus, and other math courses through NCVPS and RCCC. Students must earn 4 math credits in order to earn their high school diploma. Math substitutions are available for students who do not wish to attend college. Please discuss this option with your counselor.
Left to right in picture
Mr. Furr, email@example.com
Ms. Myers, firstname.lastname@example.org
*Mr. Williams, richard.williams@Cabarrus.k12.nc.us
Ms. Seaford, email@example.com
**Miss Ziegler, firstname.lastname@example.org


And the veteran teachers I know say the same thing as the veteran doctors I know — their jobs used to be enjoyable and make them feel like they were making a difference; now they feel overworked, unappreciated, and trapped in mountains of paperwork. In jargon terms, locally within h there is no trend.
Would-be musicians leave the orchestras behind to go work in the higher-paying factories, and the orchestras have to raise their prices if they want to be assured enough musicians. This is the only use of this order relation for schema processing.
Making decisions is certainly the most important task of a manager and it is often a very difficult one.
Following Thompson's paper, the compiler builds an NFA from a regular expression in postfix notation with dot. The green dots suddenly appear.
The distance at which samples become independent of one another is denoted by a and is called the range of influence of a sample. Second, college is even worse: Students will broaden their knowledge of quadratic functions, exponential functions, and systems of equations.
Students will connect previous knowledge from Algebra I to Geometry through the coordinate and transformational geometry strand. Rob Pike clarified some of the history surrounding his regular expression implementation. There are multiple ways to translate regular expressions into NFAs.
Some areas are expected to be rich, some to be poor. This document uses conventional prefixes to refer to these namespaces. Specifically, the problem is NP-completemeaning that if someone did find an efficient implementation, that would be major news to computer scientists and would win a million dollar prize.
Every value space inherently has an identity relation. Start states are depicted with lone arrowheads pointing at them, and matching states are drawn as a double circle.
It is no wonder that decision-makers sometimes postpone choices for as long as possible. The final value after 12 months is: Just like every number can be considered a scaled version of 1 the base unitevery circle can be considered a scaled version of the unit circle radius 1and every rate of growth can be considered a scaled version of e unit growth, perfectly compounded.
All of these involve the same basic assumption -- that the relationship between the value at point A and any sample value depends on the distance and possibly direction between the two positions, and on nothing else.
Let us make an assumption that the difference in value between two positions in the deposit depends only on the distance between them and their relative orientation.
Historical data about the device or system under consideration Many organizations maintain internal databases of failure information on the devices or systems that they produce, which can be used to calculate failure rates for those devices or systems.
Decision-makers often face a severe lack of information. So the general formula for x periods of return is: Now suppose we let the two samples move a little distance apart.Write an exponential function y = abx whose graph passes through (1, 6) and (3, 24).
S OLUTION Substitute the coordinates of the two given points into y = ab x to obtain two. Precalculus Exponential and Logistic Modeling Exponential Growth and Decay. How do you write an exponential function to model each situation & solve given the population of Warren Michigan wasin How do you write an exponential function to model each situation & solve given whole milk consumption in the U.S.
For those primarily interested in the changes since versionthe appendix Changes since version (§I) is the recommended starting point. An accompanying version of this document displays in color all changes to normative text since version ; another shows changes since the previous Working Draft.
Exponential Growth and Decay Write an exponential growth function to model each situation.
Then find the value of the function after the given amount of time. 1. Annual sales for a clothing store are $, and Write an exponential decay function to model each situation. Then. In statistics, the t-distribution was first derived as a posterior distribution in by Helmert and Lüroth.
The t-distribution also appeared in a more general form as Pearson Type IV distribution in Karl Pearson's paper. In the English-language literature the distribution takes its name from William Sealy Gosset's paper in Biometrika under the pseudonym "Student". SOLUTION: Write a exponential function to model the situation.
The predict the value of the function after 7 years(to the nearest whole number) A population of animals that decreases at Algebra -> Exponential-and-logarithmic-functions -> SOLUTION: Write a exponential function to model the situation.Download


Research Techniques and Data Analysis
|Unit(s): 6.0||Level(s): III||Term(s): Summer||Offered?: Yes|
This course provides an introduction to the basic principles and techniques of statistics used in social science research. My approach involves extensive use of examples from real research to illustrate ideas, applications, and interpretations of statistics. Students will also have an opportunity to apply the techniques learned in class to actual data. I should emphasize up front that this is NOT a mathematics course. Students are expected to understand the basic rules of math, but the focus will be on selecting, applying, and interpreting statistical techniques for data analyses. Overall, this course is intended to get students thinking about why statistics are important to social science research and when and how to apply relevant statistical techniques to answer specific questions.


Tip: To find your correct size, measure your dominant hand.
Halti indicate the size of the gloveswith letters that correspond to the widest part of the palm in inches. This is how you measure the glove size that suits you: Measure the circumference of your palm from the widest point with a centimeter and divide the result by 2.54. If the circumference of the palm is, for example, 23 cm and it is divided by 2.54, the result is 9.06. The suitable glove size for you is M = 9.


Thursday, December 01, 2011
The Bible of Math and the Cal Ripkens
Conor kneels before his bible--a Grade 4 math workbook. He bought this on his own, by his request, with his own money, and does it for fun. Craziness. (Forget word problems, I don't even make change.)
All under the watchful eye, of course, of the autographed jersey of his holiness Baltimore Oriole Cal Ripken Jr.
Conor calls the Baltimore Orioles the "Cal Ripkens". As in, what's your favorite baseball team, Conor? The Cal Ripkens.
Behold, the workbook.


Phone: (559) 386-9083 Fax: (559) 386-5303
Reef-Sunset Unified School District is committed to providing a rigorous, inspiring and nurturing educational program.
Stadium Renovation Approved Design
2nd ANNUAL RSUSD MATH BOWL
Students in 4th, 5th & 6th grades from AES, TES & KCES participated in the district math bowl on Friday, May 17, 2013.


General Online Session with Ashani DasGupta (IV – VII)
Discussion of Pappus Theorem, where he also discussed the extension of the idea of Pappus Theorem to conic sections’ curves like circle and parabola.
Some links of the tutorials and the students’ activities are given below:
- The video of the online sessions with the children enjoying the video.
- The video explaining the whole thing briefly by Cheenta.
Few students tried to test the validity of the theorem on another curve that looks like a flower as follows.
Construction of Weights (VI – VII)
Puzzle: There are eight weights. Seven of them are equal weights and the other one is a bit defective and doesn’t weigh the same. Explain how can you find out the odd one out by using a double pan weighing balance.
Symmetry & Permutations (VI – VII)
The idea of this project is to introduce the idea of permutations, odd permutations and even permutations by examples. We took the example of GALOIS and took permutations on it and repeated on it till GALOIS comes back again. We love to let the children learn by working themselves.
We also gave examples to the students by symmetrical arguments. Reflection, Rotations as operations and tried to introduce groups.
The students were just awesome. We gave an example of a three legged person to explain the symmetry same as an equilateral triangle.
One student actually has cut the figure by her hand. It is beautiful.
The World of Dimensions (Class IV – V)
The children were shown clips of the film Flatland to show how the life of two-dimensional objects looks like. It also let the students realize how different dimensional creatures interact with each other.
Also, we discussed the ideas of intersections and dimensions. Also, why time is a dimension. Some students gave ideas of a time machine and their use to interpret time as a dimension.


The Traveling Salesman Problem, also known as the Traveling Salesperson Problem or the TSP, is a well-known algorithmic problem in computer science. It consists of a salesman and a set of destinations.
The salesman has to visit each of the set of destinations, starting from a particular one and returning to the same destination.
Let us take a deep dive into what the challenge of the Traveling Salesman Problem is and how the TSP solutions can help in optimizing last-mile deliveries.
The Traveling Salesman Problem:
- The Traveling Salesman Problem was first formulated in 1930 by Merrill M. Flood, who looked to solve a school bus routing problem.
- It is one of the most intensively studied computational problems in optimization, used as a benchmark for many other optimization methods.
- The Traveling Salesman Problem (TSP) refers to the challenge of determining the shortest yet most efficient route for a traveling salesman to take to visit a list of specific destinations.
- The goal is to find the shortest route from a set of different routes to minimize the total distance traveled and the travel cost.
- The TSP is classified under combinatorial optimization problems known as “NP-complete.” It is classified as “NP-hard” because of two reasons:
- There are no quick solutions.
- The complexity of calculating the most optimum route increases when you add more destinations to the TSP.
- You can solve the TSP by analyzing every round-trip route to determine the shortest one.
- As the number of destinations increases, the corresponding number of routes increases exponentially. This exponential increase surpasses the computational capabilities of even the fastest computers.
- A set of ten destinations alone can have more than 300 thousand permutations and combinations of routes. A set of 15 destinations can have more than 87 billion possible routes.
- The Travelling Purchaser Problem (TPP) and the Vehicle Routing Problem (VRP) are generalizations of the TSP.
- The TSP has several applications, including planning and logistics.
Most Popular Solutions for the Traveling Salesman Problem:
- The Brute-Force/Naive Approach:
- The Brute-Force Approach calculates and compares all possible permutations of routes to find the shortest unique solution.
- The steps involved in solving the TSP using the Brute-Force Approach include:
- Calculating the total number of routes
- Drawing and listing all possible routes
- Calculating the distance traveled in each route
- Choosing the shortest route, which is the optimal solution.
2. The Branch-and-Bound Method:
- The Branch-and-Bound method involves breaking the problem into a series of sub-problems, each of which may have several possible solutions.
- The solution selected for one sub-problem may affect the possible solutions of subsequent sub-problems.
- The steps involved in solving the TSP using the Branch-and-Bound Method are as follows:
- Choose a start node and then set bound to a high value, say infinity.
- Select the cheapest arch between the unvisited and current node and then add the distance to the current distance.
- Repeat the process until the current distance is less than the bound.
- Then add up the distance so that the bound equals the current distance.
- Repeat this process until all the arcs are covered.
3. The Nearest Neighbor Method:
- This method is perhaps the simplest method to solve the TSP
- This method involves always visiting the nearest destination and then going back to the first destination when all other destinations are visited.
- The steps involved in solving the TSP using the Nearest Neighbor method are as follows:
- Choose a random destination
- Look for the nearest unvisited destination and go there.
- Once all destinations are visited, the salesman must return to the first destination.
4. Recent Solutions by Academics:
- Zero Suffix Method solves the classic symmetric TSP
- Biogeography‐based Optimization Algorithm solves the problem of optimization using the animals’ migration strategy.
- The African Buffalo Optimization Algorithm is derived from careful observation of the African buffalos.
- Meta-Heuristic Multi Restart Iterated Local Search (MRSILS) is more efficient than the Genetic Algorithms when clusters are used.
- Multi-Objective Evolutionary Algorithm solves multiple TSPs based on NSGA-II.
- Multi-Agent System solves the TSP of N cities with fixed resources.
Real-Life Solutions for The Last-Mile Delivery Problem:
Efficient solutions found through the Traveling Salesman Problem help to optimize and minimize the cost of last-mile deliveries.
These solutions help delivery businesses find a set of routes or paths to reduce delivery costs. The delivery problem domain involves a set of warehouse locations, delivery locations, and several delivery vehicles.
An efficient routing and delivery optimization software can provide the best solutions to logistic companies.
Are you ready to implement real-time routing and last mile route optimization software to plan your routes quickly and efficiently?


Many courses at LCC have minimum skill level requirements in reading, writing, and/or mathematics. These skill levels must be met before a student will be permitted to enroll in those courses. One way students meet these skill prerequisites is by achieving the required scores on placement tests.
Placement test results also play a large role in determining both the level and number of required courses. It is important that you do your best. You are encouraged to use the review materials listed below—both to refresh your knowledge and to become familiar with the question format.
DO YOU NEED TO TEST?
If you have completed the ACT or SAT you may be able to waive placement testing and receive levels based on your score. Click here for information on submitting test results for placement levels.
If you have previously attended college or have AP or CLEP scores, visit the Waiver Team Webpage to determine if you can waive the tests.
Information, Test Overviews, & Preparation Materials:
- Frequently Asked Questions
- Reading, Writing & Math Assessments
- English as Second Language (ESL) Assessments
- Official ACCUPLACER Study App - IOS, Android, & Web-Based (Free)
- Accuplacer Sample Questions - PDF
- The WritePlacer Guide - PDF
- Math Resources on the Web (links to helpful websites)
- Preparation Resources and Websites - LCC Library
- Accuplacer Cut Scores and Placement Levels
Alternative Testing Locations
- Testing Off-Campus - Information & Proctor Request Form
- Testing Options at Other LCC Campuses & Learning Centers
Additional Testing Information:
- Health Biology Proficiency Test (HBPT)
- Proficiency and Core Exams
- How to view test scores
- ACT/SAT Placement Test Waiver Form
The Reading Comprehension Test is an untimed multiple-choice test. There are two types of questions:
- A passage followed by a question based on the text.
- Sentence relationships: Presents two sentences followed by a question about how they are related (such as supporting, contradiction, or repetition).
The WritePlacer is a timed essay (70 minutes).
You will be asked to write a 300-600 word essay that draws on your experiences, learning, and ideas in support of your point of view in relation to the issue in question.
Responses do not require any technical or specific knowledge. Your score will be based on your ability to express, organize and support your opinions and ideas.
The following components are considered in the score:
Focus - The clarity of the main idea or point of view
Organization - The clarity of the structure and the logical sequence of ideas
Development and Support - Elaboration of ideas and supporting details
Sentence Structure - Effectiveness of the sentence structure
Mechanical Conventions - Extent to which the writing is free of errors is usage and mechanics
The WritePlacer Guide has sample essays representing the full range of possible scores.
There are 3 possible math assessments. You will choose which test to start at. A high or low on the score of the first test may result in a second test.
The Arithmetic Test has three types of questions:
- Operations with whole numbers and fractions
- Including: addition, subtraction, multiplication, division, recognizing equivalent fractions and mixed numbers, and estimating.
- Operations with decimals and percents
- Including: addition, subtraction, multiplication and division with decimals. Percent problems, recognition of decimals, fraction and percent equivalencies, estimation
- Applications and problem solving
- Topics: rate, percent, and measurement problems, simple geometry, distribution of a quantity into its fractional parts.
The Elementary Algebra Test has three types of questions:
- Integers and rational numbers, computation with integers and negative rationals, the use of absolute values, ordering
- Operations with algebraic expressions using evaluation of simple formulas and expressions; adding, subtracting, multiplying and dividing monomials and polynomials; evaluation of positive rational roots and exponents, simplifying algebraic fractions, factoring.
- Solution of equations, inequalities, and word problems; solving linear equations and inequalities; solution of quadratic equations by factoring; verbal problems in an algebraic context, geometric reasoning and graphing; the translation of written phrases into algebraic expressions.
The College Level Math Test assess intermediate algebra through precalculus. Including:
- Algebraic operations: simplifying rational algebraic expressions, factoring, expanding polynomials, manipulating roots and exponents
- Solutions of equations: solution of linear and quadratic equations and inequalities, equation systems, other algebraic equations
- Coordinate geometry: plane geometry, the coordinate plane, straight lines, conics, sets of points in the plane, graphs of algebraic functions
- Applications and other algebra topics: complex numbers, series and sequences, determinants, permutations and combinations, fractions, word problems
- Functions and trigonometry: polynomials, algebraic, exponential, logarithmic and trigonometric functions.
Khan Academy and Math.com are good resources for additional math review. However, these websites are NOT designed specifically for the Accuplacer tests. Review the subjects listed in the overviews above to narrow your focus before visiting math related websites.
NOTE: ESL students who have graduated from an English speaking high school or have academic admission on their I-20 take the college-level placement tests (which are also available after high scores on the ESL tests or upon request).
There are 3 ESL assessment tests. Students will use the average score of the ESL Reading Skills and ESL Language Usage tests along with the ESL Listening score to determine their courses.
ESL Reading Skills - Evaluates comprehension of short passages. Including: paraphrasing, locating information, vocabulary on a phrase level, pronoun reference, main idea, fact vs. opinion, cause/effect logic, identifying irrelevant information, author's point of view, applying author's logic to another situation.
ESL Language Usage - Measures grammar and usage
Subjects for both of the above tests include: Subject-verb agreement, verb tenses, irregular verbs, noun forms and pronouns, modifiers and comparatives, prepositions of direction and place, comparatives, connectives and commands, sentence fragments or run-on sentences.
ESL Listening - Assesses the ability to listen and understand one or more people speaking English - not on ability to read English. First, student will listen to the conversation and the question that follows, while looking at pictures of the speakers. Below are four answers from which to choose, written on the screen or with a drawing next to each choice.
Health Biology Proficiency Test
The HBPT is a 50 question multiple choice test. A passing score meets one of the prerequisites for BIOL 201. This test can only be attempted once and does not require a scheduled appointment. For additional information about this test contact the Science Department at 517-483-1092.
- Log into myLCC from the LCC main page
- Click on the "Profile" tab
- On the right side of the screen you will see "Placement Test Scores"
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MATHEMATICS ANXIETY AND SELF EFFICACY IN DOING MATHEMATICAL PROOF
Self-Efficacy or a lack of confidence is one of the causes of mathematical anxiety. This paper discusses the best way to overcome mathematical anxiety, self efficacy in proving mathematics. The method used is literature review. Self efficacy has an important role in eliminating the anxiety of mathematics, where if someone has confidence in their abilities, they will be more happy and active in proving mathematics. But sometimes most do not believe or believe in themselves so they tend to be lazy in doing mathematical proof, therefore a learning community is needed where they are able to interact and exchange ideas so that they can open up opportunities to be able to prove mathematics without the math anxiety.
Epp, S. (2003). The role of logic in teaching proof. The American Mathematics Monthly, 110(10), 886-899.
Gowers, W.T. The Language and Grammar in Mathematics. Diunduh dari https://www.dpmms.cam.ac.uk/~wtg10/grammar.pdf tanggal 16 juni 2017.
Jamison, R.E. (2000). Learning and Language in Mathematics in Language and Learning Across the Disciplines. Diunduh dari wac.coloasate.edu. tanggal 16 juni 2017.
Johnson, D. (2003). Math Anxiety. Literature Review. Knuth, E. (2002). Secondary school mathematics teachers’ conception of proof. Dalam Journal for Research in Mathematics Education, 33(5), 379-405.
Khatoon, T. & Mahmood, S. (2010). Mathematics Anxiety Among Secondary School Students in India and its Relationship to Achievement in Mathematics. European Journal of Social Science, 16 (1), 75-86.
Lestari, E.K, Ridwan, M. (2015). Penelitian Pendidikan Matematika. Bandung:PT Refika Aditama.
Lunenburg, F.C. (2011). Self efficacy in the workplace: implication for motivation and performance. International Journal of Management, Bussiness, and Administration, vol 14, no 1
Ma, X. (2003). Effect of Early Acceleration of Students in Mathematics on Attitude toward Mathematics and Mathematics Anxiety. Teachers College Record, 105 (3), 438-464.
Martin, W. G,, & Harel, G. (1989). Proof frames of preservice elementary teachers. Journal for Research in Mathematics Education, 20(1), 41 – 51.
Moore, R.C., (1994). Making Transition to Formal Proof. Journal of Educational Studies in Mathematics 27: 249-266. Kluwer Academic Publisher: Netherlands.
Nawangsari, N. A. F. (2001). Pengaruh self-efficacy dan expectancy-value terhadap kecemasan menghadapi pelajaran matematika. Jurnal Psikologi Pendidikan: Insan media psikologi, 3,2, 2001, 75
Peker, M. (2009). “Pre-Service Teachers’ Teaching Anxiety about Mathematics and Their Learning Styles”. Eurasia Journal of Mathematics, Science, & Technology Eductaion. 5 (4), 335-345.
Remillard, K.S. (2010). Exploring the learning of mathematicak proof by undergraduate mathematics majors through discourse analysis. Proceedings of the 13th Annual Conference in Researh in Undergraduate Mathematics Education.
Santosa, C. (2013). mengatasi kesulitan mahasiswa ketika melakukan pembuktian matematis formal. Jurnal Pengajaran MIPA, Volume 18, Nomor 2, Oktober 2013, hlm. 152-160.
Van Dormolen, J. (1977). Learning to understand what giving a proof really means. Educational Studies in Mathematics, 8, 27-34.
Vanspronsen, H.D. (2008). Proof Processes Of Novice Mathematics Proof Writers. Dissertation University of Montana, Missoula.
Wahyudin. (2010). Monograf: Kecemasan Matematika. Bandung: Program Studi Pendidikan Matematika SPS UPI.
Yanti, D., Fauziah, A., & Friansah, D. (2017). Pengaruh model pembelajaran kontekstual terhadap kemampuan koneksi matematika siswa kelas X SMA Negeri 4 Lubuklinggau Tahun Pelajaran 2015/2016. Jurnal Pendidikan Matematika Raflesia, 2(2).
Zakaria, E., Nordin, N. M. (2008). “The Effects of Mathematics Anxiety on Matriculation Student as Related to Motivation and Achievement”. Eurasia Journal of Mathematics, Science, & Technology Eductaion. 4 (1), 27-30.
Zandieh, M. & Sean, L. (2008). Proofs and refutations in the undergraduate mathematics classroom. Educational Studies in Mathematics, Vol. 67, No. 3.
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
This work by Journal of Mathematics Science and Education is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.


2017-05-08 22:06:52 UTC
I have implemented my Universal Scalability Law progam..
Where do you use it ?
You use it for example to optimize more the cost/performance ratio on
multicores and manycores.
With -nlr option means that the problem will be solved with the
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Please read more about my Universal Scalability Law for Delphi and
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I have included a 32 bit and 64 bit windows executables called
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You can read about it and download it from here:
Amine Moulay Ramdane.


The notion of a hash is one that you’ll come across repeatedly in any discussion regarding cybersecurity.
These seemingly random sequences of numbers and letters are created and employed in a variety of ways. Even though this is a very restricted and easily overcome method of detecting current viruses, hashes bring a lot of value and help to prove identification but are also used in a variety of ways. We’ll go through a few of them in this post as we learn more about what a hash is and how it works.
What Is a Hash?
Hashes are the result of a mathematical function that converts a text string (no matter the length) into an encrypted string of a fixed length. For every given piece of data input, algorithms such as MD5 (Message Digest 5) or SHA (Secure Hash Algorithm) fundamentally generate a unique, fixed-length string – the hash value.
How Do Hashes Work?
Hashing is basically a one-way cryptographic function. Because hashes are irreversible, knowing the output of a hashing method does not allow you to recreate the contents of a file. It does, however, allow you to assess whether two files are similar without knowing their contents.


All Disciplines Postgraduate Award, Queen Mary, University of London - Biology
With a BS in mathematics from the University of Michigan, Jeremy is pursuing a career in biology research, applying mathematical techniques to problems in cancer and chromatin biology. He has already worked with a number of experts in this field. With Professor Marisa Eisenberg, he has developed models for the 2014-2016 West African Ebola epidemic, and studied the identifiability of infectious disease models. With Professor Arul Chinnaiyan and Dr. Sethu Pitchiaya, he has also developed a computational pipeline for microscopy images, in order to study spatial and transcriptional heterogeneity in cancer cell populations. Jeremy is delighted to be working with Professor Trevor Graham at Barts Cancer Institute during his Fulbright where he will develop spatial models of the interaction between tumours and the immune system. The goal is to better understand the parameters influencing the tumour-immune interaction, which could inform future immunotherapies. In addition to his research, he plans to form connections within the UK mathematical biology community. He also hopes to play chamber music (as a violinist) and rekindle his involvement in choral music.


Are you getting confused with the puzzle questions on mathematics? Then this Assignment help will definitely help you to summarize the solution of such absurd proof related to basic mathematics. Mathematics is fun. To be skilled in mathematics needs not much effort, rather it needs to clear the basic concepts. It is a capability that one can acquire by practicing and solving various problems. Here we are to make your mathematics exciting.
Practice makes a man perfect. This is a proverb applied mainly to students. Most of the students in their academic careers are afraid of mathematics subjects. They do not realize the interesting background behind the subject. It is very hard to believe that most of the students harshly follow their academic syllabus. Apart from that, they do not think something extra, something that violates basic calculation.
In mathematics, a conceptual theory is the BODMAS rule. BODMAS is an acronym that is used to remember the order of operations to be followed while solving the given expressions in a mathematics problem. BODMAS is a part of simplification. The full name of BODMAS stands for B – Brackets, O – Order of powers or roots, D – Division, M – Multiplication A – Addition, and S – Subtraction. This is a stepwise rule, which means as the letters are arranged, the computation needs to be done in that sequence.
According to the BODMAS rule, when a given simplification needs to solve, the student first solves the expression with brackets then with the exponents, then the division, multiplication, addition, and subtraction. It is necessary to remember and apply for the order as mentioned. If the student just does without following this rule they will make mistakes and obtain answers wrong. For example:
With the given equation (11+19)8+3-12,
According to BODMAS:
- The first step is to sum the numerical values given within the bracket,11+19=30
- The next step is to multiply the result with 8, 30×8 = 240
- The next step is to sum the result by 3, 240+3=243
- Now 12 is subtracted from the obtained result, 243-12=231.
In mathematics, the concept of squaring a number is the consequence of multiplying a given number by the number itself. “To square” a number this multiplication operation is done. Squaring is the same as putting a power 2, and is denoted by a superscript 2 of the given number. For instance, the square of 10 may be denoted as 102, which gives the value 100.
Next, comes the concept of square root. In mathematics, the Square Root Law states that the total security store can be calculated by approximation by multiplying the total stock of an item by the square root of the number of future logistics locations divided by the present quantity. For example: Using the square root law the future logistics = (4000) * √ (3/2) = 4000 * 1.22474 = 4898.979 units.
When the above concepts are clear and easy to apply, we try to prove 2+2=5. Normally we know that 2+2 equals 4 but by applying realistic conceptual mathematics, we can prove that 2+2 equals 5.
Mathematics gives 2 + 2 = 4
Now LHS, 2 + 2 = 4 +1-1 (1-1 = 0 means we have written 4)
Similarly we can write,
2 + 2 = 4 + –
= + (here = (any number) (2*1/2) = any number.
The algebraic formula of (a – b)2 = a2 – 2ab + b2
Thus we can write = 42 – 2*4* + = 16 – 36 + .
2 + 2 = + = +
= + (16-36 = -20)
= + (here to make a new formula, we can write -20 = 25-45)
= + (25 is represented as 52 and 45 can be represented as 2*5* )
= + (here we get a2 – 2ab + b2, so we can write (a – b)2 )
= + (any number =(any number) (2*1/2) = )
= + (eliminate the bracket)
Thus, 2+2 =5 (any number – any number = 0)
Thus it has proved that 2 + 2 = 5.
What we have learned from this mathematics?
Is, mathematics proves mathematics is wrong?
What do we consider 2 + 2= 4 or 2 + 2=5? It’s an interesting matter in mathematics. 2+2 equals 4 this is known by all. 2+2 = 2*2 = 4, this is what mathematics originally explains. But 2 + 2 = 5 is mathematics that has been proved by intelligence and forcefully.
Students will definitely learn the theory 2 + 2=4 but at the same time, they need to understand the logic behind the 2 + 2=5. While going to prove this interesting logic we have applied or learn some important rules of mathematics like indices, surds, and BODMAS. These learning and applications mean a lot for the student.
Conclusion: After reading this blog I hope you have got an idea of how to proof 2 + 2=5.
If you have any doubt, you can ask our assignment help experts and take help from them at any time. For more details log on to our official website GotoAssignmentHelp and check the necessary details of hiring them.


I'm a developer and this site shows some programs I developped. Feel free to send me your feedbacks.
Have a nice visit.
Here you can find an eclipse plugin. It gives to the eclipse developers a way to check there is no inconsistency in their project classpath.
Here is a Sudoku program. It will help you to find the solution of any Sudoku grid.
Here is a mathematical equations solver. It can resolve your NxN equations and gives you all details of the calcul.
Here are little games
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here is my Curriculum Vitae.
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MATH 280 Introductory Statistics
This course covers elementary topics from the probability and statistics of both discrete and continuous random variables. Topics include independence and dependence, mean, variance and expectation, and distributions of random variables. Statistics is applied to hypothesis testing. This course provides the student with a broad, general knowledge and understanding of statistics. The emphasis of this course is on the utility and practical application of statistics rather than on the mathematical derivation of statistical principles.
Course ID: MATH 280
Semester Hours: 3


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Jeff Atwood discusses the "Monty hall" problem
. I made a comment about why I believe people's intuition is often wrong when presented with the problem: I believe it is due to the way probability theory is taught in schools and universities. The notion of probability simply as an extension of classical logic as presented by Edwin Jaynes matches intuition much more closely. To solve the Monty Hall problem we need three simple principles (which apply to a wide
range of problems):
- Probability is about information. Forget notions of "random" experiments, e.g., the outcome of throwing a die is about the laws of physics - there is no magical randomness built into the die causing it to come up with each side equally often "in the long run" (what ever that means). If we know the laws of physics and have enough information about the experiment we might assign other probabilities to the outcomes. This means that if new information is obtained the probability changes!
- In the name of science, we shall not make any unwarranted conclusions, and we promise to use all the information at hand, not deliberately discarding information (for what ever reason).
- We use the laws of probability theory.
The first point is where the problem lies. In fact the probabilities are just a formalization of the information
we have. This is why we always condition the probability on some information e.g., P(A | I) is the probability of proposition A given the information I.
Let's solve Monty Hall using the principles presented in Jaynes' book. Notice that these techniques are completely general and can solve many different problems of this nature; the key in Monty Hall is not to make any unjustified conclusions, but simply consider all the information at hand!
Lets name the doors A, B and C, and let us assume that we initially selected door A (the argument applies for any other initial choice as well). Let us write I for the information we have initially (before opening any doors) - this includes the rules of the game. More precisely I is the conjunction of statements:
* We have chosen door A.
* The host knows where the car is, and may only open a door that does not contain the car.
* The host may not open the door we selected (A) (even if it does not contain the car).
We formalize the information I in probability equations below. Let us consider three mutually exclusive and exhaustive propositions
A = the car is behind door A;
B = the car is behind door B;
C = the car is behind door C
By the principle of indifference, given only the initial information, I, we have
P(A | I) = P(B | I) = P(C | I) = 1/3
Notice also that so far intuition is completely clear.
Let us now assume that the host opens door C. Let H be the statement:
H = the host opened door C
(the argument is similar for any other choice). The important point here is that we are given additional information beyond our prior information, I. Now let us first derive the correct solution, we then analyze where peoples intuition usually goes wrong.
By the rules of probability theory (specifically Bayes theorem) we have
P(A | HI) = P(A|I) P(H | AI)/P(H|I)
The quantity P(A|HI) is what we are interested in: the probability of the car being behind door A given all the information available to us
We know P(A|I) is 1/3 so we can focus on P(H|AI) and P(H|I) - notice these are both probabilities about the host's actions - probabilities that are very relevant to the problem (by the equation above), but also probabilities that most people would not consider to analyse (because probability is taught the way it is)! The former is the probability of the host opening door C given the car is behind door A; the latter is the a-priori probability of the host opening door C given only the information I. The former, P(H|AI), is the most simple: given we know that the car is behind door A what is the probability of the host opening door C. Since we have no information about which door the host opens when the car is behind the door we selected, the principle of indifference applies and we have:
P(H|AI) = P(not H|AI) = 1/2
Now consider P(H|I): the a-priori probability of the host opening door C. Since propositions A, B and C are mutually exclusive and exhaustive, the rules of probability theory imply
P(H | I) = P(H | AI)P(A|I) + P(H | BI)P(B | I) + P(H | CI)P(C | I)
We know that P(H | CI) = 0 because by information I, the host may not open door C if the car is behind door C. We already figured out P(H | AI) and P(A|I) so the first term is 1/2*1/3 = 1/6. Also we know P(B | I) = 1/3. Now we can focus on P(H | BI): the probability of host opening door C when the car is behind door B and we have chosen door A. But here the rules of the game are clear: the host must
open door C in this case since he may not open A and may not reveal the car. Hence P(H | BI) = 1. We get:
P(H | I) = 1/6 + 1*1/3 = 3/6 = 1/2.
We now have all the quantities needed to calculate P(A | HI):
P(A | HI) = 1/3 * [(1/2)/(1/2)] = 1/3. Hence P(B | HI) = 2/3 and we should switch doors!
The technique is completely mechanical. I have not used any clever arguments or mathematical ingenuity: only the rules of the game, the principle of indifference and the laws of probability theory. All calculations could be performed by a machine with these inputs.
So where does our intuition go wrong? Two places, I believe. First because of schooling our intuition tells us that somehow we can only reason about "random" events. Instead we should focus on information
e.g., 'the car is placed "at random" behind a door' versus "we are given the information that there is a car behind one door and sheep behind the two others." Once we free ourselves to consider probabilities as expressing the information we have available, it is natural that the probabilities change when we obtain more information. This is crucial. The second, I believe, is a consequence of the first: most people seem to identify the following two statements in the Monty Hall problem:
* the host opens door C
* the car is not behind door C
But these two pieces of information are not equivalent when we know the rules of the game (i.e. given our prior information). Considering them equal would violate our commitment to science, to be objective and to consider all
the information at hand :-)
To illustrate let us analyse a variant of Monty Hall where "H" means the latter instead.
Given this alternate piece of information, our first step is still to apply Bayes theorem so:
P(A | HI) = P(A|I) P(H | AI)/P(H|I)
We still have P(A|I) = 1/3. P(H|I) is the probability that the car is not behind door C given our initial information. Since H = not C, and since A, B, C are mutually exclusive and exhaustive, the rules of probability theory imply
P(H | I) = P(not C|I) = P(A or B|I) = P(A|I) + P(B|I) = 2/3
Now P(H | AI) is calculated by classical logic: since A implies not C we have P(H | AI) = 1. Hence:
P(A | HI) = 1/3 * 1/[2/3] = 1/2
Which is the false result that most people's intuition prefer. This is the correct conclusion, but for a different game than Monty Hall, namely the game without a host where you simply get an additional information about where the car is not.
Notice that we easily analysed both variants of the game using simple probability theory, and in its interpretation as an extension of classical logic, the intuition follows along nicely. The key is to use all the information at hand
, not discarding any information that could be of relevance to the problem (i.e. we got the information that host selected C, not that door C had a sheep behind it).


Abacus makes mathematics easy.
Mathematics is an important and compulsory subject in every school. It’s not a difficult subject, but it needs a bit more effort compared to other subjects. Abacus is a beautiful method to make few parts of mathematics easy. The abacus has been around for thousands of years, and is still used in some parts of the world. Sometimes blind people will use an abacus, because they can feel the numbers easily. It is also a fun way for small students to solve math, who feel the subject difficult.
But not every school provides the facilities to learn abacus. In urban places, we find special classes which provide abacus knowledge. But, in the case of rural areas, we hardly find. So, LEADer Vinay from Bapuji Polytechnic College, Davangere started an initiative of teaching abacus to school students. He too has learnt abacus for around six years and has an excellent knowledge about it.
He went to a school named Bachpan school, Davangere and seemed for the permission from the principal of the school to teach students how to use an abacus. The school principal was pleased to his offer and allowed him to take the classes for some time everyday for a week. He started his classes by first introducing the students to the instrument used. He then briefed them about its origin, existence, value, and importance of its use and then he taught them how to carry out the calculations on it. It was really fascinating to all the students which created an eagerness to learn to them. On the last day, he also conducted a small test which gave a good result.
Students, teachers and the school principal were impressed by it. It helped students not only in calculations, but also made math interesting subject for them. Teachers appreciated LEADer with a warm gratitude and asked him to carry on the classes for another week. During the project, he overcame upon the stage fear which he had earlier. He learnt leadership skills, teaching skills, confidence, and courage.
Written by : Priyanka Kammar
Email ID : firstname.lastname@example.org