More than 20 years ago (1996), Vic Reiner and I wrote a computer lab for a senior-level course in algebraic geometry at U Minnesota. The cardioid is also a familiar shape around St. Valentine's Day, when it very nearly matches the traditional "heart" shape. You can also determine the direction of the cardioid. Cardioid can be understood by comparing its shape to that of the cross section of an apple without stalk. The cardioid curve is in the form of a spiral sinusoid. In this blog post, we present a few favorite places that cardioids appear. In 1637 Étienne Pascal—Blaise’s father—introduced the relative of the cardioid, the limacon, but not the cardioid itself. The two dimensional shapes include triangles, quadrilaterals, circles and other polygons. I didn’t know about the coffee cup. The microphone is so-named because the graph of the sensitivity of the microphone in polar coordinates is a cardioid. Cardioid: The value of ‘a’ is equal to that of ‘b’. Did you notice that examples 1 and 3 will produce horizontal cardioids? (So in our numbering, n=0 sits at the point P.). Got your coffee? Since arc PQ equals arc QR arc PR is twice arc PQ. Author: Clarissa Grandi Created Date: 02/10/2013 14:42:37 Title: Drawing a cardioid Last modified by: Clarissa Grandi Company: Thurston Community College The envelope of these lines is a cardioid. Area of cardioid = 6 π a2 = 6 x 3.14 x (6)2 = 678.24 square units. A Cardioid as an Envelope of Lines. Find a tutor locally or online. 1-to-1 tailored lessons, flexible scheduling. complex_number Calculator skills revision lesson. A parabola whose focus is at the center of inversion can be inverted to form a cardioid curve. The parametric equations of ‘x’ and ‘y’ in the above cardioid equation is given as: where ‘a’ is the radius of the circle which is traced. (The tedious calculations require both algebra and further applications of the double angle formula.) In particular, as we see below, arc QR is twice arc PQ. Examples 2 and 4 are vertical cardioids. Area of cardioid = 6 π a2 = 6 x 3.14 x (6)2 = 678.24 square units, Length of the arc = 16 a = 16 x 6 = 96 units. The pages are designed so that the mathematical figure is on one side and the flip book page number is on the reverse side. The word cardioid is derived from the Greek word which means ‘heart’. But then segment QR is a line that we would have drawn in the previous construction. (Let's stop here to give away an equation for a flawless, vertical, valentine heart: You can plug this into a graphing calculator, Google search, or online plotter and get a lovely little valentine.). Polar Form of Representing Cardioid Equation: The polar equation of a cardioid graph is represented with respect to ‘r’ and ‘θ’ coordinates as follows: In the above equation, ‘a’ is the radius of the circle that is traced and θ is the polar angle. Thanks for the comment and the link! In 1741, Johann Castillon gave the cardioid its name. Cut out each page, put in numerical order, and secure with a binder clip. Let’s see why this is the case. Playing the probabilities in Settlers of Catan, Coffee stains and the Simpsons in your LaTeX document, Trigonometric functions and rational multiples of pi. That main heart-shaped region? x (t) = 2r * cos (t) * (1-cos (t)) y (t) = 2r * sin (t) * (1-cos (t)) This way its easier to calculate. Since θ can be any angle, the resulting cardioid can orient horizontally or vertically.


Ticket Seat Plan = The total number of plans people have pledged. For example, if John J. pledges 4 20-game plans in the the Upper Outfield, that equals 4 Ticket Seat Plans and if John H. pledges 4 full season plans in the lower infield, that too equals 4 Ticket Seat Plans. Because this only tells part of the story, we also report Dollars Pledged.
Dollars Pledged = The cumulative value of all the plans everyone has pledged. We take the dollar value from the matrix on the Pledge Page and assign it to each pledge, then add it up. So that means that John J's pledge of 4 20-game plans in the Upper Outfield equals $2,400 and John H's pledge of 4 full season tickets (which include the one-time Stadium Builders License fee) in the lower infield equals $42,400.
In the future we plan to break out these statistics in other ways, such as Season Ticket Equivalents and total people who have made pledges.


Highest Readouts and Number of Decimals
There is a maximum distance which the Plan Wheel can display. This varies depending on the units of readout chosen. Also depending on the units of readout, a different number of digits will be displayed following the decimal. The following chart shows the maximum reading and number of digits for each unit of readout possible on the Plan Wheel:
Units of Readout
No of Decimals
If you roll past the maximum reading, the display will show all dashes (-------). However the Plan Wheel continues to accumulate distance internally. The measurement can be recovered by switching to larger units; for example, from feet to yards.
The number of digits after the decimal does not necessarily reflect the resolution of the readout. Resolution of readout = 1.0 mm (0.04") wheel resolution times the scale factor.
Examples: For a scale of 1:100 and reading out in meters, the resolution is 1.0 mm times 100 = 0.1 meter. For a scale of ¼" = 1' (1:48) and reading out in feet, the resolution is 0.04" times 48 = 1.92 inches or 0.16 feet.
This chart applies to the Plan Wheel PC as well as the Plan Wheel.


A Consistent Pricing Model for Swaptions and Forward Volatility Contracts on Swaptions
In the financial markets many different types of contracts are traded in order to control the risks of a portfolio. One of the most traded financial product is the swaption. A risk associated with a swaption, is the so called volatility risk. A tool for hedging this risk is the forward volatility contract, which allows an investor to lock in the forward volatility embedded in the shape of the volatility surface observed today. The objective of this thesis, is to construct a mathematical model, which is able to price these forward volatility contracts consistent with the pricing of vanilla swaptions.
Student: Asbjørn Snitkjær Meinhardt
Education: Mathematics - Economics


Bore Da. Dydd Gwyl Dewi Hapus.
Apologies, I thought this had posted on Monday.
Here is this week’s learning grid. As more children are now accessing the 2 day offer or are back to school full time (Foundation Phase) we have reduced the number of links etc on the presentation. While in school the children will be working on their focussed maths and phonics activities as well as activities that are related to the story / topic. Within the learning grid there are additional links to phonics and maths sites. It is so nice to have the children back in school and hopefully we will all be back together very soon.
Today’s activities will be uploaded to seesaw shortly.
Thank you so much for your continued support and engagement through these unusual times


STEM Project - Formula 1
Beth and Jo decided to combine their subjects Science and Maths to create a Formula One based project for the students. Over a course of four weeks the students looked at speed and power of formula one cars - they calculated the speeds of various drivers from the 2014 Monaco Formula One. We also looked at the design of Formula One cars and they completed their own research into them. They also looked at stopping distances of cars and did their own hazard perception tests. From aspects of Physics such as Newton’s Laws and speed calculations from Maths – it was a collection of these subjects that created this project. All students took part in the activities – but would like to specially congratulate the students that completed the full work pack: Jonathon Crosbee, Tommy Black, Mikey Hope, Abdul Ahmed, Curtis Doughty and Dan Scott. These students were then taken out for their own version of high speed racing with Go-Karting at Wessex Raceway.


Bearing problems practice problems online brilliant. Bearing problems on brilliant, the largest community of math and science problem solvers. Fill in the boxes at the top of this page with your name, centre number and candidate number. Find out how much you can recall about compass bearings with this convenient quiz and worksheet. In order to determine the classification and applicability of antidumping duties, please provide the requested information for each bearing. Kevin pedalled his pushbike along a road for 4km in the direction s650e. Apr 07, 2008 a bearing is a measurement of direction between two points.
Nskhps high performance standard bearings for industrial machinery. Bearings are generally given in one of two formats, an azimuth bearing or a quadrant bearing. If ball bearing not including ball bearings with integral shafts or parts of ball bearings. Worksheet 1 working with angles name standard angle. An azimuth bearing uses all 360 of a compass to indicate direction. Reference meridians geodetic northsouth reference line that passes through a. Mathematics linear 1ma0 bearings materials required for examination items included with question papers ruler graduated in centimetres and nil millimetres, protractor, compasses, pen, hb pencil, eraser. Failure to provide full and accurate data may result in clearance delays andor penalty actions by customs and border protection. Now let us look at some examples of writing compass bearings and true bearings. He then changed course to n25 0e and pedalled a further 3km. I have a pair of bearing angle values and want to draw two lines using these bearing angles. Release of imporations could be delayed unless this information is provided. Mark the location of these points and calculate the bearings between them. A worksheet which allows students to practise and apply their understanding of bearings.
How to plot compass bearings as lines in excel i was wondering if anyone might be able to help me find a way to plot a couple of lines on a chartgraph that represents a pair of compass bearing. Maths made easy complete tuition ltd 2017 bearings 1. Super precision sealed angular contact ball bearings. Reference meridians geodetic northsouth reference line that passes through a mean position of the earths geographic poles.
As the author of the video says, when using bearings there should be three things to have in mind. Together the two parts of this activity will teach reading bearings from a map and following bearings in the field. Course the direction a vessel has traveled or plans to travel. Bearing name and part number manufacturer case number country. Jul 14, 2009 this interactive application has been designed to teach pupils to accurately estimate and draw a bearing. Following a bearing once you have your magnetic bearing, and the compass is pointing to your objective, you need to start walking do not walk and look at the compass at the same time its easy to veer off your bearing you cant see whats in front and around you find an intermediate point that is on your bearing, put your compass. Bearings classification worksheet bearings are a highly regulated product due to various outstanding antidumping cases. Bearings in trigonometry examples, solutions, videos. List the direction and degree reading for each point. Answers to the course are provided after the course outlines. Please check the one box that describes the bearing, and fill in any blanks below the selected description.
For this online bearings worksheet, students complete a variety of online exercises involving traveling in different directions. Angles, azimuths and bearings christian brothers university. Edexcel gcse mathematics a foundation tier 1ma01f you must have. I hereby certify that i have entered into any agreement or understanding for the payment or for the refunding to me, by the manufacturer, producer, grower, seller or exporter of all or any part of the special antidumping duties assessed on the importation of these bearings. To transfer the bearings and set the same course outside on the ground. A bearing is an angular direction of one point in relation to another point. Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, hb pencil, eraser. Bearings worksheets bearings questions maths made easy. Bearing worksheet pdf bearing worksheet word this free teaching resource is provided by ngfl cymru your gateway to teaching and learning resources online. The bearings from a point p of two points a and b are 34 0 and 124 0 and their distances from p are 230 m and 760 m respectively. Bearings foundation tier for this paper you must have. Watch this gcse maths revision video its really helpful. Using a compass to measure both possible bearing angles of the line. Read each question carefully before you begin answering it.
Its advisable for a scouter to monitor the activity to give a hand if needed. Pencil, pen, ruler, protractor, pair of compasses and eraser you may use tracing paper if needed guidance 1. We take north as 0000 degrees and mark off the direction in degrees in a clockwise direction. In this workshsheet, students calculate bearings from the given angles. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. Using an orienteering compass you will need to align the indicated north lines on your worksheet with north on the compass.
Hand this paper to your classmate and have them stand in the same spot. More lessons for gcse maths math worksheets a collection of videos, games, activities and worksheets that are suitable for gcse maths. Year 10 bearing practice 2 with answers mr patels maths blog. Department of commerce initiates antidumping duties cases when they find shippers are selling a commodity at less than fair market value thus putting u. The reason for having these rules is probably because sailors needed a way to communicate their locations to each other, but that can get confusing when youre in the middle of the ocean. So south is a bearing of 180 degrees, east is 090, west is 270. Bearings worksheets contents compass bearings page 2 add 3figure bearings to a compass rose calculating bearings page 3 plot points using coordinates and find simple bearings bearings homework page 4 measure bearings and find changes in direction bearings map page 5 for use with next activity designed for a3 size map tasks pages 67. Draw the bearing, then use the scale on the map to convert the distance to cm and measure. The principal problem with hydrodynamic bearings, however, is that the thickness of the hydrodynamic layer, and hence the accuracy of the bearing, depends on speed. To find the bearing of b from a, draw a line from a to b, draw a northline at a and measure the angle clockwise from the northline to your line.
In the asn, standards are hierarchically structured. Bearings a bearing is used to represent the direction of one point relative to another point. The numbers in brackets are the true bearing readings. The scouts copies down on their card the letter on each marker along their route. Direction on a grid or map are described in terms of the four main.
They help locate objects or positions within a twodimensional plane, such as a. Find compass bearings lesson plans and teaching resources. Compass bearing displaying top 8 worksheets found for this concept some of the worksheets for this concept are bearings work, finding directions using a compass, the compass taking a bearing, getting to the point, orienteering curriculum packet nov17final, layout, basic map compass skills, compass parts purpose. Each lot is defined using bearings and line lengths. Rotate to landscape screen format on a mobile phone or small tablet to use the mathway widget, a free math problem solver that answers your questions with stepbystep explanations. Hi here are bearing questions practice with answers. The following information is required for the importation of bearings per. It is important to know what direction various compass bearings represent. The application allows the practice of drawing bearings and the estimation of bearings. This worksheet will give you practice at using this knowledge combined with elementary geometry.
Perhaps this is what led to the development of externally pressurized, or hydrostatic bearings. Click on popout icon or print icon to worksheet to print or download. Given that r is 35 km from p, calculate the bearings of x and y giving your answers to the nearest whole number. How to get a bearing with a compass isu geosciences. Students check their twentyone answers as they go and the computer computes their final overall score at. This video shows how to use the cosine rule to solve a problem involving bearings. Compass directions and bearings teaching resources.
Use a compass to find the bearings between the checkpoints shown on the orienteering course on your worksheet in the order given. Bearings catalogs and cad drawings services nsk global. In your school yard, and without letting anyone see you, take a bearing on a particular object tree, building, car, etc. A bearing is measured in a clockwise direction from north. Worksheets are bearings work, finding directions using a compass, the compass taking a bearing, getting to the point, orienteering curriculum packet nov17final, layout, basic map compass skills, compass parts purpose. Note the bearing in degrees, and write the answer in the box below. Bearings are a way of expressing the angle between two objects, and there is a specific set of rules about how bearings should be calculated and expressed. May be measured in degrees true, magnetic, or compass. A bearing is a measurement of direction between two points. Solutions for the assessment compass directions and bearings 1 a northeast is 045 b southeast is 5 title.
Feb 10, 20 a worksheet which allows students to practise and apply their understanding of bearings. Bearing name and part number manufacturer case number. Youll answer questions about the format of various kinds of bearings. Compass bearings are used as methods of navigation in relation to the north direction by angles. You will probably learn about bearings in maths as well as geography. The compass is numbered clockwise with north as 0, east 90, south 180, and west 270. Follow the links to the cymru website to use interactive activities. The drawing below shows the compass bearings for the 8 directions.399 1030 1473 794 113 596 680 1540 1604 737 916 190 218 654 1624 1074 890 897 329 1585 906 617 732 611 322 1325 33 338 555 1150 1183 328 1045 1454 469 334


This article is about scale, nominal scale, principal scale, representative fraction, and scale factor of a map. For bar scale on a map, see Linear scale.
Large scale, medium scale, small scale.
A map is classified as small scale or large scale or sometimes medium scale. Small scale refers to world maps or maps of large regions such as continents or large nations. In other words, they show large areas of land on a small space. They are called small scale because the representative fraction is relatively small.
Large scale maps show smaller areas in more detail, such as county maps or town plans might. Such maps are called large scale because the representative fraction is relatively large. For instance a town plan, which is a large scale map, might be on a scale of 1:10,000, whereas the world map, which is a small scale map, might be on a scale of 1:100,000,000.
The scale of a map is the ratio of a distance on the map to the corresponding distance on the ground. This simple concept is complicated by the curvature of the Earth's surface, which forces scale to vary across a map. Because of this variation, the concept of scale becomes meaningful in two distinct ways. The first way is the ratio of the size of the generating globe to the size of the Earth. The generating globe is a conceptual model to which the Earth is shrunk and from which the map is projected.
The ratio of the Earth's size to the generating globe's size is called the nominal scale (= principal scale = representative fraction). Many maps state the nominal scale and may even display a bar scale (sometimes merely called a 'scale') to represent it. The second distinct concept of scale applies to the variation in scale across a map. It is the ratio of the mapped point's scale to the nominal scale. In this case 'scale' means the scale factor (= point scale = particular scale).
If the region of the map is small enough to ignore Earth's curvature—a town plan, for example—then a single value can be used as the scale without causing measurement errors. In maps covering larger areas, or the whole Earth, the map's scale may be less useful or even useless in measuring distances. The map projection becomes critical in understanding how scale varies throughout the map. When scale varies noticeably, it can be accounted for as the scale factor. Tissot's indicatrix is often used to illustrate the variation of point scale across a map.
The terminology of scales.
Representation of scale.
Map scales may be expressed in words (a lexical scale), as a ratio, or as a fraction. Examples are:
'one centimetre to one hundred metres' or 1:10,000 or 1/10,000
'one inch to one mile' or 1:63,360 or 1/63,360
'one centimetre to one thousand kilometres' or 1:100,000,000 or 1/100,000,000. (The ratio would usually be abbreviated to 1:100M
Bar scale vs. lexical scale.
In addition to the above many maps carry one or more (graphical) bar scales. For example some modern British maps have three bar scales, one each for kilometres, miles and nautical miles.
A lexical scale on a recently published map, in a language known to the user, may be easier for a non-mathematician to visualise than a ratio: if the scale is an inch to two miles and he can see that two villages are about two inches apart on the map then it is easy to work out that they are about four miles apart on the ground.
On the other hand, a lexical scale may cause problems if it expressed in a language that the user does not understand or in obsolete or ill-defined units. On the other hand ratios and fractions may be more acceptable to the numerate user since they are immediately accessible in any language. For example a scale of one inch to a furlong (1:7920) will be understood by many older people in countries where Imperial units used to be taught in schools. But a scale of one pouce to one league may be about 1:144,000 but it depends on the cartographer's choice of the many possible definitions for a league, and only a minority of modern users will be familiar with the units used.
The following table describes typical ranges for these scales but should not be considered authoritative because there is no standard:
Classification Range Examples
large scale 1:0 – 1:600,000 1:0.00001 for map of virus; 1:5,000 for walking map of town
medium scale 1:600,000 – 1:2,000,000 Map of a country
small scale 1:2,000,000 – 1:∞ 1:50,000,000 for world map; 1:1021 for map of galaxy
The terms are sometimes used in the absolute sense of the table, but other times in a relative sense. For example, a map reader whose work refers solely to large-scale maps (as tabulated above) might refer to a map at 1:500,000 as small-scale.
Mapping large areas causes noticeable distortions due to flattening the significantly curved surface of the earth. How distortion gets distributed depends on the map projection. Scale varies across the map, and the stated map scale will only be an approximation. This is discussed in detail below.
Large-scale maps with curvature neglected.
The region over which the earth can be regarded as flat depends on the accuracy of the survey measurements. If measured only to the nearest metre, then curvature of the earth is undetectable over a meridian distance of about 100 kilometres (62 mi) and over an east-west line of about 80 km (at a latitude of 45 degrees). If surveyed to the nearest 1 millimetre (0.039 in), then curvature is undetectable over a meridian distance of about 10 km and over an east-west line of about 8 km. Thus a plan of New York City accurate to one metre or a building site plan accurate to one millimetre would both satisfy the above conditions for the neglect of curvature. They can be treated by plane surveying and mapped by scale drawings in which any two points at the same distance on the drawing are at the same distance on the ground. True ground distances are calculated by measuring the distance on the map and then multiplying by the inverse of the scale fraction or, equivalently, simply using dividers to transfer the separation between the points on the map to a bar scale on the map.
Point scale (or particular scale).
As proved by Gauss’s Theorema Egregium, a sphere (or ellipsoid) cannot be projected onto a plane without distortion. This is commonly illustrated by the impossibility of smoothing an orange peel onto a flat surface without tearing and deforming it. The only true representation of a sphere at constant scale is another sphere such as a globe
Given the limited practical size of globes, we must use maps for detailed mapping. Maps require projections. A projection implies distortion: A constant separation on the map does not correspond to a constant separation on the ground. While a map may display a graphical bar scale, the scale must be used with the understanding that it will be accurate on only some lines of the map.


Product features. Part of the Osmo Genius Starter Kit for kids ages 6-10. Develop confidence with numbers in a hands-on, interactive way! Play with physical Numbers Tiles, including dots and. But be careful doing that with Amazon. The website The Daily Scam says fraudsters are posting fake Amazon customer support phone numbers that then show up in a Google or.
Here is how we can get the seller to reach the threshold with the minimum number of additional five-star reviews: Before we add more five-star reviews, the percentage for this seller is ( (4 / 4) + (1/2) + (3/6))/3 = 66.66%. If we add a five-star review to the second product, the percentage rises to ( (4 / 4) + (2/3) + (3/6))/3 = 72.22%. There will be an input of an array of numbers, called "bad numbers", for ex: [23, 3, 35, 9]. Your sequence counting will be break when you hit the bad number. cremepan • 9 mo. ago, Does any of them exist on LeetCode? 1 more reply, [deleted] • 9 mo. ago, [removed] FlyAdministrative605 • 9 mo. ago, Completed my OA 23 days back.
Listen to your favourite songs from Oa Nkalosa by Maureen R now. Stream ad-free with Amazon Music Unlimited on mobile, desktop, and tablet. Download our mobile app now. Orthomen OA Unloading Knee Brace for Osteoarthritis Lateral Off Loader Support (Left) 394. ₹21,240 (₹21,240/Count) ₹69,377.46 (69% off) 10% Off on ICICI BankCards. Get it Tuesday,. Listen to your favourite songs from Oa Nkalosa by Maureen R now. Stream ad-free with Amazon Music Unlimited on mobile, desktop, and tablet. Download our mobile app now.
Problems. Question 1: Amazon Music Pair. Given durations of songs and the rideDuration of the bus, return the pair of songs which when added is exactly equal to rideDuration-30 seconds. You cannot repeat the song.Return the index of the songs. Ex: RideDuration: 250. songDurations = [100,180,40,120,10].
Lloyds Banking Group is investing £3 billion (€3.35 billion) in technology and staff to improve its digital services. As a result, the Group has announced The move reflects the growing shift towards digital service provision by the world's biggest banking firms, with the amount of transactions in high-street. Search: Charged Twice For Same Transaction.
thomaddox444 • 7 mo. ago. OA1 was easy for me as well (back in January), and my final interview question that I did last Friday was also pretty simple. My OA wasn't that bad, but certainly more.
The website the Daily Scam says fraudsters are posting fake Amazon customer support phone numbers that then show up in a Google or Bing search. The real number is 888. Did Amazon OA today.First problem all test cases passed and gave most optimal solution.Second problem, I was on right track but while the code had some runtime exception..
Why do lottery numbers repeat ? The statistical probability of lottery drawings producing the same winning numbers rises as the number of drawings increases, meaning that a short window of time with fewer drawings is less likely to produce duplicate drawings than a longer window of time with more drawings. .
The Satisfied Workbook: A Spiritual Guide to Recovery and Food Freedom. by Dr. Rhona Epstein | Jan 12, 2021. 74.
where can i buy tree stumps near me


The common core state standards describe what students are expected to learn in mathematics and language arts. The standards are designed to be robust and relevant to the real world.
Changes in curriculum- Administration and curriculum leads have been attending workshops and planning for the curricular shifts. Our work has placed Waggoner on the path to success with common core. There is much learning ahead for students, parents, and staff members, which is exciting!
Changes in assessments- The CST measured knowledge in specific content areas. By contrast, the new common core assessments will be performance-based. Exams will be administered to 3-5 grade students and will now be online by the Smarter Balanced Assessment Consortium.


Formula 1 Lotto System Support Desk
Formula 1 Lotto System - Support Desk
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US PowerBall - Choosing The Powerball Number.
If you play US PowerBall or Mega Millions, the question is often asked…”why are only 5 boxes available to input my numbers into. What about the 6th number?”….
For those games the F1LS allows you to input the first 5 numbers.
Then when you click the ‘generate button’ the system auto-generates the 6th number.
The reason for this is the system uses its algorithm to maximize the total the number spread. (also see the attached )
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Learn financial and statistical terms to understand the investment language.
A measure of the volatility, or systematic risk, of a security or a portfolio in comparison to the market as a whole.
Compound Annual Growth Rate is a number that describes the rate at which an investment would have grown if it grew at a steady rate.
A statistical measure of how two data sets move in relation to each other. Perfect positive correlation (a correlation co-efficient of +1) implies that as one security moves, either up or down, the other security will move in lockstep, in the same direction.
The peak-to-trough decline during a specific record period of an investment, fund or commodity. A drawdown is usually quoted as the percentage between the peak and the trough.
An exchange-traded fund (ETF) is an investment fund traded on stock exchanges, much like stocks. An ETF holds assets such as stocks, commodities, or bonds, and trades close to its net asset value over the course of the trading day. ETFs are attractive as investments because of their low costs, tax efficiency, and stock-like features.
A statistical measure used to describe the distribution of observed data around the mean.
A ratio developed to measure risk-adjusted performance. The Sharpe ratio tells us whether a portfolio’s returns are due to smart investment decisions or a result of excess risk. The greater a portfolio’s Sharpe ratio, the better its risk-adjusted performance has been.
Short selling (also known as shorting or going short) is the practice of selling securities, that have been borrowed from a third party (usually a broker). The short seller hopes to profit from a decline in the price of the assets between the sale and the repurchase, as the seller will pay less to buy the assets than it received on selling them. The short seller will incur a loss if the price of the assets rises.
Describe asymmetry from the normal distribution in a set of statistical data. Skewness can come in the form of “negative skewness” or “positive skewness”, depending on whether data points are skewed to the left (negative skew) or to the right (positive skew) of the data average.
A method of evaluating securities by analyzing statistics generated by market activity, such as past prices and volume. Technical analysts do not attempt to measure a security’s intrinsic value, but instead use charts and other tools to identify patterns that can suggest future activity. Technical analysts believe that the historical performance of stocks and markets are indications of future performance.
An investment performance measure that combines two components; any change in the price of the security and any dividends or interest paid to shareholders over the period being measured.
Upside/Downside Capture Ratio
A statistical measure of an investment manager’s overall performance in up and down-markets. The up/down-market capture ratio is used to evaluate how well an investment manager performed relative to an index during periods when that index has risen/fallen. An investment manager who has an up-market ratio greater than 100 has outperformed the index during the up-market. For example, a manager with an up-market capture ratio of 120 indicates that the manager outperformed the market by 20% during the specified period. An investment manager who has a down-market ratio less than 100 has outperformed the index during the down-market. An investment manager who has positive performance when the index is negative will have down-market ratio less than 0.
Value at Risk (VaR)
A technique used to estimate the probability of portfolio losses based on the statistical analysis of historical price trends and volatilities. For example, if a portfolio of stocks has a one-day 5% VaR of $1 million, there is a 0.05 probability that the portfolio will fall in value by more than $1 million over a one-day period if there is no trading.
Source: Wikipedia, Investopedia


Jul 14 2011
Here’s a Thursday math quiz for all you brainiacs out there:
Question: How far must a plastic jug of milk fall in order to split open?
Answer: If you guessed, “The approximate distance between a 3-year-old’s arm and the grocery store floor,” then you win!
Answer: this is a trick question. Because the magazine rack and checkout conveyor belt slow the milk’s progress, causing it to pool. But if you guessed “about the length of the checkout line and under the candy store rack,” then you get a gold star!


Numerical Integration Utility: Definite Integral of square-root(x) * sin(x)
This page contains a routine that calculates the definite integral of √ x sin(x) on an interval specified by the user.
Author: David K. Kahaner. Scientific Computing Division, NBS
From the book "Numerical Methods and Software" by
D. Kahaner, C. Moler, and S. Nash
Prentice Hall, 1988
To use this utility, the user must enter two values: b and c, which specify the range [b, c], over which
∫ √ x sin(x) dx will be computed. b and c must be entered as radians, NOT degrees, and they must both be greater than or equal to zero. If a negative value is entered for either of them, an error message appears asking the user to try again.
Note that over intervals for which the function is negative the integral is negative too.
IMPORTANT: Note the Error Code returned.
Error Code = 0: Normal Completion. e < eps (= 1.0e-12) and e < eps*abs(I).
Error Code = 1: Normal Completion. e < eps but e > eps*abs(I).
Error Code = 2: Normal Completion. e < eps*abs(I) but e > eps.
Error Code = 3: Normal completion but eps was too small to satisfy absolute or relative error request.
Error Code = 4: Aborted calculation because of serious rounding error. Probably e and I are consistent.
Error Code = 5: Aborted calculation because of insufficient storage. I and e are consistent.
Error Code = 6: Aborted calculation because of serious difficulties meeting error request.
Error Code = 7: More than 2*NMAX (= 100) iterations of main loop. Subroutine aborted.


Assignment Help for Linear Regression
The fact that linear regression is used in all sorts of scientific work is great. It makes the job of professionals who want to understand how people make decisions easier, and easier means less time is wasted. It also reduces frustration for the many people who have a hard time getting past the initial math or which one they use. So how do you go about obtaining do my statistics homework?
Before getting into the specifics, there is one main reason why the Linear Regression method is so popular. It is often used when taking the question of causation to other disciplines, particularly sociology.
Linear regression is often used when dealing with the personal habits of those who follow the law. The individual who is involved in either the corporate or academic setting will often find himself or herself working with a person of interest, who might show certain behaviors.
Often times these behaviors are not displayed by people all the time. As a result, it is difficult to determine whether the actions are due to the circumstances or are rather “bad luck.” Linear regression is a great way to figure out which may be the case.
The first step in trying to determine causation using linear regression is determining the best fitting curve, which is known as the x-intercept. When the data is divided up into two or more parts that represent observations (corresponding to part A and part B), and when a group of points (corresponding to A and B) is fitted to the original data, the best fitting point is the x-intercept of each of the parts.
In some cases the x-intercept may not be the same for each part. The best fit point will often be the last x-intercept in both parts, or the x-intercept of the sum of the two x-intercepts, but it does not necessarily have to be this way.
There are two other factors that can cause the x-intercepts of parts to differ, and these can cause the best fit to vary. The first of these is the slope of the regression line. The slope tells you how the linear regression line becomes steeper or gentler with each step down the x-axis.
To determine whether this slope is a good fit to the data, a model should be fitted to it, and the model should be ranked according to the number of parameters that change, and the number of variables that change by more than one level. This will help determine the best fit to the data.
The second reason why the x-intercept and the slope of the regression line are different for each part is known as the cointegration. The integration occurs when the slope of the line moves slightly but still remains steeper than the x-intercept.
With this method, the y-intercept is not used. The y-intercept is the lowest value of the line, and the slope is then calculated using the y-intercept of the line with respect to the x-intercept.
The advantage of this method is that it accounts for the fact that the slope of the line may be steeper than the y-intercept, and the y-intercept should be the most important part of the equation. The disadvantage is that the regression line will be slightly steeper than the y-intercept, and this will make the slope of the line is slightly steeper than the y-intercept.
The model is evaluated by determining how the parameters change, and the relative importance of the x-intercept and the y-intercept. By comparing the two models and determining the better fit, this method will usually reveal a new model that is most likely a good fit.


The Department of Natural and Quantitative Sciences (NQS) is dedicated to serving the educational needs and aspirations of its students in the fields of natural sciences and mathematics. Through high quality learning experiences, the effective integration of technology, project based learning, practical investigation and research, the Department seeks to establish in students a solid knowledge base in natural sciences and mathematics which will enable them to assume technical, managerial and leadership roles in a technologically advanced and rapidly changing society.
The Department of Natural and Quantitative Sciences aims to achieve six main goals:
Attract quality students and serve their educational needs and aspirations with the goal of attracting ten percent of the major student body
Provide high quality learning experiences for students
Ensure that teaching will be provided by dedicated, quality faculty
Ensure that learning experiences will incorporate in an integrated way the use of technology, project based learning, practical investigation and research
Provide students with a solid knowledge base in science and mathematics in line with world standards
Enable students to assume technical, managerial and leadership roles
The Department of Natural and Quantitative Sciences fulfills three important roles in Zayed University.
First, regardless of a student′s major area of study, the General Education program requires all students to complete a total of fifteen credits in the Science, Mathematics and Technology knowledge domain. Students must take a minimum of three credits in Science, three credits in Mathematics, six credits in Information Technology and a further three elective credits. The Department provides a variety of courses to help students fulfill these requirements.
Second, Natural and Quantitative Sciences acts as a service department for other colleges within the University. The College of Business Sciences, the College of Education and the College of Information Systems all require their majors to enroll in a selection of courses offered by the Department of Natural and Quantitative Sciences. In some cases, such as Quantitative Methods for Business (MTH 291), the course has been tailor-made, according to the particular college′s requirements. In other cases, a college may require a course that is generic and not specific to their discipline, such as Precalculus (MTH 201).
Finally, the Department offers a major leading to a Bachelor of Science degree in Natural and Quantitative Sciences. Students may choose from three streams: one with an emphasis in the physical sciences, one in biological sciences and one in mathematics and statistics. The major seeks to provide students with the knowledge and hands-on skills necessary to pursue a career in the areas of science and mathematics.


The BBC published a story today about a 91 year old woman finally getting her dream job. Like everyone, I have a fantasy job. Unlike most, mine involves math. And prisons.
Perhaps sad but totally true: I long to teach algebra to women who are incarcerated. It’s a plan I’ve thought through. First, they would be a “captive audience” (ouch); why not do some homework and come to class? What else is going on? Second, there would be the luxury of time — time to make sure multiplication tables are memorized; time to explain the underlying concepts. Third, conquering algebra would build confidence and brain power. Might even help someone get a better job when their time was served. Fourth, I wouldn’t be expected to use fancy “new math” and computer teaching programs. My favorite form of instructional technology is a piece of chalk and an eraser. And of course, we would only do the easy word problems.
You wouldn’t have to pay me to work this dream job of mine and I might not face much competition to get it. I probably have a better chance at this one than my other fantasy: to make a living from the writing I want to do, which is not to be confused with the kind of writing that pays.
You’d be amazing at that job. Hope you find a way to do it.
This reminds me that I loved math in K-12, but was a year ahead and back then they didn’t offer the second AP Calc class at my school, so I took no math in 12th and then went to Eckerd and became one of those “math is scary and for boys” girls and OMG I REGRET IT! It’s not a job, but just dreams? Having the ability to get a BS in math without the computers and whatnot. I would definitely feel less like I gave up on part of myself I was really proud of. So if you get that job, tell me where, and maybe I’ll get myself arrested!


Let’s assume the following:
The goal of this section is to introduce some key terms necessary for expressing Bayes’ theorem. To facilitate this, it is helpful to have a working example.
This information can be represented using a probability tree (see Figure 1).
First, let’s define what are known as unconditional probabilities or prior probabilities. These are probability that do not depend upon (are not conditioned by) something else being the case. In our example, there are three prior probabilities.
This information can be put in the language of hypothesis and evidence / data / observation. First, suppose we have the hypothesis that we have VX. Call this hypothesis . The prior probability of is the probability of independent of (or prior to) any test for VX.
Definition 1 (prior probability of ) the probability of before we take into consideration some evidence . Let stand for “the probability of the hypothesis ()” independent of evidence .
Second, with this hypothesis in mind, we can characterize the results of VX as evidence. Call either a positive or negative test . The prior probability of is the probability of independent of whether or not we have the VX disease or not.
Definition 2 (prior probability of ) the probability of before we take into consideration some hypothesis (theory) . Let stand for “the probability of an observation ()” independent of a hypothesis .
What we have then is two different unconditional probabilities: and . Note, however, that incoming information influences the probability of the hypothesis and that scientists want to know the probability of a hypothesis given some piece of evidence. In other words, given some incoming evidence , we should adjust the probability of the in light of .
Definition 3 (conditional probability) The conditional probability of A given B is the probability of A on the condition that B.
There are two important conditional probabilities in our example.
Definition 4 (posterior probability of - ) on the assumption (condition) that the hypothesis is true, the probability of the evidence . That is, the likelihood of some observation given (in light of) the hypothesis . Let stands for the probability of assuming is true.
Definition 5 (posterior probability of - ) on the assumption (condition) that some observation is the case, the probability of the hypothesis (). That is, the likelihood of the hypothesis given (in light of) the evidence . Let stand for the probability of given .
The posterior probability of given , that is is what we want to know. Bayes theorem tells us how to calculate this information.
At the core of the Bayesian approach to science is Bayes’ theorem. What is the theorem? Let’s consider three different, increasingly precise articulations of Bayes’ theorem.
Definition 6 (Super simple Bayes’ theorem) Belief (hypothesis) + new evidence = new and improved belief (hypothesis)
Definition 7 (Bayes’ theorem in English) The probability of a hypothesis given some new evidence is equal to the probability of the evidence given the truth of the hypothesis times the probability of the hypothesis independent of the evidence divided by the probability of the evidence independent of the hypothesis.
Definition 8 (Bayes theorem)
In what follows, some step by step examples are provided to show how Bayes’ theorem can be used to determine the posterior probability of some hypothesis given some evidence. In using Bayes’ theorem, the following step-by-step method will be followed:
Example 1 (Cancer screening)
Now take John. What is his probability of having VX ? In looking at the probability tree, we would say it is 1%. Now suppose John is tested for VX and he tests positive. What now is his probability of having VX given that he has tested positive ?
The answer, in this case, is obvious, but it can be computed using Bayes’ theorem. First, let’s write out Bayes’ theorem:
Next, let’s input the values from our probability tree beginning with the prior probability that John had VX:
Next, input the probability that he tests positive given that he has VX
Next, we input the probability that he tests positive prior to determining whether he does or does not have VX. For this, we add the probability that he has VX to the probability that he tests positive (.01*1) to the probability that he does not have VX and tests positive (.99*0):
Finally, we do the calculations and, as expected, we find that the probability that John has VX given a positive test is 100%.
What we see from the above is that Bayes theorem can be used to determine the probability of the hypothesis that someone has the VX-disease given
What it does is allow us to update the probability of a hypothesis given new information. Let’s consider a more complicated and realistic example. We cannot expect every test to be 100% accurate.
Example 2 (Cancer screening)
Suppose a woman between 40-50 goes to have a mammogram. Her doctor meets with her to tell her that her test has come back positive. Since the test is not 100 percent reliable, she does not know if, in fact, she has cancer. It could be a false positive.
What is the probability that she actually has breast cancer.
We now can use the diagram and Bayes’ theorem to determine the probability that an individual has cancer given a positive test. First, we determine the probability that an individual who tests positive actually has cancer . This is multiplied by the probability that an individual has cancer independent of whether they tests positive or negative .
Next, we determine the likelihood that someone will test positive for cancer independent of whether they have cancer or not: .
Then using Bayes’ theorem we can calculate the probability that one has cancer given a positive test.
Discussion 1 Suppose you are working for a large corporation that drug tests employees. To keep things simple, let’s suppose that the drug is cocaine. If any individual fails the drug test, they are immediately fired and the employer informs the police.
Now suppose someone tests positive for cocaine. What is the probability that they are on cocaine given the positive test?
Bayes’ theorem has a wide variety of applications. What role does it play in the philosophy of science?
Note 1 (Bayes’ theorem and the confirmation of a scientific theory.)
Bayes theorem can be used to formulate a theory of incremental confirmation. Namely, we can say that some evidence confirms if and only if . That is, if the posterior probability of a hypothesis is greater than the prior probability of a hypothesis, then the hypothesis has been confirmed by the evidence.
This does not mean that the hypothesis is true, likely, or that we should believe the theory when . Notice that in the case of cancer screening, even though the probability that you have cancer given a positive test is greater than the probability that you have cancer independent of a test (), it is still more likely that you don’t have cancer than you do have it.
Note 2 (Bayes’ theorem largely corresponds to how we think observation and evidence influences the probability of a scientific theory)
First, if is likely whether is the case or not, won’t (strongly) support a hypothesis . That is, if is true under a variety of competing hypotheses, then won’t increase the probability of being true.
For example, suppose a hypothesis and two competing hypotheses . If under each hypothesis on the condition that the hypothesis is true, then it is the case that the sky is blue (that is, ), then does not change the likelihood of the . In short, evidence that supports a variety of competing hypotheses equally or is true whether is the case or not won’t be strongly supportive (see Figure 2).
Second, if is extremely unlikely unless is true and it turns out that is the case, then will significantly increase the likelihood of . The idea here is that if a hypothesis makes a novel (or unusual) prediction – one that is not likely given other hypotheses –, and this prediction is confirmed, then the probability of the significantly increases.
Note 3 (Bayes’ theorem and ad hoc modifications.)
Bayesianism is capable of accounting for problems associated with ad hoc modifications to theories. For suppose runs into conflict with some observation . A proponent of theory might, however, modify the theory in an ad hoc way in order to preserve the theory.
However, the Bayesian can account for why ad hoc modifications to theories fail to be better than the original theory simply because they are less susceptible to being falsified.
Objection 1 (How do we know the prior probability of the hypothesis?)
The use of Bayes’ theorem requires that we know the (i) prior probability of the hypothesis, (ii) the prior probability of the evidence, and (iii) the conditional probability of the evidence given the hypothesis. How is the prior probability determined before applying Bayes’ theorem? For example:
Response 1 (All hypotheses have equal prior probability) One response is to take an objectivist position. Namely, all hypotheses are equal until the evidence makes them more or less probable. Call this the objectivist position.
Imagine two boxers: Ryan and Frank. To determine the likelihood of one boxer beating the other, we begin by simply supposing that each has an equal chance. So the likelihood that Ryan will beat Frank is 50% and Frank beating Ryan is 50%. From there, we look at features in the world, using Bayes’ theorem, to adjust the likelihoods, e.g. injury, training, etc.
Objection 2 (Probability of scientific hypotheses) The objectivist approach might work in simple cases where there are two options, but it cannot work in science where there are potentially an infinite number of hypotheses. For if there are an infinite number of hypotheses, then probability of each is 0 and Bayes’ theorem won’t work if the prior probability of a hypothesis is 0 (no matter the evidence).
Response 2 (The prior probability of a hypothesis is determined subjectively) In contrast to an objectivist view of probability, let’s consider the subjectivist view. The subjectivist accepts Bayes’ theorem and interprets the prior probability that in terms of the degree of confidence that people have in occurring.
There are, however, some important caveats to this claim:
So, in the case of two boxers: Ryan and Frank, the probability that Ryan will beat Frank is whatever individuals would be willing to bet. From there, we look at features in the world, using Bayes’ theorem, to adjust the likelihoods, e.g. injury, training, etc.
Objection 3 (This makes probability rest on subjective considerations.) The problem seems to be that individuals might have different prior probabilities for the same probability. For example, I might say that the prior probability of astrology being true is 99% and the prior probability of it not being true is 1%. Where you might say that the prior probability of astrology being true is 1% while it being false is 99%.
Response 3 (Initial subjectivity is fine, probabilities converge.) Consider a hypothesis that you would not take to be very probable. Let’s suppose that I strongly believe that a certain man in an alley has psychic powers. I think the hypothesis that he can predict the future is 99.9% probable and you think it is closer to .1%. With this hypothesis in hand, we can subject him to various tests and this incoming information will (hopefully) lead us to assign the same probability to his ability to predict the future.
For example, suppose you and I go to test the hypothesis. You ask him to guess what number you are thinking of from 1-100, and he answers correctly, then 1-10,000 and he answers correctly. You are slightly more convinced. There are alternative explanations, but these seem less and less likely the more he guesses correctly. Finally, you ask him to guess tomorrow’s lottery numbers. He guesses correctly. This prediction is staggering and with each unbelievable predication, your re-use of Bayes theorem would lead you to change the probability of the man having psychic powers from .1% to 99.9%.
In short, the initial probability of a hypothesis is unimportant. What is important is that the hypothesis is allowed to adjust to incoming information.


Can it really be that hard to determine the time? It’s either 25 or 26 minutes before 4:00! Pretty simple. Today, we can better answer such questions with digital clocks. It’s either 3:34 or 3:35—no question at all.
Science is usually pretty precise so you would expect numbers to be fairly set as well. Science would tell us the time down to nanoseconds for extra precision. It’s for that reason that I found an article to be especially annoying. The expected accuracy was missing.
If one car drives at 7 miles per hour and another drives at 70 miles per hour, wouldn’t it be safe to say that the second car is travelling 10 times faster? Can you imagine a scenario in which you would say, at the same speeds, that it was travelling five times faster? Seven times faster? Of course not! We can easily see that 7 x 10 = 70 and the statement that it is travelling 10 times faster is accurate.
I read an article today about interstellar space travel. It was written by “Richard Obousy is co-founder and President of Icarus Interstellar Inc., a nonprofit foundation dedicated to researching the science and technologies that will enable interstellar flight by 2100.”
Here’s what this very intelligent man says:
“…Voyager 1, launched in 1977, is the furthest manmade object from Earth, and travels at over 10 miles per second (36,000 mph). Even traveling at this incredible speed, it would take just over 70,000 years to reach the closest star to our solar system.
Recently, NASA began developing Solar Probe plus, which will study our own sun. Through a series of seven gravitational assists with the planet Venus, the probe will reach the extraordinary speed of 125 miles per second. This is a full seven times faster than Voyager 1, which would allow it to make a trip to another star (if that were its objective) in 6,450 years.”
According to his math, 125 miles per second is a full seven times faster than 10 miles per second!
My calculations tell me it’s 12.5 times faster but who am I to argue with a rocket scientist???
(OK—he did say “over 10 miles per second”. Fact is, 125 is seven times faster than 17.857 miles per second. You would think he’d at least say “over 15 miles per second!)


Elementary staticsprincipally designed for the use of candidates for the first and second class certificates, and for the intermediate examinations; with numerous examples and exercises.
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Marty is the author of Essentials of Statistics, Elementary Statistics Using Excel, Elementary Statistics Using the Graphing Calculator, and he is a co-author of Biostatistics for the Biological and Health Sciences, Statistical Reasoning for Everyday Life and Business Statistics/5().
Marty is the author of Essentials of Statistics, 5th Edition, Elementary Statistics Using Excel, 6th Edition, Elementary Statistics Using the TI/84 Plus Calculator, 4th Edition, and he is a co-author of Biostatistics for the Biological and Health Sciences, 2nd Edition, Statistical Reasoning for Everyday Life, 5th Edition, and Business by: Access our elementary statistics book online for free.
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Do a quick audit of your day to consider whether you’re working hard or smart. The value we place on each minute of every day will have a cumulative impact on the remainder of our lives. He did a little arithmetic and figured the average person lives about 75 years. He multiplied 75 times 52 and came up with 3,900, which is the number of Saturdays that the average person will live. He ran, stumbled and breathlessly said, “God, I asked you to help me, but don’t push me.”Don’t let your time push you.


The department provides range of mathematics courses for the engineering undergraduate programmes, as well as courses in Technology, Value and Ethics for both the undergraduate and postgraduate levels..
Engineering Mathematics 1 (MATH 1310)
Complex numbers, vectors and geometry in space, matrix algebra, eigenvalues and eigenvectors, linear system of equations, differentiation and integration with applications.
Engineering Mathematics 2 (MATH 1320)
Multivariable functions, quadratics surfaces, partial derivatives and applications, multiple integrals with applications, vector valued functions, vector calculus, infinite power series, series solution of linear differential equation, Laplace transformation.
Differential Equations (MATH 2310)
Complex functions and derivatives, analyticity of function, complex integration, ordinary differential equations and modelling, partial differential equations and modelling, numerical methods to solve ordinary and partial differential equations.
Differential Equations and Statistics (MATH 2320)
Linear ordinary differential equation (ODE) with constant and non-constant coefficients, systems of ODEs, numerical solutions of ODEs. Probability, discrete and continuous random variables, estimation, hypothesis testing, simple and multiple linear regressions analysis, experimental design.
Computational Methods and Statistics (MATH 2330)
Numerical solution of linear systems, curve fitting and interpolation, numerical differentiation and integration, numerical solutions of ordinary differential equations. Probability, discrete and continuous random variables, estimation, testing hypothesis, simple and multiple linear regressions analysis, experimental design.
Complex Analysis and Numerical Methods (MATH 2340)
Complex functions and derivatives, analyticity of function, complex integration, Taylor and Laurent series, orthogonal functions and Fourier series, Fourier-Legendre series, Fourier-Bessel series, numerical solution of linear system, curve fitting and interpolation, numerical differentiation and integration, numerical solutions of ordinary differential equations.
Partial Differential Equations (MATH 2350)
Orthogonal functions, Fourier, Fourier-Legendre and Fourier-Bessel series, Laplace and Fourier transforms, underlying theory of partial differential equations, heat, wave and Laplace’s equations, orthogonal series expansions, partial differential equations in polar, cylindrical and spherical co-ordinates, numerical methods to solve partial differential equations, applications in modelling of engineering problems.
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This course relates religion, ethics and important themes of humanity and nature to engineering studies. The central theme of this course is to relate Engineering Professionalism to Islamic ethical foundations. The course also focuses on Occupational Safety and Health Administration (OSHA) and the different industrial hazards and disasters that may affect human lives and the ecological system. In a nutshell, the course is designed to infuse religious and ethical conscious into Muslim future engineers.
Values, Technology and Society (RKGS 6000/6001)
Lessons from the past Muslim achievements in science and technology; comprehend the social, economic and political impacts of technology in the Muslim world; Islamic worldview and valuesof science and technology development.
Islamization of Engineering Studies (RKGS 7000)
This course focuses on the intellectual content of “Islamization of Knowledge”. Attention will be given to the role of Islam in the development of engineering sciences within the perspectives of morality. Topics to be discussed include: the role of revelation and reason on engineering studies, the Islamic paradigm of knowledge and methods of Islamizing engineering studies.


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California Institute of Technology
1200 E. California Blvd., MS 252-21
So. Mudd Building, Rm 265E
Pasadena, CA 91125
Fax: (626) 564-0715
I am currently working on the CUDA-based coding and computation on a parallel sampling algorithm called CATMIP (Cascading Adaptive Tempered Metropolis In Parallel), which is based on the Bayesian Markov chain Monte Carlo sampling algorithm. The CUDA version CATMIP will be used to enable the fast computation for high-dimensional finite fault earthquake source modeling.


Market cycles of similar size – or degree – share certain mathematical properties widely found throughout nature.
The Fibonacci sequence of numbers was discovered (actually rediscovered) by Leonardo Fibonacci da Pisa, a thirteenth century mathematician. When R.N. Elliott wrote Nature’s Law: the secrets of the universe, he referred specifically to the Fibonacci sequence as the mathematical basis for the Wave Principle. It is sufficient to state at this point that the stock market has a propensity to demonstrate a form that can be aligned with the form present in the Fibonacci sequence. (For a further discussion of the mathematics behind the Wave Principle, see “Mathematical Basis of Wave Theory,” by Walter E. White, in New Classics Library’s book.)
In the early 1200s, Leonardo Fibonacci of Pisa, Italy published his famous Liber Abacci (Book of Calculation) which introduced to Europe one of the greatest mathematical discoveries of all time, namely the decimal system, including the positioning of zero as the first digit in the notation of the number scale. This system, which included the familiar symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9, became known as the Hindu-Arabic system, which is now universally used.
In Liber Abacci, a problem is posed that gives rise to the sequence of numbers 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on to infinity, known today as the Fibonacci sequence. The problem is this:
How many pairs of rabbits placed in an enclosed area can be produced in a single year from one pair of rabbits if each pair gives birth to a new pair each month starting with the second month?
In arriving at the solution, we find that each pair, including the first pair, needs a month’s time to mature, but once in production, begets a new pair each month. The number of pairs is the same at the beginning of each of the first two months, so the sequence is 1, 1. This first pair finally doubles its number during the second month, so that there are two pairs at the beginning of the third month. Of these, the older pair begets a third pair the following month so that at the beginning of the fourth month, the sequence expands 1, 1, 2, 3. Of these three, the two older pairs reproduce, but not the youngest pair, so the number of rabbit pairs expands to five. The next month, three pairs reproduce so the sequence expands to 1, 1, 2, 3, 5, 8 and so forth. The Rabbit family grows with logarithmic acceleration. Continue the sequence for a few years and the numbers become astronomical. In 100 months, for instance, we would have to contend with 354,224,848,179,261,915,075 pairs of rabbits.
The diagram below illustrates the concept:
The Fibonacci sequence resulting from the rabbit problem has many interesting properties and reflects several interesting relationships among its components:
Each term equals the sum of the preceding two terms;
As the series goes to infinity, the ratio between a term and the next higher term tends to 0.618.
In other words as n tends to ∞, the Xn-1/Xn ratio tends to 0.618;
As the series goes to infinity, the ratio between a term and the second next higher term tends to 0.382.
In other words as n tends to ∞, the Xn-2/Xn ratio tends to 0.382 (or 1 – 0.618);
As the series goes to infinity, the ratio between a term and the next lower term tends to 1.618.
In other words as n tends to ∞, the Xn/Xn-1 ratio tends to 1.618 ( or 1 + 0.618 );
In math, 0.618 is the only real number r for which the property 1/(r) = 1 + r holds true.
In other words, 1/(0.618) = 1 + 0.618;
Because of that, 0.618 is the only real number r for which the relationship (r)n+1 = 1 – (r)n holds true for any natural number n.
In other words (0.618)n+1 = 1 – (0.618)n;
Market movements of similar degree tend to be connected at such fibonacci ratios. Something really intriguing is that what seems to matter most is ratio not actual nominal sizes measured and this adds evidence to the idea that the Fibonacci ratios are in fact a mathematical property of all series that represent processes of additive growth.
Very interestingly, it can be demonstrated that for any series starting with any two terms X1 and X2 for which subsequent terms can be formed as the sum of the preceding two, i.e. Xn = Xn-1 + Xn-2 , the following properties hold true as n tends to ∞:
the Xn/Xn-1 ratio tends to 1.618 (or 1 + 0.618 ) ;
the Xn-1/Xn ratio tends to 0.618 ;
the Xn-2/Xn ratio tends to 0.382 or (1 – 0.618).
It can be seen in the pictures below that the Fibonacci series can form the basis of the so-called golden spiral (as shown in the first two diagrams). A remarkable trait is that the golden spiral is the mathematical law that seems to apply to virtually all processes of additive growth found in nature, from structures as small as the DNA molecule to as large as the shape of the galaxies and everything else in between (including the eyes of hurricanes, the horns of animals, the shapes of sea shells or the cones and flowers of plants).
Login Correlation patterns at the asset class level stem from two sources, that is discounting factors and the way sectors and industry groups absorb higher or lower interest rates based on […] The wave principle is unique in the perspective it can give on market trends. Many technicians find themselves confused with Elliott and present as criticism the subjective nature of wave […]
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Correlation patterns at the asset class level stem from two sources, that is discounting factors and the way sectors and industry groups absorb higher or lower interest rates based on […]
The wave principle is unique in the perspective it can give on market trends. Many technicians find themselves confused with Elliott and present as criticism the subjective nature of wave […]


The words consider and median are easily mis persuade terms which a majority of the public does not understand. The deuce terms are often wrongfully used as synonyms to the word average. Many politicians understand the publics misinterpretation of the terms and take advantage of it. What is worse is for those who actually understand the conflict between mean and median, they fail to see any practical difference between the two terms. First, it will be necessary to square off the terms and next to give a realistic supposed example of the terms in order to fully dig out the true meanings of the each one.
To square up the mean in a quantitative set of data, one must add the metrical composition together and then divide by the quantity of be in the set. Take for example the side by side(p) set of amount: 1, 2, 5, 6, 7, 9. First, the sum of all of the total is 30. Next, the sum is divided by the quantity of patterns in the set which, in this case, is 6. Therefore, 30 divided by 6 equals 5, which is the mean for this specific numerical set of data.
Now, take the same set of numbers and find the median. The first step in finding the median is to enthrone the numbers in numerical order (which they already are).
The succeeding(a) step is to find which number is the middle number, or in other words, which number has the same quantity of numbers ahead and after it. In some cases, where the numerical set has an hitherto quantity of numbers (like the example), the median is the two middle numbers divided by two. In the example the median number is 5.5.
To put the difference of the two terms into perspective, consider the following example: A town of 200 households has a mean income of $40,000 per year. With an income of $40,000 the town seems very much blue-collar in its status. Then, comes along millionaire who earns $2 million per year. Suddenly, with the addition of the millionaire, the towns mean income goes up to most $50,000. Just because one new person moved into the town, the...If you emergency to get a full essay, order it on our website: Orderessay
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Do Preschool Children Have An Innate Ability To Do Math?
Psychologists at Harvard University have found that five-year-olds are able to grasp numeric abstractions and arithmetic concepts even without the formal education or language to express this knowledge in words. The discovery of these inborn skills among preschoolers could point the way to new teaching techniques, making arithmetic easier and more pleasant for elementary school children.
A paper describing the findings will be published in the Proceedings of the National Academy of Sciences and is now on the journal's web site.
"Teaching symbolic arithmetic is one of the primary tasks of the first four years of elementary education," says co-author Elizabeth S. Spelke, a professor of psychology in Harvard's Faculty of Arts and Sciences. "Some children have enormous trouble mastering this skill, and most children find symbolic arithmetic challenging and, at times, confusing. Our studies say, however, that children already have a basic understanding of this domain. I hope our work points the way to improving mathematics education by building on this understanding."
Spelke and her colleagues asked 16 preschoolers to compare arrays of dots on a computer screen, or to merge two sets of dots and then compare these with a third set. Even without the symbolic knowledge of arithmetic that formal schooling brings, the five-year-olds could consistently tell which sets of dots were larger. Further successful comparisons between arrays of dots and sounds reinforced that the children understood the basic concept of amount.
These skills contrasted sharply with the preschoolers' ability to comprehend symbolic arithmetic, as is taught in school. For instance, children were unable to answer verbal questions about numerical addition, such as: "Suppose you have 15 marbles and your mom gives you 10 more, while your sister has 20 marbles. Who has more marbles, you or your sister?"
However, the children were able to solve this same problem when it was presented in non-symbolic form, such as an array of 15 blue dots, then a second array of 10 blue dots, and finally a sequence of 20 tones. When asked whether there were more dots or tones, the youngsters were able to give correct answers.
"A fundamental question for psychology is, 'Where do abstract number concepts come from?'" Spelke says. "Some have suggested they come from human language or are constructed by children during formal instruction; our studies provide evidence that children have abstract number concepts, and that they can operate on these concepts to perform addition, before they start school. We conclude that abstract number concepts do not depend either on language or on instruction."
Spelke's co-authors on the PNAS paper are Hilary Barth, Kristen La Mont and Jennifer Lipton, all of Harvard's Department of Psychology. The work was funded by the National Science Foundation, National Academy of Education and the Spencer Foundation.


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In a similar way, a 4 inch pump converts to 101.6mm but would ordinarily be referred to as a 100mm (10cm) heel.For example, using the chart below allows the user to see that 26 millimeters is equal to 1.02 inches.The Metric scale ranges from 0 to 25.4 mm. The inch scale is in decimal inches.Convert 146 mm x 70 mm to inches. mm to inches conversion chart.
If you know the inch to millimeter formula all you need for in to mm is a calculator.Converting from millimeters to inches, 8 millimeters (mm) is equal to 0.3150 inches.
Converting millimeters to inches - what is 700 mm inYou can also request quotes or samples online to skip the phone call for fast delivery.To start simply enter Centimeter or Inch into the correct box below.To convert 70 cm to in multiply the length in centimeters by 0.3937007874.Enter a number into the box and the results will be calculated automatically.
70 Centimeters To Inches Converter | 70 cm To in Converter
ENGLISH/ METRIC BOLT SUBSTITUTION TABLEInches to feet, yards and meters - Conversion Chart - Convert from inches to feet, yards and metre Length Units Converter - Convert between common length units like meters, feet, inches, nautical miles and more.
Note that all whole-number inch designations on the following chart convert to multiples of 25 mm except for 3-inch pipe, which ISO designates as 80 mm.To convert 70.3 mm to in use direct conversion formula below.
This Online Conversion Calculator converts in both directions.
Nominal Pipe Size Conversion to Metric SizeAn inch is the name of a unit of length in a number of different systems, including Imperial units, and United States customary units.
Conversion Table / Millimeter to Decimal Inches - RAFThe following charts will help understanding the Threads and Diameters in metric fasteners and their conversion to US Standard Inches.
To convert any value in millimeters to inches, just multiply the value in millimeters by the conversion factor 0.039370078740157. So, 0.7 millimeter times 0.039370078740157 is equal to 0.02755905511811 inches.Assumed you have seven inches and want to convert them into millimetres.
Millimeters Per Second to Inches Per Second (mm/s to in/sTo convert 8mm to inches, one simply multiplies 8 by 0.0394 inches to arrive at 0.3150 inches.
The Millimeters to Inches conversion calculator is used to convert millimeters (mm) to inches (in).
P-Metric Tire Sizes – P-Metric to Inches Conversion Chart
How Tall Is 70 Inches? | Reference.comIn 1958 the United States and countries of the Commonwealth of Nations defined the length of the international inch (in) is to be exactly 25.4 millimeters (mm).This conversion calculator produces results in inch decimals and not inch fractions.
Millimeters to Centimeters Converter - convert mm to cm onlineThe inch and the millimeter come from the imperial and the metric systems of measurement, respectively.
Metric/SAE Conversions - rcramer.com
DECIMAL EQUIVALENTS - gfii.comYears ago it was a basic unit in formerly used CGS (centimeter-gram-second) unit system, but in modern times the role of basic unit of length is played by meter.To convert 70 millimeters to inches, it is important to determine the number of inches that are equivalent to one millimeter.
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You can use the Centimeters to Inches unit converter to convert from one measurement to another.How to convert 64 millimeters to inches To calculate a value in millimeters to the corresponding value in inches, just multiply the quantity in millimeters by 0.039370078740157 (the conversion factor).How to convert 70 millimeters to inches To convert 70 mm to inches you have to multiply 70 x 0.0393701, since 1 mm is 0.0393701 in.


Bill Sykes' Newsletter
An ex-Brit gives his views-(without fear
or favor)---of the American Scene
This one is for the mathematicians amongst you:
(Please read the following very carefully and
you will find that if you accentuate the positive and
eliminate the negative then it will all add up). These
words of mathematical and geometrical ingenuity come from
an unknown author.
At New York’s airport some weeks/months ago, or
so the story goes, an individual, (later to be discovered
to be a public school teacher), was arrested trying to
board a flight while in possession of a ruler, a protractor,
a set square, a slide rule, and a calculator.
At the following mornings press conference, Attorney General
John Ashcroft was reported to have said that he believes
that the man is a member of the notorious al-gebra movement.
He is being charged with carrying "weapons of math
"Al-gebra is a fearsome cult", Ashcroft declared.
They desire average solutions by means and extremes, and
sometimes go off on tangents in search of absolute values.
They use secret code names like "x" and "y"
and refer to themselves as "unknowns". But we
have determined that they belong to a common denominator
of the axis of medieval with coordinates in every country,
and as the Greek philanderer Isosceles used to say, "there
are three sides to every triangle".
When asked to comment on the person’s arrest,
President Bush was reported to have said, "If God
had wanted us to have better weapons of math instruction
he would have given us more fingers and toes".
The President then said, "I am gratified that our
government has given us a sine that it is intent on protracting
us from these mad dogs who are willing to disintegrate
us with calculus disregard", and added "statisticians
love to inflict a plane on every sphere of influence”.
He then went on to say. "Under the circumferences
we must differentiate their root, make our point, and
draw the line", and warned that, "These weapons
of math instruction have the potential to decimal everything
in their math on a scalene never before seen, unless we
become exponents of a higher power and begin to factor-in
random facts of vertex".
Attorney General Ashcroft was then reported to have said,
"As our great leader would say, read my ellipse.
There is one principal to be sure of, that although they
continue to multiply their days are numbered as the hypotenuse
tightens around their necks".
We welcome feedback about any of the contents of these
newsletters. Please send all correspondence to firstname.lastname@example.org


Dr. Uda received the 2018 MSJ Prize for Excellent Applied Mathematicians
Dr. Tomoki Uda, Assistant Professor at AIMR, received the 2018 MSJ Prize for Excellent Applied Mathematicians.
The Prize is awarded to young researchers who have obtained outstanding results in the field of Applied Mathematics. Dr. Uda was recognized for his work in “Discrete formulation of Reeb graphs and its application to topological flow data analysis.”
The award ceremony was held on March 17 at Tokyo Institute of Technology as part of the MSJ Spring Meeting 2019.
PR & Outreach Office, Advanced Institute for Materials Research (AIMR), Tohoku University


In this site you will find information about the contents and the instructors of the course, as well as useful materials and references.
BACHELOR DEGREES: Economics, Economics and Law, International Studies and Economics.
We will learn the basic tools of calculus of functions of several variables.
Student must be familiar with calculus of functions of one variable.
Larson, Hostetler & Edwards. Calculo Volumen II.
Sydsaeter & Hammond. Matemáticas para el análisis económico. Prentice-Hall.
The final grade is the weighted average of the final exam and the class grade. The final exam is the same for all the Mathematics for Economics II groups and consists of practical exercises and theoretical questions. The class grade is determined by each professor and is based on quizzes done in the classes.
The quizzes will be held at the end of the second half of lesson 2, at the end of lesson 3 and at the end of the course.
The quizzes mentioned before will be notified in advance with enough time.
Ordinary exam: The final grade is the weighted average of 60% the grade in the final exam and 40% the class grade.
Extraordinary exam: The final grade is the maximum of the following grades:
a) A weighted average consisting of 60% the grade in the final exam and 40% the class grade.
b) The grade in the final exam.
© 2018 uc3m - Departamento de Economía


Project: Analysis of marathon results¶
Project weight: 10 points
Download the following csv file which contains race results of about 26,000 marathon runners:
Analyze the marathon data. In particular:
Compute 1-dimensional kernel density estimate (KDE) of male and female runners using finish times, and use it together with the Bayes theorem to compute the probability that a runner with a given time was a female. Use this to make predictions if a runner was a male/female based on their finish times and check accuracy of these predictions.
Repeat part 1, but using 2-dimensional KDEs computed using finish times and ages of runners.
Compare accuracy of predictions obtained in parts 1 and 2 to the predictions made using k-NN with the same input data.
Use linear regression to predict finish times of runners based on their 5K times. Evaluate accuracy of these predictions. Then use other data beside the 5K time (the age of a runner, whether the runner was a male or a female) together with the 5K times to predict finish times using linear regression, and check if this meaningfully improves the predictions.
Add anything else that you find relevant and interesting.
Note: Tools for computing KDE are implemented by several Python libraries. You can use, for example,
scipy.stats.gaussian_kdewhich is a part of the scipy library. On the other hand, you must not use ready-made Bayes classification tools implemented in
sklearn and other machine learning packages. You can use
sklearn to compute k-NN classification. For linear regression you can use the
implementation provided by


| Animal traction |
|2. Draft animal selection|
To determine an animal's weight, first measure the length of the animal from point of shoulder to point of rump (A-B) and the circumference of its torso at point of heart (C) with a tape or rope. (See the drawing on page 20.) When taking the torso or girth measurement, observe these rules:
• Measure in the morning before the animal drinks. Don't give it hay the night before.
• Have the animal stand squarely with its head in a normal position.
• Pull the tape snugly around the torso, at the smallest circumference behind the shoulders.
Next, follow these formulas:
For bovine animals
Substitute measurements A-B (length) and C (circumference of torso at point of heart, or girth) into this formula:
(girth x girth x length)/300 = weight
For this formula, measurements must be taken in inches. If a metric tape or rope/rule is used to measure the animal, centimeters must be converted to inches before the formula can be used. One inch = 2.54 cm.
Girth of bull measures 152 cm, length measures 135 cm.
152/2.54 = 60 inches (girth)
135/2.54 = 53 inches (length)
(60 x 60 x 53)/300 = 636 lbs
Since one kg = 2.2 lbs, the weight of the animal in kg is obtained by dividing 2.2 into the answer above (636 lbs).
636/2.2 = 289 kg
The bull weighs 636 lbs or 289 kg.
An alternate method for estimating the weight of a steer (castrated bull):
Live weight • 1.04 [27.5758 x heart girth) -1.04967]
Substitute measurements A-B (length) and C (girth) into this formula:
(girth x girth x length)/300 + 50 lbs = weight
Measurements must be taken in inches, or converted into inches, before the formula is used.
Donkey's girth measures 37 inches, donkey's length measures 35 inches.
(37 x 37 x 35)/300 + 50 = weight of donkey
160 + 50 = 210 lbs
If the animal's weight is to be expressed in kg,
210/2.2 = 95 kg
The donkey weighs 210 lbs or 95 kg.