In their article “Modeling Time-dependent Randomness in Stochastic Dual Dynamic Programming“ , Nils Löhndorf and Alexander Shapiro, compare the effectiveness of two prominent approaches on how to represent inflow uncertainty in models of long-term hydropower planning. The planning problem is formulated as a multistage stochastic program and solved with QUASAR®’s dual dynamic programming solver.
Numerical results indicate that discretizing the stochastic inflow process to a scenario lattice yields lower system cost than sample average approximation when evaluating decisions out-of-sample. The article also demonstrates how dynamic risk measures can make the solution of a stochastic programming model robust against the model risk of using a mis-specified stochastic process.
Interested to see the model in action and learn more about its benefits?
Interested to learn more about how to model and solve a stochastic hydropower optimization problem with QUASAR®?
 Löhndorf N, Shapiro A. 2019. Modeling time-dependent randomness in stochastic dual dynamic programming. European Journal of Operational Research 273(2), 650-661.


Theory, Computation, and Numerical Simulation
Why this book?
This book offers an introductory course in theoretical and computational fluid dynamics, presented in a way that unifies theory and numerical computation. Computational algorithms are developed immediately after problem formulations are discussed, and numerical methods are introduced along the way. The approach is truly introductory in that a minimum of prerequisites are required. Intended audience includes undergraduate and entry-level graduate students, and a broad class of scientists, engineers, and other enthusiasts with a general interest in scientific computing.


Buy now on amazon.com New
This teacher-approved Step Ahead workbook from Golden Books is a great guide to math skills for 2nd-3rd graders--now in a deluxe edition with twice the pages and over 70 colorful stickers. Perfect for back to school--no matter what that looks like!
Carefully planned by teachers to complement the school curriculum, every Step Ahead workbook provides positive learning experiences through a variety of interactive, kid-friendly activities. In Math Skillbuilders (Grades 2-3), children will learn about:
- Greater than and less than
- Practicing adding and subtracting
-Money and fractions...


What are the vocabulary and the names of geometrical Shapes in Welsh?
In this blog about “Names of Geometrical Shapes in Welsh”, we are going to study in detail about the following topics with tons of example sentences in Welsh and English.
- What are the names of Geometrical Shapes in Welsh?
- What are the different two dimensional Geometrical shapes in Welsh?
- What are the different three dimensional Geometrical shapes in Welsh?
- What are the different types of Triangles in Welsh?
- Learn Geometry in Welsh.
Why should I learn the names of geometric shapes in Welsh?
In real life, learning the list of geometrical Shapes in Welsh is a very important activity. Why? Let’s start at the very beginning. Even for babies, we start off the process of learning by introducing the baby to different shapes such as circle, triangle, square and rectangle. Then we move next to teaching babies about 3D shapes (toys) such as cubes, cuboids, cylinders, spheres etc.
Whether you’re in school or in college, whether you’re working or retired, in a developed country or a third world country, you cannot live without about the different geometrical shapes (both 2D and 3D). You will need to mentally process images that you see and they are nothing but geometrical shapes. So it becomes very important that you learn the names of geometrical shapes in Welsh quite well.
- The ball is spherical
- The bottle is cylindrical shaped.
- The party hat is a cone.
- I need a square sized paper.
Here you need to know how to say the names of geometrical shapes in Welsh and also the statement in Welsh. This is what you will be learning in this blog called Shapes in Welsh.
What are the names of Geometrical shapes in Welsh?
The classic example of how important shapes can be in your lives is the game “Minecraft”… It basically shows that any structure in the world is nothing but a combination of basic shapes.
There are so many shapes and sizes which we would have studied as a child in our mathematics classes. We do come across these shapes on a daily basis for everything and sometimes we are asked to use them in our conversations.
In Mathematics, the shapes are categorized into 2 broad categories: 2D and 3D or two dimensional and three dimensional. Let us go through the different Geometrical shapes in Welsh.
Names of Two Dimensional (2D) Shapes in Welsh
Everything that have only an X Axis and a Y Axis and no Z Axis is 2 dimensional. If you draw something on a piece of paper, its 2 dimensional. Most movies that you see are labelled as 2D since the screen only has length and breadth and no depth (not talking about the new funky 3D movies though). It is thus very important that you learn some of the Three Dimensional (3D) Shapes in Welsh
What is a 2D shape called in Welsh? The translation for 2D or two dimensional shape in Welsh is “Siapiau dau ddimensiwn” or “Siapiau 2d”
|The triangle has three sides.
|Mae tair ochr i’r triongl.
|The rectangle is my favorite Shape.
|Y petryal yw fy hoff Siâp.
|She drew a trapezium.
|Tynnodd hi drapesiwm.
|A rhombus has four sides.
|Mae pedair ochr i rombws.
|The parallelogram is an interesting shape.
|Mae’r paralelogram yn siâp diddorol.
|A rectangle is a long square
|Mae petryal yn sgwâr hir
|She has square glasses.
|Mae ganddi sbectol sgwâr.
|A pentagon has five sides.
|Mae gan bentagon bum ochr.
|A hexagon does not have seven sides
|Nid oes gan hecsagon saith ochr
|The heptagon has 7 sides.
|Mae gan yr heptagon 7 ochr.
|The green octagon.
|Yr octagon gwyrdd.
|Can you draw an ellipse?
|Allwch chi dynnu llun elips?
|A circle is not a poygon.
|Nid poygon yw cylch.
|A triangle is a polygon.
|Polygon yw triongl.
|A semicircle is half a circle.
|Mae hanner cylch yn hanner cylch.
Names of Three Dimensional (3D) Shapes in Welsh
Everything that you see in the real world is a 3D shape. You might see a cylindrical drum, a conical bottle. The sun is spherical and the earth as well. The dice from Dungeons and Dragons is an 8 sided Octahedron or a 12 sided dodecahedron. It is thus very important that you learn some of the Three Dimensional (3D) Shapes in Welsh
So the question is (and one which many ask), will you encounter an octahedron in real life? Of course. Take a hexagon and extend it and there you go. An example… A screw is nothing but a cylinder mounted on an octahedron.
What is a 3D shape called in Welsh? The translation for 3D or three dimensional shapes in Welsh is “siapiau tri dimensiwn” or “Siapiau 3d”
|Tetrahedrons are beautiful.
|Mae tetrahedronau yn brydferth.
|Ciwb / giwb
|A cube has 6 sides.
|Mae gan giwb 6 ochr.
|A cube is a hexahedron.
|Mae ciwb yn hecsahedron.
|An octahedron has 8 sides.
|Mae gan octahedron 8 ochr.
|A dodecahedron has 12 sides.
|Mae gan dodecahedron 12 ochr.
|A icosahedron has 20 faces.
|Mae gan icosahedron 20 wyneb.
|The box is cylinder shaped.
|Mae’r blwch ar siâp silindr.
|The house is cone shaped.
|Mae’r tŷ ar siâp côn.
|I want to make a pyramid.
|Rwyf am wneud pyramid.
|The earth is a sphere.
|Sffêr yw’r ddaear.
|My school has a glass Prism.
|Mae gan fy ysgol Prism gwydr.
Types of Triangles in Welsh
What is an Equilateral Triangle in Welsh?
- An Equilateral Triangle is one wherein all the sides of the triangle are of the same length. In Welsh, an Equilateral Triangle is called as “triongl hafalochrog”
- This is an equilateral triangle
- Triongl hafalochrog yw hwn
What is an Isosceles triangle in Welsh?
- An Isosceles triangle is one wherein two sides of the triangle are equal in length. In Welsh, an Isosceles triangle is called as “triongl isosgeles”
- Mae hwn yn driongl isosgeles.
- This is an isosceles triangle.
#2D shapes in Welsh , #3D shapes in Welsh , #Equilateral Triangle in Welsh, #Isosceles triangle in Welsh , #List of all Shapes in Welsh , #Right Angled Triangle in Welsh , #Types of Triangles in Welsh , #Names of Geometrical Shapes in Welsh


An introduction to statistics and probability geared toward enabling attendees to understand the capabilities and limitations of statistics and probability and to help them implement calculations in their projects. Where possible/feasible, attendees will build their own tools to help them grasp the underlying concepts. In addition, attendees will be introduced to the pre-built tools in world-class Python and data science libraries to help them capitalize on the efficiencies and utility that those libraries offer.
Talk given by Chalmer Lowe at PyCon 2018.
Thanks to PyCon for giving us permission to post this talk. freeCodeCamp is not associated with this talk. We’re just excited to bring more exposure to to it!
Learn to code for free and get a developer job: https://www.freecodecamp.org
Read hundreds of articles on programming: https://medium.freecodecamp.org
And subscribe for new videos on technology every day: https://youtube.com/subscription_center?add_user=freecodecamp


Supercomputer Exceeds Previous Performance Numbers on Graph 500 Benchmark Test by 3.5 Times
MILPITAS, CA -- (Marketwired) -- SGI (NASDAQ: SGI), the trusted leader in high performance computing, announced today that the SGI® UV? 2000 became the first single node SMP to exceed 100 GTEPS, as verified by the Graph 500 benchmark test for measuring large data volume processing by supercomputers. In addition to this new performance world record, the Green Graph 500 test also revealed the SGI UV 2000 to be the commercial supercomputer with the lowest power-consumption figures.
The Kyushu University Institute of Mathematics for Industry (IMI), in conjunction with the Institute of Statistical Mathematics (ISM) and SGI Japan, Ltd., have conducted the Graph 500 (*1) benchmark test on the SGI UV 2000, which is officially known as the Data Assimilation Supercomputer System at ISM. It recorded a figure of 131.427 GTEPS, becoming the first single-node SMP system to exceed 100 GTEPS. The test measures the performance of supercomputers in processing large amounts of data. The Green Graph 500 (*2) benchmark test showed that it was also the commercial supercomputer with the lowest power consumption performance of 12.481 MTEPS/W.
A research team at the IMI Laboratory of Advanced Software in Mathematics was responsible for running the dual benchmark tests on one rack of SGI UV 2000, which had 640 cores per node.
The exceptional performance of the SGI UV 2000 was primarily due to its inherent capability of providing high-frequency memory access and wide memory spaces required by the Graph 500 benchmark.
"We are delighted to have one of our most innovative HPC solutions achieve these kinds of results on such a widely respected industry test," said Jorge Titinger, president and CEO of SGI. "And by doing so in such an energy-efficient manner, we have proven it is possible to accomplish high-performance computations reliably and stably at a lower power consumption. It truly is possible to have one single supercomputer provide high-density, industry-leading performance, and do so within a stringent power envelope."
"Attention is increasingly being turned to the use of new supercomputers in big data computing, such as processing massive amounts of graph data," said Katsuki Fujisawa, professor, Institute of Mathematics for Industry, Kyushu University. "This requires large-scale memory utilization and high-speed parallel processing, making supercomputers more important than the cloud for big data processing. The software developed at the Kyushu University Institute of Mathematics for Industry has shown even greater than expected processing performance and energy savings when processing massive graph data on the SGI UV 2000. Other major advantages of the SGI UV 2000 are the ability to migrate existing software to it, and the ability to apply past experience and expertise."
"The Institute of Statistical Mathematics is a leading inter-university research institute engaged in data centric science research in the big data age," said Yoshiyasu Tamura, vice director-general, The Institute of Statistical Mathematics. "We have chosen the SGI UV to be our 'extreme' supercomputer, which is providing the institute's researchers access to the world's largest coherent shared memory of 64 TB optimum performance in analyzing large amounts of data on graph theory and is essential to our research. This system is a critical factor in our university's output and is used in HPCI work and through the ISM Cooperative Research Program arranged by our institute."
SGI is a global leader in high performance solutions for compute, data analytics and data management that enable customers to accelerate time to discovery, innovation, and profitability. Visit sgi.com (sgi.com/) for more information.
© 2014 Silicon Graphics International Corp. All rights reserved. SGI, the SGI logo and SGI UV are trademarks or registered trademarks of Silicon Graphics International Corp. or its subsidiaries in the United States and/or other countries. All other product and service names mentioned are the trademarks of their respective companies.
(*1) The Graph 500 is a benchmark for testing graph search performance of supercomputers and other computers. The test uses the number of edges found in a 1-second breadth first search of a graph as an index. TEPS (Traversed Edges Per Second) is the unit used by this index. A high TEPS value indicates faster graph search capability. A GTEPS (Giga TEPS) value of 131.427 indicates capability to search approx. 131.4 billion edges in a graph per second. Visit the Graph 500 website at: http://www.graph500.org/
(*2) The Green Graph 500 is a benchmark for testing graph search performance similar to the Graph 500 that uses TEPS/W (Traversed Edges Per Second/W) as an index unit. A high TEPS/W value indicates a high graph search capability per unit of power consumption, or in other words low power consumption. A 12.418 MTEPS/W (Mega TEPS/Watt) value indicates that the computer can search 12.41 million edges in a graph using just one watt of power. Learn more at the Green Graph 500 website: http://green.graph500.org/
Contact Information: Grayling Public Relations Jessie Adams-Shore (415) 593-1400 [email protected]


"Last night I dreamed so many circles in front of me. What does this dream mean? Why do I sometimes see in a dream geometric shapes such as circles, rectangles, diamonds, squares, triangles, trapezoids, cubes, spheres, straight lines, etc...? Last night I dreamed to draw a geometric figure with something written inside. What does it mean to draw geometric elements? Last night I dreamed of a circle, a triangle, a square, a cube, a sphere with numbers inside. Why dream these geometric shapes?" What is the meaning and interpretation given to triangles, to squares, circles and straight lines or curves in dreams? The geometric figures in a dream, have a precise symbolic value and are not absolutely meaningless. Let's figure.
If you dream of a square or a rectangle: this figure when it appears in a dream is a sign of pragmatism, stability, unity and balance. When you say "be between four walls", means just to be safe. And the shape of a house, a city, a room, it is usually a square shape. When you dream then a square or rectangle you are in a phase of life very balanced, in which you are confident about yourself, what you are doing. This figure also represents the precision and constancy in work. So it is a dream especially favorable to pursue ideas and work projects.
If you dream of an equilateral, isosceles, scalene triangle: the figure with three sides instead refers to our idealism, our practical spirit that can find an outlet in our action, in busy. Dreaming then a triangle means that we are idealistic people but at the same time practical, so we go from idea to action thanks to a spirit, a way of thinking very smart.
If you dream of a circle, an ellipse, a circle, a sphere: the circle is considered a perfect figure because every point on its circumference is equidistant from a central point and this distance we know to be the radius of the circle. So dream a figure like that is to be balanced people, perfect, self-confident and in some cases indicates selfless people. Generally, it is always a positive symbol, favorable to the dreamer who can then experience a period of great personal achievement.
If you dream of a straight or curved line, a figure without a side: straight lines or curves in a dream usually indicates a great imagination, a very lively mind, and an independent spirit who wants to learn, to discover new things and not be subject to the orders of others and the obligations of life. Those who dream straight lines, curves, geometric figures without one side is usually a very imaginative or otherwise is in a phase of life where it is.
Have you had another dream? Do you want to read an interpretation of it? Look in the dictionary of dreams this site the item that you have dreamed and read the interpretation. If you do not find anything you perform a search on one of best dedicated website to the world of dreams and not only, ilmigliorweb.blogspot.com. If you want more clarification on a dream or nightmare that you can write using the contact form and we'll try to answer you as soon as possible.
DREAMS MOST POPULAR AMONG THE PEOPLE:
You may also be interested in these items:


The Geometer's Sketchpad is developed by KCP Technologies, Inc. and is published in the United States by Key Curriculum Press.
- Key Curriculum Press
Publishes middle school and high school mathematics textbooks, high school science textbooks, mathematics software, supplemental workbooks and materials, and manipulatives. Also maintains the list of Sketchpad's International Publishing Partners.
Mathematics resource site for students, parents, and mentors sponsored by Key Curriculum Press.
- KCP Technologies
Develops mathematics education software including The Geometer's Sketchpad and Fathom Dynamic Data.


1. Сортируем инструкции по возрастанию степени свободы инструкции (степень свободы – количество функциональных блоков, на которых инструкция может выполняться).
2. Берем следующую инструкцию a из списка. Для каждого ресурса r: прибавляем сколько раз a использует r к UsageCount(r). Выбираем альтернативный блок с минимальным UsageCount.
The resource-constrained lower bound on the II, ResMII, is calculated by totaling, for each resource, the usage requirements imposed by one iteration of the loop. The exact ResMII can be computed by performing an optimal bin-packing of the reservation tables for all the operations, a computation that is of exponential complexity. Complex reservation tables and multiple alternatives make it worse yet and it is impractical, in general, to compute the ResMII exactly. Instead, an approximation to this exact lower bound is computed.
The ResMII is computed by first sorting the operations in the loop body in increasing order of the number of alternatives, i.e., degrees of freedom, and initializing the usage count of each resource to zero. At each step in the algorithm, the partial ResMII is defined to be the usage count of the most heavily used resource at that point. The operations are processed in sort order. For an operation with multiple alternatives, each alternative is selected in turn. The number of times it uses each resource is added to the current usage count for that resource in order to determine the partial ResMII that would result if this alternative were actually used. For each operation, that alternative is selected which yields the lowest partial ResMII. When all operations have been considered, the usage count for the most heavily used resource constitutes the ResMII. It is important to note that this selection between the alternatives is only for the purpose of computing the ResMII. During scheduling, the scheduler has complete freedom to select the alternative that will actually be used.
The method above yields an integer-valued ResMII. In general, the ResMII is a real-valued number and ought to be computed as such. For instance, if the floating-point adders are the most heavily used functional units, there are three of them and there are 8 add operations, the ResMII is 8/3. More generally, if the functional units can be partitioned into equivalence classes, such that all of
the functional units in a given equivalence class can perform exactly the same set of operations, and if the operations are such that each one can be performed by precisely one equivalence class, then the ResMII can be computed by taking ratio of the number of operations to be executed on a given equivalence class and dividing that number by the number of functional units in that equivalence class. The largest such ratio, across all of the equivalence classes, is the ResMII.
Unfortunately, many real machines do not possess any such structure, and there exists no good technique for computing the real-valued ResMII. One approximate way to do so is to conceptually unroll the loop U times, calculate the integer-valued ResMII for this unrolled loop, and then divide that by U.


Must register card to collect points.
Up to 5 cent off per gallon next fill, if registration complete.
When entering your Card Number, please enter all 13 digits.
**** Points System****
Every dollar you spend in the store is worth 1 points. Every gallon you fill up with is worth 1 points.
60 PTS = 1c/gallon
120 PTS = 2c/gallon
180 PTS = 3c/gallon
240 PTS = 4c/gallon
300 PTS = 5c/gallon
360 PTS = 6c/gallon
Sign up to start earning points, and we will give you 5c/gallon off.
Points expire in 90 days


My daughter is now in kindergarten and is very interested in trying out a lot of things. She is still learning to read but she absolutely likes counting to 100. Her interest in Math is something I want to encourage so I tried one time to teach her addition.
I have had this workbook – Kindergarten 2 Mathematics Worksheets Revised Edition by Kimberly Teh and I skipped teaching her the addition and we covered only the counting part at first. I know kids learn faster while they’re younger so thought I would take advantage of that and tried to teach her addition of numbers from 1-5 through finger counting.
Then I found out she already did those skipped pages with her Lolo (Grandpa).
Constant reinforcement is needed when teaching these little ones so I give her “games” on sheets of paper. Yes, I call them games and she thinks they ARE games.
Just today Iet her try addition games online on mathplayground.com
This one is a little harder because it includes numbers up to 20 but still quite enjoyable.
I am hoping she won’t forget these and that we would be able to practice it on paper at least twice a week. I’m not sure if it would interfere with her learning to read because the last time we tried out Kumon, they told us they recommended to complete the learning to read part first before enrolling in the math program. Eventually we took her out of the Kumon reading program and hired a private tutor that she was already comfortable with instead – her nursery teacher.
There are a lot more resources online like this one that I would like to try out soon =D
If you have tips for me on how to go about this and if you want to share how you introduced math to your daughter, feel free to comment!


Many employers with Defined Benefit Plans provide an option for a retiree to take a lump sum instead of a monthly pension. With interest rates rising quickly, the calculations used to value a lump sum will likely change dramatically and may offer a significant timing opportunity.
Lump Sum Math: Lump sums are computed with a mathematical calculation very similar to the math used in mortgage loans. The Lump Sum is the present value of the monthly pensions. It’s based on three ingredients:
· The monthly pension
· The rate of interest used to compute the lump sum, and
· The life expectancy of the individual
The Benefit. The monthly pension is simple: the bigger the monthly pension, the bigger the lump sum, all things being equal.
Life Expectancy. The life expectancy, or mortality, of the individual, also has an effect. Two employees with identical monthly benefits will have different lump sums based on their age. For example, suppose Tom and Susan both work at a company for 30 years and have monthly pensions of $3,200. Tom is 62, Susan is 66. According to IRS Mortality Table for 2022, Tom will live about 23.08 years and Susan about 19.68 years. Note the IRS mortality table is a little bit of a math lift; you have to actually build a life expectancy table. Drop me an e-mail if you’d like an explanation of how to do it.
Interest Rate: Threat and Opportunity. Because of the mathematics, interest rates have a major effect on a lump sum calculation, particularly considering the rising rate environment. The mathematics of lump sums are a present value calculation, meaning the lump sum is the present value of a stream of payments at an interest rate for a period of time. Think of a mortgage – a mortgage loan is the present value of the payments. A $3,000 monthly mortgage payment on a 3%, 30-year mortgage would sustain a mortgage loan of $711,518. If the rate was 5%, the amount of a mortgage loan would be $558,845. If these were pension lump sums, the higher interest rate causes the lump sum to decrease substantially (by over 21%).
The method the IRS uses to compute interest on lump sums affects the outcome as well – there is a blended rate for the first five years of payments, years 6-20, and payments 20 years or later. Using the IRS Minimum Present Value Segment Rates for May 2022, the first segment is 3.23%, the second segment is 4.59% and the third segment is 4.69%. With those rates, Tom would have a blended rate of about 4.502%, and Susan a rate of 4.69%, however, it’s the interest rate calculation that has the biggest impact.
The rates used by the IRS in the Minimum Present Value Segment are divided in three segments: the first segment is for the first five years (of the participant’s life expectancy) of the calculation, the second segment is for years six through twenty, and the third segment for years after twenty. Using the IRS computed mortality for a 66-year-old, the life expectancy is 19.68 years, which would utilize only the first and second segments. The life expectancy of a 62-year-old is 23.08 years, which would use all the segments. A blended rate can be used to approximate the valuation of a lump sum.
These are the IRS Present Value Rates for the last 12 months:
The rates have substantially increased in the last 12 months. The consequences on a lump sum calculation are significant. Here are calculations based on the IRS life expectancy and the blended rate. Note that we did not take in to account the mortality change (the individual got older), nor did we switch mortality, but instead chose to illustrate the change from the rising rates.
The Threat. In 2022, we are experiencing a rising interest rate environment, with more prospective interest rate increases on the horizon. As the above chart illustrates, the present value of a lump sum for a 62-year-old computed in June of 2021 was over 19% greater than the same present value in May of 2022. A further 1% increase in rates for the above illustration would reduce the present value of the lump sum by another 8-9%. By way of illustration, in December of 2021, the Moody’s seasoned Aaa bond yield was 2.65%. In May 2022, it was 4.12%. Rising rates decrease the lump sum.
The Opportunity. The opportunity lies in the fact that pension plans typically change their lump sum calculations once a year. Many large plans use an October or November rate to make computations for an entire year. This means that many eligible retirees can get their lump sum based on the older lower rates. Using the calculations above, there is a significant difference between the October 2021 calculation versus the May 2022 calculation. Here’s the opportunity: You may be able to get a large lump sum going into a down market. For example, the 62-year-old in the above example may be able to take a $617,452 lump sum, when the market itself, both stocks and bonds, are down. Check with your company to see when they compute the lump sum.
Bottom Line: Rising rates reduce lump sums. Pension Plans offer lump sums periodically, but typically change once a year. If you are eligible for a lump sum, you may be able to get a significantly larger lump sum by timing the payment before the re-set. You might also get an opportunity to buy into a down market. As always, I’ll do my best to answer questions at firstname.lastname@example.org. I also have a White Paper on the topic with more detail, you can download it HERE.


Sacred Geometry - Ascribes symbolic and sacred meanings to certain geometric shapes and certain geometric proportions. It involves patterns used in the design of everything in our reality most often seen in sacred architecture and sacred art. The basic belief is that geometry and mathematical ratios, harmonics and proportion are also found in music, light, cosmology. The study of sacred geometry has its roots in the study of nature.
Platonic Solids - Platonic Solids are regular polyhedra. “Polyhedra” is a Greek word meaning “many faces.” There are five platonic solids, and they are characterized by the fact that each face is a regular polygon, that is, a straight-sided figure with equal sides and equal angles: Tetrahedron, Cube, Octahedron Dodecahedron, Icosahedron


WW.Math 4.0 Features
WW.Math is a math component targeted at computational geometry.
- 2D and 3D points and vectors (plus 4D vectors).
- 2D, 3D and 4D matrices (addition, subtraction, multiplication, adjoint, inverse).
- 2D, 3D lines, rays, segments, polylines, polygons.
- 2D segment-segment, segment-line, line-line, ray-segment, ray-ray intersection.
- 3D planes (including 3D line, ray, segment intersection).
- Vector and matrix multiplication, matrix inversion etc.
- Constrained Delaunay Triangulation (2D, holes allowed).
- 2D polygon boolean operations (intersection, subtraction, union).
- 2D convex hull calculation of polygons or ordered or unordered point sets.
- 2D polygon area, centroid calculation.
- Uses structs for optimal speed.


Given a list of places you want to go, what is the shortest possible route that visits each place and returns to the place where you first started? This is the basic idea behind the Travelling Salesman Problem (TSP).
Most of us have faced this problem before, either when planning a trip with many cities/tourist attractions, or maybe when dealing with more complex stuff like optimizing public transport systems, air line operations, shipping routes etc. Computationally speaking, this used to be a difficult problem, but things are changing and the number of programs to solve the TSP is increasing.
Todd W. Schneider has created a brilliant code to build interactive solutions to the Traveling Salesman Problem using R and Shiny . In this post here, you may read in detail how the simulation process works and you may also play trying to find the shortest route through some world cities or through all of the US State capitals. (ht Tariq Khokhar).
[image credit: Todd W. Schneider]


|FINDING THE ANSWERS|
|Up to now you've just been getting used to the feel of the computer. Now we'll actually use the computer to do a few sums.
THE LET STATEMENT
Nearly all arithmetic operations are done by using the LET statement. It is of the form
LET variable = expression.
In this case the variable (which can have any name you assign to it) is what you want to find out. The expression describes how you want to define the variable.
LET A = 2+4
means "add 2 to 4 and set A equal to the result (6)". You can use other variables:
LET A = 2 + B
LET A = B + C
One condition: the computer must already know what the values of B and C are before it comes to the LET statement.
The equal sign (=) isn't used in quite the same way it is in ordinary arithmetic or algebra. For instance:
LET J = J +1
Obviously J isn't equal to J + 1. What the LET statement means is: "Take the existing value of J, add one to it and then set J to this value."
The + sign is called an operator and defines the operation you wish to be performed. The other arithmetic operators are:
* (multiply - there is no x sign to avoid confusion with letter x)
** (raise to the power)
For the moment we'll leave / and ** out of it.
Here is a program for multiplying two numbers together
10 PRINT "MULTIPLICATION"
20 PRINT "ENTER FIRST NUMBER"
30 INPUT A
40 PRINT "ENTER SECOND NUMBER"
50 INPUT B
60 LET C==A * B
70 PRINT "THE ANSWER IS", C
Notice line 70. It's a PRINT statement with a string between inverted commas, but it's got a C added to it. This form allows you to economize on PRINT statements.
Enter the program and try running it, using two quite small numbers — such as 17 and 25.
The computer will come up with the answer:
THE ANSWER IS 425
Run the program a few more times, increasing the size of the input variables. At about 255 * 129 or just a bit larger you will get another error message — 6/60. The 6 is the code for arithmetic overflow because the answer is larger than 32767, which is the largest number the computer can hold as an integer variable.
Now try editing the program so that it does addition instead - just change the * to a + in line 60. You can also try subtraction and check that you get negative numbers when A is less than B.
All fairly straightforward so far.
Now let's try division. Alter line 60 to
60 LET C = A/B
Run the program for A (first number) = 24
B (second number) = 12
The computer will come up with: THE ANSWER IS 2
Run the program again, this time for A=18 and B=12
THE ANSWER IS 1 ??!!
Shouldn't that be 1.5? Well, yes, but the ZX-80 uses integer arithmetic — only whole numbers can be expressed. What the computer does is to do a division normally and the truncate the result towards ZERO. As examples:
-2.58 would become-2
-0.01 would become 0
-212.1 would become -212
-5941.98 would become -5941
This means that you may have to be careful when you use division — it's always fairly accurate when you're dividing a large number by a small number, but may be less accurate when the two numbers are closer together in size.
Luckily there are ways of getting round this problem. For instance, here is a program which will give quotients to 3 decimal places using integer arithmetic only.
10 PRINT “DIVISION PROGRAM”
20 PRINT “DIVIDEND = ?”
30 INPUT X
40 PRINT “DIVISOR = ?”
50 INPUT Y
60 LET Z = X/Y Divides X by Y
70 LET R1 = X-Z*Y Calculates Remainder
80 LET D1 = 10*R1/Y Divides 10*remainder by Y to give first decimal
90 LET R2 = 10*R1-D1*Y Calculates 2nd remainder
100 LET D2 = 10*R2-D2*Y Divides to give 2nd decimal place 110 LET R3 = 10*R2-D2*Y Calculates 3rd remainder
120 LET D3 = 10*R3/Y Last decimal place
130 PRINT “THE ANSWER IS “;Z;”.”;D1;D2;D3
This program does a long division in exactly the same way as we would do it on paper.
Try running it!
Notice the PRINT list in line 130 — it contains several literal strings and variables separated by semicolons. The semicolons tell the ZX-80 that each thing to be printed must be printed immediately after the preceding item, without spaces between them.
Also notice the LET statements from line 70 on. There's no fiddle — you can use more than one operator per statement. There is a snag, though.
Operations are not necessarily carried out in order from left-to-right.
The order in which they are carried out depends on what sort of operations are present in the statement.
Here is a list of priorities for arithmetic operations:
First A**B (A to the power B)
Second —A (Negation, or multiplication by-1)
Fifth A+B or A-B
Now for some experiments
10 REM TEST PROGRAM (REM is a keyword — key Y)
20 PRINT "ENTER A"
30 INPUT A
40 PRINT "ENTER B"
50 INPUT B
60 PRINT "ENTER C"
70 INPUT C
80 LET Z = A + B * C
90 PRINT Z
Try running this with A=1, B=2, C=3 but before you start, use the priority rules to predict what answer the ZX-80 will give: 7 or 9?
O.K. — run it now.
The answer was 7. First the computer multiplied 2 by 3 to get 6, then it added 1 to get the final answer.
Try a few other combinations by editing statement 80 - like
A/B*C (watch out for truncation!)
A**B (A to the power B — try using small numbers with C = 0)
Here's a golden rule: when in doubt either use more than one LET statement and build up that way, or use brackets.
Brackets make life much easier when it comes to complex arithmetic operations. Take example Z = A/B*C
The normal sequence would be for the computer to evaluate B times C and then divide A by the result.
If we put brackets round A/B thus:
80 LET Z = (A/B)*C
then the computer will carry out the operation within the brackets first, even though it has a lower priority.
A more subtle example is:
Z = A*B/C
At first sight you would think that these would give the same answer. Well, they do — sometimes!
Try them both using A == 100, B = 25, C = 5 (the answer is 500).
Now try it both ways using A = 100, B = 3, C = 5 (the answer should be 60).
What happened when you used the brackets? Think about it.
The phantom truncator has struck again!
The computer evaluated 3/5 first and truncated it to ZERO - then it multiplied 100 by ZERO and naturally got ZERO as a result.
All this emphasizes that you have to be very much on the alert when you use integer arithmetic for multiplication and division. Multiplications can cause arithmetic overflow problems (which will cause the program to stop), whilst small numbers used in division may give rise to funny answers which don't give error codes.
If you think that you're going to run into truncation then do multiplications first — on the other hand it may be better to do divisions first to avoid overflow.
That's probably enough arithmetic for now. Let's move on to more interesting things.


Many students live in fear of math.
Some students say that their biggest pain of theirr school life is “Math.”
The National Center for Education Statistics repots, for the year 2003, that 79% of 4th grade students were not proficient in math. The number for 8th graders was 72%.
Math skills are critical today with the technological advancement in our society. Students with math problems frequently have the following problems:
Slow processing skills
Poor auditory analysis skills
Weak logic & reasoning skills
Inadequate math facts
Poor understanding of math processes
A fear of math.
Our system will build your child’s confidence and math skills rapidly
All people who say they can’t do math are really saying is that they can’t count. They don’t realize how easy math is because that is all it is, counting..They often do a very good job of fooling themselves into thinking it’s hard. They may even think they have bad “math genes…” Well, here at our center we are going to explode those myths, answer a lot of questions and make math so easy it’s child’s play.
It is paradoxical that many educators and parents still differentiate between a time for learning and a time for play without seeing the vital connection between them. -Leo Buscaglia, author (1924-1998)
Here at our center we are using algebra to teach 5 year olds how to count…they factor trinomials as an added bonus. They have a blast learning algebra.
Our Math Program is for Math Students all the way up to High School and College.
We start with


How to use addition(+) plus operation in php program to get sum total of two or more numbers.
Addition also known as plus( + ) operator is used to get total numbers of two or multiple numbers inside every programming language so inside php program web developer can easily get sum of multiple numbers using addition operator. So here is the complete step by step tutorial for Php Addition Arithmetic Operator Example Tutorial.
Php Addition Arithmetic Operator Example Tutorial.
Code for Addition-Program file.
<!doctype html> <html> <head> <meta charset="utf-8"> <title>Php Addition Arithmetic Operator Example Tutorial</title> </head> <body> <?php //Declaring three variables with values. $one = 1 ; $two = 2 ; $three = 3; // Storing all variables values to $sum variable using addition + operator. $sum1 = $one + $two + $three; // Printing sum on screen using echo function. echo "Total = ".$sum1; ?> </body> </html>


Introduces the methods of statistics including sampling from normally distributed populations, estimation, regression, testing of hypotheses, point and interval estimation methods. Prerequisites: a placement recommendation for MTH 146 and Algebra I or equivalent. 3 credits
**Prerequisite Introduction to Elementary Statistics: A prerequisite means students are not allowed to take this course unless they have a placement recommendation. This is determined by a test given by the community college to make sure students have enough mathematical knowledge to take this course. Successful completion of Algebra I or equivalent with also meet the prerequisite for this course. Parents and/or students should speak to their school’s guidance counselor make sure qualifications have been met.
No textbook required
Ordering Info: http://cnx.org/contents/MBiUQmmY@18.11:2T34_25K@11/Introduction
Sherri Gardner is a mathematics instructor at Gate City High School, Virginia Highlands Community College and Northeast State Community College. She has a B.A. degree in mathematics from the University of Virginia at Wise and a M.S. degree in mathematics from East Tennessee State University. In...


Maths problems can be related to neuro-motor immaturity in the following ways:
- Difficulties with visual tracking (horizontal) necessary for reading instructions or (vertical) for aligning columns correctly
- Vestibular problems which can influence spatial skills necessary to understand spatial relationships, geometric forms, patterns etc.
- Visual-motor integration difficulties
- Visual perceptual problems
- Sequencing necessary for remembering sequences of information (eg multiplication tables), and following instructions and carrying out procedures
- Inter-hemispheric communication necessary to solve problems
Our Dyscalculia page has more information on maths problems and dyscalculia which you may find interesting.


main sage calculus page
We can try to guess a limit by trying numbers close to our target point.
You can take limits. Try sin(1/x) at a=0 to see what happens.
You can (graphically) test against the definition of a limit. The default delta is too large, so the function goes outside the interval [L-epsilon,L+epsilon]; make delta smaller until it makes the function stay in the interval. Then make epsilon smaller and then find a sufficiently small delta for that epsilon. Repeat. What would happen if we had the wrong L?
You can take limits from the left or right.
You can define a function and take limits involving it. We had to declare that h was a variable, otherwise it would be undefined and give an error; only x is assumed to be a variable.
You can illustrate the Squeeze Theorem.
You can take limits at infinity. Try it for sin(x).
You can evaluate limits that are infinite.
Last modified: Thu Aug 3 19:20:10 UTC 2017


Saxon Math 1- $20
QR Code Link to This Post
Saxon Math 2, homeschool meeting book, student workbook(pt 2)- $40
Saxon Math 3, student workbook (part 1&2) -$40
Saxon Algebra 1, 3rd edition, Test forms, home study packet- $20
Saxon Algebra 2 2nd edition, Test forms, home study packet- $20
Saxon Advanced Mathematics 2nd edition x2, Test forms, home study packet-$40
Saxon Phonics 1, rule book, student workbook (part 2),box of teaching tools- $30
Saxon Phonics 2, student workbook (part 1&2), rule book, box of teaching tools- $30
LifePac Science 5th & 8th grade- $40
Various Pathway readers- $5
Christ centered math workbooks level A&B- $5
K-1 Math Manipulatives- $5
7 books in the Dover children's thrift classics series- $5
Reading made easy book- Free
Christian Liberty press: History for pilgrims- $5
Early American History- $5
The Prairie Primer, The little house cookbook- $10
The writing road to reading book- $5
Who is God? biblical worldview of God and truth+notebooking journal $20
Some of the Math student worksheets have been used.
The beginning 8th grade unit 1 LifePac is written in.(with pencil)
Pathway readers are well used.
Everything else is in good condition.
Call or text for more info.


By Olver P.J.
Read Online or Download AIMS lecture notes on numerical analysis PDF
Best Computational Mathematicsematics books
This e-book offers a primary advent to numerical research. This e-book covers various themes together with Interpolation and Polynomial Approximation, Curve becoming, Numerical Differentiation, Numerical Integration, and Numerical Optimization. For engineering and machine technology fields.
This can be the 1st e-book on confident tools for, and functions of orthogonal polynomials, and the 1st to be had number of appropriate Matlab codes. The booklet starts with a concise advent to the speculation of polynomials orthogonal at the genuine line (or a element thereof), relative to a good degree of integration.
The sphere of molecular evolution has skilled explosive progress lately end result of the swift accumulation of genetic series information, non-stop advancements to computing device and software program, and the advance of refined analytical equipment. The expanding availability of huge genomic info units calls for robust statistical the way to study and interpret them, producing either computational and conceptual demanding situations for the sector.
Additional info for AIMS lecture notes on numerical analysis


3 edition of An effective multigrid method for high-speed flows found in the catalog.
An effective multigrid method for high-speed flows
by National Aeronautics and Space Administration, Langley Research Center, National Technical Information Service, distributor in Hampton, Va, [Springfield, Va
Written in English
|Statement||R.C. Swanson. E. Turkel, J.A. White.|
|Series||ICASE report -- no. 91-56., NASA contractor report -- 187602., NASA contractor report -- NASA CR-187602.|
|Contributions||Turkel, E., White, John A., 1939-, Langley Research Center.|
|The Physical Object|
A recent development in application of multigrid and multilevel adaptive methods for fluid flow by the numerical simulation group at Louisiana Tech University is reviewed. The multigrid method has been successfully applied for a number of flow cases including both steady and time-dependent flows. () A Cost-Effective Smoothed Multigrid with Modified Neighborhood-Based Aggregation for Markov Chains. Mathematical Problems in Engineering , () Theoretical bounds for algebraic multigrid performance: review and analysis.
Multigrid cycle We describe a geometric multigrid method for the Poisson problem deﬁned in (2). Our approach uses a V-Cycle of the Multigrid Correction Scheme [TOS01] and the pseu-docode for each V-Cycle iteration is given in Algorithm 1. The V-Cycle procedure requires a discretization of the Poisson problem at L+1 levels of resolution. A nonlinear primal dual method for Total Variation based image restoration, in ICAOS'96, 12th Int'l Conf. on Analysis and Optimization of systems: Images, wavelets and PDE's, Paris.
Robust Multigrid Methods by Wolfgang Hackbusch, , available at Book Depository with free delivery worldwide. multigrid algorithms are applied to the two-dimensional advec_ion equation, and Fourier analysis is used to determine their damping properties. The capabilities of the multigrid methods are assessed by solving three different hypersonic flow problems. Some new multigrid schemes based on semicoarsening strategies are shown to be quite effective.
TOO MANY TRAITORS (HB #14) (Hardy Boys Casefiles
Systems and procedures for business data processing
Masterpieces of Japanese poetry
truth will out
Taken care of. --
comparison of the V/STOL handling qualities of the VAK-191B with requirements of AGARD report 577 and MIL-F-83300
International Wheat Conference, 1967.
Rural Local Broadcast Signal Act
Casting Kaiser aluminum
J. S. Bach
St. Lawrence project
The use is considered of a multigrid method with central differencing to solve the Navier-Stokes equations for high speed flows. The time dependent form of the. An effective multigrid method for high-speed flows. A Multigrid Method for High Speed Reactive Flows Scott G. Sheffer*, Antony Jameson*, and Luigi Martinellr CFD Laboratory for Engineering Analysis and Design Department of Mechanical and Aerospace Engineering Princeton University Princeton, New Jersey U.S.A.
Abstract This paper presents a multigrid method for com-Cited by: 6. An Effective Multigrid Method for High-Speed Flows R. Swanson NASA Langley Research Center Hampton, VA E. Turkel * Tel-Aviv University Tel-AvivIsrael and Institute for Computer Applications in Science and Engineering Hampton, VA J.
White Analytical Services and Materials. Inc. Hampton, VA Abstract. Multigrid methods belong to the most promising methods for convergence acceleration and are widely used for non-reactive subsonic and transonic flows.
This paper presents the application of an implicit multigrid algorithm to non-reactive and reactive turbulent high speed : Peter Gerlinger, Dieter Brüggemann. Among the topics discussed are a novel three-dimensional vortex method, unsteady viscous flow around circular cylinders An effective multigrid method for high-speed flows book airfoils, a time-accurate multiple grid algorithm, the numerical solution of incompressible flows by a marching multigrid nonlinear method, the Navier-Stokes solution for hypersonic flow over an indented nosetip, graphics and flow visualization in computational fluid.
Sheffer, A. Jameson, L. Martinelli, A Multigrid Method for High Speed Reactive Flows Google Scholar CPRF J.R. Edwards, An implicit multigrid algorithm for computing hypersonic, chemically reacting viscous flows, J.
Comput. The application of multigrid methods is complicated if the set of governing equations contains strongly nonlinear source terms.
This is the case for finite-rate chemistry as well as for turbulence conservation equations. In most cases strong nonlinearities within the chemical production rates prevent convergence of standard multigrid methods.
Overlapping grids and multigrid methods for three-dimensional unsteady flow calculations in IC engines International Journal for Numerical Methods in Fluids, Vol. 15, No. 6 An effective multigrid method for high-speed flows. this method to three-dimensional flows.
This is unique in that existing methods (see Refs. ) using multigrid methods are attuned to computing thrpp-dimmsional subsonic/transonic flows bv ~.~.~.~ applying multigrid in three dimensions. For the case of very high speed flows, the effectiveness of applyiig a multigrid algorithm to all three.
A simple and effective method is presented that enables the multigrid scheme to converge. A strong reduction in the required number of multigrid cycles and work units is achieved for different test cases, including a Mack 2 flow over a backward facing step.
In numerical analysis, a multigrid method (MG method) is an algorithm for solving differential equations using a hierarchy of are an example of a class of techniques called multiresolution methods, very useful in problems exhibiting multiple scales of behavior. For example, many basic relaxation methods exhibit different rates of convergence for short- and long-wavelength.
In the present work, a 3-level V-cycle multigrid method is implemented as a simple but extremely effective method for accelerating the convergence of the Runge-Kutta time stepping.
At each multigrid cycle, the numbers of iteration for each level are 5, 10 respectively. Get this from a library. An effective multigrid method for high-speed flows. [R Charles Swanson; E Turkel; John A White; Langley Research Center.].
An Effective Multigrid Method for High-Speed Flows R. Swanson NASA Langley Research Center Hampton, VA E. Turkel * Tel-Aviv University Tel-AvivIsrael and Institute for Computer Applications in Science and Engineering Hampton, VA J.
White Analytical Services and Materials, Inc. Hampton, VA Abstract. 4 MULTIGRID METHODS c Gilbert Strang u2 = v1 2+ = 2 u1 0 1 j=1 m=1 m=3 j=7 uj 2 8 vm 4 sin 2m = sin j (a) Linear interpolation by u= I1 2 h hv (b) Restriction R2h 2 (2h h) T h Figure Interpolation to the h grid (7 u’s).
International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 11, No. 4 Geometric multigrid with applications to computational fluid dynamics Journal of. Part of the Lecture Notes in Mechanical Engineering book series (LNME) Abstract. Matrix dissipation scheme is known to give more accurate solutions than scalar dissipation scheme.
An effective multigrid method for high-speed flows. Commun. Appl. Numer. Methods () Google Scholar. Thibert, J.J., Grandjacques, M., Ohman, L.H.: NACA.
The application of the multigrid method to accelerate the conventional Navier-Stokes calculations for two-dimensional incompressible steady state turbulence flows is presented.
The calculation solves time averaged Navier-Stokes equations in primitive variables using a decoupled manner. Two equations model of turbulence (k-epsilon model) is employed to predict turbulent flow problem, and the. The main difficulty of developing robust and effective multigrid methods for the saddle point system is to design an effective smoother with the consideration of the constraint div u = g.
We shall use the Peaceman-Rachford iteration developed in [ 15 ] as a smoother since the nonlinearity can be handled efficiently and the constraint is always.
An effective multigrid method for high-speed flows. By J. A. White, R. C. Swanson and E. Turkel. Abstract. The use is considered of a multigrid method with central differencing to solve the Navier-Stokes equations for high speed flows. The time dependent form of the equations is integrated with a Runge-Kutta scheme accelerated by local time.() Parallel multigrid method for finite element simulations of complex flow problems on locally refined meshes.
Numerical Linear Algebra with Applications() Parallel characteristic finite element method for time-dependent convection-diffusion problem.An effective multigrid method for high-speed flows.
By J. A. White, E. Turkel and R. C. Swanson. Abstract. The use is considered of a multigrid method with central differencing to solve the Navier-Stokes equations for high speed flows. The time dependent form of the equations is integrated with a Runge-Kutta scheme accelerated by local time.


Given any function in the slope-intercept form, whether linear or non-linear, the area between the curve and the x-axis between two points can be easily approximated with the Riemann Sum using a
This is a simple pseudo-code example, where
Y1 is the function and
Y1(I) is the value of
X = I:
N = 0 For (I, Left Limit, Right Limit, Step Interval) N = Y1(I) + N End Display N
To determine the step interval, use this:
Step Interval = (Right Limit - Left Limit) / Number of Steps
To improve accuracy, there are multiple ways of using this approximation, which distinguish between which end of each step to use. To adjust the limits and intervals for the desired method, use this code:
If LRAM (using left end) Right Limit = Right Limit - Step Interval End If If MRAM (using middle of step, often most accurate) Left Limit = Left Limit + (Step Intverval / 2) Right Limit = Right Limit - (Step Intverval / 2) End If If RRAM (using right end) Left Limit = Left Limit + Step Interval End If
For anyone wishing to have a complete program for a TI-83 or TI-84 calculator, use my Riemann Sum Program (dead link).
Please note that this is an approximation. You can find exact answers using integrals.


The Division Algorithm: If a and m are any integers with m not zero, then there are unique integers q and r such that a = qm+r with 0 < r < |m|. For example, if a is 36
SITA-standard är 2 gånger snabbare än Full Avhandling: Phase-Noise Compensation for Space-Division Multiplexed model, two pilot-aided algorithms are developed using i) the sum–product algorithm Technical report, Division of Industrial Electrical Engineering and Automation, Lund University, Samuelsson, O. (2002), Development of Damping Algorithm. Thesis: “A Time Multiplexing Algorithm for Active Jamming Countermeasures”. -Division of Fluid Mechanics, Luleå University of Technology,. 2002-present.
- 8 d
- Huddinge psykiatri
- Manusförfattare sökes 2021
- Vikens montessori
- Nydala pizzeria umeå
- Xxl göteborg sisjön
- Lediga jobb tma chauffor
Solution : As we have seen in problem 1, if we divide 400 by 8 using long division, we get. Dividend = 400. Divisor = 8. Quotient = 50. Remainder = 0 Combinational Division Algorithm, approach to use floating point numbers and implementation of look-up tables to provide values of trigonometric function (cosine, inverse cosine etc) in Very High Speed Integrated Circuits Hardware Description Language is briefly introduced. 2021-01-01 This video introduces the Division Algorithm and its use to find the quotient and remainder when dividing two integers.
Lesson 15: The Division Algorithm—Converting Decimal Division into Whole. Number Division Using Mental Math. 156. This work is derived from Eureka Math
00:06:52 · The Division Algorithm (Screencast 3.5.1) · skoleflix | 7 Visninger. Maths : multiplication et Dividend Synthetic Division. How to solve polynomials with long division | StudyPug Long Division Algorithm and Synthetic Division!!!
dilatera v. dilate. dilation sub. dilation. dimension sub. v.
Apr 15, 2021 - Multiplication Algorithm & Division Algorithm - Computer Organization and Architecture | EduRev Notes is made by best teachers of Computer Science Engineering (CSE). This document is highly rated by Computer Science Engineering (CSE) students and has been viewed 24718 times. This page is based on the copyrighted Wikipedia article "Division_algorithm" ; it is used under the Creative Commons Attribution-ShareAlike 3.0 Unported License. You may redistribute it, verbatim or modified, providing that you comply with the terms of the CC-BY-SA. Cookie-policy; To contact us: mail to firstname.lastname@example.org
2020-11-26 · Euclid’s Division Algorithm is a technique to compute the Highest Common Factor (HCF) of two given positive integers. HCF of two positive integers a and b is the largest positive integer d that divides both a and b.
Pt utbildning gavle
Let's learn how to apply it over here and learn why it works in a separate video. No, the polynomial division algorithm does not immediately generalize to multivariate rings. Here is a simple proof. Just as for $\rm\:\Bbb Z,\:$ a domain having an algorithm for division with smaller remainder, also enjoys Euclid's algorithm for gcds, which, in extended form, yields Bezout's identity. 2020-07-08 · Ex 1.1 , 1Use Euclid’s division algorithm to find the HCF of :(i) 135 and 225Since 225 > 135, We divide 225 by 135Since remainder is not 0We divide 135 by 90Again, since remainder is not 0We divide 90 by 45Since remainder is now 0HCF of 135 and 225 is We thought it might be helpful to include some long division worksheets with the steps shown.
In Chapter-II, Number theoretic functions are discussed with some well-known
The Euclidean algorithm for the computation of the greatest common divisor of Given integers a,b, you perform the division algorithm on a,b, a = qb+r; if r = 0,
A cursory look at other search engine results did not reveal the division algorithm in the top ten, and even in Russian Wikipedia the article was still waiting for its
keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves. Vi har ingen information att visa om den här sidan. TrueCue (a division of Concentra Analytics) - Sales Forecasting · Single source of truth: the prediction algorithm is run centrally and written to database.
Hexagon aktie wasserstoff
jeremiasgården äldreboende örebro
matematik 1a 1b eller 1c
investera csn lan
olle svenning katalonien
- Intel(r) computing improvement program
- Why would you put that on the internet
- Lovdata engelsk
- Strömstad kommun skola
- Herzberg motivationsteori
- Kontakt unionen akassa
Implementation and evaluation of a polynomial-based division algorithm. Uppsats för yrkesexamina på grundnivå, Linköpings universitet/Institutionen för
(2) It is very useful therefore to write f(x) as a product of polynomials. What we need to understand is how to divide polynomials: Theorem 16.1 (Division Algorithm).


At Brunswick South-West Primary School we use a combination of the Australian Curriculum and the Victorian Essential Learning Standards (VELS) as a framework for what we teach in Maths.
We believe all students can succeed in numeracy. Our focus is on making maths meaningful. We want students to be able to use their number knowledge to solve problems. Games and concrete materials are used to support learning.
Maths has 5 hours per week of designated teaching time. Maths is also integrated into other learning areas.
We hold a whole school math activity day celebrating 100 days at school.
The school is fortunate to have two maths consultants working with the staff.
Katherine Palmer Every Child Counts
Dr Gaye Williams Deakin University
More information about Maths and AusVels can be found at: ausvels.vcca.vic.edu.au


The following is a paper by H. Aspden published by the Institute of Physics (UK) in J. Phys. A.: Math. Gen., v. 13 pp. 3649-3655 (1980).
Abstract: Using generalized mathematical considerations the inverse-square law of force is shown to imply specific spatial energy distribution relative to the interacting bodies. The retardation effects associated with energy redeployment when the bodies are in motion are examined. It is found that, as applied to the gravitational interaction between sun and planet and provided there is no discontinuity in the spatial energy distribution, retardation will give a law of motion conforming with Einstein's law of gravitation. A necessary condition is that the energy in transit in the field system is ineffective in determining force for a retardation period equal to the time required for a photon to travel from one body to the field and then return from the field to the other body. The implication is that gravitation could be a quantum interaction which assures causality and balance of action and reaction by this dual photon exchange interaction.
Commentary: This paper was, for the author, a breakthrough, in the sense that referees of a journal published by the U.K. Institute of Physics had yielded a little ground and allowed the publication of a paper that so clearly aimed to undermine Einstein's theory.
The paper was strictly a mathematical exercise to establish where the mutual interaction energy between two interacting particles was deployed, given that the particles were subject to an inverse square law of force. Although the solution was indeterminate so far as full three-space energy distribution was concerned, the range distribution of energy from either charge was determinate as one of two alternatives. The Coulomb interaction fitted one case and the magnetic interaction fitted the other case. The latter option, as applied to gravitation, was found to yield, on a retarded energy transfer basis, with a three-dimensional space metric, the identical equation to that which Einstein had derived from his complex four-space theory.
Even so, readers interested in this, will see that the eventual solution of the problem of the Neumann potential [1988a] was needed to justify why the retarded energy transfer was local to each particle and involved sequential action centred on the two interacting particles, coupled with an instantaneous action-at-distance directly between the particle centres.
Reference is now made to a criticism raised by Allen D. Allen concerning the validity of the mathematical case presented in this U.K. Institute of Physics paper. His comments were directed at the counterpart text in the author's book 'Physics Unified'. The following quotation is drawn from this author's paper [1983b] of these Web pages:
"The author has shown in 'Physics Unified' how Einstein's General Relativity equation for the law of gravitation can be explained by energy propagation. The theory depends upon analysis of the spatial energy distribution corresponding to the inverse square law of force. Allen D. Allen, in his review, quotes an equation (27) from the book:
-r-3[sum]cn(n+2)(x/r)n=0from which the author deduced that n was -2 and that the coefficients cn, were zero for values of n not equal to -2. [Note that the expression 'sum' is used instead of a summation sign.]
Allen D. Allen pointed to the difficulty of justifying this conclusion.
The author therefore seeks here to amplify the argument. The above equation is derived from a general formulation subject to the condition that with x larger than r it holds for all x. The summation applies for all negative integer values of n. Imagine that there are N coefficients Cn that are not zero and bear in mind that x can have an infinite number of values. We may take N+k different values of x to formulate N+k equations, each with N unknowns. r is fixed. k can be as great as we like. In these circumstances the only solution is that for which each term in the summation is itself zero, as one readily sees by solving:
y+2z=0 3y+4z=0 5y+6z=0Here we have three equations and two unknowns and both y and z must be zero. Then, given that each term in the summation is zero, one is led to the conclusion that n is -2 and that the coefficients cn with n as -1, -3, -4, etc. are all zero."


Has humanity just became even more meaningless?
The laws of physics demand that we cannot see through a black hole’s event horizon; it is fundamentally impenetrable. Even light cannot escape it.
But in a new study, a physicist from the University of Michigan has proposed a technique to do just that, and his findings could help solve one of science’s most challenging problems.
The study, published in the journal PRX Quantum, even adds weight to the theory that the universe is a hologram.
Wait, the universe is a hologram?
The idea that the universe is a hologram has been misinterpreted as the theoretical physics equivalent of Plato’s Cave, an ancient allegory about mankind’s inability to truly perceive reality, perhaps partially due to the popularity of films such as The Matrix.
But the theory, formally known as Holographic Duality, is actually a mathematical model to reconcile one of science’s greatest conundrums.
“In Einstein’s General Relativity theory, there are no particles, there’s just space-time. And in the Standard Model of particle physics, there’s no gravity, there’s just particles,” explained Enrico Rinaldi, a research scientist at the University of Michigan.
“Connecting the two different theories is a longstanding issue in physics – something people have been trying to do since the last century,” added Dr Rinaldi, one the paper’s authors.
What is Holographic Duality?
Holographic Duality suggests that the theory of gravity and the theory of particles are actually mathematically equivalent. The problem is the theory of gravity requires three dimensions, while the particle theory only has two.
Black holes are a valuable object for the sake of reconciling these theories. They are so dense that they warp three-dimensional spacetime, but we observe them because of their mathematical connection to particles, effectively projected through two-dimensional space.
One of the mathematical tools used to represent particle theory are known as quantum matrix models. Solving these models would show that the maths which represent particle theory could equally represent gravity.
But solving them is a hard problem. The models are basically blocks of numbers that represent particles. They are solved by finding the best configuration of particles to represent the system’s lowest energy state.
To find the solution, the team used quantum circuits – doing the equivalent of shaking a bucket of sand to level out the top – and ran the system through a special neural network to find the wave function of the matrix with the lowest possible energy.
The problem is that most modern quantum circuits are not powerful enough to solve these models if they are too complicated, so Dr Rinaldi and his team had to develop an exceptionally simple one to prove that their approach works.
As the technology develops they hope that researchers will be able to solve even more complicated matrix models.
“Because these matrices are one possible representation for a special type of black hole, if we know how the matrices are arranged and what their properties are, we can know, for example, what a black hole looks like on the inside,” added Dr Rinaldi.
“What is on the event horizon for a black hole? Where does it come from? Answering these questions would be a step towards realising a quantum theory of gravity,” he said.
He added that the results have provided an important benchmark for future work on quantum computing and machine learning algorithms that researchers can use to explore quantum gravity through the idea of holographic duality.
If you like our content please keep us going for as little as £2 a month https://dorseteye.com/donate/


Watch the video:
What do you notice?
What do you wonder?
How many carpet squares would be needed to cover the whole room?
What is a number that you're sure is too small?
What is a number that you're sure is too big?
Notice that the Teachers' Study Room's floor is not a rectangle. It's a kind of L shape:
It looks like, from the plan that this is its shape, measured in carpet tile lengths:
Show your thinking when you work out the number of carpet tiles to cover the room.
Next door is the staff room:


How to determine ceiling height inside of a metal building.
When planning a metal building, it's important to know how to determine the final height of the inside from floor to ceiling. To determine the height, you must know:
- The Eave Height
- The Roof Pitch
- The depth of the roof purlins
- the type of slope
- the width of the building.
To determine the ceiling height of a gabled building:
First, take the total width and divide by 2
Total width = 72' 0" / 2 = 36' 0"
Next, look at the roof pitch. The roof pitch is a measure of the slope. It is always measured in twelfths.
If you have a 1/12 pitch, you have 1 foot of rise vertically for every 12 foot of run horizontally
If you have a 2/12 pitch, you have 2 foot of rise vertically for every 12 foot of run horizontally
If you have a 5/12 pitch, you have 5 foot of rise vertically for every 12 foot of run horizontally
In the example above we have 36 foot of horizontal and a 1/12 pitch (in speaking, we say this is a "one on twelve pitch")
So take the horizontal run of 36 feet and divide by 12 (36 divided by 12 = 3)
Next multiply the Rise by this number. So 3 x 1 foot = 3 feet.
This gives you the change in height from the eave to the peak.
Again, looking at the example above, the eave height is 20 feet. Add 3 feet to that and you get the height at the peak, which would be 23' feet.
If you wanted to measure what the height would be 18 feet from the perimeter of the building, you would divide 18 by 12 and add it to the eave height ( so 18 / 12 = 1.5+20 = 21.5' , or 21' 6" )
Now because the eave height is always measured from the bottom to the top corner of the structure, it's important to know that this only gives you the OUTSIDE HEIGHT of the building.
To determine the inside height of the building, you must subtract out the purlin height. Looking at the example above again, we can determine the height of the purlin by looking at the engineering diagrams (not shown). In this case, our purlins are 8" tall.
So to determine the INSIDE HEIGHT of the steel building, subtract the purlin height (8").
- At the eaves, this building is 20' subtract 8" = 19' 4" interior height
- At the peak, this building is 23' subtract 8" = 22' 4" interior height
- At 18' from the outside wall, this building is 21'6" subtract 8" = 20' 10" interior height
For a single slope building, the calculation is the same except you don't divide the width by 2.
Now it's also important to consider that the main frame support columns that sit under the purlins. So at every Main frame column, you will lose anywhere from 10 inches to 36 inches, depending on the height of the main frame beam, or the "web". Often, if we are planning interior walls in the building, we will position the main frame columns so that they coincide with the interior walls.
It's not possible to know the depth of the main frame column beams until the Metal building engineer has actually designed the structure. There are many factors that can affect the size of the main frame columns, such as:
- height of the building
- distance apart of main frame columns
- snow zone
- ceiling loads
- wind storm zones
- other collateral loads
The depth of the web will usually vary across the width of the building. By tapering the I-beam supports, engineers can put strength where the building experiences the largest structural forces. This strategy minimizes unnecessary steel used in fabrication.
If you want to guess, typically the larger the building, the larger the depth of the main frame columns. I anticipate 12 to 24 inches for building less than 50', and 20 to 36 inches for buildings up to 80' in width.


I spent this past school year teaching 6th, 7th, and 8th grade math in the mornings and K-4 PE in the afternoons. As much as I love teaching math and PE, I've accepted a job teaching preschool at Riley County. I've taught summer preschool there the past three summers and will now teach year round.
I'm very excited to make this big change. I'll also be starting my Master's Degree in Early Childhood Education, so things probably won't slow down too much!


We were both trying to convince the other of whether width or height comes first in the world of 2D measurements. Thus, the inspiration for this article. Whether . Aug 20, 2015 – When we describe the image of something on a computer screen, it’s nearly universal to give the width first, before the height: W x H. When describing the . People often ask about the “correct” use of length, width, height, and depth. In the most common contexts in elementary school, mathematics does not have a . Both the length and width had the same measurement; it was laid out as a perfect square . The first foundation [stone] was jasper, the second sapphire, the third . This is the first question to ask yourself before buying a TV. . Once you’ve chosen the location, measure the height, width, and depth of that spot; . next level so you can enjoy all of your favorite shows, movies, and games in glorious Ultra HD. To calculate the heightof each layer, the projected height of the wall was divided . shovelto cut a slabof stiff mud about 30–35 cm long ×18–20 cm wide × 8–10 cm thick. . Figure 7.3Professional mason and assistant (left) layingthe first slabs of. For dykes they gave the height, top width, base of slopes, sectional area, the . supplied to the Zahsildars, who received full instructions and were first taken over . For dykes they gave the height, top width, base of slopes, sectional area, the . supplied to the Zahsildars, who received full instructions and were first taken over . Apr 23, 2016 – Compare and order objects of different length, width and height . 18This level is generally aligned with the objectives for First and Second Glorious! Chilled soups cost €3.75 per kg after a 25% saving has been applied. We know that on the true “glorious 1st of June” namesakes of the “Invincible,” . Drinking and toasting in this connection would have seemed to us the height of bad volcano, were separated by a belt of silence nearly 100 kilometers in width.


Headmaster's Office, Yulin Normal University, 299 Jiaoyuzhong Road, Yulin (537000), Guangxi P.R. China
Nonlinear programming (smooth constrained optim.; minimax optim.; cone optim.; math. prog. equili. constraints): sequential quadratic programming (SQP) methods, norm-relaxed SQP methods, sequential quadratically constrained quadratic programming (SQCQP) methods, sequential systems of linear equations (SSLE ) methods, sub-feasible and strongly subfeasible directions methods, interior point algorithms, generalized projection methods and so on.
Variational inequality problems (VIP): continuation methods and so on.
Convex analysis: generalized convex sets and generalized convex functions.
Optimization in power systems
Education for Jin-bao Jian
Dr. Sc. (June 2000) Xi'an Jiaotong University,China Specialty: Computational Mathematics. Direction: Optimization Theory and Methods Tutor/Supervisor: Prof. Kecun Zhang. Thesis topic: Researches On Superlinrarly and Quadratically Convergent Algorithms for Nonlinearly Constrained Optimization.
M. Sc. (Mar. 1989) Guangxi University, China. Specialty: Applied Mathematics. Tutor/Supervisor: Prof. Shengjia Xue. Thesis topic:A Sort of Reduced-Variable Metric Algorithm with Superlinear Rate of Convergence.
B.Sc. (June 1986) Guangxi University , China.
Honors or Awards
Researches on Fast Algorithms for Constrained Optimization and Generalized Convexity, The Second Prize for Natural Science in Guangxi Province of China, J.-B. Jian, Z.-B. Zhu, C.-M. Tang, R. Quan, J.-L. Li, Q.-J Xu, et al. 2010
An advanced worker in the national education system of China, J.-B. Jian, 2009
The State Council special allowance of China, J.-B. Jian, 2007
An outstanding expert in Guangxi Prvince of China, J.-B. Jian, 2006
Superlinearly Convergent Algorithms for Optimization and Methods for Varational Inequalities, The Second Prize for Scientific and Technological Advance in Guangxi Province of China, J.-B. Jian, Y.-L. Lai, K.-C. Zhang, 2003
Scientific and Technological worker with outstanding contribution in Guangxi Province of China, J.-B. Jian, 2001
Researches on Globally and Superlinearly Convergent Algorithms for Optimization, The Second Prize for Scientific and Technological Advance in Guangxi Province of China, J.-B. Jian, 1998.
Memberships and Services
Director of the science & technology division (2006-)
Council Member of the Operations Research Society of China(ORSC)
Council Member of the the Mathematical Programming Society of China
1993&2007, Visiting scholar, The Chinese University of Hong Kong, Hong Kong


A direct admission pathway is for high school students wishing to pursue the Doctor of Pharmacy degree.
Steps for Admission into the Pathway Program:
- High School:
- Graduating GPA ≥3.5
- ACT Composite Score ≥ 26 or a SAT composite ≥ 1250
- ACT Math Score ≥ 26, or a SAT Math Score ≥ 620,
or ALEKS placement in Math 150,153 and 154, or 155 and Chem 115
or transferrable math credit for college algebra AND college trigonometry
- Apply to WVU as a pre-pharmacy major
- WVU Undergraduate:
- Enroll in pre-pharmacy courses (semesters 1-4)
- Maintain GPA of ≥ 3.0
- Participate in the School of Pharmacy First Year Experience Seminar Course PHAR 191 and Kaplan PCAT Prep Course PHAR 199
- Join APhA-ASP
- Register for July PCAT during the 2nd semester of first year
- Score ≥ 50th percentile composite score
- Apply through PharmCAS for WVU School of Pharmacy Early Decision
- Admission to School of Pharmacy:
- Late September-early October interview
- Notification of admission by mid-October
- Finish prerequisites by end of 4th semester and maintain GPA of ≥ 3.0
WVU Tech Direct Admit Pre-Pharmacy coming soon!
Requirements to enter the Direct Admit program will be the same as listed above when the program is launched.


Improving the H2MLVQ algorithm by the Cross Entropy Method
Schlagworte:Generalized Learning Vector Quantization, Relevance Learning, Cross Entropy method, Initialization sensitiveness, DDC: 004 (Data processing, computer science, computer systems)
AbstractThis paper addresses the use of a stochastic optimization method called the Cross Entropy (CE) Method in the improvement of a recently proposed H2MLVQ (Harmonic to minimum LVQ) algorithm, this algorithm was proposed as an initialization insensitive variant of the well known Learning Vector Quantization (LVQ) algorithm. This paper has two aims, the first aim is the use of the Cross Entropy (CE) Method to tackle the initialization sensitiveness problem associated with the original (LVQ) algorithm and its variants and the second aim is to use a weighted norm instead of the Euclidean norm in order to select the most relevant features. The results in this paper indicate that the CE method can successfully be applied to this kind of problems and efficiently generate high quality solutions. Also, good competitive numerical results on several datasets are reported.


“This is the fourth edition of this interesting graph theory textbook. The author marked paragraphs recommended for a first course and also some exercises. Reinhard Diestel. Graph Theory. Electronic Edition There is now a 4th electronic edition, available at You should be able. Title Graph Theory, 4th Edition (Graduate Texts in Mathematics); Authors Reinhard Diestel; Publisher: Springer; 5th ed. edition (July 21, ), 4th Edition.
|Published (Last):||24 November 2018|
|PDF File Size:||17.60 Mb|
|ePub File Size:||8.57 Mb|
|Price:||Free* [*Free Regsitration Required]|
Alamsyah 5th International Conference on Information…. Boundedness and Finite Spreading.
Reinhard DiestelChristof Rempel: On the excluded minor structure theorem for graphs of large tree-width. Simplicial tree-decompositions of infinite graphs, I.
Diestel, Graph Theory (4th ed’n), Professional Edition
Graph Theory can be used at various different levels. Direct comparison method of information dissemination using legacy and Social Network Analysis A. Discrete Mathematics 71 2: Infinite matroids in graphs. Johannes CarmesinReinhard DiestelM. To the professional mathematician, finally, the book affords an overview of graph theory as it stands today: Showing of 27 extracted citations.
The eBook includes the entire book, including the index. Journal of Graph Theory 50 3: Citations Publications citing this paper. It is also available in translation: ParyastoFeriza J. A topological approach, I.
Diestel, Graph Theory (4th ed’n), Professional Edition by Reinhard Diestel – PDF Drive
Discrete Mathematics 1: The American Mathematical Monthly 7: Social network data analytics for market segmentation in Indonesian telecommunications industry IndrawatiA. Twins of rayless graphs.
End spaces and spanning trees. A topological approach, III. MacLane’s theorem for arbitrary surfaces. A Short Proof of the Path-width Theorem.
For Weather, Flights, Runways of Airports all over the world, etc, click here. Journal of Graph Theory 11 1: On Infinite Cycles in Graphs: This standard textbook of modern graph theory, now in its fifth edition, combines the authority of a classic with the engaging freshness of style that is the hallmark of active mathematics.
Menger’s Theorem for a Countable Source Set.
Reinhard Diestel Graph Theory 4 th Electronic Edition c © – Semantic Scholar


Website Plaza Heights Christian Academy
Private Christian School
PHCA is currently accepting applications for a secondary teaching position in Math. Applications should possess a minimum of a bachelor’s degree in the related field along with a desire to minister to students. Extra curricular positions are available/can be added as well. Prior teaching experience is a plus, but not required. This position would be teaching subjects of Pre-Algebra, Algebra 1 and 2, Geometry, Personal Finance courses.
To apply for this job please visit www.plazaheightschristianacademy.org.


There are 25 students in my AP Calculus course at Letcher County Central High School. The AP Calculus course at LCCHS has always been taught using lecture. However, some students struggle to keep up with other members of the class, while others must wait for the class to catch up before moving on to new learning. I am utilizing the “Flipped” Classroom model to personalize learning for my Calculus students. Using the “Flipped” Classroom model, students complete knowledge-level assignments outside of class (previewing new learning resources, generating questions, applying knowledge to complete assignments, etc.) By doing this work outside of class, students come to class prepared to ask questions and prepared to
apply higher-level thinking skills to solve problems and complete projects.
Letcher County High School, Letcher County Project Title: Flipping OUT in AP Calculus STEM Grant Recipient


William Thomson, mathematician and university administrator, was educated at the University of Edinburgh, where he was awarded the degrees Bachelor of Science (BSc) and Master of Arts (MA) with honours in mathematics and natural philosophy (physics) in 1878. That same year he wrote a substantial article on "Mensuration" (the science of measurement) for the ninth edition of the Encyclolpaedia Britannica. After some years as assistant in the Department of Mathematics at Edinburgh he succeeded George Gordon* in January 1883 as professor of mathematics and natural philosophy at Stellenbosch College (later Victoria College, which became the University of Stellenbosch in 1918). He soon added a course in electricity and magnetism to the syllabus. In June 1887 he resigned for health reasons, but was reappointed the next month. From the beginning of 1892 he was professor of mathematics only. He also became a member of the council of the University of the Cape of Good Hope in 1883, holding both positions until 1895. In 1884 he married Annie Catherine van der Riet, with whom he had two daughters.
Thomson's publications included An introduction to determinants (Edinburgh, 1881), Algebra for the use of schools and colleges (London, 1886), A text-book of geometrical deductions (with J. Blaikie; London, 1891-1892), and Elementary algebra (London, 1901). In 1887 he was an examiner in mathematics for the University of Edinburgh.
In June 1895 Thomson gave up his academic career and succeeded Reverend James Cameron* as registrar of the University of the Cape of Good Hope - an examining body and the only university in southern Africa at the time. He served in this position until 1918, when the institution became the University of South Africa and moved its headquarters to Pretoria, and continued as registrar of the latter until his retirement in 1922. During this period he served as secretary of the Inter-Colonial Conference on University Education in 1908, as chairman of the Higher Education Commission of 1911, and as a member of the University Statutes Commission in 1916.
From 1895 he was a member of the South African Philosophical Society for a few years, and from 1902 a member of the South African Association for the Advancement of Science. Honorary Doctor of Laws (LLD) degrees were conferred upon him by the University of Edinburgh (1904) and the University of Cape Town (1922) and he was elected a Fellow of the Royal Society of Edinburgh. He was knighted in 1922 for his contribution to tertiary education in South Africa and the next year returned to Scotland.
In 1924 Thomson represented the University of South Africa at the conference on university education of the League of the Empire in London. In October that same year, following the resignation of J.H. Hofmeyr as principal of the University of the Witwatersrand, he agreed to return to South Africa to fill this post until a permanent appointment could be made. This only happened early in 1928, when H.R. Raikes was appointed. Thomson also resumed his services to the University of South Africa as a member of its council from 1924 until his death in 1947. After his final retirement he lived in Simonstown.


Skip to main content
Make the most out of any wiki by using our free sister product,
Blendspace by TES
, to create interactive lessons and presentations!
Come Teach With Us Math - Lesson
Pages and Files
Directory of Users
High School Lesson Ideas
Middle School Lesson Ideas
Template for Lesson Plans
Math Olympiad Questions
Email whole class
Sequence, arithmetic sequence, common divisor
Grades/Course: 11, Algebra 2
Lesson Number: Arithmetic Sequences
Time Required: 40 minutes
Original Author: Marion Blanchard
Essential Question(s) for this Lesson
What patterns exist in Math?
How can you use Math to make problems simpler?
Addressed for this Lesson
A2.A.29 Identify an arithmetic or geometric sequence and find the formula for its nth term
A2.A.30 Determine the common difference in an arithmetic sequence
A2.A.32 Determine the specified term of an arithmetic or geometric sequence.
G.PS.2 Observe and explain patterns to formulate generalizations and conjectures
Math B – Modeling / Multiple Representations
-- 4A Represent problem situations symbolically …
-- Use symbolic form to represent an explicit rule for a sequence.
Evidence of Student Understanding (Assessment) for this Lesson
Worksheet in class
Student Preparation Prior to this Lesson
None, this is the first class in the unit
Number and Patterns worksheet – I per student
Challenge problem – 1 per student
Unit tile blocks for manipulative approach to sequences if necessary
Specific Purpose(s) or Objective(s)
Use of mathematical notation
See that tedious and repetitive math problems may have a simpler pattern / solution
Arithmetic sequence notation and usage
A rich relative is leaving you money. You get a penny today, 2 pennies tomorrow, 4 pennies the next day, this continues. On which day do you get $10.01?
Step by Step Explanation of Activities/Strategies
1. Do Now – (3 minutes)
Put these sequences on the board. Students to find the next 3 numbers:
2, 4, 6, 8, … (arithmetic)
1, 4, 9, 16, …
15, 13, 17, 15, 19, ….
5, 10, 20, 40, …. (geometric)
1, 1, 2, 3, 5, … (Fibonacci)
1, 7, 13, …
2. Talk about each sequence. (6 minutes)
Any pattern you can explain is valid, as long as you can explain it to me.
Mention Fibonacci sequence, geometric sequence.
Our lesson will be on arithmetic sequences”
What is the first term? What is the next term? What did you do to get there?
3. Hand out number patterns worksheet and challenge worksheet (5 minutes)
Class start working on them. Stop after 5 minutes. Save this worksheet. You will need it again
4. Introduce notation: a1, an, d (common difference) (15 minutes)
backwards terminology! – we are adding and the word refers to subtraction
Write out the a1, a2, a3,.. of some of the series from the worksheet. Go forward 2 terms, what is answer? Two more. Then ask for the 105th term.
Look for general definition of nth term: an = a1 + (n-1)d
So back to the starting problem – How do we set this up?
an = a1 + (n-1)d;
an = $10.01,
d = .02
10.01 =.01 + (n-1) * .02,
n = 501.
It takes more than 500 days to get to $10.00. When we start doing summations of sequences in a few days I will show you something interesting about this problem.
5. Define homework (2 minutes)
Homework will be to finish worksheet. Write these instructions on the worksheet. Next to each sequence write a big “A” if it is an arithmetic sequence. If it is - write the a1 term and the d term. Write that on the work sheet now so you don’t forget. The challenge problem is optional.
In class – everyone make up an arithmetic sequence. Give it to your partner to solve. The person who is solving: be sure to define a1, d. Find the 243rd term of your sequence. You will hand in to me as you leave. Put both of your names on the sheet.
I will use some of these as tomorrow morning’s do-nows.----
Accommodations for Students with Disabilities or Diverse Learning Styles
Auditory learning – repeat key words – Common difference, nth term, sequence
Manipulative learning – have small unit square tiles available. Students can create piles of blocks, each pile a term in a sequence.
Challenge problem for advanced students
help on how to format text
Turn off "Getting Started"


Degrees and Certifications:
Mrs. Melissa (Missy) Halvorson has taught Mathematics at West Fargo High School for 23 years. She was born and raised in West Fargo and graduated from WFHS. Go Packers! She earned her Bachelor of Science degree in Mathematics from Minnesota State University Moorhead and her Master of Education degree from Minot State University. Missy and her husband have three daughters. In her spare time, she enjoys spending time with her family and friends, cheering for her daughters at their activities, spending time outdoors, and taking pictures.


احصل على Problems And Solutions Of Rot Mill Square السعر(WhatsApp)
يمكنك الحصول على سعر Problems And Solutions Of Rot Mill Square وسيتصل بك ممثل A&C في غضون يوم عمل واحد.
Question Corner What is the .
What is the Square Root of i? Asked by a student at Eastwood High on May 9, 1997: What is the square root of i? There are two square roots of i: and .learn more
Practice Questions of Square Root .
Solved Practice Questions for NTSE, Free question bank for Square Root Cube Root Mathematics NTSE with solutions, Chapterwise test for Square Root Cube Root NTSElearn more
3 Tomato Plant Problems and How .
· 3 Tomato Plant Problems and How to Prevent Them. ... tomato growing problems has an easy solution. ... the fruits that already have blossom end rot, ...learn more
How to Solve Square Root Problems .
· Встроенное видео· How to Solve Square Root Problems. ... For quick solutions, ... Cookies make wikiHow better. By continuing to use our site, ...learn more
Square root Wikipedia
In Ancient India, the knowledge of theoretical and applied aspects of square and square root was at least as old as the Sulba Sutras, ... with solutions = = ±. The ...learn more
Roots and Solutions. There is a .
What is the deal with roots solutions? The solution of a polynomial equation, f(x), is the point whose root, r, is the value of x when f(x) = 0.learn more
Square Root Word Problems TuLyn
Square Root Word Problems. Are you looking for word problems on square root? ... Radicals Word Problems . Find word problems and solutions on radicals.learn more
Root Solutions | Creo Parametric .
Root Solutions UK Resellers of the 3D Product Design Software ... Creo is PTC''s landmark initiative to redefine CAD and solve the big problems in mechanical CAD, ...learn more
problems and solutions of rot mill .
Quantum mechanics and the square root of Brownian motion | The ... 25 Jan 2012 ... TartagliaPascal triangle gives, in the proper limit, the solution of the heat ...learn more
Differentiation Using the Chain Rule .
SOLUTIONS TO DIFFFERENTIATION OF FUNCTIONS USING THE CHAIN RULE ... ( The outer layer is ``the square ... Click HERE to return to the list of problems. SOLUTION ...learn more
IXL Square roots (Algebra 1 practice)
Fun math practice! Improve your skills with free problems in ''Square roots'' and thousands of other practice lessons.learn more
problems and solutions of rot mill .
Barite processing plant. Baryte, or barite, is a mineral consisting of barium sulfate. The baryte group consists of baryte, celestine, anglesite and anhydrite.learn more
Quadratic equation Wikipedia
Solutions to problems equivalent to the quadratic equation were ... The solutions of the quadratic equation ax 2 + bx + c ... a square root, so the solution ...learn more
Ratio Word Problems with Solutions .
Ratio word problems with solutions and detailed explanations for grade 9. ... What is the ratio of the area of square A to the area of square B? Solutionlearn more
Calculus II Root Test Lamar .
Most of the classes have practice problems with solutions available on the practice problems pages. ... Root Test. Suppose that we have the series .learn more
Statistics Problems With Solutions
· Statistics and Probability Problems With Solutions. Use the dropdown text boxes to describe the problem you want to review.learn more
Radicals: Introduction .
Covers basic terminology and demonstrates how to simplify terms containing square roots. Skip ... Radicals: Introduction Simplification. ... or no, solutions) are ...learn more
Solving Math Problems : How to .
· Встроенное видео· In math, the square root of one number is found by looking for another number that will equal the first when multiplied by itself. Solve square .learn more
Free square root worksheets (PDF .
Make free worksheets worksheets for square ... Word problems relate algebra to ... equations and inequalities intuitively before formal solutions are ...learn more
Root Square Mean Velocity Example .
· Root Square Mean Velocity Example Problem ... Solution: Root mean square velocity is the average ... Practice Chemistry with Worked Chemistry Problems.learn more
Tomato Problems Tomato Growing
Low temperatures, over watering and wet weather are often the cause of common tomato problems in the earlier part of the growing season.learn more
Solving squareroot equations (basic) .
· Встроенное видео· Solving squareroot equations: no solution. Practice: Solve squareroot equations. Next tutorial. Extraneous solutions of radical .learn more
Algebra Equations with Radicals
Most of the classes have practice problems with solutions available on the ... and Inequalities / Equations with Radicals. ... equations involving square ...learn more
Root Cause Analysis Problem .
· Use Root Cause Analysis to look deeper into problems ... Learn how to use Root Cause Analysis to fix problems more ... who implement the solutions, ...learn more