Introduction This page or section is a stub. You can help the wiki by accurately contributing to it. Floating point numbers are a way to represent real numbers inside computer memory which usually operates with binary digits. As opposed to fixed point numbers which have a fixed number of digits before and after the decimal markfloating point numbers can be considered to have a certain amount of significant digits or 'accurate leading numbers' that we consider to carry an accurate approximation to some value.
The DX—Core2 microprocessors contain their own built-in arithmetic coprocessors. Be aware that some of the cloned microprocessors from IBM and Cyrix did not contain arithmetic coprocessors.
The instruction sets and programming for all devices are almost identical; the main difference is that each coprocessor is designed to function with a different Intel microprocessor. This chapter provides detail on the entire family of arithmetic coprocessors.
Because the coprocessor is a part of the DX—Core2, and because these microprocessors are commonplace, many programs now require or at least benefit from a coprocessor. The family of coprocessors, which is labeled the 80X87, is able to multiply, divide, add, subtract, find the square root, and calculate the partial tangent, partial arctangent, and logarithms.
Data types include, and bit signed integers; l8-digit BCD data; and, and bit floating-point numbers. With the improved Pentium coprocessor, operations execute about five times faster than those performed by the microprocessor with an equal clock frequency.
Note that the Pentium can often execute a coprocessor instruction and two integer instructions simultaneously. The Pentium Pro through Core2 coprocessors are similar in performance to the Pentium coprocessor, except that a few new instructions have been added: The multimedia extensions MMX to the Pentium—Core2 are instructions that share the arithmetic coprocessor register set.
The MMX extension is a special internal processor designed to execute integer instructions at high-speed for external multimedia devices. For this reason, the MMX instruction set and specifications have been placed in this chapter.
See Table 14—1 for a listing of all Intel microprocessors and their companion coprocessors. These data types include signed integer, BCD, and floating-point. Each has a specific use in a system, and many systems require all three data types. In order to accomplish any such modification, the instruction set and some basic programming concepts are required, which are presented in this chapter.
Signed Integers The signed integers used with the coprocessor are the same as those described in Chapter 1. When used with the arithmetic coprocessor, signed integers are worddoubleword integeror bits quadword integer wide. The long integer is new to the coprocessor and is not described in Chapter 1, but the principles are the same.
Conversion between decimal and signed integer format is handled in exactly the same manner as for the signed integers described in Chapter 1. Integer data types are found in some applications that use the arithmetic coprocessor.
See Figure 14—1, which shows these three forms of signed integer data. Data are stored in memory using the same assembler directives described and used in earlier chapters. Example 14—1 shows how several different sizes of signed integers are defined for use by the assembler and arithmetic coprocessor.
Each number is stored as an digit packed integer in nine bytes of memory as two digits per byte. The tenth byte contains only a sign-bit for the digit signed BCD number. Figure 14—2 shows the format of the BCD number used with the arithmetic coprocessor.
This form is rarely used because it is unique to the Intel coprocessor. Floating-Point Floating-point numbers are often called real numbers because they hold signed integers, fractions, and mixed numbers.
A floating-point number has three parts: Floating-point numbers are written in scientific binary notation. The Intel family of arithmetic coprocessors supports three types of floating-point numbers: See Figure 14—3 for the three forms of the floating-point number.
Please note that the single form is also called a single-precision number and the double form is called a double-precision number. Sometimes the bit temporary form is called an extended-precision number. The floating-point numbers and the operations performed by the arithmetic coprocessor conform to the IEEE standard, as adopted by all major personal computer software producers.
This includes Microsoft, which in stopped supporting the Microsoft floating-point format and also the ANSI floating-point standard that is popular in some mainframe computer systems.
The float is a bit version, double is the bit version, and decimal is a special version developed for Visual studio that develops a very accurate floating-point number for use in banking transactions or anything else that requires a high degree of precision.
The decimal variable form is new to Visual Studio and Converting to Floating-Point Form.Nov 08, · Lets an analysis of the floating point coprocessors in the design of a microprocessor in computer science start right off with a controversial claim: Forth is the hackers programming language Coding in Forth is a little bit like writing assembly.
The term floating point is derived from the fact that there is no fixed number of digits before and after the decimal point; that is, the decimal point can float. There are also representations in which the number of digits before and after the decimal point is set, called fixed-point representations.
Floating point number, normalization, exceptions, latency, etc. 1. INTRODUCTION An arithmetic circuit which performs digital arithmetic operations has many applications in digital coprocessors, application specific circuits, etc. Because of the advancements in the . For example, a math coprocessor performs mathematical computations, particularly floating-point operations.
Math coprocessors are also called numeric and floating-point coprocessors. Most computers come with a floating-point coprocessors built in. Note, however, that the program itself must be written to take advantage of the coprocessor.
smart-memory coprocessors to a microprocessor. This Introduction The Data-IntensiVe Architecture (DIVA) project  is building a workstation-class system using (Integer to floating-point) instruction, the fraction is first converted to sign-magnitude format by conditionally inverting if the sign is negative.
Then the result is shifted. Introduction to Many Integrated Core (MIC) Coprocessors on Stampede. Intel Xeon Phi™ SE10P coprocessors to change the power/performance curves of supercomputing • Over 70% provided by Xeon Phi moderate floating point throughput –2x E on Stampede: Tflop/s, W.


Mathematics is a formal subject, but most of us enjoy it as a fun and interesting subject.
It is a subject that is both intellectually challenging and culturally intriguing. A lot of people have not been introduced to it in their early years and like to experiment with it and see how far they can push it.
Maths is an issue that encircles ideas and notions , you might never have examined custom paper it in 1 lifetime. Distinct areas of math involve various regions of the mind. A person’s capacity is essential in this respect. Elements of math treat various mindsets.
Certainly one of the greatest challenges to your thoughts is math. You can find a number of good reasons for this. Mathematicians have also and all of the period the urge to multiply to figure out why matters come out. The response to the question’why would this happen?’ Is not found in the past web page of the text book or by means of multiplication tables.
All https://internationaloffice.berkeley.edu/students/new these mathematicians feel some thing called curiosity. They’ve been always looking for better and new means to interpret a set of data. Once you understand that the answer is not accessible any textbook and also have a take a look in the listing of mathematical difficulties and difficulties, you receive yourself a sense of invincibility. Then you’re worked up about math.
The odyssey to get a person considering mathematics starts out of the following. The very first thing to do is to obtain an thought of the’terminology’ of one’s pick. The second thing to do is to know it. The third step is to find out good enough to enhance your comprehension of other issues. https://www.grademiners.com/article-writing-services The next step is to produce it a discipline, not simply an enjoyable pastime.
This last step is also important because these natural aspects of mathematics have interesting patterns to them. You may be fascinated by the patterns of the use of the different numbers. Then you can put them together to create a pattern that explains why and how something happens. That is when you understand mathematics.
After finishing their initial one diverse students go onto choose this course. You should pursue several, if you are serious about any of this. There are a lot of ideas which might be heard by way of this course. You want to think about your future aspirations, so you want to continue to keep matters in outlook. It can sound confusing, but you may find that the mathematical aptitude has blossomed once you grab this.


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Lehigh's Master's of Science in Data Science allows students from a wide range of backgrounds to gain the qualifications necessary to tap into the wealth of data science jobs, many of which require an advanced degree. The U.S. Bureau of Labor Statistics projects jobs in the field to grow more than 30 percent between 2020 and 2030. Lehigh's Data Science program provides access to the skills and tools of data science to people who want to develop that skill set, even if they don't have a background in computer science or statistics. Prospective students need a strong foundation in math and some basic training in computer science, but no prior data science coursework is required. Classes will be taught in a hybrid (both in-person and remote) format.
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14 October 2020 10:00am–11:30am
We have secured funding through the Inclusive Learning Project in the South East for a four week online course hosted by the National Numeracy Project. This is a project which aims to advance maths in the workplace; there is absolutely no maths tutoring/ training or learning involved. The purpose of the sessions are to understand anxiety around and towards maths, looking at ways you can help members to overcome it (if they ask).
Within the UK 49% of adults are operating with a maths level of that expected of primary school children and we can help tackle this. The National Numeracy Project understand that as soon as you start talking maths people start to switch off, they propose a much more subtle approach to advancing maths learning in the workplace and as part of that you will learn how to run a successful project.
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On the first day of school Superintendent Noflin visited MJH 6th grade classes and encouraged the students to do their best. Pictured with him is Principal Rene Fonte and a 6th grade student in Ms. Davis' Science Class.
Mr. Fonte telling the students how much he believes in their success this year and they attentively listens.
Students going over their handbooks with Mr. Fonte, Ms.Dollie Martin and Ms. Sheila Minor.
Mrs. Robinson and Ms. Perry taking a moment to pose before preparing lunch for the students. Ms. Denise getting the Annex Building's bulletin board ready for the new year.
8th Graders Learn About College
Representative Jackson of Louisiana Connect spoke to 8th grade students at Morehouse
HAPPY BOSS'S DAY
Anti-Bullying Day was held on Wednesday, Oct. 10 and several students at MJHS participated to show their support "against" bullying by wearing orange shirts. A few of the students are featured below with Mrs. J. Kelly, Instructional Facilitator and Mrs. K. Martin,Secretary.
MJH students collect 1,635 pounds of canned food for the Northeast Louisiana Food Bank where the food will benefit the surrounding communities!
Morehouse Junior High Helping Students Reach for the Stars
A new “Math Academy” for the top 6th grade math students will let students achieve far beyond their peers
Bastrop, LA; August 27, 2012: A new concept in education has come to Morehouse Junior High School with the addition of a Math Academy class.
On Thursday night, August 23rd, a group of students, parents, and educators gathered at MJH with the purpose of introducing a new concept in classroom math education that involves using the computer as the primary source of instruction and then depends on the classroom teacher to monitor and mentor students when they come to an area of mathematics where they may struggle.
Known as the Khan Academy (MJH has chosen the name “The Morehouse Junior High Math Academy”), this web-based program offers a “FREE WORLD CLASS EDUCATION TO ANYONE”. The Khan program began as one man attempted to offer You-Tube videos to help tutor a cousin in another city and became overwhelmed with the response from strangers all over the world. The successes in other schools around the country has prompted MJH to begin this pilot program to see just how far a motivated student can climb in this first year of offering a class of this sort.
Each student in this new class was hand selected based on their i-LEAP scores from their 5th grade year. What is truly unique about this new class is that they will be using a computer based learning program that is geared to allow them to grow well beyond the 6th grade curriculum. The students will, after completing the required modules for a particular grading period, be able to move at their own learning pace to any level of math they wish. The program offers instructionin math from basic addition through Advanced Calculus.
The teacher in the class will track each student and will work one-on-one with any student who runs into a “bump in the road”. Meanwhile, all of the other students will be working on different modules at their own pace and based on their own curiosity or weaknesses.
The teacher in the course said that he is expecting this class of students to move from Basic to Mastery or from Mastery to Advanced by the time the i-LEAP tests are given again in April of 2013 and that if this occurs the program could be expanded in the next school year.
The MJH principal, Mr. Rene’ Fonte, said that it would be possible, assuming success is shown, that the initial students in this class would be allowed to continue in the Math Academy throughout their junior high school careers.


Anita’s whole-school approach to primary maths
Anita believes a consistent whole-school approach to maths is essential to improve student understanding and achievement in primary schools.
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Anita grounds her approach in Anita Chin’s Primary Maths Framework (2020) which is the culmination of more than 25 years’ experience in leading and teaching mathematics in Australian primary schools.
Anita’s Primary Maths Framework
The Framework combines a strong evidence base with Anita’s extensive knowledge of what works best in primary maths classrooms.
The Framework provides a structure to support schools to implement a consistent and sustainable whole-school approach to maths. It contains four components:
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All of Anita’s professional learning links to her Framework which is complemented by her 360 Degree School Reflection Tool. The Reflection Tool is designed to be used at key milestones on your learning journey to gather the data you need to demonstrate progress towards your school’s goals for mathematics.
Anita’s tools for leading primary maths
Anita has developed a suite of tools to support leaders to implement a consistent whole-school approach to maths K–6.
Anita’s 360º School Reflection Tool
Designed to be used at key milestones on your learning journey with Anita, the Reflection Tool allows you to analyse your situation and plan the next steps to meet your school’s strategic goals for maths.
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Anita’s Accountability Tools
Anita’s Accountability Tools are used by your maths team and classroom teachers to assist them to plan and record their implementation and progress towards their strategic goals in maths.
Anita’s Ultimate Toolkit for Leaders
Using her trademark practicality to bring the research alive, Anita’s Ultimate Toolkit folder is jam-packed with the tools and strategies you need to drive sustainable improvement in maths.


Hey, I’m Ty! And I think for a living.
Mostly, I think about how to describe nature using concepts from math and physics. I specialize in adding spatial movement to ecological and evolutionary processes, and I’m especially fascinated by the idea of relative motion—i.e. the spatial patterns that emerge when we consider how different parts of the natural world move in different directions or at different speeds relative to each other.
I test these ideas using a mix of theory, simulations, and highly replicated experiments with an emphasis on testing mathematical theory using experimental data. Over the last ten years as a scientist, I have shown that motion is a powerful ecological mechanism that alters how natural systems operate. I have also shown that taking account of relative motion in our mathematical models can unlock secrets about the ways ecological and evolutionary processes operate.


Have you ever made a transaction on your bank’s website? Do you feel 100% secure when using an HTTPS encrypted connection? Well, you shouldn’t. A recent publication  proves how the encryption behind HTTPS may fail in practice. You better read what’s next.
Related post: Do Quantum Computers Mean the End of HTTPS?
HTTP over TLS (also called HTTPS) ensures a secure communication between two parties by using a cryptographic protocol called TLS (Transport Layer Security) – successor of SSL. TLS expects two parties (Client and Server) to negotiate a stateful connection by using a handshaking procedure. During this phase, a session key must be generated for encrypting all messages in the communication session. Generally, in order to generate this key, the client uses the Diffie-Hellman key exchange, an algorithm which allows two parties to exchange cryptographic keys over a public channel.
The Diffie-Hellman method expects two entities to agree upon the usage of a public prime number p and a public prime base g, part of a cyclic group G. Given a and b are two numbers secretly and independently chosen by the two parties, one entity sends ga mod (p), the other sends gb mod (p) and each can compute a shared secret key gab mod (p). An attacker who can find the discrete log(x) from y = gxmod (p) can easily find the shared secret key. However, there is no known efficient algorithm for solving that problem. Thus, by imposing the order of G to a very large prime factor, the complexity of the problem is high enough to prevent attackers from obtaining a or b.
This publication released last October 2015 introduces the existence of an attack named Logjam, able to exploit the security vulnerability (CVE-2015-4000) released in March 2015, which allows the hackers to break a TLS connection using a 512-bit prime key. This is possible because of the algorithm used to solve the aforementioned discrete logarithm. Actually, it has been proved that the first three computational steps of the four necessary for solving that equation depend only on the order of G, and not on the specific number. Thus, by pre-computing those steps for all the single 512-bit primes in about a week, it is possible to solve the fourth step of the algorithm in about a minute, thereby having the key to decrypt the connection. The researchers found 8.4% of HTTPS - TOP 1 Million Domains being vulnerable because they use a 512-bit prime key.
Researchers found that 18% of HTTPS - TOP 1 Million Domains and 25% of SSH Servers are using 1024-bit primes instead to encrypt their connections. The researchers estimated the cost of creating logjam precomputation for one 1024-bit prime at hundreds of millions of US Dollars. Given the $10.5 billion allocated by the US Government for the Consolidated Cryptologic Program of 2012 and taking the claims of leaked NSA papers released by Snowden, the researchers speculate that the NSA can break much of current crypto.
First of all, update your browser, since all of them (IE in May 2015, Safari and Mozilla in June 2015, Chrome in September 2015) have provided fixes for defeating this vulnerability. Then if you run a server, you should disable support for export cipher suites and use a 2048-bit Diffie-Hellman Group.
So what should we learn from this? As is always the case in security, the mathematics work but the implementation and configuration are the weakest links in the chain most of the time.


Infinity puzzles are jigsaw puzzles with no beginning and no end. They have no fixed shape, no starting point, no edges, and can be assembled in thousands of different ways.
The “Infinity Puzzle” is based on the Klein bottle, a non-orientable surface; it is a two-dimensional manifold against which a system for determining a normal vector cannot be consistently defined.
The puzzle, created by Nervous System, is configured using science, math, and lasers. “Our infinity puzzles build on that tradition with a new mathematical twist that would be almost impossible with hand cutting, a puzzle that tiles in every direction,” the company wrote on their blog.
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Online Exam » Aptitude » Clocks
1. A clock is a circle which is divided into 60 minute spaces. The minute hand passes over 60 minute spaces. The minute hand passes over 60 minute spaces in one hour. By the hour hand goes over 5 minute spaces. In 60 minutes, the minute hand gains 55 minutes on the hour hand.
i. In every hour, both the hands coincide once
ii. When the hands are in opposite directions, they
iii. When the hands are at right angle, they are 15 minute spaces apart. This happens twice in every hour.
iv. The minute had moves through 6o in each minute whereas an hour hand moves through in each minute.
v. The hands of a clock are at right angles 44 times in a day.
vi. The hands of a clock coincide in 22 times in a day.
vii. The hands are straight (coincide and opp. direction) 44 times in a day.
2. Between x and (x+1) how they coincide at (5x) min. past x o’ clock.
3. Between x and (x+1) they will be right angle at (5x+15) min. past x o’ clock.


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Ever dream of a foolproof lottery system? Thanks to the wonders of 3D printing, you just may be able to make it a reality.
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In statistics, there are 3 common techniques to discover the average of a group of information. paramountessays com To locate the median, your numbers need to be listed in numerical order from smallest to largest, and that means you might need to rewrite your list before it’s possible to discover the median. If there’s a finite number of elements, the median is no problem to find.
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The second one is multiplied by a scalar to correct the brightness, causing an extremely dark red. To put it differently, it’s the value that is probably to be sampled. The end result is that k is going to be given the worth of 21.
You also ought to opt for a proper Function Type depending on your real circumstance. Science is full of rather big and very smallish numbers that are not simple to read and write. A High Dynamic Range representation of the image has a greater range than the normal 0-1 and so includes the appropriate luminances.
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Be aware that the number will appear with all its zeroes should they fit on the monitor. It’s possible to even press two numbers in sequence. It would have just become the number in the center.
Mean is the average of each of the numbers. It is basically the average number. It is only unique if the sample size is odd.
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Before you can start to understand statistics, you ought to understand mean, median, and mode. Median is the middle price, dividing the range of information into 2 halves. The mean is http://msnonline.arizona.edu/resources/webinars/ utilized to show us the authentic average of a set of information.
A median is effective if you get a high outlier or a very low outlier. It is basically the average number. It is only unique if the sample size is odd.
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Many forms of predefined glues exist to satisfy different needs that may arise with typesetting. The division by 2 comes from the simple fact a parallelogram can be broken into 2 triangles. This solution won’t return an answer once the angles cancel out to a very small magnitude.
It can be difficult to work out, as it’s the number found in the center of the set when they’re listed in numerical order! It’s possible to even press two numbers in sequence. The range of places have to be a non-negative integer.
The particular cases are the very same as for Log. At the base of the Function Body page, you can locate a group of controls called Quick Check which may help to look at the validity of the function. The results change significantly once you have a bigger selection of numbers.
In the event the end result of a single operation has more digits than specified, it’s rounded. There are two issues that have to be resolved. The median grade isn’t recalculated to take into consideration grade changes or resolution of incompletes.
Grouping brackets do not need to match in style. Most of the fundamental operations will act on an entire vector and may be used to quickly carry out a substantial number of calculations with a single command. The next example demonstrates the way the mgf of an exponential random variable is figured.
The mean of these distribution is 26. The mode is easily the most frequent member of the group. Probability is a means of describing the likelihood an event will occur.
It has average of 2, three or four numbers with different difficulty levels. To try to remember the definition of a median, just consider the median of a road, that’s the middlemost area of the road. You should not presume that your mean is going to be one of your initial numbers.
LaTeX fragments don’t need any special marking whatsoever. Most of the fundamental operations will act on an entire vector and may be used to quickly carry out a substantial number of calculations with a single command. Type these commands in MATLAB.
Still, we don’t need the extreme upper tail to have a lot of influence. Ultimately, there are different approaches to understand non-integer powers. There are many ways of entering greek symbols.
Later, you might want to read more about the way to include more packages and the way you can create packages of your own. For instance, if you take a look at the minimum of two vectors utilizing the min command you will find the minimum of all the numbers. The Lighter Color Blend mode is a bit more aggressive when it comes essay helper to applying the White areas of the best layer to the bottom layer.
By utilizing algebra, economists can build theories and structures which can be used with diverse scenarios regardless of specific quantities. Calculator manufacturers use it in order to display numbers in scientific notation because the longhand version is hard to display and would be even more challenging to read. By remembering this easy test, you’ll never should panic if you can’t remember the way your calculator works in the center of a test.


Differential Equations Notes & Study Guide
This semester I am taking differential Equations and this is a study guide/cheatsheet I’m writing to help me better understand my notes and to help anyone else understand the topic who maybe in similar boat.
A First Course In DIFFERENTIAL EQUATIONS with Modeling Applications (11th Edition)
Florida Polytechnic University
Note: I will try to not use textbook language wherever possible but I will include Book definition in some form to allow me to elaborate on what the book definition means.
Calc 2 skills such as
- Logarithms and their properties
- Complete the square
- Partial Fraction decomposition
Table of contents:
ii. Exam 1
iii. Exam 1 Summary
iv. Exam 2
v. Exam 2 Summary
vi. Exam 3
vii. Exam 3 Summary
viii. Final Exam
What is a Differential Equation?
“An equation containing the derivatives of one or more unknown functions ( or dependent variables), with respect to one or more independent variables, is said to be a differential equation (DE).”
The video above goes into detail about what this definition means but basically:
Differential Equations are equations written to express real life problems where things are changing and with ‘solutions’ to these equations being equations themselves. We are using math to represent real life scenarios, usually meaning a rate of change.
ie. beats per minute (bpm) , meters per second (m/s), or anything that isn’t exactly a finite value but rather a changing one.
Now to the goal in this class is to find the original function that has a derivative of the one in the equation you are given.
That may sound complex but this class is usually taken after Calculus 2 and that means Im assuming you have a simple understanding of Derivatives and integrals.
d/dx (x²) = 2x
and your job is to find:
integral of (2x)
which is x²+c
Where your answer is still a function but that’s very basic calculus, I will go back and write a Calculus 2 and 3 Article later but for now thats all you need to know.
Types of Differential Equations
Now the equations you’re given in differential equations problems will involve 1 or more derivatives of many unknown functions as defined below as ODE’s but eventually you will be doing Differential Equations with partial derivatives (PDE’s) from Calc 3 (More on this later)
- If a differential equation contains only ordinary derivatives of one or more unknown functions with respect to a single independent variable, it is said to be an ordinary differential equation (ODE)
2. An equation involving partial derivatives of one or more unknown functions of two or more independent variables is called a partial differential equation (PDE)
Initial Value Problems:
“ An initial value problem is an ordinary differential equation together with a specified value, called the initial condition, of the unknown function at a given point in the domain of the solution.”
To Solve the above:
y’ is equal to 𝑑𝑦/𝑑𝑥 in this case so:
Then we move the y+1 and 𝑑𝑥 around
Then Integrate both sides to get
Now to remove the ln we need to make each side the base of e^x
hint: e^[ln(y+1)] is just y+1
(𝑒^c) is still just C and we move the +1 to get:
𝑦= 𝑐𝑒^x -1
to arrive at the general solution of:
y = 𝑐𝑒^𝑥 -1
but the could be:
1𝑒^𝑥-1, 2𝑒^𝑥-1, 3𝑒^𝑥-1 etc.
The C represents a constant that we don’t know yet,
But we were given some initial condition in the problem y(0) = 5, then we can now use this to solve for our C value by plugging it in to our
5 = C𝑒⁰-1
5+1 = C𝑒⁰
5+1 = C(1)
and Then we get
which means C = 1
And this means we now have a single function answer of:
y = 6𝑒^𝑥 -1
as our solution, rather than a family of functions as a solution (The general solution)
We didn’t know that without knowing the initial condition but thats how we would solve for the C value given an initial condition but otherwise we just look for the general solution.
And thats only with there being one derivative which means the equation is of the first order.
First order differential equations:
The number of derivatives you have relates to the Order of the equation (equations with second derivates are said to be of the second order, equations with third derivative are said to be of the third order, etc)
for every extra derivative in your problem, you will get an extra C value which can be denoted
x being the order of derivative taken for that value
These Values are necessary for accuracy but eventually can be combined later so just make sure you never forget your +C
We will go into detailed examples but for now this is the basic theory behind the equations to help as it maybe a little tricky or obscure at first but we’ll get there.
Exam 1 :
Sections 1.1 to 4.2
Our professor is testing us on Chapter 1 through chapter 3 section 1 (3.1)
Here’s the notes we’ve covered of the chapters covered (not skipped)
This first exam will be on ODE’s of any kind using the different techniques covered so I will go through each of the techniques and when they would be used to solve a ODE
To solve Any Differential equation, you must first start by deciding on which technique is most suitable for the equation in question.
The most effective way solve ODE’s is through this list of techniques, checking to see if the equation can be solved by each method in this order.
Note: Most problems tend to be solvable through multiple techniques but the optimal technique will make your solution much easier which makes it so important to pick the correct and best method.
The later techniques above often will turn your original equation into an equation solvable by the earlier methods (ex. A Bernoulli can sometimes create a separable equation which are much easier to solve)
A differential equation is said to be separable if the variables can be separated. A separable equation is one that can be written in the form dy/dx. Once this is done, all that is needed to solve the equation is to integrate both sides. Our example in the introduction is considered a separable equation as with the one below:
- If you can split of the X and Y terms to be on opposite side of the equal sign, then it is a separable equation
- Once separated, take integral of both sides
A differential equation can be homogeneous in either of two respects. A first order differential equation is said to be homogeneous if it may be written f(x,y)dy=g(x,y)dx, where f and g are homogeneous functions of the same degree of x and y. In this case, the change of variable y = ux leads to an equation of the form dx/x=h(u)du, which is easy to solve by integration of the two members.
- Every term must be of the same degree
A substitution problem is essentially a problem where you do a u-substitution for portion of the problem to make the problem easier to manipulate or solve.
Usually look for a term that when replaced with a u, makes the problem simpler
dy/dx =( some term)² could be u = some term
and hopefully you’d get
u = some term
dy/dx = du/dx + d/dx( some term)
You then substitute in your u term and new dy/dx term
and solve accordingly
- Can be made separable
4. Linear (y or x)
To start a linear equation, you must first write it in standard form
y’ P(x) + y = Q(x)
Once this is done, the integrating factor is
I(x) = e^integral of P(x)dx
And then the general solution is now
y = 1/I(x)[integral of I(x)Q(x) dx + C]
5. Bernoulli (y or x)
Basically, if in the form M(x,y) dx + N(x,y)dy = 0,
then you can separate the
M(x,y) and N(x,y) terms
Take the partial derivative of each of x and y and if they are equal,
your equation is exact.
7. Integrating Factor
Format your equation as such:
y’ + yP(x) = Q(x)
Integrating factor → I(x) = e^integral(
Use accordingly (Look at exact)
y = 1/I(x) * int[ I(x)*Q(x) + C ]
Growth & Decay
rate of change of x with respect to time
Modeling with First order Differential Equations
Now that you’ve practiced these different techniques for solving differential equations, Our next objective is to apply these differential equations to rate of change problems that we can now solve now that we’ve created am equation of the differential type.
Usually our differential equations are either separable or non-separable.
If separable, split up the variables and integrate
If not separabale, we must
- Label the variables in the equation
- List any given constants or given initial conditions
- Write out equation in terms of words/variables
- Write equation in standard form
- Solve this differential equation
- Plug in the initial condition in to get C
Exam 1 Summary
The best way to go about first order differential equations
- Does the problem fall under SHEILDS — Separable, homogeneous, Exact, Linear, Direct Integration, or Substitution. (I know the order is different but shields is a good acrynonm
- Separate the variables into the dy and dx terms on the respective sides of the equal sign and then integrate and solve in terms of y
- Replace y = ux or x = vy
- Find dy/dx and then substitute in y or x and dy/dx
- Integrate the two sides
- Look at the equation and see if you can identify a M(x,y) and N(x,y) term which is set equal to 0
- Find the partial derivative of M(x,y) and N(x,y) and see if they are equal
- Put the equation in standard form:
y’+yP(x) = Q(x)
Your integrating factor is now
I(x) = e^integral(P(x))
You then multiply the equation by your integrating factor
I(x)* y =integral ( I(x) * Q(x) dx
For Direct Integration
- Just integrate the equation, shouldn’t be too complicated
- If the equation can be made simpler, substitute in a u = some term and then find du and apply that to the equation
When given a modeling word problem, you need to memorize a couple of different problem types and their associated differential equation type so that you can solve for their general solution and for C if given the initial conditions
Bacterial Growth, Half-Life of Plutonium, Age of a Fossil
dx/dt = kx or dA/dt = kA
Cooling of a Cake
dT/dt = k(T-70)
Mixture of Two Salt Solutions
dA/dt = (input rate of salt) -(output rate of salt) =>R in — R out
Exam 2 :
Sections 4.2 to 7.1
Reduction of order
Homogeneous Linear Equations with Constant Coefficients
Undetermined Coefficients — Superposition Approach*
Undetermined Coefficients — Annihilator Approach
y’’ + y’ + … = 0
y c: complementary function
y p: particular solution
y p = u1(x)cosx + u2(x)sinx
u1(x) = negative integral of y2 f(x) / w(x) dx
u1(x) = integral of y1 f(x) / w(x) dx
w(x) is the Wronskian
To find wronskian we do a crossproduct of |y1 and y2|
y = yc + yp
Exam 2 Summary
At the present moment in time, classes were now moved completely online meaning we did receive a lecture video review which I will be breaking down into sections, steps and explanations as best I understand.
The video that was made to cover our second exam material is from sections 4.1 to 4.8 and it is mainly solving homogenous and non-homogenous linear differential equations.
I took hand written notes that can be found here
I will write out verbal explanations with light equations due to the inability to type the mathematics properly with sub notation but I will do my best to describe steps in full
Topics and Examples
Prove that given solutions are indeed solutions to the homogenous, linear, second order differential equation
Show that [e^x , e^-3x] is a fundamental set of solutions of the equation
y’’ + y’ — 6y=0
First we must check if the given solutions are linearly independent or not
so we use each of the provided solutions as inputs for y and take their respective first and second derivatives to see if they satisfy the equation.
In this problem the y’s and their derivatives satisfy the differential equation so now we must check if they are linearly linearly independent by finding the general equation and since the equation is a second order differential equation so there are only two solutions.
so e^(2x) & e^(3x) are our f(x)1 and f(x)2
To find the general solution we need to find the wronskian which is
the cross product of the f(x)’s and their derivatives.
If the final solution is never 0 then the solutions are linearly independent
In this case e^(2x)•-3e^(-3x) + -2^(2x)•e^(-3x) = -3e^(-x) — 2e^(-x)
- This equals -5e^-x so they are linearly independent
- Therefore both of the provided solutions are the fundamental set of solutions
Reduction of order formula
Given the equation: x²y’’ — 3xy’+4y=0 and the solution: y1 = x² ,
Find the other solution
This is a second order linear differential equation that has a non-constant coefficient so we take the original equation and divide by the term in front of the y’’ to get it by itself
In this case we divide by x² to get
y’’ — 3y’/x + 4/x²y = 0
The coefficient of y’ is P(x)
The coefficient of y is Q(x)
Now at this point we need to use the reduction of order formula
Then using this formula we can plug in and solve for the the second solution the to the differential equation.
Find the general solution of the homogenous linear equation
Solving non-homogenous differential equations using the method of undetermined coefficients
Solving non-homogenous linear differential equations with constant coefficients using the method of variation of parameters
1.1: Definitions and Terminology
1.2: Initial-Value Problems
1.3: Differential Equations as Mathematical Models
2.2: Separable Equations
2.3: Linear Equations
2.4: Exact Equations
2.5: Solutions by Substitutions
3.1: Linear Models
4.1: Preliminary Theory — Linear Equations
4.2: Reduction of Order
4.3: Homogeneous Linear Equations with Constant Coefficients
A homogeneous linear ordinary differential equation with constant coefficients is an ordinary differential equation in which coefficients are constants (i.e., not functions), all terms are linear, and the entire differential equation is equal to zero (i.e., it is homogeneous).
4.4: Undetermined Coefficients — Superposition Approach*
4.6: VARIATION OF PARAMETERS
Thanks for reading! Buy me coffee? https://ko-fi.com/jonngan


From EP 4, we could know all 3 types of Linear regression. Linear regression is just one of 4 Machine Learning (ML) algorithms.
Supervised Learning is ML on labeled output and we use the label to train our models. For example, we have data of age and income. We want to predict income at any age as labeled output is income.
In other hand, Unsupervised Learning is working on unlabeled output that means we have no initial result data to train models. We will talk about this later.
And Continuous means quantitative output as Discrete means qualitative output.
As the figure above, there are main 4 ML algorithms:
Discrete Supervised Learning. This is for predicting group in limited values. For example, we want to predict which group of interests for a customer when we have customer data as ages, occupations, genders, and interests.
Continuous Supervised Learning. This is to predict output as it can be any values. The example is the previous episode.
Discrete Unsupervised Learning. It is to group our data. For example, we want to group customers into 8 types leading to the hit advertisements from customer data.
- Dimensionality reduction
Continuous Unsupervised Learning. This is working on data optimization. One day we will have tons of data in thousands columns, and Dimensionality reduction helps us find the most important columns to deal with in terms of data processing.
And this time, I am proud to present…
Logistic Regression predicts the probability. Despite its name, its algorithm is classifier as the result is a member of labeled output.
Now it’s the time.
We reuse Titanic data again. Assign
x as “Pclass”, “is_male” that is calculated from “Sex”, “Age”, “SibSp”, and “Fare”.
y as “Survived”. We are going to predict the survivability.
Utilize the module
sklearn.linear_model.LogisticRegression() and run
solver='lbfgs' to avoid a warning.
fit(). Just peeking
coef_ and find the second column, “is_male”, has negatively impact on “Survived”.
Once we get the model then go to test. We create a crew with “Pclass” is 30, male, no “SibSp”, and paid 25 as “Fare”.
Our model predicts he was dead (“Survived” is 0). Please mourn for him 😢.
.predict_proba() and we realize his survivability is just 10%.
Ok. Let’s see the correctness of the model. We create a
DataFrame to combine “Survived”, predicts, and a correction flag as “is_correct”.
Average correctness of our model is 83%. Quite great.
Besides, we shall meet Dummy Classifier. This one provides the “baseline” classification model. It means we can apply this as a standard to evaluate our model.
Dummy Classifier run the model with simple rules and we can define the rule by the parameter
strategy. This time is “most_frequent” that is to predict base of frequent values of the training set.
Now we check the baseline correctness as it is just 52.7%. Our Logistic Regression model above works.
Classifiers is useful for data categorizing works and I hope this blog can be great for you to understand ML overview.
Let’s see what’s next.


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Institute of Mathematics and Informatics
Bulgarian Academy of Sciences
Eight International Conference
New Trends in the Applications of Differential Equations in Sciences (NTADES 2021)
6-9 September 2021, Sts. Constantine and Helena (Bulgaria)
The conference will be held in the Joliot-Curie International House of Scientists, St. Constantine and Helena, Bulgaria.
Last modified: 2021-01-13


How do I interpret the test results?
These tests are for potency and the units are mg/g or mg/1000mg. So, if you’re interested in the percentage of cannabinoid in a given product, you just move the decimal over three spaces. Ex: 2.6mg/g = .0026g/g or 0.26%.
To calculate the amount of CBD in your product, you multiply the mg/g by 29g/bottle (oil is less dense than water so 30ml weighs 28.8g). So for our Calm tincture, 37.2mg/g x 28.8g = 1071mg CBD.
In our high-potency tinctures, one bottle contains ~1000mg CBD which translates to 1.2mg CBD per drop (there are slight variations in drop size depending on the viscosity of the oil).
Our products are high potency, full-spectrum and all guaranteed to be below 0.3% THC.
Start low and go slow. Begin with 4 drops-1/4ml (5-8mg CBD) and slowly work your way up to what is ideal for you.


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A car accident in 1975 stops time for a gifted math professor, after which he can only remember what has happened in the last 80 minutes. He lives his life through numbers as he draws correlations from birthdays, phone numbers, and shoe sizes to snippets of his past. Every morning the professor meets his housekeeper and her 10-year old son anew. Together the three of them learn about the beauty of numbers and what it means to live in the present. Praise for Yoko Ogawa’s The Housekeeper and the Professor has come from the New York Times, the San Francisco Chronicle, the Guardian UK, and UHS Math Department’s own Minh Nguyen:
“What is the most beautiful equation (or result) in mathematics? Ask a number of mathematicians and you will get many different answers. In Yoko Ogawa’s beautiful novel, The Housekeeper and the Professor, you can find out the Professor’s favorite. But along the way, you will learn, among other things, about memory, love, giving, baseball, and, of course, math. Yet the most remarkable of Ogawa’s feats is not so much how she finds a way to weave so many topics (and math nuggets) into a book, but how her simple and elegant prose makes you feel a deep sense of compassion for all the characters. Ultimately the novel is about humanity, despite a Plato-nistic view of mathematics, it’s not really about the purported most beautiful equation, it’s really about the beauty of math (and the present moment).”
Don’t just take Minh’s word for it (although I would!), read a passage of The Housekeeper and the Professor for yourself.


Myra Norton is the President & CEO of Arena, a technology company that helps organizations vitalize, stabilize, and diversify their workforces to improve organizational performance and impact. Previously, she was the CEO of Community Analytics, an analyst at Northrop Grumman, a professor in Mathematics and Statistics at Temple University, Towson University, and the US Naval Academy, and an Administrator in the College of Science & Technology at Temple University. She serves as Immediate Past Chair on the Executive Committee of TEDCO, an organization founded to serve and expand the entrepreneurial ecosystem in the State of Maryland. She also chairs the BmoreSTEM Infrastructure Workgroup, working to increase student access and retention in STEM fields.
Norton has been featured as a presenter, speaker and facilitator at several industry events such as the AHA Leadership Summit, ACHE Congress on Healthcare Leadership, SXSW, and several Modern Healthcare events. She has collaborated with researchers from Harvard University, Babson College, University of Virginia, the National Institutes of Health, University of Maryland, and the University of Chicago.
Norton graduated from the University of Alabama as a Faculty Scholar, earning a BS in Math Education, and was then awarded a Future Faculty Fellowship and earned an MA in Mathematics and an MS in Statistics at Temple University.


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How to calculate loans using online calculator to calculate the loan amount
How to calculate the loan amount. Home loan calculator. The amount you borrow when you take out a home loan is called the loan amount. An interest rate is a term used in finance that refers to the amount of money you must pay the lender. Loans (such as mortgages and car loans) typically carry interest rates that go up over time. Fixed rates (also known as. I have a rate of 5.,000 fixed and I have to pay 4,000 on it. I have a rate of 5.00 and I have to pay 4.00 for it. I have a rate of 4.25 and I have to pay 3.50 on it. How to calculate the amount of interest you will pay on your home loan.
calculating mortgage payments – How to calculate mortgage payments.
You can use this online Calculator to calculate loan amounts, mortgage payments, loans on cars, education loans etc.


Mrs. Lahar’s 3rd Grade
We begin 2016 with renewed enthusiasm for learning!
For math instruction, the 3rd graders are in the Eureka Math program. We have just started a unit focusing on place value and
problem solving using units of measure. This unit will include problem solving using time, measuring using weight and volume and rounding to the nearest ten and hundred. We will also learn and use the standard algorithm for addition and subtraction.
At the end of math class, the 3rd graders have time to practice their facts. By the end of 2nd grade, it is expected that students know their addition and subtraction facts. By the end of 3rd grade, they need to know their multiplication facts. Each 3rd grader is working on the facts they still have not mastered. Some students are still working on addition and subtraction. While others will soon be pushing themselves to learn their division facts.
During our literacy time, we have been using the Reader's Workshop model. We begin with a whole class read aloud and a minilesson on a specific skill or a reading strategy. Then students practice the skill or strategy by independently reading. While students are independently reading, I conference with individual students or I meet with small reading groups. Reader's Workshop is an approach that provides students with the conditions that are supported by reading research. We will be focusing next on the skills needed to read nonfiction.
In addition to Reader's Workshop, students are challenging themselves to read and test on books through the Accelerated Reader program. After reading and successfully passing a test on five books, students choose a small prize. For each additional five books, they may choose another prize. Prizes are also given out at the end of the school year to students that participated.
In writing, we are focusing on information writing. We will be working hard to create organized pieces with many paragraphs.
We have gotten off to a great start in 2016! If you have questions or concerns, please contact me (firstname.lastname@example.org).


The Statistical Society of Australia (SSA) will host the Early Career & Student Statisticians Conference (ECSSC) 2021 virtually from July 26th to August 1st 2021. As part of the conference, we have set side a day (July 31st 2021) for our future budding statisticians! High school students (year 7 – 12), or teachers of high school and primary students are encouraged to join in the conference.
Workshop: An introduction to statistical programming and analysis
The day will begin with a hands-on workshop were students and teachers will be introduced to the freely available software package R and learn the fundamentals of statistical programming (no experience required!). Participants will have opportunities throughout the workshop to implement what they learn as they work through a statistical problem, from data exploration to data visualisation and more. Our workshop presenters are experienced R users and statisticians, spanning industry and academic researcher.
- Dr. Emi Tanaka, Department of Econometrics and Business Statistics, Monash University
- Dr. Kevin Wang, Statistician at CSL Behring
- Patrick Robotham, Nimble Australia Pty Ltd
- Daniel Fryer, Department of Mathematics and Physics, The University of Queensland
High School Day Career Panel
Following the workshop, a careers panel will provide information on the many possible career pathways in statistics and how to navigate statistical learning. Hear from recent statistics graduate and early career statisticians on there experiences studying statistics at varying levels of education, and how they use data in their everyday work to solve a wide variety of problems.
Soraya McPhail is a current methodology graduate at the Australian Bureau of Statistics, ABS. She completed a Bachelor’s degree in Economics, Mathematics and Statistics at the University of Western Australia in 2020. At the ABS, Soraya works within the Statistical Methodology Branch, where she assists her team in providing statistical and sampling advice to ABS Business Surveys. Over her short time at the ABS, Soraya has worked on a wide range of projects including investigating the feasibility of using administrative data for ABS publications, confrontational analysis, sample design and estimation support for internal ABS clients.
Ever since graduating from Macquarie University in 2018, I have had the opportunity to work across multiple sectors, industries and organisational scales. From being an analyst at Australia’s largest debt purchaser to catching internal fraud for Westpac, and now with NSW Health as a Trainee Biostatistician. Let me just tell you, I’ve been in the trenches and I’ve seen some things. So, if you got what it takes, let me share my insights about this wild world.
Dr. Elena Tartaglia
Dr. Elena Tartaglia is a Research Scientist at CSIRO’s Data61. She is part of the Analytics and Decisions Sciences program and mainly works on consulting projects with external clients. Elena completed her PhD in Mathematics at the University of Melbourne in 2016 and moved into data science three years ago. Since joining Data61, she has used statistics and data science to solve problems in manufacturing, education, risk management and bushfire prevention.
Registration is free of charge for school students. Simply upload a copy of your student ID at the time of registration as proof of your student status. As part of your registration, you will also have access to all other conference days which include an amazing line-up of keynote speakers from all occupations, and a diverse range of selected talks from early career & student statisticians.
Register for the conference!
Online registration and information on the conference, keynote speakers, workshops, and abstract submissions are available at: http://ecssc2021.com.au/.
A number of door prizes will be drawn during the High School Career Day, courtesy of the Australian Research Council Centre of Excellence for Mathematical & Statistical Frontiers (ACEMS). These will include some introductory statistical textbooks and book vouchers to help foster your learning in statistics!
If you have any questions, concerns, or feedback, please contact the ECSSC Chair via email at firstname.lastname@example.org.
We look forward to welcoming you to our conference!


In a previous post, I argued for restricting the Law of Likelihood to mutually exclusive hypotheses and claimed that this restriction would not exclude cases of genuine scientific interest because scientists don’t test hypotheses against one that are not mutually exclusive.
Chandler (2013) argues for this restriction as well. He considers the objection that Forster and Sober (2004) claim that in the context of model selection, scientists sometimes say that data favor a given model over a logically weaker one. For instance, they might say that a set of observations of a variable Y taken for different X values that fall roughly along a straight line favor the model (LIN) according to which Y is a linear function of X plus a noise term over the model (QUAD) according to which Y is a quadratic function of X plus a noise term. But (LIN) is a special case of (QUAD) obtained by setting the coefficient of the X2 term in (QUAD) to zero. Thus, the scientists who speak in this way are speaking of an evidential favoring relation between compatible hypotheses. As a result, restricting the Law of Likelihood to apply only to mutually exclusive hypotheses excludes cases of genuine scientific interest.
Chandler’s response to this objection is that, “as Forster and Sober use the term, ‘E favors model M1 over model M2’ is actually shorthand for ‘E favours the likeliest (in the technical sense) disjunct L(M1) of model M1 over the likeliest distinct of model M2,’ with L(M1)∩L(M2)=∅.“ This reply may be true, but it does address the whole problem. Forster and Sober may use the phrase “E favors model M1 over model M2” in this way, but scientists use it in other ways as well. For instance, they might use the phrase “E favors (LIN) over model (QUAD)” to mean their data favors the claim that the element of (QUAD) that is closest to the true model in some sense has a nonzero coefficient for the X2 term over its negation. If they are a bit more sophisticated then they will realize that it is implausible in typical applications that the coefficient of the X2 term is exactly zero. What they might mean instead is that their data favors over its negation the hypothesis that a nonzero coefficient for the X2 term is necessary for producing a statistically adequate curve, meaning roughly a curve the residuals of which look like white noise to a degree that is adequate for their aims.
On both of these interpretations, “E favors (LIN) over (QUAD)” actually means “E favors (LIN) over (QUAD)(LIN).” In general, when scientists talk about evidence favoring one model over another when those models are nested, they typically mean either that it favors the best element of the first over the second or that it favors the smaller model over the set-theoretic difference of the larger model minus the smaller model or vice versa. Unless there are cases in which scientists clearly mean what they say when they speak of evidence favoring one model over another when those models are nested, such examples do not indicate that there are cases of scientific interest that involve testing compatible hypotheses against one another.
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Vedic maths: multiplying numbers by 11-19 in less than five seconds. Multiplying tens multiplying a 2 digit number multiplying hundreds multiplying a 3 digit number multiplying with renaming multiplication of two digit numbers multiplication the four basic operations multiply 2 by 2 digit numbers multiply 3 by 2 digit numbers multiply 3 by 3. Kids learn about long multiplication including the steps needed such as lining up the numbers, adding zeros, and adding the total. Multiply two numbers - powered by webmath webmath - solve your math problem today explore the science of everyday life click here for k-12 it doesn ' t just give you the answer the way your calculator would, but will actually show you the long hand way to multiply two numbers this selection can be sort of fun. Fun math practice improve your skills with free problems in 'multiply numbers ending in zeroes' and thousands of other practice lessons. 10 ways to do fast math: tricks and tips for doing math in your head you don't have to be a math teacher to know that a lot of students—and likely a lot of parents (it's been awhile) step 1: take the number being multiplied by 5 and cut it in half, this makes the number 4 become the number 2 step 2.
Well leilani, the number goes to a used arithmetic-part store, and borrows what he needs no ok alright so in mathematics, regrouping (borrowing) is the reorganization of numbers from one column to another to perform addition and subtraction equations typically, regrouping is referred to as “carrying” and. To multiply decimal numbers: multiply the numbers just as if they were whole numbers line up the numbers on the right - do not align the decimal points starting on the right, multiply each digit in the top number by each digit in the bottom number, just as with whole numbers add the products place the decimal point in the. Students are always happy to learn shortcuts to solving math problems therefore, your students will be eager to know about regrouping when multiplying for example: multiplication problem your students can then adapt these same concepts to multiplying with numbers that contain zeros using the distributive property.
Multiplying large numbers is fully explained learn how to multiply large numbers step by step you will bean expert in no time my name is chris and my passion is to teach math learning should never be a struggle which is why i make all my videos as simple and fun as possible i cover all subjects from. In this topic, we will multiply and divide whole numbers the topic starts with 1- digit multiplication and division and goes through multi-digit problems we will cover regrouping, remainders, and word problems. Method 1 multiplying numbers not close to one hundred write down your numbers sitting on top of each other, like you would do when multiplying normally image multiply multiply the numbers in the ones place and put the product directly under the ones. Here's a way to multiply numbers visually suppose you want to multiply 22 by 13 draw 2 lines slanted upward to the right, and then move downward to the right a short distance and draw another 2 lines upward to the right (see the magenta lines in figure 1) then draw 1 line slanted downward to the right, and then move.
Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction relate the strategy to a written method and explain the. Other articles where multiplication is discussed:a second binary operation called multiplication is defined the number 5 is called the multiplicand the number 3, which denotes the number of summands, is called the multiplier and the result 3 × 5 is called the product the symbol × of this operation is read “times ” if such. Japanese kids learn to multiply with a completely different method than the one kids in the us do the japanese math voodoo/magic is more of a visual technique where you draw lines and count the intersections.
Ever dreamed of being able to multiply large numbers in your head math dude provides 5 easy tips to help you become a master of mental math. In table 1, we are multiplying the decimal 02658 by powers of 10 each time we multiply by a power of 10, the decimal point is moved one place to the right in table 2, we are dividing the whole number 265,800 by powers of 10 each time we divide by a power of 10, the decimal point is moved one place to the left. Multiplication tricks for mental math in this post will let you do multiplication faster than a calculator there are many multiplication tricks to do mental math, but the ones covered here can be applied to multiply any set of numbers learning the techniques in this post will be like learning to ride a bi-cycle once you learnt it, it is. This visual method is very valuable to teach the basis of multiplication to children however, it isn't very useful when handling large numbers the math behind the fact: the distributivity of multiplication the method works because the number of parallel lines are like decimal placeholders and the number of dots at each.
Instructor: yuanxin (amy) yang alcocer amy has a master's degree in secondary education and has taught math at a public charter high school in this lesson, you will learn how to multiply numbers that end in zeroes you will see that multiplying numbers that end with zeroes is an easy process that requires some counting.
Multiplication is one of the four elementary mathematical operations of arithmetic with the others being addition, subtraction and division the multiplication of whole numbers may be thought as a repeated addition that is, the multiplication of two numbers is equivalent to adding as many copies of one of them, the. Here is another math trick that will help you multiply any given number with 25 and 125 in your head and under 5 seconds just follow these simple steps. When we think about multiplication, we usually think of the times tables in my opinion, you should not teach your child the times tables until he or she understands what it means to multiply two numbers after your child has understood the concept, then the times tables are useful as a short cut to carrying out the.


Within the 2014 National Curriculum maths falls into two areas, arithmetic and reasoning.
At Dymchurch Primary School we follow the White Rose Scheme of Work in maths to ensure that across all year groups children are being taught skills which are essential to achieve success.
Arithmetic skills and fluency in calculation is key to achieving well in reasoning.
Oral and mental mathematics is essential, particularly so to aid speedy calculation; this being so, we have MOG Maths (Mental and Oral Games) daily.
By ensuring children develop this knowledge we are laying the foundations of success. We provide children with a good understanding of how the four operations build on efficient counting strategies. We know the importance that a secure knowledge of place value and number facts has, so ensure that children develop these skills.
We follow Singapore maths strategy of concrete, pictorial, and abstract understanding.
Children use practical apparatus to give hands-on learning experiences. They may use concrete objects such as counters, dice, or cubes, as the visual and kinaesthetic ‘hook’ to help them process this their understanding of a concept.
drawing pictorial representations of mathematical concepts e.g. drawing circles to represent the counters they were using in their earlier learning.
Students then solve mathematical problems in an ...
way, by using numbers and symbols to represent the calculation. Once arithmetic has been taught in this way, the children move to reasoning questions where they problem solve using the skills they have previously honed.
The ability to calculate mentally forms the basis of all methods of calculation and has to be maintained and refined. A good knowledge of numbers or a ‘feel’ for numbers is the product of structured practice and repetition. It requires an understanding of number patterns and relationships developed through directed enquiry, use of models and images and the application of acquired number knowledge and skills.
The National Curriculum demands that by Yr4 children have instant recall of all multiplication facts
up to 12x12.
Times tables are crucial, and are learned through KS1 and into KS2. We have the Times Table Factor Challenge for KS2 children in school. The National Curriculum demands that by Yr4 children have instant recall of all multiplication facts up to 12x12. Through challenges and practice we are engaging children in achieving this target. In upper KS2 we move to mental calculation of decimals – it is challenging, but our pupils are rising to the challenges set.
Children will develop the ability to use what are commonly known as ‘standard’ written methods – methods that are efficient and work for any calculation, including those that involve whole numbers or decimals.
By the end of Key Stage 2, the great majority of children should be able to use an efficient written method for each operation with confidence and understanding. Children will develop the ability to use what are commonly known as ‘standard’ written methods – methods that are efficient and work for any calculation, including those that involve whole numbers or decimals. They are compact and consequently help children to keep track of their recorded steps. Being able to use these written methods gives children an efficient set of tools they can use when they are unable to carry out the calculation in their heads. We want children to know that they have such a reliable, written method to which they can turn when the need arises.
We have a clear calculation policy which develops skill progression in the strategies used to makes calculations. Our curriculum has a thorough coverage of all elements of mathematics and we use the White Rose Scheme of Work to support the curriculum. Children engage daily in mental maths skills through timed papers, games paired work and challenges. The maths curriculum crosses over in to many areas of learning so children apply skills in other areas of learning such as Science and Cookery
For further information on the Maths curriculum and assessment criteria for your child(ren)s year group please see the Assessment page.


Evolutionary theory is attractive for the same reasons that theoretical physics is: there is the hope of solving some of the mysteries of existence. Evolution takes on additional meaning because the mysteries are not just about “stuff”, but about life itself. Evolution is a fertile field for emergent phenomena, both within the products of evolution – the organism – and in the dynamics of evolutionary change itself. Mathematics is the discipline that enables one to explain these emergent phenomena. By “explain” I mean to show relationships between things that no one suspected or understood.
Adaptation and diversification are spectacular emergent phenomena in and of themselves. But evolutionary dynamics are rich enough to host other, higher order phenomena. I have focused on identifying and explaining phenomena in evolution beyond adaptation and diversification. These include the evolution of inheritance mechanisms (i.e. the maintenance and expansion of information in the organism and species), the evolution of evolvability, and the evolution of modularity in the genotype-phenotype map.
These phenomena appear in evolutionary computation as well. Evolutionary algorithms are computer programs that solve problems by evolving the answers in analogy to Darwinian evolution with artificial or natural selection. I have introduced the evolution of evolvability and Price’s equation into the evolutionary computation literature. The theory of evolutionary computation has many attractive open questions.
When the analysis of these questions becomes mathematically difficult, one has two options. The first option is computer simulation – numerical results can provide illustrations of phenomena. But as Murray Gell-Mann astutely said, “What is the point of studying a complex system that we don’t understand by making a complex computer model that we don’t understand?” The second option is to hunker down and find the mathematical results one needs or produce them oneself. I have pursued all of these options.
For some of these problems, the mathematic analysis leads one to matrix theory. The student of complex systems hears at the beginning that nonlinear dynamics are the fountain for complexity. A closeup lens on nonlinear dynamics often reveals eigenvalues and eigenvectors as the key objects in analyzing the larger system. Eigenvalues and eigenvectors are themselves emergent properties of linear operators. Much of my research has therefore focused on understanding that “first emergent property”, the spectral properties of matrices and linear operators. Some biological questions have results from the linear algebra literature there waiting for them; others require new mathematics to answer. I pursue such results as the logic of the phenomenon in question requires.
The process of organic evolution has produced spectacular results and left many mysteries. Nothing is more pleasing that to shine a little light on some of these mysteries.
Learn more at http://dynamics.org/Altenberg/
Contact Lee at firstname.lastname@example.org


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In society different jobs tend to have different levels of recognition or acclaim. Those that are athletes tend to receive the most publicity and mainstream recognition. People like scientist and mathematicians are always regarded as the most impressive and most people would be proud to say that they are a doctor in a scientific or math-based field of study. One person who embodied what it is to be a mathematician despite these societal notions is Michael Lacey. His work will help develop our next phase and is important to the future.
Michael Thoraeu Lacey was born on September 26, 1959. He was always intelligent and attended the University of Illinois at Urbana-Champaign. He studied faithfully and received a PhD in 1987. This was under the direction of Walter Philipp. It was apparent that even from this early age that Lacey was special at math as his thesis was on Banach spaces. This early worked solved an issue to do with the law of iterated logarithm of empirical characteristic functions. After this early breakthrough he did work in the mathematical fields of primarily harmonic analysis, probability, and ergodic theorem. He soon got his first job following his doctorates degree. This was as a professor at Louisiana state university and the university of North Carolina in Chapel Hill. While here he worked with Walter Phillippe and contributed to the almost solved central limit theorem helping close the book on it. He continued to work, study, discover, and teach for many years. During a tenure at Indiana State University he began a study on the Hilbert Transform which was the topic of much debate at the time. Michael Lacey along with Christoph Thiele solved it in 1996 to much acclaim and a Salem Prize. Lacey remained with Indiana University from 1989 to 1996 and received a National Science Foundation Postdoctoral fellowship membership for his work and studies.
Michael Lacey has contributed to mathematics a vast amount over the years. As recently as 2004 he received a Guggenheim Fellowship for work with Xiachun Li and became a member of the American Mathematical Society in 2012. Lacey’s ability to balance life as a professor and mathematical problem solver is impressive and he has received many awards. Though he probably doesn’t care about mainstream popularity I hope one day he and many other scientist and mathematicians get mainstream coverage to match their prestigious awards.


Information on how to start and run a singles leagueDarts is a numbers game. We like to use number to determine where people should play. Yes, there are levels; there are levels in every single sport out there and our goal is to get EVERYONE playing darts and wanting to be competitive.
Not every player can be at the top, but that doesn't mean they are not competitive and trying the best they can. By offering different levels of play with a statistical tracking method for advancement, we're trying to encourage new or lower players to improve.
Each PlayDartsAmerica league is designed to last about 1 hour 10 minutes, so you can have different levels of play going on at the same time and have your schedules work out the same.
|League||3-dart avg / darts per game / Darts Index||Format||PlayDartsAmeria|
|Other League Comparison|
|Premier||71+ / < 22 darts per game / <= 7.0||Best of 18||Masters||A+ or AA|
|1||60+ / < 26 darts per game / <= 8.4||Best of 16||AA||A or AA|
|2||52+ / < 30 darts per game / <= 10.0||Best of 12||A||A|
|3||42+ / < 36 darts per game / <= 12.0||Best of 8||B||B|
|4||31+ / < 48 darts per game / <= 16.0||Best of 6||C||C|
|5||Under 31 / 48+ darts per game / > 16.0 )||Best of 4||D||D|
You can start with as little as 2 players and you can have a league. Granted the more players you have the better, but anyone can start with the smallest amount. Our first associated league started with 2 players 3 years ago and now has 5 different venues across multiple skill levels.
More details to come soon...


Having the use of money for a period of time has value, a value that is real and measurable. Borrowers pay and lenders or investors receive interest for use of As long as the interest rate and the time period are reasonably small, then compounding won't have much effect so 5% for 10 years is 5%*10=50% plus a bit. 24 Sep 2015 CAGR is used to measure the value of an investment and its growth over a given period of time to estimate the total return on a particular Compound Annual Growth Rate - CAGR: The compound annual growth rate (CAGR) is the mean annual growth rate of an investment over a specified period of time longer than one year. The compound growth rate is a measure used specifically in business and investing contexts, that indicates the growth rate over multiple time periods. It is a measure of the constant growth of a data series. The biggest advantage of the compound growth rate is that the metric takes into consideration the compounding effect. Compound annual growth rate (CAGR) is a business and investing specific term for the geometric progression ratio that provides a constant rate of return over the time period. CAGR is not an accounting term, but it is often used to describe some element of the business, for example revenue, units delivered, registered users, etc. CAGR dampens the effect of volatility of periodic returns that
Here's a look at how to calculate compound interest. The simplest way is probably to just take your starting balance and multiply it by the interest rate: $1,000 times 0.05 (for a 5% interest rate) gives you $50, which is 5% of $1,000. Add that to the starting balance, and your ending balance is $1,050,
CAGR stands for the Compound Annual Growth Rate. It is a measure of an investment’s annual growth rate over time. with the effect of compounding taken into account. It is often used to measure and compare the past performance of investments, or to project their expected future returns. CAGR, or compound annual growth rate, is a useful measure of growth over multiple time periods. It can be thought of as the growth rate that gets you from the initial investment value to the ending investment value if you assume that the investment has been compounding over the time period. Compound annual growth represents growth over a period of years, with each year's growth added to the original value. Sometimes called compound interest, the compound annual growth rate (CAGR) indicates the average annual rate of growth when you reinvest the returns over a number of years. Growth rates refer to the percentage change of a specific variable within a specific time period, given a certain context. For investors, growth rates typically represent the compounded annualized Calculate Compound Annual Growth (CAGR) The CAGR calculator is a useful tool when determining an annual growth rate on an investment whose value has fluctuated widely from one period to the next.
The compound growth rate is a measure used specifically in business and investing contexts, that indicates the growth rate over multiple time periods. It is a
Compound annual growth rate (CAGR) is a business and investing specific term for the geometric progression ratio that provides a constant rate of return over the time period. CAGR is not an accounting term, but it is often used to describe some element of the business, for example revenue, units delivered, registered users, etc. CAGR dampens the effect of volatility of periodic returns that Compound annual growth rate, or CAGR, is the mean annual growth rate of an investment over a specified period of time longer than one year. It represents one of the most accurate ways to calculate
Compound annual growth rate measures how an investment grows over a specific number of years. Investors looking at your small business examine the compound annual growth rate (CAGR) as a way to gauge past returns on investment in order to predict how their investments may pay off in the future.
The compound growth rate is a measure used specifically in business and investing contexts, that indicates the growth rate over multiple time periods. It is a 6 Jun 2019 IRR is also commonly used by venture capital firms to decide which company acquisition targets could provide the highest returns. What's the
13 Jun 2019 Compound annual growth rate (CAGR) is the rate of return that would be required for an investment to grow from its beginning balance to its
If you have no absolute values you can set the first year to 1 and construct an an annual index [prior period index * (1+ Annual Growth Rate)] for each year. The Compound Growth Rate of this calculated index, calculated using the Logest function as I suggested in above comments, will be the same as if you had all the actual values. However, simply use the RRI function in Excel to calculate the compound annual growth rate (CAGR) of an investment over a period of years. 1. The RRI function below calculates the CAGR of an investment. The answer is 8%. Note: the RRI function has three arguments (number of years = 5, start = 100, end = 147). The formula for Compound Annual Growth Rate (CAGR) is very useful for investment analysis. It may also be referred to as the annualized rate of return or annual percent yield or effective annual rate, depending on the algebraic form of the equation. Many investments such as stocks have returns that can vary wildly. CAGR or Compound Annual Growth Rate is one the most often used financial tool to evaluate an investment over a time period. You can use our online CAGR Calculator to easily get the CAGR value with in-depth table report and chart graphics. Calculate a Compounded Annual Growth Rate (CAGR) - Duration: 7:52. Doug H 85,339 views
8 Oct 2019 The Average Annual Return is a percentage figure used to report a historical return of a Compounding or Compound Annual Growth Rate. The average annual percentage growth rate for a series of n observations. The formula for determining the CAGR % is as follows: (((last value/first For example, if you wanted your business revenues to grow from $400,000 to $1 million over the next 10 years, you can calculate the annual growth rate you need 7 Apr 2011 But there's also a compound annual growth rate formula, often shortened But simple growth rates can also be used for other periods, such as 3 Aug 2016 Strictly speaking, it's not an accounting term, but it is often used by financial analysts, investment managers and business owners to figure out 7 Apr 2011 CAGR stands for compound average growth rate. The active word there is “ compound.” It means that the growth accumulates, like interest. So if


Welcome to Year 1
Firstly thank you so much to everyone for coming to join in with our Harvest celebrations on Friday. We hope you enjoyed it as much as we did.
Next week in Maths we will be ordering 3 groups of numbers from the smallest to the greatest and vice versa. We will then be ordering these numbers on a blank number line. In English we are revisiting the Three Little Pigs and thinking in particular about the Wolf who has gone missing! We will be planning and making our own missing wolf posters focusing on adjectives and descriptive phrases. In Art we will be taking a closer look at Autumn and will use leaves, pastels, paint and other media to create an Autumn scene. We will be looking at high and low pitch in Music, practising our computing skills using bug club and learning more about our value of the month - Happiness.
Maths at home
- Writing numbers 0-10 the correct way round. All numbers are written starting from the top.
- Use the vocabulary, greater than, more than, fewer than, less than and equal to and discuss what each mean.
- Practise ordering 3 numbers from 0 - 10 from smallest to biggest and vice versa. Where possible use every day objects eg pasta to help with representing each number first before ordering.
Don’t forget Infants parents evening this week. Tuesday 3.15 - 6pm and Thursday 5.00pm - 8.00pm
Thank you for your continued support.
Year 1 Team
Curriculum evening handouts:


Hello everyone! Welcome to my new video series called 300 Writing Prompts! I recently bought a book by the same title and I wanted to make it fun in allowing you all to choose random numbers between 1 and 300 and I will make the video based on the numbers you choose. If you want to see your number made into a video, please comment below. I can only do 10 requests at a time so please leave your number in a comment or feel free to put it in my inbox. Thank you!
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