Use the following form to generate some simple math problems for children. After clicking the Submit button, you will be brought to another page. Print that page off and hand it to your young-un to get some practice in :) More explanation follows the actual form application.
I’ve come to notice that my son needs some extra work with math. It seems he is finding certain things harder than others. I figured I could actually take what knowledge of programming I have and apply it to something useful. This isn’t nearly as great as, say, sitting down with your child and doing some flash cards, but it’s nice if you have some stuff to do around the house and your child is in need of some extra work with their early years in mathematics.
Anyway, another reason is because I searched the web (rather quickly, and not in-depth) for something similar. All the links that turned up high ranking in Google had some basic worksheets, but they also had pop-up ads. What kind of site that has things for children has pop-up ads??? Well, my site isn’t exactly for children, but you parents out there can rest easy knowing you can come here for a worksheet for your kids and not get any of those annoying pop-ups :)
I’ve noticed that there are a lot of hits for this page when searching for math problems for children. If there are any requests for features, please post them in the comments section at the bottom of this page. I can’t make any promises, because I’m no guru at this stuff, but I can at least know what people would like to see.
What is each option?
Here’s the breakdown:
- Smallest Number
- This is the smallest number that you want to appear in the math problems. So, if here you enter a 100, no number below 100 will be generated.
- Largest Number
- Similar to Smallest Number, this is the largest number that you want to appear within the generated math sheet. Entering 100 here would cause no number above 100 to appear.
- Number of Columns
- This is simply saying how many columns of problems you want. You have the option of having between 4 and 10 columns for the worksheets.
- Number of Rows
- Yup, you guessed it! Same as columns, but rows this time.
- Type of Math
- Choose from addition, subtraction, or multiplication problems. Simple.
- Display Name Line
- This is here in case some teacher stumbles on this page and wants to use a generated worksheet. I know that’s a long shot, but hey, you never know haha
- Display Date Line
- See above, same thing.
A quick note. When printing out the following worksheet page, you can turn off the header and footer so the URL doesn’t show up on the print out. Just a heads up for those that don’t know. Your browser should have an option called Page Setup, or something similar. This is where you can do that.
- When there are alot of problems, sometimes there are repeats. Maybe come up with some sort of array in RAM to counter this
- Include a mixture of both addition and subtraction as a worksheet type
- Maybe work in the use of decimal numbers
- Include an option to make it so it doesn’t matter if the top number is highest or not (right now it’s defaulted to have the highest number on top of the problem)
- Figure out a good way to make division problems generate to have no remainder
- Come up with a decent way to display division (bracket-style)
- Maybe pretty up the form a little bit
- Add in a fix for the way Internet Explorer separates math problems at the bottom of the print out
- Ignore the next-to-last To-Do on the list because no one should ever use Internet Explorer anyway
Who can use this?
EVERYONE! This is free to use, and I don’t need any kind of moolah or whatever for it. Let’s see… oh, no warranty, blah blah. Just use it if you would like, and I hope you find it useful for your child!


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Go Math - Think Central
This site contains our textbook, practice pages, and many interactive tools for our math series, Go Math! Please explore the many useful tools availabe to you.
Illuminations - NCTM
This site contains resources and interactive games from the National Council of Teachers of Mathematics.
This site contains many exciting math games!
This site has many different games to reinforce multiplication facts.
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Welcome back to what is already turning out to be a fun filled year of learning at our school. Our students and our teachers have quickly settled in and begun their lessons. As I wander through the classrooms I can see and hear students engaged in explicit lessons throughout all learning areas.
At St Joseph’s we are fortunate to have iPads and laptops for all students. This week you will have received a copy of our ICT policies to review and discuss with your children. Please ensure you return these notes as soon as possible so that your child can begin to take their device home to use for homework. At St Joseph’s we ask that our devices are only used for educational tasks set by the classroom teacher.
You may have heard teachers talk about getting their students to work mathematically. So, what is working mathematically?
Working mathematically is integral to the learning process in mathematics. It provides students with the opportunity to engage in genuine mathematical activities and develop the skills to become flexible, critical and creative users of mathematics.
Working mathematically encompasses five interrelated components.
Communicating– we want our students to develop the ability to use a variety of representations, in written, oral or graphical forms to be able to formulate ideas and explain their thinking.
Problem Solving– through problem solving develop the ability to make choices, interpret, model, and investigate problems.
Reasoning– as part of reasoning students develop an increasingly sophisticated capacity for logical thoughts and actions by being able to prove and justify their thinking.
Understanding– when students understand they are able to adapt and transfer mathematical concepts.
Fluency– a fluent student can carry out procedure flexibly, efficiently and accurately.
In our classrooms we use variety of number talks as one way to develop these five components. A number talk is a short whole class maths activity where students find the answer to problems in their heads, then share aloud the strategies they used to find the answers. Sometimes, we give students the problem and ask them to represent their thinking visually.


By Hiroaki Hijikata,Heisuke Hironaka,Masaki Maruyama
The dialogue starts off with an outline of numerous formulation for enumerating specific sorts of gadgets, that could be tabular preparations of integers referred to as younger tableaux or a few varieties of monomials. the subsequent bankruptcy explains the way to determine those enumerative formulation, with emphasis at the position performed via differences of determinantal polynomials and recurrence family chuffed via them. The ebook then turns to a number of purposes of the enumerative formulation and common identification, together with together with enumerative proofs of the straightening legislations of Doubilet-Rota-Stein and computations of Hilbert services of polynomial beliefs of definite determinantal loci. Invariant differentials and quaternion extensions also are tested, besides the moduli of Todorov surfaces and the type challenge of embedded strains in attribute p.
This monograph may be an invaluable source for practitioners and researchers in algebra and geometry.
Read or Download Algebraic Geometry and Commutative Algebra: In Honor of Masayoshi Nagata: 1 PDF
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Algebra is a type of math that uses symbols to calculate instead of numbers all by themselves. It looks to many like a secret code, but once you learn the “key,” it opens up a lot of knowledge. There are many books out there to learn about algebra. This list provides twenty for students, teachers, parents, and everyone who needs them.
What Is Algebra?
The average person does not remember lots of stuff that they are taught in school. Many will remember this formula: a2 + b2 = c2, which is also known as the Pythagorean theorem.
The formula itself is a form of algebra. Algebra is a type of math where symbols are used instead of numbers themselves. The word “algebra” was first used by a medieval Arabic mathematician and roughly means “reunion of broken parts.”
Algebraic formulas (which can look like a form of secret code) are a basic way this can be done. If we break down each formula, it is easier to understand. And, as in everything out there, algebra has its rules and jargon.
Why Should I Read About Algebra?
Algebra is one of those things people learn in school that leads to people asking “why do I have to know about this?” Many people have problems learning algebra.
I myself did better in social sciences like history than mathematics. But, difficulty does not make something pointless.
The basic reason why you should learn algebra is that it is a simplified way to learn the answer to various questions. Algebra helps to train your brain in ways that the humanities do not.
It’s also required in secondary and college level education. Love it or hate it, you’ll have to at least muddle through to graduate.
Maybe you simply are interested in mathematics and algebra in particular. That is one more reason to read about it.
Best Books About Algebra
An important thing to do here is to find a good book that will help you learn it in a clear and accurate way. There are many books out there, but what ones should you choose?
As a parent, you may be thinking, “I have been out of school for years, I have no idea about this sort of thing!”
You are in the right place. Below is a summary of the top algebra books with some basic information that will help you pick the one best for you or the person you are assisting.
After looking at the top 10, I will then provide a list of ten more that are also useful.
TOP TEN ALGEBRA BOOKS
Hot X: Algebra Exposed! By Danica McKellar
Parents and some viewers of “classic television” might recognize Danica McKellar as “Winnie” from the show The Wonder Years. Others might recognize her from various Hallmark Channel movies.
She also has a degree in mathematics and is the author of multiple mathematics books, including Kiss My Math: Showing Pre-Algebra Who’s Boss, geared for tween and teenage girls, though boys can learn a lot from them as well. McKellar knows her stuff and explains algebra in a down-to-earth fashion with a twist of girl power.
Algebra Exposed is a great book to explain algebra in an engaging, real-world manner.
It does not offer many problems for students to practice their newly learned knowledge.
Amazing Algebra Activities by Jacqueline Medori Lynch
A veteran secondary math teacher with a specialization in special education, Jacqueline Medori Lynch has compiled over 50 practice worksheets in the form of puzzles and riddles.
Her aim is to create engaging activities to encourage the practice of algebra skills. It’s also a great way to activate both the right and left hemispheres of the brain.
Linear equations, functions and polynomials are just a few of the exercises included.
This book is good for a parent who wants to offer their child extra practice. Its 8.5” by 11” size is also perfect for teachers who want to copy the puzzles for their students.
There are lots of fun worksheets covering all algebra topics that add fun the practicing math.
This will not replace a textbook that details the theory behind algebra.
Algebra I Workbook For Dummies by Mary Jane Sterling
Mary Jane Sterling taught algebra, business calculus, geometry, and finite mathematics at Bradley University for more than 30 years. She knows her stuff and is no dummy.
This book provides down-to-earth explanations of Algebra I basics plus the tougher stuff with step-by-step examples you can understand and apply in the classroom.
Other books available in the series: a workbook, a review guide, practice problems, or a bundle of everything all in one.
The same is available in Algebra II.
This is a great refresher book for those going back to school.
It does not include many practice problems and may be too difficult for a novice.
The Cartoon Guide to Algebra (Cartoon Guide Series) by Larry Gonick.
Larry Gonick is both a cartoonist and Harvard instructor, making him a good choice to provide a fun graphic novel that provides a comprehensive look at algebra.
Do not be confused by the format. A range of educational subjects have been put in cartoon form. The book is good for students of all ages.
The book covers algebra’s history, practical applications, and all the essentials such as linear equations, polynomials, quadratic equations, and graphing techniques.
This is a great intro to algebra and will even work for middle school students.
There are no answer keys to the chapter quizzes.
Regents Algebra I Power Pack Revised Edition (Barron’s) Revised Edition by Gary M. Rubinstein M.S. [Algebra II also available]
Gary Rubinstein is a high school teacher living in New York City. Who is better to go to help study for the New York Regents exams?
This two book “power pack” provides a comprehensive review, administered exams, and practice questions to help students prepare for the Algebra I Regents exam. Part of the nearly one hundred years long Barron’s study guide collection.
This is a great prep review for those taking the New York State Regents
Though it can be helpful as a supplemental tool it’s really focused on 1 state test.
No-Nonsense Algebra: Part of the Mastering Essential Math Skills Series (Stepping Stones to Proficiency in Algebra) 2nd ed. Edition by Richard W Fisher
Richard Fisher is an award-winning teacher of over thirty years. This easy-to-follow text combined with tutorial videos is part of his well-developed teaching system. Thousands of his students have thrived using his technique, regularly skipping ahead in the process.
This gets kudos from homeschool parents. It also includes video tutorials.
There are some typos in the answer keys.
The Complete Idiot’s Guide to Algebra by W. Michael Kelley
W. Michael Kelley is an award-winning calculus teacher and author of multiple math books, including the The Humongous Book of Algebra Problems (Humongous Books). His goal is to make math hurt less. Good luck with that!
This well-received addition to the familiar series makes the reader not feel like an idiot about algebra by breaking it down into easy to understand basics. The book is good both for the student in school and the adult learner of the subject matter.
It’s a very well-received book to up your algebra skills.
There are not many exercises to practice the skills.
Mathco College Algebra: The Step-By-Step Study Guide by L. Muriel Locke
Prof. Locke, an associate professor of mathematics, enjoys helping students to successfully improve their math skills in various math courses. She has used her doctoral education to help provide clear and understandable presentations of the concepts of college mathematics.
This study guide provides the fundamental concepts of College Algebra, which should be helpful for students in various courses. It gives you easy-to-learn Math notes, definitions, and study notes in a range of algebraic areas including polynomials, algebraic fractions, radicals, logarithms, and more. The many examples will help clarify all the material covered.
Easy to follow study guide for college students
May be too difficult for beginners.
Arithmetic and Algebra Again: Leaving Math Anxiety Behind Forever by Britta Immergut and Jean Burr Smith.
The authors have combined over fifty years experience teaching mathematics in middle school, high school, and colleges. Immergut wrote many books; Burr Smith was one of the originators of the concept of math anxiety, and received numerous awards for teaching techniques.
This is the second edition of the continuous best seller, which provides an expert approach in teaching the subject, particularly for those with math anxiety. The first section eases you in with basic math and then you are ready to tackle algebra.
Good review of the fundamentals of algebra.
The more advanced topics can be confusing. The answers are not explained.
Algebra Essentials Practice Workbook with Answers by Chris McMullin
Chris McMullen is a physics instructor at Northwestern State University of Louisiana. He earned his Ph.D. in participle physics.
This is one of a series of algebra workbooks that can be found on the linked Amazon page.
Each chapter has many practice exercises geared to build fluency in the subject matter. If you get an answer wrong, study your solution, rework the problem, or review the examples so that you can learn from your mistake.
If you’re looking for a TON of practice problems this is the book for you.
It’s very light on explaining the concepts; definitely geared as a workbook.
Algebra: Chapter 0 (Graduate Studies in Mathematics) by Paolo Aluffi
Paolo Aluffi has a Ph.D. with a dissertation in algebraic geometry and is a professor at Florida State University. He has visited many universities around the world. Aluffi has published over sixty research papers in algebraic geometry. He knows his stuff.
This book is a one-volume introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level.
The book does not only provide a reliable discourse on the material but readers have praised its style of writing. Prof. Aluffi shows the reader that a college textbook need not be boring.
Excellent for higher-level post-secondary students.
Not a beginner’s guide.
SOME MORE GOOD ALGEBRA BOOKS
Unknown Quantity: A Real and Imaginary History of Algebra by John Derbyshire
Many are familiar with John Derbyshire for his writings on conservative subjects. He is a mathematician and linguist by education, a systems analyst by profession, so a book on the history of algebra is right up his alley.
Along with the instruction and workbooks, it is good to have some books on history and philosophy in your scientific library. This book is an excellent account of the story of the development of algebraic thought from the beginning until now.
Publisher’s Weekly called this a “very entertaining survey of the development of algebra.”
Dr. Ron Larson is a professor of mathematics (began teaching in 1970) and is a pioneer in using multimedia to teach mathematics, having authored more than 30 software titles since 1990.
This book uses his basic basic techniques including learning by example, a down to earth writing style, emphasis on visualization through the use of graphs, and comprehensive exercise sets. Larson has also written many other math books, including a pre-algebra practice workbook.
Abstract Algebra by W.E. Deskins
W.E. “Gene” Deskins, a professor and mathematician was chairman of the math department at the University of Pittsburgh during the 1970s and 1980s. He was well known for cultivating both his students and his garden. This book is more mathematical related.
This is an excellent college textbook, appropriate for undergraduates, which has received much praise over the years. The book is not “chatty” but is chock full of material for those learning algebra in college. It is not geared to advanced students of algebra.
Algebra: 100 Fully Solved Equations To Explain Everything You Need To Know To Master Algebra! (Content Guide Included) by Math Wizo.
This is a small book of equations, part of the Math Wizo series (“Our mission at Math Wizo is to end the fear and pain around Math forever.”)
One reviewer said this is like doing work problems, but with numbers, and that is exactly what algebra is about. Helpful to practice and keep your skills sharp.
Algebra Part 1 (Quickstudy Reference Guides – Academic) by Inc. BarCharts
These quick study pamphlets are a useful set of laminated instructional materials with Algebra, Part 2 and Algebraic Equations also available. Six pages long, chock filled with details that will provide essential information at your fingertips.
Helpful for refreshers and as a research guide.
Everything You Need to Ace Pre-Algebra and Algebra I in One Big Fat Notebook (Big Fat Notebooks) by Jason Wang and Workman Publishing.
The BIG FAT NOTEBOOK covers everything you need to know during a year of Pre-Algebra and Algebra 1 class, breaking down one big fat subject into easy-to-understand lessons. Study better with ways to remember things, definitions, diagrams, education doodles, and quizzes to recap. And, in the end you (or your student) will learn and get better grades. Win win for all.
Forgotten Algebra 4th Edition by Barbara Lee Bleau, Meg Clemens, and Glenn Clemens
This “self-teaching” workbook is designed especially for students who need to go back to algebra basics as preparation for starting a college-level math course.
It’s also a helpful review for those preparing to take standardized exams that include math testing, such as a math placement exam, the GRE or GMAT.
Good to use with Bleu’s Forgotten Algebra book.
Jim Libby taught high school mathematics for over twenty years and at the end was an administrator. As he says:
“While I was teaching, I always thought there should be a resource for teachers to find appropriate high school math applications for students; one that would answer the question all math students seem to have: “Where are we ever going to use this?”
This book, particularly written for teachers, provides such a resource. It provides hundreds of practical applications for mathematics–from baseball statistics to the theory of relativity–that can be understood by anyone with a high school knowledge of mathematics.
Algebra for Fun by Yakov Perelman
Yakov Perelman (1882-1942) was a Russian and Soviet science writer and author of many popular science books. He was known for mixing humor with an ability to educate the average person on a range of math and science subjects.
This book, one of many he wrote, was an early mathematical best seller. Maybe, a new generation will appreciate this down-to-earth introduction to algebra. An example of his approach: an early problem using changing weather to introduce algebraic ideas.
The Algebraist by Ian M. Banks
A book with this title basically has to be included on a listicle about algebra.
Ian Banks was a Scottish sci fi writer, and this is a work of science fiction. He is particularly known for “Culture Series” novels, but had an award-winning career with many short stories and books. This book takes place in 4034 and crafts a whole new world among gas planets out there in space. The story involves a scholar on a mission to discover long-lost knowledge that will, if found, reshape the entire structure of the known universe. X+y=N (Nirvana)?
Math will remain scary for some people. It will also remain a basic part of our lives and education. These books help students of all ages, though some are particularly geared for certain ages and education levels, to learn about algebra. And, help break the code.


Marketing is a method used by
Monthly and annual plans Are Available. However, I prefer using Calculator on my mobile for everything that is more difficult. Are you still unsure whether CalcWorkshop is the right fit for you?
Explore the website and learn how memberships can ease the stress of the process of learning math. Comments.1 You can join in the discussion by subscribing the feed of comments on this blog post.
Mathematics, Algebra and Geometry and its place in Business. Thank Simon. A business is described as an enterprise or organisation that engages in industrial, commercial or even professional pursuits.
Thank you Simon for your helpful shares.1 The term "business" can refer to a non-profit entity that is able to perform its business in pursuit of an ecumenical purpose or to advance its social mission or a non-profit corporation to earn money from the sale of a specific item or product. Regards, Jennifer. When it comes to managing a business math is essential.1 Thank Simon for this.
Businesses are primarily concerned with the money and mathematics is utilized in all dealings of money. Simon for this fascinating article . You can't make a profitability without knowing how to manage your money. I will answer the questions in different ways . Mathematical tools can be utilized to keep track of and manage the the business operations of the commercial business. 1.) When did you first begin to study mathematics? "Mathematics, Algebra and Geometry and their Use in the World of Business" when I was just age 6 .1 Get custom essay. 2.) Do you like maths?
Why/why you don't? Commercial companies use mathematics to manage inventory and sales forecasting, accounting marketing and analysis of financials. Yes . Mathematical calculations is used for calculating financial formulas to determine tax calculations of hiring rates, calculations for salary as well as the calculation of interest and much more.1 I enjoy maths for several reasons . Companies may also employ statistical data and have the capability to offer solutions to some issues.
For one, maths can be exercises in my brain . There are many issues which a business faces and these need been addressed in a timely manner so to ensure that they do not occur again when they do.1 It is a challenging subject that require me to take my time to think about how to solve them . The issues that arise can be solved effectively using the basic mathematical tools. Additionally, it's a important to me in my everyday life . Mathematical concepts can be utilized to analyse and calculate business issues, which allows firms to solve and rectify any issue they face.1 I often use maths at the bank, shop as well as in school. Mathematics is the science that deals in the theory of quantity, arrangement , and shape. 3 Is it essential for all to study mathematics.
Math is everywhere throughout our lives on a daily basis. Yes, definitely . It's employed in all aspects of our life.1 Like I mentioned in the last question.
It is the basis of everything we do which includes art, architecture, engineering as well as mobile devices, money and even sporting occasions. 4.) Would you rather using a calculator for math? Since mathematics was first discovered and embraced, math has been at top of the world, and can be observed being utilized even in the most impoverished of civilizations.1
It's all about the difficulty of the problems and also on the amount of time . In the past, tribes utilized math to calculate the sun's position and to master the science of hunting. I'll make use of calculators in the event that the problem is complicated and I'm trying to get them solved in rush.1 When civilizations began to evolve mathematical scientists began to working with geometry. 1.) When did you first begin to study mathematics? While geometry allows you to calculate volumes, as well as the ability to measure angular angles and can be used in many different ways. I'm afraid I can't give you a precise point of time.1
Geometry has a lot of ties with algebra. But, I vaguely remember when i began to do some basic maths at age six, when I started the elementary schools. Algebra provided civilizations with the ability to divide the inheritances of families as well as a method to distribute resources. 2.) Do you like maths?1 Why/why you don't?
Mathematicians could use math to tackle linear problems and system. it also allows negative and positive solutions. Absolutely. Ancient civilizations, like the Greeks have developed a system of abstract mathematics that utilized geometry.
I used to be in a gifted course for students who were good in math.1 Because Greece had such a complicated and impressive architecture, together with a complicated system of government that they became the models of mathematic accomplishment in the past until the current. I really enjoy it because I enjoy doing math.
Numerous commercial enterprises will utilize various aspects of math which include marketing, accounting, sales estimation, stock management, along with financial analysis.1 Additionally, I always feel satisfied when I have solved math problems. The use of financial formulas is for interest calculation as well as tax calculations, salary calculations, as well as internal hiring rates. It's the satisfaction of success. Accounting is the procedure that records the financial transactions that affect the company. 3 Is it essential for all to study mathematics.1 The procedure involves analysing as well as presenting information to the oversite agencies as well as tax collection agencies and the regulators.
Yes , absolutely. Accounting makes use of these statements as an account on all transactions in the financial system throughout the accounting period. Since mathematics is really essential for everyday life.1 They also provide a summary of its financial situation in terms of cash flow, as well as business operations. But I think that math should be simple in this particular instance. Marketing is a method used by companies to market either the sale or purchase of the product manufactured by its company.1 In other words, we don't have to do complicated maths.
It includes advertising as well as selling 4.) Would you rather using a calculator for math? Geometry. In reality, it is dependent on how difficult the maths are. and also delivering goods and services to consumers or other businesses. If I am required to deal with lots of numbers, complex calculations I'll definitely be glad to have a calculator.1 The use of math is to determine the costs of the marketing performed by the business. I'm taking IELTS for the first time in my entire life on December 5th. If companies employ sales forecasting, they're making use of a process to determine the future sales of their company.
Absolutely nervous. With accurate forecasts, businesses to make more informed choices and even determine the company's short- as well as long-term performance.1 I face a huge obstacle in writing and speaking. Forecasts can be made determined by past sales figures along with economic trends, as well as broad industry-wide comparisons. Your website has really helped me.
In an organization, it oversees the flow of the goods manufactures by the business to warehouses and also from the warehouses until the point of sale.1 I am truly grateful. Inventory managers take care of capitalized assets that are not capitalized as well as stock items. P.s Is there anyone who willing to do some speaking practice with me? My goal will be 7.0 overall. It is vital to record exact calculations of products being imported and products being sold so to let the company know when the inventory is sufficient to allow another shipment, or not.1
Skype ID: blackangel_jen. Financial analysis is the process that evaluates budgets, plans, businesses and other transactions involving finance that determine company performance and its suitability. Please feel free to add me to your Skype account. as a friend on Skype. Financial formulas businesses utilizes are crucial and they are considered to be relevant when they give the business accurate results and the answers to queries, which help to organize and structure the business.1 I'm looking for someone who can practice their English with me.
Common formulas include: simply interest = Prt P is the principal formula, the interest rate is r and t is the amount of length in years. skype id: golgedur. Compound interest . 1). P is the basic principle and that is r, which is the rate that compounding is at, that is compounding's, and t represents the years.1 I started studying mathematics at the age of six years old. old.It is very helpful to use in everyday math. Also, an effective rate. that is, r represents interest, and n is the compounding's. To make quick decisions in shops"school" and more . 2.) I do like maths because it can be used in daily life and also in professional settings as I work for a the banking industry where I utilize calculations during my work.1
3.) Yes , I believe it is important for each one to master basic calculations regardless of their preferences, since math is an integral aspect of our lives throughout our work. 4.) It depends on the job likely to use calculators in difficult tasks. Calculations of salary are utilized by businesses to figure out the amount of money they will pay to each employee by multiplying the number hours an employee has to work per week by the wage established by the business.1 However, it is not needed in simple calculations. Then, you multiply that number by 52 that is the total number of weeks that a year. Anyone looking to exercise their speaking, can reach me at skype.
If an employee earns $30 an hour and was working at 44 hours per week, your salary is $30x44x52, which equals an annual salary of $68,640.1 My target is 7,5. Tax calculations for a business is taking the business's annual earned income and subtracting credits and deductions to arrive at the taxable amount.
I passed my test of speaking on October 9th. Whatever the earnings are at the time will place the company into a particular tax bracket.1


In my introductory post I talked about fake difficulties. It will take some time and several more posts before I can say what I really mean by that notion, but this post will get me a bit closer. So far I have mentioned that if you can’t solve a problem because you haven’t been bothered to look up what the words mean, then your difficulties are not genuine. A more interesting category of fake difficulties is a failure to grasp a few basic logical principles. I call this a fake difficulty even though for some people it is genuinely difficult; the reason I do so is that when mathematicians consider a problem to be hard, it is not for basic logical reasons. To put that another way, with a little bit of practice one can make basic logical deductions completely mechanically, and it is absolutely essential to learn how to do so. It is a simple skill (which is not to say that no work is needed), and it underlies all mathematical reasoning. Trying to understand university-level mathematics without a secure grasp of basic logic is like trying to learn long multiplication without knowing your tables — only a lot harder.
What am I talking about when I use the phrase “basic logic”? I am talking about having a good understanding of the following.
Logical connectives. The main ones are “and”, “or”, “not” and “implies”.
Quantifiers. The phrases “for all” and “there exists” come up a lot in mathematics and you have to be capable of dealing with sentences like this: for every there exists such that for every
Relationships between statements. Given a statement, you should have no trouble forming its negation, its converse and its contrapositive. Of course, for that you need to know what those three things are.
Each of the items above is a potential source of confusion. In particular, quantifiers take a lot of getting used to. However, when you are used to basic logical principles you will find that in many situations you can apply them in a purely mechanical way, sometimes without even needing to understand the statements to which you are applying them. In the next few posts I will try to help you develop that ability if you don’t already have it.
These posts, all with titles of the form “Basic logic — <subtitle>,” are not intended to be typical of the posts in this series, since they are introductory and not tied to any particular course. But basic logic is something that I have to get out of the way before we move on to the more interesting stuff. So let me now discuss a couple of logical connectives in more detail. I’ll save “not”, “implies”, quantifiers, and sentence relationships for later posts.
If you think your basic logic is not quite 100% secure, then I recommend that you read through all the posts that I shall put up on the topic. If put together, they are quite long, and therefore you probably won’t want to reread them too often, so I intend to write a brief summary of the main points, for easy reference later. But that summary will just give you the basic facts, without the justifications and explanations that will be presented in the posts.
AND and OR.
It may seem at first as though there is not much to say about the words “and” and “or”. After all, are they not just common English words that mathematicians happen to use as well? In a sense they are, but their meanings are subtly different from their usual everyday meanings, and it is important to understand the differences.
For the purposes of this discussion I am going to do something that you may not have seen before. You will be very familiar with the idea that letters can be substituted for numbers. But at university, letters (or other symbols) get substituted for absolutely everything. Here I am going to use letters to stand for statements. For some reason the traditional letters to use seem to be p and q, or sometimes P and Q.
How might we explain what “and” means? It seems difficult to do so without being circular and saying something like this: “P and Q” is true if and only if P is true and Q is true. I appear to have defined “and” using the word “and”. If I substitute actual sentences for P and Q I get something like this: “London is in England and Paris is in France” is true if and only if “London is in England” is true and “Paris is in France” is true, which is a bit of an odd observation to make.
And yet somehow it does tell me something. It tells me that if I want to establish the truth of the compound sentence “London is in England and Paris is in France” then it is enough to establish that London is in England and also to establish (possibly by a completely different method) that Paris is in France.
However, that observation is not enough to stop the example feeling odd. In my opinion, one gets a much better idea of the role of logical connectives in mathematics by considering statements with parameters. I’m talking here about statements like, “n is prime”, where all you know about n is that it is a positive integer. The statement “London is in England” is either true or false (and happens to be true). The statement “n is prime” involves the parameter n, and is true for some values of n, such as 13 and 17, and false for others, such as 14, 15 and 16.
The great advantage of thinking about statements with parameters is that their truth value is not fixed, but depends on the parameters. That this is an advantage will become particularly clear when we come to think about the word “implies”. But for now let us return to the word “and” and consider the statement, “n is prime and n is even.” For this to be true, we need n to be both a prime number and an even number, which tells us that n=2. For all other values of n it is false. For example, if n=3, then n is prime but n is not even, and because n is not even we cannot say “n is prime and n is even.” Similarly, if n=4 then the statement is false because n is not prime.
Here is another example that is perhaps even more typical of how mathematics uses the word “and”. One of the topics in the Numbers and Sets course is, needless to say, sets, and one of the definitions associated with sets is that of the intersection of two sets (which you may have met at school and represented in Venn diagrams). If A and B are two sets, then their intersection is defined to be the set of all objects x such that x belongs to A and x belongs to B. I am trying to avoid using symbols here, but for those who have seen them, the definition would normally be written like this:
Another way of expressing the same idea would be this: x belongs to if and only if x belongs to A and x belongs to B.
What does this tell us? Well, when we try to solve a problem, we usually have a statement that we are trying to prove, and some statements that for one reason or another we know to be true. Suppose that one of the statements we know to be true is that x belongs to the intersection or in symbols Then the meaning of the word “and” tells us that we can replace this information by the two bits of information that x belongs to A and that x belongs to B. That is, if we were to keep a list of statements that we knew to be true, and on that list we had
x belongs to
we would know that we could replace that list item by the two items
x belongs to .
x belongs to .
This might be a very useful thing to do: for example, perhaps the information that x belongs to A is used in one place in the argument and the information that x belongs to B is used in another place.
I still haven’t really demonstrated an interesting difference between the mathematical use of the word “and” and the everyday use. But here’s one. In everyday usage the following sentence makes good sense: “Jack and Jill went up the hill.” But in mathematics, at least when it is written formally, the word “and” connects statements (which is why it is called a logical connective) rather than connecting objects. So a mathematician would feel an urge to rewrite the well-known nursery rhyme in the following rather less catchy way: “Jack went up the hill and Jill went up the hill.” That’s not to say that you never see a sentence like “x and y are positive”, but you should be very aware that that is a different use of the word and should think of it as a useful shorthand for “x is positive and y is positive”.
The first thing to say about the word “or” as it is used in mathematics is that it is always the inclusive or rather than the exclusive or. In abstract terms, the statement “P or Q” is true if and only if P is true or Q is true or both. As with “and” one can illustrate this in a rather unilluminating way with examples such as the following.
London is in England or Paris is in France.
London is in England or Paris is in Pakistan.
London is in Scotland or Paris is in France.
London is in Scotland or Paris is in Pakistan.
Of those four sentences, the first three are true (because in each case at least one of the two constituent parts is true) and the fourth is false (because neither constituent part is true).
But again the real use of the word “or” is much better illustrated by statements with parameters. For instance, the statement “n is prime or n is of the form 4m+1” is true if at least one of “n is prime” and “n is of the form 4m+1” is true. (Here I’m imagining that n is a positive integer but m can be zero.) Let’s list the first few values of n for which this statement is true:
For all the other positive integers up to 60 it is false (unless I’ve made a slip). Had I been using the exclusive or (so called because the two statements “exclude” each other) then I would not have included 5, 13, 17, 29, 37, 41 or 53 because those number are both prime and of the form 4m+1. But I was following conventional mathematical practice and using the inclusive or, so I did include them.
Perhaps the single most important thing you need to know about “or” is how to respond to it if it comes up in proofs. For example, suppose you find that amongst the list of statements you know a statement of the form “P or Q”. In other words, you know that either P is true or Q is true (or possibly both). In most cases, P and Q will be statements with parameters: an example might be “n=2 or n is odd”, which would follow if you knew that n was prime.
If you know that “P and Q” is true, then you can add both P and Q to your list of things that you know and can use. But if all you know is that “P or Q” is true, then your task is more difficult. This time what you have to do is split your argument into cases. If you are given that “P or Q” is true, and you want to deduce R, then you must show that you can deduce R if you assume P (and whatever else you know) and that you can also deduce R if you assume Q (and whatever else you know). That way, since at least one of P and Q is guaranteed to be true, R must be true. So in a proof you might write something like this: “First let us assume that P. Then … blah blah … so R follows. Now let us assume that Q. Then … blah blah … and again R follows. Therefore the result is proved.”
What I mean when I say that you need to be on top of basic logic is that you should get to the stage where reacting to a statement of the form “P or Q” in the way I have just described is a pure reflex: you see that you know that either P or Q, so you just automatically go into “If P, then … and if Q, then …” mode.
What about if the statement “P or Q” is the statement you are trying to prove (as opposed to what I have just been discussing, when “P or Q” is one of the statements you are trying to use to prove something else)?
If P and Q are fixed statements, then you can prove “P or Q” by picking one of P and Q and proving that. For instance, if I want to prove the statement “There are infinitely many primes or every group of prime order is cyclic” then I could simply prove that there are infinitely many primes and have done with it. But that is not the situation that usually occurs. Usually when one wishes to prove “P or Q” it is a statement with parameters. For example, an important result in the Numbers and Sets course is this.
Theorem. Let p be a prime number and let a and b be positive integers. Suppose that p is a factor of ab. Then either p is a factor of a or p is a factor of b.
Before I say anything more about this, note that the result would be false if I were not using the inclusive or. For example, p could be 5, a could be 10 and b could be 15. Then p is a factor of ab (which equals 150) but it is a factor of both a and b. Part of the reason I’m mentioning this is that the word “either” suggests to many people that one is using the exclusive or, probably because in many ordinary-language contexts we use the word “either” to emphasize that the two alternatives we then go on to lay out are incompatible. An example: if I say, “I don’t know where I’m going to go on holiday next year. I think I’ll either go to the South of France or to Greece.” then it would be quite reasonable of you to interpret me as ruling out going to both places. But in mathematics the word either does not have this implication. If it sounds to you as though it does, then you need to get into the habit of ignoring the word whenever you see it.
Returning to the theorem, what is the statement we are trying to prove. It is “p is a factor of a or p is a factor of b.” Now because we don’t actually know anything about p, a or b, beyond the fact that p is a prime and a and b are positive integers, we can’t just say, “Right, I’m going to prove that p is a factor of a,” or “Right, I’m going to prove that p is a factor of b.” Instead what we have to do is more like this.
1. Assume that p is not a factor of a.
2. Draw some consequence of that assumption and use it to prove that p is a factor of b.
If we can do that, then the result is proved, since either p is a factor of a or the above argument can be used to show that p is a factor of b. The consequence one uses if p is not a factor of a is that the highest common factor of p and a is 1. I won’t say any more at this stage but in a future post I shall discuss this proof in detail.
Sometimes when one wishes to prove a statement of the form “P or Q” a slightly more complicated plan of attack works. It goes something like this.
1. Attempt to prove P, and try to identify what has to happen for your proof not to work.
2. Show that if that happens, then Q must be true.
Here is a simple example: the infinite pigeonhole principle. I will state the result and its proof.
Theorem. Suppose that the positive integers are each coloured either red or blue. Then either there are infinitely many red integers or there are infinitely many blue integers.
Proof. [First comes the attempt to prove one of the two statements.] Let us attempt to find infinitely many red integers. We’ll try to do it in the simplest way imaginable: we’ll just pick a red integer then a larger red integer then a larger red integer and so on. If we succeed, then we have produced an infinite sequence of distinct red integers and we have therefore obtained the first statement.
[Next comes the process of understanding what must be the case if the proof of the first statement doesn’t work.] The only way we can fail is if for some k we find that we have identified red integers and cannot find any red integer that is bigger than (If we could find such an then we could have used it for so we wouldn’t have been stuck at )
[And now, having drawn a consequence of our failure to prove the first statement, we go ahead and use it to prove the second.] But in that case all the integers from onwards are blue, so in particular there are infinitely many blue integers.
The associativity of AND and OR.
There is a rule that I ought to mention briefly, even though you will either be aware of anyway or will happily use it without even thinking about it. It is the rule
and the companion rule
For “P or (Q or R)” to be true, we need at least one of P and “Q or R” to be true. And for “Q or R” to be true we need at least one of Q or R to be true. Putting all that together, we find that for “P or (Q or R)” to be true we need at least one of P, Q and R to be true. And clearly the same argument shows that the same condition needs to hold for the statement “(P or Q) or R” to be true. So we just drop the brackets and write “P or Q or R” and think of this as saying that at least one of the three statements is true.
Similarly, we don’t bother with brackets for repeated ANDs, writing “P and Q and R” for the statement that all three of P, Q and R are true. And similar considerations hold for larger collections of statements as well.
The distributivity of AND over OR and vice versa.
Consider the following sentence.
What does this mean? Does it mean this?
Or does it mean this?
The answer is that the sentence as written could mean either. Since mathematicians don’t like ambiguity, they do not allow themselves to write such sentences, or their symbolic equivalents, which are and
Before I talk about distributivity, let me briefly mention another context where there are expressions we are not allowed to write. Nobody writes because the numbers and are in general different. But hang on, you might say, the numbers and are in general different, but it is considered perfectly OK to write That is indeed true, and all I can say in response is that we have a very strongly established convention that when you’ve got a string of pluses and minuses, you bracket them in such a way that you do the calculations from the left. For instance, is understood to mean (More intuitively, it means “start with then take away then take away then add then take away then take away ) We could easily use an exactly analogous convention for division, so why don’t we? That’s a historical question, but I suspect the answer is closely related to the fact that we usually don’t use the division symbol , preferring to write things as fractions. With that notation, we can distinguish clearly between and . (Of course, we don’t write because that would go back to being ambiguous.)
Returning to AND and OR, that tells us that an expression like is invalid until it is given some brackets. So let’s do so and consider the expression And to do that, let us continue with analogies from arithmetic. (You might prefer the word “algebra” since I’ll use letters rather than numbers, but in university mathematics, the word “algebra” has rather different connotations and we’ll happily talk about arithmetic even if the numbers we’re adding, subtracting, multiplying and dividing are unknown and represented by letters.) The distributive law in arithmetic is the one that says that By a miracle, exactly the same rule applies to and That is,
Before I continue, let me say that you should always be suspicious of anything in mathematics that looks like a remarkable coincidence. Nearly always there is an explanation, and nearly always that explanation takes the form of some more general statement of which the two parts of the coincidence are separate manifestations. If you want something to think about, see whether you can come up with some general statement that contains the distributive law for times and plus and the distributive law for OR and AND as special cases. And if you’re interested in the question of whether there is such a thing as a genuine coincidence in mathematics, you might like to read a very nice article on the topic by Philip Davis.
Oh, and if you do try to find that general distributivity statement, then while you’re at it you might as well throw in the fact that AND is distributive over OR. That is, not only do we have the rule I’ve just stated, namely
but we also have the same thing with AND and OR reversed. That is,
That may come as a bit of a surprise, seeing that addition is not distributive over multiplication, by which I mean that it is not a correct rule that always equals This tells you that finding a general framework that encompasses times/plus and or/and can’t be too simple, since otherwise it wouldn’t explain why plus/times doesn’t work but and/or does.
I’ve just stated these distributivity rules, so before I stop, let me briefly discuss why they are true. Let’s go back to the sentence about primes, but this time put brackets in. Suppose we wanted to show that
Well, if we can show that is prime, then we’ll be in great shape, since that will make both brackets true, which is exactly what we need. But if we can’t show that is prime, then the only way of making both brackets true is to show that is prime and is prime. And now if you look carefully at what I’ve just written, you’ll see that I’m saying that it is both necessary and sufficient to show that
A similar justification can be given for the other distributivity law. That is, if you want to show that
then it is necessary and sufficient to show that
I recommend that you stare at these two sentences until you have convinced yourself that they are indeed saying precisely the same thing.
One last question to finish the post: why do you think that the conventional way of interpreting expressions like is what it is?


12-16 November 2018 – Tremough Innovation Centre, Penryn
April 2019 (Date TBC) – Cardiff
Course open to: All years
Course Organiser: Dr Rob Thomas
Course fee for students not funded through the NERC GW4+ DTP: £480
Register here for November course: https://nercdtp.onlinesurveys.ac.uk/statistical-analysis-with-r-november-2018
Deadline for registration: 29 October 2018
Register here for April course: https://nercdtp.onlinesurveys.ac.uk/statistical-analysis-with-r-april-2019
Deadline for registration: 1 April 2019
Objective: To develop competence and confidence in data analysis, encompassing the majority of statistical methods that most earth and environmental scientists need to use in their day-to-day research, as well as a conceptual framework for learning more specialised methodologies for particular research fields. This course is aimed at those students who will be using statistics during their PhD and extra support during the course is provided for those students with a basic knowledge of statistics.
Composition: A 5-day practical workshop introducing students to the theory and practice of statistical analysis and the opportunity to apply the methods to their own data sets and/or class example data sets.
- Using (and not abusing) Generalised Linear Models (GLM),
- Analysing count data data with GLM,
- Analysing binomial, proportional and ordinal data with GLM,
- Generalised Additive Models (GAM),
- Mixed models (GLMM) and alternatives to GLMM,
- Multi-model inference and model averaging,
- Time-series analysis,
- Survival analysis,
- Spatial analysis,
- Multivariate methods,
- Where to go from here; onwards and upwards with R.
These sessions will include relevant material for researchers using both R and other analytical software such as Arc-GIS, Q-GIS and Matlab.


Health researchers commonly use logistic regression when profiling health providers. Data from the patients treated by the providers are used to construct models predicting the expected number of outcomes for providers and the ratio of observed to expected outcomes (O/E ratio) used as a risk-adjusted measure of provider performance. Typically, when calculating the standard deviation (SD) of O/E ratios, only O is treated as a random variable. We used the propagation of errors (Pe) to derive a SD estimate that accounted for variability in O and the estimate of E. Using data previously used to profile Canadian cardiac surgery providers, we compared Pe-SD estimates with typical SD (SDT) estimates. The SDT estimates and confidence intervals were always larger than the Pe estimates, most notably when one or more providers treated a large proportion of the patients. This was confirmed using computer simulations. SDT estimates should be abandoned in favor of more sophisticated estimates.
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- Comparing outcomes across providers.in: Iezzoni L.I Risk adjustment for measuring healthcare outcomes. 2nd edition. Health Administration Press, Chicago1997: 471-516
- Confidence interval estimates of an index of quality performance based on logistic regression models.Stat Med. 1995; 14: 2161-2172
- Expected values: mathematical statistics and data analysis. 2nd edition. Duxbury Press, Belmont (CA)1995 (p. 111–62)
- Coronary artery bypass grafting in Canada: national and provincial mortality trends, 1992–1995.CMAJ. 1998; 159: 25-31
- CABG in Canada.CMAJ. 1999; 161: 941
- for the APPROACH Investigators. Overview of ‘APPROACH’ the Alberta provincial project for outcome assessment in coronary heart disease.Can J Cardiol. 2000; 16: 1225-1230
Accepted: January 10, 2003
Received: September 17, 2002
© 2003 Elsevier Inc. Published by Elsevier Inc. All rights reserved.


报告题目：Applying solid state physics to classical waves: Bound states in the continuum and non-Hermitian physics
报 告 人：Dr. Yixin Xiao (Hong Kong University of science and technology）
This report comprises two parts: one is about bound states in the continuum, and the other is about non-Hermitian physics. Bound states in the continuum are eigenstates (waves) that remain localized even though they coexist with a continuous spectrum of extended eigenstates (radiating waves in the context of wave systems). In this talk I will introduce the existence of bound states in the continuum in two kinds of systems: one utilizes the concept of topological subspace, and the other uses Anderson localization. Bound states come from topological interface states and Anderson localized states, respectively, in these two systems. In the second part, I will introduce some interesting phenomena in non-Hermitian systems. The most prominent phenomenon in non-Hermitian systems is the occurrence of exceptional points, where several eigenvalues as well as their eigenvectors coalesce. I will first introduce the phenomenon of anisotropic exceptional points of arbitrary order and exceptional ellipses in a 1D system with asymmetric hoppings. Universal power laws for the asymptotic behaviors of both eigenvalues and phase rigidities will be shown. Next I will introduce the phenomenon that exceptional points form a star-like shape in the Lieb lattice with gain/loss added. The evolution behavior of the exceptional points will be shown. A topological invariant called the discriminant number is used to characterize the robustness and creation/annihilation of some discrete exceptional points.
Yi-Xin XIAO is currently a postdoc researcher at Hong Kong University of Science and Technology. He obtained his Ph. D. from the Hong Kong University of Science and Technology (Advisor: Prof. C. T. Chan) and bachelor’s degree from Wuhan University. Dr. Xiao is now working on non-Hermitian systems and the topological properties therein.


- Includes 6 dice
- 1 score pad
- Rules of play and in Spanish
- Reinforces probability, math and strategic thinking
- Playing time: 15 minutes
The addictive award winning dice game that launched the “roll and write” genre of games – but has some surprisingly varied reviews
This quick-playing dice game will have you on the edge of your seat from beginning to end! Qwixx is simple to play but each decision is crucial – the more numbers you cross off, the more points you score. With no downtime between turns you’ll have a chance to gain from each and every roll. Just one round of this thrilling game and you will be caught up in Qwixx-fever!


ALEKS Most Asked Questions
ALEKS is an online math placement and learning program that Western uses to assess student readiness for math and math dependent courses. This video on the ALEKS website explains how the ALEKS Math Placement Assessment (also known as ALEKS Placement Preparation and Learning) works.
You must take both ALEKS MPA #1 (un-proctored/practice) and MPA #2 (proctored/official). Your first ALEKS score will not count for math placement at Western; we treat MPA #1 as a practice test for our students. The scores for MPA #2 (or highest of scores from MPA 2, 3, or 4 if you should decide to reassess) will count as official for math placement and registration purposes.
The computer requirements for taking the practice assessment (MPA#1) are straight-forward, but you will need access to high-speed internet. Review the system requirements for MPA#1
The requirements for the proctored/official assessment (MPA#2) are more rigorous but you can verify that you meet the following minimum requirements with a quick test.
Requirements for taking the MPA#2 beginning July 1, 2020:
- Operating System: Windows 9.1 or higher; Mac OSX 10.13 or higher
- Browser: Google Chrome (minimum version 83)
- Internet: Speed: 1.5 Mbps download, 750 Kbps upload
- Web Camera and Microphone
Students who took the former MPT can use those scores for math placement. Score Requirements
ALEKS scores can be transferred from another institution if it was a proctored exam:
- Log into your ALEKS account
- Click on the three vertical dots on the right of the cohort in the “My Classes” section
- Select “Send Results” drop down option in the “My Classes” section
- Search by the college code: 2ECD42 for Western Washington University
If the other institution does not allow automatic transfers through ALEKS, you can print out their scores from the ALEKS website and bring to the Registrar’s Office to be entered into SOATEST. Students can also send to Registrar.Office@wwu.edu provided the score report shows their full name and has their Western ID# on the score report.
Please note that Western will transfer in only proctored exams taken within the past five years.
Learn about Math Course program requirements
ALEKS is not a multiple-choice test. It is open-response and requires you to work out solutions with a paper and pencil, then enter them into ALEKS. Be sure to have scratch paper with you.
ALEKS is an online, adaptive system that covers a broad spectrum of mathematics topics. The length of the Placement Assessment will vary, but can be up to 30 questions. You will see some, but not all, of the math you have learned in high school. It is a Placement Assessment, not a preview of math courses at your institution. It is designed to identify if you are prepared for a particular course. After you take your first Practice Placement Assessment, you will have the opportunity to review and master additional topics to reassess and improve your official placement score. You must take the MPA a second time in order to place into an appropriate course.
- Real numbers (including fractions, integers, and percentages)
- Equations and inequalities (including linear equations, linear inequalities, systems of linear equations, and quadratic equations)
- Linear and quadratic functions (including graphs and functions, linear functions, and parabolas), exponents and polynomials (including integer exponents, polynomial arithmetic, factoring, and polynomial equations), rational expressions (including rational equations and rational functions
- Radical expressions (including higher roots and rational exponents)
- Exponentials and logarithms (including function compositions and inverse functions, properties of logarithms, and logarithmic equations)
- Geometry and trigonometry (including perimeter, area, and volume, coordinate geometry, trigonometric functions, and identities and equations).
Your first assessment is a Practice Assessment (MPA#1), that will not count as an official score. ALEKS will begin with a brief tutorial to make sure you are comfortable with the online math tools before your Placement Assessment begins. The tutorial shows you how to enter different types of answers, how to use the ALEKS calculator, and how to graph. If you aren’t sure how to input an answer, or need help while you are taking the ALEKS Placement Assessment, select the Help button below the answer input tools. Going to the tutorial during your Placement Assessment will NOT impact your Placement Assessment results.
No. ALEKS will provide an on-screen calculator, if you need one to complete a particular problem. Otherwise, you may not use a calculator. Be honest about your skill level. There is no benefit to cheating on the placement assessment – the result could be that you are placed into a class that is too difficult for your current level of mathematical knowledge, with a high potential for failure. Therefore, while you are taking the assessment, do not consult any other source for help (friends, family, internet searches, etc.). The purpose of the placement assessment is to give an accurate measure of your current mathematical skills so that you will be successful in your mathematics courses.
Allow 24 hours for your ALEKS score to be loaded into the system after completing ALEKS. Remember that Assessment #1 does not count for purposes of registration. The day after you have completed Assessment #2 you should be able to register for any math course for which you qualify – within your scheduled registration timeframe.
You will be able to see your ALEKS placement score immediately after you finish the MPA.
The math course you take usually depends on your intended major. You should consult the WWU catalog to see what math course is required for your intended program of study. Once you determine the course you need, visit the ALEKS Placement Scores page to see what ALEKS score is necessary to register for that course.
You should first try to work through the Prep and Learning modules to improve your MPA score. If you have already done that, you should take the course for which you qualify. There is no other way to get into the course for which you wish to qualify other than having met the course prerequisite.
ALEKS access is valid for one year from the initial practice assessment. The cost to register again after the initial enrollment has expired is $40.
ALEKS results can be transferred to another institution if the receiving institution will accept automatic transfers through ALEKS. Students log into their ALEKS account, click on the three vertical dots located to the right of cohort in the “My Classes” section, and select the “send results” drop down option in the “My Classes” section. The college code and institution should appear if the institution has accepted to receive automatic transfers.
Most students, including transfer students, who plan to register for a course at Western that has a mathematics prerequisite must first take the ALEKS Math Placement Assessment (MPA) twice.
The MPA serves as a prerequisite for math courses, but also serves as a prerequisite for some courses in other departments such as Astronomy, Chemistry, Computer Science, Decision Sciences, Economics, Environmental Sciences and Studies, Geology, Physics and Science Education. Taking the MPA may save students both time and money.
Students may take the MPA any time after they activate their Universal Account. It is recommended that students take the MPA early, so as to allow time to work through the preparation and learning modules and to retake the MPA to improve their score. Students should complete the MPA at least two weeks before attending a new student Advising & Registration session – if they plan to register for a math course during their first quarter of study. Please be aware that failure to take both MPA #1 (practice) and MPA #2 (proctored/official) before orientation will delay registration for a math course or other courses that require a math prerequisite, such as Astronomy, Chemistry, Computer Science Decision Sciences, Economics, Environmental Science, Environmental Studies, Geology, Physics and Science Education.
ALEKS (Assessment and Learning in Knowledge Spaces) MPA is an adaptive assessment instrument covering material from Basic Math through Precalculus. ALEKS is designed to determine a student’s knowledge base in mathematics. Each Assessment has 30 questions and will take approximately 60-90 minutes to complete, and you will need to take a minimum of two assessments. While each MPA takes only 60-90 minutes to complete, the system will allow access for three (3) hours once each assessment is started, so no need to panic if you should have internet connectivity issues. Note that the proctored assessment #2 (not #1) is the score that will count for math placement in registration.
Prep and Learning Modules FAQs
You will have 12 months of access to your Prep and Learning Module. Access to the prep course will not begin until you select start on the top of your screen. DO NOT select into the Prep and Learning Module until you are ready to start working.
No. Access to a Prep and Learning Module is included along with the additional Placement Assessments.
You can take the Placement Assessment up to four times – the practice assessment plus three additional assessments. The highest score (after the practice assessment) will be used for math placement. Students are required to work in a Prep and Learning Module for a specific amount of time prior to the third and fourth MPA to increase success.
- #1 MPA – Practice MPA
- #2 MPA – Official for placement; Prep & Learning Module advised but not required
- #3 MPA - Requires 3 hours of work in a Prep and Learning Module and 72 hour wait before attempting MPA #3.
- #4 MPA - Requires 3 additional hours of work in a Prep and Learning Module and a 96 hour wait before this final assessment is attempted.
While working in a Prep and Learning Module, you will periodically complete a Knowledge Check to make sure you have mastered the topics you gained in Learning Mode. If you do not show mastery during the Knowledge Check, the topics will be added back into your Learning Plan so you can review them again.
No. You must complete a new Placement Assessment to change your placement result. Select the placement tab in the upper right corner of the ALEKS page to start a new Placement Assessment.
No! You may only use one Prep and Learning Module. Choose carefully; if you are unsure which module to select, use the module recommended by ALEKS or consult with the Math Department.


The fine books and manuscripts auction at Bonhams New York on April 13 will feature a number of computing relics, the house announced today, including a recently discovered 56-page handwritten manuscript by British mathematician and computer scientist Alan Turing, which is expected to fetch at least seven figures.
Dated around 1942-44, at the time when Turing was working to break the German Enigma Code at Bletchley Park, the document is thought to be the only extensive autograph manuscript of Turing’s in existence. Besides depicting the foundations of mathematical notation and computer science, the blank center pages of the notebook also contain Turing’s dream journal, written by fellow mathematician and friend Robin Gandy.
The auction will also present a rare German Enigma I Enciphering Machine (also known as the Heeres Enigma) in working condition. The machine, one of few of its kind to have survived WWII, was manufactured for the German military in July 1944, and is estimated at $140,000 to $180,000.
And there’s more: a 1839 handwritten letter signed by the mathematician and world’s first computer scientist Ada Lovelace, estimated at $25,000 to $35,000. Her algorithm, written for Charles Babbage’s Analytical Engine, is considered to be the first code ever used on a computer.
“One of the truly gratifying aspects of auction is the sometimes magical juxtaposition of important historical figures,” Christina Geiger, director of fine books and manuscripts at Bonhams, said in a statement. “Here we have Ada Lovelace and Alan Turing, two computing pioneers who lived almost exactly a century apart, both of whom were impeded by the prejudices of their time but vindicated by history.”


Oooh, I really like this. Brilliant idea. It would take some time to get the wording right, but the end result would be worth it.
I'm going to add to this in an extremely geeky way below the fold...
There is, however, one axiom, called the "axiom of choice", that is up for some debate. It cannot be proved from the other axioms; you either take it as an axiom or you reject its validity. In its simplest form, it says that if you present me with a whole bunch of sets, I can pick one element from each. Simple, right? How can anyone disagree with such a harmless thing? Well, it directly leads to the following result, called The Banach-Tarski paradox: we can take a ball of any size, cut it into 5 pieces, and re-assemble the pieces to get two balls, both of equal size to the first. Despite this (and other) paradoxes, the axiom of choice is good in so many ways that the vast majority of mathematicians believe it.
You can probably see where I'm going with this -- the axiom of choice in mathematics seems to me to be intimately related with the right to privacy in politics. (The axiom of choice is conveniently named for this discussion, as the right to privacy is roughly equivalent to a woman's right to choose.) We have a large group of people (the majority, in fact) that believe it exists and a smaller group that believes it doesn't. So why not make it an axiom? It's good in so many ways.


Best Probability of Winning in Internet casino Gambling
A casino game is some of a variety of casino games that use random chance as a way of determining the outcome of the game. The outcome of 온라인 바카라 a single game is not influenced by the choices of any longer than one person. Casino action is often known as “payback” or “cash out” in comparison to conventional casino games where there is no payout; these games are as an alternative characterized by the “pot”, which can be won or lost. In recent years, there has been an increase in the usage of casino game machines as a means of recreation, gambling, and even as revenue generators for operators of the modern casino hotels.
There are three basic categories of casino game games: table games, gaming machines, and random number machines. Gaming equipment, including pachinko and slot machines, are generally played by one individual at a time and don’t require the dynamic participation of casino personnel to play. Random number equipment on the other hand, like roulette, craps, baccarat, and keno, require the dynamic participation of the players to make the odds get in the casino’s favor. The random number machines used in many movie poker casinos are referred to as blackjack, roulette, and poker equipment.
All three forms of casino game devices are governed by exactly the same mathematical laws of probability. Blackjack, roulette, and poker devices all utilize random number generators or random amount processors to determine the probability of success. These same laws of probability govern the results of most other games including slots. In most cases, it is possible to alter the odds slightly through the use of a number of the many slot gaming devices on the market, though it should be noted that even this small change will have little effect on the final outcome of the game.
The most popular of the casino game devices may be the slots. Slots are carefully identified with gambling thrillers, given that they require luck and are made to keep people playing for long periods of time. Of all the games available on the Las Vegas strip, slots are the most popular attraction, drawing thousands of visitors each night. As the prospect of winning huge may entice some individuals, the long wait necessary for a single get poses another barrier to entry, making slots one of the appealing casino game choices for the traveler.
Blackjack, like slot machines, is really a game of chance. Fortune is involved in a great deal of casino game outcomes, although ability also plays a component. A well-planned strategy can help one improve the odds of winning, but there is absolutely no inherent strategy that guarantees success. For this reason, no matter which casino game is performed, skill, patience, and a bit of knowledge can help one improve the odds of hitting the jackpot. One useful strategy would be to analyze casino game outcomes utilizing the binomial distribution.
Binomial distribution probabilities may be used to examine casino game titles at any level of play, including the novice participant. The binomial distribution functions as a robust tool for identifying the very best odds of hitting in certain slot odds and table video games. In roulette along with other table games with regular deviation probabilities, the binomial distribution can be used to identify the best odds of hitting in a set number of trials. Typical deviation probabilities take random measurements of casino results and will be used to examine the likelihood of casino results from a random event. Once again, a simple understanding of statistics is essential to comprehend how these probabilities can be used to identify the best odds in casino game titles.
It ought to be noted, even so, that the binomial model will not connect with all casino games and to all casino gaming machines. It applies most effectively to games with standardized random outcomes, such as for example roulette, blackjack, and the slots featured in many casinos. Since the outcome of any casino game is totally random, the probability of hitting a jackpot with one machine is the same whether you’re playing at an online internet casino or at a brick and mortar casino. Hence, in this instance, the binomial model would not put on.
Slot machines are by far the most popular games of all casino floors and so are the focus of a lot of the entertainment at casinos around the world. Blackjack, craps, baccarat, along with other slots are the most popular games in NEVADA, Atlantic City, and Macao, and there are literally hundreds of slots per floor at most NEVADA hotels. The large variety of slots on any given casino ground raises the odds of striking a jackpot and helps it be more likely that players will be successful within their bets. Slots are the most dependable way to increase your chances of winning for the most part casinos.


Ancient Egyptian cultures expressed fractions using (distinct) unit fractions. For example they might have written 2/5 = 1/3 + 1/15. In addition to having practical applications for fair division problems, this interesting way of writing fractions raises many interesting mathematical questions which we will explore:
- How do you write a "regular" fraction as an Egyptian fraction?
- Can you write every fraction as an Egyptian fraction?
- How many unit fractions do you need to express 4/n for an arbitrary whole number n?


1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, … was first discussed in Europe by Leonardo of Pisa (whose nickname was Fibonacci) in the early 13th century, although the sequence can be traced back to about 200 BCE in Indian literature.
The sequence follows the rule that each number is equal to the sum of the preceding two numbers. The Fibonacci sequence begins with the following 14 integers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 … Each number, starting with the third, adheres to the prescribed formula.
Fibonacci discovered the Fibonacci sequence primarily through his travels in the Middle East and India. While talking to other merchants and… See full answer below. mathematicians, he was able to discover that Indian culture had developed a numeral sequence system referred to as the Hindu-Arabic numeral system.
Key Takeaways. The golden ratio is an irrational number that is equal to (1+√5)/2, or approximately 1.618… The ratio is derived from an ancient Indian mathematical formula which Western society named for Leonardo Fibonacci, who introduced the concept to Europe.
The Fibonacci sequence shows up in many places, in mathematics and, remarkably, in nature. The Fibonacci sequence can describe branches on a tree, sequences in music, the number of petals on a flower, Pascal's triangle, paintings, structural design, human anatomy, the shape of a spiral, and more.
Solution: By the use of the Fibonacci number formula, we can calculate the rest of the Fibonacci numbers like 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89. (a) Therefore, the 8th term will be 21.
Hence, 63 is the correct answer. The pattern followed in the series is first number multiplied by 2 and plus 1 = second number. Thus, 63 is the correct answer.
triangular numbers: 1, 3, 6, 10, 15, … (these numbers can be represented as a triangle of dots). The term to term rule for the triangle numbers is to add one more each time: 1 + 2 = 3, 3 + 3 = 6, 6 + 4 = 10 etc.
The first known mention of the golden ratio is from around 300 BCE in Euclid's Elements, the Classical Greek work on mathematics and geometry.
18th-century mathematicians Abraham de Moivre, Nicolaus I Bernoulli, and Leonhard Euler used a golden ratio-based formula which finds the value of a Fibonacci number based on its placement in the sequence; in 1843, this was rediscovered by Jacques Philippe Marie Binet, for whom it was named "Binet's formula".
The Fibonacci sequence can describe branches on a tree, sequences in music, the number of petals on a flower, Pascal's triangle, paintings, structural design, human anatomy, the shape of a spiral, and more.
Egg is an example for Fibonacci spiral.
Maths is needed in every step of our life and we cannot live without it. Numbers are the basic foundation and building blocks in our life. If we do not have numbers there is no time, no calendar and the list goes on. We won't even know our birthday, festivals, price of an item etc.
What is the Fibonacci sequence The Fibonacci sequence is a famous group of numbers beginning with 0 and 1 in which each number is the sum of the two before it. It begins 0, 1, 1, 2, 3, 5, 8, 13, 21 and continues infinitely.
The Fibonacci sequence is the series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34… In this series, the next number is found by adding the two numbers before it. Hence, the next term in the series is 8 + 13 = 21.
Solution: The Fibonacci series is the series of numbers 1, 1, 2, 3, 5, 8, 13, 21, … Therefore, the next Fibonacci number in the following sequence is 34.
1, 2, 6, 15, 31, 56, 92, 141, …
The Fibonacci sequence is a series of numbers where a number is the addition of the last two numbers, starting with 0, and 1. The Fibonacci Sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…
These numbers are in a sequence of 1, 3, 6, 10, 15, 21, 28, 36, 45, and so on. The numbers in the triangular pattern are represented by dots. The sum of the previous number and the order of succeeding number results in the sequence of triangular numbers.
According to a study conducted by Dr. Julian DeSilva, supermodel Bella Hadid had the most perfect face as per the Golden Ratio, followed by singer Beyonce and actress Amber Heard.
Regé-Jean Page was named the most handsome man following the Golden Ratio of Beauty Phi.
Phi is an irrational mathematical constant, approximately 1.618.., and is often denoted by the Greek letter φ. Other commonly used names for Phi are: Golden Mean, Extreme and Mean Ratio, Divine Proportion and Golden Ratio. Phi is a naturally occurring ratio which exhibits aesthetically pleasing properties.
Others think that we tend to perceive a face more aesthetically appealing when it features the Golden Ratio because the human eye can process it faster and that causes our brain to feel 'pleased'. The Golden Ratio is not just observed in humans, but it is actually used in architecture and art work as well.
The Fibonacci sequence is a set of steadily increasing numbers where each number is equal to the sum of the preceding two numbers. The golden ratio of 1.618 is derived from the Fibonacci sequence. Many things in nature have dimensional properties that adhere to the golden ratio of 1.618.
Spiral Galaxies is another example of where Fibonacci's sequence is apparent. The milky way has several spiralled arms that follow in the Fibonacci sequence.


Lauren Zundel named Goldwater Scholar
Posted: April 13, 2018
Founded in recognition of U.S. Senator Barry M. Goldwater, a scholarship fund that recognizes distinguished students in the fields of mathematics, science and engineeringhas been bestowed on Lobo Lauren Zundel, a physics & mathematics major, who plans to conduct research in the area of theoretical nanophotonics and teach at the university level after obtaining a Ph.D.
Her mentors include Alejandro Manjavacas, Bernd Bassalleck, and David Dunlap.She was selected based on academic merit from a field of 1,280 natural sciences, mathematics and engineering students nominated by the campus representatives from over 2,000 colleges and universities nationwide.


What is a MySQL DECIMAL? Simply put, it is just a number that can have a decimal in it (2012.56 and -2013.0034 are examples). Let’s take a look at how to declare a MySQL DECIMAL.
M is the maximum number of digits (IE precision) and has a range from 1 to 65 (Take note that versions of MySQL prior to 5.0.3 allowed the range from 1 to 254). This is the total number of digits INCLUDING decimal digits.
D is the number of digits to the right of the decimal point (IE scale) and has a range from 0 to 30 AND cannot be larger than M.
Why use a MySQL DECIMAL?
You would generally use a decimal type when you need to store exact fractional values like money. It doesn’t suffer from the rounding errors of other number types in MySQL.
How do you use MySQL DECIMAL?
Here is some example mysql code…
CREATE DATABASE IF NOT EXISTS Testing; USE Testing; CREATE TABLE WeightCalculation (WeightCalculationID INT NOT NULL, Weight DECIMAL(10,5) NOT NULL); INSERT INTO WeightCalculation (WeightCalculationID, Weight) VALUES (1,54.3445); INSERT INTO WeightCalculation (WeightCalculationID, Weight) VALUES (2,928.23017); SET @a = (SELECT SUM(WEIGHT) FROM WeightCalculation); INSERT INTO WeightCalculation (WeightCalculationID, Weight) VALUES (3,@a); SELECT * FROM WeightCalculation; DROP DATABASE Testing;
WeightCalculationID|Weight 1 54.34450 2 928.23017 3 982.57467
So let walk through this code and see what is going on. To start, I create our Testing database if it doesn’t exist. Then I create a table called ‘WeightCalculation’ and give it two columns ‘WeightCalculationID’ and ‘Weight’ in order to store some simple data. Notice that column ‘Weight’ has been declare a DECIMAL of total length 10 digits and up to 5 decimal places. Next, I insert two rows of data into the table. Just for fun I calculate the sum of all the Weight column values and store them in a user-defined variable named @a then insert the sum into another row of the table. Lastly, I perform a SELECT operation on the table to get it’s contents. To clean up I drop the Testing database.


In September , Edward Frenkel gave a series of four lectures at MSRI, ” Elementary Introduction to the Langlands Program”. The videos of the lectures. An Introduction to the Langlands Program present a broad, user-friendly introduction to the Langlands program, that is, Elementary Theory of L- Functions I. Discover Archives, a shared portal for exploring archival holdings at the University of Toronto and its federated colleges.
WaldspurgerCorrespondance de ShimuraJ. Drinfeld, Langlands conjecture for GL 2 over function fieldsProc. Gross, On the evolution of non-commutative harmonic analysisAmer. Cartier, Representations of p-adic groups: MR [Langlands 5] R. MR [R S] S. PlatonovArithmetic theory of algebraic groupsUspekhi Mat. MR [Shimizu] H. MR [Mackey] G. Lipsman, Group representationsLecture Notes in Math.
Shelstad, Notes on L-indistinguishability based on a lecture of R. MR [Art 3] J. MR [Mac] I. Monthly 85no. MR [Shel 4] D.
Mathematical Sciences Research Institute
Gelbart, Elliptic curves and automorphic representationsAdv. Langlands, Base change for GL 2Ann. MR [Rib] K. MR [Kaz] D. MR [God 2] R. Schiffmann, Automorphic forms constructed from the Weil representation: II, Lecture Notes in Math.
MR [Kudla] S. MR [Tate 2] J.
“An elementary introduction to the Langlands Program” / by Stephen Gelbart – Discover Archives
Wiles, Class fields of abelian extensions of Q, Invent. Langlands, Euler productsYale Univ.
Nauk 7no. Tunnell, Artin’s conjecture for representations or octahedral typeBull. Langlands, L-indistinguishability for SL 2Canad. Springer, Reductive groups Proc. Jacquet, Automorphic forms and automorphic representationsProc. MR [We 3] A. Gelbart, Examples of dual reductive pairsProc. MR [Cas Fro] J. rhe
Shalika, On Euler products and the classification of automorphic representations. MR [Rob 3]A. MR Robert E.
MR [Langlands 9] R. Shelstad, Embeddings of L-groupsCanad. Arthur, The trace formula in invariant formAnn. Piatetski-Shapiro, L-functions for GSp 4preprint, MR [Tate] J. MRhttps: MR [Flick 1] Y. References [Enhancements On Off] What’s this? I, II, Duke Math. MR [Shalika] J.
Gelbart : An elementary introduction to the Langlands program
Flicker, Automorphic forms on covering groups of GL 2Invent. MR [We 2] A. Warner, Harmonic analysis on semi-simple Lie groups. MR [Langlands 1] R.


High-Performance Designs for Linear Algebra Operations on Image Processing
Keywords:Salt and Pepper, Adaptive, Pipeline, FIFO, Rank order, Non linear
Numerical linear algebra operations are key primitives in scientific computing. Performance optimizations of such operations have been extensively investigated. With the rapid advances in technology, hardware acceleration of linear algebra applications using field-programmable gate arrays (FPGAs) has become feasible. In this paper, we propose FPGA-based designs for several basic linear algebra operations, including dot product, matrix-vector multiplication, matrix multiplication, and matrix Factorization. By identifying the parameters for each operation, we analyze the trade-offs and propose a high-performance design. In the implementations of the design a convolution filter using dot product, this is especially useful in noise removal. The proposed designs are implemented on Xilinx FPGAs. Experimental results show that our designs scale with the available hardware resources. Also, the performance of our designs compares favorably with that of general-purpose processor-based designs.
2. Olli Vainio, Yrjö Neuvo, Steven E. Butner, A Signal Processor for Median-Based Algorithms, IEEE Transactions on Acoustics, Speech, Processing VOL 37. NO. 9, September 1989.
3. V.V. Bapeswara Rao and K. Sankara Rao, A New Algorithm for Real-Time Median Filtering, IEEE Transactions on Acoustics, Speech, Processing VOL ASSP-34. NO. 6, December 1986.
4. M. O. Ahmad and D. Sundararajan, Parallel Implementation of a Median Filtering Algorithm, Int. Symp. on Signals and Systems, 1988.
5. Dobrowiecki Tadeusz, Medián Sz?r?k, Mérés és Automatika, 37. Évf., 1989. 3.szám  Xilinx Foundation Series Quick Start Guide, 1991-1997. Xilinx. Inc.
Authors need to sign following agreement with International Journal of MC Square Scientific Research before publishing their articles:
- Authors need to return copyright form to Journal Editor-in-chief to proceed their articles for publication. Meantime, the journal licensed under a Creative Commons Attribution License, which permits other user to distribute the work with an acknowledgement of the authors for International Journal of MC Square Scientific Research.
- Authors are also able to share their separate, additional contractual arrangements for the non-restricted contribution of the journal with an acknowledgement of publication in International Journal of MC Square Scientific Research.
- Authors are allowed and encouraged to share their work during the submission process for increasing citation and exploring to increase the paper availability in worldwide way. The Effect of Open Access.


In the last very short post here, we saw how a special value is used to vary the hash of the block. You may also recall that this value is called the Nonce. So now, its time to continue our journey deep into the fundamentals of what makes a blockchain. This time we will be taking a closer look at The Cryptographic Puzzle.
So at the beginning of this post let's just make a statement very loud and clear.
The hash is just a number.
Now, many of you may already know this but for those of you who don't let's explore how. For example,
7eb720cb71f1bf1d0b4c2f6442d0148d775fdd473ea3f33a28bd893a21d7e5b4 is a real SHA-256 Hash. Now, you may have already noticed that this is not a number, it has characters like e, f etc. Let's explain how. This my friends is a hexadecimal number. The hexadecimal format has 16 characters. These are the numbers
0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and then some alphabets
a, b, c, d, e, f. Here
a denotes 10,
b denotes 11,
c denotes 12 and so on. Got it? Good. Now you may ask but why are you telling me this? Let's find out, shall we?
The Leading Zeroes
To begin, let's take another hash number for example.
Notice how this number has some zeroes in the beginning. But, why in the world does it matter if it is a number or a bunch of characters. Well because, numbers are special because the have a value. And as you may remember from your elementary school math class that zeroes in the front of a number don't have a value.
Look at this diagram, it represents all the hashes that can exist. Since, these hashes are hashes are numbers, we can compare them and easily determine which one is bigger and which one is smaller. Also, you should take notice that the more the leading the zeroes, lesser will be the value of the number.
Now, the blockchain system sets a target. The hash of this block along with the nonce should be lesser in value than this target. Let's put our hashes in the table once again.
Let's say that the target was
00000000000062b4fccaebda5722f9d4d22465eab2ac0285b43f794ed71ee704. Our seconds hash would clearly be below the target and that is what we (or the miners) want. Now, this is where the nonce comes into play. The miners can easily change the nonce and try to get an acceptable hash value.
Quick Trivia: The nonce that gives us the accepted hash is called the golden nonce.
You may already know that the hash itself is unpredictable and changes rapidly due to The Avalanche Effect. If you don't then, I suggest reading my post on the same.
That was it, folks! Today, you learnt about one of the key aspects of a blockchain. See you in the next one!


Position of the outermost perimeter of shear reinforcement: the value of k
Eurocode 2 part 1-1: Design of concrete structures 6.4.5 (4)
The control perimeter at which shear reinforcement is not required, uout (or uout,ef see Figure 6.22) should be calculated from Expression (6.54):
|uout = βVEd / (vRd,c d)||(6.54)|
The outermost perimeter of shear reinforcement should be placed at a distance not greater than k⋅d within uout (or uout,ef see Figure 6.22).
The recommended value of k for the calculation of the position of shear reinforcement is 1,5.


Multiple Y-Axis Scales
Okay, I have a graph that I will need up to 3 different Y-axis scales.
I see how to add multiple scales manually, but I dont always want all
3 scales to be visible. Is there a way to use the property node to
turn on or off the extra Y-axis scales?
Leave a comment...
- 1 Comments
- Thanks! That did it.#1; Tue, 29 Apr 2008 21:02:00 GMT