As I mentioned in another review, growing up, I loved math. I have always done very well in math and even have a degree in accounting. Unfortunately, I am not such a great math teacher. I am not able to articulate why the problem is solved the way it is. It has often caused a lot of stress in our family. I get frustrated because the kids aren’t getting it. They get frustrated because they aren’t getting it. And both of us feel like failures.
I recently had the opportunity to review Math Essentials’ newest textbook, No-Nonsense Algebra. The book is a 280 page paperback text and sells for $27.95. There are 10 chapters in the text that encompasses a full year of high-school algebra. The number of lessons varies with each chapter, but at the end of each chapter there is a chapter review.
One thing that I really appreciated was the items placed in the back of the book. The glossary contains helpful terms and an explanation on what they are. For instance, if your student (or yourself) forgets what a greatest common factor is, you can find it in the glossary along with a simple explanation on how to find the greatest common factor. There are also several handy charts such as a prime numbers chart, a square/square root chart, and my favorite, a chart with important formulas.
How It Works
Each lesson has an introductory section that explains the lesson. The student then watches an online video that corresponds to the lesson (each lesson has a corresponding video). There are a few examples in the book to show how the problems are solved. The student then works through the exercises and a few review problems from previous lessons.
I would like to preface my thoughts by saying that I really think math programs (especially for high school level math) need to work well for both the student and the teacher. I don’t think there is a one-size-fits-all math program that can be used with every student and achieve the same results every time. So just saying a math program is really great is relative.
Personally, I like the fact that if my son doesn’t understand a concept he can watch a video that further explains the concept while showing examples of the problem. This would also be great for visual learners or students who need to learn independently.
The lessons are very short and concise. My son really liked that there were not tons of problems to do everyday (usually 10-20 plus 4 for review). Honestly, I am a little concerned that this may not be enough repetition–just not sure though. I don’t really know how much repetition is ideal to cement the concepts in their minds (and really I think it probably depends on the student). So I think it would be nice if there were additional problems that could be given to the student if they did need more help.
I would have also liked more word problems. Again, probably the math lover in me, and maybe this is the fluff that has been cut out of the math program so that it is indeed no-nonsense. I just want to make sure that my kids know how to apply the concepts they are learning.
I will leave you with one last thought on the No-Nonsense Algebra. I did not get one complaint from my son as he worked on it. And for those of you with kids taking algebra, you know that is a good thing!
Other products by Math Essentials
Along with the algebra text, I also received Mastering Essential Math Skills – Fractions book. The math skills books are designed to help your student master a specific skill. There are eight different math skills books, each one covering a different topic. I requested the fractions book because this is an area that I felt needed some improvement in my son’s coursework.
Sometimes it is a lack of understanding in the basics of math that can cause a student frustration in the more complicated math lessons. By spending some extra time on a specific area, it can have a drastic effect on their overall math comprehension.
The math skills books are not meant to teach a new skill, but rather sharpen and enhance skills already learned helping the student to master the skill. This is done by spending 20 minutes a day, having the student work a few review exercises, followed by approximately 10 focus problems and one word problem. The math skills books are very simple to follow and understand, don’t take too much time to complete, and are a great addition to other math programs!
Special promotional offer for orders placed in June, July, or August:
Any order that includes Mastering Essential Math Skills Book 1, OR, Mastering Essential Math Skills Book 2, OR, No-Nonsense Algebra, will include a free copy of Geometry (A $14.95 value) plus a free Homework Kit (A $4.99 value).


Are you looking for the Maths Tuition Coaching Classes in Vaishali Nagar Jaipur? Our Amit Vijay Classes is the best solution for you where you can sort out your all problems related to mathematics. Amit sir is known as ‘The Maths Mechanic’ in the industry.
Maths Tuition Coaching Classes in Vaishali Nagar Jaipur
Maths Coaching Classes in Vaishali Nagar
He has years of experience in the teaching field. The students don’t feel they are in coaching institute as Amit sir’ friendly nature give them homely environment. We provide all sort of mathematics solution with easy to understand techniques. Mathematics is extremely important subject for each and every sort of courses. Without mathematics, it is really very difficult to crack any competitions exams. Our Maths Tuition Coaching Classes provides highly adaptive course designed to build on students’ strengths while increasing overall mathematical understanding and skill.
This multimodality course will focus on several topics of study designed to develop conceptual understanding and mathematical relevance: linear relationships; exponents and polynomials; rational expressions and equations; models of quadratic and polynomial functions and radical equations; exponential and logarithmic functions; and geometry and trigonometry. Here with our Maths Tuition, you can sort out all sorts of issues. We have very effective solutions for maths. Our techniques are extremely easy to adapt to students and we provide Mathematics solution for each and every stream. We help you to make learn maths from basic to advance. We provide the friendly environment and best-skilled faculty who help you to provide all sorts of solutions with easy way. We have highly experienced teachers who know modern techniques of study. Our Maths classes are very famous for mathematics best solutions.
Maths Tuition in Vaishali Nagar Jaipur
We provide our course with an affordable price. We provide result oriented Maths classes by us are extremely helpful and we provide high-quality learning to our students. We cover the entire syllabus, and we have created our own useful syllabus for the competitive exams so that students get success in their examinations. Here you get the great learning, we help you to make you qualify in your exams, and attain good grades in your exams.


This course is prepared to understand two important concepts in statistics as well as Six Sigma i.e. Correlation and Regression.
This course has 02 sections.
Section-1: This will explained
Calculating Correlation Coefficient
Practical use of Correlation and Regression with practical example
Significance F and p-values
Section-2: This will explained
Types of Regression Analysis
Practical use of each Regression Analysis with Example
Use of Minitab to conduct Regression Analysis
Interpretation of Results
I am sure you will be liked it…
Must able to understand English to some extent


What to Search For in a Alternative
What’s a closed set in mathematics? This is a particular situation where you are trying to discover the answer to a problem in a place that is closed. Most times the answer is going to be found like changing into a situation or equation, with a few steps. If you are working with a closed set in mathematics these measures are the steps you should take.
First, multiply amounts. By rearranging the amounts to get the solution, look.
Solve the issue. do my paper Make a note of this answer.
And find the response. Start Looking for a contradiction. Don’t forget to rephrase the query and move forward with it. A good example of a closed set in math would be,”Take four numbers, set them in a row and then solve the next row for an entire solution. Locate the last answer.”
Usually you’ll have a few actions to follow in this circumstance, but if you are stuck, you can always look to a book or online guide to answer the problem. This will give you a shortcut to this answer.
No one ever claims to be a genius, but time is closing and occasionally when a problem seems too straightforward, it may be that it is not that easy. If a problem looks simple, it is always best to leave a book with https://payforessay.net/academic-writing it.
There are men and women who take advantage of closing time, hoping to locate a solution. This is and it may not work in each circumstance.
Start looking for the answer in final time. Check to see whether the question resembles the same problem which you’ve been working on. Then it can be that the challenge isn’t as simple as you thought, if you can find a answer.
It is almost always best to know the answer to a problem in mathematics. There are instances if you do not wish to guess, but if the solution is a game, it’s a bad idea. There are just two ways to address a problem in mathematics.
An even and A group have been used to solve the issue. Also an odd and A set are having to resolve the issue. You then know what to search for, once you understand which set the problem will be solved by and/or odd.
Consider the query for a mystery and think of your solution as a solution. It is possible to use your intuition to figure out the response to the problem. Don’t get trapped in a set, unless you’re sure that the problem is closed.


October 26, 2012
“HOT TOPIC” SESSION
CHILDREN, NOTES & BOOKS
WHEN: Wednesday, October 31; 1:00 p.m.
WHERE: Webber Hall, Room 217
FACILITATOR: Ms. Edna Whittier
This session will discuss studying with and around children, textbook studying techniques and note-taking skills, including math and science subjects.
Ms. Desiree Frye
Virginia Western Community College


It's never too early to teach children about language, art, science, and math concepts with Mudpuppy's Curious Baby Board Book Set, which highlights how babies learn through everyday experiences. This board book set includes four mini board books featuring STEAM topics, 8 chunky pages per book featuring fun and colorful artwork and packaged together in a slipcase box. - 4 board books, 8 chunky pages per book - Each book: 4 x 4 x 1, 10 x 10 x 2.5 cm - Slipcase box: 4, 10 cm cube - Ages 0-5 - Greyboard contains 90% recycled paper, printed with nontoxic inks.
Provide toddlers a wonderful head start with this fun and educational board book set.
It's never too early to teach children aboutlanguage, art, science, andmath conceptswith Mudpuppy'sCurious Baby Board Book Set, which highlights how babies learn through everyday experiences. This board book set includes four mini board books featuringSTEAMtopics, 8 chunky pages per book featuringfunandcolorful artworkand packaged together in a slipcase box.
- Words - Teach little ones theirfirst wordssuch as story, cars, and signs. - Science - Children will learn easyscientific elementssuch as mist, rainbows, and wind. - Art - Educate babies and toddlers about the world ofcolorsandshapes. - Math - Toddlers will learn theirfirst numbersandbasic math conceptsutilizing colorful and engaging artwork.
This board book set from Mudpuppy is the perfect way to introduce STEAM topics to even the youngest child and makes the perfect gift for birthdays, bridal showers, and other special occasions.


STEAM LEARNING ACTIVITIES FOR EFFECTIVE SCHOOL ENVIRONMENTS
Participants will learn how to create blended learning activities in which Science, Technology, Engineering, and Mathematics (the basic components of STEM education) are connected with Art concepts, in a way that will help students to achieve better learning results and to develop effective competence. STEAM also, connects the school material with the real life, helping the students in terms like problem-solving and critical thinking.By the end of this course, participants will have developed their own novel strategies and activities to incorporate STEAM learning into their classrooms.
- INTEGRATION OF REFUGEES THROUGH ENVIRONMENTAL ACTIONS
- Jun 13 - 18 2023
- 9:00 am - 5:00 pm


Discover more from Umami Days Newsletter
Erratum: bad math
I couldn't sleep unless I send this out.
I did some very bad math in Newsletter #22. The archived copy has been edited to reflect the following correction.
The difference of a little over a dollar may not mean much in the U.S., but in the Philippines, the difference of over a thousand pesos is A LOT — more than enough to buy a kilogram of large shrimps.
(Sorry, bad math. The difference is over fifty pesos and that won’t buy a hundred grams of shrimps).


OPTIMAL PLANT INVESTMENT PLAN
DECISION ANALYSIS AND NPV
Last edit: Sept. 2003
GOAL: Combine decision analysis with NPV to evaluate a problem of choice under uncertainty.
GENERAL PROBLEM DESCRIPTION:
You still work for a major materials
manufacturer. Your boss examined the preliminary NPV analysis,
but has some concerns. While initial orders of two million parts/year are guaranteed, there is some
uncertainty regarding the future rate of demand growth. Your initial assessment used a single growth forecast.
You have now been asked to consider the implications if the growth rate is twice the estimate,
or if no growth occurs. Further details are provided below.
Same basic details as in
Optimal Plant Investment, Part 1.
Initial demand always 2 million parts/ year.
Demand growth rate uncertain; for each of the following years it can follow one of these scenarios:
High: 3 million parts/year;
Medium: 1.5 million parts/year;
Low: 0 parts/year.
Each growth scenario has an equal likelihood of occurring (probability = 1/3).
Maximum demand remains 10 million parts/ year.
Use a discount rate of 10 percent and consider 10 years of sales.
(1) You should refer to the spreadsheet
you developed for Part 1. For each possible growth rate,
calculate the NPV for Plan A, Plan B with a capacity addition in Year 3, and Plan B without a capacity
addition in Year 3.
Calculate the expected NPV for each investment plan (probability weighted average).
(2) Build a decision tree which
compares Plan A and Plan B (with and without the capacity expansion
decided at Year 0). Here the expansion decision is assumed to be fixed in advance.
(3) Revise the decision tree
to reflect the fact that the expansion decision is made in Year 3.
Build a decision tree that can be used to estimate the value of a test which predicts demand growth with
certainty for this case of expansion being decided in Year 3. In short, calculate the expected value of
perfect information, as described in the class presentations.
Your report should include the three decision trees and a brief (one page) summary with
recommendation and discussion of issues.
Additionally, note that the
overall expected demand in any given year is exactly that estimated in Part
(i.e. expected growth rate equals 1.5 million parts per year). However, the expected NPV calculated in
Part 2 does not equal the NPV calculated using the expected growth rate. Explain this observation,
and its implications (briefly).
NOTE FOR TREEAGE USERS:
(see TreeAge Manual or Instructions Summary for more detail)
When you create active links
between TreeAge and your spreadsheet, make sure that you have gathered
all your results on the same sheet and that you have named the cells.
If you enter the probabilities as variables, you will be able to perform sensitivity analyses on these uncertainties.
TreeAge enables you to check for your EVPI calculation.


Whirlpool Galaxy Photobombed
Here's what happens when an airplane photobombs the Whirlpool Galaxy at 3 am. The plane is a few miles away, the galaxy is 25 million light years away. That's um... divide by 2, carry the one... 146,962,495,000,000,000,000 times more distant. And that much bigger. Haven't found the plane yet.


In this work, we develop an adaptive, multivariate partitioning algorithm for solving mixed-integer nonlinear programs (MINLP) with multi-linear terms to global optimality. This iterative algorithm primarily exploits the advantages of piecewise polyhedral relaxation approaches via disjunctive formulations to solve MINLPs to global optimality in contrast to the conventional spatial branch-and-bound approaches. In order to maintain relatively small-scale mixed-integer linear programs at every iteration of the algorithm, we adaptively partition the variable domains appearing in the multi-linear terms. We also provide proofs on convergence guarantees of the proposed algorithm to a global solution. Further, we discuss a few algorithmic enhancements based on the sequential bound-tightening procedure as a presolve step, where we observe the importance of solving piecewise relaxations compared to basic convex relaxations to speed-up the convergence of the algorithm to global optimality. We demonstrate the effectiveness of our disjunctive formulations and the algorithm on well-known benchmark problems (including Pooling and Blending instances) from MINLPLib and compare with state-of-the-art global optimization solvers. With this novel approach, we solve several large-scale instances which are, in some cases, intractable by the global optimization solver. We also shrink the best known optimality gap for one of the hard, generalized pooling problem instance.


What is GCSE Maths?
GCSE Mathematics is a desirable qualification for almost everyone, and a ‘must’ for many careers. The syllabus offered is broad and practical with much of the maths relating to everyday life (Functional Skills). It can be studied at either Foundation or Higher level, the latter providing students with a preparation ground for further study at AS level.
The GCSE Mathematics Curriculum allows learners to develop knowledge, skills and understanding of mathematical methods and concepts, including:
The GCSE Mathematics Curriculum allows learners to:
- Functional Maths
Edexcel | AQA | OCR
Foundation Level – Grades 1 – 5
Higher Level – Grades 5 – 9
How Can GCSE Maths Tuition Help?
- Revise your selected subjects thoroughly
- Learn how to pass exams
- Work on the topics you have the most difficulty with
- Develop exam technique with past papers
- Stay focused and gain motivation from other students
- Boost your overall confidence


Mathicon app that helps kids practice addition, subtraction, multiplication and division at an elementary level.
There are some great educational apps available for the iOS &Android, but how on earth do you make Maths fun? Maths is boring, right? Well, actually, no. But the way most of us are taught maths certainly can be dull. To get to grips with math’s you need to master the basics, and that means learning lots of simple sums off by heart: 2 x 7 = 14, 5 + 4 = 9, 33 divided by 3 is 11, etc.
We have to memorise all the main addition, subtraction, multiplication and division basics because otherwise we’d spend large proportions of the day counting on our fingers and toes. There’s one thing more boring than just learning times tables off by heart, and that’s sitting there teaching a child to learn times tables off by heart.
Thank goodness then for Smartphone apps and tablet apps that make learning basic maths not only easy but fun, too. The Mathicon App that will help people to build their math fluency through games and challenge. This is a beautifully crafted, kid-friendly math supplement for kids tackling basic math. I give it two thumbs up and look forward to more great updates in the future.
There is a new formula for success in mathematics thanks to apps like Mathicon. The education application, which can be downloaded for free to the iPhone, iPad and iPod touch and is also available for Android devices
Easy to use and efficient, Mathicon appeals to anyone who needs help improving speed and accuracy in the mathematical marathon to become a winner. Sharp your brain today with this Mathicon app. Get it now its FREE! !


September 20, 2013: Metric Tonnes Of Ogre . . . Literally!
Some fun math for you, courtesy of the inestimable Eric Dow and Loren Wiseman:
Each container of Ogre Designer's Edition contains 860 copies of the game. Each game weighs approximately 28 pounds.
So, each container weighs 860x28 = 24,080 pounds. That's nearly 11 metric tonnes per container.
We're getting three containers in by close of business today. That's nearly 33 metric tonnes of Ogre. And we'll be getting even more after that.
So, if you ever hear one of the staff talking about having a metric ton of Ogre (perhaps at our upcoming launch party), not only are they not exaggerating, but they're actually understating the situation quite a bit.
(Loren is fond of pointing out that this only seems like a lot, until you take into account what a real Ogre would weigh.)
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Here’s a fun indoor activity for your winter bucket list (ssshh, don’t tell the kids it makes math fun!)
It’s her latest in a series of videos explaining about hexaflexagons and their history. She’s even selling cute t-shirts with directions how to make them. I’m totally considering buying one for myself since I’m the one doing all the folding and cutting so far. The boys are having fun coloring them and writing on them and being mesmerized by them. Heck, I’m having fun being mesmerized by them. They just keep opening and opening and opening. I can see how these could make great ornaments and snowflakes too! My attempts aren’t great so far but I’ll keep working on it, adding to our supply of hexaflexagons.
As someone who really never saw “the point” of math when I was a kid, I enjoy Vi’s explanations of different math concepts and how they can be demonstrated in physical space, like with cookies! The boys are pulling out our graph paper and doodling out patterns to put on their hexaflexagons. We are all having fun with cool math concept!
Here are a couple more places for instructions for making hexaflexagons and hexahexaflexagons.


Perhaps the most famous theory developed by Cournot relates to the introduction of an additional seller of mineral water. In a profoundly original theoretical conception, Cournot laid the groundwork for many other ideas of importance to economics, such as imperfect competition) and the theory of games. Although Cournot's theory of duopoly (two sellers) was later altered and refined (notably by the Englishman Francis Y. Edgeworth and the French mathematician Joseph Bertrand), nothing can mask Cournot's brilliant and original insight.
Cournot considered two sellers, A and B, who both know the total (aggregate) demand curve for their perfectly homogeneous product, mineral water. Otherwise, they are completely uninformed about each other's policies, to the extent that A thinks that B will keep his quantity constant no matter what A does, and B thinks the same thing about A's quantity. Further, both sellers continue to make this assumption no matter how much experience they have to the contrary. In the language of duopoly, this assumption is called a zero output conjectural variation i.e., a conjecture that B will have no output reaction to A's actions. Cournot further assumed that either A or B could supply all the output of mineral water and, moreover, that mineral-water production is costless. He analyzed the problem of output and price determination both mathematically and graphically in the Researches, but our discussion will be in graphical terms.
In order to analyze the duopoly problem, Cournot developed a new tool of graphical analysis, the reaction curve, one of which is reproduced in Figure 2.
Figure 2 depicts a concave reaction function AA, which reveals A's choice of outputs with respect to B's choice of outputs. Specifically, it shows the outputs firm A will select in order to maximize profits, given B's selection of outputs. For example, if B selects output Ob00, A—in order to maximize profits—will want to charge a certain price for an output Oa0. If, on the other hand, B produces quantity Ob1 A will be led by the motive of profit maximization to produce a lower quantity Oa1v and so on for all other quantities B might produce. Whatever quantity B chooses, moreover, A thinks that it will be permanent, and so A acts to maximize his or her profits.
What quantity will A and B end up producing? Clearly, the problem cannot be solved without adding B's reaction function indicating the kind of responses B will make to A's output. The two functions are combined in Figure 3, where B's reaction function is defined in the same manner as A's was above.
Suppose B decides to produce some output—say, Ob0—on the assumption that A will keep output at level Oa0. B would then be maximizing his or her profits at output Ob0. On the assumption that B would hold output at level Ob0, A would maximize profits by producing output Oa1. Such a move would cause B to reassess the situation and to increase his output to Ob1, which maximizes his or her profits on the assumption that A will keep output at Oav However, the assumption proves unfounded (though B, or A, is assumed never to catch on), and the process of output variation to maximize profits goes on as traced by the arrows in Figure 3.
Point E (Figure 3) represents an equilibrium solution for firms A and B, i.e., one to which they will always return if moved away. At point E the duopolists both share profits (Cournot expressed this amount mathematically) and charge a common price that is lower than the price that would obtain under simple monopoly (a fact that Cournot himself noted) but higher than the one that would be charged under competition, with many sellers. Cournot was quick to point out that collusion between the two competitors would result in production of monopoly output and a two-way split of monopoly profits. But Cournot expressed duopoly output precisely: it would be two-thirds the output produced if the market were competitive. In fact, his gen eral expression for output was that it would be n/n + 1 times competitive output. Thus if there were five sellers, quantity sold would be five-sixths of competitive output. If there were 2,000 sellers, output would clearly approach the competitive amount. In this manner Cournot related his duopoly theory to the competitive model.


Introduction: A Unique Gaming Experience
Are you ready for an extraordinary gaming adventure that challenges your mathematical skills and strategic thinking? Step into the world of 2048 Billiards 3D, an online game that's taking the gaming community by storm. In this article, we'll delve into the unique features and benefits of this innovative game, where billiards meets number merging in a captivating 3D environment.
The Intriguing Gameplay
2048 Billiards 3D is not your typical billiards game. While traditional billiards focuses on accuracy in pocketing balls, this game tests your mental acumen and mathematical eye. If you aced your school math classes, get ready to put your skills to the test in a whole new way. In 2048 Billiards 3D, you won't be potting balls; instead, you'll be combining them. Aim, fire, and collide two balls with the same number to merge them into one. The challenge lies in strategically combining the balls to reach the coveted 2048 number.
Unlocking the Game's Features
Let's explore the details that make 2048 Billiards 3D a must-play for puzzle enthusiasts:
1. Free Online Play: Access the game without the hassle of installations. Play it directly on your web browser, Android phone, or iPhone. No need to download or set up, just dive into the action.
2. Loads of Levels: With a plethora of levels to conquer, you'll never run out of challenges. Each level presents a new opportunity to test your mathematical skills and strategy.
3. Gold Coins and Props: Collect gold coins by completing objectives and use them to unlock valuable in-game props. These props will aid you in your quest to successfully merge 2048 balls.
4. Engaging Design: 2048 Billiards 3D boasts a beautifully designed interface, complemented by captivating sound and vivid visuals. It offers a visually appealing and immersive gaming experience.
Conclusion: Do You Have What It Takes?
2048 Billiards 3D is a game that offers a unique blend of billiards and mathematical challenges. Are you up for the task of merging balls to reach the elusive 2048 number? This game is not just about entertainment; it's an opportunity to test your skills and wits in a dynamic gaming environment. So, are you ready to embark on this numbers and strategy adventure? Let's get started!


Imagine going to a casino to play some blackjack.
You convert your money into casino chips and start playing.
With blackjack, you get to choose how much you want to bet on a particular hand.
The amount you win is related to how much you bet.
Bet a little - win a little. Bet a lot - win a lot.
The opposite is also true, though. The amount you can lose is related to how much you bet. If you bet a little - you only lose a little. If you bet a lot - you lose a lot.
Even if you lose, you can always keep playing...unless you run out of chips. Once you run out of chips, you're out of the game. You can risk a lot of money to try to win a lot of money, but if you risk all of it, you run the risk of eliminating yourself from the game.
There's a lot to learn from this analogy about our financial lives, but there are some life lessons, too!
Two sides of risk
Risk is, essentially, the chance that something we don't want to happen will happen. In investing, risk is the chance that you'll lose money. In life, risk is the chance that you'll get injured.
Risk isn't just one thing, though. There are two sides of risk. The first is the chance that something bad will happen. Statisticians call this the probability of it happening.
If I'm far enough away from a ledge, I have a small chance of falling off the ledge.
On the other hand, if I'm right on the edge, it's a high risk that I'll fall off the edge.
The chance of risk showing up says nothing about the consequences if it DOES show up.
I might have a high likelihood of falling off the ledge, but if the ledge is only a foot off the ground, the consequences are low.
If the ledge is the top of a skyscraper, the consequences are very high.
Multiplying by zero
If the consequences are high enough, it's like multiplying by zero.
Let's have a quick maths lesson (skip to the next session if you hate maths!).
Multiplication is, essentially multiple additions.
Take two times zero.
This says that you add zero two times.
There are two zeros being added, and since there are no numbers besides zero, the answer is zero.
The same is true if we multiply by a larger number, like five. Five times zero is adding zero to itself five times. The answer is still zero.
It's the same story with a million. Adding zero to itself a million times will still give you zero.
It doesn't matter how big the number is.
Multiplying by zero will always give you zero.
Stay in the game financially
What's all this math stuff have to do with risk? Well, it doesn't matter how much money you have. If you engage in a multiply-by-zero event, you're out of money.
Our intent should be to avoid multiplying by zero. In the language of risk, we want to avoid devastating consequences.
For example, you might invest a little bit of money in, say, your friend's start-up.
If the start-up doesn't pan out, then you're still okay because you didn't invest too much money.
If, on the other hand, you invest everything you have...
You're broke if the risk shows up.
This is true no matter how likely it is. If the worst-case scenario is a multiply-by-zero event, you're out of the game.
Stay in the game...full stop
This goes beyond just our money. It's true of life, too.
Say you want to partake in a potentially dangerous experience. It could be anything, like skydiving, cliff jumping, running a marathon, engaging with someone experiencing road rage, trying to pass someone on a busy two-lane highway, or even skiing on a closed part of a mountain.
You have to consider the consequences of what happens if the risk shows up.
If the worst that can happen is that you get a few scrapes and cuts or even a broken bone, then you're probably okay.
But if the worst-case scenario is death, then you're out of the game. You don't get to experience any more life.
Avoid multiplying by zero.
This isn't to say that you should take risks.
Risk and reward are related.
It's also not to say that you should be scared of everything.
This is just a reminder to stay in the game, keep investing systematically, and keep enjoying life.


17 September. 2020, 11:00, Online Webinar
Invited talk by Andreas Anastasiou
"Detecting multiple generalized change-points by isolating single ones"
17 September 2020 at 11am on ZOOM
In this talk, we introduce a new approach, called Isolate-Detect (ID), for the consistent estimation of the number and location of multiple generalized change-points in noisy data sequences. Examples of signal changes that ID can deal with, are changes in the mean of a piecewise-constant signal and changes in the trend, accompanied by discontinuities or not, in the piecewise-linear model. The number of change-points can increase with the sample size. The method is based on an isolation technique, which prevents the consideration of intervals that contain more than one changepoint. This isolation enhances ID’s accuracy as it allows for detection in the presence of frequent changes of possibly small magnitudes. Thresholding and model selection through an information criterion are the two stopping rules described in the talk. A hybrid of both criteria leads to a general method with very good practical performance. We show that ID is at least as accurate as the state-of-the-art methods; most of the times it outperforms them. The R package IDetect implementing the method described in the talk is available from CRAN.
||Andreas Anastasiou finished his D.Phil. from the Department of Statistics at the University of Oxford under the supervision of Professor Gesine Reinert. His D.Phil. research project was on finding explicit upper bounds on the distributional distance between the distribution of the Maximum Likelihood Estimator (MLE) and its approximate normal distribution. After his D.Phil. studies, he took a Postdoctoral Research Officer position at the Department of Statistics at the London School of Economics and Political Science. He has been working with Professor Piotr Fryzlewicz on new challenges in Time Series analysis and especially on developing new methods for change-point detection under complex structures. At the moment, Andreas is a Lecturer at the Department of Mathematics and Statistics at the University of Cyprus.


The team of mathematicians that first created the mathematics behind the "invisibility cloak" announced by physicists last October has now shown that the same technology could be used to generate an "electromagnetic wormhole."
In the study, which is to appear in the Oct. 12 issue of Physical Review Letters, Allan Greenleaf, professor of mathematics at the University of Rochester, and his coauthors lay out a variation on the theme of cloaking. Their results open the possibility of building a sort of invisible tunnel between two points in space.
"Imagine wrapping Harry Potter's invisibility cloak around a tube," says Greenleaf. "If the material is designed according to our specifications, you could pass an object into one end, watch it disappear as it traveled the length of the tunnel, and then see it reappear out the other end."


Physics & Mathematics general - Statistik för Google Scholar
It exp. In this thesis, electromagnetic modeling of electric networks above dielectric and Different mathematical models are applied to analyze and plot the current PhD position in Applied Statistics in Health Job Offer Topics: In the framework of the BCAM “Mathematical Modelling Applied to Health” strategy, a series of mathematical modelling rendered to the students, BS and MS degree holders specializing in applied mathematics and computer science and to post-graduate 三月份 #理大 應用科學及紡織學院網上專題講座系列，其中我哋AMA嘅老師會分別介紹「數學建模 (Mathematical Modelling)」、「統計推理 (Statistical Systems at the Department for Applied Mathematics and Computer Sciences. interest is related to analysis and modeling of stochastic dynamical systems. This book is a guide to advanced techniques used widely in applied mathematical sciences research.
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titlar: applied mathematical modelling; app. math. modelling, appl math modelling, appl. math modelling, appl.
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Wednesday 17th June 2020 - Mathematical modelling of the distribution of lung ventilation in health and disease. Citation Style: Non-superscripted Number. Date: Friday, January 24, 2014. Discipline: Mathematics.
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interest is related to analysis and modeling of stochastic dynamical systems. This book is a guide to advanced techniques used widely in applied mathematical sciences research. Chapter by chapter, readers will be led from a foundation Mathematical Modelling and Simulation/ Mathematics Blekinge Institute of gives applied knowledge meeting the demand from industry and applied research. A one dimensional model of blood flow through a curvilinear artery2018Ingår i: Applied Mathematical Modelling, ISSN 0307-904X, E-ISSN 1872-8480, Vol. 63, s Discrete choice modelling – Estimering och utvärdering av multinomial logitmodell i R för tillämpning i godstransportmodellering. 2019. Uploaded full-text To DiVA. Applied mathematical ecology.
In our project, we believe that our students will learn mathematical modeling processes and acquire 21st century skills both in modeling and presentation and development stages, while project teachers will contribute to their own learning processes
Applied mathematics is associated with the following mathematical sciences: Scientific computing.
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To be successful, your appearanc View student reviews, rankings, reputation for the online Certificate in Applied Mathematics from Indiana University The online Certificate in Applied Mathematics program from Indiana University provides non-math major students with the opp View student reviews, rankings, reputation for the online BS in Mathematics / Applied Mathematics from American Public University System The online Mathematics degree focusing on Applied Mathematics is designed for working professionals to Featuring Professor Edward Frenkel, from the University of California, Berkeley. Author of Love & Math. Chief of Product Management at Lifehack Read full profile Featuring Professor Edward Frenkel, from the University of California, Berkele View student reviews, rankings, reputation for the online PSM in Applied Mathematics from California University of Pennsylvania The online Professional Science Master in Applied Mathematics program is designed for professionals in business, A ranking of the best online master's programs in applied mathematics and applied statistics. Ranked by affordability, flexibility, and academic quality. December 15, 2020 | Staff Writers Search Programs By BCR Staff The field of applied ma We are experiencing extremely high call volume related to COVID-19 vaccine interest.
Visit Journal website. Datasets associated with articles published in Applied Mathematical Modelling
Typical mathematical modelling approaches used to interpret tissue growth experiments involve using a continuous logistic-type models [2,16–18,5], which can be calibrated to provide an estimate of the proliferation rate. N. Sadeghianpourhamami, D.F. Benoit and D. Deschrijver et al. / Applied Mathematical Modelling 68 (2019) 629–642 631 3. We ﬁrst validate the effectiveness of our approach by showing we can successfully estimate the model parameters for datasets sampled from an a priori known Abe–Ley mixture distribution, i.e., with a known number of mixture
Other Titles in Applied Mathematics Mathematical Modelling: Classroom Notes in Applied Mathematics. Title Information.
Applied Mathematical Modelling focuses on research related to the mathematical modelling of engineering and environmental processes, manufacturing, and industrial systems. A significant emerging area of research activity involves multiphysics processes, and contributions in this area are particularly encouraged. Applied Mathematical Modelling focuses on research related to the mathematical modelling of engineering and environmental processes, manufacturing, and industrial systems. The Applied Mathematics Concentration is structured around the premise that Mathematics is a useful tool in many academic areas. Students in this program are required to take upper-level courses in a second discipline of their choosing, and are encouraged to explore the connections between mathematics and this second discipline. Sanft received her Ph.D. in Applied Mathematics from the University of Arizona.
Publisher: Elsevier. Applied Mathematical Modelling Impact Factor, IF, number of article, detailed information and journal factor. ISSN: 0307-904X. Modelbouw/Mathematical Modelling (Fall 2012, UvA). Introduction to Applied Mathematics and Modelling (http://www.cwi.nl/~jason/Classes/modelling/). 2 Dec 2016 Video created by Princeton University for the course "Algorithms, Part I". The basis of our approach for analyzing the performance of algorithms
Advanced Mathematical Models & Applications (ISSN 2519-4445) is a peer- reviewed, open access journal meant to publish original and significant results and
Mathematical Modeling Basics - TU Delft OCW ocw.tudelft.nl/courses/mathematical-modeling-basics
How to Make a Mathematical Model. A mathematical model is a description of a system using mathematical language.
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Applied Mathematical Modeling: A Multidisciplinary Approach: Shier
applied. Figures 4 and 5. How de we decide on the size of changes to make to each CANCELED - Mathematical Models Applied to Molecular Dynamics and Oncology to foster the scientific interaction in Applied Mathematics between Cuban, Applied Mathematical Modelling http://www.zotero.org/styles/applied- mathematical-modelling 0307-904X 2018-03-09T05:06:46+00:00 This work is licensed with a strong emphasis on how these techniques can be applied in industry.
Applied mathematical modellin... - LIBRIS
N. Sadeghianpourhamami, D.F. Benoit and D. Deschrijver et al. / Applied Mathematical Modelling 68 (2019) 629–642 631 3. We ﬁrst validate the effectiveness of our approach by showing we can successfully estimate the model parameters for datasets sampled from an a priori known Abe–Ley mixture distribution, i.e., with a known number of mixture Other Titles in Applied Mathematics Mathematical Modelling: Classroom Notes in Applied Mathematics. Title Information. Published: 1987.
5 poäng. Mathematics/Applied mathematics B, Mathematical Modelling. Naturvetenskap. 100%. This work is intended for use in graduate courses of engineering, applied mathematics and applied computation where tools as mathematical and computational Applied Mathematics and Statistics at Department of Mathematical Sciences (More Mathematical Modelling and Numerical Analysis, Journal article 2017 Sökning: "MATHEMATICS Applied mathematics Mathematical statistics" Some mathematical models that employ these extreme points such as curve fitting, Head of the Interdisciplinary Centre for Mathematical Modelling and Professor of Applied Mathematics & Theoretical Physics at Loughborough University, UK. av JB Ärlebäck — Applied mathematical problem solving, modelling, applications, and links to other subjects: State, trends and issues in mathematics instruction. Educational What is mathematical modelling? See and describe the world mathematically!


We are pleased to introduce Dr. Alan Anderson. Alan is one of the best tutors in the world with a gift for explaining complex concepts in an easy to understand manner.
Alan holds an M.A. and a Ph.D. in Economics from Fordham University in Bronx, New York as well as an M.S. in Financial Engineering from Polytechnic University in Brooklyn, New York. He also holds the FRM (Financial Risk Manager) certification from the Global Association of Risk Professionals. Alan’s primary areas of expertise are risk management, quantitative methods, derivative securities, investment analysis, international finance and corporate finance. He tutors a variety of subjects including finance, economics and statistics.
Alan worked at various financial positions in the “real world” for ten years for companies such as Reuters and Westdeutsche Landesbank before moving on to academia. He has taught an extensive array of courses in economics, finance, math and statistics at several schools over the past eleven years, both at the graduate and undergraduate level. The schools include New York University, Fordham University, Fairfield University and Manhattanville College. He also conducts corporate training courses for the consulting firm Wall Street Training.


|Min. Avg. Density (lb/ft3)||Class|
|Less than 1||500|
Calculating Density & Linear Footage
Formula 1 - Finding Cubic Feet
(Length x Width x Height)
_____________________ = Cubic Feet
Formula 2 – Calculating Density
________________ = Pounds Per Cubic Foot
Formula 3 – Finding Linear Feet
____________ = Linear Feet
*Shipment dimensions are calculated using inches. Shipments that occupy a total of 750 cubic feet or more with a density of 6 pounds per cubic feet or less will fall into cubic capacity and are subject to inflated freight charges.
*To calculate the density of shipments with several pallets and identical dimensions, multiply the cubic feet by the number of equal pallets. For pallets of different dimensions, find cubic feet for all shipments and add them together. To find linear footage of non-stackable standard pallets, multiply the number of skids by two.


This course will place a strong emphasis on the continued study of integers, order of operations, variables, expressions, and equations. Students will solve and graph equations and inequalities, write and solve proportions, and explore geometry, statistics, and graph concepts. Problem solving will be emphasized throughout the course.
Algebra 1: Prerequisite – Pre-Algebra or Math 7/8
Algebra I is a course in which students learn how to solve problems by using variables to represent unknown quantities and then solving for those unknown quantities by writing equations and inequalities. Course topics include a review of the order of operations with integers, solving equations, and simplifying expressions. Students will work extensively on solving and graphing linear equations and inequalities. Additional topics will include rules of exponents, factors and polynomials, polynomial fractions, quadratics and radicals.
Geometry: Prerequisite – Algebra 1
The course includes the following topics: geometry terminology, inductive and deductive reasoning, the development of a postulate system, and the geometric proof. Various algebraic techniques are incorporated. Students will also study area, volume, circles, and right triangles.
Algebra 2: Prerequisite – Algebra 1
This course is designed to build on algebraic and geometric concepts. It develops advanced algebra skills such as systems of equations, advanced polynomials, imaginary and complex numbers, quadratics, and concepts and includes the study of trigonometric functions. It also introduces matrices and their properties. The content of this course are important for students’ success on both the ACT and college mathematics entrance exams.
Algebra 3: Prerequisite – Algebra 2 & Geometry
This course is designed for the student who has successfully completed Algebra 2, but is not ready for the academic rigor of Pre-Calculus. The course will review solving equations and inequalities, graphing, factoring, and systems of equations. Course content includes the study of many types of
functions: linear, quadratic, polynomial, exponential, logarithmic, rational, radical, and trigonometric.
Pre-Calculus: Prerequisite – Algebra 2
This course is designed to provide a comprehensive study of functions, which are the basis of calculus and other higher mathematics courses. The students will study the properties and graphs of trigonometric, polynomial, rational, inverse, exponential and logarithmic functions in the first semester. During the second semester, the students will explore inequalities, polar coordinates, complex numbers, conic sections, matrices, vectors, sequences, series and limits.


Evelyn Lamb: Hello, and welcome to My Favorite Theorem, a math podcasts where there's no quiz at the end. I’m coming up with a new tagline for it.
Kevin Knudson: Good.
EL: I just thought I'd throw that in. Yeah, so I'm one of your hosts, Evelyn Lamb. I'm a freelance math and science writer from Salt Lake City—or in Salt Lake City, Utah, not originally from here. And here's your other host.
KK: I’m Kevin Knudson, professor of mathematics at the University of Florida in Gainesville, but not from Gainesville. This is part of being a mathematician, right? No one lives where they're from.
EL: Yeah, I guess probably a lot of professions could say this, too.
KK: Yeah, I don’t know. It’s also a sort of a generational thing, right? I think people used to just tend to, you know, live where they grew up, but now not so much. But anyway.
KK: Oh, well, it's okay. I like it here.
EL: Yeah. I mean, it's great here right now it's spring, and I've been doing a ton of gardening, which always seems like such a chore and then I'm out smelling the dirt and looking at earthworms and stuff, and it's very nice.
KK: I’m bird watching like crazy these days. Yesterday, we went out and we saw the bobolinks were migrating through. They're not native here, they just come through for, like, a week, and then they're gone.
EL: The what?
KK: Bobolinks, B-O-B-O-L-I-N-K. They kind of fool you, they look a little bit like an oriole, but the orange is on the wrong side. It's on the back of the neck instead of underneath.
EL: Okay, I'll have to look up a picture of that later.
KK: And then this morning for the first time ever, we had a rose-breasted grosbeak at our feeder. Never seen one before and they're not native around here, they just migrate through. So this is
EL: Very nice. Yes.
KK: This is what I'm doing in my late middle age. This is what I do. I just took up bird watching, you know?
EL: Yeah. Well, I can see the appeal.
KK: Yeah, it's great.
EL: Yes. But we are excited today to be talking with Adriana Salerno. Do you want to introduce yourself?
Adriana Salerno: Hi. Yeah, I'm Adriana Salerno. Now I am an associate professor of math at Bates College in Maine. And I am also not from Maine. I live in Maine. I'm originally from Caracas, Venezuela, so quite a ways away.
AS: Again, you don't choose where you live, but maybe you get to choose where you work. So that's nice.
EL: Yeah. And you're you're not only a professor there, but you're also the department chair right now, right?
AS: Oh, yeah. Yeah, I'm trying to forget. No, I’m kidding.
KK: You know, speaking of, before we we started recording here, I spent my afternoon writing annual faculty evaluations. I’m in the first year as chair. I have 58 of them to write.
AS: Oh, I don't have to do those, which I'm very happy about. But we are hiring a staff position, and I'm in charge of that. And that's been a lot.
EL: And we actually met because both of us have done this mass media fellowship for people interested in math or science and writing. And so you've done a lot of writing not for mathematicians as well, throughout your career path.
AS: Yeah, yeah. I mean, I did the mass media fellowship in 2007. And since then, I've been trying to write more and more about mathematics for a general audience. These days, I mostly spend time writing for blogs for the AMS. And right now I'm editing and writing for inclusion/exclusion. I wish I had more time to write than I do. It's one of those things that I really like to do, and I don't think I do enough of, but these opportunities are great because I get to use those—or scratch that itch, I guess, by talking to you all.
KK: Well, so speaking of, we assume you have a favorite theorem that you want to tell us about. What is it?
AS: Well, so it's always hard to decide, right? But I guess I was inspired by a conversation I had with Evelyn at the Joint Math Meetings. So I've decided my favorite theorem is Cantor's diagonalization argument that the real numbers do not have the same cardinality as the natural numbers.
EL: Yes, and I’m so excited about this! Ever since we talked at the Joint Meetings, I’ve been very excited about getting you to talk about this.
AS: Good. Good.
EL: Because really, it’s such a great theorem.
AS: Yeah. Well, I was thinking about it today. And I'm like, how am I going to explain this? But I have chosen that, and I'm sticking with it. Yeah.
AS: So yeah, it’s—one of the coolest things about it is sort of it’s this first experience that you have, as a math student—at least it was for me—where you realize that there are different sizes of infinity. And so another way of saying that is that this theorem shows, without a doubt, I believe—although some students still doubt me after we go over it—it shows that you can have different sizes of infinity. And so the first step, even, is to say, “How do you decide if two things have the same size of infinity?” Right? And so it's a very, very lovely sort of succession of ideas. And so the first thing is, how do you decide that two things are the same size? Well, if they're finite, you count them, and you see that you have the same number of things. But even when things are finite—and say, you're a little kid, and you don't know how to count—another way of saying there's the same number of things is if you can match them up in pairs, right? So you know, if you want to say I have the same number of crayons as I have apples, you can match a crayon to an apple and see that you don't have anything left over, right?
AS: And so it's just a very natural idea. And so when you think about infinite sets—or not even infinite sets—but you can think of this idea of size by saying two things are the same size if I can match every element in one set to every element in another set, just one by one. And so I really like, I'm borrowing from Kelsey Houston-Edwards’ PBS show, but what I really like that she said that you have two sets, and every element has a buddy, right? And so then I love that language, and so I'm borrowing from from her. But then that works for finite sets, but you can extend it to an infinite set.You can say, for example, that two infinite sets are the same size if I can find a matching between every element in the first set and every element in the second set. It’s very hard to picture in your head, I think, but we're going to try to do this. So for example, you can say that the natural numbers, the counting numbers, 1, 2, 3, 4, etc, have the same size as the even numbers, because you can make a matching where you say, “Match the number 1 with the number 2 on the other side. And then the number 2, with the number 4 on the other side.” And you have all the counting numbers, and for every counting number, you have two times that number as the even buddy.
EL: Yeah. And I think this is, it's a simple example that you started with, but it even hints at the weirdness of infinity.
EL: You’ve got this matching, but the even numbers are also a subset of the natural numbers. Ooh, things are going to get a little weird here.
KK: Clearly, there aren’t as many even numbers, right?
KK: This is where you fight with your students all the time.
AS: That’s exactly—so when you're teaching this, the first thing you do is talk about things that have the same cardinality. And then everybody, it can take a while, you know, like, infinity is so weird that you can actually do these matching. So Hilbert’s infinite hotel is a really great way of doing this sort of more conceptually. So you have infinitely many rooms. And so for example, suppose that rooms numbers from 1, 2, 3, to infinity, mean, and so on. Yes, you have to be careful because infinity is not a number. You have to be careful with that. But say that all the rooms are occupied. And so then, you know, say someone shows up in the middle of the night, and they say, “I need a room.” And so what you do if you're the hotel manager is you tell everyone to move one room over. And so everyone moves one room over and you put this person in, and room number one. And so that's another way of seeing that. So the one-to-one pairing, or the matching here is every person has a room. And so the number of rooms and the number of people are the same—the word is cardinality because you don't want to say number because you can't count that.
AS: And so you you say cardinality instead. But it's really weird, right? Because the first time you think about this, you say, “Well, you know, there's infinity, and there's infinity plus one.” That's like the kind of thing that you would say as a kid, right? And they're the same! When you have the natural numbers and the natural numbers and one extra thing, or like with zero, for example—unless you're in the camp that says zero is an actual number—but we're not going to get to that discussion right now.
KK: I’m camp zero is a natural number.
AS: Okay. I feel like I know maybe half people who say zero is a natural number and the other half say it's not. And I don't think anyone has good arguments other than, ah, it must be true! And so then the cool thing is, once you start doing that, then you start seeing, for example—and these are, these are kind of tricky examples, it can get tricky. Like, you can say that the integers like the positive whole numbers, negative whole numbers and zero, that also has the same cardinality as the natural numbers. Because you can just start with zero—I mean, basically, when you want to say that something has the same cardinality as the natural numbers, what you're really trying to do is to find a buddy, so you're trying to pair someone with one or two, or three. But really, what you can do is just list them in order, right? Like you can have like the first one, the second one, the third one, the fourth one, and you know that that's a good matching. It's like the hotel. You can put everyone in a room. And then you know they're the same number. Everyone has a room. So with the integers, for example, the whole numbers, positive, negative and zero, then you can say, “Okay, put zero first, then one, then negative one, and two, then negative two then three, then negative three,” and then they're the same size, right? And so once you start thinking about this—I remember this pretty clearly from from college—once you start thinking about this, then you're like, “Well, obviously, because infinity is infinity.” That’s the next step. So the first step is like, well no, infinity plus one and infinity are different. But then you get convinced that there is a way of matching things that where you can get things that seem pretty different, or a subset of a set, and they have the same cardinality. And then you go the other direction, which is “Well, of course, anything infinite is going to be the same size as anything else that's infinite.” And so then it turns out that even the rationals are the same size as the natural numbers. And that's way more complicated than we have time for. But if you add real numbers, meaning irrationals as well, then you have a whole different situation.
KK: You do indeed.
AS: It’s mind blowing, right? And so if you just think about the real numbers between zero and one, so just get go real simple. I mean, small, relatively. So you're just looking at decimal expansions. And so if those numbers had the same cardinality as the natural numbers, then you should be able to have a first one and a second one and a third one, and a fourth one. Or you can pair one number was the number 1, one number with the number 2, etc. And that list should be complete, and in the words of Kelsey Houston-Edwards, everyone should have a buddy. And so then, here's the cool thing, this is a proof that these two sizes of infinity are not the same, and it's a proof by contradiction, which is, again, your favorite proof when you are learning how to prove things. I mean, when I was learning proofs, I wanted to do everything by contradiction. So proving something by contradiction means you want to assume, “Well, what if we can list all the all the real numbers?” There’s a first one, a second one, a third one, etc. So Cantor’s amazing insight was that you can always find a number that was not on that list. Every time you make this list: a first one, a second one, a third one… there is some missing element.
And so you line up all your decimals. So you have the first number in decimal. And so you have like, you know, 0.12345… or something like that. And then you have the next one. And the next one. And like, I mean, this is really hard to do verbally, but we're going to do it. And so you sort of line them up, and you have infinite decimals. So you have point, a whole bunch of decimals, point, a whole bunch of decimals. And so you can make a missing number by taking that first number in the first decimal place a just changing that number. Okay, so if it was a 1, you write down a 2. And so you know, because we’ve known how to compare decimals since we were little kids, that what you need to compare is decimal place by decimal place. So these are different because they're different in this one spot, right? And then you go to the second number, and the second decimal point. And then you say, “Well, whatever number I see there, I'm going to make the second decimal point of my new number different.” So if you had a 3, you change it to a 4, whatever it is, as long as it's not the original number. And and this is why it's called the diagonalization argument, or the diagonal argument, because you have lined all those numbers up, and you can go through the diagonal, and for each one of those decimal points, at each decimal place, you just change the value. And what you're going to get is a number, another real number, infinitely many decimals, and it's going to be different from every number on your list, just by virtue of how you made it. And so then, what that shows is that the answer to the “what if” is: you can’t. The “what if” is, if you have a list of all real numbers, it's not complete. So there is never going to be a way that you can make that list complete. And this is the part where every time I tell my students, at some point, they're like, “Wait, there are different sizes of infinity? What?” Then—and that’s sort of lovely, because it's just this this mind-blowing moment where you've convinced yourself, by the way, that you were to infinity is infinity, and then you realize that there's something bigger than the cardinality of the natural numbers. And and then it's really fun when you tell them, “Well, is there something in between?” They’re like, “Of course! There must be!” And then you're like, “Wait, no one knows.”
KK: Maybe not.
AS: So yeah, I just love that argument. And I love how simple it is. And at the same time, it's, simple, but it's very, very deep, right? You really have to understand how these numbers match up with each other. And it requires a big leap of imagination to just think of doing this and realizing that you could make a number that was not on this infinite list by just doing that simple trick.
AS: And so I just think it's a really, really beautiful theorem. And then I also have a really personal connection to this theorem. But it's one of my favorite things to teach. And I'm going to be teaching at this term, and I’m really looking forward to seeing how that how that lands. Sometimes it lands really well. Sometimes people are like, “Eh, you’re just making stuff up.” Yeah.
KK: Well, then you can really blow their minds then when you show them the Cantor set, right?
AS: Yeah, yeah.
KK: And say, “Well, look, I mean, here's this subset of the reels that has the same cardinality, but it's nothing.”
AS: Exactly. Yeah, there's nothing there. Yeah.
EL: Yeah. I remember, then, when I first saw this argument, really carefully talking myself through, “Like, okay, but what if I just added that number I just made to the end of the list? Why wouldn't that work?” And trying to go through, like, “Why can't I—Oh, and then there must be other numbers that don’t fit on the list either.” It's not like we got within 1 of being the right cardinality.
EL: For these infinite number. So yeah, it's a really cool idea. But you said you had some personal connections to this. So do you want to talk more about those?
AS Sure. So I am from Venezuela, and I went to college there. And I liked college, it was fine. I knew—Well, one thing that you do have to decide when you're a student in high school is, you don't really apply to college, you apply to a major within the college. And so then I knew I wanted to do math. And I signed up for math at a specific university. And so then the first year was very similar to what you would do in the States, which is sort of this general year where everybody's thinking calculus, or everybody's taking—you have some subset of things that everybody takes. And then your second year, you start really going into the math major. And so this was my first real analysis class. This was my first serious proof-y class in my university. And we learned Cantor’s diagonalization argument, which was pretty early. But I loved this argument. I felt so mind-blown. You know, I was like, “This is why I want to do math,” you know, I was just so excited. And I knew I understood everything. And so I took the exam, and I got horrible grade. And in particular, I got zero points on the “prove that the real and the natural numbers don't have the same cardinality.” And so I went to the professor, and I saw my exam, and I was really confused. And I went to the professor, and I said, “I really don't understand what's wrong with this problem. Could you help me understand?” Because I thought I understood this. And then—you know, that's a typical thing. I probably said it in a more obnoxious way than I remember now. But I felt like I was being pretty reasonable. I was not the kind of kid that would go up to my professors too often to ask for points. I really was like, “I don't know what I did wrong.” And especially because I felt like I really got it.
AS: And so then he just looked at me and said, “If you don't understand what's wrong with this problem, you should not be a math major.” And that was it. That was the end of that conversation. Well, I still don't know what's wrong with this problem, and now you just told me I need to do something else. Just go do something else at a different school. Right? And I mean, I don't know that that was particularly sexist. But I do know that I was the only woman in that class, and I know that I felt it a lot. I think he probably would have said that—I really do think that he in particular would have said that to any student. I don’t think it was just me being female that affected that at all. But I do think that if I had been less stubborn about my math identity, I might have taken him up on that. But I was just like, “No, I'm going to show you!” And eventually I got an A in his class. He taught real analysis every semester, so I had to take the class with him every time and at some point, I cracked his code. And he at some point respected me, and thought I deserved to be there. But he was just very old-fashioned. You know, I don't think it's even sexism. It's just very, very, like, this is how we do things. And then I went—eventually, I did talk to someone. I think it was a teaching assistant. And I was like, “I don't know what's wrong with this problem.” And he looked at it. And he said, “Well, here's the problem. When you were listing—so you needed to list all these generic numbers and their decimal expansion. And I did, “Okay, the first number is point A1, A2, A3, etc. The second number is point B1, B2, B3, etc. The third one is point C1, C2, C3, etc, dot dot dot, right? And he said, “You have listed 26 numbers. And that's not going to be an infinite list.” Right?
KK: That’s cheap.
AS: And I was just like, “Okay, but I got the idea, right?” I was like, “Okay, it's true.” He’s like, “The way you wrote it is incorrect.” And I'm like, sure.
EL: Sort of.
KK: I’ve written that same thing on a chalkboard.
AS: You know, this shows you—like, fine, you can be more careful, you can be more precise, but from this, you shouldn't be a math major? That’s pretty intense.
AS: And I knew the mechanics, I knew what was supposed to be happening, I knew how to make the missing number, right? Like you just need A1: you change it to some other number, B2: you change it to some other number, C3: you change it to some other number. And so, I just thought—I mean, that was a moment where I was just literally told I should not be in math because I made a silly mistake. And it was a moment where I realized that—now looking back, I realize my math identity was pretty strong, because I just said, “Well, ask someone else to see what was wrong, and I'm not going to ask this guy anymore because it's clear what he thinks.”
AS: And sort of the stubbornness of, “Well, I’ll show him that I do deserve to be here.” But I think of all the students who might have taken classes with him, who would have heard that and then been like, “Yeah, maybe I need to do something else.” I mean, it just makes me really sad to hear, especially now that I'm a professor, and teaching these kinds of things. It just makes me sad to see which people were just scared away by someone like that, you know?
AS: So that was a big moment for me. Yeah.
EL: Yeah. Quite a disproportionate response to, what’s basically a bookkeeping difficulty.
EL: So, you know, we like to get our mathematicians to pair their theorems, with something on this show. And what have you chosen as your pairing for Cantor's diagonalization argument?
AS: Well, now that you suggested, music and other things, I'm maybe changing my mind.
EL: You could pair more than one thing.
AS: I was trying to find something that was just like—I need to sort of express the sort of mind-blowing nature of this, right? And so I was like, a tequila shot! You know, really just strong. And like, “Whoa, what just happened?” And so that was one thing that I thought about. And then—I don't know, just mind-blowing experiences, like, when I saw the Himalayas from an airplane, or when—you know, there are some moments where you're just like, “I can't believe this exists.” I can't believe this is a thing that I get to experience. So I guess, you know, there's been—most of these have been with traveling, where you just see something that you're just like, “I can't believe that I get to experience this.” And so I think Cantor's diagonalization argument is something like that, like seeing this amazing landscape where you're just like, “How does this even exist?”
EL: Yeah, I like that. I mean, I've had that experience looking out of airplane windows too. One time we were just flying by the coast of Greenland. And these fjords there. Of course, an airplane window is tiny and it's not exactly high-definition picture quality out of the thick plastic there, but it just took my breath away.
EL: Yeah, I like that. And we can even invite our listeners to think of their own mind-blowing favorite experiences that they've they've had. Hopefully legal experiences in their jurisdiction.
KK: Well, oh wait, it's not 4/20 anymore. Oh, well. So we also like to invite our guests to plug anything they want to plug. So you write for the AMS, the inclusion/exclusion blog, are there other places where we might find your mathematical writing for the general public?
AS: Well, that's my main plug and outlet right now. But I I do write for the MAA Focus magazine sometimes. That's sort of my main, and sometimes the AWM newsletter. So you might find some of my writing there. And the blog. I mean, again, now that I'm chair and doing a lot of other things, I'm not writing as much, but I definitely like to—I’ve gotten really into maybe this is a weird plug, but I've gotten really into storytelling.
EL: Oh yeah, you’ve been on Story Collider?
AS: Yeah, I was on one Story Collider. I've done some of the local stuff. But you can find me on the internet telling stories about being a mathematician. Some of them about some pretty fantastic experiences, and some not so great experiences.
EL: Yeah. Okay. Yeah. Well, we'll link to your Twitter, and that can help people find you too.
AS: Oh, yeah. Cool.
EL: Thanks a lot for joining us.
AS: Yeah. Thanks for having me and listen to me ramble about infinity.
EL: Oh, I just love this theorem so much.
KK: Yeah, we could talk about infinity all day. Thanks, Adriana.
AS: Yeah. Thank you so much.
We were excited to have Bates College mathematician Adriana Salerno on the show. She is also the chair of the department at Bates and a former Mass Media Fellow (just like Evelyn). Here are some links you might enjoy along with this episode.
Salerno on Twitter
AAAS Mass Media Fellowship for graduate students in math and science who are interested in writing about math and science for non-experts
Hilbert’s Infinite Hotel
Evelyn’s blog post about the Cantor set
Salerno’s StoryCollider episode
The inclusion/exclusion blog, an AMS blog about diversity, inclusion, race, gender, biases, and all that fun stuff


Additionally, each group of nine shaded cells must also contain the digits 1 to 9. I stopped my timer after I broke it the first time and this went on for a total of 4 times .Though I knew that the kropki rules was applicable only on the lines, for some reason I kept on using vice versa rule of kropki for digits not on the line...That totally messed my solve. If the digit is a half of digit in the neighboring cell, then they are separated by black dot. A black circle marks all adjacent squares where the value in one is double that in the other, such as 3 and 6. This blog deals with grid-based puzzles and the various types of logic and ideas used to solve them. Ask a question or add answers, watch video tutorials & submit own opinion about this game/app. Kropki Sudoku: 200 Puzzles: Moore, Gareth: Amazon.sg: Books. About this Sudoku Solver. PUZZLE NO. If absolute difference between two digits in neighboring cells equals 1, then they are separated by a white … It also contains notices, information and results about various puzzle and sudoku championships across the globe. 4) If the digit in a cell is half of the digit in a neighbouring cell, then black dot is indicated. Walk through on the Kropki Sudoku that was posted on our website on 28th July. Sudoku is a challenging logic puzzle. Kropki Sudoku (the Polish word "kropki" means "dots"; also known as "Dots Sudoku") is the variation of the original sudoku. Additionally if absolute difference between two digits in neighboring cells equals 1, then they are separated by a white dot. Kropki Sudoku adds circles between squares which indicate two different types of relationship. Stuck on a puzzle in a newspaper or magazine? Rules of 'Kropki' Place numbers of the given range in the grid such that each number appears in every row and column exactly once. Solve Online. Sudoku ist ein Logikrätsel, bei dem der Rätselnde in ein einem 9-mal-9-Rechteck, das teilweise mit Ziffern von 1 bis 9 gefüllt ist, fehlende Ziffern nach einem bestimmten System ergänzen muss. Jun 14, 2016 - 6x6 Kropki Sudoku puzzle is solved by applying Mini Classic Sudoku Rules. Beiträge: 1.240 Themen: 113 Registriert seit: May 2007 Bewertung: 7 #3. Sudoku Kropki 9x9 #9 to solve free online puzzles (Dots Sudoku, Black and White Sudoku) Due to the huge number of Sudoku Kropki puzzles, carefully selected in order of increasing complexity, this unique collection of many puzzles is full of attractively designed tasks from the author of this site. Hello Select your address All Hello, Sign in. What is kropki sudoku... By: Staceym [6-July-12 5:06PM] posts: Final one for the moment that I'm going to look at - called kropki sudoku. Sudoku has enormous depth and while this solver has grown up enough to crack 99.9% of puzzles there are many weird and wonderful examples that defeat it. This solver offers a number of features to help you improve your solving skills and practice solving strategies. These white and black dots are placed on the lines between two different cells. Greater Than Kropki Sudoku Place a digit from 1 to 9 into each of the empty squares so that each digit appears exactly once in each of the rows, columns and the nine outlined 3x3 regions. Additionally if absolute difference between two digits in neighboring cells equals 1, then they are separated by a white dot. Additionally if absolute difference between two digits in neighboring cells equals 1, then they are separated by a white dot. In all cases where two digits have a consecutive value or one digit is two times as big as the other digit (or both), a greater than sign is placed. Feb 3, 2018 - Standard 6x6 Kropki Sudoku can be solved by applying Mini Classic Sudoku Rules. Homepage Suchen. The dot between 1 and 2 c… Cart All. 194 : Consecutive Pairs Sudoku RULES : Classic sudoku rules apply. Dec 5, 2016 - These 9x9 Kropki Sudoku puzzles can be solved by placing a digit from 1 to 9 into each of the empty squares so that each digit appears exactly once in each of the rows, columns and the nine outlined 3x3 regions. Zitieren. Autor: Gabriele Argiolas: Quelle: Argio-Logic: Lizenz: Freundliche Genehmigung des Autors Account & Lists Account Returns & Orders. Die Kropki sind fast das selbe wie die Pünktchensudoku, nur dass die Gebiete fehlen. Die ultimative Herausforderung für alle anspruchsvollen Sudoku-Freunde. PUZZLE NO. Il risolutore ti determina un errore nel gioco, cosi puoi continuare a concentrarsi sugli altri giochi. To that end I've added new graphical tools and features which I hope you'll enjoy. 15.07.2012, 13:18 . Sudoku is a logic-based, combinatorial number-placement puzzle. This is a fun variant of sudoku where one sees the usual sudoku grid, but also sees lots of little white dots or black dots. Enter the digits into the app and get the solution instantly! Wenn die Differenz zweier benachbarter Zahlen gleich 1 ist, werden die Zellen durch einen weißen Punkt getrennt. Skip to main content.sg. If absolute difference between two digits in neighboring cells equals 1, then they are separated by a white dot. Kropki Sudoku adds circles between squares which indicate two different types of relationship. Sudoku FAQ Was ist Sudoku? The dot between 1 a… The dot between 1 an… Online Solving . Brilliant creations.I think arguably the best of the Sudokus in this blog. Search This Blog. Sudoku-Löser (Sudoku solver) Dieser Online-Sudokulöser versucht Sudokus durch reine Logik zu lösen. You can solve the puzzle completely, partially or solve a single cell using the buttons in the Solving section of the Features block. A white circle indicates all numerically-consecutive adjacent squares, such as 3 and 4. About Sudoku. Sudoku Kropki 9x9 #9 to solve free online puzzles (Dots Sudoku, Black and White Sudoku) Due to the huge number of Sudoku Kropki puzzles, carefully selected in order of increasing complexity, this unique collection of many puzzles is full of attractively designed tasks from the author of this site. Printed on large, top-quality paper ideal for solving on, the 200 Kropki Sudoku puzzles vary in difficulty from easy to hard so whatever your preference or experience you'll always find a puzzle here to suit you. Das raubt dem Rätselnden eine Menge Zeit, in der er sinnvollere Dinge tun könnte. Zu meiner eigenen Überraschung lassen sich damit die meisten Aufgaben aus diversen Zeitschriften lösen. Avoid kropki Sudoku hack cheats for your own safety, choose our tips and advices confirmed by pro players, testers and users like you. Hinweise zur Sudoku-Variante mit kreisförmigem Aufbau, wobei die gleichen Regeln wie beim klassischen Rätselpuzzle gelten. If the digit is a half of digit in the neighboring cell, then they are separated by black dot. Enter the numbers of the puzzle you want to solve in the grid. KROPKI SUDOKU Rules : 1) Rules of Classic sudoku apply. An Arrow Kropki Sudoku posted on the Daily League Facebook group by Ella Torch. Puoi usare il Sudoku risolutore anche se alla fine si scopri che la risoluzione non corrisponde ai … If the digit is a half of digit in the neighboring cell, then they are separated by black dot. Pünktchen-Sudoku - einfach bis schwierig: Die Kropki-Variante der Meisterschaften (Heines Rätselbibliothek) | Heine, Stefan | ISBN: 9783939940159 | Kostenloser Versand für alle Bücher mit Versand und Verkauf duch Amazon. uvo Moderator. Der Sudokulöser soll vorrangig Menschen helfen, Warum gibt es hier einen Sudokulöser? Visit www.PuzzleBooks.org for a full list of other titles in this series. ROQA: Ensaimada in der Kategorie Anleitungen, Hilfen und FAQs. Kropki-Sudoku (im Polnischen wörtlich "Punkte"; auch bekannt als "Dots Sudoku") ist eine Variante des Original-Sudoku. kropki Sudoku tricks hints guides reviews promo codes easter eggs and more for android application. Wenn die Zahl die Hälfte der benachbarten Zahl ist, werden die Zellen durch einen schwarzen Punkt getrennt. 25 Kropki Sudoku 41 26 Windoku 50 27 Diagonal Sudoku 53 28 Round Off Sudoku 64 29 Clone Sudoku 64 30 Untouchable 123-789 Sudoku 66 31 Minimax Sudoku 86 32 Pünktchen Sudoku 94 33 Mathrax Sudoku 100 34 Partial Twins Sudoku 102 Insgesamt 900 Runde 3 Gemischte Runde 15.30 – 17.00 (90 Minuten) Namen eintragen: Nr. Rätsel Punkte 35 Standard Sudoku 26 36 Standard Sudoku 29 37 Standard Sudoku … 3) If the absolute difference between two digits in neighbouring cells is 1, then a white dot is indicated. This program is designed to automatically solve puzzles of following types: * Sudoku (9x9) * Futoshiki (4x4, 5x5, 6x6, 7x7, 8x8 and 9x9) * Binary (from 4x4 to 14x14) The main reason to keep this solver in development is to analyse these difficult ones. Dazu befolgt er drei einfache Regeln, die weiter unten auf dieser Seite beschrieben werden. Jun 14, 2016 - 6x6 Kropki Sudoku mini puzzle is solved by applying mini Classic Sudoku Rules. 199 : Extra Region Sudoku RULES : Classic Sudoku rules apply. It had a very narrow break in and nearly 50% people could not find it. 2) Place digits 1-9 in each row, each column and each 3*3 region. Attenzione: Sudoku Solver non è qui per facilitare il lavoro, ma soprattutto per scoprire gli errori. Solve Features. Solve Sudoku puzzles to challenge yourself, to relax, to train your brain, or to kill some time. Fill in the missing numbers in such a way that the numbers 1 to 9 occur exactly once in every row, in every column, and in every block. Falls Sie bei einem Sudoku aus diesem Heft oder bei irgendeinem anderen nicht weiter wissen, haben Sie hier die Möglichkeit, sich Schritt für Schritt den logischen Weg zur Lösung erklären zu lassen: —> […] Featuring a huge number of Kropki Sudoku puzzles, all carefully sorted into order of increasing difficulty, this unique collection of 200 puzzles is full of attractively-designed challenges from best-selling puzzle author Gareth Moore, author of many international books. If the digit is a half of digit in the neighboring cell, then they are separated by black dot. The dot between 1 and 2 can be either white or black. Each puzzle has only one solution, which can be reached with logic reasoning, no guessing needed! PUZZLE NO.


CPM homework help will always be part of class work. Therefore, it is beneficial for students to have homework assignments done on time. We can’t deny that sometimes these tasks can be overwhelming. In addition, students with other responsibilities beyond school are more likely to find it difficult. For example, students who work might have difficulty working on homework because they are required to work. In this scenario, CPM homework help companies are of great use. This subject is already very tedious and students need to focus completely on their studies. In such a scenario, assignment work becomes an extra burden. So, if you want to save your time and effort then employing a CPM homework helper can work in your favour.
What is CPM?
CPM stands for College Preparatory Mathematics. This educational program is for students studying at universities and colleges. This program will introduce formulas, functions, diagrams, and diagrams. You might have heard of the CPM textbook, but what is CPM? CPM is as shorthand as College Preparatory Mathematics and is an instructional approach at its base. Still, there are a variety of courses known under the title CPM Core Connections, which classroom teachers developed.
The lessons within these books are thoroughly tested in the field and proven effective. There are a lot of issues in the college preparatory mathematics class, CPM for short can bring to high school. Courses aren’t free, but the good news is that many studies have proven that CPM students score more effectively on SAT or ACT than those who utilize other programs. But do you require CPM eBooks homework assistance? Do you have the ability to do it by yourself?
The majority of classes are composed of CPM, which is also known as College Preparatory Mathematics. This can be a fascinating world for anyone who wants to understand the basics of mathematics. However, it can be terrifying for those who don’t know how to handle it.
Types of CPM
This is the best course to help students prepare for the SATs and other competitive exams. Below are the three types of CPM modules. However, we can also say that these courses might pose challenges and that you may need CPM homework help. These are the three types of CPM:
CC1: This course covers percent conversion, fractions and decimals, calculation of central tendencies, rate, time and distance mathematical problems, volume and surface area problems, data representation, tabular and graphical data representation, and simplification of variable data.
CC2: This course covers percentages, discounts and markups. It also includes ratios and unit rate calculations. Angles and their measures. Perimeter and area of compound shapes. Pair of angles.
CC3: This course covers linear functions problems, along with the rules and tables, as well as graphs and tables; solutions using tables and graphs; unit rate and slope ratios; data representation; associates, scatterplots and data representation; and theorems such as Transversality Theorem and Pythagorean Theorem and Triangle Angle Sum Theorem.
CPM also deals with Algebra I & II. There is a possibility you could get confused by these courses and may need CPM homework help assistance.
Many students find mathematics difficult because they believe it is the most complex subject. Students need to put in a lot of time and effort to solve math problems. Many students fail to solve these problems, but everyone knows the situation. Here we have tried to help students understand CPM homework help and why they require it.
CPM’s goal is to help students do better in math to get good marks in their courses. CPM homework helps you understand the various methods of solving mathematical problems. It also clarifies the basics of mathematics. Before we get into the details, let’s first discuss CPM homework assistance.
Every course must be solved with unique methods and methods. In case you do not know the subject, you may be unable to complete the course, but don’t worry about it. There are various CPM homework help companies.
Some students may need to be more focused on school-related tasks. For example, students working on their thesis may not have the time or energy to complete their homework assignments.
Are You Looking For CPM Homework Help For Geometry?
If you find geometry complicated and getting anxious, it’s time to put all your concerns aside and contact the assistants with your query. The way it works is:
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Contact the tutors to get CPM homework help assistance in geometries-related subjects. You will receive prompt support. The most effective answer comes with clarified explanations. This will help you understand the significance of a CPM question and why it is essential.
Instead of feeling the anxiety that comes with finishing your CPM homework, you should be respectful of your grade in geometry. Engage a CPM homework helper in the manner you have established.
Mathematics can help you develop your career in the direction you’d like and will put you ahead of others trying to make it into the most prestigious Ivy League schools. If you need help with your CPM homework for the CC2, CC3, or integrated 1 level, you can submit a query on the CPM homework help site and seek assistance in overcoming the difficulties.
You can receive all types of assistance by hiring CPM Homework Help Geometry tutors. You just need to search for reliable sites and drop your query. The experts there will provide you with the best assistance.
Here is where CPM homework help service comes in. These service providers can offer complex educational tasks such as research papers, essay writing and online classes. Moreover, these service providers are easy to find online.
Be careful when selecting these service providers because some may not be able to assist you with your homework. They are only there to make money off their clients. When looking for CPM homework help service providers, it is essential to consider several factors.
Find out their area of focus
The first step is to determine the company’s focus area. For example, some companies will only be able to help you if you have a Math homework assignment, while others can help you only if it is related to Science. If you have any questions about your History homework assignment, don’t hesitate to contact them.
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Before you hire a CPM homework help geometry service provider, it is essential to check their reputation. You should only hire a company with an excellent reputation. Find reviews online to see what other clients think about them. You should also only choose a service provider with an outstanding rating.
When doing homework, it is essential to know the turnaround time for the CPM homework helper company. It is useless to ask for their help if the service provider fails to complete the homework within the time frame. You must ensure they are efficient enough to complete the homework on time. You should also ensure that you get the best possible output.
The above points that are mentioned here will help you in reaching out to the best CPM homework helper company. Don’t forget to ask questions. Curiosity regarding your subject can also help you in understanding your subjects.


|Time:||December 7, 2022, 9:15 a.m. (CET)|
|Download as iCal:||
As part of his oral doctoral examination, Robin Merkle from the Institute of Applied Analysis and Numerical Simulation will give a public talk
on Wednesday, 7 December, 2022
at 9:15 am
at Pfaffenwaldring 57, 70569 Stuttgart, Room 8.122
He will talk about:
Subordinated Fields and Random Elliptic Partial Differential Equations.


Standard form is a way of writing numbers that are very big or very small. It makes calculations easier in mathematics.
To write a number in standard form, we use the power of 10 to express its size.
You can easily convert a number to a standard form with just a single click with a standard form calculator by calculator-online.net.
When calculating the speed of light and distances between galaxies, which are incredibly large, scientists utilize standard form. Because the size of atoms and bacteria or small microorganisms are so small therefore they are also described in standard form.
The standard form is sometimes called the scientific notation of a number. You can find a standard form with a standard notation calculator without any difficulty.
Either very small or very large numbers do not fit into standard calculators and it takes time to write them if finding a calculator. The standard form makes it easier to write such numbers and use them anywhere.
The method to write an ordinary number to standard form:
Steps to writing in standard form
- Note down the first digit from the given number
- Add the decimal point after the first number
- Now count the number of digits after the first number from the given number and write it in the power of 10
You will better understand with the help of examples:
87300000000 is the number hence the standard form of a number is obtained by
- The first number is 8
- Add a decimal point after 8 it becomes “8.”
- The number of digits after 8 is 10
- The standard form will be written as 8.73 x 10^10
The method to write Decimal Numbers in Standard form.
Decimal numbers consider 10 as a base and may require 10 different numerals and a dot to represent its number. Depending upon the position of digits decimals are either moved from left to right.
Consider an example 451.221 its place values are 4 as hundreds 5 as tens 1 as ones after decimal 2 as tens 2 as hundred and 1 as thousand. Its standard form is written as 4.51221 x 10^2. With the help of a standard form calculator, you can find the standard form of a number easily.
How to write decimal numbers in the standard form
- Write the first non-zero digit of a number
- Add a decimal point after the first non-zero digit
- Find how many digits the decimal point has shifted from its original position and write it in the power of 10
You will get a better understanding of writing decimal numbers in standard form in the following example:
For example, 0.00000054 in standard form
- The first non-zero digit is 5
- So add a decimal point after 5 written as “5.”
- Here decimal point has moved 6 places to the right
- Its standard form will be 5.4 x 10^-6
- Note that the power of 10 will be negative as the decimal is shifted to the right if the decimal shifts to the left it is written in positive.
Standard form is an important technique in mathematics that makes it easier to represent different mathematical expressions. It allows us to compare big numbers.
Standard form improves precision and clarity and it is easy to communicate information for efficient problem solving. standard form calculator An online tool finds standard notation in a few seconds.


We all live according to time. Time guides us in
everything that we do. Spatial Mathematics seeks to draw a
relationship between space and time by using special
mathematical subscripts that represent time. It also uses
inequalities to define how the value of fields change at different points in time. Let look at a
simple business problem to illustrate this point.
account has an initial value of $5,000 on 1/17. The value of
the account increases by $250 every week. What is the value
after one week?
the value of the account, (BA) denotes the name of the bank
account, [1/17] and [1/24] denote the dates of the events that changed the account.
values of variables represent the value of a field at a point in
time. Events change the value of fields. The value of one
field at a point in time will be different than the value of a
field at a later point in time. You can use Spatial Mathematics
notations to state the variable of the field as being the same
before and after the event. What changes is the value of the
field and the points in time of the events in relation to the
changes in the numerical value of the fields in question.
You can read more about the Spatial
Mathematics by going the Downloads Page and downloading ôSpatial
Mathematics: A New Theory of the Mathematical Representation of
Space and Time" for free in Adobe PDF format.