Published: Sep 27, 2022 | Updated at: Sep 27, 2022
In the past, the internet was viewed as a distraction in schools. It took students' attention away from the important work of learning. Now, online programs have been created to be a part of a student's learning journey.
Online software tools let students take learning to new heights. They help students who struggle to absorb challenging concepts and those who want to to improve and excel. Programs like Delta Math assist teachers in the classroom and help them save time.
A high school math teacher developed the online program specifically to help his students improve their work on test problems. It has since become a practical model for online that has launched across hundreds of schools.
Keep reading to learn about Delta Math and how this program boosts math education in schools.
What is Delta Math
Delta Math is an online platform developed by teachers for teachers. It helps teach students math by working directly with test problems and providing lessons based on key problem areas.
Students have the opportunity to practice an unlimited amount of math problems. They then get feedback from the program about the specific problem they just worked on. This creates a highly individualized student-led learning experience that empowers young people to be independent learners.
For teachers with busy classrooms, the Delta Math platform saves them a lot of time spent on menial grading work. The input test questions that give students automated results and feedback. Students don't get left unattended because they can work on their own online.
Delta Math offers the following benefits for classrooms in grades 6-12 with valuable math tools, including:
- Problem explanations catering to appropriate grade level
- Curriculum aligns to Common Core problems and targeted goals
- Automatically tracks students progress using analytics
- Randomly generates math problems for students
- Software designed to reduce cheating
How Does Delta Math Work
Students receive a special code from their teachers through their email. This gives them access to their own dashboards, which tracks their progress. They also can access all of their assignments from there, including past due assignments as well as current and completed assignments.
Teachers use the Delta Math platform to provide digital math assignments for middle school and high school. The platform also lets teachers show test corrections. Students can learn from explanations and improve from their mistakes.
Delta Math uses multiple types of math problems including the following:
- multiple choice
- questions with interactive models
- timed problem sets
Teachers link each problem to a specific skill. The program can also filter out problems based on Common Core grade level or specific curriculum targets created by the teacher specially for their class.
Because it's an online platform, teachers and students can keep tracks of problems they've attempted and what skills they need to work on. The programming offers simple and easy-to-understand explanations that helps students.
How Can Teachers Use Delta Math
While teachers can link test problems online, they have to do so manually. That means they input one question at a time, which can be tedious. But the convenience and autonomy it allows for students makes up for it.
Teachers can use test questions to help remedial students or those struggling with certain concepts. Students can work through problems as a repetition to solidify math skills.
Delta Math lets teachers create specific learning units that they link math problems too. They can set up special units for students as warm-up problems or catching up through review. They can also set up activities to correct test problems.
Classrooms can benefit from an online tool that regularly updates data of students' progress in real-time. Teachers can see exactly where their class is at in their learning goals. They can also coordinate class-wide learning online, which students can log onto anywhere that has internet access.
Solving Math Problems with Interactive Features
Delta Math relies on several visual and interactive features that help students gain a real understanding of different mathematical concepts. Its interface utilizes a hands-on self-guided approach where students can take as much time as they need on whatever problems they want to work on.
One cool thing that Delta Math offers for test problem solutions is that you can work with both 2D and 3D models. They do this using the "show solutions" option. Once in the "show solution" function, users can slide across the graph problem to see the solution as solid shapes.
Students can choose from a range of shapes, including triangles, rectangles, squares, or circular disks. For 2D displays, the sliding option fills in the solution area. Using this future, students can choose whether to work with 2D or 3D settings.
Check out this teacher-created blog post to watch videos testing out these interactive tools.
Does DeltaMath Cost Anything
Teachers can access a lot just by using Delta Math's free version, known as DeltaMath Teacher. The free version, naturally, costs nothing and includes many of the basic and key tools and features to assist teachers in their classrooms.
Delta Math also features different priced packages, which include the following:
- DeltaMath Plus
- DeltaMath Integral
DeltaMath Plus offers extra tools for digital math assignments that include video instruction for all problems and the ability to upload instructional videos from Youtube. Teachers can also create their own problems, assign problems to one student or a group, and add on co-teachers, along with many other perks.
DeltaMath Integral offers everything from the first two levels plus advanced administrative tools. Integral lets teachers upload students' own work and notes. They can also print out assignments and assessments through PDF files.
The Integral package allows teachers to run diagnostics for their classes. And one of the biggest features for Integral is that you can integrate other platforms with DeltaMath, including Clever, ClassLink, Schoology, or Canvas.
You can access Delta Math from their site.
Revolutionize Your Teaching
Delta Math works so well for teachers because it was made by teachers. The program intuitively works with what classrooms need to guarantee success for all students.
Halsell is a platform that delivers special tools for project managers, CRM, and databases. They use the same tools that DeltaMath benefits from in their programming.
Visit Halsell's site today to sign up.


Mathematics is fun and it becomes more amazing once we integrate maths with another awesome topic i.e hacking and arithmetic help in hacking?. There could also be many questions inside your mind like why hackers should need knowledge of mathematics and the way to use mathematics for hacking. If you ever consider this question then this post is for you. Let’s start our article fellow members of toptechpal!
Let’s begin Mathematics in hacking !
Shall we start how mathematics help in hacking? Let us assume that a web application uses following algorithm for their password.
First_four_letters_of_alphabet_in_uppercase + year_of_birth
This seems easy to crack but think once brute-forcing this may take ages as there are 4 uppercase alphabets & 4 digits involved. in order that they create 2821109907456 combinations and it might take 90 years to crack the password if we try 1000 combinations per second.
Now, Who will spend 90 years to hack a singe account?
But if you’ve got some knowledge about mathematics and a few brain you’ll be able to easily hack that account with in few seconds.
Let’s apply some mathematics in this scenario
Now let’s examine more how mathematics help in hacking. First let target the algorithm. the mixture is within the form:
([A-Z][A-Z][A-Z][A-Z])([0–9][0–9][0–9][0–9]) (4 uppercase letters) (4 digits) (Group 1) (Group 2)
The alphabets are during a group and lie before the digits which also are grouped so there’s no possibility that they’ll be mixed to create a mixture like S2N65GE1 . So what percentage combinations are possible after considering that?
Lets calculate the amount of combinations of 4 letters which might be formed by 10 digits i.e. 0-9 :
(10)⁴ - 1 = 9999
So there’ll be 9999 possible combinations. Great! Now let’s calculate the identical process for alphabets.
(26)⁴ - 1 = 456975
And all the combinations of 9999 digit and 456975 alphabets combinations will be:
456975 * 9999 = 4569293025
And if we try 1000 combinations in 1 second we’ll need this much of your time
4569293025 / 1000 = 4569293.025 seconds or 52 days 21 hours 14 minutes and 53 seconds
Just using some brain and arithmetic We just decreased the time required from 92 years to 53 days!
The change is orgasmic but it’s still an excessive amount of time. What else may be done?
Here’s the catch, these are just not 4 alphabets and 4 digits, these are four alphabets & year of birth of somebody.
A human can live up to 100 years which suggests someone born in 1642 can’t be alive and hence can’t have an account.
Time traveling is additionally impossible at the instant which suggests someone who goes to turn in 2594 can’t travel back to the time to make account.
So the combinations starting from 0000–9999 aren’t valid. We just need the 1920–2020 range which covers humans old 0 to 100.
So now the amount of combinations and time required is:
456975 * 100 = 45697500 combinations 45697500 / 1000 = 45697.5 seconds or 12 hours 41 minutes 37 seconds
We just decreased the time required from 92 years to 53 days and now to 12 hours! It’s all thanks to mathematics.
Now if there’s slight change in algorithm we will further decrease our time. If the algorithm is like:
first_four_letters_of_first_name_in_uppercase + year_of_birth
We can decrease the time from hours to seconds. Let’s apply maths here again:
Just like all the combinations of digits weren’t valid years of birth, similarly AAAA or PZVS aren’t valid for the first four letters of a name.
So what would an attacker do?
They used Photon to scrape names from an internet site which was basically a directory of names and let’s say we found 3283 unique names! you’ll follow this link for photon. Use the subsequent command to extract the primary 4 letters and filtering out the duplicates
grep -oP ”^\w” custom.txt | sort | uniq | dd conv=ucase
There are 1598 entries!(say) It may be even less as there are many duplicates, for instance the primary four letters within the names Sanjeev & Sanjit are same.
Anyway, let’s calculate the time required now
1598 * 100 = 159800 combinations 159800 / 1000 = 159.8 seconds or 2 minutes 39.8 seconds
Hmmm? Decreased time from 92 years to 2 minutes to crack a password by just using simple mathematics. Now can we further decrease the time? the solution is yes.
Let’s use some facts for that!
WORLD HAS over 50% OF ITS POPULATION BELOW THE AGE OF 25 AND over 65% BELOW THE AGE OF 35.
So rather than creating combinations with age 01–100, a sensible move would be to do this:
25 – 01 (reversed because young ones don’t seem to be likely to own an account online)
25 – 35
36 – 100
So if we take the age statistics into consideration, the prospect of matching the right password in first 1598 * 25 = 39950 combinations is 50% which implies we’ll crack half the passwords in 39950 / 1000 = 39.95 seconds! And within the next (1598 * 10) / 1000 = 15.8 seconds , we’ll have %15 more passwords! So basically we’ll have 65% of the passwords in 55.9 seconds . we’ve come a very long way!
This is just a theoretical example of how we are able to use mathematics help in hacking.
#In association with Thetechrim
Hope you enjoy it!
This was just a fun article on how mathematics help in hacking. If you want to get such awesome and interesting articles then feel free to subscribe to our newsletter and turn on notification of our website on your browser. Feel free to share and support us. Bye till next post.


Apple's Secret Calculator
The iMac’s Spotlight search is an amazing tool that lets you swiftly search your entire iMac for any media, program, or document. You can click the magnifying glass in the upper right hand corner, or just hit Command + Spacebar and the Spotlight search bar will drop down, ready for you to type any text in to begin your search. But did you know that the bar actually does basic math too? Instead of having to actually open your Calculator, just type in some basic math right into the spotlight search bar and… voila! You will see the Icon for Calculator appear, and your math problem will be solved right in the spotlight window.
One more secret - if your Mac doesn't have a number pad, you might make a few simple mistakes based on how the calculator keys appear visually. If you want to use multiplication, remember to use Shift-8 to get the star icon (*) and not the letter X. For keying in division problems, the forward slash (/) is the way to go.
Keep reading for more handy iMac tips and tricks!


Subject: Parameter estimation of ordinary delay differential equations
Contains: 73 pages, 11 tables, 33 figures, 90 formulae, 13 references
The goal of this paper is to develop and implement fast and robust algorithm for parameter estimation of ordinary delay differential equations.
Based on the modern numerical methods the parameter estimation algorithm is proposed and its implementation is done in the MATLAB language.
Parameters of one demographical model are estimated.
The topicality of the paper – lack of theoretical basis and ready solutions for such problems.
Keywords: PARAMETER ESTIMATION, ORDINARY DELAY DIFFERENTIAL QUEATIONS, SPARSE SYSTEMS, LEAST SQUARES, NUMERIC INTEGRATION, CYCLIC REDUCTION, SQP, MATLAB


Mar 15, 2017
I’ve been working with threejs a bunch lately. Here’s a pretty shiny tessellation of a space-filling polyhedron called the rhombic dodecahedron:
Oct 14, 2015
Make your delaunay triangulation squirm in the updated version of this project, here.
This version also allows you to toggle between wallpaper and wireframe mode.
I decided to build in this functionality because I wanted to make my polygonal background wallpaper be constantly moving slightly, but it’s way too computationally expensive to do that atm. In other words, be warned: your fan will spin up.
Oct 4, 2015
My initial goal was to make a dynamically generated triangle pattern for a site, like so:
That site will generate a new pattern on each visit.
Here you see a set of points, randomly generated, that has been triangulated. In other words, every generated point has become the vertex of a triangle and all triangles are non-overlapping.
In the demo, drag points to see the triangulation recalculate.
Jan 10, 2015
I want random data! But…I want them to be distributed normally!
Nov 13, 2014
If you are at all interested in SVG or Bézier curves, you’ve probably seen something like Jason Davies’ animation. I found that those animations are an excellent way of intuitively grasping how Bézier curves work. However, the math behind it all is less intuitive.
I just read this really illuminating article.
Something I hadn’t realized before reading the article is that, mathematically, Bézier curves are not defined as run-of-the-mill functions. Whereas generally one would plug an
x value into a function to determine a
y value, à la
f(x) = y = ax + b , Bézier curves are defined parametrically. The values of
y are determined independently, according to a third parameter, dubbed
This is the general formula for a cubic Bézier:
B(t) = (1-t)3·P0 + 3·(1-t)2·t·P1 + 3·(1-t)·t2·P2 + t3·P3
P3 are the start and end points, and
P2 are the first and second control points.
Sep 3, 2014
I’m currently reading a book on graph theory.
A graph, in the mathematical sense, is a completely abstract object made up of sets. However, it definitely lends itself to visual representation, so I’m having a bit of fun making visualizations of some of the concepts.
Sep 3, 2014
This paper demonstrates an extremely accurate approximation of a circle using cubic bezier curves.
It takes 4 curves, one for each 90° circle arc.
As you can see above, I’ve implemented that approximation. The black dots represent the start (
P_0) and end (
P_3) of each segment, and the red dots represent the control points (


- Colors of Infinity Alternative
Retraces the steps that led to the discovery of the Mandelbrot set in 1980. Dr Arthur C Clarke explains the mathematics and the basic computer operations that generate the Mandelbrot set and the associated imagery. He also demonstrates how the discovery of the set, which gave birth to the science of fractal geometry, is significant to all the sciences. The study of fractals is leading to a better understanding of chaotic systems such as weather and galaxy clusters. The fractal method of digital image compression developed by Michael Barnsley is also discussed. Includes animated images of the Mandelbrot set. Contributors include Dr Benoit Mandelbrot, Prof Stephen Hawking and Prof Ian Stewart.


Ive heard the greatest real life application for a math problem. Its about parabolic and linear systems
A renegade dictator lauches a scud missle at a US troop installment. The troops launch a Patriot missle to intersect it. Due to satellite imaging. We see the world as a grid. The scud missle is stationed at (6,0). Its path can be represented by the parabola y=-X(X)+8X-12. The Patriot missle was lauched from the point (0,0). Its path can be represented by the line y=x. Graph the system of equations. Find the point(s) where the Patriot missle will intercept the scud missle.
I don't know about you readers, but that's the most creative math problem I've ever seen.
Very Truly Yours, Happy Ostriching,


#3 Question: Does every single dollar of tax deductions means a $1 reduction in taxes due?
If you thought that every single dollar of your tax deductions actually equals a dollar reduction in taxes, you were wrong. The dollars you deduct only minimize your tax bill based on the amount of your actual marginal tax rate. The marginal tax bracket for you refers to the tax rate you actually pay on your last dollar of income.
For instance, if your marginal tax rate is 22 percent, and you have, let’s say, a $1,000 deduction, you have to multiply the amount of your deduction by your marginal rate in order to know exactly the amount of money you actually save (in this case the amount of money saved is $220).


Maths Family Equation Print
Units Sold: 0
100000 in stock
About Maths Family Equation Print
Maths Family Equation
What makes up the maths for your family equation? This understated but meaningful art is personalised to your family numbers. making it an adorable addition to your home.
Comes fully framed ready to hang.
Method: Royal Mail
Dispatch time: 5-7 days
As the Maths Family Equation Print is personalised, it cannot be returned unless it is faulty.


Successful learning and practising of maths relies on a range of factors. This includes motivation, language ability, attention, attitudes, IQ and social and educational experiences.
Due to the complex nature of maths, kids learn at different paces and in different ways. Some require hands-on practise, others need repetition, whereas some just get it! What’s more, some kids will struggle more than others, and could have a specific learning difficulty with maths called Dyscalculia. Studies have shown children who do not have opportunities to practise maths may be at a loss when it comes to starting school. Moreover, it has been found that introducing maths in the early years is important for schooling success.
Here are some tips for at home:
Play maths games!
Maths games make the process fun and motivating. This is because it helps kids develop number sense without the threat of grades or embarrassment they may experience in a classroom. Check out our full range here
ThinkFun Zingo! 1-2-3 Game
Introduce maths in everyday life!
Practising maths in context makes introducing maths in the early years more relevant to a child. This also provides an opportunity to deepen their overall understanding. These activities are helpful for home:
- With your child, take a handful of marbles, paper clips, pencils – anything that can produce ‘a bunch of’. Ask your child to guess and write down an estimate of how many are in the bunch, then count to confirm. Counting while using their hands is perfect for kids who learn better with tactile validation.
- For older children, open your wallet, separate coins and notes into their denominations and together add up the total amount of money
- Collect a group of toys or items in their room and line them up from lightest to heaviest – then get out scales and weigh them to confirm their estimations.
Don’t worry if maths is not your strong suit!
A study of first and second grade children found those with maths-anxious parents tended to learn less maths and were more likely to have maths anxiety themselves –when their parents provided were involved frequently in helping with maths homework.
Though parents had great intentions, conveying their own attitudes towards maths can be detrimental to the child. If an individual experiences maths-anxiety, their performance is affected as their working memory is consumed with worry and anxiety – and they don’t have enough left to do the actual maths. So, how can maths-anxious parents help their children at maths? Dr. Cooper suggests that parents of young children create a maths-positive environment by modelling “maths behaviour.” The game plan: Tell your child, “‘You have your maths homework, and I have mine,’” he said, and show them whenever you “count your change, calculate when dinner will be ready, look at prices in a grocery store.
Stearns, M. (2013). LEARNING MATH: Why kids get frustrated and what parents can do: Ideas to share with parents. The Education Digest, 78(5), 38.


My research has focused on developing statistical methods to analyze correlated data and to remove biases that emerge from informative cluster size, study design, missing data, or misclassification in multilevel observational studies and complex surveys. I have collaborated with researchers from various disciplines including oncology, nephrology, anesthesiology, and oral health.
If you are a student and interested in working with me, please contact me by email at aya.mitani(at)utoronto.ca.
Education and Training
- Postdoc, Harvard T. H. Chan School of Public Health
- PhD, Biostatistics, Boston University
- MPH, Biostatistics, Yale University
- BA, Mathematics, Pitzer College


From the Deputy Head (Academic), Dr Andrew Daniel
Wellington School’s curriculum is designed to fulfil three principal objectives:
- to stimulate pupils’ curiosity and inspire a life-long interest in independent learning
- to equip pupils with the essential skills in Mathematics, English and Science to tackle future learning and careers with confidence and success
- to give older students the chance to make their own choices through experiencing
many subjects, then specialising in their chosen field
Subject specialist teachers provide the full range of traditional subjects, using modern techniques and a balance of didactic, interactive and independent learning activities.
We place great emphasis on monitoring students’ performance and ensuring they continue to make progress – and we achieve excellent exam results.
Students have an entirely free choice of A level subjects and a free choice of GCSE options outside of a compulsory core of Mathematics, English, Science and Religious Education. House staff and the Deputy Head (Academic) are always available to advise and support students’ academic studies.
Years 7 and 8
The curriculum is notable for the range of subjects included. It builds on foundations previously laid in the core subjects, but adds new ones to stimulate and extend students’ thinking. There is setting in Mathematics and banding in French
Students are taught French in Year 7 and Year 8 and begin the study of either German or Spanish in Year 8.
Latin provides a matchless grounding in the structure of language, as well as opening students’ eyes to the ideas and culture of the ancient world that continue to exercise influence today.
The curriculum offers genuine breadth to allow students the maximum choice of GCSE subjects. Students with aptitude for or experience of Latin continue this subject, gaining a real appreciation of the language, ideas and culture of the ancient world. A course in Classical Civilisation gives a similar insight for those without experience of Latin.
Years 10 and 11
A wide range of GCSE options is available, complementing the core subjects of Mathematics and English. Students have a choice of Separate Sciences or Dual Award Science and must study at least one Modern Foreign Language. Courses in Religious Education and Physical Education are also compulsory.
Students take at least 10 subjects at GCSE. The most able Mathematicians take GCSE Mathematics at the end of Year 10, allowing them to take an Additional Mathematics qualification in Year 11. The full list of subjects available is:
The Mathematics and Science courses lead to International GCSE (IGCSE) qualifications. Universities and employers accept these as equivalent to GCSE qualifications, although they do not appear in government league tables, and the benefit is an excellent preparation for A level.
Students have a free choice of four, or occasionally five, AS courses. These are complemented in the Lower Sixth by courses in Information Technology, Careers, University Entrance, Critical Thinking, Philosophy and Cooking. Visiting speakers and academic societies also extend the curriculum.
In the Upper Sixth students continue with their A2 studies and have the option to take qualifications in Critical Thinking and the Extended Project. The full list of subjects available is:
Please visit our Pastoral section to find out what Sixth Form life is all about.


ANOVA. If you have been analyzing ANOVA designs in traditional statistical packages, you are likely to find R's approach less coherent and user-friendly. A good online presentation on ANOVA in R can be found in ANOVA section of the Personality Project. If variances are unequal, then a Welch’s one-way ANOVA is appropriate. One-way ANOVA Example in R. In this example, an experiment is performed to compare the dry weight of plants with one of three potential treatments. Each plant is treated with one out of three available treatments to enhance the weight of each plant. 05/12/2019 · What is ANOVA? Analysis of Variance ANOVA is a statistical technique, commonly used to studying differences between two or more group means. ANOVA test is centred on the different sources of variation in a typical variable. ANOVA in R primarily provides evidence of the existence of the mean equality between the groups. Implemented are various tests for semi-parametric repeated measures and general MANOVA designs that do neither assume multivariate normality nor covariance homogeneity, i.e., the procedures are applicable for a wide range of general multivariate factorial designs. In addition to asymptotic inference methods, novel bootstrap and permutation. I am wanting to see if differences in mean home range size differ across sites and periods. Based on having two categorical variables site and period, I assume this would be done using a repeated measures ANOVA? I was needing to see what code would be used since I have never done an ANOVA in R before. rm list = ls hrdata=read.csvxxx hrdata.
- two factor ANOVA with repeated measures on both factor =two-way within subject ANOVA Se outcome è il valore del parametro che viene misurato, mentre factor1 e factor2 sono i due fattori di classificazione, tra i quali si vuole stimare se vi è differenza, le formule da applicare in R sono rispettivamente: per il mixed model.
28/06/2017 · How to do a repeated measures ANOVA n R using lme4 and lmerTest. Also the difference between repeated measures ANOVA and ANOVA. Reddit: reddit.co. 02/04/2011 · Compute two-way ANOVA test in R for unbalanced designs. An unbalanced design has unequal numbers of subjects in each group. There are three fundamentally different ways to run an ANOVA in an unbalanced design. They are known as Type-I, Type-II and Type-III sums of squares.
NOTE: This post only contains information on repeated measures ANOVAs, and not how to conduct a comparable analysis using a linear mixed model. For that, be on the lookout for an upcoming post! When I was studying psychology as an undergraduate, one of my biggest frustrations with R was the lack of quality support for . This site is powered by knitr and Jekyll. If you find any errors, please email winston@. ANOVA mit Messwiederholung: Voraussetzungen Insgesamt sechs Voraussetzungen sind zu erfüllen, damit wir eine rmANOVA berechnen dürfen. Allerdings sind nicht alle Punkte, die wir im nachfolgenden nennen werden, echte Voraussetzung die strikt eingehalten werden müssen. The repeated measures ANOVA compares means across one or more variables that are based on repeated observations. A repeated measures ANOVA model can also include zero or more independent variables. Again, a repeated measures ANOVA has at least 1 dependent variable that has more than one observation.
04/01/2018 · Lecturer: Dr. Erin M. Buchanan Missouri State University Spring 2018 This video replaces a previous live in-class video. This video covers "doubly" or two-way repeated measures designs focusing on data screening, ANOVA using ezANOVA, post hoc tests, and effect sizes. Examples of graphs in ggplot2, and write ups in APA style are. REPEATED MEASURES ANOVA Repeated measures ANOVA RM is a specific type of MANOVA. When the within group covariance matrix has a special form, then the RM analysis usually gives more powerful hypothesis tests than does MANOVA. Mathematically, the within group covariance matrix is. Clear examples for R statistics. Two-way anova, repeated measures, mixed effects model, Tukey mean separation, least-square means interaction plot, box plot. Repeated measures data require a different analysis procedure than our typical two-way ANOVA and subsequently follow a different R process. This tutorial will demonstrate how to conduct two-way repeated measures ANOVA in R using the Anova function fr.
ANOVA mit Messwiederholung in SPSS Generell gelten Versuchsdesigns mit Messwiederholung als sehr effiziente Art der Forschung. Bei solchen Designs werden meist dieselben Versuchspersonen mehrmals gemessen. 18/12/2019 · Analysis of Variance ANOVA in R: This an instructable on how to do an Analysis of Variance test, commonly called ANOVA, in the statistics software R. ANOVA is a quick, easy way to rule out un-needed variables that contribute little to the explanation of a dependent variable. It.
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Graphs.jl provides several traversal and shortest-path algorithms, along with various utility functions. Where appropriate, edge distances may be passed in as a matrix of real number values.
Edge distances for most traversals may be passed in as a sparse or dense matrix of values, indexed by
[src,dst] vertices. That is,
distmx[2,4] = 2.5 assigns the distance
2.5 to the (directed) edge connecting vertex 2 and vertex 4. Note that for undirected graphs
distmx[4,2] also has to be set.
Default edge distances may be passed in via the
Any graph traversal will traverse an edge only if it is present in the graph. When a distance matrix is given:
- distance values for undefined edges will be ignored;
- any unassigned values (in sparse distance matrices) for edges that are present in the graph will be assumed to take the default value of 1.0;
- any zero values (in sparse/dense distance matrices) for edges that are present in the graph will instead have an implicit edge cost of 1.0.
Graph traversal refers to a process that traverses vertices of a graph following certain order (starting from user-input sources). This package implements three traversal schemes:
The package also includes uniform random walks and self avoiding walks with the following functions:
The following properties always hold for shortest path algorithms implemented here:
- The distance from a vertex to itself is always
- The distance between two vertices with no connecting edge is always
yen_k_shortest_paths functions return path states (subtypes of
Graphs.AbstractPathState) that contain various information about the graph learned during traversal.
The corresponding state types (with the exception of
YenState) have the following common fields:
state.distsholds a vector with the distances computed, indexed by source vertex.
state.parentsholds a vector of parents of each vertex on the shortest paths (the parent of a source vertex is always
In addition, with the appropriate optional arguments,
dijkstra_shortest_paths will return information on all possible shortest paths available from the source.


Creative indie game lets you play puzzles without needing math degree.
I remember not too long ago that I really got hooked on a puzzle game called Threes. In that game, you swipe your finger left-right-up-down to move squares around your screen. To win, you combine the numbers to form multiples of three (3, 6, 9, 12 and so on). Because of its simplicity, it’s highly addicting and very fun. There is another game called 2048, that has the same principle. You just have the goal of combining numbers until you reach the total of 2048. Now, you can do the same thing with cupcakes in Cupcake 2048.
Cupcake 2048 is a cute indie game that launches today. It’s based off of puzzle games like 2048 except that instead of combining numbers to reach your goals, you are building cupcakes. The thought was that you could enjoy the puzzle-based game without having to have a math degree.
“I decided to create Cupcake 2048 because I was so addicted to 2048 and I thought it would be great to play with some nice cupcakes instead of numbers.” says Wolfgang Knecht. “Development time took longer than expected because I was hooked to my own game. Sometimes that kept me from work.” he concludes.
- 2048 game without numbers
- Charming vintage style graphics
- 3 different yummy cupcakes
- Smooth animations
- Supports English and German
I was fortunate enough to be able to test out Cupcake 2048 before its official release. It is indeed a very entertaining, very addicting game. It’s one of those games that you start playing and then realize it’s been an hour since you started. It goes by quickly and it plays like an endless runner style game. This type of game is also very challenging – especially the longer you play.
Cupcake 2048 is free to download with an option to remove ads for $0.99.
For more information, visit http://www.wolfgang-knecht.com.
Find Wolfgang Knecht on Twitter.


Joseph Priestley Award Celebration Lecture
Synchronization in Nature
Monday, October 12, 2015
Anita Tuvin Schlechter Auditorium, 7 p.m.
Strogatz will discuss spectacular examples of synchronization in nature, from rhythmically flashing fireflies to crowds of pedestrians that inadvertently caused London’s Millennium Bridge to wobble on its opening day.
The Joseph Priestley Award recipient is chosen by a different science department each year. The Department of Physics and Astronomy has selected this year’s recipient, Steven Strogatz. The event is supported by the College’s Priestley Fund and is sponsored by the Clarke Forum for Contemporary Issues, Student Senate and the Churchill Fund and co-sponsored by the departments of physics and astronomy, biology, chemistry, earth sciences, environmental studies, math & computer science, and psychology.
Steven Strogatz is the Jacob Gould Schurman Professor of Applied Mathematics at Cornell University. He works in the areas of nonlinear dynamics and complex systems, often on topics inspired by the curiosities of everyday life. He studied at Princeton, Cambridge, and Harvard and taught at MIT before moving to Cornell in 1994. A renowned teacher and one of the world’s most highly cited mathematicians, he has blogged about math for the New York Times and has been a frequent guest on RadioLab. His honors include a Presidential Young Investigator Award; MIT’s highest teaching prize; a lifetime achievement award for the communication of mathematics to the general public; the Lewis Thomas Prize for Writing about Science; and membership in the American Academy of Arts and Sciences. He is the author of Nonlinear Dynamics and Chaos, Sync, and The Calculus of Friendship. His latest book, The Joy of x, has been translated into 15 languages.
Joseph Priestley Lecture
The Priestley Award is presented by Dickinson College in memory of Joseph Priestley, discoverer of oxygen, to a distinguished scientist whose work has contributed to the welfare of humanity. The Priestley Award, first presented in 1952, recognizes outstanding achievement and contribution to our understanding of science and the world.
Video of the Lecture


Numbers play a vital role in our day-to-day lives.
From the day we make our appearance known, right down to the minute, we enter into the visible and invisible realm of numbers.
Before we can count, it is being done for us. The date and time of our birth is recorded. We are whisked off to check vital statistics. Our length is measured, our weight is recorded and we are given an APGAR score.
Two eyes, check! Ten toes, yes! Ten fingers, great!
Later on in life, we learn to not only count on our fingers, but we learn to number our friends. We are very blessed if we have a handful of best friends we can count on.
Numbers Are Everywhere
Numbers permeate every area of life. There isn’t anything that does not involve them; everything from the microcosm to the macrocosm, and everything in between. They even encompasses The Secret of Life, which I will discuss below.
Even the hairs on our head are numbered. (Matthew 10:30)
We use numbers to:
- add, subtract, multiply and divide.
- chart progress and productivity.
- detect patterns.
- entice customers. Today only… two for one.
- find out the truth, to obtain proof. Deductive reasoning tells when the numbers don’t add up.
- keep track of time, to schedule appointments. Is the train late?
- measure area, distance, growth, intelligence, sizes of population, time, volume, and weight.
- provide excellence in service.
- record important events.
- report a crime. How many were involved? How long ago did this happen? How tall? What weight? Did you get a license number?
- solve problems. How much do they cost? How many are needed?
We could do none of these things without numbers.
Curious, Fascinating Numbers and The Secret Of Life
Some cultures treat numbers with a certain reverence; that they are lucky and control destiny.
Such is the popularity of such things as Fung Shui, horse races, and lottery tickets.
Some people treat numbers with superstition. A good example of this is the number thirteen.
Some think it is good luck, and others a curse.
The number sixteen is interesting. In the Old Testament, there were sixteen prophets.
In the New Testament, you will find sixteen apostles and evangelists.
The number 153 is also a curiosity. If you cube each number, it returns to itself.
1 + 125 + 27 = 153
The Beauty, Goodness & Truth of Numbers
There is a purity to numbers. They are the voice of truth. They never lie, even if they get fudged.
To date, no one has been able to figure out the determinant pattern of prime numbers.
Prime numbers are positive, non-zero numbers that have just two factors; the number one and the number itself.
They certainly have held my imagination captive for many years now. I have written high-level encryption programs, and others involving prime numbers. One such program treats prime numbers as linguistic elements.
Here is an example:
The phrase, “The Secret of Life” consists of eleven elements, each of which is a prime number.
When the elements are joined together, they produce six hundred eleven thousand nine hundred fifty one.
This is also a prime number. to see for yourself, check here.
But wait! Aren’t these eleven elements more than two factors?
No. The elements are added, whereas factors are multiplied.
In providing one more example, The Secret Of Life shows up in a different way.
The gathering of the eleven elements is a picture of unity in diversity.
Collectively, they are equally important.
For example, is it possible that three can be one? …. or any number of things be one?
When you add them together, one plus one plus one equals three.
But, when you multiply them, one times one times any number of ones will always equal one.
Perhaps, one day, the poet-philosophers will write about the day that humanity became one.
Teach Us To Number Our Days
The Bible says, “Teach us to number our days, that we may gain a heart of wisdom.”
When we are small, naïve, and our life experience matches our size, the number of our days
seems infinitely large. We have a small number of memories, and a lifetime to unearth beauty.
When we are older, wiser, and perhaps becoming small again, the number of our days seems to be
in short supply. The brevity of life looms larger. We have many memories, some which are buried and long forgotten.
If we are wise, we also learn to make the most of our days.
You Have A Voice… Let’s Hear It
Do you have a favorite number?
Do you enjoy the elegance and beauty of numbers?
Please contribute you thoughts here.
I appreciate each and every one. Thank you kindly! 🙂


In order to calculate the Customer Retention Rater, there are three pieces of information we need to use.
- E is the number of customer at the end of a period;
- N is the number of new customers acquired during that period;
- S is the number of customers at the start of that period.
We are interested in the number of customers remaining at the end of the period without counting the number of new customers acquired. Remaining customers can be calculated by subtracting N from E. To calculate the percentage, we divide that number by the total number of customers at the start and multiply by 100.
So, in formula, we have: ((E-N)/S)*100


Please use this identifier to cite or link to this item:
|Title:||Algorithm to determine the intersection curves between bezier surfaces by the solution of multivariable polynomial system and the differential marching method|
multivariable polynomial systems
|Publisher:||The Brazilian Society of Mechanical Sciences|
|Description:||The determination of the intersection curve between Bézier Surfaces may be seen as the composition of two separated problems: determining initial points and tracing the intersection curve from these points. The Bézier Surface is represented by a parametric function (polynomial with two variables) that maps a point in the tridimensional space from the bidimensional parametric space. In this article, it is proposed an algorithm to determine the initial points of the intersection curve of Bézier Surfaces, based on the solution of polynomial systems with the Projected Polyhedral Method, followed by a method for tracing the intersection curves (Marching Method with differential equations). In order to allow the use of the Projected Polyhedral Method, the equations of the system must be represented in terms of the Bernstein basis, and towards this goal it is proposed a robust and reliable algorithm to exactly transform a multivariable polynomial in terms of power basis to a polynomial written in terms of Bernstein basis .|
|Appears in Collections:||Technology and Engineering|
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The Mathematician II supports a team of developers and artists producing video casino games by creating fresh game content and iterating on current gameplay formulas, to deliver high quality, captivating and performing games.
ESSENTIAL DUTIES AND RESPONSIBILITIES:
Essential Duties and Responsibilities include but are not limited to the following:
- Evaluate game design to ensure all points (features, frequencies, etc.) are cohesive with an exciting math model given system, mathematical and jurisdictional restraints.
- Follow rules from the game design to produce the mathematical calculations for features.
- Develop in-house simulations and theoretical calculations.
- Perform validation calculations through an in-house simulator.
- Under minimal supervision, develop varying math models for different markets, including creating Class 2 math models using in-house tools. Review outcomes for all game specific metrics and make all necessary adjustments.
- Review all math models through game play as they are implemented to ensure they reflect the correct math model. Make any adjustments as needed to create world class math models.
- Prepare documentation to include math models in game software.
- Under minimal supervision, provide documentation for certification labs and casinos.
- Under minimal supervision, validate outcomes in the field or investigate unusual player sessions as requested.
- Participate in the game design for basic games.
- Develop tools to support new game mechanics including Office extensions and/or WPF applications.
- Trouble shoot and identify simple technical issues/challenges and develop potential solutions.
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- Other projects and duties as assigned by manager.
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- While performing the duties of this job, the employee is regularly required to talk or hear. The employee is also regularly required to stand, walk, sit, and use hands to finger, handle, or feel objects, tools or controls.
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I saw my math teacher walk into her office with a piece of graphing paper.
I think she was plotting something.
They’re all kinds of weird fetishs out there. Some people even get off on graphing.
Thats where I draw the line.
I’ll see myself out.
My son used to be horrible at graphing trig functions.
Luckily he's made excellent sines of improvement.
I have been graphing my past relationships...
There's an Ex axis and a Why axis.
My graphing calculator works really well...
Some would say it functions perfectly.
I am pretty good at almost all areas of Math
But graphing is where I draw the line
This joke may contain profanity. 🤔
A man was in a Terrible fire.
Third degree burns covers his legs torso arms and face. Luckily he had enough skin intact for skin grafts. The doctor worked tirelessly graphing him from top to bottom. They were almost finished when they got to his eyelids. The doctor was stuck trying to figure out what to do to graft this youn...
Jimmy approached his teacher
After looking at the syllabus for their next lesson on graphing, Jimmy approached his teacher with a stern look on his face and said, “I’ll do algebra, I’ll do trig, I’ll even do statistics, but graphing is where I draw the line!”
I may be willing to solve equations..
but graphing is where I draw the line!


I’ve been using a lot of different EdTech tools in my math classroom, but I found no tool which is more powerful than GeoGebra. Some of the reasons, I would love to share with you.
Great tool for beginners and for experts
First of all, it is incredible easy to use. Is it easy to construct a triangle, a straight line, or a circle. Even teachers, who consider themselves not very tech-savvy, will have results in a few seconds. Students don’t need a long time to learn how to handle the software. For GeoGebra novices, it is a great opportunity to create easy geometrical constructions.
Easily constructed triangle – ready to copy and paste
But simple to use does not imply limited usage. When you start to go deeper in GeoGebra, you will find a plethora of applications to use in math classroom.
Applet: Find the correct parabola…
View original post 699 more words


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Parameter and Statistics the two terms are immovably consolidated that are vital for the computation of the example size. The boundary portrays the entire populace, while Statistics express a piece of the populace. At times it is hard for a person to comprehend the distinction between these two terms, however it is critical to know both the terms and what recognizes them and furthermore learn about Statistics vs Parameter.
WHAT IS PARAMETER?
A Parameter is a valuable idea of factual examination. It makes reference to the properties that are applied to depict a given populace. It is predominantly used to characterize the highlights of the whole local area or society. While doing a theory about the general population, the Parameter is new in light of the fact that it is unbelievable to gather the insights regarding each person in the populace.
For example, in the event that you request the businesses from an organization what sort of food or lunch you will like and assuming the portion of the representatives’ answer is Maggi, the Parameter is half of laborers like Maggi in their lunch.
The most standard boundaries which are utilized to compute the information are Mean, Median, and Mode. These are the most natural boundaries that are the proportion of focal propensity. They used to clarify how the information acts when the information is dispersed.
WHAT IS STATISTICS?
All things considered, Statistics is characterized as the part of applied math that incorporates the assortment, clarification, and examination of the proposal from quantitative information. In basic words, it examines the attributes of something about the example of the populace.
For instance, as we talked about, Parameter is the point at which half the number of individuals like exactly the same thing as in their lunch, yet on account of Statistics, it gets hard to figure the number of individuals who like to have Maggi in their lunch. You can not get some information about their decisions; all things being equal, you need to do the overview. What’s more, figure generally speaking of what are the inclinations of individuals in food or lunch. This estimation is known as Statistics.
The two significant spaces of measurements are known as Descriptive Statistics and Inferential Statistics. The first portrays the properties of test and populace information, and the subsequent one uses these properties and checks speculations and makes the end, individually and get biostatistics task help.
Contrast BETWEEN PARAMETER AND STATISTICS
- The Parameter states something about the whole populace, and measurements indicate an example of the populace. For instance, we need to know the normal length of butterflies. The Parameter tells the whole populace of butterflies, yet we gather 100 butterflies and study the butterflies’ normal length in Statistics. The mean length of butterflies is Statistics and afterward dependent on the mean length, we close the length of the whole butterflies populace.
- Besides, the Parameter’s worth remaining parts unblemished, while the worth in Statistics can vary starting with one example then onto the next. For example, Group A of butterflies’ normal length is 6.5mm, and the length of butterflies from bunch B is 6.8mm.
- It isn’t in every case clear that the number you are managing is a Parameter or a Statistics. To realize which kind of numbers are they, pose the accompanying inquiry to yourself:
> Does the number give the subtleties of the entire or complete populace?
> Is it conceivable to gather the data on this trademark from each part in a sensible time period?
The number is most likely to be a boundary. For a little populace, subtleties can be gathered from the entire populace and closed in Parameter.
Nonetheless, on the off chance that the appropriate response isn’t right for both the inquiries, the number is bound to be insights. Examining is utilized for the assortment of data from numerous populaces and sums up the measurements to a wide populace in an apparently decent manner.
HOW TO ESTIMATE PARAMETER AND STATISTICS?
A Statistic is an attribute of the gathering of the populace or test. You get the Sample Statistic when you gather the example and compute the standard deviation or the mean. You can utilize the example to do the proposal about the whole populace with inferential measurements.
Be that as it may, it would help you when you had a particular examining strategy to assemble a legitimate induction. By utilizing these techniques, ensure that examples give impartial gauges or are right by and large.
To ascertain the populace boundary in inferential measurements, you need to utilize the example insights. For example, in the event that you gather an arbitrary example of female youngsters in Canada and gauge their loads, you need to ascertain the example mean.
As we learn over that, the Parameter and Statistics both are like some degree, yet the two of them have diverse estimation techniques. As Parameter depicts the entire populace, then again, Statistics portrays a piece of the populace. Best since they correspond to one another.


2 edition of Combinatorics found in the catalog.
Advanced Study Institute on Combinatorics Breukelen, Netherlands 1974.
|Statement||M. Hall, J. H. van Lint, ed[itors].|
|Series||Mathematical Centre tracts ; 55-57, Mathematical Centre tracts ;, 55-57.|
|Contributions||Hall, Marshall, 1910-, Lint, Jacobus Hendricus van, 1932-, North Atlantic Treaty Organization.|
|LC Classifications||QA164 .A34 1974a|
|The Physical Object|
|Pagination||3 v. ;|
|LC Control Number||75321319|
1 An Introduction to Combinatorics 3 2 Strings, Sets, and Binomial Coefficients 17 3 Induction 39 4 Combinatorial Basics 59 5 Graph Theory 69 6 Partially Ordered Sets 7 Inclusion-Exclusion 8 Generating Functions 9 Recurrence Equations 10 Probability 11 Applying Probability to Combinatorics 12 Graph Algorithms vii. Combinatorics Introduction This set of texts in combinatorics is accompanied by numerous quizzes that can help you check whether you understood the material. The collection of problems and the set of texts is under construction and you should expect it to expand continuously. Table of Contents Sets Functions Introduction to the theory of counting.
The book provides a theoretical background for several topics in combinatorial mathematics, such as enumerative combinatorics (including partitions and Burnside's lemma), magic and Latin squares, graph theory, extremal combinatorics, mathematical games and elementary : Springer International Publishing. One book not mentioned yet is Brualdi's "Introductory Combinatorics" It looks to be at a good level for beginning undergraduates while still maintaining a reasonable level of rigor. Some of the comments at Amazon seem say that the most recent edition is . Combinatorics - Combinatorics - Graph theory: A graph G consists of a non-empty set of elements V(G) and a subset E(G) of the set of unordered pairs of distinct elements of V(G). The elements of V(G), called vertices of G, may be represented by points. If (x, y) ∊ E(G), then the edge (x, y) may be represented by an arc joining x and y. Then x and y are said to be adjacent, and the edge .
Books For Combinatorics Well I am starting to crave for proofs seem so elegant and I haven't gone through any book that deals with only combinatorics. I am not a complete beginner in combinatorics but still I'd like to have your views on the books you've read on combinatorics so that I can get one and start. -- click on the image for a free PDF copy of the whole book. ANALYTIC COMBINATORICS: This book, by Flajolet and Sedgewick, has appeared in January , published by Cambridge University Press.. Free download linkp.+xiv. Electronic edition of J (identical to the print version). This is the version of Introduction to Combinatorics and Graph Theory. It contains new sections and many new exercises. The book was last updated Janu , When there is a substantive change, I will update the files and note the change in the changelog. The book is available in two formats, as a PDF file and as HTML .
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SyntaxTextGen not activatedFront Matter 1 An Introduction to Combinatorics pdf Strings, Sets, and Binomial Coefficients 3 Induction 4 Combinatorial Basics 5 Graph Theory 6 Partially Ordered Sets 7 Inclusion-Exclusion 8 Generating Functions 9 Recurrence Equations 10 Probability 11 Applying Probability to Combinatorics 12 Graph Algorithms 13 Network Flows 14 Combinatorial.In addition to the above, on the general combinatorics front (towards the enumerative side) I'd recommend the Combinatorial Species book and Flajolet & Sedgwick's Analytic Combinatorics.
Edit: Oh, and Wilf's generatingfunctionology is an useful and easy read. Applied Combinatorics is an open-source textbook for a course covering the ebook enumeration techniques (permutations, combinations, subsets, pigeon hole principle), recursion and mathematical induction, more advanced enumeration techniques (inclusion-exclusion, generating functions, recurrence relations, Polyá theory), discrete .


This book was geared towards scientists, researchers, and engineers. It was very technical, very scientific and had lots of math formulas. I did find it interesting though. It dealt with erosion and other problems that in particular effect metal and other substances used in airplanes, turbines, etc. I had never thought, for instance, that a 1 or 2 mm drop of water falling 1000 feet, at many hundreds of feet a sec, was the equivalent of a bullet hitting metal (which of course would be of particular interest to aeronautical engineers). The book also looked at craters such as on the moon to compare with similar craters on materials on earth. The scientists state that the evidence in some of the lunar craters (with a raised portion in center) would suggest that the impact from whatever produced said crater hit with such force that both projectile and surface of moon were momentarily liquefied, the almost instantly (because of the extreme temps) frozen. I think that because of the vast amount of technical data, and math problems many people would find the book extremely boring, but I learned some things.


Dr. Laurel Travis received a both her MBA and her Ph.D. in Business-Quantitative Analysis from the University of Wisconsin-Madison. She obtained a bachelor’s degree from the University of Michigan in Mathematics. Since that time, she has taught at 7 universities in the United States, Canada, and most recently, China. She has taught at both the undergraduate and graduate levels, in subjects including management science, management information systems, engineering, mathematics, and computer science. She has published a textbook entitled Simulation for Decision Making, with Arne Thesen.
Laurel's research and teaching interests focus on international programs, gerrymandering, discrete event simulation, and applied optimization. Laurel’s recent volunteer activities include caring for the Hokie horses, and teaching STEM on a schooner in the Great Lakes.


Werkhoven P., Toet A. & Koenderink J.J. (1990). Displacement estimates through adaptive affinities. IEEE Transactions on Pattern Analysis and Machine Intelligence 12(7), 658‑663. Algorithms for the computation of optic flow from image sequences by means of "local constraint" (relating spatial to temporal gray value variations in the image plane) often postulate an additional "oriented smoothness constraint" (assuming that the flow vector field varies smoothly). Oriented smoothnes in addition to "local constraint" proves to be a mathematical foundation for many iterative algorithms that compute optic flow. In this correspondence we present a new technique that is functionally equivalent to the oriented smoothness concept and reduces numerical complexity and computational costs by eliminating the smoothness requirement from the iteration process. We applied local affine transformations for propagating uniquely computed flow vectors into homogeneous regions and along edges, in a single step. The window within which the local affine transformation is performed, is adaptive to the local structure of the intensity pattern, which is accordance with the oriented smoothness concept as formulated by Nagel.
Werkhoven P. & Koenderink J.J. (1990). Extraction of motion parallax structure in the visual system I. Biological Cybernetics 63, 185‑191. We present a paradigm to estimate local affine motion parallax structure from a varying image irradiance pattern. The method is based on a matching of jets of irradiance rather than the local image irradiance pattern or features of it. It does not put any constraints on the structure of the image irradiance pattern. Moreover, the aperture problem does not arise and additional ad hoc constraints on the velocity field like the 'smoothness constraint'' are superfluous. An implementation is designed such that the affine structure of the local motion parallax field is represented through simple combinations of the outputs of physiologically plausible receptive fields and their temporal derivatives.
Werkhoven P. & Koenderink J.J. (1990). Extraction of motion parallax structure in the visual system II. Biological Cybernetics 63, 193‑199. We have developed an algorithm to extract local affine motion parallax structure of a varying image irradiance pattern in part I. In part II, we present computational results of this algorithm for situations where the information about the affine structure is contained in only two successive images. This applies to a large class of problems (e.g. two-image motion sequences and stereoscopic vision). The results show the effects of spatio-temporal discretisation and internal noise on the performance of this algorithm.


The aim of the quantity is to supply a aid for a primary path in arithmetic. The contents are organised to charm particularly to Engineering, Physics and computing device technology scholars, all components within which mathematical instruments play a vital position. easy notions and techniques of differential and vital calculus for services of 1 actual variable are offered in a fashion that elicits severe examining and activates a hands-on method of concrete purposes. The format has a specifically-designed modular nature, permitting the teacher to make versatile didactical offerings whilst making plans an introductory lecture path. The e-book could in reality be hired at 3 degrees of intensity. on the effortless point the scholar is meant to understand the very crucial principles and familiarise with the corresponding key ideas. Proofs to the most effects befit the intermediate point, including numerous feedback and complementary notes improving the treatise. The final, and farthest-reaching, point calls for the extra research of the cloth inside the appendices, which permit the strongly prompted reader to discover additional into the topic. Definitions and houses are offered with large examples to stimulate the training approach. Over 350 solved routines whole the textual content, a minimum of half which advisor the reader to the answer. This re-creation beneficial properties extra fabric with the purpose of matching the widest diversity of academic offerings for a primary process arithmetic.
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Additional info for Mathematical Analysis I (UNITEXT)
Then: a) If f expanding on I, then f′(x) ≥ zero for all x ∈ I. b1) If f′(x) ≥ zero for any x ∈ I, then f is expanding on I; b2) if f′(x) > zero for all x ∈ I, then f is exactly expanding on I. evidence. allow f be the map. consider first f is continuous, for this reason for each x zero ∈ I, the variation quotient , with x ∈ I, x ≠ x zero, is 0. Then f‱(x zero) = zero via definition of by-product. Vice versa, consider f has 0 spinoff on I and allow us to end up that f is continuing on I. this may be resembling challenging Take x 1, x 2 ∈ I and use formulation (6. thirteen) on f. For an appropriate among x 1,x 2, we now have therefore f(x 1) = f(x 2). □ 6. 7 6. 7 Monotone maps within the mild of the consequences on differentiability, we take on the problem of monotonicity. evidence. allow us to turn out declare a). believe f expanding on I and think about an inside aspect x zero of I. For all x ∈ I such that x < x zero, we now have therefore, the adaptation quotient among x zero and x is non-negative. nevertheless, for any x ∈ I with x > x zero. the following too the adaptation quotient among x zero and x is confident or 0. Altogether, Corollary four. three on yields f′(x zero) ≥ zero. As for the potential extremum issues in I, we arrive on the comparable end via contemplating one-sided limits of the variation quotient, that's constantly ≥ zero. Now to the results in elements b). Take f with f′(x) ≥ zero for all x ∈ I. the assumption is to mend issues x 1 < x 2 in I and turn out that f(x 1) ≤ f(x 2). For that we use (6. thirteen) and notice that through assumption. yet because x 2 − x 1 > zero, now we have proving b1). contemplating f such that f′(x) > zero for all x ∈ I as an alternative, (6. thirteen) implies f(x 2) − f(x 1) > zero, accordingly additionally b2) holds. □ the theory asserts that if f is differentiable on I, the next common sense equivalence holds: additionally, The latter implication isn't really reversible: f strictly expanding on I doesn't suggest f′(x) > zero for all x ∈ I. we have now somewhere else saw that f(x) = x three is in all places strictly expanding, regardless of having vanishing spinoff on the foundation. an identical assertion to the above holds if we modify the observe ‘increasing’ with ‘decreasing’ and the symbols ≥, > with ≤, <. Corollary 6. 28 permit f be differentiable on I and x zero an inside severe aspect. If f′(x) ≥ zero on the left of x zero and f′(x) ≤ zero at its correct, then x zero is a greatest element for f. equally, f′(x) ≤ zero on the left, and ≥ zero on the correct of x zero implies x zero is a minimal element. Theorem 6. 27 and Corollary 6. 28 justify the hunt for extrema one of the zeroes of f′, and clarify why the derivative's signal impacts monotonicity periods. instance 6. 29 The map f : ℝ → ℝ, f(x) = xe2x differentiates to f′(x) = (2x + 1)e2x , whence is the only serious element. As f′(x) > zero if and provided that is an absolute minimal. The functionality is exactly reducing on and strictly expanding on . □ 6. eight 6. eight Higher-order derivatives enable f be differentiable round x zero and permit its first by-product f′ be additionally outlined round x zero. Definition 6. 30 If f′ is a differentiable functionality at x zero, one says f is two times differentiable at x zero. The expression is termed moment spinoff of f at x zero.


Learning to Love Math
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Reflexmath Login: Reflex is a student login portal. It gives students creative and exciting ways to learn maths. The founder of Reflexmaths was David Shuster in 2011. Reflex offers to learn through an easy method, assessment, practice, coaching. This Portal gives students fun games and activities to play and learn. It is a more effective way to learn and find the best and easiest way to teach students with research. It helps students with maths solutions or studies, and it grows students’ confidence and interest in maths.
Reflex provides students maths-related fun activities including subtraction, multiplication, division, addition and more for upto grade 2 elementary students. It can gain students interest in maths and confidence to solve maths problems. Reflex math gives a 30 days trial, and it can be accessible for parents to log in. It will cost school and personal teachers the amount would vary, and school amount will be dependent on the per school, and teachers cost on the per student.
Reflexmaths gives Login to students, educators, and parents. Students can log in through a teacher name, and parents can log in to the parent reporting account and view their child’s progress on Reflexmaths. Parents will get the weekly progress of their child via email.
Benefits of Reflexmath login account
Reflexmaths gives students innovative ways to learn and have fun while studying online. Here are the benefits of it:
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Students Login requirements of Reflexmath Login
Here are the login requirements of Reflexmaths include:
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Reflexmath Login Procedure of student
If you want to successfully log to the Reflexmaths portal, follow the mentioned below steps:
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Reflexmath login procedure of teacher’s
If you’re a teacher, follow the mentioned below steps to access your teacher login account.
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If you have forgotten the password of your educator login account so you may follow the mentioned steps below. The steps would be:
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Mentioned below contact details of Reflexmaths will help you in any trouble during Login or anything. You may contact the given points.
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Charlottesville, VA 22902 USA.
You may check Reflexmaths social media handles, and they are available over there as well. Such as Twitter, Facebook and YouTube.
Frequently asked questions (FAQ)
Q. Can parents view their child’s progress on Reflex?
Ans. Yes, Parents can view their child’s progress through Login to the parent reporting account. Reflex gives a free login portal to Reflex.
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Ans. The per school subscription of Reflexmaths is $3,295 (USD).
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Ans. This Portal is specially designed for students that already know basic maths. So it gives students a fun way to learn and become fluent in maths. Such as games, fun activities, practice, and more.
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Ans. You may visit the customer care service of Reflexmaths, or you may contact the teacher as well for any queries.
This article is about the Reflex Math Students login portal, and we describe the login process, its benefits, and contact information. If you find this article interesting and helpful, let us know in the comment section below. You can also leave your queries over there, and we would like to help you. You can also provide us with your feedback.
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