SAN ANTONIO -- At one point in history, a typewriter was useful for homework. Fortunately for students in the North East Independent School District, iPads have replaced the clunky machine.
"The iPads have been amazing to have in the classroom. They are very motivating. They help in all subject areas. Our focus right now is math," said Courtney Cleveland.
Cleveland teaches at Clear Spring Elementary School. Third and fourth graders at her campus and students at Olmos Elementary are participating in a new program that puts the electronic devices in the hands of students to help with math in the classroom and at home.
Through the Technology Lending Program, NEISD was awarded a grant providing 3000 iPads.
"Kids, they usually say math is boring. Once they get an iPad, and it's in a game, it's 90 percent more fun," insisted one 4th grader.
"I was really, really excited, because I have always wanted an iPad and never got one,” said Destiny Carter.
Students believe learning is more fun with the iPad. Parents might wonder if it really enhancing learning or just fun and games.
“They can really see what a fraction is all about and how much this fraction is divided into, and then the brain is so powerful,” said Mercedes Carter.
If the benefits outweigh the costs, the NEISD would like expand the use of iPads to more students throughout the district.
"It's wonderful," grandmother Mercedes Carter told us. "And one thing also, I think U.S. students should be tops in technology, and this is a good start."


We are continuing with the second lesson of our program study, and this time we focus on the announcement and explanation of Variety.
What is the difference? They are machines that will allow us to temporarily save any information we need to interact with our systems. In fact, in this second tutorial we also explain what kind of data you are and will show you, for example, how to work with numbers or ones that contain a decimal part.
In addition, we will learn to use general mathematical operations when using numerical values, as well as other aspects of a particular personality to consider … and make the transition between numbers and text, and vice versa!
But don't be comfortable … pay attention to the definitions! Because for every video accompanying this tutorial some questions will arise … and I'll leave you space to think about it and give your answer (press & # 39; stop & # 39; if you need more time).
But don't worry, because if you don't get the answer yourself … you can find the answer in the descriptive video for this article.


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Math Games Framework
Toward a Conceptual Framework for Designing Math Games
Full recording (text chat, audio, video, web tours)
About the event
Wednesday, February 17th 2010 we will meet in the LearnCentral public Elluminate room at 6:30pm Pacific / 9:30pm Eastern time:
has been focusing on the subject of serious games for learning mathematics since the Fall of 2009. It also
met in September 2009
. We are working on a conceptual framework for evaluating and designing math games. It is based on the series of decisions in design. Definitions of decisions come from game theory research and gaming studies. The gameplay consequences of each decision are analyzed based on existing games viewed through the lens of these definitions. The mathematics education consequences of each decision are then analyzed based on the pedagogy embodied in the gameplay, and viewed through the lens of learning theories. A series of parallels between gaming concepts and pedagogical notions helps mathematics educators make sense of game theory concepts, and apply these concepts to teaching. The resulting structure makes it clear that some types of math games are overused, and other promising types are rarely employed by
education game developers.
The decisions, as well as their mathematics and math education parallels, are made along these dimensions that provide dichotomies, gradients or levels:
narrative-based vs. abstract; situated vs. formalized
full disclosure to hidden information; open-book to closed-book
strategic to typed; problem-solving to exercises
bounded rationality gameplay or not; level or stage learning theories
Agency and autonomy gradient:
high to none; open-ended to closed-ended tasks
interactions, tasks, tactics, strategies; order of math tasks
expert to superficial knowledge; deep learning to expository learning
sandbox play to clear goals; conceptual learning to procedural fluency
Dmitri Droujkov has more than 10 years of experience with programming, design, requirements and development management. Dmitri's interests include integration of all aspects of the development cycle, agile development methodologies, and facilitation of distributed development using integration of web based collaboration tools and development tools. Currently Dmitri is the CTO for Phenix Solutions, Inc., a software services organization that empowers innovation.
Chris Hazard is the founder of Hazardous Software and is a PhD candidate in the Computer Science Department at North Carolina State University. His research interests can broadly be described as the mathematics of computational strategy and dynamics of multiagent systems, which includes topics such as computational trust and reputation, game theory, mechanism design, and artificial intelligence.
Previously, he worked for Motorola Inc. for 3 years designing and developing simulation software for CDMA infrastructure, directing global development teams. Mr. Hazard has also had experience at Kiva Systems, a warehousing robotics startup company, performing algorithms research. Mr. Hazard enjoys teaching, and has taught courses ranging from teaching game programming to gifted and talented high school students to teaching upper-level undergraduate E-commerce courses. He has won numerous academic and programming awards, including a best paper award in an international conference, University Outstanding Teaching Assistant Award at NCSU, the NCSU Dean's Fellowship, and Valparaiso University Board of Directors' Independent Research Award. He obtained his B.S. in Computer Science from Valparaiso University with departmental honors. His academic website can be found here:
Maria Droujkova is founder and director of Natural Math. Her research interests include Early Algebra, Multiplicative Reasoning, and social media ("Math 2.0"). Maria organizes Math Clubs and other local math groups and events, and online networks.
Maria's web site:
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Computer science is one of the most popular fields of activity. If You want to become a competitive specialist with fundamental and applied knowledge in the field of information technology, skills for research, professional and practical activities in the modern conditions of the labor market - we invite You to the bachelor of science program in "Informatics". You will get skills of application of methods of applied mathematics and Informatics, information technologies in professional activity.
Introduction to computational mathematics Numerical methods Equations of mathematical physics Basis of mathematical and computer modeling Mathematical modeling packages Decision theory Operations research Modeling of computational mathematics problems
Programming languages and technologies Algorithms and data structures C++/C# programming Introduction to Net application development Python programming Software application design Java programming Mobile application design
Mechatronics and robotics Educational robotics Methods of teaching Informatics and mathematics It project management Professional oriented foreign language Application packages Computer simulation
Operating systems Human-computer interaction Architecture of parallel computing systems Web-technology Telecommunication technologies Routing and switching basics Information security systems Database theory Computer networks Development of client-server applications Big Data
Graduates can work in management organizations, scientific organizations, computer and information centers using the methods of applied mathematics and computer science, computer technology in professional activities. Graduates may hold positions of mathematician-programmer, software developer, database administration specialist, system analyst, system and network administrator, software maintenance specialist.


Fully qualified, very experienced teacher available in the Chichester area as a maths and English tutor.
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How to Identify the Top Equivalent Ratio Calculator
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Should I tell you that I use a calculator when I grade student papers?
30 total points minus 2.5. Ummmm.
Do it in your head, dad would say. This was usually at the kitchen table, with a box of Kleenex and a math book sitting in front of him. Bless him. No dad tried harder to work numbers into his kid’s head.
In grieving my dad’s departure from us, I had a little weep one day when I was writing in my checkbook. A long time dad spent teaching me how to make a 2, 3, 4, 5, 7, and 8 –so that they would never be mistaken for other numbers. This lesson came in high school algebra. The three has a solid line on the top, so it can never be confused for an eight. The left line of the four curves to the left, so it can never be confused for a nine. The eight is made with two circles, like a snowman, so that…not sure. I think he just liked how that looked.
Algebra equations –I think that was the last time I was able to comprehend a math problem. It was downhill into geometry and calculus. Many tears to follow.
If A = B and B = C, then A = C.
Math is good for something after all, because I’ve been taking this mathematical equality to church with me.
If Jesus was raised from the dead and my dad knows Jesus, then my dad is raised from the dead.
By his power God raised the Lord from the dead, and he will raise us also. (1 Corinthians 6:14 NIV)
More Easter math…
God’s power raised Jesus from the dead, and now that same power is inside of me, so my everyday problems can be resurrected.
That power is like the working of his mighty strength, which he exerted in Christ when he raised him from the dead… (Ephesians 1:18, 19, 20 NIV)
Now that’s not so hard, is it? Dad would say.


IT254 Spreadsheet Applications
This course is designed to introduce the basic computer spreadsheet application skills, with an emphasis on essential design, format, functions, and formulas of spreadsheet operations in solving real-world problems. Electronic spreadsheets are used in a variety of business calculations to analyze, graph, and manage data. Applications of spreadsheets can be used to generate reports to maintain large amounts of data, make accurate calculations, and accelerate repetitive tasks.
MAT143 or MATH143 or MATH140 OR MATH140-L or MAT150 or MATH150 or MATH105 or MATH102
DistributionComputer Science/Engineering/Information Technology


How to Calculate an NPS Margin of Error
One critique sometimes heard about NPS scores is that they can’t be stat tested. That is not true. Though I know of no statistical packages that do it automatically, it is an easy calculation you can do on your own. Here’s the math:
n = sample size
a = % promoters
b = % passives
c = % detractors
NPS = a – c
First, calculate the standard error:
With that, you can easily calculate the 95% confidence interval (or margin of error) for the NPS score:
NPS ± 1.96 (SE)
If you want to compare two groups: Calculate the difference between the two NPS scores. Then calculate the standard error for each group separately. Then calculate this 95% confidence interval:
If this interval contains the zero value, then the difference is not statistically significant.
Note that applying the typical z-test for percentages normally used in market research is not appropriate, and indeed these calculations are not the same as the margins of error for simple proportions.
So, while there are lots of reasons you might want to avoid using NPS as your be-all and end-all customer satisfaction measure, don’t let your inability to figure out statistical testing be one of them. Toss these formulas into an excel spreadsheet and you’re good to go.
P.S. Many thanks to Mark Schieffer, Kanglung Wong, and Dong Xiaoming at Sprint for pointing out a formula typo in our original post on this topic!


neitheranswer explanation . ∠1 and ∠3 are vertical angles. measure of angle CEA. One of the angles in the pair is an exterior angle and one is an interior angle. Check all that apply. say we know, we're given, that this angle right over here, Notice also that x and y are supplementary angles … Angles that add up to 90° Tags: Therefore, each of these pairs is also a pair of supplemental angles since their sum is a straight_ angle. m∠2 and m∠4 are vertical angles. SAVAGE_CRIP17. see people write, angle BED plus angle CEB Or we could say the Vertical angles. This is the first Section 3: Angles 59 Position the buildings on the map by meeting the following conditions: Ø The park and the city building form a linear pair. And that might even make Angles a° and c° are also vertical angles, so must be equal, which means they are 140° each. They are abbreviated as vert. Flashcards. we know so far and not using a protractor, So what's the measure of angle Let me make that B You see that angle BED and intersecting line segments. The precise statement of the conjecture is: vertical angles are equal. I'll leave you there. So once again, subtract m∠2 = m∠4 for them is vertical angles. going all the way around. Now plug –5 and 15 into the angle expressions to get four of the six angles: To get angle 3, note that angles 1, 2, and 3 make a straight line, so they must sum to 180°: Finally, angle 3 and angle 6 are congruent vertical angles, so angle 6 must be 145° as well. The angles that are opposite to each other when two lines intersect each other are known as vertical angles. angle CEB are adjacent.
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ALP Math Teacher Resources
Level IV Digital Technologies
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Level IV Academic Math Resources
Level IV Graduate Math Resources
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Level III Math Resources
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In this lesson for grades 4-7 from Cyberchase – the program that shows kids that math is everywhere and everyone can be good at it! — students are introduced to concepts of fairness in games based on the probability, or odds, of winning and losing a game of chance. It includes media resources, assessment materials, and Common Core State Standards. (more…)
Posts Tagged ‘math’
PBS LearningMedia’s newest math collection, Math at the Core: Middle School, contain media-rich lessons designed to help middle school students visualize math concepts. The lessons align to Common Core standards for grades 5-8 and address critical concepts, such as ratios and proportions, adding negative integers, and probability and statistics. (more…)
- The Sweet Science of Chocolate | Grades 4-13+ | Video | Chocolate makers explain the elaborate engineering and chemistry behind this tasty treat
Proponents of blended learning are like the early settlers forging west — the path is full of unexpected obstacles. So states a report by staff writers in the January 27th issue of eSchool News. As school leaders consider adopting blended learning to provide more opportunities for their students, the article highlights five key considerations gleaned from the thousands of schools engaged in this approach. (more…)
Cyberchase is the Emmy award-winning animated math mystery show featuring a team of curious kids who use their math and problem solving skills to outwit and outsmart the villain Hacker in their quest to save Cyberspace. In addition to segments from the animated portion of the show, the PBS LearningMedia collection of Cyberspace resources includes live-action For Real segments, in which hosts Bianca and Harry explore the show’s math topics in everyday life. (more…)
Posted in Lesson Plans, Professional Development, Teaching Tools, tagged grades 6-8, grades 9-12, learning, lesson plan, math, pbs learningmedia, professional development, reading, teaching, video on January 3, 2014 |
This vast collection of resources, including lesson plans and professional development, is from Thirteen/WNET in New York. It’s designed to engage students in financial awareness, economic empowerment and personal responsibility. The 25 resources for grades 7-12 that comprise (more…)
The holiday season can be financially challenging as we purchase gifts and other creature comforts that may have come to be expected in traditional celebrations. Students, who may struggle with financial matters over the holidays as well as in their daily lives, can benefit from education on the subject of fiscal responsibility. (more…)
A new study has found that the acquisition of essential early math skills — counting, recognizing numerals, recognizing shapes, and patterning — increased significantly among four- and five-year-old children from economically disadvantaged communities who participated in a 10-week PBS KIDS Transmedia Math Supplement initiative.
Materials featured videos and interactive content from several PBS KIDS programs such as Sid the Science Kid, The Cat in the Hat Knows a Lot About That!, Curious George, and Dinosaur Train, as well as non-digital activities including books and foam shapes. (more…)
Posted in Uncategorized, tagged common core, grades 6-8, health and nutrition, history, lesson plan, literacy, math, National Standards, pbs learningmedia, reading in the content areas, writing in the content areas on December 2, 2013 |
Common Core State Standards set requirements not only for English language arts but also for literacy in history/social studies, science, and technical subjects — making content-area reading more important than ever.
Because students usually need practice with content-area reading, PBS LearningMedia provides ways to boost literacy using the Middle School Literacy Initiative, which is funded by the Walmart Foundation and supported by other PBS LearningMedia resources. With these self-paced online lessons, perfect for blended learning environments, students can read, review vocabulary, and practice writing in the content areas.
You can visit any of the following individual lessons:
Science: On the continental drift, students learn how an idea that started with a man looking at a map of continent became a scientific theory.
Mathematics: On unit conversion, students figure out how much water various activities use and also learn about water conservation.
Health: Should I eat this? Students learn about nutrition values of different foods and meet two students with diabetes.
Social Studies: Students meet four teen immigrants and learn about the challenges they face as they adapt to American culture.
To use the lessons, students simply need to register for an account on PBS LearningMedia, or use their existing account.


Back when multisampling first showed up, GPU hardware was slow, so triangle counts were low. Complex curved shapes were approximated by a small number of faceted triangles, each of which was big enough to cover many screen pixels.
This created an odd situation where early articles about multisampling focused on how it could smooth jaggies along the straight edges of these enormous triangles. We’d become so used to the faceted appearance of computer graphics that we could geek out over how beautifully antialiased our triangle edges were, without ever stopping to notice “whoah, that dude’s entire head is made of just 5 triangles!”
But hardware improved. Triangle counts went up. A high end modern game typically uses somewhere between 4000 and 6000 triangles for a main character.
Consider a typical gameplay situation:
With this much detail in our models, faceted geometry is a thing of the past. Instead we have a new problem: we just got Nyquisted!
Remember: to avoid aliasing we must take at least twice as many output samples as our highest frequency input signal. But here we have FEWER output pixels than input triangles. It is intuitively obvious that this must cause aliasing. With fewer pixels than triangles, some triangles will inevitably not appear in the output image at all. As the object moves, which triangles are lucky enough to get themselves a pixel will randomly vary, so the image shimmers with aliasing as individual triangles pop in and out of view.
In fact there is a narrow sweet spot for how many triangles a model should contain. For best quality, you want each triangle to cover exactly two screen pixels. If triangles are smaller than this, you cross the Nyquist threshold and get aliasing. If larger, your silhouette will appear polygonal and faceted.
It is not entirely intuitive that the sweet spot is two pixels per triangle as opposed to just one, yet this is true. Consider a circle being approximated as a series of straight line segments. As you increase the number of segments, the circle becomes more perfectly round. By the time each line segment reaches two pixels in length, the circle is perfect. Adding more line segments beyond this point will not give any improvement to the curvature of the shape.
It is obviously impractical to keep all our triangles exactly the same size on screen, given that models must be drawn at different sizes as they or the player move around the world. So how can we draw high detail geometry without aliasing?
Multisampling (or supersampling if you can afford it) helps by giving more headroom before we hit the Nyquist threshold, but this alone is not enough to avoid all geometry aliasing.
Normalmaps can be a powerful technique. We have great features for avoiding aliasing when resampling textures, so any time we can take fine detail out of our geometry and replace it with a normalmap, that will help control aliasing. We often think of normalmaps as purely a performance optimization (replacing expensive geometry with a cheap texture map) but they can also boost visual quality (replacing a data representation that cannot be easily filtered with one that supports anisotropic filtering and mipmaps).
Finally, it is important to consider level-of-detail model variants. When the object is far away, replacing that 6000 triangle model with a simpler 1000 or 500 triangle alternative will not only boost perf, but also reduce geometry aliasing artifacts.
Moral: when it comes to triangle counts, more is not always better! Beware of trying to draw more triangles than you have screen pixels to represent. That way lieth the land of aliasing.


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Geometric Analysis and Partial Differential Equations Seminar
September 25, 2013 @ 10:30 am - 11:30 pm
Mr Scott Parkins (University of Wollongong)
Gap Lemma for the Triharmonic Equation on Surfaces with small energy
We use energy methods to establish a gap lemma for solutions to the Triharmonic flow on surfaces with small energy. We then talk about an extension to high general Poly-Laplacian flows.


Defining Mathematical Reasoning
To explore and operationally define types of mathematical reasoning present in elementary students.
This project is to examine mathematical reasoning in elementary students in order to operationally define types of reasoning. For the last two years our team has worked to better understand the reasoning of elementary students in mathematics. Our primary focus has been on students in grades 3-6. Two primary studies have been conducted to meet this objective. Study 1 consisted of two phases and used a sample of students performing below the 35th percentile (N = 105) and Study 2 consisted of students in the general education population (N = 418).
Study 1 used two separate analyses to examine types of reasoning that emerged based on student responses (N = 1,928) to a psychometrically validated measure of mathematical reasoning for Whole Number and Fraction items. In the first phase of Study 1 a cluster analysis was performed on 36 categories of student strategies, and the data dispersed into three clusters. Based on these results and a review of the literature on reasoning, the research team created a set of operational definitions encompassing three types of reasoning: (1) faulty reasoning, (2) algorithmic reasoning, and (3) plausible reasoning.
Study 2 was conducted to examine the reasoning of a larger, more diverse population. We replicated the cluster analysis performed in Study 1 conducted on the 36 reasoning strategies to determine the findings from Study 2 were comparable. Findings from this study were promising for our proposed categories and provide initial evidence in the development process of an evaluation tool for assessing students’ mathematical reasoning intended for research and practical application.
- Lindy Crawford
- Jacqueline Huscroft-D’Angelo
Graduate Student Researchers
- Hannah Alvis
- Madeline Cranford
- Pei Pei Gong
- Shelley Shirley
- Shayla Sigler
The Mathematics eText Research Center (MeTRC) is located at the University of Oregon. Currently, under the leadership of Dr. Mark Horney and Dr. Lynne Anderson-Inman of the University of Oregon's Center for Advanced Technology in Education (CATE), the center is in the process of conducting a systematic program of research that has spanned over five years in collaboration with five teams across the country, each focusing on a specific student population, curriculum, or technology.


Who is it aimed at?
Level 5 upwards
Duration: 1 hour
The aim of this session is to provide participants with an introduction to Statistics and the common causes of their misuse, including an exploration of the factors participants need to consider when analysing statistical data…with some fun examples!
By the end of the session participants will;
- Have an understanding of the problems when using statistics
- Be able to identify factors which influence statistical results
- Have an understanding of the difference between Correlation and Causation
- Be able to critically use statistics and apply it to their research/assignments


Algorithm Design and Analysis
These notes are for a version of the course taught by Prof. Bahman Kalantari in the spring of 2017.
Professor’s Website - http://www.cs.rutgers.edu/~kalantar/
- Homework & Quizzes: 15%
- Midterm I & II: 20% each
- Final Exam: 45%
Exam 1 Date: Feb. 15th, 2017
Lecture 1 - 1/18/2017
The aim of this course is to study algorithms - routines or sets of steps to solve problems.
In this course we wish to analyze the runtime and memory efficiency of algorithms. We will explore how to best go about designing algorithms which have optimal runtimes.
Lecture 2 1/23/2017
In this lecture we explore the growth of functions and some asymptotic notation.
Given two functions which map natural numbers to all real numbers
To put that into english we can that that, if and only if (double implication) there exists some constant which is greater than 0 such that the condition that is satisfied for every which is greater than some reasonable then we can say that . (f is big-oh of g)
Example: , Our restriction is that is 1
Q: In this case, is ?
A: Yes, if we set then we get which is true for any which is greater than or equal to 1.
There are two other definitions similar to big-oh as well.
Review - The L’Hopital Rule
Given two functions such that then we can also say that
Suppose two functions: and . Our claim is that
Also suppose we look at functions that are exponential in nature (vs polynomial functions). Given the two functions and
Then if we continue to differentiate we find that we get .
If we are then to continuously differentiate our other function we get
Then if we are to take the limit of the ratio (now that we have applied L’Hopital’s rule) we get
We see from this that exponential function of a base raised to an input value power is infinitely worse than a high order polynomial function.
Transitive Property of Big-Oh
The sequence is defined as
A naive algorithm might do something like
def fib(n) if n == 0 return 0 if n == 1 return 1 if n > 1 return fib(n-1) + fib(n-2)
However this algorithm isn’t efficient because we keep computing many of the same values over and over again for just a single calculation, while a simpler lookup array could be far faster.
Another way to calculate fibonacci values is via the following equation
Homework in the book. Pages 8 and 9.
Lecture 3 - 1/25/2017
Review of last lecture:
Given , and , which is larger (asymptotically)?
- Take log of each
- We immediately see that is smaller asymptotically smaller than
Given the functions floor and ceil we know
We also know that
We should also say that
Which gives us that is bounded.
Useful Summation Formulas
What about the summation: ??
We can generalize and make it
From this we can simply see that
Moving on to algorithms - searching for a key in a sorted array
A sorted array is an array with the condition such that
- One option is to run binary search.
Let be the worst case number of comparisons for binary search. We can then say that
We can say now that the worst case is , but what about the average case? Or the best case.
Let be the average # of comparisons in binary search, assuming all numbers are distinct.
Given that and
For Let the number of positions where is takes comparisons to find the correct location.
Assume the following table for
The average time is then given by
In more mathematical terms there are locations plus gaps which gives us locations.
The Average time then becomes
Lecture 4 - 1/30/2017
Given a list of elements, we want to determine whether a specific element is contained in a list of the elements. We define
- - The worst case run time
- - The average case run time
In binary search we fine that .
Representing the number of items as giving
To calculate the average case we get
where is the number of position where it takes comparisons.
Divide and Conquer Algorithms
Many algorithms are recursive in nature and call themselves one or more times. This is called using a “divide and conquer” approach because the algorithms solve small subproblems before coming back together to complete the entire problem.
- Divide the problem into smaller subproblems
- Conquer: Solve the subproblems recursively. If the subproblem size is small we solve it with a straightforward approach.
- Combine solutions for subproblems into solutions for the original problem.
One of the classic divide and conquer problems is mergesort.
The key problem in mergesort is combining two sorted lists. The function might be defined as where
- A is an array
- p, q, and r are indices.
Assume is sorted and is sorted
The best approach will take no more than comparisons. This works by using two pointers and incrementing one of them on the list until we find a value which is larger than the other pointer. We switch pointer comparisons until we reach the end of one list. Then we append the rest of the other list.
Given the list 5 2 4 6 1 3 2 6 Show the mergesort steps 5 2 4 6 | 1 3 2 6 5 2 | 4 6 | 1 3 | 2 6 5 | 2 | 4 | 6 | 1 | 3 | 2 | 6 2 5 | 4 6 | 1 3 | 2 6 2 4 5 6 | 1 2 3 6 1 2 2 3 4 5 6 6
The algorithm for mergesort can be written:
margesort(A, p, r): if p < r q <-- floor( (p + r) / 2) mergesort(A, p, q) mergesort(A, q+1, r) mergesort(A, p, q, r)
To analyze this type of algorithm we can relate the overall runtime to the runtime of the subproblems.
For mergesort, given number of comparison to sort a list of numbers with mergesort
This formula can be generalized to the form
- number of subproblems
- = size of each subproblem
- time to divide
- time to combine
If we apply the mergesort algorithm to this to analyze the runtime we can first state that
If we plug in into our final answer we find
In multiplying two numbers together we find that the way we normally do it on paper takes approximately operations. Wheras the c algorithm implemented in computers are able to do it in approximately
Lecture 5 - 2/1/2017
In divide and conquer algorithms we can represent the runtime as the following function
- : Number of subproblems
- : size of each subproblem
- : Cost to divide
- : Cost of combining
Proving that the non-base case for is
More proofs for solving recurrence relations
Using recurrence relations we can find the runtime of divide and conquer algorithms.
Master Theorem -
Lecture 6 - 2/6/2017
- Split and compare elements of the from from left to right with A starting with A
- If an element is greater than A it stays in place
- Otherwise, swap with the first key which is either greater than or equal to it in the greater section
- Finally swap A with the last of the smaller keys (n-1 comparisons)
In the worst possible case, quicksort is
With randomized recursion where we choose a random pivot index from 1 to n, then which is the average number of comparisons in randomized recursion.
We get that Theorem: $$A(n) \leq cn\cdot log(n)
Lecture 7 - 2/8/2017
Sorry! No notes for today
Lecture 8 - 2/13/2017
A structure which satisfies the heap property:
In human terms this means that given a key that we can say that a structure satisfies the heap property if the parent element of is always greater than or equal to its children.
This is different from a binary tree where we know the relationship between the left and right nodes must be that the left node is always less than the right. In a heap this isn’t true. In a heap all we know is that the parent is always greater than the children.
So when popping a new item from a heap we must ensure that the heap property is still satisfied. In order to do this we remove the item from the heap, then we fix the heap by sifting the new largest value of the roots children as the new root. Then look at that nodes children and bring the larger one up, and so on.
The recurrence relation for heapsort is
If we break this down by setting we can get
Then breaking down the recurrence relation we
By going until we get
Lecture 10 - 2/27/17 - Graphs
Graphs are special constructs which include vertices and edges. We represent a graph by
Where represents the set of all vertices in the graph. represents the edges in the graph. When drawing a graph, an edge is associated with two vertices and is typically represented by a line drawn between the two vertices which it connects.
BFS (Breadth-First Search)
Breadth-first search means starting from a specific node and searching for a value within a graph by exploring all nodes within a similar distance of the first before moving outwards to search more distant nodes.


Technical Tuesday: Exploring financial market data with Z-Scores in Python
Nothing says festive season quite like a post on statistics and programming! Welcome to the inaugural Technical Tuesday, a fortnightly series on data science, machine learning and programming with Python. I am often asked about topics in those areas and if I have some good answers I plan to share them here — in a short and digestible format. Most articles will be written with finance use cases in mind, but many insights can be applied to other fields as well.
We’ll start with Z-Scores, or Standard Scores, today. Z-scores are ubiquitous in descriptive and inferential statistics. Moreover, they are often a core methodological part of financial index construction. Standardisation is also a key step in machine learning to transform all input features to the same scale or distribution. (This ultimately helps deal with the curse of dimensionality, a tricky problem in ML.)
Getting started: definition, formula and introductory example
Put simply, the Z-score shows how far away a data point is from the mean. More specifically, the distance of a data point (or raw value) from the mean is measured in terms of standard deviations.
Let’s use an example to illustrate this. We have a sample of five people’s heights measured in centimetres. The mean height of our sample is 174.2cm and the standard deviation is 9.12cm (calculated with one degree of freedom as it a sample and not the population).
We’re interested in the Z-Score of George’s height of 189cm (which is not part of the above sample). With the below code block, which also creates the Pandas DataFrame table shown above, we manually calculate the Z-Score using the formula introduced earlier. The Z-Score for George’s height is 1.62, i.e. 1.62 standard deviations above our sample mean.
The challenges of sequential data
We could have calculated the Z-Score of Alice’s height (second row of the table) as well — order does not matter here. Many phenomena in nature have attractive statistical properties such as being close to normally distributed and stationary. By contrast, time series — and in particular financial market data — are more complicated in many ways. We need to take into account the sequential nature of the data, especially if we are planning to make predictions.
Imagine you have 30 daily data points from December 1st to 30th. If you calculate the mean and standard deviation for the whole period and use both to compute the Z-Score for December 10th you will have entered the statistical danger zone. This is called look-ahead bias (or data leakage) because on December 10th you would not have had the other 20 “future” data points to calculate the mean and standard deviation necessary for the Z-Score. If you do this any predictive model will look much better than it actually is because you’ve peaked into the future. The first day for which you could use the above data points is the following day, December 31st. So in contrast to the earlier example with human heights, order does matter if the data is sequential!
Building early warning signals with the right look-back window: Lockdown news volume example
Our first time series example involves news volume for the keyword “lockdown” from Marex Spectron’s NowCast. In this case we need to make sure we only use means and standard deviations computed on data prior to the observation for which we wish to calculate the Z-Score. Finding the appropriate lookback methodology and windows is tricky business.
One option is to define fixed rolling lookback windows, e.g. the past 30 days or 6 months. For the below analysis of “lockdown” news volume I picked another option: the expanding window methodology with data going back to 2015. The expanding method takes all data points going back to the first one for each calculation instead of having a fixed rolling window (where data prior to the window is not used as the window rolls forward).
This approach produces means and standard deviations that tend to react more slowly to changes than (often shorter) rolling windows. Both results are shown in the green and orange lines in the top part of the chart right below. That means extreme short-term moves (of the raw data we’re interested in) are compared to slower-moving means and standard deviations. This produces faster and bigger moves in the Z-Scores, highlighting extraordinary developments. Using expanding lookback windows can often work well as “early warning systems” when big shifts, or regime changes, happen.
The expanding window Z-Score above reacts very strongly to what look like little tremors in January 2020 when Wuhan and parts of China were locked down. In that sense it served well as an early warning system.
This is easily implemented with Python and the Pandas library. First let’s create three variables (e.g. smoothing) containing parameters (e.g. 14 days) in the first few lines and then an empty result DataFrame. Line 5 calculates the rolling mean using an expanding lookback window (where the DataFrame df contains the raw daily data points). Line 6 then computes the rolling standard deviation also with an expanding lookback window. I set degrees of freedom (ddof) to 0 as the Marex Spectron NowCast data is considered population data instead of sample data (in contrast to the human height samples above). The last column “zscore_expand” implements the Z-Score calculation subtracting the “ma_expand” mean from our daily data points (or to be precise, the slightly smoothed 14 day moving average of it) and then dividing the result by “st_dev_expand”.
Spotting recurring outliers with Z-Scores: Trade war example
Let’s hope we will not have to face another pandemic and damaging lockdowns any time soon. Certainly 2020 has felt like a once-in-a-century outlier. Other market-moving developments such as the trade disputes between the US and China have been of a recurring nature. How do we know when it’s critical and when it’s a blip? If we use expanding lookback windows for our Z-Score calculation the means and standard deviations tend to remain elevated for quite some time in both in the lockdown and trade war cases. It can make sense to use shorter, rolling windows so the Z-Score does not “get used to” high levels and fails to highlight new, big moves.
The methodology and parameters (shown below in the code block) produce a reasonable result that picks up the first tremors in 2016 and 2017 quite well. The raw news volume in those years is tiny compared to what was about to come in 2018 and afterwards. The Z-Score also picks up the 2018 and 2019 spikes (in the absolute count) quite well — in contrast to what expanding window Z-Scores would have shown for those later years.
The key difference to the code block above is that we use the .rolling() method instead of the .expanding() method to calculate mean and standard deviation. The method also requires that we pass an argument, i.e. the length of the lookback window, expressed in the number of days: 350 in our case.
Comparing time series with disparate absolute levels: Inflation v Deflation example
Drawing on Marex Spectron’s NowCast data again, we are able to compare related topics such as growth and recession, supply and demand (for a range of commodities) and inflation and deflation. Often the news volume for these related topics might differ enormously. As the chart right below shows, daily mentions of inflation are five to ten times as high as those for deflation.
If we took the difference of the absolute figures we would end up with the result shown right below. In a time of minimal concerns about deflation (from mid-2015 onwards), the chart looks almost the same as the one for inflation itself as the news volume for deflation is miniscule.
Should concerns about deflation resurface, it would be hard to detect this in the absolute difference chart above. One way to adjust the imbalance between the two is to standardise the time series for each topic by calculating the Z-Scores. We then subtract the Z-Scores (inflation minus deflation) and end up with the below chart showing the difference.
When the COVID/lockdown crisis hit in Q1 2020 the conversation was strongly swinging towards deflation — and this is only visible in the Z-Score chart below. The Inflation/Deflation net figure went to almost -3, i.e. three standard deviations below the mean of the past year.
Parts of the code will look familiar as we calculate the individual Z-Scores for inflation and deflation with a 350-day rolling lookback. As an aside, repeating the code to compute the two results violates the DRY principle of programming (Don’t Repeat Yourself). A reusable function could be written that processes the computation of both scores instead, but an explanation of this is beyond the scope of this introductory post. The second-to-last line of code takes the difference of both Z-Scores and the last line adds a horizontal line at zero.
Standardising inputs for Machine Learning
Apart from data exploration and time-series comparison Z-Scores can also be used as a key data pre-processing step in Machine Learning pipelines. The three code blocks below describe a quick example. First, we import the preprocessing module from the widely-used Scikit-Learn library and also Numpy. We then create some dummy data in the shape of a real-valued matrix containing three feature vectors (columns) and three training samples (rows).
The next step is to instantiate StandardScaler() from the preprocessing module and then passing the training data set (X_train) into the fit() method, which computes the mean and standard deviation — as we had done manually in our prior examples. The second line of code performs the standardisation, i.e. it calculates the Z-Scores for each feature vector (column).
Finally, we print the re-scaled matrix and take a look at the first column, which shows Z-Scores of 0, 1.225 and -1.225. The mean of our raw inputs of 1, 2 and 0 equals 1 so a Z-Score of 0 for the first row entry is correct. The standardised matrix can now be fed into the next pre-processing steps or directly into the algorithm fitting part of the ML pipeline.
To summarise, we explained what Z-Scores are and then explored the basic steps of how to compute different variations of them with practical examples using data from Marex Spectron’s NowCast. Standard scores can be used e.g. as early warning signals, to spot recurring outliers and to compare disparate time series. We also explained how Z-Scores are implemented in a machine learning pipeline using Scikit-learn.
Future posts will include a whole range of issues — from data engineering questions like how to handle very large financial market data sets to machine learning applications to more time series analysis and other topics. This article is also cross-posted on LinkedIn.


The material I recently posted as Metamorphosis, Identity, and Metaphysics in Dumbo and Fantasia started out as a piece on topology in Pink Elephants on Parade. And then it went somewhere else. In that context the topology material didn’t quite hold together. But it has some interest in itself, not so much for the topology but for Piaget’s remarks on children’s acquisition of intuitive topology and geometry. So I’m posting that material as a separate piece.
The mathematics of space comes in several varieties, of which ordinary Euclidean geometry is the most familiar. Topology is a more recent mathematics of space, one that is considerably more general than geometry. Robert Bruner at Wayne State observes that “the thing that distinguishes different kinds of geometry from each other ... is in the kinds of transformations that are allowed before you really consider something changed,” a view he attributes to Felix Kline, who is most popularly known for the Klein Bottle, which manages to be both inside and outside itself at the same time.
As Bruner explains, geometry is quite restrictive with respect to identity-conserving transformations while topology is quite liberal:
In ordinary Euclidean geometry, you can move things around and flip them over, but you can't stretch or bend them. This is called "congruence" in geometry class. Two things are congruent if you can lay one on top of the other in such a way that they exactly match.In projective geometry, invented during the Renaissance to understand perspective drawing, two things are considered the same if they are both views of the same object. For example, look at a plate on a table from directly above the table, and the plate looks round, like a circle. But walk away a few feet and look at it, and it looks much wider than long, like an ellipse, because of the angle you're at. The ellipse and circle are projectively equivalent.
And it wasn’t only Renaissance mathematicians who were interested in projective geometry. As Bruner’s remarks imply, artists were also interested in it, and used it in their painting. Animators, obviously, must be intuitive masters of projective geometry, for they have draw many carefully calibrated views of complex objects, such as people and animals, moving in space.
In topology, any continuous change which can be continuously undone is allowed. So a circle is the same as a triangle or a square, because you just `pull on' parts of the circle to make corners and then straighten the sides, to change a circle into a square. Then you just `smooth it out' to turn it back into a circle. These two processes are continuous in the sense that during each of them, nearby points at the start are still nearby at the end.
This is the crucial point, all points have the same neighbors when a circle is transformed into a square.
The circle isn't the same as a figure 8, because although you can squash the middle of a circle together to make it into a figure 8 continuously, when you try to undo it, you have to break the connection in the middle and this is discontinuous: points that are all near the center of the eight end up split into two batches, on opposite sides of the circle, far apart.
Donuts and teacups are the same from a topological point of view, but not a geometrical point of view. The hole in the teacup handle corresponds to the hole through the middle of the donut. Teapots are more complex. There’s the hole through the handle and the hole through the spout. Put another hole through your donut—anywhere (think about it, visualize it)—and it becomes topologically equivalent to a teapot.
[You can find illustrations and discussion of children’s spatial and geometric thinking at this site.]
In a slender volume, Genetic Epistemology (Colulmbia UP 1970) has some remarks on topology, noting that, in children’s active understanding “the first intuitions are topological. The first operations, too, are those of dividing space, of ordering in space, which are more similar to topological operations than to Euclidean or metric ones” (p. 31). That is to say, the developmental order is opposite from that in the history of mathematics, where Euclidean geometry came long before topology.
Of course, we are talking about very different things here. Mathematics involves explicit assertions involving language and mathematical symbols. Those things are taught more or less in the order in which they arose in the history of mathematics. One learns plane geometry in middle or high school. Topology is reserved for college if it is learned at all.
Piaget is talking about what children draw and what they point to. Here’s what he says (pp. 31-32):
Pre-operational children can of course distinguish various Euclidean shapes—circles from rectangles, from triangles, etc.—as Binet has shown. They can do this at about 4 years of age, according to his norms. But let us look at what they do before this age. If we show them a circle and ask them to copy it in their own drawing, they will draw a more or less circular closed form. Once again, if we show them a triangle, they will draw just about the same thing. Their drawings of these shapes are virtually indistinguishable. But if, on the other hand, we ask them to draw a cross, to copy a cross, they will draw something totally different from their drawings of the closed figures. They will draw an open figure, two lines that more or less come to a cross or touch each other. In general, then, in these drawings we see that the children have not maintained the Euclidean distinctions in terms of different Euclidean shapes, but that they have maintained the topological distinctions. Closed shapes have been drawn as closed, an open shapes have been drawn as open.
I note further that Piaget’s discussion is not limited to geometry and topology. Following the Bourbaki mathematicians he also discusses the algebraic group (which Lévi-Strauss employed as a rhetorical device in Mythologies) and “the order structure. This structure applies to relationships, whereas the algebraic structure applies essentially to classes and numbers” (Genetic Epistemology, p. 25).
Finally, I want to quote a passage which has to do with identity, which IS relevant to the problem of metamorphosis (pp. 56-57):
The last experiment that I should like to mention is carried out by Boyat on plant growth. He started by experimenting with the growth of a bean plant, but that took too long, so instead he uses a chemical in a solution, which grows in a few minutes into an arborescent shape looking something loike a seawee. Periodically, as a child watches this plant grow, he is aked to draw it, and then with his drawings as reminders he is asked whether, at the various points in its growth, it si still the same plant. We refer to the plant by the same term the child uses for it—a plant, seaweed, macaroni—whatever he happens to use. Then we ask him to draw himself when he was a baby, and himself a little bigger, and still a little bigger, and as he is now. And we ask the same questions as to whether all these drawings are drawings of the same person, whether the person is always he. At a relatively young age, a child will deny that the same plant is represented in his various drawings. He will say that this is a little plant, and that is a big plant—it is not the same plant. In referring to drawings of himself, however, he will be likely to say that all show the same person. Then, if we go back to the drawings of the plant, some children will be influenced by their thoughts about their drawings of themselves and will say now that they realize that it is the same plant in all the drawings, but others will continue to deny this, maintaining that the plant has changed too much, that it is a different plant now


Percentage Calculator - Tools for everyday use.
Once you have finished using our tool for learning how to do simple conversions you will no doubt want to explore other mathematical forms of theory such as calculus or long division. If this is the case then we are working on creating a guide for this information which will be available asap.
Percentage Calculator – Applying the equation
Simply Applying what you know to the equation:
You see an item that is $50.00, but it is being reduced by 15%. First you must decide what the amount is that is going to be deducted from $50.00 To do this you will need to multiply 50.009 by .15 (you need to convert 15% to a decimal). The answer is 7.5, now you will need to subtract $7.50 from $50.00, you will be paying $42.50 for the item that is on sale.
If this information is useful to you please don’t hesitate to leave friendly comments and let us know how we could improve this writing for you!


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Four -year Bachelor’s degree in mathematics teacher
Are you passionate about math? Would you like to show others the beauty and elegance of mathematics? Do you like sharing your knowledge or solving problems together with students? If the answer to any of these questions is yes, join our Mathematics Bachelor Teaching program and become a 21st century math teacher. A teacher that thinks and teaches outside of the box.
The classes occur during the afternoon. Besides our one-on-one classes, we also have our own interactive digital learning environment called ELOUA. ELOUA is exclusively for students and can be found at stone.ua.aw.
The Mathematics Bachelor Teaching program offers a four-year bachelor degree program that leads to a “tweedegraads bevoegdheid” as a mathematics teacher. As a “tweedegraads bevoegd” teacher, graduates of this program are qualified to teach at different high schools levels including MAVO, EPB, EPI and the lower grades of HAVO and VWO. If you have a mathematical academic background, you may be eligible for a shorter program.
Admission requirements: VWO mathematics A or B, HAVO mathematics B, E.P.I. level 4, Propaedeutic (technical) HBO with a proficient score in mathematics, “Derdegraads bevoegdheid” mathematics, Colloquium Doctum for applicants with HAVO mathematics A
Cost of academic year: Awg. 2.500,- Cost of books: Awg. 2.000,- Class schedule: 3:00 p.m. - 9:00 p.m. Essentials: Laptop/Tablet and the right attitude Start: End of August Registration: May 15 - July 15
Duration of study
Language of instruction
I started my journey at the UA back in 2013. One of the first skills I learned was time-management and giving presentations. Looking back at my first experience, I now feel secure and my teaching skills have improved. My teaching experience taught me how to deal with students with different characters and to manage my time and classroom better. If you enjoy working with numbers and calculations and of course teaching, I suggest you register for the Mathematics Bachelor Teaching program. "To teach is to touch lives."Darryl Wout, Faculty of Arts & Science, Mathematics Bachelor Teaching Program (Lerarenopleiding Wiskunde)
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Understanding and controlling randomness is crucial in solving global challenges including contemporary problems in biology. To unite the scientists utilizing probabilistic methods to tackle biological problems, Ivan Corwin, Professor, Dept. of Mathematics, led a symposium on March 6, 2020, co-organized by the Herbert and Florence Irving Institute for Cancer Dynamics and the Probability and Society Initiative.
The afternoon started off with a lecture by Tian Zheng, Professor and Chair, Dept. of Statistics. She discussed how to use Markov modulated Hawkes processes to model "bursty" events in which there are periods of activity followed by periods of dormancy. This talk was followed by one by Ian McKeague, Professor, Dept. of Biostatistics, which studied branching processes related to random trees and random matrix theory. Mathieu Carriere, Postdoctoral research scientist, Dept. of Systems Biology, gave a stirring talk about topological data analysis, showing how to perform statistical analysis on the results of the "Mapper" algorithm. Wesley Tansey, Postdoctoral research scientist, Dept. of Systems Biology, then explained how deep probabilistic learning methods can be used to discover which genes play important roles in cancer drug response. The final talk was presented by Khanh Dinh, Postdoctoral research scientist, Dept. of Statistics, who applied probabilistic models to understand how to infer the phylogenetic trees behind the evolution of cancerous mutations.
The talks were followed by a stimulating discussion from the audience of the departments of mathematics, statistics, biology, data science, the medical school and the school of public health. The speakers enjoyed a tour of the newly designed space of the Herbert and Florence Irving Institute for Cancer Dynamics. The event came to a close with a reception and stimulating discussion of several fascinating ideas on how to solve critical problems in biology utilizing probabilistic methods.


An entropy method is one of the methods based on the existence of information in the decision table. So, in order to solve an issue in an entropy manner, we must make a decision table. In the following, the steps of the entropy method are explained first and, in the next step, an entropy method is given as a fully functional example.
Entropy method steps
Step 1: Set up a decision table: The first step in the process of entropy is the formation of a decision table. Therefore, in order to calculate the weight of the indices using the entropy method, the problem decision table must first be formed, since, as stated, the decision table is considered as the input of the entropy method. Matters indicate the decision making as follows.
Step 2) Normalizing the decision table: The second step is the normalization of the entropy procedure or the non-scaleing of the decision table. Normalization uses a simple normalization method, the same as the arithmetic mean. The simple normalization relation is as follows.
Step 3: Calculate the entropy of each index: At this stage, the entropy of each indicator should be calculated using the following equation.
Note: The K value will cause the entropy value of each index to remain between zero and one.
Step 4: Calculate the distance of each index from its entropy (dj): at this stage, we must find the distance of each of the indicators from the amount of entropy that was calculated in the previous step. To do this, use the following equation.
Step 5: Calculate the weight of each indicator: At this stage we calculate the weight of each indicator using the following equation.
Note: Because the credibility of the weight derived from the entropy method depends on the validity of the data, so to increase the weight of the weight, this method can be combined with one another.
Example) A dam construction project has been delegated to the “A” ministry. This project can be carried out by executive personnel in the ministry (option A1), internal contractor (option A2), or external contractor (option A3). The ministry is looking to select the best contractor (option) to give it a dam construction project.
To assess contractors, five indicators of “labor hardness”, “capacity”, “national reputation”, “strength” and “cost” have been used. Calculate the weight of each index using the entropy method.
Step 1: Formulate a decision table: As stated, the first stage of the entropy process is the formation of a decision table. Using the questionnaire, the data related to the decision table was obtained as follows.
Step 2: Normalization of the decision table: Using the relationship expressed to normalize the problem-solving table.
Step 3: Calculate the entropy of each index: At this stage, we calculate the entropy of each of the indices using the proposed relationship. The table below gives the entropy value of each indicator in each option.
Note: To calculate the entropy of each index, the entropy of each indicator must be combined for all the options presented in the table above (sum of the above table columns).
By calculating the entropy of each index, we can calculate the degree of diversion of each indicator, the weight of each indicator and the rating of each payment index (stages 4 and below) by comparing the ratios presented. The following table provides the results of these calculations.


Sic Bo is a game of chance. Players place their bets on a spot on the Sic Bo table and wait for a live dealer or an automatic dealer to roll the dice and award them with a prize. This game is easy to understand and does not require complex math or technical calculations. In fact, even novice players can learn how to play this game and win without too much hassle.
The game involves three dice. Players place their bets based on how often three dice will appear on the board. Players may bet on a single number, two numbers of the same value, or three dice showing the same value. If the number appears on all three dice, the player will win one unit for every unit staked. However, the payout for this bet is much higher than a single number bet. If three of a kind appears on the dice, the player wins a large sum.
Sic Bo is a game of chance that originated in Ancient China and is a favorite among Asian gamblers. While the game is predominantly popular in Asian countries, westerners have also found it enjoyable. The name “Sic Bo” means “two dice”, and “Dai Su” is the Chinese term for “grand hazard.” Sic Bo gambling is a fun way to spend an evening at the casino.


Happy New Year from the Math Department! Problems for Round 8 have been posted on the Saint Maur Math Challenge website. For the remainder of the academic year, the SMMC problems will be posted every Wednesday 2 and should be returned to your teacher before or on Wednesday 1.
The AMC 10 and 12 will be taking place on Feb 19. Good luck to those who have been invited to participate. For more information on the contest, click on the link for the AMC website.


Decagonal coverings and quasicrystals
Gummelt's decagon with the decomposition into kites and darts indicated by dashed lines; the thicker darker lines bound an inscribed ace and thick rhomb; possible overlaps are by one or two red aces.
In 1996, German mathematician Petra Gummelt demonstrated that a covering (so called to distinguish it from a non-overlapping tiling) equivalent to the Penrose tiling can be constructed using a single decagonal tile if two kinds of overlapping regions are allowed. The decagonal tile is decorated with colored patches, and the covering rule allows only those overlaps compatible with the coloring. A suitable decomposition of the decagonal tile into kites and darts transforms such a covering into a Penrose (P2) tiling.
The painting uses the idea of Petra Gummelt.


The very sight of questions on Algebra, Geometry and Modern Maths flusters and unsettles many aspirants dreaming to bell the CAT. Since these three areas together account for more than half the Quantitative Ability (QA) questions in the CAT, it’s imperative to master them thoroughly. Let’s discuss the significance of these areas and try to zero in on some elementary concepts, which are indispensable to score well in these areas.
Algebra, arguably the most important topic for CAT preparation, constitutes around 25–35% of the QA questions. The questions of Algebra are based on Polynomials, Equations, Logarithm, Inequality, Maxima-Minima, Relations & Functions, Sequence & Series, Co-ordinate Geometry.. In order to do well in Algebra, one needs to acquaint oneself with the basics of linear, quadratic and cubic equations; graphs of some basic functions; some standard sequences and the fundamentals of inequalities.
Since the inception of the new avatar of CAT, Geometry has assumed a greater importance and sweeps around 15-25% of the QA questions. The area deals with Euclidean Geometry, Mensuration and Trigonometry. To ace the topic, one has to familiarize oneself with basic theorems involving parallel & transversal lines, triangles, circles and quadrilaterals; area and volume of solids; trigonometric ratios etc.
Modern Maths, with topics such as Permutations & Combinations, Probability and Set Theory, has not been as important for CAT as the other two discussed above, but needs to be prepared nonetheless. Usually, just a couple of questions feature from this area in the CAT and are not very difficult to handle. Also, a set of 2-3 questions based on the applications of Set Theory is known to have featured in the exam in the past, though not very frequently.
In a nutshell, if a CAT aspirant goes whole hog in familiarising himself/herself with the nuances and intricacies of the aforementioned concepts pertaining to the three areas and is able to apply them adeptly on the day of the exam, he/she can be sure of reaping rich dividends.


The simple solution to complex problems
Calculating stresses and deformations in planar structures subjected to varying loads is a standard part of any engineer’s existence. Non rectangular geometries cannot be calculated using tables or simple formulas; they require the use of finite-element calculation methods.
As part of its support, IBS can offer glass calculations using SJ Mepla.
In designs for glass components, the systems and shapes are often repetitive, so the mesh can be limited to standard geometries. Even so, new meshes always need to be created. Calculations on laminated safety glass generally require the use of volume elements.
In most cases the evaluation of the calculation results also follows the same pattern (deformation, stress, proof). Until recently, the results always had to be extracted from the finite-element data.
It is almost impossible to perform calculations on insulating glazing units (2-, 3- of 4-ply) if every planar shape needs to be considered, or if a non-linear geometry model is being used.
The consultants at IBS have found a solution in the form of SJ Mepla, a finite-element computer program for structural glass calculations developed by SJ Software.
Click here to go to the website of SJ Mepla. For more information, send a message to Ralph van der Stel at email@example.com.


I recently came up with an interesting idea for making better passwords you might like to implement. OK, so there is this website that generates true random numbers using atomic decay. It has a Java library but also an http api if you don't use Java (I don't know what language you used for keystash).
Because the numbers are true random, this makes it more ideal for password generation as it has even distribution. It also runs over an encrypted https connection making it hard to intercept the numbers used.
On the downside, you have to trust the website and the machine that makes the numbers and hope nobody takes the time to decrypt that connection you made when generating the numbers.
Well, I came up with a solution to this problem... You take a true random number from this website, then add it to a fractional pseudorandom number greater than the negative of the true random number and less than or equal to the number of choices in the array minus the true random number generated by Java's SecureRandom class and round it to the nearest whole number. This is a way of getting around the uneven distribution of even + even = even, odd + odd = even, even + odd = odd. In other words any equation involving adding numbers is more likely to end up even than odd. If you add a random fractional number, it has an equal chance of staying even or switching to odd when rounding is involved. You use the resulting number to select the character or number from the array of possible choices.
This method should lead to more even distribution of the possibilities and because there is an additional pseudorandom number added to the original number, the result is trustless. Even if the true random number website starts to broadcast the same number, over and over again to try and control the resulting password they will just end with a standard pseudorandom number between zero and the index of the last result in the array which is no worse than where you started off just using your standard pseudorandom number.
So really there is nothing to lose with this method and true random password generation to gain.


Get Assignment:Nursing essay assignment help
Assignment:Nursing essay assignment
In a sample of 100 auto parts, 12 are defective. If three parts are selected without replacement, find the probability that all three parts are defective. Find answer in reduced fraction form.
The table shows the number of male and female students enrolled in nursing at a university. A student is selected at random. Find the probability that the student is a male or a nursing student.
Twelve light bulbs are tested to see if they last as long as the manufacturer claims they do. Three light bulbs fail the test. If two light bulbs are selected at random from this group of twelve without replacement, what is the probability that at least one light bulb failed the test.
The table shows the results of a survey in which 90 dog owners were asked how much they have spent in the last year for their dog’s health care, and whether their dogs were purebred or mixed breeds.
Given that a randomly selected dog owner spent less than $100, the probability that the dog was a mixed breed is [x1]. Write answer rounded to three decimal places.
In a survey conducted by the National Family Organization, new mothers were asked to rate the difficulty of delivering their first child compared with what they expected. The pie graph below shows the results. If you selected a new mother at random and asked her to compare the difficulty of her delivery with what she expected, what would be the probability that she would say that it was the same or more difficult than what she expected?Write your answer here as a percent. [x1
The number of responses to a survey are shown in the Pareto chart. The survey asked 1005 U.S. adults what they feel is the biggest problem with movies. Each person gave one response. Find the probability that a randomly selected person from the sample feels the biggest problem with movies is not both that movies have too much violence or that the tickets cost too much. This means that you are looking for the adults who did not say these two responses. Answer should be rounded to three decimal places.
You select a card from a standard deck of 52 playing cards. Find the probability that the card is a 4 or an ace.
Write your answer here in reduced fraction form. For example: write 3/4 for the fraction three fourths. [x1]
Are these two events mutually exclusive? Answer yes or no. [x2]


It’s the last day of Maymester Math Modeling, and I am so relieved it is over! The only thing that got me through two and a half hours of quadratic functions and logarithmic equations plus five more hours of studying was knowing that it would all be over in three weeks!
I’ve never been good at math, so I avoided taking it at all costs. Unfortunately, I had to take it in order to graduate in December. I was conflicted at first about taking such a difficult course at an accelerated pace, but there is no way I could have taken that kind of stress for a whole semester. Also, I was pretty much doing math eight hours a day — something I could not have done if I had other courses to focus on as well.
Overall, I’m glad I got the math course over with, but I wouldn’t bother with Maymester for a course I could easily do during a regular semester. One thing I definitely learned in algebra was this equation: (Maymester + Math ≠ Pool Time).


Oxford Reading Buddy
Oxford Reading Buddy is a digital reading service which our children access to develop comprehension and encourage a love of reading. It matches pupils with books at the right level and tracks performance across hundreds of Oxford’s print and digital books through expertly written comprehension quizzes.
It provides a motivating and friendly virtual environment where students have their own Reading Buddy to coach comprehension skills and where they will earn badges for working well.
Times Table Rockstars
Our Maths teachers know how fundamental times table recall speed is to success in maths lessons; yet it’s not always easy fitting in daily practice. Times Tables Rock Stars is a carefully sequenced programme of daily times tables practice which children can access independently at home.
All children have a login and password for Times Table Rockstars. Please ask your child’s class teacher if you don’t know it.
Mathletics - Virtual Learning Environment
Mathletics is an inspiring and engaging online platform which our year 6 children use for improving and reinforcing maths skills. Mathletics is designed to inspire children with the desire to learn and the confidence to succeed!
• Exciting, global Live Mathletics competition
• Set tasks to encourage independent learning
• Weekly progress emails to monitor progress via the dedicated Parent Centre
• Thousands of adaptive curriculum activities with an animated support centre
• Explorative Concept Search tool containing visual clues and interactive animations
• Times Tables Toons and Rainforest Maths
• Proven to increase average marks in maths
• Immediate feedback
• Inbuilt reward system to encourage confidence and improvement
• Students have access to Mathletics 24 hours a day, 7 days a week
• Very easy to use
• Provides the perfect link between home and school
• A wide variety of curricula and courses available
• The program is based upon adaptive learning thus students can learn at their own pace


Viesti GeoGebra Cookbook työryhmältä, kokeile!!
The GeoGebra Cookbook like any other cookbook contains recipes, tips and tricks, and useful hints. The only difference is that its focus is not on food but on the free mathematics software GeoGebra and how it can be used in the classroom.
It is made for teachers of the following school levels:
Made for teachers who are:
have some experience
to use GeoGebra.
You can use it for free and the only thing we ask of you is to answer a short questionnaire related to the Cookbook in order for us being able to make it better.
The GeoGebra Cookbook is brought to you by the Nordic GeoGebra Network, which applied for and received a grant from Nordplus for a project involving GeoGebra conferences in the Nordic and Baltic countries, and key topic group meetings for mathematics teachers and mathematics education researchers to be able to meet, collaborate, and prepare materials for teachers and students. Enjoy!
the Cookbook key topic group


I am a research scientist working in the area roughly called AI. My primary interest is in bridging the gap between how we actually think and how we can usefully model that in a computer. That means I have to work on the intuitive side; after all, art is the way we naturally deal with our world. But I also have to work with the realities of mathematics and logic.
What brings me to the study of symmetry is the conviction that it can bridge these two sides, together with a concept of narrative. I was lucky enough to be advised early in my career that this might be so. As a result, I have been at the founding of the symmetry society. It has been enormously rewarding to me, and I have repaid that by investing not only in the growing study of symmetry, and the paths suggested by exposure to some members but also by helping administer the society.
I sponsor the Symmetry Society site and the Kutachi Project.


Student of mathematics are often faced with a dilemma - where to look for the best resources on math problems? Text books do provide some assistance but assistance is limited. Online assistance also exists but where does the busy student have the time to look for the correct website offering him the exact assistance? Even the experts coming home to provide coaching to the students have limited resources available on math problems. Yet it is said that the best way to get this subject become friendlier is to solve as many problems as possible to get an upper hand on the subject.
Yes, the internet is the correct place to look for a dossier of the same type of problems on the selected topic. The more you are accustomed and familiar with the problems the more you improve your chances to clear the examinations with flying colors. It is said that practice makes a man perfect - nothing could be as true.
Where to Find Math Problems
There are some eBooks available for free on the internet which offers a kaleidoscopic array of math problems to suit the requirement of the students. The teachers, examiners and research associates are always looking out for as many different assortments of problems as possible to prepare the students for the examinations from all angles.
Math problems are also found in a wide variety of books on the subject. Most large bookstores have racks dedicated to specific subjects and a browsing through of these books will give you an idea of the huge number of problems that are there in these books. For those who cannot afford to buy these books or have the luxury of a laptop or a desktop to solve as many problems as possible, there is the public library where some good books are always available. There are some very good old style libraries that have volumes of books on mathematics. The young student or the mature researcher can access these volumes and note down the problems to be solved later from the comfort of their own homes.
Math problems usually come with a limited number of solved problems as well. The student would do well to first grasp the technicalities of these problems. Initially before going all out for math problems it is always advisable to have a thorough reading of the theory part of mathematics to gain as much relevant knowledge as possible on the chapter. So if you are looking for exclusive problems on trigonometry the best thing is to understand the basics of trigonometry first in all its magnitude and then go ahead looking for problems in as many resources as you can. You would be prepared to the hilt on trigonometry on your own.
Care should be exercised as much as possible about the source of the problems. Sometimes math problems are printed in such a manner that the problem itself becomes a problem till someone is able to figure out what the problem exactly is. Only authentic resources should be used in learning and solving problem is mathematics. Well begun is half done, so the saying goes, and how true when applied to the study of mathematics as well.
If we learn the basics in the earliest year when we were being introduced to the subject thoroughly well we would not really have a major difficulty in solving the problems that are given at the end of the chapters in the books. Unfortunately and very sadly this is not the case. Formative years in mathematics are a waste if time is not given and the correct investment done to prepare well in advance for the future.
In case you have any question, you can contact us.


Practice Review Quiz. Can be used as classwork, homework, Quiz, or test review. Envision Math Grade Five Topic 4 Quiz Lessons 1-3. Multiply Decimals By Powers of 10, Estimate the Product of a Decimal and a Whole Number, Use Models to Multiply a Decimal and a Whole Number.enVision Math, 4th Grade, Topic 3 Practice Test Quiz - Quizizz
Envision Topics 3 & 4 Subtraction Test. by . Jamie Seymour. This is an assessment for the third grade Envision Math series Topics 3 & 4 subtraction units. The assessment includes 25 questions assessing various forms of subtraction. There are a variety of multiple choice and free response questions. Also to make life easier for you this download ...Envision Math Grade 3 Topic 4-3 Visual Learning
Envision Math Grade 4 Topic 3. STUDY. Flashcards. Learn. Write. Spell. Test. PLAY. Match. Gravity. Created by. saraha_moody TEACHER. Terms in this set (6) The Associative Property of Multiplication states that you can change the grouping of the factors and the product stays the same.enVision MATH Common Core 3 answers & resources | Lumos ...
Envision math grade 4 answer key pdf. Fill out, securely sign, print or email your Envision Math Grade 4 Answer Key. envision math grade 4 answer key instantly with SignNow. The most secure digital platform to get legally binding, electronically signed documents in just a few seconds. Available for PC, iOS and Android. Start a free trial now to save yourself time and money!enVisionmath2.0 Common Core (K-5) - Savvas Learning Company
Topic 12 Adding & Subtracting Fractions & Mixed Numbers with Like Denominators. R12-1 P12-1 R12-2 P12 R12-3 P12-3 R12-4 P12-4 R12-5 P12-5 R12-6 P12-6Grade 3, Mrs. Johnston / 3rd Grade Math Pearson Realize
Topic 3. Topic 4. Topic 5 Topic 6. Topic 7. Topic 8. Topic 9. Topic 10. Topic 11. Topic 12. Topic 13. Topic 14. Topic 15. Topic 16. Step Up to 5th grade ... Step Up to 5th grade Jami Patterson. 4th Grade vCard. Home. Info. News. Newsletter. Blog. Photos ... Envision Math Common Core Practice "Unsinkable Ships" Project Page "Unsinkable" Ships ...End-of-the-Year Test - Grade 3 - Math Mammoth
Topic 3 Envision Math Grade 4. Multiplication. STUDY. PLAY. array. A way of displaying objects in rows and columns. factors. The numbers multiplied together to find a product. product. the answer to a multiplication problem. multiple. the product of any two whole numbers. Identity Property of Multiplication.Envision Math 1-3, Topic 1 Lesson 3, Arrays and Multiplication
What's Included Included in this pack are 10 worksheets on all the lessons in the fourth grade enVision Math book for topic 3 - Use Strategies and Properties to Multiply by 1-Digit Numbers These can be used as a quiz, formative assessment, homework, or just extra practice! Answer keys are includeEnvision Math Grade 3 Topic 4-1 solve and share
The Super Mario Effect - Tricking Your Brain into Learning More | Mark Rober | TEDxPenn - Duration: 15:09. TEDx Talks Recommended for youenVision 2.0 Fourth Grade Unit 4
This is a detailed lesson plan for Grade 4 Topic 6 Lesson 1 for the enVision math 2.0 2016 version. It is editable so you can change it to fit you and your student's needs! I plan on uploading more lessons as I create them!enVision MATH Common Core 6 answers & resources | Lumos ...
Overview *4 Entries Included *Use these interactive notebook activities as a companion to Envision Math 2nd Grade Topic 5. *Focus Standards: 2.NBT.A.1a, 2.NBT.A.3, 2.NBT.A.4, 2.NBT.B.8, 2.OA.C.3 *Interactive notebook activities could be used to cover the focus standards even if your classroom does ntest 3 envision math Flashcards and Study Sets | Quizlet
4th Grade EnVision Math Topic 4 Study Guide with Answer Key This study guide is created for the fourth grade envision math series topic 1 to help prepare students for their end of topic test. Fourth Grade Math 4th Grade Classroom Math Study Guide Math Teacher Teaching Math Teacher Pay Teachers Teaching Ideas Envision Math Daily 5 Math. https ...Rosendale Newland 3rd Grade / Envision Math Practice Pages
9 3 Envision Math Practice. Displaying all worksheets related to - 9 3 Envision Math Practice. Worksheets are Ixl skill alignment, Third grade envision math curriculum map canyons school, Name practice 9 5 comparing and ordering fractions and, Name practice 9 2 fractions and division, Envision math common core reteaching and practice, Grade 3 math practice test, Practice workbook grade 2 pe ...Curriculum & Instruction / Math 2-5 enVision Support and ...
I flipped my classroom. I use this video to "pre-teach" my students. You can even use them in an Edpuzzle and get some feedback to help form your next day's lesson. Enjoy!enVisionmath2.0 Program for Grades K-8 - Savvas Learning ...
enVision Topics 7 & 8: Multiplying by 2-Digit Numbers. Large Numbers by 2-Digit Numbers. Large Numbers by 3-Digit Numbers . enVision Topics 9 & 10: Dividing by 1-Digit Divisors. Introduction to Long Division & Remainders. Long Division & Remainders . enVision Topic 11: Understanding FractionsFourth Grade enVision Math Topic 4 | Smore Newsletters
Play this game to review Mathematics. There are 24 dancers in Joy’s recital. ... enVision Math, 4th Grade, Topic 10 Practice Test - Version 1. DRAFT. 4th grade. 13 times. Mathematics. 70% average accuracy. 8 months ago. sbradford. 0. Save. Edit. Edit. enVision Math, 4th Grade, Topic 10 Practice Test - Version 1 DRAFT. 8 months ago. by ...enVisionmath2.0 Common Core (K-5) - Savvas Learning Company
The math topics we cover in fourth grade are listed below. To help you at home we have an online math book plus worksheets, and videos. Just click the link at the right for enVisionMATH. Topic 1 Multiplication and Division: Meanings and Facts.Your child should be practicing their multiplication facts!4th- Mrs. Young / 4th Grade Math
Student Links > Math > Envision worksheets & lesson videos - Lesson Topics. Topic 1: Place Value. Topic 2: Adding & Subtracting Decimals. Topic 3: Multiplying Whole Numbers. Topic 6: Multiplying Decimals. Topic 4: Dividing by 1-Digit Divisors. Topic 5 ... Geometry Topic 1: Place Value Topic 1: Place Value Topic 2 (4th grade): ...Fourth Grade enVision Math Topic 7 | Smore Newsletters
Pearson Texas, enVision MATH 2.0, Grade 3, Volume 2, Topics 9-16, 9780328767281, 032876728x. Jan 1, 2015. 4.2 out of 5 stars 5. Paperback $15.29 $ 15. 29. $3.99 shipping. More Buying Choices $1.35 (40 used & new offers) Envision Math Grade 3, California Edition, Common Core Edition, 9780328784035, 0328784036, 2015. by Grant ...Fourth Grade enVision Math Topic 13 | Smore Newsletters
Fifth Grade Math Topics and Corresponding Lessons. enVision math 2.0 . TOPIC # 1 Understand Place Value. 1-1 Patterns with Exponents and Powers of 10; 1-2 Understand Whole Number Place Value; 1-3 Decimals to Thousandths; 1-4 Understand Decimal Place Value; 1-5 Compare Decimals; 1-6 Round Decimals .enVision Math, 5th Grade, Topic 9 Practice Test Quiz - Quizizz
Fourth Grade enVision Math Topic 11 - Adding and Subtracting Fractions with Like Denominators by Nancy Torres | This newsletter was created with Smore, an online tool for creating beautiful newsletters for educators, nonprofits, businesses and moretest topic envision math Flashcards and Study Sets | Quizlet
The materials for Grade 4 enVision Math 2.0 partially foster coherence through grade-level connections. Most lessons in the Grade 4 program focus within a single domain and cluster. Of 109 lessons, 70 lessons focus within a single cluster and domain. In Topic 1, 0 of the 5 lessons address standards within two or more clusters.4th grade Math map - canyonsdistrict.org
enVisionMATH Grade 6. Scott Foresman enVisionMATH (©2009) Grade 6 hardbound edition, organized by math Topics contains daily lessons that provide a Visual Learning Bridge, teaching math concepts step-by-step with purposeful, sequential illustrations while connecting Interactive Learning with Guided and Independent skill and problem solving practice.enVision MATH Common Core 5 answers & resources | Lumos ...
Oct 15, 2015 - Envision Math Grade 4 Topic 2 Test Page 2Envision 2.0 Math Centers Grade 3 Topic 2 (With images ...
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Topic 3 Test Grade 4 Envision Math Mybooklibrary
The most popular ebook you must read is Topic 3 Test Grade 4 Envision Math Mybooklibrary. I am sure you will love the Topic 3 Test Grade 4 Envision Math Mybooklibrary. You can download it to your laptop through easy steps.