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Support for metacognition in the mathematics classroom often looks like either a lot of teacher-led modeling and thinking out loud or giving students loads of problems to solve in the hope that they will somehow discover the most useful approaches and strategies on their own.
Most teachers will tell you that in practice, neither of these approaches works very well. And they really don’t work for students who are already struggling. According to William Emeny, for many students, it’s better to “show them the [metacognitive] toolkit and teach them how to use it one tool at a time…teaching one’s brain to control the thought processes it has for the purpose of directing it towards the management of their own learning.”
Why Foster Metacognition?
When students hit difficult problems that leave them feeling frustrated — it can be tempting for them to give up and resort to the words “I can’t do it.” That’s why it is important for teachers to support and model the metacognitive process. Asking questions gets the metacognitive work going internally so that students begin to gain conceptual understanding and procedural skill and fluency and to be able to apply what they have learned. Encouraging students to talk about their learning stimulates their thinking about their thinking. In short, it fosters their mathematical metacognition. The more students are able to understand their own learning process and articulate it, the easier it will be for them to figure out what strategies and supports work best for them — knowledge that will help them succeed — both now and as they grow up.
Fostering metacognition in mathematics requires a balance of explicit instruction, teacher modeling, student-centered exploration, and responsive coaching that helps students first learn the kinds of questions and thought processes they can apply, and then grow to use them on their own. These metacognitive skills come naturally to some students but not to others. Therefore, teachers must play an active role in teaching them and helping students own their mathematical learning.
Why metacognition? Recent research has shown that students who were taught metacognitive strategies made an average of eight months more progress than students who were not. And that, according to Emeny, was over the course of just one year.
It’s clear from this data that metacognition is important, but what is it really, and how can it be taught?
Metacognition and the Strands of Math Proficiency
Larson and Kanold suggest that for too long, judgments about what constitutes “good” math instruction have been based on false dichotomies. Learning is either student-centered or teacher-directed, and its goal either conceptual understanding or procedural fluency. Both of these either/or propositions vastly oversimplify the complexity of what our brains need to know and to do to engage in mathematical thought.
Indeed, the influential report of the National Mathematics Advisory Panel found that “all-encompassing recommendations that instruction should be entirely ‘student-centered’ or ‘teacher-directed’ are not supported by research,” and that “the curriculum must simultaneously develop conceptual understanding, computational fluency, and problem solving skills.”
That report underscored the key findings of another seminal report from the National Research Council (NRC), Adding It Up: Helping Children Learn Mathematics, which found that, much like literacy, attaining proficiency in math requires learners to weave together multiple strands all at once. These key strands of mathematical proficiency drew on and further refined mathematical process standards that had been developed over the previous two decades by the National Council of Teachers of Mathematics (NCTM).
The Common Core State Standards for Mathematics brought together this vast array of research and instructional expertise to present a clear framework for metacognition in mathematics by placing a strong emphasis on the equal importance of procedural skill and mathematical understanding. And, they are clear in what they mean by mathematical understanding.
“One hallmark of mathematical understanding is the ability to justify, in a way appropriate to the student’s mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from. There is a world of difference between a student who can summon a mnemonic device to expand a product such as (a + b)(x + y) and a student who can explain where the mnemonic comes from. The student who can explain the rule understands the mathematics, and may have a better chance to succeed at a less familiar task such as expanding (a + b + c)(x + y).”
Knowing this, it is easy to see why the math standards incorporated standards of two very different types, the Standards for Mathematical Content and the Standards for Mathematical Practice. By articulating both content and practice, the standards define both what students should know and be able to do in mathematics and how they should be thinking about mathematics.
Defining the Practices for Metacognition
The Standards for Mathematical Practice grew out of the NCTM process standards as well as the NRC strands of proficiency. They acknowledge that weaving together all of the strands of mathematical proficiency is a complex process that requires students to acquire both content knowledge as well as a variety of skills and practices.
The Standards for Mathematical Practice present a helpful framework for this complex and important work. They are the same for all grade levels and represent ways that students can engage with mathematics. A few examples are included of how students at different levels or studying different topics might apply or demonstrate the proficiencies described.
But, while these brief descriptions are helpful for figuring out what the standards mean, they are not specific enough to provide much practical guidance for classroom implementation. In short, the practice standards lack the elements of focus, coherence, and rigor that the standards as a whole were created to achieve. In order to bring clarity around each element as they relate to the practice standards, let’s examine the goals and issues for each.
As teachers, helping students do this cognitive work is just as complex as the work the students themselves are doing. It requires us to understand the standards themselves, their issues, and the processes involved—to think about the thinking—and thereby help students develop the necessary conceptual understandings as well as the procedural and metacognitive skills required to be successful with math.
The Learning Brief
In this article you learned…
- Metacognition in the math classroom is essential for increasing student achievement in mathematics.
- Fostering metacognition requires a balance of explicit instruction, teacher modeling, student-centered exploration, and responsive coaching that helps students first learn the kinds of questions and thought processes they can apply, and then grow to use them on their own.
- Mathematics instruction must simultaneously develop conceptual understanding, computational fluency, and problem-solving skills and teaching the Standards for Mathematical Practice can support this development.
Can you imagine building an environment full of motivated, engaged, and eager students who own their learning?


Why Minus Times Minus Is Plus: The Very Basic Mathematics Of Real And Complex Numbers
MATHEMATICS / ALGEBRA This book is written for a very broad audience. There are no particular prerequisites for reading this book. We hope students of High Schools, Colleges, and Universities, as well as hobby mathematicians, will like and benefit from this book. The book is rigorous and self-contained. All results are proved (or the proofs are optional exercises) and stated as theorems. Important...
Paperback: 136 pages
Publisher: iUniverse (July 8, 2010)
Product Dimensions: 7.5 x 0.3 x 9.2 inches
Format: PDF ePub TXT book
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points are covered by examples and optional exercises. Additionally there are also two sections called "More optional exercises (with answers)." Modern technology uses complex numbers for just about everything. Actually, there is no way one can formulate quantum mechanics without resorting to complex numbers. Leonard Euler (1707-1786) considered it natural to introduce students to complex numbers much earlier than we do today. Even in his elementary algebra textbook he uses complex numbers throughout the book. Nils K. Oeijord is a science writer and a former assistant professor of mathematics at Tromsoe College, Norway. He is the author of The Very Basics of Tensors, and several other books in English and Norwegian. Nils K. Oeijord is the discoverer of the general genetic catastrophe (GGC).


I am so glad I packed the Hape wooden numbers for our holiday. I just knew that A’s interest in numbers would keep growing.
I was at a discount store and spotting packets of cats. They came in a pack of 6 so I grabbed three knowing I would have enough for A to use them as counters up to 5.
I introduced the toy cats to A just after we were playing with our real cats. ‘I love these! These are my favourite animals!’
I started with the number 1 and then we worked out way down the mat; going back to check if A had enough cats for each number.
After this I also added the zero and showed him how there were no cats beside zero because it means ‘none’ or ‘nothing’. Such a hard concept to understand!
I think I’ll go back and get some more packets of cats so he can keep counting up to 10.
I remembered that I had kept some wooden Christmas craft buttons and shapes, so I got them out to see if I could use them as counters.
There was enough to create counters from 1 to 5, and A was interested in counting them with me. I got the Montessori numbers and counters puzzle down off the shelf so that we could also put numbers to our counters. Basically I showed A a number and said, ‘This is the number 2, can you find the collection that has 2 in it?’
I then put the Christmas counters to the side and pulled the counters part of the puzzle out of the box.
I repeated the activity, pointing out the number and asking him to find the puzzle that had that many dots.
A then grabbed some cars and started using the completed puzzles as car parks or truck pads. 😅
You just got to ‘roll’ with it.
I really wish I owned the sandpaper numbers. I want to DIY some basic number tiles instead of buying them but I haven’t gotten around to it yet.
I do like this puzzle. I could have DIYed them easily, but I like the tactile warmth of the wooden puzzle that a laminated piece of paper doesn’t have.
I have removed the parts for 6 through to 10 to make it easier for A. When he can count the dots half of the puzzle, and it actually matches up to the number half it’s pretty satisfying. A was proud of his efforts during this activity.
Our shelves needed some rotations!
We’ve swapped out the scales and weights for a number puzzle and a stacking game!
A really enjoyed the puzzle - an improvement from last time I had it out.
I asked A to pick up a number and I told him the name of that numeral. Once he knew what the numeral was, he could then count the animals on the jigsaw before putting the number in place. I think this is also helping with estimating how many items are in a group which has a name but I can’t remember it.
The other shelf we swapped over is the miniature tray. We put out the Safari Toob Nativity set.
I printed out a picture from this link which was from this YouTube video. We watched the video and A had to find the figurine as it was displayed.
We can match up the figurines with the image for a later activity.
I thought I had read my little man right because he has been counting heaps lately. I wasn’t really interested in teaching him the actual numbers just have them out so he can see them and get used to numerals. Even then he wasn’t really interest them.
This activity should have been a winner. A loves stickers but he did not want to do this at all. In the end I think he put one sticker on the page and called it done 😆
This Melissa & Doug puzzle was too hard for A to put back together but he really enjoyed taking the numbers out. We also counted some of the pictures underneath.
This tray was a winner! I bought the plastic numbers from Riot! And got A to thread them all up.
A then played fishing boat in the washing basket - just too cute.
The book we had on display was the ‘Montessori Number Work’ by Bobby and June George.
A liked runningbhis fingers over the numbers and we did some counting but he go bored pretty quickly.
Hi, I'm Pamela. A nail crazy lady with green hair. I live in outback Queensland with my toddler and my husband. I love books, writing and crafting. For more info about me go to my 'About' page.


Nonlinear System of Equations
Nonlinear system of equations consists of more than one algebraic equations that must be solved together, whether linear
or non-linear. In effect, we see each equation as a graph, and when we solve the equations, we are looking for the points where those graphs cross or touch.
You're looking at y = x2
– 2 and y = -x2
+ 3. The intersections are marked by the circles. Below are a few more examples.
This is an intersection of y = x3
and y = x, at 3 points.
There are no intersections between y = x2
- 2 and y = 4x2
In a special case, where two graphs touch at ALL points, then the two graphs are identical.
As you can see, graphs provide a clear an easy way to spot where the intersections are, but it is usually unable to provide an exact answer unless the line falls on a corner of a grid box when plot using a computer. Plotted by hand, it can only give you a good estimate but not the exact answer. To get the exact answer, you'll need to use algebraic methods to solve the system of equations.
Give y = 2x2
+ 3x and y = 9x2
– 2, solve for x and y up to 3 decimal places.
Example 1 Solution
First we list the equations out.
y = 2x2 + 3x (Equation 1)
y = 9x2 – 2 (Equation 2)
Then you need to substitute one equation into the other. In this case, I choose to substitute Equation 2 into Equation 1. If you choose to substitute Equation 1 to Equation 2, it's okay too.
Since we have a quadratic equation, we can use the quadratic formula to solve for x.
We find that there are 2 values for x. Now we can substitute these values into either one of the equations to determine the respective values of y. For convenience, I choose to use Equation 2. For the first value of x up to 3 decimal places,
So we get the coordinates (0.790, 3.617). Substituting the second value of x into Equation 2 up to 3 decimal places,
So we get the coordinates (-0.362, -0.823). To check our results, we can plug in the x values into Equation 1 to see if the resulting y values match. Alternatively, if we plot the equations and mark the points where they cross, we can roughly determine that we have obtained the correct answer.
Hence, the coordinates (0.790, 3.617) and (-0.362, -0.823) are the intersections of these equations.
Continue to Example 2
Continue to Example 3
Continue to Examples 4 to 6
Continue to Example 7
Continue to Examples 8 and 9
Return from Nonlinear System of Equations to Intermediate Algebra
Return Home to Algebra-by-Example.com
Unclear about a concept? Or see something missing?
Do you have questions about what you've read in this section? Is something missing? Post your question or contribution here and I'll get to it as soon as I can.
If you're sending in a problem you need help with, please also describe what you've tried to get a response.


How many people does it take for there to be a 50% chance that a pair in the group has the same birthday only 23 people what about a 99% chance maybe even more. The birthday game this rather popular party game seems counterintuitive problem as given the people at a party agree to tell their birthdays. As an application of the poisson approximation to binomial, we consider the birthday problem, which is quite interesting do you know whether there are two students. Of the birthday paradox, be asked in homework or exams to write down the exact probability for a birthday-type problem (step 3 above),. On this page we'll investigate the probability that at least two people in a room with n people share a birthday and allowing for the possibility that some may have a.
'when is cheryl's birthday' the maths problem set for teenagers that has baffled the world a maths problem for 14-year-olds has baffled people across the world. El equipo que rompió la clave utilizó un ataque masivo en paralelo basado en el 'birthday attack',. Birthday problem is a draft programming task it is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
- [voiceover] so, this is a fun deductive reasoning problem that's being forwarded around the internet several people have actually forwarded it to me, and so, i. Which is calculate the odds that 365 people in a room will find someone else with their birthday the problem itself is actually very easy to understand. The probability that at least 2 people in a room of 30 share the same birthday. Finding p(at least two students with the same birthday) directly will be extremely difficult consequently, we must look for a different way if we find the.For all of you who have been trying to figure this out today, here’s my solution (with workings) and for those of who who’ve yet to read the problem, here it is. What if somebody offered to bet that at least two people in your math class had the same birthday would you take the bet how large must a class be to make the. Sandra writes: i was given this problem for extra credit and i am just stuck btw - i am not asking for source code and i am not asking anyone to do. This phenomenon is known as the birthday paradox “the uniformity assumption in the birthday problem, math mag 53 1980, no 5, 286-288. Download and read birthday problem simulation matlab birthday problem simulation matlab no wonder you activities are, reading will be always needed. Probability and the birthday paradox a mysterious math problem from science buddies. // this is the birthday paradox program // for 2 - 50 people, it detemines the chances of any 2 of the group to have their birthday on the same day. One version of the birthday problem is as follows: how many people need to be in a room such that there is a greater than 50% chance that 2 people share the same. Generalized birthday problem (n items in m bins) suppose n items are randomly distributed into r bins so that each item has a (independent) probability of 1/r of.
The “cheryl’s birthday” problem has attracted a lot of press, with cnn, the washington post, slate, and the telegraph and countless others weighing in there. @journal of the american statistical association june1972, volume 67, number 338 theory & methods section the generalized birthday problem. Birthday problem the birthday problem pertains to the probability that in a set of randomly chosen people some pair of them will have the same birthday.
The great birthday problem you walk into a room with a group of people in it and make the following wager, i'll bet $50 that there ( are / are not ) two people in. The first step in solving a problem is admitting you have one and, in this essay, i come clean about some pain that has been clawing at me for some time in the hope. Writing in 1866, john venn (of venn diagram fame) wrote: to many persons the mention of probability suggests little else than the notion of a set of rules, very. In a group of $n$ people, which is the probability of finding at least any two people which have their birthday the same day along the year.
Using a monte carlo simulation performing graphical analysis of the birthday-problem function. We can conclude that the number of people with a given birthday is a binomial distribution with mean=np=131428 (32857 for feb 29) and variance=npq=131341.Download


Today we did pgs 60-65 in The Comprehensive Curriculum for Preschool focusing on Triangles. We practiced writing the word triangle, tracing triangles, counting their sides and writing the number 3.
For our first project I drew some black triangles on black paper and had J cut them out with craft scissor. Once she finished her triangles, J glued them on a pumpkin to make a fun, fall face!
For our last project I cut some slits in the bottom of a toilet paper roll then shaped each square into a point to make triangles. This was a really fun stamping project and was great to make the sun and flowers. We also ended up with a color blending lesson where J got to see that blue and yellow make green and purple and yellow make brown!


The geometric coordination concept is the simplest of the three models. The basic idea is, that each point in space belongs to the nearest atoms. The mathematic basics are already described by Voronoi . Niggli  used the concept in crystallography by defining the 'Wirkungsbereich'. Frank and Kasper  used the concept in intermetalic systems and Ruban  defined an inverse construction of the same polyhedra.
To construct a Wirkungsbereich, it is necessary, to draw lines from a center atom to all atoms around. Then in the middle of each of this lines, we construct a perpendicular plane to the vector along the line.
The smallest possible convex polyhedra is the Wirkungsbereich or Frank-Kasper-Polyhedra.
A two-dimensional picture is shown below.
All five atoms in the polyhedra, which contribute a face are coordinated and are included in the geometrical coordination. Atom A only shares a single point, but still is treated as lying in the coordination. Atom B is lying shortly outside the coordination.
For practical purposes, the geometrical coordination may be reduced to a chemical coordination by only counting electronegative and electropositive neighbours and ignoring faces between two electronegative or two electropositive neighbours.
Last Updated: 26 October 1996


Modeling, Mining, and Machine Learning in Astronomy
Tuesday-Thursday 1:25-2:40 pm
301 Space Sciences Building
520 Space Sciences Building
This course builds upon a foundation of probability and statistics to explore, develop, and apply algorithms for discovering objects and events in astronomical data, for inference of sophisticated models for populations of objects using frequentist and Bayesian methods, and for visualization and presentation of results to address fundamental questions using persuasive, data-based arguments. Topics include time-series analysis; clustering and classification algorithms; genetic algorithms; Markov Chain Monte Carlo methods; and neural networks. Analysis projects include investigation of simulated and real data using Python and Jupyter notebooks. The emphasis is on understanding the fundamentals of algorithms and developing expertise for choosing appropriate methods to address top-level goals.
Lectures, reading material, and assignments will be posted here as we go.
Lecture 1: Introduction to the Course
Reading for the next two lectures:
Probability basics: here are several reference options.
After reading item 1, make a quick run through items 2, 3 or 4.
Key features to be emphasized in class include random variables,
probability density functions, examples like the Gaussian distribution, and the Central Limit Theorem.
Relevance: we will treat data as 'processes' that
are collections of random variables and we need to be able to
manipulate their probabilities.
1. Chapter 1 and portions of Chapter 5 from Gregory:
all sections except
5.5.4, 5.6, 5.7.3, 5.8.3, 5.8.4, 5.11.1, 5.13.2, 5.14, 5.15
2. Course Notes (slides 2,3 summarize main elements we will use)
3. Another approach: Laws of Probability, Bayes' theorem, and the Central Limit Theorem
4. Another approach: Basics of Probability from CS229 Stanford
Lecture 2: Basics of Probability and Processes.
Lecture 3: Probability Applications.
Homework: Assignment 1 A simple demonstration of Frequentist and Bayesian methods
Jupyter notebook: Frequentist_Bayesian_Example.ipynb
Lecture 4: Correlation functions, transformation of variables, Fourier transforms
Address the questions asked in the notebook by writing up what you did and what your conclusions are. You can add this to the notebook but RENAME the notebook with your name prepended to the notebook name. Alternatively you can submit (by email) a text-edited document converted to PDF (also with a name that includes your name). Due Thursday Feb 7.
1. Fourier transforms: Appendix B sections B.1 through B.4.2 of Gregory
2. Fourier transforms: Course notes
3. Linear Shift Invariant Systems
Notes: Correlation Functions as a Diagnostic Tool
Lecture 5: Linear models, cost functions, solutions, covariance matrices
1. Linear least squares
2. Sections 10.1-10.6 in Gregory
Homework: Assignment 2 Due February 21 (Thursday)
Lecture 6: Iterative linear regression; overfitting, detection and classification
1. DFT, FFT Usage, Fourier-based Power Spectra
Lecture 7: Detection/classification of aligned features, Matched Filtering
1. Matched Filtering (first 18 slides)
2. Chapter 39.4 The Single Neuron as a Classifier, in
Information Theory, Inference, and Learning Algorithms (MacKay)
3. Single layer neural networks (notebook from Sebastian Raschka)
Lecture 8: Detection/classification of misaligned features, Matched Filtering II
Jupyter notebooks: these are for the hackathon in the Lecture 9 class
1. Classical least squares demonstration (matrix algebra, covariance matrix, cost function, etc.)
2. Least squares fit done iteratively in a simple network
3. Pulse detection (classification) with a simple network (aligned pulses)
4. Misaligned Pulse detection (first take)
5. A neural net in 11 lines of Python
Lecture 9 (19 Feb) Hackathon to investigate simple networks


St. Petersburg becomes the center of attraction for mathematicians from all over the world!
Only a few days left before the start of the 62nd International Mathematical Olympiad, which will be virtual this year. St. Petersburg will be the organizer of this world event again and will become a center of attraction for participants from all over the world.
St. Petersburg is the city with an amazing history, the city of drawbridges and white nights, the city that inspires the greatest minds of mankind.
It is from St. Petersburg that Russian science, Russian mathematics, Russian higher and, above all, mathematical and technical education began. In 1724, by decree of the Russian Emperor Peter I, the St. Petersburg Academy of Sciences, the first higher scientific institution in the Russian Empire, was founded in the city on the Neva River.
For three centuries, the St. Petersburg Mathematical School has been one of the leaders not only in Russia, but also in the world. We invite you to get to know the city even closer and present you a short film about the history of mathematics in St. Petersburg.


On Mathematical Modeling and Data Science Education
Mathematical modeling with data can connect people with mathematics. These powerful tools empower choices and decisions. As modelers gather and analyze relevant data, they make creative decisions that depend on the context of the problem and the objectives of the client. Scroll down for some free resources for teaching!
Modeling and data science almost always require simplifying assumptions. Models can embed preferences, ethics and even biases. The mathematical sciences help us understand when algorithms and models work, how they work and under what conditions they can fail.
I have been passionate about educating teachers in mathematical modeling since the early 1990s when I was teaching middle school and Everly Broadway invited me to provide professional development for Durham Public School Teachers.
Recently Cynthia Anhalt and I co-organized the Critical Issues in Mathematics Education March 2019 meeting on Mathematical Modeling in K-16: Community and Cultural Contexts at the Mathematics Sciences Research Institute (MSRI). See this article by one of our participants and facilitators, Greta Mills.
You can download SIAM and COMAP’s free Guidelines for Assessment and Instruction in Mathematical Modeling Education (GAIMME Report). Readers can “look over the shoulder” of expert facilitators of mathematical modeling and gain a gentle introduction to mathematical modeling from Kindergarten to Undergraduate classrooms.
The National Science Foundation funded a project called IMMERSION (STEM-C 1441024). The program has been sustained in California as the Pomona Unified School District Math Modeling Summer Institute. In 2019 PUSD held the 5th summer institute in mathematical modeling for elementary school teachers, taught at Harvey Mudd College by elementary teachers who were former participants. These PUSD teachers are available to provide professional development in mathematical modeling education to teachers from other school districts!
If you are looking for resources to teach mathematical modeling, check out Mathematical Modeling: Computing and Communicating, one of the many free resources offered by SIAM as part of the Mathworks Math Modeling Challenge (M3 Challenge) which welcomes high school student teams to the world of modeling and data science.
The Math Modeling Hub is an online community and resource suite to support mathematical modeling education.


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A few weeks ago , I realized that my GLM knowledge was pretty rusty as I was struggling to get meaningful estimates from a poisson regression.
Decided to immerse myself over the weekend on what I gather to be one of the best books on GLM , written by Annette J Dobson. Well , there is always the classic monograph by Nelder & McCullagh , “Generalized Linear Models”, that one can refer to , which to me was a little too dry to go over. So, there is that little guilt feeling in me that I have never read the classic monograph from the father of GLM(J.A.Nelder) . I have always found this to be the case in quite a few stuff that I have learnt over the years. For example, I have never read till date, Bjarne Stroustrup’s C++ , the supposedly classic book on C++. However I have coded C++ like crazy and have used C++ to perform whatever that was needed . So, I always have this guilt trip whenever I think of C++. Well, may be someday I will go through the classic book . In a similar vein, I will go through Nelder’s classic stuff someday, hopefully 🙂
Ok, coming back to this book, I could only get the second edition of the book. Basically will have to wait for a kind soul to upload the third version on the net 🙂 .. Till then second edition will do 🙂 . The third edition has some chapters on Bayesian stats appended towards the end of the book.
The brilliant stuff about this book is organization of ideas and thoughts with just enough math to get you going on coding your own GLM estimation and diagnostic functions.
There are about 11 chapters in the book neatly organized based on the type of data that one is dealing, namely, Continuous, Binary, Nominal with > 2 categories, Ordinal, Counts, Failure times, Correlated Responses. Basically one can visualize this book as learning the GLM tool box for various combinations of dependent and independent variables. GLM toolbox broadly comprise all the elements mentioned under the methods column in the following table.
Chapter 1 : Introduction
This lays out the basic notation that has been followed in the book. Some basic results relating to normal distribution, Chi-Square , Non Central Chi Square distribution, F distribution, Quadratic forms, Cochran’s theorem are mentioned. Also the basic MLE method is described. If I had read this book a few years ago, I would be wondering why should one talk about distributions in the introduction. Pick up any book and you will usually find some angrezi about the book, meaning some general gyan about why some topic is important , why the author is writing the book, blah blah… But this books cuts all the crap and gets to THE MOST IMPORTANT thing that is needed to specify, estimate the model parameters, DISTRIBUTIONS. Typically these are stuffed in the appendix. The fact that they are mentioned in Chap1 talks a lot about the way author presents this book as compared to the run-of-the mill kind of books.
Chapter 2 : Model Fitting
Two basic examples of competing model evaluation are mentioned to kick off the discussion. Poisson with one general parameter Vs two parameters, Linear Regression with same beta Vs different beta’s for specific categories are discussed and ways to choose competing models are discussed. As clearly and repeatedly mentioned through out the book, GLM broadly comprises 2 major aspects, the first aspect being, the choice of the distribution of dependent variable from the exponential family of distributions, the second aspect being the link function between the expectation of dependent variable and covariates. Both examples more than reinforce this thinking.
Chapter 3 : Exponential Distributions
This chapter talks about the various forms in which Y , the dependent variable can appear in GLM. Normal , Poisson and Binomial are the widely used distributions that fall under exponential distributions. Density relating to each of these variables is written in the exponential form and their properties are discussed. The chapter ends by giving 3 examples where the link function is indentified so that one can apply GLM framework.
Chapter 4 : Estimation
This chapter is one of the key chapters of the book as it talks about the estimation framework that needs to be followed in developing a GLM model. Well one can formulate any fancy model but one needs to keep in mind the estimation methods. In the case of regression , the estimation procedure is known to everyone. Least squares is almost always the chosen method to get the estimates. In the case of GLM , there is a twist in the tale. The twist is that , the relation between dependent variable and independent variable is not a linear one but is dependent on the link function. So, here you are with a set of values , supposedly a dependent variable following any of the distribution from the exponential family. You also have a set of covariates and you have a link function. How does one use MLE to get estimates is the central question answered in this chapter. The procedure behind the math can be summarized as follows
- Form the log likelihood function for the Yi’s.
- Compute the score statistic with respect to one of the covariates.
- The score statistic unlike the usual MLE will contain a term which captures the link function.
- At this junction, Information matrix needs to be computed as it is needed for the Newton Raphson formulation of the equation relating to estimating of beta’s
- At this step , it becomes very obvious that Newton Raphson equation becomes equivalent to an iterated Weighted least squares procedure.
Thus an estimation of any simple GLM model connects a whole lot of concepts like MLE, score statistic, link function, Newton Raphson method, Iterated least square method. When one uses off the shelf stuff to get estimates, one doesn’t get to the see what happens behind the scenes and a novice can fail to appreciate the beauty behind the procedure.
The chapter ends with a poisson regression example which can be worked out manually, thus allowing one to appreciate the connections between various aspects of GLM estimation. The beauty of this chapter is that it allows you get in to the intricate details of estimating the parameters for a GLM using nothing else but matrix algebra and Newton Raphson method. Once you work out an example from scratch, you will obviously be amazed at the power of stat software like SAS, R, Matlab which give the output in a jiffy.
Chapter 5 : Inference
This chapter provides the link between score statistic and the distribution of MLE estimates by explaining the procedure to find the sampling distribution of score statistic and MLE estimates. It also talks about deviance function for some common models. Deviance function, as the name implied would be the difference between the null model and the hypothesized model. Asymptotics are invoked on this Deviance estimate to choose between competing models. A few examples of Hypothesis testing are show using Wald Statistic and Deviance statistic
Chapter 6 : Normal Linear Models
This chapter deals with the Normal Models. Basic Multiple Linear Regression concepts are discussed along with outlier detection methods based on metrics like Influence measure and Cook’s distance. The discussion about ANOVA and ANCOVA has been presented with great clarity. Until I read this chapter, I had never known that deviance function of a one factor anova is the same irrespective of the linear model specification. In most of the texts that I have read till date, there was no special emphasis on the fact that deviance function is the key to this entire ANOVA, ANCOVA business 2 factor ANOVA and ANCOVA models are also discussed with complete derivation of the estimates, thus making a reader appreciate the Fstats that are available at the call of a simple command. One thing which is common across all these jargon models is , “the basic matrix algebra is similar to simple linear regression”. However I have not seen till date , any powerful application of these ideas such as ANOVA , ANCOVA etc in stat arb . I guess it falls under “nice to know” stuff. I do vaguely remember of an example where anova was used to get some information about the seasonality of the spreads.. However I haven’t still come across a WOW application till date for this ANCOVA stuff in finance.
Chapter 7 : Binary Variables and Logistic Regression
Logits and Probits are discussed in this chapter. Various stats for model selection such as Pearson Chi Square statistic, Hosmer-Lemeshow statistic, Deviance statistic , likelihood ratio chi-squared statistic , pseudo Rsquare statistic are derived. Even though knowledge about these models and estimations look nice on paper, I sometimes wonder about the usefulness of models based on such simplistic equations. Shouldn’t the logits be a stochastic process ? What about the covariates ? Unlike social science applications, in finance, almost always the covariate is going to be a arma process or a non stationary series. The information in this chapter will help one understand a basic logit model math, but if you have to apply this to the real world, one quickly realizes that most of the assumptions for plain vanilla logit /probit model are useless atleast to the models applicable to the trading world. You have to bring in the stochasticity in to variables. I guess for a successful application of any of these models in the real world, one requires solid intuition + deep understanding of the contextual knowledge of the variable being studied + skills to model systematic randomness not gaussian types + LUCK 🙂 to get it right. …LUCK factor , sometimes, might be the only variable that seems to be a sane explanation of the success of your model :) .
Chapter 8 : Nominal and Ordinal Logistic Models
At this stage of the book , the reader can actually guess the contents and structure of a chapter. As the title of the chapter goes, the models considered are nominal logistic and ordinal logistic. There are two approaches to modeling the response variable if it is a categorical variable with multiple levels. First is by using nominal and ordinal logistic models and Second is by framing it as a poisson regression. This chapter dwells on the first method. One of the first observations made is that a multinomial distribution is not in the form of generalized exponential distribution family and hence will not directly fit the framework described in the book. However a multinomial distribution can be regarded as the joint distribution of Poisson random variables, conditional upon their sum. This result provides a justification for the use of generalized linear modelling.
Nominal logistic models can be used when there is no natural order in the categories shown by the response variable. Any random category can be picked up as the reference category and logit models are built with respect to the reference category. This clearly means if there are any correlations between the levels of the response variable, then plain vanilla logistic is NO GOOD.
The usual summary statistics are derived such as Pearson chi square, Deviance, Likelihood ratio Chi Squared, Pseudo R squared. Good thing about this chapter is the usage of single example to illustrate both nominal and ordinal logistic models. In the former case, the variable is assumed to be nominal and modeled. In the latter case, the variable is enhanced with the natural ordering present and a ordinal logit model is built. Both the examples illustrate the importance of not relying on just a single goodness of fit statistic. The more goodness of fit measure you compute , the better it is for you to get an idea of the strength of the model. The biggest learning for me is to keep in mind Likelihood Chi square statistic and Pseudo R Squared statistic, besides the usual deviance statistic which is mentioned in everywhere.
Chapter 9 : Count Data, Poisson Regression and Log Linear Models
As the title of the chapter suggests, this deals with the case when the response variable is a count variable. First method discussed is the plain simple poisson regression where the response variable for each covariate pattern is modeled a poisson variable and log function is used to link the expected value of the response variable and the covariates. In the case of contingency tables, based on the number of constraints of the data, the appropriate models are formulated. For example a contingency table where the sum of all elements is fixed, one can use a multinomial model. If there are more fixed marginal totals than just the overall total n, then appropriate products of multinomial distributions can be used to model the data. One good take away from this chapter is the case where data in the contingency tables are not independent and there is a suggestion to use negative binomial distribution to take care of this over dispersion problem.
The last two chapters of the book applies the GLM framework to Survival analysis and Longitudinal Data.


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Now that we have completed all the pages in our shape book, it was time to make the cover. Before we started I passed out the laminated shapes we used each week to introduce the shape. As we sang our shape songs, the children had to decide which shape we were singing about and hold it up. The triangle is still tricky.
The cover is a bit of a more involved skill time activity so that was all we did today. At the table each child got the four shapes already cut out. We made little shape people for our cover. After the children glued down the shapes, we added eyes, faces, arms, and legs. They are very basic, but they have a bit of character.
I just have to staple them all together and off to home they go!


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Today we will look at two official criteria corp aptitude test sample questions and we will try to apply simple tricks that will shorten our response times and will allow us to answer more questions, thus increasing our overall raw score. try to find the answers for numbers with more digits and by heart. Our math puzzles are designed to supplement our in-depth units of instruction. Sudoku Puzzles: Easy The modern version of Sudoku was invented in 1979 by Howard Garns in USA (where it was called `Number Place'). Contents 1 R. com THESE FUN MATH GAME PRINTABLES are brought to you with compliments. Unit 1-1 Everything in Order; Unit 1-2 Patterns Can Be Fun! Unit 1-3 Write the Number. It is the time consuming part for most of the Aspirants. Fourth graders love these tricks! Most of them (and even some younger children) are also ready to understand how they work and even to learn to make up their own tricks! Without the high-school notation, what they are learning is the beginnings of algebra! The trick. This trick comes down to the order of operations—adding and subtracting occur in the same step and can happen in either order. When you learn these mathematical tricks, you'll be able to show off your skills to friends and prove to them that you have a talent for mathematics. Detailed explanations and solutions to these questions are also provided. Manipulate the Pythagorean Identities. My brain is telling me the answer is $3 or. His book is a narrative about what he did, what he tried, what worked, what failed, but most important, what the kids experienced. Download free ASSET Math Level 1 PDF Sample Papers for Class 3 or practice with online worksheets at India's leading online Olympiad practice platform. All Trigonometric Functions Exercise Questions with Solutions to help you to revise complete Syllabus and Score More marks. Math tricks are as entertaining as they are practical. 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In particular, this unit aims to identify and help students who have difficulties with: The traditional multiplication algorithm. add a constant, subtract a constant, multiply by a constant, and divide by a constant) to both sides of the equation, the equality is still an equality. Find Kerala PSC Maths Tricks Tips PDF, Questions and Answers, Equations, Study Materials. Detailed explanations and solutions to these questions are also provided. Bedtime Math Fun and lively daily math problems centered around real-life topics and offered in three levels: Wee Ones, Little Kids, and Big Kids. minister was asked to give the answer to 7 x 8 and he gave the answer of 54, instead. Math can be a daunting subject for many kids but puzzle-solving will take away the fear of numbers and help the child to develop an enthusiasm for numeracy. A Mind For Numbers How To Excel At Math And Science Even If You Flunked Algebra also available in format docx and mobi. SSC CGL Questions and Answers PDF. The best thing about mental math is that anyone can learn it! Mental math tricks are what all practitioners of mental math rely on. Math magic tricks can liven up any math class and create a sense of wonder and curiosity about math. There are many \cartoon" type images for the important theorems and. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. speed of a Ferris wheel. Bedtime Math Fun and lively daily math problems centered around real-life topics and offered in three levels: Wee Ones, Little Kids, and Big Kids. "That's an interesting observation," Mr. Sometimes these hacks will save you time on the exam, other times they will actually be a little bit more time consuming, but they will always be really great problem-solving tools to keep in your arsenal of test-taking strategies. At Pizza Hut, your bill was $15. First of all: Memory is your best friend! With the whole table in your memory you will just know that 3×5=15, 6×8=48 etc. I wonder why topics examined in high school math contests are so different from the maths learned by those who are seriously studying a math major at a university. Students can take printable Division 210 timestables, Multiplication 210 timestables, addition 210 timestables and Subtraction 210 timestables from this page. First published in 1947, Mathematics Magazine offers lively, readable, and appealing exposition on a wide range of mathematical topics in five issues each year. Put your math knowledge to the test with this fun math quiz for kids. And it never hurts to have a couple of tricks up your sleeve, either. Instantly, one six-year-old came up with the solution. This is the fastest way to improve score. I used them for CAT and IBPS exams. • If the signs are different, subtract the num-bers and keep the sign of the number with the largest absolute value. On difficult questions, eliminate as many incorrect answers as you can, then make an educated guess. SSC CGL Questions and Answers PDF. Find Kerala PSC Maths Tricks Tips PDF, Questions and Answers, Equations, Study Materials. Also, see Aptitude Shortcuts so that you will clear/ slove question answers easily. Know Grammar easy way on Kerala PSC exams general for English. Math facts are a very small part of mathematics but unfortunately students who don’t memorize math facts well often come to believe that they can never be successful with math and turn away from the subject. Search www. Test yourself on calculating numbers, fractions, angles, areas, volumes, pythagorean theorem and etc. Quicker mathematics for competitive exams pdf free download If you need a job then you have to passed a Competitive exam. Memory is fast, too. The NRICH Project aims to enrich the mathematical experiences of all learners. Gmat Premier 2017 With 6 Practice Tests Online Book Videos Mobile Kaplan Test Prep. Then, he pulls back the curtain to show how the trick is done, explaining in detail the mathematical ideas underpinning the illusion. Addition Add the numbers and write the answers in the crossword puzzle. We ensure straight A’s with all our math solutions; For swift solutions to “Answer my math problems,” consult our team of experts right away. SSC MTS will declare on the official website that they will release the SSC MTS. pdf Practice Exam 3. Aspirants looking for admission in B. The remaining choices are possible values of x. Example Problems with solution pdf download notes video for exam sum. Ten Amazing Mathematical Tricks Magicians have invented a fantastic variety of self-working mathemat ical tricks in which the outcome of seemingly random choices can be predicted in advance. To achieve a good score on the math section, it is essential that you memorize the necessary GMAT math formulas. short tricks of maths for ssc in hindi pdf Shortcut tricks on Mensuration Methods will help you to do Mensuration Methods. Fun Math Tricks: 1. Every question you answer correctly is worth 1 point toward your raw score on the test. First published in 1947, Mathematics Magazine offers lively, readable, and appealing exposition on a wide range of mathematical topics in five issues each year. It contains a list of basic math formulas commonly used when doing basic math computation. Aggarwal Math Book In HINDI Pdf Download2 R. Therefore, teachers must also remember to incorporate mental. Math Puzzle Answers. The more math you can comfortably do in your head, the better you’ll perform on the Core Math exam. AAA Math Hundreds of math pages. These questions are all frequently used in all Exams. The 11 Rule. com! On this page, you will find Math word and story problems worksheets with single- and multi-step solutions on a variety of math topics including addition, multiplication, subtraction, division and other math topics. Choose the answer which the test maker intended. As long as you do the same mathematical operation (e. Each topic wise questions for practice with detailed solutions for SSC CGL Tier-1 and Tier-2 exam. Add Comment. pdf - Free download as PDF File (. Once you show them the trick, it'll most likely just shut down their thinking. Why Verbal Reasoning Arithmetic Reasoning? In this section you can learn and practice Verbal Reasoning Questions based on "Arithmetic Reasoning" and improve your skills in order to face the interview, competitive examination and various entrance test (CAT, GATE, GRE, MAT, Bank Exam, Railway Exam etc. recruitmentresult. Get ready to give your undivided attention, because you’ll need it to solve these fun math riddles. SSC CGL Questions and Answers PDF. G R A D E 6 + 6 +. Use the above tricks with accuracy in order to increase your speed. Almost all puzzles were told to us by a computer/math genius Vlad Mitlin. She put the same number If you know how to get an answer, Math Squares 12 15 8 50 9 1 1 6 4. There are many \cartoon" type images for the important theorems and. The book draws heavily on the IAE-pedia document "Good Math Lesson Plans" you are currently viewing. Available: MATHCOUNTS coaches only please. Learn these MATHS TRICKS For Bank Exams to Speedup the calculation ability and to learn maths shortcuts. The answers are provided and are located at the lower part of the page. Clickhereto see some of their work. Welcome to The Mystery Number Trick (A) Math Worksheet from the Number Sense Worksheets Page at Math-Drills. Enter key or OK button finalizes answer. Most children should have developed an automatic recall of the basic addition and subtraction facts by the end of the second. SSC MTS will declare on the official website that they will release the SSC MTS. Aggarwal Maths Book Content List :3. What is come in place of question mark (?) in the following series?. A video Launch for this lesson is available in two parts. This gem of a question hit the webz back in April. These methods can save two third of your time. We will provide you all question of Assam TET of all subjects. Here are eight tips for quickly figuring out a tip, saving time doing math in your head. x + 6 = 10) is to realize that the equation is an equality. These word problems worksheets are appropriate for 4th Grade, 5th Grade, 6th Grade, and 7th Grade. Glosser's Math Goodies Interactive math activities and puzzles. UPTET Question Paper Download PDF Subject Wise:. them in classic math-circle style: He doesn’t ask and then answer a ques-tion, but shows us a problem—be it mathematical or pedagogical—and describes to us what happened. A jar contains 100 marbles, identical except that 30 are red, 20 black, 5 green and the rest white. "Think-of-a-number" tricks. Multiply or Divide by 5. math and reading b. Math Home >> Student Home >> Grade 4 >> Use Place Value to Represent Whole Numbers >> Place Value Through Hundred Thousands To go to an online lesson, pick the chapter number and lesson number. For example the same trick can be demonstrated with four digits. Fun Math Tricks: 1. The answer is rounded to the nearest whole number for an approximate result. For subscribers, read recent issues online (requires MAA membership). From the main page parents or children will find a simple and easy to navigate menu featuring the different levels of math games and the various math concepts that are available. PREPARING FOR YOUR DIPLOMA EXAM.


Next week we will be learning how to double and half numbers.
Please support your child’s learning by doing some fun doubling and halving activities at home. This will help develop a deeper understanding and make links from what is learnt in the classroom to home. Here are some ideas:
- When eating, half the items on your plate into two piles, count the items on each side of the plate.
- Share sweets between two people – How many have you each? How many altogether?
- When shopping – I need double that amount? Use money when doubling and halving.
- Quick fire double and halving – say we are going to double the number. Say a number 1-10 – child calls back the double, try different numbers at speed. Repeat with halving numbers.
- When cooking. e.g. I have two eggs, I need double that amount, show child how to double.
- When sharing a family meal. e.g. A pizza – I am going to half the pizza, 1 + 1 = 2, I’m going to half it again, 2 + 2 = 4
Please note at this stage halving will be taught by sharing rather than using division.


23rd, October, 2018
|Job type||Full time|
We seek to establish the best quantitative investment research team by recruiting and nurturing extraordinary talents.
– Study transaction data of stocks, futures and foreign exchange markets, explore patterns that are predictable over different periods and build mathematical models with trading logic.
– Implement mathematical models into program codes, and perform historical data backtesting.
– Monitor actual model performance in real trading and make revisions when necessary.
– Comprehensive and professional training in trading strategy building, backtesting and analyzing.
– Cutting-edge research platform.
– Opportunity to work with experienced fund managers
– Inspiring and academic research and discussion atmosphere.
- Bachelor degree or above.
- Mathematics, Physics, Computer Science or other science and engineering background, with experience in mathematical modeling.
- Familiar with Python, and experience in Matlab/R is a plus.
If you think you have what it takes to succeed in a dynamic, fast-paced environment, send your CV, salary expectation and availability details to [email protected]
Tel: 0965725068 (Zalo,…)


I got kind of tired of rewriting the same OpenSCAD code to build rounded boxes for things and messing up the minkowski sum math in the process, so I built a simple module to do it for me.
Usage is simple:
The paramaters are:
rounded_case(25, 25, 10, 2);
rounded_case(X, Y, Z, T, LID, LID_OFFSET)
X, Y, Z : Inside dimensions of box
T : Thickness of walls
: optional, bool : true to also make a lid
LID_OFFSET : optional : how much smaller to make the "lip" of the lid that fits inside the top of the box
The outside dimensions of the box will be the inside dimensions + 2 x T. E.g. if the X dimension is 20mm, and T is 2mm, then the width of the box will be 24mm (20 + 2 + 2). The example above will make a box that is 29mm x 29mm x 14mm (with the lid on) on the outside, and 25 x 25 x 10 on the inside.
Get it here: rounded_case.scad


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Scientists have been pretty long exploring space with many dimensions. In the twentieth century, it became natural to operate with a unified space-time with various number of dimensions. But it turns out that geometry and even physics can be studied using a model in which all the dimensions are temporal. Due to the unique additional symmetry, this model has many advantages and can better describe the surrounding reality than common space-time construction we use today. Then what kind of world do we live in? Maybe the idea of space and
space-time is only a simplified representation of reality in which all the dimensions are actually temporal? The answer to these questions can be given by fairly simple experiments in which instead of particles there are point events, and instead of rulers there are high precision clock.
"Multi-Dimensional Time" is a continuation of the previously released films, "The geometry of the universe from different points of view" (2006) and "Anisotropic World" (2009).
In order to become more familiar with the issues raised in the film and to discuss them in more detail visit our website and forum at : http://www.polynumbers.ru


What is it about mathematics that scares so many students? Why do the simple tasks of addition, subtraction, division or multiplication appear horrifying monsters to many? Eminent Kashmiri educationist Prof A G Madhosh says that a lot of students have an ingrained fear of maths from early schooling. “When we ask students as to why they don’t like maths, they simply reply that they cannot do it. This is because of the initial fear which they have faced in the beginning of their studies,” said Madhosh.
Are we raising smart kids armed with gadgets and technology, or are the gadgets intruding childhood. Nishah Zargar reports.
Gone are the days when mothers and grandmothers would soothe crying babies by singing lullabies or making stories. Now everyone knows how to make a weeping baby smile - just pop a smart phone with a video playing in their hand.
Humaira, a mother of two says, she has to hide her phone from her seven-year old.


To bring up a scatter plot for a correlation pair, click the correlation in the correlation table to make it appear in the correlation historical chart. Then, click on the correlation name listed to the right of the chart.
The scatter plot shows how the correlation is calculated:
- the number of samples used (each sample is a monthly return)
- the regression line, characterized by its slope and intercept.
- the r-squared, which is equal to the squared correlation
In this chart, the horizontal axis measures the monthly returns of one of the assets being correlated, while the vertical axis represents the other.
Each point on the plot corresponds to a month. Hover the mouse over a point to display the details of the returns for that month. If the option "Show time weights" is selected, the points are colored according to their age. Recent months appears brighter, while older months appears faint, reflecting their weight in the correlation calculation.


On-line Registration is now open for all K-12 students. If you
completed Spring Registration at the Elementary, you are finished.
Click Here to Begin
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36386 Highway 58, Pleasant Hill, OR 97455Phone: (541) 736-0400 Fax: (541) 736-0446 Contact Us
◼ District ◼ High School ◼ Elementary
Oregon State Standards by grade level for the following curriculum areas:
English Language Arts, Math, Health, Science, Social Studies, Art, Physical Education and Technology.


Mike’s background is focused on research methods and statistical analysis. He holds both B.S. and M.S. degrees in statistics with emphasis on business analysis. Mike has experience in a wide variety of statistical methods, including multivariate regression, ANOVA, sample and survey design, structural equation modeling, Bayesian hierarchical models, mixed models, stochastic processes, experimental design, meta-analysis, and non-parametrics. He has worked on a variety of statistical projects from exit polling and election prediction to the relationship between job performance and satisfaction to the effectiveness of prerecorded lectures in academic programs.
Mike has been with The RBL Group since May of 2009 and has proven to be a valuable asset in analyzing and organizing our many research studies (including the HRCS, Leadership Code, and talent management research). He has worked with ADIA, NuSkin International, Ernst & Young, the Singapore Ministry of Manpower, and Pfizer, among others.


Using geometry, Keith explores the concept of our original wholeness and that of the natural world and treats flowers as a source of remembering as well as learning about our inner power of recognition and consciousness.The beauty of a flower draws on some universal truths (permanent principles) similar to the truth of mathematics. He uses the Fibonacci Law to explain the spiral at the centre of many flowers and the symmetry that helps to create their appeal. This spiral follows the ‘flow’ of the life journey of the flower from seed to mature plant and then back to seed again.
We have chosen some flowers to help demonstrate the geometry and spiralling beauty of flowers– look at the centre of each flower, to see its spiral that represents the winding up and down of its life, the set of the petals in each flower, the formation, the shapes and patterns formed by the petals– and since patterns are at the heart of ‘recognition’ and the power of consciousness, flowers serve to remind us of the laws of mathematical and spatial order, the ‘laws’ under lying beauty. “As Socrates said: ‘Geometry is the art of the ever -true’ – the constant reminder that flowers are emissaries of the ‘ever-true’ makes what we live in a cosmos not a chaos.”
This is part of a series of works celebrating nature,sustainability, environmental awareness and craftsmanship


tldr: The goal of this post is to find an accurate and robust get_mouse_screen_position() for the community.
Big thanks to @Unryze for helping me find stuff in the 1.26 game.dll!
So for a few patches now, there is a way to get the mouse world coordinates. However there is no way to get the...
How to find the x, y, and z when a projectile move by m basing on the parabolic line?
Basically, if the projectile move to the green dot, what is the distance (xy) and what is the length of z?
And also, how to find the length of the arc?


Solving constraint satisfaction problems (CSPs) is a notoriously expensive computational task, for example, Sudoku, Boolean Satisfiability Problem, etc. In this work-group, we will build a network to solve some typical constraint satisfaction problems on neuromorphic chips.
To accelerate the searching of optimal solutions, we will utilize the randomness brought by the intrinsic noise on neuromorphic hardware.
We will first fit this network into one Dynapse board (4096 excitatory and inhibitory analog neurons in total). Then when the problem's scale is increased, we can scale the network up by using multiple Dynapse boards.
Login to become a member send
||15:00 - 00:00
1. Binas, J. and Indiveri, G. and and Pfeiffer, M. Spiking Analog VLSI Neuron Assemblies as Constraint Satisfaction Problem Solvers, International Symposium on Circuits and Systems (ISCAS) 2094-2097, 2016
2. Hesham Mostafa, Lorenz K. Muller, Giacomo Indiveri Recurrent networks of coupled winner-take-all oscillators for solving constraint satisfaction problems, NIPS, 2013


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