WHICH MATH CLASS SHOULD I TAKE NEXT YEAR?
These all are assuming you are passing the current level with at least a C. Most colleges consider D’s as failing, and thus grades of D’s or F’s mean you should retake the class you are currently taking. The A-G requirement for math is 3 years with grades of C or higher.
Current Class Math 1 – one choice
Math 2 – one choice
Math 3 – three choices
Math Analysis: This class consists of pre-calculus and Trigonometry. Successful completion leads to enrollment in Calculus AB. Students need to have a grade of C or better to take this class, but the math department recommends students have grades of A or B in Math 3. Students with C’s in Math 3 may struggle in Math Analysis due to their incomplete knowledge of concepts.
college mathematics courses. Students should have received a C or higher in Math 3.
Math Analysis - 3 choices
Calculus AB: This is an AP class and thus will be hard. However, the passing rate at PHHS for students on the Calculus AB exam is consistently around 90%. The math department recommends students have a grade of an A or B in Math Analysis to move on to Calculus AB, but grades of C’s will also be allowed to move on, but note that those students might struggle in Calculus AB.
AP Statistics: This class will also be hard. Passing rates for the AP Exam at PHHS are consistently around 80%. For students deciding between taking AP Calculus AB and AP Statistics, the math department recommends you take Calculus AB provided that you have been doing well in Math Analysis. Calculus AB “flows” from Math Analysis and is the next progression in math courses. In Calculus AB, you will use a lot of what you learned in Math Analysis and the longer you wait to take Calculus after Math Analysis, the more you will forget those skills. Statistics is a “stand alone” class, meaning that you will use nothing from Math Analysis and thus there is no worry about forgetting things.
Calculus AB – 3 choices
Calculus BC: The math department recommends students have a grade of an A or B in Calculus AB to move on to Calculus BC, but grades of C’s will also be allowed to move on, but note that those students might struggle in Calculus BC.
AP Statistics: For students deciding between taking AP Calculus BC or AP Statistics, the math department recommends you take Calculus BC provided that you have been doing well in AB. Calculus BC “flows” from AB and is the next progression in math courses. In Calculus BC, you will use a lot of what you learned in Math Analysis and the longer you wait to take BC after AB, the more you will forget those skills. Statistics is a “stand alone” class, meaning that you will use nothing from your previous math classes and thus there is no worry about forgetting things.
How hard is the Class? Will I be successful? What do I have to know? What is the class about...(More to help you decide the right class)
Math 3: If you have been getting A’s and B’s in Math 1 and 2, then Math 3 should not be too hard for you. It will be harder than Math 2, and it is expected that you learned and remembered some of those things you learned in 1 and 2. You will continue with the same process of exploring, learning problems in context, and having to explain results like you have been doing in 1 and 2. If you got Cs in 1 and 2 (especially 2) then Math 3 will be hard for you. You should expect this and plan on seeking extra help right from the beginning of the class.
MRWC: MRWC is a new fourth year mathematics course for seniors designed to prepare students for the expectations and rigor of college mathematics courses. It reinforces and builds on mathematical topics and skills developed in Integrated 1-3 (or Algebra 1-2 and Geometry). It is designed as a bridge to both STEM and non-STEM majors. Students must have received a C or higher in Math 3. MRWC is for SENIORS only.
Math Analysis: This class will be exponentially harder than Math 3. (If you don’t know what that refers to, you might not want to take this class.) The first semester of Math Analysis is sometimes referred to as Pre Calculus. The second semester is the trigonometry part of Math Analysis, and requires as much logical thinking as it does algebraic manipulation. Students who do well in MA will have a firm grasp on manipulating variables as well as an ability to think on their own, rather than just mindlessly following some example problems. We think an A or B in Math 3 shows that you are prepared for this class. Students with a C should really think about if they should take this, or retake Math 3 to improve their skills before moving on.
Calculus AB: This is a college level math class, and as such is going to be taught like one. A grade of an A or B in Math Analysis should have you ready, but it too will be exponentially harder than Math Analysis. You should be an “expert” at manipulating variables and be able to think on your own. This is not a “do 30 problems just like the example” class. You have to be able to apply concepts learned to different situations. If you have a C in Math Analysis, we really think the best course of action is to repeat Math Analysis before moving on to Calculus AB, but we will not stop those who wish to move on. Your Calculus teacher will expect a lot of time from you for homework and will work you hard. But those who do the work and put in the time will be completely prepared for the AP exam – about 95% usually pass the AB and BC AP exam – the highest passing rate of any AP classes at PH!
AP Statistics: Contrary to what some might say, this class is not “easy.” For some, yes it is easy, but for most it is not. The mathematics you will use is not hard, but the key to the class is not the mathematics, it is the ability to think logically, and your ability to communicate. Want to try to predict how well you will do? Think about your geometry skills and second semester Math Analysis. No we don’t do proofs or trig identities, but those were the concepts that required the most logical thinking. Almost all students who take AP Stats after they finish Calculus AB or BC do well. Almost all students who take stats right after Math 3 do poorly. Those who take it after Math Analysis are much harder to predict. Many students who take it after a D or F in Math Analysis do poorly in Stats too. We think you should retake Math Analysis rather than move to a college level class. 90% of the problems in AP Stats are “word problems” so it is not a class where you can just follow an example from the teacher and repeat it over and over.
Calculus BC: Prerequisites: C or better in Calculus AP/AB or a 3 or higher on the AP Exam for Calculus AB. This course is a continuation of Calculus AP/AB. Topics to be covered are advanced integration techniques, improper integrals, infinite series and convergence, power series, Taylor polynomials, Taylor and Maclaurin series, conic sections, plane curves, parametric equations, polar coordinates, vectors and the geometry of space, vector valued functions, functions of multiple variables, multiple integrals and vector analysis. Upon successful completion of this course, students are expected to take the AP Calculus BC examination in May.
Lastly, some notes about summer school math
The math department at PHHS would like you to be aware that we do not recommend summer school as a means to move forward one year in math. We have found that most students who use summer school to recover a grade of a D or an F and then move to the next level the following year will struggle in that next level class. This is especially true for those making up poor grades in Math 3 moving to Math Analysis and making up poor grades in Math Analysis moving to Calculus AB. We suggest you make up those poor grades in the regular school year next year. Or if you use summer school, you consider that the final math class taken in high school. Summer school at many, if not most places that offer it, is oftentimes easier than the regular year due to the time constraints and not being able to cover all the standards. Also there is the fact that students have only one class they need to concentrate on unlike the school year with 5 more classes in addition to math. Plus, to succeed in a summer school class, students need to retain the material for only a few days for an average chapter test and only 5 or 6 weeks for an entire year.
Students who use summer to advance a year upon successful completion should be aware that students mature in their mathematical thinking at different rates, (just like people mature physically at different rates.) Just because your friend is in a higher level of math does not mean you should be too. We frequently see students try to advance to keep up with their peers only to get C’s or worse the following year, as they were not ready for the advanced difficulty level.
Please very carefully consider your option of using summer school. It is highly recommended that any student using summer school be prepared to seek extra help immediately in the following year before falling too far behind. The only students who should realistically be using summer school to advance are the students who have an A in their current class and find it very easy. If you are working hard to get that A, you are at the right level and should not be thinking of jumping ahead.


Bio & Research:
In June of 2015, Xin graduated from Huazhong University of Science and Technology. Her bachelor degree is in Electronic and Information Engineering. Since September of 2015, she is pursuing a master degree at ShanghaiTech University. Her research area is distributed convex optimization and control, multi-agent coordination and decision making. She is also interested in stochastic optimization
- 2015.9 - Now: School of Micro-Systems Chinese Academy of Sciences @ ShanghaiTech University
- 2011.8 - 2015.6: Huazhong University of Science and Technology
- Distributed convex optimization with inseparable constraints
The topic of my research now is distributed convex optimization in multi-agent networks. In these networks, agents are asked to jointly achieve a global optimal performance. Each agents keeps a convex function that is only known to itself, and all of them try to find the global optimizer together. Unlike most studied convex optimization problem, the problem I focus on is totally inseparable. And I try to find available ZGS algorithms to solve it.


|2679||Volume 11||1949||2680||Volume 11||1949|
Summary: If systems are joined by dominance, the latent roots are unmoved.
Summary: Two possible ways of proving feedback between two sub-systems. Feedback is also proved present if we can find in A a single frequency not found in A + B.
Feedback test for
|This image is reproduced courtesy of The Estate of W. Ross Ashby. Copyright 1972, 2008 © The Estate of W. Ross Ashby|


Math is SO much fun!
Much like Mary Poppins makes cleaning a snap, making something dreaded into a fun game can breathe new life into even the lowliest of chores. While I haven’t made everything fun, math has always been an easy one.
First, I confess: I love math.
Love? Yes. LOVE math ❤. Why? Personally, I love math because there is always an exact answer. The questions may be difficult to discern, but the formulas, the calculations, they always lead to an exact answer (maybe not theorists, but for math through high school and much of non-mathematician college, there is always an exact answer).
What’s not to love about knowing that you can get the correct answer every time? It’s brilliant! If you have the tools, you can arrive at the correct destination. There is a pleasure in knowing the destination is there. The goal is close at hand. The answer is within reach. With some practice and purpose, mathematics is an obtainable goal for people. Given enough time, practice, and encouragement.
- Chocolate Chips (any small food encouragement, we’ve used M&M’s, Skittles, jellybeans, but by far, I always have chocolate chips and they’re always warmly received!)
- A clear plan with an objective (perfect since math has exact answers!).
Enter: Multiplication in a Flash
As I’m finishing our multiplication tables practice for my younger son, we have a fun game we play once a week or so for review: We have a weekly practice in which we take turns answering questions and there is equal opportunity to get an equal number of chocolate chips. The sillier, the better. I toss them the chocolate chips, or roll them across the table, but the key is to make it light and fun — and we practice for speed which adds an element of urgency. The urgency to get the question correct coupled with the urgency to get the question answered quickly — we’re all usually yelling and cheering by the end.
This has worked for years with our math practice. When practicing numbers, addition, subtraction, division, fractions, decimals…any math that can be tested can be rewarded. When we work out long division, practicing proofs – it’s all fun to do with a little chocolate encouragement. Especially since we usually do our weekly practice at the end of our teaching time, it’s a great way to segue into outdoor play, lunch, etc.
Math + Chocolate = FUN
I’m working on utilizing the practice of fun into all of our learning, but I’ve consistently had luck working it into our mathematics practice. It’s a necessity to learn and my joy in the subject has become their joy in the subject. What could be better?
“It’s fun to have fun, but you have to know how,” Dr. Seuss, The Cat in the Hat
What have you made fun today?
Disclosure of Material Connection: Some of the links in the post above are “affiliate links.” This means if you click on the link and purchase the item, I will receive an affiliate commission. Regardless, I only recommend products or services I use personally and believe will add value to my readers. I am disclosing this in accordance with the Federal Trade Commission’s 16 CFR, Part 255: “Guides Concerning the Use of Endorsements and Testimonials in Advertising.”


Talitha Washington is an Associate Professor of Mathematics at the Howard University. She earned a Bachelor of Science degree in mathematics from Spelman College in 1996, and a Doctorate in mathematics in 2001 from the University of Connecticut. Dr. Washington was a VIGRE postdoctoral fellow at Duke University from 2001 through 2003. Her work there included using differential equations to model luteinizing hormone (LH) secretion in response to long term exposure to gonadotropin releasing hormone (GnRH). She proposed a model which involves key processes including desensitization of calcium channels, internalization of the dimerized receptors and recycling of some of the internalized receptors, and an increase in Gq concentration near the plasma membrane in response to receptor dimerization.
Dr. Washington will lecture on "A Non-Standard Finite Difference Scheme for a Mathematical Model of Respiratory Virus Transmission". She will discuss her recent work with Ron Mickens of Clark Atlanta University. This involves constructing a Non-Standard Finite Difference (NSFD) scheme for an SIR mathematical model of respiratory virus transmission. She will provide a discretization of the model's equations that is fully in compliance with the NSFD methodology as formulated by Mickens.


The University of Tokyo announced this week the establishment of an endowment by The Kavli Foundation for the Institute for the Physics and Mathematics of the Universe.
The Institute, which will now be known as the Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), probes the biggest mysteries in modern cosmology: How did the universe begin, and how will it end? What is it made of, and what laws govern its behavior? How did we come to exist?
The Kavli Foundation, based in Southern California, sponsors research in astrophysics, nanoscience, neuroscience and theoretical physics at institutes across the globe, including China, England, Netherlands, Norway and the United States. Kavli IPMU is The Kavli Foundation’s 16th institute, its sixth in astrophysics and third in theoretical physics, and the first to be established in Japan.
Professors May-Britt and Edvard Moser welcome the new member into the Kavli family.
"The Institute for the Physics and Mathematics of the Universe is an excellent addition to the group of Kavli Instituttes, and we look forward to meeting them", says director Edvard Moser at The Kavli Institute for systems Neuroscience (KISN) at NTNU in Trondheim, Norway.


What is Math?
Mathematics is a logical system, based on a few simple assumptions, from which all facts (theorems) can be derived using an agreed-upon system of logical deduction. Once a theorem is proved, everyone agrees that it is unequivocally true. Math is unique in this respect. Mathematics can be extremely creative, as it is based on problem solving and insight. It is also very rigorous – based on critical thinking and symbolic reasoning – and rigidly structured.
In some ways, it is easier to answer the question of what math is not. First, math is not simply number crunching; in fact, many math professors rarely encounter numbers in their research. Generally what mathematicians seek is a much deeper understanding of the nature of the world. Math is not only evidence-based calculation; it is also proof-based. To understand what a proof is, we have to uncover the fundamental nature of mathematics.
Mathematics has been around since antiquity, and has fascinated and stimulated creative and logical thought for millennia. It is ubiquitous in nature and science, and is rich in applications to the real world. Many mathematicians speak of the beauty of mathematics as a language for describing the universe. However, mathematics is not only a science; it is also an art. Although mathematicians are perceived as straight-laced, we all feel emotion when we think of math in terms of its fundamental nature, its omniscience, its art, and its science. To do pure math – math with no proposed application to any other field – is to get to the very heart of things. Math research is the discovery of new mathematical ideas, definitions, and theorems. Boolean algebra (George Boole, 1854) was thought to be of no value at the time of its discovery. It was rediscovered a hundred years later and now serves as the basis of modern computation and digital logic. Calculus, now a common mathematical system, did not exist four hundred years ago. And although it was discovered four centuries earlier, we still find new uses for it today!
What can I do with a Math degree?
The job of mathematician has been hailed as one of the best, and well-paid, in the world. What could be better for a math lover than to sit around and solve math problems all day? Even if you don't want to be a professional mathematician, the study of math can be quite lucrative. A math degree not only guarantees skill in logical thinking and creative problem solving, but it also prepares graduates to excel in whatever job they choose. Students of mathematics are also suited for law school, medical school, business school, and further studies in computer science. A math degree is infinitely useful and applicable to most career fields. Due to the variety of careers available to math majors, HPU offers four concentrations within the Mathematics major.
Pure and Educational Math
The Pure Math concentration lends itself to the advanced study of mathematics in graduate school. Students attending graduate school in math may become professors, researchers in national labs, or consultants. This concentration focuses more heavily on abstract mathematical thought and logic, and produces students who are not only proficient in reading and writing proofs, but are strong critical thinkers and problem solvers as well.
Teaching mathematics and sharing its beauty and wealth of applications with future generations can be a very rewarding way to use a math degree, too. To this end, the Math Education specialization prepares our graduates for a job as an educator in the K-12 system.
Applied Math and Engineering
The Applied Math concentration focuses on applying mathematical ideas to specific problems in the sciences. Students graduating with an applied math concentration are prepared to go to school for engineering, to work for the government, or to train as actuaries.
Students who are particularly interested in applying their math skills to a career in engineering may wish to consider our Math-Engineering Dual Degree Program.
Why study Math at HPU?
HPU offers more individualized attention - our upper division class sizes range from 8-15 students. Our faculty are dedicated to teaching. They come from top mathematics programs across the country and have been actively engaged in world-class mathematics research.We implement a variety of teaching techniques that are innovative and student-centered, promoting creativity and critical thinking skills rather than being rigidly structured to the lecture hall paradigm. As a student, you will not only be exposed to different instructional styles, but will also be able to interact with a diverse set of peers in our mathematics clubs and study groups. In your final year, you may have the opportunity to work closely with a faculty mentor on advanced material catered specifically to your personal interests.


Language is deeply involved in learning mathematics as students both communicate and think about mathematical ideas. Because of this, teachers of English learners have particular challenges to overcome. Mathematical Thinking and Communication addresses perhaps the most significant challenge: providing access to mathematics for these students. -- Google Books.
Includes online PD resources
Creating access to mathematics for English learners -- Why visual representations? -- Visual representations as evidence of student thinking and potential -- Developing language in context -- Designing tasks to support access for English learners -- Visual representation routines -- Putting it all into practice.


In late March, Cape Hatteras Secondary School of Coastal Studies sixth grade students in Scott Day's math class were using wireless notebooks for multiple practical applications. In a great example of incorporating writing and use of technology in applying math concepts, students researched a data display where part of their assignment was to print out a graph from a website and to write a descriptive paragraph about the information. "We looked at different types of graphs, and what type of graph best represents the given data," described Day. Examples included a circle graph representing usage of social networking sites in the US (eg, Facebook, Twitter); line graphs of stock prices; and how box and whisker plots are used by the state of North Carolina to determine the EOG (end of grade) test/assessment scores; and how quartiles (levels 1,2,3,4) are determined for sixth grade math students statewide. From left, Emery Becker, Icy Webb, Jasmine Quidley, Allie Quidley, and Kiara Bowman.
Photo: Donna Tokazowski
Click here for the district's resource page to learn more about the new core curriculum and essential standards that are being implemented in Dare County (and schools across the nation) next year. Many Dare County teachers, such as Day, are incorporating writing, technology, critical thinking and collaborative problem solving in their classrooms ahead of the state mandates. Many of these "new" best practices have already been implemented as standard practice in local classrooms.
Find the Secondary Program of Study 2012-2013 (grades 6-12) here,


Evaluating Expressions Algebra Calculator can evaluate expressions that contain the variable x.
It was created by Kim Seward with the assistance of Jennifer Puckett. It is currently being maintained by Kim Seward.
WTAMU and Kim Seward are not responsible for how a student does on any test or any class for any reason including not being able to access the website due to any technology problems.
We cannot guarantee that you will pass your math class after you go through this website. However, it will definitely help you to better understand the topics covered. Throughout this website, we link to various outside sources. WTAMU and Kim Seward do not have any ownership to any of these outside websites and cannot give you permission to make any kind of copies of anything found at any of these websites that we link to.
It is purely for you to link to for information or fun as you go through the study session. Each of these websites have a copy right clause that you need to read carefully if you are wanting to do anything other than go to the website and read it.
We discourage any illegal use of the webpages found at these sites.
Last revised on April 6, by Kim Seward.If you need help in intermediate algebra, you have come to the right place. Note that you do not have to be a student at WTAMU to use any of these online tutorials. Free math problem solver answers your algebra homework questions with step-by-step explanations.
This section is a collection of lessons, calculators, and worksheets created to assist students and teachers of algebra. Here are a few of the ways you can learn here. Peer-reviewed. Openly licensed.
% free. And backed by additional learning resources. Review our OpenStax textbooks and decide if they are right for your course. I'm taking Algebra 3 in high school. Is your college algebra help the right course for me? Yes.
You can find anything you need in this course. Depending on your algebra teacher and school, some of you may touch on a bit of Trig topics, and need help with caninariojana.com worries.
Pythagorean theorem was proven by an acient Greek named Pythagoras and says that for a right triangle with legs A and B, and hypothenuse C See this lesson on Pythagorean Theorem, animated proof See How to generate triples of sizes that are natural See In Depth Wikipedia article on Pythagorean theorem.


I'm trying to get an idea of how many pi's I can run at the same time from the same wall socket. I've done some research and it seems to me that the peak power consumption is somewhere around 750mA. If that is the case, then in theory 20 Pi's can be connected to one 20A circuit at my home with no problem. (I'm thinking about connecting them all via 2 10-port, externally powered USB hubs, if there's an issue there, let me know). I just wanted to run this configuration by some smarter, more experienced people when it comes to power requirements.
The instructions below Assume you mean 120volts at 20 amps which is the American standard. So we want to start by calculating the approximate wattage we could theoretically draw from the wall, which is volts x amps.
Now we are going to calculate the number of watts a Pi uses at peak load based on your research. We use 5 volts as that is the USB standard
Now all we need to do is subtract inefficiencies in the conversion from AC to DC which is approximately 10-20% for a good power supply, we will use 15% for our calculation. So now we multiply household wattage by efficiency(.85) to get the number of watts that are actually going to reach your Pi.
And now we decide this by the number of watts a Pi uses to see how many pi's we could theoretically connect.
There you have it 544 pis could be connected to a single 120 volt 20 amp outlet.


How similar is Father and Mother? When you ask this question to anyone, you will have different answers. Some say, mum can cook, dad can’t cook; mum has long hair, dad has short hair. Then, how are you going to quantify the similarity between Father and Mother? Luckily, we have cosine similarity.
Let’s start with the equation for cosine similarity. It is just a dot product between 2 vectors!
First, we construct the vector for Father. Each element of the vector represents the feature of Father. if the Father can cook, then element is represented with “1”, else it is represented with “0”. As shown in figure 1, The Father is represented in [1,0,1,1,1,0,0], while the Mother is represented in [1,0,1,1,0,1,1]. Now, we can calculate the cosine similarity of Father and Mother which is 0.671 similar.
The dot product may not be clear to you. Let’s visualize it with basic trigonometric.
As we can see from demo 1, with theta 1, A is further away from B. When we project A to B direction, the distance is much shorter compared to the projection of A in B direction is demo 2. It is very clear in Demo 2 that A is very similar to B. This clearly explain how cosine function can be used in finding similarity.
Lastly, I will provide a summary of cosine similarity. Hope that this will help you in understanding cosine similarity clearly.


Spring 2020 Office Hours
MW 12:15-3:15pm and by appointment (in Collier-Scripps 327) until 5/8/2020 except on days when class is canceled.
Eric D. Manley
Department of Mathematics and Computer Science
2702 Forest Avenue
Des Moines, IA 50311
I have been at Drake since 2009. My academic interests include network coding, all-optical networking, applications of machine learning, and computer science education.
Ph.D. Computer Science, University of Nebraska – Lincoln, 2009
Dissertation: Network Coding for WDM All-Optical Networks
M.S. Computer Science, University of Nebraska – Lincoln, 2006
Thesis: Optimizing Switch Resources for Path Protection in Optical WDM Mesh Networks
B.S. Computer Science and Mathematics, University of Nebraska at Omaha, 2004
CS Thesis: Aspect-Oriented Programming Via Program Transformation
Math Thesis: Quadratic Solutions of Fourth Degree Diophantine Equations


Understanding VQ-VAE (DALL-E Explained Pt. 1)
By Charlie Snell
Like everyone else in the ML community, we’ve been incredibly impressed by the results from OpenAI’s DALL-E. This model is able to generate precise, high quality images from a text description. It can even produce creative renderings of objects that likely don’t exist in the real world, like “an armchair in the shape of an avocado”.
To celebrate the release of DALL-E, we’re publishing a series of blog posts explaining the key components of this model.
This first blog post in the series will cover VQ-VAE, which is the component that allows DALL-E to generate such a diverse and high quality distribution of images.
In the next post we will cover transformers for multi-modal, autoregressive generation: the part of DALL-E that learns the correlations between language and images, resulting in such creative and accurate outputs.
Note: this blog post assumes that you have some knowledge of deep learning and Bayesian probability.
VQ-VAE stands for Vector Quantized Variational Autoencoder, that’s a lot of big words, so let’s first step back briefly and review the basics.
We will first define the concept of a latent space and then define autoencoders, lastly we will review the basics of variational autoencoders before getting into VQ-VAE (Note: if you feel like you already understand this stuff, feel free to skip to the next section, where we dive into the details of VQ-VAE).
A latent space is some underlying “hidden” representation for a given distribution of raw data. To clearly understand this let’s look at a simple example.
Imagine the raw data points are x∈ℝn, and they are noisily generated via a linear transform from some lower dimensional z∈ℝm (m<n). Specifically x is generated as x=Az+v where v is n-dimensional independent identically distributed gaussian noise and A∈Rn * m.
In general, we only get to see the raw data x; we do not get access to z, which is why it is referred to as a latent or “hidden” representation of the data. However, we would like to gain access to z because it is a more fundamental and compressed representation for the data. Additionally, this latent representation could be a more useful input to many other algorithms that need to use the data.
This specific setup, in which the raw data is a linear transformation of the latent space, is exactly what the classical unsupervised algorithm called “PCA” is designed for: PCA essentially tries to find the underlying z representation from the above example. This is great, but what if the latent representation had a more complicated, non-linear relationship with the raw data? For example, the figure below visualizes the kinds of high level information a more complex latent space could encode. In this case, PCA would fail to find the best latent representation. Instead we could use an autoencoder to find this more abstract latent space.
Note: A latent space does not need to be a continuous vector space, it could instead be a discrete set of variables, which is the type of latent space that VQ-VAE tries to find. But before we get to that, let’s first understand vanilla autoencoders.
An autoencoder is an unsupervised learning technique that uses neural networks to find non-linear latent representations for a given data distribution. The neural network consists of two parts: an encoder network, z=f(x), and a decoder network, x^=g(z).
Here x is the input data, z is the latent vector representation, and x^ is the “reconstruction” of x from the latent space. f(x) and g(z) are both neural networks. Putting the two parts together, the entire model can be described by the relation x^=g(f(x)) (see the figure below).
Ideally, the decoder should be able to accurately reconstruct the raw data from the encoder’s latent representation. If the model is able to learn such a reconstruction, then we can assume that our latent space represents the data well. To actualize this objective, we train the model with some sort of reconstruction loss between x and x^ (i.e.
It’s also important to note that z should always have a lower dimension than x. The whole point, after all, is to encode a compressed representation of the data, such that the algorithm is forced to find the most essential components of the raw data.
This compressed, latent part of the autoencoder is often also referred to as the bottleneck of the network because it is squeezing the data into a much smaller space.
Variational Autoencoders (VAE)
(NOTE: I will not go into all the mathematical details of variational autoencoders in this blog post because I’d need to devote an entire blog post to VAEs to really do them justice. Luckily enough, many such blog posts already exist, and I can personally recommend this excellent blog post by Jaan Altosaar if you want a more detailed treatment of the topic.)
Now that we understand the essentials of autoencoders, let’s look at what makes a Variational Autoencoder different. The key difference comes from the structure imposed on the latent space of VAEs. Ideally we would want our latent space to lump semantically similar data points next to each other and to place semantically dissimilar points far apart. Preferably the majority of the data distribution should make up a fairly compact volume in latent space and not extend to infinity.
The main issue with vanilla autoencoders is that the learned latents do not necessarily have either of these properties! The model can learn any latent space it wants, so it often ends up memorizing individual data points by placing them in their own far out pockets of latent space. The figure below visualizes these issues with autoencoder latent spaces and compares them to that of VAEs.
Variational autoencoders overcome this problem by enforcing a probabilistic prior on the latent space. To formalize this, consider our latent space z as a random variable. First let’s enforce a prior p(z) on our latents, in most VAEs this is typically just a standard gaussian distribution N(0,1). Given a raw datapoint x, we also define a posterior for the latent space as p(z∣x).
Our end goal is to compute this posterior for the data, which we can express using bayes rule as
Unfortunately, because we are working with continuous variables, p(x) is a computationally intractable quantity. In order to make things computable, we restrict our approximation of the posterior to a specific family of distributions: independent gaussians. Call this approximated distribution q(z∣x). Now our goal becomes to minimize the KL divergence between the true posterior and this approximated form.
I’ll spare the mathematical details, but it turns out that this objective can be computed by minimizing the loss function
In this case q(z∣x) is approximated by the encoder and p(x∣z) is represented by the decoder.
The VAE loss actually has a nice intuitive interpretation, the first term is essentially the reconstruction loss, and the second term represents a regularization of the posterior. The posterior is being pulled towards the prior by the KL divergence, essentially regularizing the latent space towards the gaussian prior. This has the effect of keeping the latent distribution compactly distributed around 0.
Given sufficiently expressive neural networks, the VAE latent space can fit complex data distributions very neatly. Generally you can expect to see smooth transitions between the different types of data points in the latent space. For example, if a VAE is trained on MNIST, you could expect a cluster for the 6’s and a separate cluster for the 5’s. If you go between the two clusters, you should get a digit that looks like a weird mix of a 5 and a 6.
Latent spaces are compressed representations of data, which often emphasize the most important and semantically interesting features of the data in their representation.
A learned latent representation can be useful for many downstream algorithms.
Autoencoders are a method for finding latent spaces that are complicated non-linear functions of the data.
Variational autoencoders add a prior to the autoencoder latent space. This gives the learned latent space some very nice properties (i.e. we can smoothly interpolate the data distribution through the latents).
Now that we have a handle on the fundamentals of autoencoders, we can discuss what exactly a VQ-VAE is. The fundamental difference between a VAE and a VQ-VAE is that VAE learns a continuous latent representation, whereas VQ-VAE learns a discrete latent representation.
So far we have seen how continuous vector spaces can be used to represent the latents in an autoencoder. But latents do not necessarily need to be continuous vectors, it really just needs to be some numerical representation for the data. And one such, potentially desirable, alternative to a vector space is a discrete representation.
In general, a lot of the data we encounter in the real world favors a discrete representation. For example, human speech is well represented by discrete phonemes and language. Additionally, images contain discrete objects with some discrete set of qualifiers. You could imagine having one discrete variable for the type of object, one for its color, one for its size, one for its orientation, one for its shape, one for its texture, one for the background color, one for the background texture, etc…
In addition to the representation, there are a number of algorithms (like transformers) that are designed to work on discrete data, so we would like to have a discrete representation of the data for these algorithms to use.
Clearly discrete latent representations can be useful, but how do we learn such a representation? This might seem very challenging at first because in general discrete things do not play too nicely with deep learning. Luckily enough, VQ-VAE manages to make deep learning work for the task with just a few tweaks to the vanilla autoencoder paradigm.
VQ-VAE extends the standard autoencoder by adding a discrete codebook component to the network. The codebook is basically a list of vectors associated with a corresponding index. It is used to quantize the bottleneck of the autoencoder; the output of the encoder network is compared to all the vectors in the codebook, and the codebook vector closest in euclidean distance is fed to the decoder.
Mathematically this is written as
where ze(x) is the encoder vector for some raw input x, ei is the ith codebook vector, and zq(x) is the resulting quantized vector that is passed as input to the decoder.
This argmin operation is a bit concerning, since it is non-differentiable with respect to the encoder. But in practice everything seems to work fine if you just pass the decoder gradient directly through this operation to the encoder (i.e. set its gradient to 1 wrt the encoder and the quantized codebook vector; and to 0 wrt all other codebook vectors)
The decoder is then tasked with reconstructing the input from this quantized vector as in the standard autoencoder formulation.
Producing Multiple Codes
You might be puzzled by the fact that there is such a restricted set of vectors that can be fed to the decoder (just the set of codebook vectors). How could one ever expect to generate the huge quantity and diversity of possible images when the decoder can only accept the set of codebook vectors as input? We would need a unique discrete value for each training point to be able to reconstruct all the data. And if this is actually the case, then wouldn’t the model effectively be memorizing the data by mapping each training point to a different discrete code?
This would be a very valid concern if the encoder were to output just one vector, but in actual VQ-VAEs the encoder usually produces a series of vectors. For instance, with images, the encoder might output a 32x32 grid of vectors, each of these are quantized and then the entire grid is fed to the decoder. Or similarly, for processing audio, the encoder could output a long 1-d sequence of vectors. All vectors are quantized to the same codebook, so the number of discrete values doesn’t change, but by outputting multiple codes we are able to exponentially increase the number of datapoints our decoder can construct.
For instance, imagine we are working with images, we have a codebook of size 512, and our encoder outputs a 32x32 grid of vectors. In this case, our decoder can output 51232 * 32=29216 distinct images! Just to make it clear how enormous this number is, I have computed it in python in the figure below… it is truly an unfathomably large number. There is absolutely no way anyone could ever visualize every possible output from this model. The size of the discrete space really is no longer a problem here.
Of course the model could still memorize the training data, but with the right inductive biases baked into the encoder (i.e. using a conv-net for images) and the right structure for the latent codes (i.e. a 32x32 grid for images), the model should learn a discrete space that represents the data well.
Learning the Codebook
Just like the encoder and decoder networks, the codebook vectors are learned via gradient descent. Ideally our encoder will output vectors that are generally close to one of the learned codebook vectors. There is essentially a bi-directional problem here: learning codebook vectors that align to the encoder outputs and learning encoder outputs that align to a codebook vector.
Both of these problems are solved by adding terms to the loss function. The entire VQ-VAE loss function is
Here we use the same notation from the previous section, and sg[x] stands for “stop gradient”, it prevents the gradient from flowing through that part of the equation.
The first term is just the standard reconstruction loss. The second term is the codebook alignment loss, whose goal is to get the chosen codebook vector as close to the encoder output as possible. There is a stop gradient operator on the encoder output because this term is only intended to update the codebook. And the third term is similar to the second, but it puts the stop gradient on the codebook vector instead because it is meant to solve the inverse problem of getting the encoder output to commit as much as possible to its closest codebook vector. This term is called the codebook commitment loss, and its importance to the overall loss is scaled by the tunable hyperparameter β. Of course these last two terms are averaged over each quantized vector output from the model, if there is more than one.
This loss function basically completes our description of the VQ-VAE.
With this, we can fully train a VQ-VAE capable of reconstructing a diverse set of images that are almost imperceptibly different from the original images as seen in the figure below. We can also train VQ-VAEs to reconstruct other modalities like audio or video.
Interpreting VQ-VAE in the Language of VAEs
Now that we know how VQ-VAEs work, let’s try to understand them in the context of the probabilistic formalism that VAEs provide. Recall that VAEs enforce a pre-defined prior on the latent space p(z), and the encoder is tasked with approximating the posterior distribution of the latents p(z∣x). Lastly, the decoder approximates the reconstruction from the latent space p(x∣z).
During training, VQ-VAE assumes a uniform prior over all the latent codes, so all latents are considered equally likely. Additionally the posterior is deterministic in that p(z∣x)=1 if z=zq(x) and 0 otherwise. Lastly, the decoder distribution p(x∣z) is unchanged and learned as usual. Using these definitions, it can easily be shown that the KL divergence term from the VAE loss becomes a constant and therefore can be dropped for VQ-VAEs, leaving just the reconstruction term. The VQ-VAE reconstruction loss is therefore consistent with VAE formalism.
Learning the Prior
Once a VQ-VAE is fully trained, we can abandon the uniform prior imposed at training time and learn a new, updated prior p(z) over the latents. If we learn a prior that accurately represents the distribution of discrete codes, we will be able to generate new data from the distribution by sampling from this prior and feeding the samples to the decoder (see the figure below for original VQ-VAE samples).
Training the prior also has compression benefits. If the distribution of latents is non-uniform, then the bits representing the sequence of latents can be further compressed by applying standard huffman or arithmetic coding to the prior distribution.
Assuming the encoder outputs a sequence of latent codes for each datapoint, we can use any autoregressive model we want (i.e. RNN or transformer) to train the prior. The autoregressive factorization is, given all previous latent codes in the sequence, predict the next one. This breaks the latent distribution down as
where zi is the ith latent in the sequence.
If we are working with a 1-d signal like audio, casting the problem into an autoregressive form is very simple: just predict the next latent in the 1-d sequence encoded from the audio. This approach assumes that the encoder is configured such that later latents in the sequence are representative of later sections of audio (this property should be expected if using convolutions to encode). For images we can cast the problem similarly, by first rolling out the 32x32 grid of latents into a 1-d sequence, such that the sequence goes from top left to bottom right, we can then apply autoregressive learning to this sequence.
State Of the Art
This paradigm of training a VQ-VAE and then learning an updated prior, is the exact formula that OpenAI has successfully used in several of their groundbreaking recent releases. OpenAI’s jukebox, a model that is able to generate original songs from raw audio, trains a VQ-VAE on audio and then uses a transformer trained on the latents to generate new audio samples. Their recently released text to image model, DALL-E, involves a transformer that takes as input both the embeddings from text and the latent codes from a VQ-VAE trained on images. Of course, some of these works are using a few additional tricks that are outside the scope of this blog post, like hierarchical VQ-VAEs and different relaxations for making the VQ-VAE bottleneck differentiable.
VQ-VAEs can represent diverse, complex data distributions better than pretty much any other algorithm out currently. And since these models play so nicely with transformers, the generative possibilities can be scaled almost arbitrarily given a large enough compute budget (unfortunately, for state of the art results, this is a budget that very few individuals or even organizations can afford). For these reasons, I expect VQ-VAEs to remain a popular component in the deep learning ecosystem for quite a while.
The next blog post in this DALL-E Explained series, will more closely examine transformers for autoregressive modeling on both single-modal and multi-modal data.
Edit: part 2 is out now ! Check it out here.
VQ-VAE paper: https://arxiv.org/pdf/1711.00937.pdf
OpenAI DALL-E blog: https://openai.com/blog/dall-e/
OpenAI Jukebox blog: https://openai.com/blog/jukebox/
Comp Three Inc. Autoencoders blog: https://www.compthree.com/blog/autoencoder/
Jaan Altosaar VAE blog: https://jaan.io/what-is-variational-autoencoder-vae-tutorial/


the next number on our list is odd? N 1 where, n is any integer. Thus, 62 is not an kirkens bymisjon fredrikstad odd number and the answer to the question "Is 62 an odd number?". Trying to have me killed is an odd way of saying thank you. When we did this, we found that the answer is a whole number. Some sequential odd numbers are: And. If you divide by 2 and there is not a remainder left, then the number is even. This is because the number cannot be divided by 2 evenly.
An odd number
Elisabeth odden, Fra odda til bergen, Ferge aarhus sjllands odden,
all negative numbers can also be either odd or even. I understand that you fotograf oslo sentrum will use my information to send me a newsletter. To find the set of odd integer numbers, we use. The membership of the boards of directors of such organizations must be equitable, and if the total number of members is an odd number, the difference between the number of men and the number of women may not exceed one. Well, that is an odd compliment. Formal definition of an odd number: A number n is odd if there exist a number k, such that n 2k 1 where k is an integer, this is formal way of saying that if n is divided by 2, we always get a"ent. 62,357,178,870.5, notice the number is not a whole number and has a remainder (the.5)? The next four bigger odd numbers are three, five, seven, and nine. Since odd and even numbers are defined only in reference to the set of integers (., 3, 2, 1, 0, 1, 2,.


The Best Way to Obtain Things is Zeros in Z
Math is not easy to know, but it’s not impossible to locate a very simple means to learn what can be zeros in mathematics. The method we’ll use is quite straightforward therefore you can discover the response to your question instantly, and it makes use of one’s favourite internet search engine. Your result will be under this post.
The question http://graftpoint.com/notion-of-arithmetic/ will be”What is zeros in math?” This really is one of those questions which I always see on math homework duties. With this question, you will need to know that there are just two kinds of amounts. These two types of sums are linear and non-linear.
Linear amounts are 1 of the ways to sum stuff up. By way of instance, let us say you have to know whether one number occurs before or after a second. Inside This Circumstance, you can multiply the numbers all and Try to Find a linear sum:
If you discover a linear sum, then the response sneak a peek at this web-site. is yes, the solution is yes. The other option is always to use the factors you heard. Within this case, you want to multiply the numbers all.
The word that occurs before that amount will be called the multiplier. This may be the best option for finding out everything is zeros in mathematics. The reply is some thing such as 1.3.
You’ll have to locate. This word is called x ray. You have to know the square root of x ray and also you’ll be able to find out that this term is just three times the square root of five.
Therefore that your answer is, you guessed itx^3. The choice to this particular question is to combine the exact additional options with each other. For this you can multiply the number you are looking all for and locate the points of the saying.
As a way to figure http://paramountessays.com/ out what really is zeros in mathematics, you will want to achieve this. That is, you may utilize the method to locate this expression’s variable. One other way will be to multiply the digits and then find a sum that is linear.


Normally I try to come up with some sort of catchy title for my blog posts. For some reason I just blanked on this one. Sorry 'bout that.
To make up for it though, I thought I'd share a few interesting lesson ideas and web resources that I've sent out to our teachers during the first two weeks of school. Here goes...
Futures Channel (www.futureschannel.com)
Ever have kids in your science and math classes ask you, "Why do I need to know this stuff?" Here's your answer. This site has videos of real people using real math and real science in real life! The videos also have printable (PDF) classroom activities.
Math Playground (www.mathplayground.com)
Need an activity for your students in the computer lab? Or would you like to recommend something they could use to practice their math skills at home? This is it. I actually met creator Colleen King, or rather her Second Life alter ego Kristy Flanagan, while chatting at the Bloggers Cafe. (NOTE: Second Lifers should also check out the Math Playground Virtual Math Center on EduIsland II)
HM Technology Resources (hmtech.wikispaces.com)
For those of you using Houghton Mifflin's Reading series, here's a site with links to supporting web resources compiled by Eva Wagner.
ReadWrite Think: Student Materials (www.readwritethink.org/student_mat)
This site contains a whole collection of online activities for your students to work on at school or at home. Browse through this rather extensive list and try out a few that look interesting. When you click on the tool, you'll get a list of grade specific lessons that could be used with it. See how these tools might fit into your Language Arts or Literature curriculum.
Back to School PhotoStory3 Project (web.mac.com/jennifergingerich)
Jennifer Gingerich comes up with yet another one of those "its so simple why didn't I think of it" ideas. This great project for primary grades can be created using a digital camera and Microsoft's PhotoStory3 or Apple's iMovie. I love hearing the kids' voices on the video.
Now the race is on! Who will be the first to use one of these ideas or resources in their classroom this year? Will it be one of our teachers? Or will it be you? If it's you, please post a comment and let me know how it went.


Kalgoorlie-Boulder Community High School teachers use NAPLAN data, teacher judgement and diagnostic tasks to determine student capability. Learning programs are adjusted accordingly. In Year 10 there is a strong focus on preparing students for upper school, offering specialist Mathematics classes in term 4 to students who elect to do Year 11 specialist Mathematics courses.
The Mathematics program is based on the new Australian Curriculum. There are three content strands in the Australian Mathematics curriculum.
Numbers and algebra
In this content strand the concentration will be on number and algebra. Recent research has emphasized the connections between these. An algebraic perspective can enrich the teaching of numbers and the integration of numbers and algebra, especially representations of relationships, can give more meaning to the study of algebra in the upper secondary years. This combination incorporates pattern and/or structure and includes functions, sets and logic.
Measurement and geometry
While there are some aspects of geometry that have limited connection to measurement, and vice versa, there are also topics in both for which there is substantial overlap, including newer topics such as networks. In many curricula the term space is used to cover mathematical concepts of shape and location. Yet many aspects of location, for example maps, scales and bearings, are aligned with measurement, and the term geometry is more descriptive for the study of properties of shapes, and also gives prominence to logical definitions and justification.
Statistics and probability
Although students are familiar with the terms data and chance, statistics and probability more adequately describe the nature of the learning goals and types of student activity. For example, it is not enough to construct or summarize data — it is important to represent, interpret and analyze it. Likewise, probability communicates that this study is more than the chance that something will happen. The terms provide for the continuity of content to the end of the secondary years and acknowledge the increasing importance and emphasis of these areas at all levels of study.


Take a look at these: Upon accomplishing those levels, a trader has to closely watch behavior of price to make a decision and enter trade on time. Gann in the first half of the 20? If cookie is disabled in your Internet browser, you may have problems with accessing Client Area. Fractals are often constructed by repeating a process recursively over and over.
Nov 20, · Murrey Math The basic concept of my strategy is to use the break of a Murrey Level to enter our trades and pick our targets. I have added the indicators, template, and two versions of a Trade Management EA I had made called Stealth.
Not a client yet?
Here are some of the trading conditions you want to avoid in the forex market. Conclusion The Murrey Math Trading Lines Strategy is the ultimate support and resistance system because unlike the simple support and resistance levels the Murrey lines are mathematically driven and possess a greater influence on how the price reacts to each of these levels.
Thank you for reading The Murrey Trading Strategy. Please leave a comment below if you have any questions about Murrey Trading Strategy! Defining the murrey math lines The Murrey math is based on observations that were made by WD Gann in the first half of the 20th century. A picture speaks a thousand words, so here is what you should be looking at: Now, all we have to establish is where to enter our long trade, which brings us to the next step of our Murrey Math Trading Lines Strategy: Also, please give this strategy a 5 star if you enjoyed it!
The main assumption in Murrey Math is that all markets behave in the same manner akin to a herd. This agrees with our concept of reflexability, that the market in a constant state of flux or perpetual chaos. As such the market is seeking to find equilibrium, which is the point of extreme chaos, i. Tops and bottoms or inflexion points. These are also the points of extreme market behavior, and why we place so much value on sentiment indicators. What we found was that The Murrey Math trading system is primarily based upon the observations made by W.
Gann in the first half of the 20? While Gann was purported to be a brilliant trader in any market his techniques have been regarded as complex and difficult to implement. The great contribution of Murrey Math T. Murrey was the creation of a system of geometry that can be used to describe market price movements in time.
Significantly it added the turning point methodology that eluded us in refining Fibonacci levels. Murrey Math is a trading system for all equities. This includes stocks, bonds, futures index, commodities, and currencies , and options. The main assumption in Murrey Math is that all markets behave in the same manner i. The Murrey Math trading system is primarily based upon the observations made by W.
Gann in the first half of the 20th century. The Murrey Math trading system is composed of two main components; the geometry used to gauge the price movements of a given market and a set of rules that are based upon Gann and Japanese candlestick formations. The Murrey Math system is not a crystal ball, but when implemented properly, it can have predictive capabilities.
Because the Murrey Math rules are tied to the Murrey Math geometry, a trader can expect certain pre-defined behaviors in price movement. By recognizing these behaviors, a trader has greatly improved odds of being on the correct side of a trade. Time interval defines width of the interval and its further change. Using big values of this figure can lead to missing profit, whereas small values give a lot of false signals that can lead to losses. As per Murrey math trading theory, the best possible time interval is 64 used for building levels on day charts.
However, practical application of ML by traders allowed finding one more interesting value as of Simultaneous application of ML with and 64 parameters provide a more profitable trading both for short- and long-term periods of time. Near these levels the most verifiable movements of price take place the most frequently, which allows to enter market at a lowest Stop Loss. Upon accomplishing those levels, a trader has to closely watch behavior of price to make a decision and enter trade on time.
More often, this level acts as resistance and support level on market. Upon completing a strong trend movement, price gets back to this level. When trend rolls back to this level, entrance to market is the best possible option.
The rest Murray levels are less important and entering market on these levels can lead to losses.
Murrey Math is a description of the Murrey Math Trading Method. Murrey Math Trading System - Forex Strategies - Forex Resources - Forex Trading-free forex trading signals and FX Forecast Free Forex Strategies, Forex indicators, forex resources and free forex forecast. Dec 15, · The Murrey math trading lines strategy is the most attractive Forex trading strategy because it’s suitable for all time frames and it can be used to trade different markets likes stocks, commodities and Forex currencies.5/5(2). Murrey math lines The indicator Murrey match lines is similar to pivot points and Fibonacci retracement. MML was created based on the observations of Gann studies and is a simple way to implement Gann.


Climate Dynamics is an advanced undergraduate-level textbook that provides an essential foundation in the physical understanding of the earth’s climate system. The book assumes no background in atmospheric or ocean sciences and is appropriate for any science or engineering student who has completed two semesters of calculus and one semester of calculus-based physics. in which mathematics takes place today. As such, it is expected to provide a ﬁrm foundation for the rest of mathematics. And it does—up to a point; we will prove theorems shedding light on this issue. Because the fundamentals of Set Theory are known to all mathemati-cians, basic problems in the subject seem elementary. Here are three simple
National Physical Laboratory, Teddington, 2nd ed., HMSO, London, and Philosophical Library, New York, 1961 (excellent annotated bibliography included). Google Scholar 22 Survey of Numerical Analysis. Solutions manual developed by Roger Cooke of the University of Vermont, to accompany Principles of Mathematical Analysis, by Walter Rudin. Subject.


- CURIOUS SPELLER as it appeared in the June 2007 issue of M-U-M magazine is reproduced here with permission of the Society of American Magicians.
- A Pack of Little Fibs by CardColm
- Martin's first and last published magic tricks spanning 80 years from Word Ways
- Mathematical Card Tricks (from Card Colm column at MAA)
- Also In His Own Words: More Mathemagical Games (and Tricks) With Cards From Martin Gardner - August 2010
- In His Own Words: Mathematical Card Tricks From Martin Gardner (1914-2010) - June 2010
- Vi Hart's Mathematical Balloon Twisting Guide
- Recreational Math Problems submitted by Dick Hess
- Penrose Tiles to Trapdoor Ciphers ... and the return of Dr. Matrix (excerpts)**
- Ten of the greatest: Maths puzzles
- Conway on Gardner
- Suggestions from Andy Liu for SNAP Math Fairs from Dana Richards' "The Colossal Book of Short Puzzles and Problems"
- Mathematically Correct Breakfast (How to Slice a Bagel into Two Linked Halves)


You might notice that:
- I can recognise the numbers 1 to 5.
- I can recognise numbers that are important to me like my age, our door number, or the bus number that I go to nursery on.
- I can touch one thing and say the number name at the same time to help me count up to 3 or 4 things.
- I can count the number of things on a page, in a book, or on a birthday card.
- I can match the right number to a group of things from 1 to 5 to begin with, and then from 1 to 10.
- I can guess how many things I can see in a bucket and then count them to see how close my guess was.
- I can tell you which basket or bucket has got “more” or “fewer” things in.
- I can put two baskets of things together and tell you how many things I have altogether.
- I can tell you what “one more” is when you say a number.
- I can tell you what “one more” or “one less” is when you give me a group of up to 5 things, then up to 10 things.
- I can use words like “more”, “add”, “less” and “take away”
- I can use marks and pictures to show you my counting.
- I can use counting to help me solve problems that are important to me, like splitting my sandwich in half to share with my friend.
How you can help me learn:
- Plan a picnic with me and let me decide how many sandwiches and bananas we will need.
- Make a number line with me using birthday cards.
- Play number snap or bingo with numbers that we’ve cut out of a magazine.
- Sing number songs where I have to count backwards like “Five Little Ducks” or “Ten Fat Sausages”.


Optimization in operations research
Prentice Hall PTR, 1998 - 919 ページ
This book is specifically designed to change the way deterministic optimization is taught to introductory students. Toward this end, it exposes students to the broad scope of the topic, reinforces the basic principles, sparks students' enthusiasm about the field, provides tools of immediate relevance and develops the skills necessary to use those tools.
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Review: Optimization in Operations Researchユーザー レビュー - Harsha - Goodreads
Review: Optimization in Operations Researchユーザー レビュー - Joecolelife - Goodreads
I thought there was only one best complete OR book is Hillier and Lieberman (H&L) until I got Rardin's book. Rardin presents the OR in different approach than H&L. The model building part is a little ... レビュー全文を読む
Problem Solving with Mathematical Models
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Pearson - Optimization in Operations Research
Optimization in Operations Research, Ronald L. Rardin, Purdue University. ISBN-10: 0023984155 ISBN-13: 9780023984150. Publisher: Prentice Hall ...
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Optimization in Operations Research: Mainpage
Comprehensive new undergraduate and beginning graduate text on mathematical programming by Professor Ron Rardin of Purdue University
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Rardin Ronald R.: Optimization in Operations Research, 1998. Winston Wayne L.: Operations Research. Applications and Algorithms, 3rd edition, 1994 ...
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The main textbook for the course is Optimization in Operations Research by rl Rardin and I strongly recommend that you either buy this book, ...
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Math 358: Methods in Operations Research
Optimization in Operations Research, Prentice-Hall, Upper Saddle River. Schrijver, A. (1986). Theory of Linear and Integer Programming, Wiley, New York. ...
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Ronald R. Rardin, Optimization in Operations Research, Prentice-Hall, Inc., New Jersey, 1998. 6. Johannes Jahn, Basic Concepts of Vector Optimization, ...
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Optimization In Operations Research. 정가, 173500원. 판매가, 173500원 + 수수료 (0% DC). 적립금, 3400(2%). ISBN10, 0023984155. ISBN13, 9780023984150 ...
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Optimization in Operations Research 1e PIE. Yazar: RONALD L. RARDIN. For first course in operations research, operations management. ...
SYS 504: Introduction to Optimization Theory Fall 2004
Required Text: Optimization in Operations Research by Ronald L. Rardin. Recommended Text: Numerical Optimization, by Jorge Nocedal and Stephen Wright. ...
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Calculation of the period of the phase signal.
Every day the UTC time difference between the zero crossing point of the phase signal obtained in the mathematical modelisation and the series of events: To, To + 23h56m4s, To + 2.[23h56m4s], To + 3.[23h56m4s], etc... is measured , where To is the UTC time of the first zero crossing point.
As after 178 days, the zero crossing point has not been away from the above events of more than 40 minutes (with an algebraic average of +12 minutes relatively to the series of events) , the mean period of the phase signal may be considered in the worst case as being the sidereal day with an accuracy of : [40*60*2]/178 = 26.9 seconds.
This result is in good agreement with the result which is obtained with a standard statistical analysis.
To show that, we must note firstly that the n=179 zero crossing points: To, T1, T2, ....T178 define (n-1)n[1/2] trials of the measurement of the period which are T1-To, T2-T1, T3-T2, etc... for one time the period, T2-T0, T3-T1, T4-T2, etc... for two times the period, etc for three times the period...until 178 times the period with a total of trials of 15931.
Thus as the worst case standard deviation relatively to the average of the measured days ( S = 23h56m12s) is : , the standard deviation of the average or uncertainty is : .
Unfortunately (but without real importance)a Fourier analysis of the phase signal has not been performed, simply due to a lack of time to program the computer to do it. Because this experiment was not really my job at the Belgian Telephone Company.
Finaly the negative linear drift (see below) of the zero-crossing points relatively to GMT days will convince anybody that the period has nothing to do with the mean solar day.
I think also important to point out here that in the experiment there is a PLL-follower between each of the two 1.5 km coaxial lines and the corresponding phase comparators which was integrated in the apparatus for an other usage in telephony (test of synchronization of noisy signals from long distance rubidium clocks) and thus difficult to extract The presence of these PLLs , due to its time constant of only 100s, is without influence on the result of the experiment and also because they have been tested with a ceasium clock to be as stable as 2 ns of non-cumulative phase rotation a day.
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STEAM (Science, Technology, Engineering, Arts, Math)
Madison Camelview Elementary School
Madison Camelview Elementary School is excited to launch their STEAM program this fall, providing students in preschool – 4th grade a strong foundation in the areas of science, technology, engineering, arts and math. Students will participate in coding classes and have the opportunity to join after-school STEAM-based clubs.
Madison Park Middle School
Madison Park Middle School‘s STEAM program provides students with a solid curriculum with an emphasis on science, technology, engineering, arts, and math, giving them an advantage when entering a STEM High School.
Students are taught to engage, explore, explain, elaborate and evaluate. All students are provided a three year engineering curriculum that includes hands on learning labs with 22 engineering lab stations that include 3D printing, pneumatics, rockets, robotics, and more.
Madison Park also offers extra-curricular opportunities for students to further develop their STEM learning including Engineering by Design, High Altitude Ballooning, and others.


When: Thu., Nov. 12, 12-10 p.m., Fri., Nov. 13, 8 a.m.-10 p.m. and Sat., Nov. 14, 8 a.m.-12 p.m. 2015
Annual conference of the Association of Mathematics Teachers of NYS. Featured speakers included internationally known Dan Meyer as well as Peg Smith. Over 150 workshops and sessions for teachers PreK-College. Presentations by the New York State Department of Education as well.
Price: Registration required.


Frequency polygons are an alternative to histograms that make it simpler to overlay multiple distributions.
freqpolygon( x, ..., panel = "panel.freqpolygon", prepanel = "prepanel.default.freqpolygon" ) prepanel.default.freqpolygon( x, darg = list(), plot.points = FALSE, ref = FALSE, groups = NULL, subscripts = TRUE, jitter.amount = 0.01 * diff(current.panel.limits()$ylim), center = NULL, nint = NULL, breaks = NULL, width = darg$width, type = "density", ... ) panel.freqpolygon( x, darg = list(), plot.points = FALSE, ref = FALSE, groups = NULL, weights = NULL, jitter.amount = 0.01 * diff(current.panel.limits()$ylim), type = "density", breaks = NULL, nint = NULL, center = NULL, width = darg$width, gcol = trellis.par.get("reference.line")$col, glwd = trellis.par.get("reference.line")$lwd, h, v, ..., identifier = "freqpoly" )
a formula or a numeric vector
additional arguments passed on to
a panel function
a prepanel function
a list of arguments for the function computing the frequency polygon.
This exists primarily for compatibility with
densityplot and is unlikely
to be needed by the end user.
how points are to be displayed
a logical indicating whether a horizontal reference line should be
added (roughly equivalent to
as in other lattice prepanel functions
center of one of the bins
an approximate number of bins for the frequency polygon
a vector of breaks for the frequency polygon bins
width of the bins
color of guidelines
width of guidelines
a vector of values for additional horizontal and vertical lines
a trellis object
This function make use of
histogram to determine overall layout. Often
this works reasonably well but sometimes it does not. In particular, when
used to overlay multiple frequency polygons, there is often too little head room.
In the latter cases, it may be
necessary to use
ylim to determine an appropriate viewing rectangle for the
freqpolygon(~age | substance, data=HELPrct, v=35) freqpolygon(~age, data=HELPrct, labels=TRUE, type='count') freqpolygon(~age | substance, data=HELPrct, groups=sex) freqpolygon(~age | substance, data=HELPrct, groups=sex, ylim=c(0,0.11)) ## comparison of histogram and frequency polygon histogram(~eruptions, faithful, type='density', width=.5) ladd( panel.freqpolygon(faithful$eruptions, width=.5 ))


SAISD Mobile App
On behalf of the faculty and staff, I would like to welcome you and your children to the 2017-2018 school year at Margil Elementary where we strive for One Team, One Dream! Here at Margil we provide education for Pre-Kinder thru Sixth grade students.
We are happy to share that Margil Elementary is predicted to meet “Met Standard” on the state accountability for STAAR. We congratulate the Margil staff, students and parents for their hard work and dedication.
This school year, third through sixth grade students will take the STAAR Reading and STAAR Mathematics state assessments. Additionally the fourth graders will take the STAAR Writing, and the fifth grade will take the STAAR Science. The fifth grade students must pass the STAAR in math and in reading to be promoted to the sixth grade.
Parents, it is in your child’s best interest to be present at school every single day, all 177 days of instruction. When your child is at school every day, your child is ensured of a successful future, which is what we wish for all of our children. Help us by having the children here every day and on time.
Thank you for working with us. I look forward to working with you in providing your child the best education opportunity possible.
Cynthia Pérez, Principal Margil School
Antonio Margil Elementary School | 1000 Perez St. | San Antonio, TX 78207 | Phone: (210) 738-9805 | Fax: (210) 228-3054
COPYRIGHT © 2016 - SAN ANTONIO INDEPENDENT SCHOOL DISTRICT


How to calculate fortune mewa -
classic phugpa calendar
1. First look after the birth year sign to find the key for the next step.
2. For a Tiger, Horse or Dog the next step starts with Metal – Monkey
For a Pig, Sheep or Rabbit the next step starts with Fire – Snake
For a Bird, Ox or Snake the next step starts with Water – Pig
For a Mouse, Dragon or Monkey the next step starts with Wood – Tiger
3. Find the key year in the same metreng as the birth year with the key found in the previous step.
4. The Life Mewa of this year is the Fortune Mewa.


Unit cost is a method of calculating the cost of producing one unit of a product or service. It can be used in various industries, including manufacturing and retail. Unit costs are typically expressed as a dollar amount per unit or can be calculated as a percentage of sales revenue.
Unit costs can be used to calculate many different financial metrics, including:
To calculate the unit cost, you need to take the average cost per unit and divide it by the number of units produced. The formula for calculating unit costs is:
Average cost per unit (ACPU) ÷
Number of units produced
The ACPU can be determined by dividing the total cost of all items produced by their total number. For example, if you make 500 glass bottles at $1,000, your ACPU would be $2 ($1,000 divided by 500). When calculating unit costs using this method and assuming that each bottle requires 3 hours of labor at $10 per hour or raw materials costing $30 per pound, then each bottle has an ACPU of 49 cents per pound, which is outlined below:
Labor = ($10 × 3 hours) + ($30 ÷ 1 pound) = $40 + $9 = 49 cents per pound
Below are a few common examples of unit costs:
Unit cost is essential for manufacturers because it helps determine the profitability of a product, the pricing of a product, and even the cost of production. It's also necessary to understand unit costs if you're going to calculate your company's gross margin (the percentage difference between the sales price and total cost).
Tracking unit costs benefits your business because it helps you make more informed decisions about pricing and production—you can use it to determine whether a price increase will be offset by higher sales volume or if increased production would be more profitable than raising prices.
For example, if you know that it costs $1 million per month to run your factory (including labor), but selling an extra ten units would generate an additional $300k in revenue, then it may make sense to increase production instead of raising prices.
Unit cost is important metric manufacturers use to measure the profitability of their products. Many factors can change the unit cost, including material prices and labor rates. Tracking these variables can provide valuable information to help you make better business decisions.
Leverage the cloud to work together, better in the new connected age of maintenance and asset


This class is used to declare objects that store running sums and averages of a series of numbers.
For each instance of the
update()method to add a value.
Get running average by accessing the
meanproperty, running sum by the
totalproperty, and number of values by the
None. The value of an instance defaults to 0 when you initiate it.
epoch_train_loss = Accumulator()
In this case, the
length property of
epoch_train_loss are all 0.
Returns the number of values in the accumulator.
Returns the number average value of the numbers in the accumulator.
Returns the total
def update(self, value: float, length: int = 1) -> None
Add a value to the accumulator.
This class is used to declare objects that calculate and track accuracy between predictions and true labels.
Call the update function to add predictions and labels.
Get accuracy score at any point by accessing the value property.


Generally garden topsoil should be about 12 inches (1 foot) deep. 750 square feet is 750 / 9 = 83.33 square yards. For larger lawn projects, consider bulk mulch to save money and trips to the store. How Many Cubic Feet of Dirt Can a Dump Truck Haul? One cubic yard is a three dimensional cube that measures 3 feet long and 3 feet tall. Step Two: Calculate Weight in Tons Depending on how you intend to use the dirt, you can either purchase topsoil or fill dirt. The formal method involved breaking the shape down into geometric shapes, calculating the area of each them and adding all the areas together for the total cross-sectional area. Mulch Buying Guide. At the center of that line, draw a new line perpendicular to the first. A cubic yard is equal to 27 cubic feet. Define Cross Section of Load - Construct "Heap" and add to Inside Load, 4.Count Up All the Whole Squares Covering the Load. 2. Next, enter in depth of the location in inches. How to calculate cubic yards for rectangular, circular, annular and triangular areas. With all due respect; that can't strictly be answered; even apporoximating, as one might define a shovel full differently, individually, and from each successive scoop up. Using 2 cubic foot bags: Square Foot Number / 12 = Total bags needed for a 2” inch thick layer of mulch. Recommended maximums are 30% compost in a soil blend, but no more than 25% compost in containers or raised beds. Yes! The Density of Red Brick Chips: 2,410 lb/yd³ or 1.21 t/yd³ or 0.8 yd³/t How long will the footprints on the moon last? Then the cost of 10m Its cost per day including driver and fuel is Rs. What is a sample Christmas party welcome address? One scoop of an excavator bucket contains half a cubic yard, so a cubic yard is also known as "two scoops." per cubic yard; Compost weighs between 1000 – 1600 lbs and soil blends weigh between 2200-2700 lbs. That should give you 61.7 cubic yards. The cubic yard is a valuable unit of measurement to help assure that you are getting the value you expect when purchasing landscaping materials. ft. = 1.5 yds @ 3″ thick) Top Soil/Mushroom Soil Yardages 1 Yard of Top Soil/Mushroom Soil = 80 sq. How much does a cubic meter of gravel weigh? All Rights Reserved. Excavating a cubic meter of dirt for a footing by hand is a serious job. Typically, mulch products weigh between 400-800 lbs. The raw materials used to make our colorants are made from naturally occurring colors found in the earth’s surface. A cubic meter of typical gravel weighs 1,680 kilograms 1.68 tonnes. SBS is based in Dallas, TX. Dyed mulch for a 160-square-foot flowerbed costs $75, and wood chips for a 500 sqft. For the best result, enter in the length and width of the location in feet. Mulch Buying Guide. Soil can be bought by the bag, and where available, in bulk too. One scoop of an excavator bucket contains half a cubic yard, so a cubic yard is also known as "two scoops." The gravel is assumed clean of dirt and other debris. Pain in the butt though! Tips. At Westminster Lawn Landscape Supply Yards, it’s one certified cubic yard of mulch per bucket. , I'd sub it out to a blower truck, and make a nice 15-20.00 yd for doing nothing, except for writing the check to the blower co. At Westminster Lawn Service Landscape Supply Yards, we have certified cubic yard buckets on our loaders to ensure the customer of an accurate measurement of the product they are purchasing. There are 25.71404638 Dry Quarts in a Cubic Foot, so a 25 quart bag of potting soil would equal approximately 1 Cubic Foot. How much is a tonne of soil? 5000. One yard of dirt is 27 cubic feet, which is an area 3 feet wide by 3 feet wide and 3 feet tall. Brian Young PlowSite Veteran. If a dump truck holds 12 cu. Mulch Cost. Top. Now, before you think about measuring dirt using yardstick, remember that it will compress down if wet and fluff up if dry. The Density of Red Brick Chips: 2,410 lb/yd³ or 1.21 t/yd³ or 0.8 yd³/t To determine how many cubic yards of soil you need for your project, measure the space’s width, length and depth in feet and then multiply them together and divide by 27 to convert to cubic yards. Types of Dirt. Next, enter in depth of the location in inches. bags of 2-cubic-feet bag $ 0: pounds $ Disclaimer: Depending on the composition of the material from your supplier, the material density, the weight, and therefore, the total price you get from the calculator above may not be 100% accurate. For the best result, enter in the length and width of the location in feet. A standard truck can hold roughly 10 to 12 cubic yards of fill dirt, which equals to about 270 to 324 cubic feet, which comes out to 20,000 to 24,000 lbs of dirt. For example, if the length is 10 feet, the width is 10 feet, and the depth is 0.25 feet, the result is 25 cubic feet (10 x 10 x 0.25 = 25) Tip Home-improvement and garden stores often sell soil in bags that indicate how many cubic feet they contain. We recommend: One truckload of dirt may weigh up to 20 tons, and a cubic yard of topsoil is about 1.3 tons. Rough number estimate: If the bucket was a rectangular box 6' long x 1.25' wide x 1.5' tall= 11.25 cu feet, but its profile is a triangle so divide by two = 5.625 cu ft = (divide by 27)= .208 cubic yard if completely full? When did organ music become associated with baseball? Soil, especially topsoil, is a valuable commodity. A full size ¾ or 1 ton pickup … You don't have to do it that way, I mean by the cubic foot. Think about it as a cube that is 3′ X 3′ X 3′. Measure the bucket of the loader to see what the cubic feet measurement is, then divide by the number of yards needed.Usually a 5' Bobcat bucket , a little heaped will be close to a cu. Recommended maximums are 30% compost in a soil blend, but no more than 25% compost in containers or raised beds. 1 ton - 2,000 lbs. 3) Divide the total cubic feet by 27, since there are 27 cubic feet in a cubic yard. One thing some guys do around here is load up one scoop and wiegh it in a truck and get your truck light loaded also but that would take all the guess work out of it. Weights for products will vary due to moisture content. ft. Or expressed as Cubic Yards is 641 / 27 = 23.7 Yards3 Where this method has only applied the angle of repose in two dimensions, the SAE Standard Formula applies it in three. That should give you 61.7 cubic yards. A cubic yard of dirt is one yard (3 feet) long, wide, and high. Soil Building Systems produces organic compost, hardwood mulch and soil mixes for the landscaping industry. Works for me. As a shortcut, try our cubic yardage calculator to conveniently calculate your volume. The company that fertilizes my yard said that I needed to add an inch of top soil on the lawn since the roots were showing. Types of Dirt. ft. x 12.33 feet = 641.33 cu. A standard truck can hold roughly 10 to 12 cubic yards of fill dirt, which equals to about 270 to 324 cubic feet, which comes out to 20,000 to 24,000 lbs of dirt. How much does a yard of product weigh? Stauffers offers mulch in 2 cubic foot bags, 3 cubic foot bags, and in scoops. When If the area to be covered is 200 cubic feet, for example, each bag of rock covers 4 cubic feet ,so you will need 50 bags of landscape rock to fill the space. Soil is assumed relatively damp, since adding water can increase or decrease the density of the soil considerably (e.g. ft. x 12.33 feet = 641.33 cu. Shop Mulch; Shop Soil & Soil Amendments; Related Articles. per bag) which equals 20.5 bags (lets round it up to 21). [For example, you have an area 6′ x 10′ x 0.25"(or 3") = 15 cubic ft divided by 27 = 0.55 cubic yards or 1 skid loader scoop. To figure out how many bags or how many scoops of mulch you will need for your space, use these formulas. A 2 cubic foot wheelbarrow typically has a shallow basin. The mulch we want to use comes in 2 cubic foot bags. Most Masons put three shovels of sand and one shovel of Mortar. Volume = Cross Sectional Area x Length A cubic meter of typical gravel weighs 1,680 kilograms 1.68 tonnes. The Society of Automotive Engineers has … A square yard of gravel with a depth of 2 in (~5 cm) weighs about 157 pounds (~74 kg). ft.) approximately 3 inches deep You can calculate the square footage by multiplying length x width (i.e. , irregular chunks influence the Weight … mulch cost half a cubic yard calculator for,... The cost of 10m its cost per day including driver and fuel is Rs Related! A ton of condensed, moderately damp soil typically fills about 0.625 3... Weigh up to 41 ) soil Amendments ; Related Articles enter in depth of the base line,. And width of the base line inches ( 1 foot ) deep alternately, a excavator... Wheel loader Buckets using the 2:1 heap, it ’ s one certified cubic yard by... Scoops will equal a cubic yard is equal to 27 cubic feet yardstick, remember that will. Multiply by.5 ft. you end up with 40 sq ft. = 1.5 yds @ thick..., you can calculate the square feet in a scoop would be the amount a backhoe would. 1.68 tonnes 1.5 which means you multiply the square footage by multiplying x. Brands and thats what they where all saying a 160-square-foot flowerbed costs $ 75 ) for the cubic. 80 sq width ( i.e 83.33 square yards bags: square foot Number / =. Labeled as to the volume in cubic yards for rectangular, circular, annular and triangular areas naturally... Recycling uses for selling bulk mulch and bulk top soil, moderately damp soil typically about., and where available, in bulk too kg ) Number is the volume in cubic yards divide... … one cubic yard calculator for topsoil, is a valuable unit of measurement to help that... Scoops ’ or bags of mulch you will need for your space use! Three dimensional cube that measures 3 feet ) long, wide, and high tells!, expressed in the length and width of the soil is assumed relatively damp how many cubic feet in a scoop of dirt since adding water increase. Hold, maybe about 1/3 cubic yard equals 27 cubic feet of area., sand, gravel, dirt ingredient for a Christmas party how much does a cubic of! To the first answer wide, and in scoops. load bulk soil is, by law, labeled to. Standard for such ratings, cubic yards = 1.5 yds @ 3″ )... Decrease the density of the soil considerably ( e.g 27 cubic feet by 27 gives you yards. But no more than 25 % compost in containers or raised beds or dryer too. Moderately damp soil typically fills about 0.625 m 3 of soil the cross-sectional of! In cubic yards ( 3/4 cu yd ), it should be about 12 (... 1.3 tons the gravel is assumed relatively damp, since there are 3 feet wide 3! Of potting soil would equal approximately 1 cubic foot bags found in the of., the perpendicular line should be 1/2 the length of the baseline to the size of a or... Some samples of opening remarks for a footing by hand is a serious job and pieces partial... 36 = 0.0833 yards by dividing by 46,656 and high a shallow basin per.. By a scoop, i assume you mean a front-end loader bucket a new line perpendicular to the.... To whole squares shop mulch ; shop soil & soil Amendments ; Related Articles feet in a yard inches 1... A shallow basin or metric units and get volume conversions to other units about! Value you expect when purchasing landscaping materials two: calculate Weight in tons i paid CDN $ (! 9 to 14 full loads to equal the specified Number of cubic yards in! By 3 feet tall are looking for cubic feet per wheelbarrow load ), it should 1/2! 88 ( approx at the center of that line, draw a new line perpendicular to the first answer is... Planimeter was used to directly measure it the mulch we want to use the dirt, can... About 0.750 cubic yards i would say 10-12 cubic feet struck and of. The landscaping industry the spill board how you intend to use comes in 2 cubic foot to cubic yards dirt. Additional squares that are made from naturally occurring colors found in the length width and depth standard-size bagged typically. Of material are required, is a serious job assure that you looking., but no more than 25 % compost in containers or raised beds 1/4... Total cubic feet of an area 3 feet long and 3 feet wide by 3 feet long and feet... The appropriate compost application depth for your space, use these formulas load bulk soil you,... Would be the amount piled on top of it truck, the load will be crowned …. First convert all the small pieces the sun so water evaporates ) an area by using the 1:1 heap the.


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Mathematics interview questions and answers pdf
Top 20 Mathematics Interview Question & AnswersDifferent types of field for maths are Calculus, Algebra, and Fractions. I use all kinds of maths, but Calculus is major. Algebra is one of the fields of maths, which uses symbols and letters to represent numbers, point, and objects, as well as the relationship between them. It is used to know the unknown variables. For example, you have lost 5 pens, and you are left with 10 pens now, to know the total number of pens you had it.
Math Teacher Interview Questions And Answers
20 math teacher interview questions and answers pdf ebook
Am I right? Your best bet is to therefore prepare for a variety of interview questions that cover a large range of themes and topics that might come up. I also believe I can contribute positively to the company culture by [ X ]…. Why do you want this job? I feel like I can provide a lot of value to the company but also grow with it. What do you know about our company? The company is based in [X] and has about [X] total employees.
But first, remember every interview is different
Completed your graduation?, Interview questions and answers, job interview tips, job search tips, cover letter and resume writing.
Best tips on how to prepare for math teacher job interview. Ebook: Killer interview Secrets -This ebook includes top 16 secrets that help you will every job interview The learning process consists of video-based instruction, computer graded assignments and a dashboard which allows the student and parent to track progress. The main focus will be on learning different techniques in solving word problems. Once the techniques are in place, solving word problems would be a breeze.


Graph papers are extremely imperative for students and young art designers. It also apply in businesses for identifying different levels of business development. Graph papers are prepared in numerous ways. Here we offer you an trouble-free way to create your own graph paper by using our provided graph paper template. You can download graph paper template free from our website. Graph paper template can edit easily as it is created in MS Word. We are hopeful that you will like graph paper template. You can see its snapshot on our website before downloading it.


I am a retired mathematics teacher/educator with a BS in Mathematics and a MS in Education. I started making functional pottery when I took classes at a community center, Richmond Arts Center, in Richmond California. After 10 years I built a log home in Mariposa California and designed a studio there. I used an electric wheel and electric and Raku kilns for firing. I made and sold functional pottery using medium range porcelain and stoneware firing at cone 5 to 6 in oxidation. I sold pottery to neighbors and tourists at the Mariposa Arts Center in town and at the Holiday Faire and the Butterfly Festivals. After 14 years in my Mariposa studio, I moved to Portland in December of 2015 and I am currently taking classes and working at the Multnomah Arts Center making functional pottery using high fire porcelain and stoneware which is fired by professional studio artists and technicians in gas kilns at cone 9 to 10 using the reduction method. I joined the Oregon Potters Association in December of 2016.