Received Date: March 16, 2015; Accepted Date: March 23, 2015; Published Date: April 07, 2015
Citation: Hasbiyati I, Suwilo S, Salim O, Tulus (2015) Simple Techniq of Projected Lagrangefora Class of Multi-Stage Stochastic Nonlinear Programs. Global J Technol Optim 6:179. doi: 10.4172/2229-8711.1000179
Copyright: © 2015 Hasbiyati I, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Visit for more related articles at Global Journal of Technology and Optimization
This paper presents a techniq for solving multi-stage stochastic nonlinear programs. The techniq is based on projected lagrange approach which generates the search direction by solving parallelly a set of quadratic programming subproblems with size much less than the original problem at each iteration. Mathamatically, can be pointed out that Lagrange’s projection method can solve problem multi-stage stochastic nonlinear programs.
Multi-stage stochastic nonlinear programs; Projected langrange; Scenario analysis; Decomposition
Multi-stage stochastic nonlinear programs emerges in there are many practical situation, as production and manpower planning, portfolio’s selection etc.. Have a lot of research that gets contribution to solve Multi-stage stochastic nonlinear programs amongst those methodics decomposition that is utilized on nonliner’s program also linear [1,2]. Most of that literature in reference to principle decomposition that introduced by Dantzig and Wide .
Decomposition method experience development which is with marks sense L-shape decomposition method that enough effective being utilized to troubleshoot multi-stage stochastic nonlinear programs.
Severally methods the other to troubleshoot multi-stage stochastic nonlinear programs is analyzed among those by Birge . Since all method is gone upon on special structure of programs characters linear stochastics, so is hard generalisation to solve nonlinear stochastic programs, Gongyun Zhao introduces iterasi’s method that bases to analisis scenario which is a method that reduces nonantisipativity constraints by lagrange dual’s approaching and combine with barrier logarithmic’s method.
Hereafter Gongyun Zhao  developing decomposition method which is by use of sequential quadratic method’s programming. Gongyun Zhao also propose conjugate’s gradient method that can determine estimation of associate dual coefficient with nonantisipativity constraints. Gongyun Zhao  also develop lagrangian dual’s method to solve nonlinear’s program multi’s stochastic phase.
Lagrange’s projection algorithm was analyzed by Murtagh and Sander  to troubleshoot sparse nonlinear constraints. Algorithm untieding to troubleshoot nonlinear large scale’s program with logistic objective and constrain smooth’s function and continu diferensiable. Algorithm is included lagrange’s projection type with logistic objectif in forms lagrange’s modification.
Base research already being done researchers former to solve multi-stage stochastic nonlinear program, in this paper, writer propose a method for solve to program multi-stage stochastic nonlinear programs which is by use of lagrange’s projection method. This method is expected gets to give alternative solution to solve multi-stage stochastic nonlinear programs.
Consider the following multi-stage stochastic program with recourse:
the recourse function
Subject to c1 (x, y1,ξ1 ) = 0 (1.2)
And for t = 2,...,T −1, recursively we have
Subject to (1.4)
QT = 0. is the deterministic vector, is the realization of the random vector is the decision vector in the i-th stage, which is generated recursively by hence represents actually. cˆ0
For the discrete random vector if ct has finite realizations then all these cti form the constraint functions on stage t. The details on the formulation of multi-stage stochastic programs can be found, e.g. in Kall and Wallace .
Let and assume that (Ω,θ , P) is the associated probability space. Suppose that we have S scenarios which has a fixed and known probability distribution Then (1.1)-(1.4) can be reformulated as the following nonlinear programming problem:
Constraints (1.7) are the so-called non-anticipativity constraints, which reflect the fact that scenarios sharing a common history up to any moment of time must have a common decision up to that moment. Readers can refer to Rockafellar and Wets  for more details on this reformulation.
Lagrange’s function in common is deep shaped as follows,
For q parameter.
Let say to be given by parameters q and r, therefore form augmented lagrange of equation upon is as follows,
Let say to be
To a f = Ax .
Therefore objective function for problem to multi-stage stochastic nonlinear programs is as follows,
In this paper, Lagrange’s projection method will be utilized for multi-stage stochastic nonlinear programs. The methods based lagrange augmented modified.
Assume that are two continu diferensiable functions, is matrix row with full rank and has special structure.
So equation (1.5) – (1.7) are formulated as forms as follows, min f (x)
A(x) = 0 Where are matrix m x n with m ≤ n .
That note function of x assumed continu diferensiable.
With Lagrange’s projection method, objektif’s function takings f(x) one equal to form commons of Lagrange augmented’s functions,
Vector λT is lagrange’s coefficient vector and ρ is penalti’s parameter.
Linear Aproksimation from constraints nonlinear is make iterasi along starting point x(k) from iterasi process followings;
A(x(k +1)) = A(x(k)) + h(k)(x(k +1) − x(k))
So algorithm that presented to solve subproblem constrain’s line linear with function objective is modify lagrange augmented and linear aproksimation f(x) on the x(k) are as follows
s.tA = 0,1≤ x ≤ u
Where is function objective is modify lagrange augmented and is aproksimasi f (x) on the x(k) and,
Where fk and Jk is cconstraints vector and jacobi’s matrix that evaluated with x(k) .
Definition 1. To ρ = 0 , one that constitute Lagrange’s solution and coefficient that corespondence to a subproblem.
Definition following to give convex requisite to form lagrange’s modification.
Solving problem multi-stage stochastic nonlinear programs by use of lagrange’s projection method depends on penalti’s parameter ρ . If ρ too large therefore will be hard to find solution. On the contrary, if ρ too little x(k), one that is expected as solution will go away to reach convergence.
Here after partision x as form xL (x linear) and form xN (x nonlinear). And partision also as [B S N] with matrix B (basic) is matrix square and nonsingular, S (super basic) are matrix m× s by 0 ≤ s ≤ n − m, and N (nonbasic) are residues column of matrix A., therefore constraints active becomes as follows;
where xB , xS , xN called by basics’s variable, superbasics and nonbasics what do accordingly with [B, S, N].
Note: basics’s variable and superbasic is variable one free on bounds.
Theorem following to give that surety nonlinear’s program have solution.
Theorem 3. Let say nonlinier’s program has t nonlinear’s variable (well on objektif’s function or constrain even), therefore an optimal solution available on each superbasics’s variable number s one accomplishes s ≤ t.
Proof. Let is variable non linear regular on appreciative optimal. Problem is rest is linear program for a basic’s solution whatever available (s=0). Its result is trivial if variable nonlinear is regarded as superbasic on early problem. If s=t, available variable nonlinear that current on bounds is nonbasic the so called. Therefore has s ≤ t.
From Theorem 3 secure to mark sense optimal solutions so base 3 get to be made by defenition followings.
Definition 4. Optimal solution available for number of smaller superbasic variable or equal to nonlinier variable number.
Hereafter been given simple algorithm for multi-stage stochastic nonlinear programs.
Set 1. Let K=0, Choose some initial estimates x0, y0 and λ0. Specify a penalty parameter ρ ≥ 0 and convergence tolerance ∈c > 0 .
Set 2. Given xk, yk, λk and ρ , solve the lineraly constrained subproblem (1.8) to obtain new quantities xk+1, yk+1, and π (where π is the vector of Lagrange multipliers for subproblem).
Set 3. Let λK+1 = the first componenets of π.
Set 4. Test convergence (see Definition 5). If optimal, exit.
Set 5. Relinearize the constraints at xk+1.
Set 6. Let K= K+1 and repeat from step 2.
Definition 5. The point (xk, yk), are solution for problem nonlinier if following condition are satisfied, (xk, yk), satisfies the first-order Kuhn Tuckere’s conditions for a solution to the linearized problem.
From the theorems, definitions and algorithm that is given gets to be seen that lagrange projection method can utilized to solve multistage stochastic nonlinear programs.
A projected Lagrangian method is a very effective approach for solving medium-size nonlinear programming. By using lagrange augmented modified, strategy a for solving a class of multi-stage stochastic nonlinear programs is proposed, which choise of ρ with size much less than the original problem at each iteration. Generelaized reduced gradient methods can be introduced to derive the estimates of the dual multiplier associated with the nonanticipativity constraints.
Make the best use of Scientific Research and information from our 700 + peer reviewed, Open Access Journals


Mathematics, Science, and Technology
The Mathematics, Science, and Technology (MST) curriculum integrates these three connected disciplines. Throughout the MST sequence, students learn to:
Understand how scientific and mathematical ideas have developed throughout history
Actively explore mathematical and scientific content
Identify new problems and pose original questions
Carry out original investigations in pure and applied mathematics and science
Apply their learning to new situations
MST classes harness students' natural curiosity about the natural and man-made world, the origins of our universe, and human history. Students learn important habits of mind, understand and assimilate information, and master technical skills through a combination of investigations, laboratory activities, and traditional approaches. These experiences make it possible for students to find answers to the questions that they pose themselves.
Division One (Grades 6 and 7)
+ Engineering with Robotics and Computer-aided Design
The essential question explored in this course is “How can we apply scientific, mathematical, and technical facts and methods to the solution of real world problems?” Beginning with the book Catastrophe! by Fred Bortz, the class develops a timeline and learns about inventors, inventions, and their impact throughout history. Students learn both the theoretical and practical sides of many disciplines as they design and build machines and then robots to address a variety of challenges. Engineering problem-solving methods guide the students as they first develop vehicles that can navigate about the room and then build robots to perform helpful tasks or compete with each other in a Robot Olympics. These projects require students to learn and apply ideas from physics (velocity and acceleration, simple machines and mechanical advantage, force, torque, energy, and material science), geometry (measurement, similarity), and algebra (proportion and linear behavior) to succeed in their efforts. Students write a research paper on an application of robotics (e.g., a self-driving car or surgical assistant). The second half of the course explores Computer-Aided Design (CAD) and Computer-Aided Manufacturing (CAM) as students use 3-D printers laser cutters, and other automated tools to produce real versions of their virtual illustrations, learning about measurement (surface area and volume) and the forms of 3-D geometry in the service of their projects. At the end of the year, they use the design/engineering process to identify a problem, evaluate possible solutions, prototype their ideas, and then write a patent application and deliver an investor pitch for their invention. The course includes themes of sustainability and appropriate technologies for developing nations.
+ Doing Research in Mathematics and Science
This course asks the question “How is new knowledge acquired in math and science?” To this end, students explore a range of scientific and mathematical settings as they practice asking questions, posing problems, and developing theories. In the first trimester, students grapple with how a conjecture differs from a theorem and how a hypothesis differs from a theory as they carry out original research for their Connect the Dots project. In parallel, students learn about classification and the structure of plants, readying them to participate in Project Budburst, a national citizen science venture. In addition to collecting data, students use an existing dataset and their growing understanding of algebra to ask rigorous scientific questions about climate change and plants. Course topics include experimental design and the statistical analysis of data, number theory, algebra, geometry, and statistics. This integrated biology and mathematics research curriculum culminates in original microbiology investigations and the application of graphing skills in the construction of flags. Some texts for this course include Reading the Forested Landscape and Tardigrades in Science.
Division Two (Grade 8)
+ Marine Science
Marine Science develops and applies biological, physical, algebraic, and geometric ideas to the study of the environment. Much of our studies are driven by questions, such as “How can we identify and describe patterns using math and science?” and “How can math and science be used to improve or optimize circumstances?” During the first term, students develop an understanding of physical oceanography and sustainability by studying the Great Pacific Garbage Patch and developing sequences to describe its projected growth. Later, building on these algebraic methods, students learn how to use linear programming to optimize a situation of their own design. In the final term, to facilitate their research of the Charles River, students build SeaPerches – remotely operated submersible vehicles designed at MIT – while in parallel working to understand electricity and currents. Students use their SeaPerches to conduct research into a question that they develop themselves. Additionally, students study ecology and evolution, presenting an independent research project on the historical and intellectual contexts in which Darwin made his discoveries. We draw from a number of texts throughout the year, including Flotsametrics, Tracking Trash, Spineless: The Science of Jellyfish, Resilience Thinking, and Into the Jungle.
Division Three (Grades 9 and 10)
+ Revolutions in Math and Science
This course compares and contrasts the relatively recent historical evolution of a truly scientific understanding of chemistry with the ancient development of a rigorous approach to mathematics and the blossoming of geometry that were reflected in Euclid's Elements. Working from this foundation, the course asks, "Within mathematics and science, what are our standards for asserting the truth of a statement?" "What types of evidence do we accept?" and "How do the mathematical and scientific communities work to reach agreement on what knowledge is valid?" Students study these questions as they explore similarity and congruence for polygons and carry out original investigations into the properties of quadrilaterals and then produce proofs of their claims. Through Chemistry experiments, students build their understanding from observation, deciding as a group what constitutes theory or truth as they explore the nature and behavior of matter and interactions between molecules and compounds. In the final trimester, students see how one intellectual revolution begets another with the surprising discovery of non-Euclidean geometries and investigations of acids, bases, and various reactions. Readings include Flatland, The Disappearing Spoon, Crucibles, Napoleon's Buttons, What Einstein told his Cook, and Radioactive: A Tale of Love and Fallout.
+ Human Biology and Decision-Making
This course compares the biology of different organisms with an
emphasis on human biology through the lens of molecular, developmental, genetic, and evolutionary concepts. In all of these contexts, we ask “How does form inform function?” Beginning with fundamentals, students explore macromolecules, cells, and how cells differentiate into complex tissues and organ systems. The class then consolidates their learning by working together to write their versions of sections of a human biology textbook. Concurrently, they learn about function families and their shapes in order to model experimental data. In our introduction to neuroscience and sensation, students make connections between trigonometry and sound, light waves, music, vision, and neural activity. As students learn modern lab techniques for exploring DNA, they discuss different bioethics questions prompted by our new biological technologies. Students read the book Predictably Irrational and connect their understanding of the brain to human behavior. Their studies of descriptive and inferential statistics prepare them to design and carry out original psychology and physiology experiments. Readings also include the books Gulp and Your Inner Fish.
Division Four (Grades 11 and 12)
+ Calculus, Physics, and Modeling
Throughout this course, students refine their abilities to model situations and see the myriad historical connections between math and science. Driven by the question “How do we describe change?” students are introduced to calculus concepts by modeling disease epidemics with a system of differential equations. Students combine algebraic analyses with numeric approximations solved using spreadsheets. These two approaches enhance student intuitions about the central calculus concepts of differentiation and integration. The concepts are reinforced through the study of Newtonian physics, enabling students to develop a rigorous analytical approach to their scientific work. Students conduct investigations and analyze data and graphs to come up with models describing different situations. They practice and deepen their understanding of these models by solving problems and posing new questions, and they apply their skills to projects such as a calculation of the efficiency of pathways that channel energy from natural resources into applications. The physics curriculum includes motion, forces, orbital motion and gravitation, work and energy, linear momentum, radioactivity, and optics. The mathematical concepts of limits, derivatives, integration, optimization, conic sections, and trigonometric, exponential and logarithmic functions are all integrated within the course. In the final term, the startling ideas of twentieth century physics, such as special relativity, are introduced. Research and current events articles, the ASU Physics Modeling Instruction program, Physics Principles with Applications, Calculus in Context: The Five College Calculus Project, Isaac Newton, and How to Teach Relativity to Your Dog are among the text resources used by the students.
+ Mathematical Modeling and Computer Science in the Social and Natural Sciences
Mathematical Modeling is the process of bringing a mathematical perspective to the study of real-world issues. In addition to its utility, math is studied because of the beauty of its patterns, the elegance of its ideas, and the pleasure one can experience exploring its structures and techniques. This course investigates the intertwined nature of applied and theoretical mathematics and how each stimulates the other. Students learn how to apply, to real problems and in original contexts, all of the mathematics they have learned and are learning with problem-posing at the heart of each project. During the first unit, students study multivariable functions of three or more dimensions and their application to rating and ranking everything from the quality of a college to whether or not a patient is a suitable organ transfer recipient. They write a 15-20 page paper describing a measure that they have developed to rank a setting of interest, justifying the operations involved in their function, and explaining the hyperdimensional geometry of their function’s graph. The class then learns computer programming in the language Python and each student develops a simulation of a stochastic model to predict the outcomes of a dice game, sports situation (e.g., the likelihood of Dimaggio’s 56-game hitting streak), or board game (e.g., expected length of a game of Chutes and Ladders). Students study probability, combinatorics, and game theory to better understand situations arising in politics, sports, business, and other competitive settings. Their modeling work culminates with a month-long project investigating an original question posed by each student pair. During the pure mathematics portion of the course, students learn more about conjecturing, methods of proof (including induction), and many of the accessible classic theorems such as the proofs of the infinitude of primes, the irrationality of the square root of two, and Cantor’s proofs about countable and uncountable infinities.
+ Introduction to Computer Programming
Students study how to analyze a problem and to design a structured solution to that problem in computer languages, such as Python and SNAP, which provide powerful and accessible graphical tools. Students learn about variables, loop structures, conditional reasoning, procedures, functions, and recursion. Projects include games, mathematics explorations, animations, and more.
+ Computer Science - Atoms, AND Gates, and Abstraction: How Computers Work
Students explore how computers work from the electronic level to logic gates, chips, and computer structure. Students study base number systems, infix and postfix representations, and other topics that help them understand the inner workings of the devices that pervade our lives. All topics are linked to new programming skills and projects that extend their understanding of Python and good programming design. Readings include Tracy Kidder's Pulitzer Prize winning book Soul of a New Machine.
+ Computer Science - Data, Algorithms, and the Ideas that Make the Internet Work
Students study how to represent data, design algorithms, and connect the two in programs. Students build a number of applications both individually and through group projects which require the class to coordinate their programming specifications. Projects include code-making and code-breaking tools, computer graphics, searching methods, games, and applications to mathematics and science. Nine Algorithms That Changed the Future: The Ingenious Ideas That Drive Today's Computers serves as a main source for understanding our networked world.
+ Non-hierarchical Systems, Fractals, and Chaos
This class instroduces programming in the graphically powerful and parallel processing programming language NetLogo, which makes possible explorations in real-world science and social science settings. Students explore how simple rules followed by many agents (e.g., termites, molecules, people, etc.) lead to unexpected emergent behaviors and patterns, such as elaborate ant homes, a zebra's stripes, cooperating communities, and more. They investigate underlying mathematical structures that explain complex behaviors and systems. Resources include An Introduction to Agent-Based Modeling: Modeling Natural, Social, and Engineered Complex Systems with NetLogo.
+ Mathematics Research Seminar
This class provides the opportunity to do sophisticated investigations in pure mathematics. Students study proof techniques including induction, proof by contradiction, and proof by exhaustion. Topics vary according to class interest, but have included combinatorics, the geometry of complex numbers, difference equations, Pythagorean triples and Fermat's Last Theorem, number theory, and graph theory. Students develop an original line of inquiry that they explore in depth.
+ Computer-Aided Design and Manufacturing
This class provides the opportunity to study Computer-aided Design (CAD) and Manufacturing (CAM) and three-dimensional geometry and algebra. Using the school's 3-D printers, laser cutter, and CNC (computer numerical control) technology, students invent, design, and build both functional objects and sculptural works of art. Students work with the powerful and professional CAD program Onshape.
+ Advanced Placement Physics
This class is offered in partnership with Boston University. Students complete some of their studies online and some on site at B.U. Course goals include: developing a deep understanding of foundational principles of physics in classical mechanics and modern physics by applying these principles to complex physical situations that combine multiple aspects of physics. Students will design and conduct inquiry-based laboratory investigations to solve problems through first-hand observations, data collection, analysis and interpretation.


Are you looking for NCERT solutions for Class 12 Maths? Here is all you need.
Class 12 is an important stage of life on which the hinge of academic life rotates. The future career largely depends on the performance you make here. Maths, as a subject is the most important subject of concern throughout life. More so, if you opt for Engineering, and wish to be qualified in the reputed universities for further studies, securing good marks in Maths is a must.
Disha Publication is here with detailed Class 12 Maths NCERT Solutions, at the same time makes the task of preparation easy and smooth. The Maths Class 12 NCERT Solutions are designed with the purpose to put you in the top of success. The biggest asset for your future endeavours will be getting well-equipped with all the basics of Maths.
Chapter-list for Class 12 Maths NCERT Solutions
The Chapters of NCERT Maths Syllabus needs additional focus as it Maths Class 12 NCERT Solutions, as it carries weightage in most of the competitive exams. Here is an outline of the chapters which you should go through to fruitfully understand the NCERT Solutions for Class 12 Maths.
Chapter 1: Relations and Functions
Chapter 2: Inverse Trigonometric Functions
Chapter 3: Matrices
Chapter 4: Determinants
Chapter 5: Continuity and Differentiability
Chapter 6: Applications of Derivatives
Chapter 7: Integrals
Chapter 8: Applications of Integrals
Chapter 9: Differential Equations
Chapter 10: Vector Algebra
Chapter 11: Three-dimensional Geometry
Chapter 12: Linear Programming
Chapter 13: Probability
Why Maths Class 12 NCERT Solutions is Important?
Class 12 Maths NCERT Solutions strengthens the base for conceptual understanding. It gives a comprehensive view of the prescribed syllabus, as the textbook does not have a detailed description of the topic nor solutions. All the important formulas and theorems of Class 12 are fully solved, which works to build the concepts and find new connections to them. Importantly, the NCERT Solutions for Class 12 Maths is the point of reference for those students preparing for competitive entrance exams like JEE Main/Advanced, BITSAT & VITEEE, in the engineering level.
When the NCERT textbook is accompanied by the solutions, the understanding of concepts becomes easy and in-depth. Moreover, students can trail into the solutions without break in concepts, as it is designed to provide a step-by-step explanation.
Try out the Maths Solutions and learn from the resources.
Why try Free Samples of Disha Publication NCERT Solutions for Class 12 Maths?
There are enough Class 12 Maths NCERT Solutions already available on the internet, and you would ask, why should I choose Disha Publication Maths Class 12 NCERT Solutions? Well, here are the practical reasons why you should and must try out the NCERT Solutions Mathematics Free Samples of Disha Publication.
- Has ERRORLESS solutions with 100% Reasoning
- Quality of solutions is incomparable
- Provides in-depth knowledge with notes immediately after the solutions with tips, shortcuts, alternative methods & points to remember
- Provides quick revision of the concepts involved along with important Formulas and definitions on the chapters, which acts as an instant refresher.
- Designed step-by-step to give 100% Concept Clarity
- Solutions are complete (each and every question is solved), & inflow (exactly on the flow of questions in the NCERT Maths book)
Why wait for some other time to try out the samples, when you can do it now? Explore and take solutions to your Maths problems.


Hey, folks, I'm Hemanth doing my 3rd year engineering at Bangalore Institute of Technology.
I can teach mathematics and physics right from secondary school up to college level.
My classes will be fun-filled, friendly, fresh and innovative.
The class structure will primarily depend upon you, as each individual is different.
Looking forward to having some fun!
I've been giving lectures in classes, participated in various seminars, attended technical talks and exposed to the real world for some time now.
My logical approach will be very helpful in understanding the student and take instant decisions depending upon the situation.
B.E 3rd year(pursuing)
Above average student
I love physics, which was the reason I chose mechanical engineering.
maths classes closeby? Here's a selection of tutor listings that you can check out.
Superprof can also suggest algebra classes to help you.
Learning isn't a problem, trigonometry classes for all!
Taking arithmetic classes has never been easier: you're going to learn new skills.
|at his home||at your home||By webcam|
|1 hour||Not available||₹500||₹300|
|5 hours||Not available||₹2,000||₹1,500|
|10 hours||Not available||₹4,200||₹3,000|


Joint and Marginal Diagnostic Tests for Conditional Mean and Variance Specifications
32 Pages Posted: 20 Jun 2007
Date Written: June 12, 2007
This article proposes a general class of joint and marginal diagnostic tests for parametric conditional mean and variance models of possibly nonlinear non-Markovian time series sequences. The use of joint and marginal tests is motivated from the fact that marginal tests for the conditional variance may lead misleading conclusions when the conditional mean is misspecified. The new tests are based on a generalized spectral approach and, contrary to existing procedures, they do not need to choose a lag order depending on the sample size or to smooth the data. Moreover, the proposed tests are robust to higher order dependence of unknown form, in particular to conditional skewness and kurtosis. It turns out that the asymptotic null distributions of the new tests depend on the data generating process, so a new bootstrap procedure is proposed and theoretically justified. A simulation study compares the finite sample performance of the proposed and competing tests and shows that our tests can play a valuable role in time series modeling. Finally, an application to the S&P 500 highlights the merits of our approach.
JEL Classification: C12, C14, C52
Suggested Citation: Suggested Citation


This is a bit different kind of help that I need compared to most other threads in this forum. I was not sure of where exactly to post this. But, since it is pretty much homework, and it's for my AP Calculus AB course, I thought this would be an appropriate place to put this thread. If not, could a moderator please tell me where a proper location would be? In order to pass the AP Calculus AB course I am enrolled in, each student must submit a project to "show their understanding of advanced mathematics". The idea behind the project is that each member of the class present a new area of math or science that uses a type of math that is considered advanced (so basically just Calculus +). It has to be something that can be taught within 30 minutes of instruction. And, that is the only restriction, basically. To give you guys an idea of the topics discussed in our class to this point, this is an appropriate list of things we have covered: -limits -derivatives of all non-polar, real-number functions -integration (definite and indefinite; by parts and substitution; reimann sums) -slope fields -applications of differentiation (related rates; optimization) -applications of integration (volume by slicing; disk/washer method; shell method; arc length) So, with that in mind, ideally, I want a topic that is advanced enough to fulfill the requirements, but not advanced enough to derail the class and confuse half of the people. I took the Calculus BC exam, so I have a good understanding of taylor series/taylor polynomials and the like. I look forward towards hearing your ideas and suggestions.


Multiplication-word-problems-3rd-grade-worksheets, subtraction with regrouping two digit multiplication multi step word problems it's all part of the third grade math curriculum and it's not always easy to digest but our third grade math. After watching this video lesson you will know how to set up and solve addition problems where you have two or more variables you will learn what steps you need to take to solve for each variable 2, order does not matter in multiplication; adding times problem or this check mocking a first grade counting exercise is being used as an example of common core math being unduly.
Alison friedman's third grade son spends his free time in math allow students like diego santiago to simply write down multiplication tables committed to memory diego had to solve a word problem, the ipads whispered and blinked to life then loaded the afternoon's work: a website chock full of long addition long multiplication long division even word problems from thomas fifth grade to. These fifth grade word problems worksheets incorporate a range of math operations including addition subtraction multiplication and division as well as concepts of place value and fractions many, would you rather read a book about mythical sea creatures or do a sheet of multiplication problems given the choice between listening to a hilarious read aloud featuring elephant and piggie or.
Greg mahar's height is written on the whiteboard in front of stephanie tham's third grade class at the josiah quincy elementary school it's being used as a way to create a word problem unable to, as applied to common core and instruction one should also be aware of problems that until fourth grade it is important to note that in ccss m the word "algorithm" appears for the first time in.
A bafflingly graded third grade maths quiz caused a firestorm on to "interpret products of whole numbers" and to "use multiplication and division within 100 to solve word problems " absent from, take quiz optional lesson 3 the commutative and associative properties and take quiz optional lesson 5 writing solving multiplication word problems with one variable score:


I want to use the "one step subgroup test".
The identity is
Therefore H is not empty since .
Now I have to show that for any two elements , is in H.
So we have:
If my working is correct so far, could anyone please show me how to manipulate this determinant to show that it satisfies the given condition, and .


Posted by arty on Saturday, March 12, 2011 at 2:59pm.
what are the steps to solve for x
calculus - Damon, Saturday, March 12, 2011 at 3:04pm
2 x^2 - 1/x^2 = 0 ???
2 x^4 = 1
x^4 = 1/2
x^2 = (1/2)^.5 or -(1/2)^.5
x = (1/2)^.25 or -(1/2)^.25 or i(1/2)^.25 or -i(1/2)^.25
calculus - arty, Saturday, March 12, 2011 at 3:12pm
thank you.i am trying to sove for critical numbers. the book is giving me an answer of
x=+square root 2/2
calculus - bobpursley, Saturday, March 12, 2011 at 3:56pm
I am wondering if the problem then is this:
x= +- sqrt (1/2)
but of course, multiplying that by sqrt(2/2) one gets
x= +- sqrt (2/4)= +- .5 sqrt 2
Answer This Question
More Related Questions
- MATH - 20. A certain computer can perform 105 calculations per second. How many ...
- Calculus - Follow the steps below for the given function. (Do not use mixed ...
- calculus - I am suposed to apply L'Hospitals rule to solve. I can't seem to ...
- Math - What steps do I take in order to solve : (101-100) = .512 times (x/.5) ...
- Math (calculus) - If y = 2x^3 - 4x and dx/dt = 4, find dy/dt when x = 1. Please ...
- calculus - can someone explain to me the steps to solve this problem? find the ...
- calculus - Implicit Differentiation question x^y = y^x I was wondering if I was ...
- Pre-Calculus - What makes a mathematical induction true? I know how to solve ...
- math calculus - Hi could someone please explain to me how i would use the chain ...
- Calculus - For the function f(x) = x/(3x+1) find the equation of the line which ...


Median, like its name suggests, it is the exact middle value in any distribution when, we are arranging any distribution in ascending or descending order.
The important thing about median is that you will have to first sort your data, you can do it in ascending or descending order, that doesn't make a difference.
But data should be sorted, and its middle value will give you the median value.
So, basically what median does is it divides our distribution in half.
So, 50% of the observations will be on the right side of the median, and another 50% of the observations would be on the left side of the median.
Now the observations can also be even, and they can also be odd.
So, suppose if I have an odd number of observations with me, okay.
And you have sorted them.
Suppose, if I have this particular distribution, in which there are 11 members, and let's consider that, this is the retirement age distribution that I have got of the 11 people.
If you see in this particular data, we have arranged them into ascending order.
So, there are 11 distributions, this means that I want its 50th ratio, I want its 50th percentile.
So, what will I do? The 6th value which is right in the middle.
If you see the sixth value, which is 57.
Five values before the distribution which is on the left and there are five values after is the distribution which is on the right.
So, 57 is the exact number which is dividing my entire distribution into half and it is giving me an exact value.
Now, if my distribution is even, even means that suppose, in the same distribution let's consider that one more value comes.
And now I have 12 values in a particular data set.
I cannot divide it in half.
What will happen in that particular scenario? I will take the mean of the middle two values.
One particular value that will come, that single value would be my median.
Suppose in this situation I took a mean of 56 and 57 which is divided by 2, 56.5 is the particular value that I got, that would be called the median.
Like we had seen, the order doesn't affect it.
You can arrange it in ascending order or in descending order.
Centre value will always remain the same.
Let's see It's advantages of the median.
This doesn't get affected by extreme values.
Basically, they are not getting affected by outliers.
Now, suppose in my data set there is any extreme value, they can be smaller values or extremely larger values.
The median doesn't consider them because it takes only the centre value.
So, this becomes an advantage, as the outliers are not affecting it, usually, median is the preferred measure of central tendency when the distribution is not symmetrical, or when we have skewed data, we may use medium at that time.
It basically converts all the disadvantages of mean into advantage, which is during outliers and skewed data, mean used to not function and in that particular scenario we can use median.
Let's also see the disadvantages of median.
Since it doesn't use all the values, it just takes the centre value and gives us a particular figure So, basically it doesn't use our entire information.
Second is, it is the same thing, because you're playing with the numbers so you cannot use median for the categorical data.
So, we are not using median and mean for categorical data.
We just use it for numerical data.
If you have any queries or comments, click the discussion button below the video and post there. This way, you will be able to connect to fellow learners and discuss the course. Also, Our Team will try to solve your queries.
(outro: 15 sec)
This course is really nice, just have one question in empirical rule explanation , SD deviation example trainer is saying mean however mean (20+30+40+50+60+70/6) value is different kindly confirm than


It doesn't take super-human powers to get stronger math skills, but lots of practice sure does help. Guide your second grader through this two-digit addition worksheet, and she'll be able to solve the mystery question at the end. Along the way, she'll boost her two-digit addition skills and mental math ability!
Try out the rest of this Super Powers! series for even more practice.


The ESA Rosetta Mission, launched in March 2004, rendezvoused with comet 67P/C-G in August 2014. The lander Philae touched down on the comet on 12 November and came to rest after bouncing twice (the harpoon tethers and cold gas retro-jet failed to fire).
Rosetta was in orbit around the comet and, after detatchment, the lander Philae was put in free fall, dropping onto the surface from a height of about 20 km in about 7 hours. It’s speed on impact was about 1 m/s.
We will have a look at the motion of Philae in the weak gravitational field of the comet and see if these numbers can be produced by simple mechanical reasoning.
For objects close to the Earth’s surface, the acceleration due to gravity is approximately constant. Newton’s law implies a force for an object of mass . Here (SI units), is the mass of the Earth and is the distance from its centre. We take to have a constant value equal to the mean radius of Earth. Then the acceleration is . For simplicity let’s take (SI units throughout).
Consider an object falling from a height at time 0 to the surface at time . From elementary mechanics, the speed at the surface is . The distance travelled is .
Juggling these equations, the time of the fall is and the speed on impact is . Thus, for example, a stone dropped from 80 metres hits the ground in 4 seconds at a speed of 40 m/s (we neglect air resistance throughout).
When the variation of distance from the centre of attraction is large, we cannot assume that is constant, and we have to integrate the equation of motion .
Multiplying by and integrating gives the equation where is a constant. Here is the kinetic energy and is the potential energy (both per unit mass), so is the (constant) total energy.
Suppose the body, initially with , falls from distance from the centre of attraction to distance . The initial energy is . The energy upon impact, , must have the same value. This gives us a formula for the impact velocity
We can integrate again: since , we get an equation involving and :
This is a standard integral, found in tables or evaluated using Mathematica or a similar package. The result is an expression for in terms of :
The Fall of Philae
Now let us apply these formulae to Philae falling towards 67P. Some relevant data: the comet mass is kg with density of about 400 kg/m³. It is of very irregular shape (see Wikipedia description), but we will replace it by a perfect sphere of radius 2km. Assuming that Philae fell from km to km, we now have values for all the factors in the above expressions. Plugging in the values for , , and in the expression for gives a value of m/s, a reasonable estimate of the impact velocity.
Now plugging the parameter values into the expression for , we get an estimate of the fall time, hours. This is much longer than the reported 7 hours.
Addendum, 1 December 2014.
To get a better estimate, we allow for non-vanishing initial velocity. If we assume that the velocity on separation (at height ) is then, from conservation of energy, the velocity as a function of height is
where . Taking the initial velocity to be , the velocity upon falling to 2km is or about one metre per second, close to the reported value.
Integrating from the release point to the surface, the time of fall now comes to almost exactly 7 hours, in agreement with the reported value.
We note that the lander has accelerated by only a tiny amount, from 0.65m/s to 1.01m/s, in the weak gravitational field of comet 67P.
An object with negative energy is held in orbit around the attracting body. If the energy is positive, then the object can escape from orbit. The minimum escape velocity is found by setting . For Philae, the energy was . The escape velocity at the surface of the comet is where km is the `radius’ of the comet. Plugging in the values given above, we get m/s.
Since Philae fell from a great height, the lander was close to escape velocity, and measures were taken to ensure that it remained on the surface. These were only partially successful, but sufficient to bring it to rest after its bumpy landing.
ESA website: http://www.esa.int/
Wikipedia article: 67P/Churyumov–Gerasimenko http://www.wikipedia.org/.


Answer: For an even function even function A function is an even function if f of x is equal to f of −x for all the values of x. This means that the function is the same for the positive x-axis and the negative x-axis, or graphically, symmetric about the y-axis. https://www.cuemath.com › calculus › even-function
- 1 What makes a function even?
- 2 What is an example of an even function?
- 3 What is an odd function example?
- 4 Is a linear function even or odd?
- 5 What types of functions are even or odd?
- 6 Which function is an odd function?
- 7 What is an example of a function that isn’t even or odd?
- 8 Is 0 neither odd nor even?
- 9 Is 2.5 odd or even?
- 10 How do you identify odd numbers?
- 11 Is 67 odd or even?
Even Function – Cuemath
, f(-x) = f(x), for all x, for an odd function odd function Odd Function. The odd functions are functions that return their negative inverse when x is replaced with –x. This means that f(x) is an odd function when f(-x) = -f(x). Some examples of odd functions are trigonometric sine function, tangent function, cosecant function, etc. https://www.cuemath.com › calculus › odd-functions
Odd Functions – Cuemath
f(-x) = -f(x), for all x. If f(x) ≠ f(−x) and −f(x) ≠ f(−x) for some values of x, then f is neither even nor odd.
A function f is even if f(−x)=f(x), for all x in the domain of f. A function f is odd if f(−x)=−f(x), for all x in the domain of f.
What makes a function even?
A function is called an even function if its graph is unchanged under reflection in the y-axis. Suppose f(x) is a function such that it is said to be an even function if f(-x) is equal to f(x).
What is an example of an even function?
Odd Function – A function \(f\) is called an odd function if \begin f(x)=-f(-x) \end for all \(x \) in the domain of \(f \text \) In other words, a function is odd if performing a reflection about the \(y\)-axis and \(x\)-axis (doesn’t matter which is performed first) does not change the graph of the function.
What is an odd function example?
What is an Odd Function? –
- Assume f to be a real-valued function of a variable that is real. The function f is odd when the equation is valid for all the values of x in a way that x and – x is present in the domain of the function f,
- -f(x) = f(-x)
- Or equivalently,
- f(x) + f(-x) = 0
- For example, f(x) = x 3 is an odd function, because for all value of x, -f(x) = f(-x).
What’s the difference between odd and even?
What are even and odd numbers? – Even numbers are divisible by 2 without remainders. They end in 0, 2, 4, 6, or 8. Odd numbers are not evenly divisible by 2 and end in 1, 3, 5, 7, or 9. You can tell whether a number is odd or even regardless of how many digits it has by looking at the final digit.
Is a linear function even or odd?
This linear function is symmetric about the origin and is an odd function : f ( x ) = f ( − x ). As shown earlier in the concept, this quadratic function is symmetric about the -axis and is an even function: f ( x ) = f ( − x ).
What types of functions are even or odd?
How are you supposed to tell even and odd functions apart? An even function is one whose graph exhibits about the y -axis; an odd function is one whose graph exhibits symmetry about the origin. Which is a fancy way of saying that, if you split the graphs down the middle at the y -axis, an even function’s halves will mirror each other exactly, while an odd function’s halves with be upside-down of each other.
In order to “determine algebraically” whether a function is even, odd, or neither, you take the function and plug − x in for x, simplify, and compare the results with what you’d started with. If you end up with the exact same function that you started with (that is, if f (− x ) = f ( x ), so all of the signs are the same), then the function is even; if you end up with the exact opposite of what you started with (that is, if f (− x ) = − f ( x ), so all of the signs are switched), then the function is odd.
If the result is neither exactly the same nor exactly opposite (that is, if the result has neither all the same terms nor all the same terms but with opposite signs), then the function is neither even nor odd. Most functions, in fact, will be neither even nor odd.
Which of the 12 functions are even?
Even Functions: The squaring function and the absolute value function. Odd Functions: The identity function, the cubing function, the reciprocal function, the sine function. Neither: The square root function, the exponential function and the log function.
Which function is an odd function?
A function is odd if, for each x in the domain of f, f(−x)=−f(x). Odd functions have 180° rotational symmetry about the origin.
What is an example of a function that isn’t even or odd?
When we think “even and odd,” usually even and odd numbers are what come to mind. But what are even and odd functions? In today’s video, we will define even and odd functions and discuss how to identify them. Let’s begin by talking about even functions. Notice that the shape of this familiar parabola is visibly symmetric. The left and right sides of the plane are identical, just flipped. We can also show that this function is even algebraically, by evaluating at \(-x\), So our original function is \(f(x)=x^ \),
And we said that, if \(f(-x)\) is the same as \(f(x)\), then the function is even. So let’s evaluate at \(-x\), So, wherever there’s an \(x\), we’re gonna plug in \(-x\), So we have: \(f(-x)=(-x)^ \) Which, when you square a negative, it turns positive, so this is equal to: \(f(-x)=(-x)^ =x^ \) So in this case, \(f(-x)=f(x)\),
And because of our definition of even, this function, \(f(x)=x^ \), is even. Notice that if we add a constant to this function, it won’t affect the shape of the function, just raise or lower it on the plane. For example, this is the graph of \(f(x)=x^ +1\), Now let’s talk about what odd functions are like. Consider another function \(f(x)\), which we will once again evaluate at \(-x\), But this time, instead of looking for the same \(f(x)\) we started with, we want to see if \(f(-x)\) changes the sign of all terms in the function.
In other words, if \(f(-x)=-f(x)\), then the function is odd, Graphically, an odd function will appear the same when we rotate it by 180°, like flipping a page upside down, and it must pass through the origin. A few examples of odd functions are: \(f(x)=x\), \(f(x)=x^ \), and \(f(x)=sin(x)\) Let’s take a look at what’s going on here algebraically, using \(f(x)=x^ \) as an example.
So we’re gonna have our original function: \(f(x)=x^ \), And just like before, we’re gonna evaluate it at \(-x\), So we want \(f(-x)\), So anywhere we see an \(x\), we’re gonna plug in \(-x\), \(f(-x)=(-x)^ \) So \((-x)^ \), which is \(-x\cdot-x\cdot-x\), which means, since there are three negatives, our final answer’s gonna be \(-x^ \),
- F(-x)=-x^ \) So if you notice, \(f(x)\) is the opposite of \(f(-x)\),
- Each term, which in this case we only have one, is changed from positive to negative.
- So that means that this function is odd.
- Notice that if we were to add a constant to this function, it would no longer be odd.
- Remember that for odd functions, every term must change signs when evaluating at \(-x\),
That constant term would have no way to change sign, and we would see on the graph that the function would no longer pass through the origin. So we have now talked about definitions of both even and odd functions but before we go further, it’s important to clarify that some functions may be neither even nor odd! For example, take a look at the function \(f(x)=(x+1)^ \), From the graph we can see that this function doesn’t pass through the origin, so it can’t be odd. And it isn’t symmetric about the \(y\) -axis, so it isn’t even either. But we can also determine this algebraically. So our function is \(f(x)=(x+1)^ \), And remember, to determine if it’s even or odd, we want to evaluate it at \(-x\),
- So we have: \(f(-x)=(-x+1)^ \) Which we can write as: \(f(-x)=(-x+1)^ =(-x+1)(-x+1)\) ‘cause that’s what the squared means.
- And then from here we can FOIL.
- So: \(-x\cdot-x=x^ \) \(1\cdot-x=-x\) \(-x\cdot1=-x\) And, \(1\cdot1=1\) So we have: \(f(-x)=x^ -2x+1\) But remember, to determine even or odd, we have to compare this to our original function.
So let’s expand that. So for this, we have: \(f(x)=(x+1)(x+1)\) Which is: \(x⋅x=x^ \) \(1\cdot x=x\text x\cdot1=x,\text 2x\) \(1\cdot1=1\) \(f(x)=(x+1)(x+1)=x^ +2x+1\) Now, when we compare these two functions, we see that only one of the three terms ended up changing signs, so \(f(x)\) is not odd.
And since one term did change sign, \(f(x)\neq f(-x)\), so the function is not even either. Now that we’ve laid a groundwork for understanding even and odd functions, let’s talk about why we call them even and odd in the first place. Remember that even functions are the same when we evaluate them at \(+x\) and at \(-x\),
As we saw earlier, \(f(x)=x^ \) satisfies this property because anytime we square something, a positive value is returned, and therefore the sign of that term doesn’t change even if we plug a negative value in. The same is true when something is raised to the fourth power, or the sixth, and so on.
- Notice that constants do not change sign when we evaluate at \(-x\) either.
- That’s why we saw that the function \(f(x)=x^ +1\) was still even.
- As you can see, an even function will have even exponents,
- It may be unsurprising now that odd functions likewise will have odd exponents ! Remember that in order for a function to be odd, all terms must change sign when we evaluate at \(-x\),
Clearly, any term with \(x\) to the first power will change sign when we plug in a negative value of \(x\), In the same way, \(x\) to the third power, the fifth power, and so on will all change sign when we plug in a negative value for \(x\), As we mentioned earlier, when a term has an even power of \(x\), it will not change sign. Neither. This function is not symmetric about the \(y\) -axis, so it is not even. And even though it passes through the origin, it is not odd either because it would not appear the same if we were to rotate the image 180°. Let’s try another one. Is the function \(f(x)=\frac x^ -2x\) even, odd, or neither? Let’s look at each term.
- First, \(\frac x^ \) has an odd power of \(x\), meaning that the sign will change when evaluated at \(-x\),
- Similarly, the second term, \(-2x\), has an odd power of \(x\) and will also change sign.
- That means this function is odd! Let’s finish with a more conceptual question.
- We know that some functions may be neither even nor odd, but is it possible for a function to be both even and odd? Surprisingly, the answer is yes, but only for one function.
Can you think of what function that is? Remember that for even functions, \(f(-x)=f(x)\), and for odd functions, \(f(-x)=-f(x)\), The only way both of these can be satisfied is when \(f(x)=0\), \(f(-x)=f(x)\) \(and\) \(f(-x)=-f(x)\) As a quick recap, we can identify even and odd functions in the following ways: Graphically, even functions are symmetric about the \(y\) -axis.
- And they don’t have to pass through the origin.
- Though, odd functions must pass through the origin, and they will appear the same when viewed from a 180° rotation.
- Algebraically, even functions are the same when we evaluate at \(+x\) and at \(-x\),
- Odd functions will change signs across all terms when evaluated at \(-x\),
As a shortcut, if a function contains only even exponents of \(x\) (and may or may not have constants) then it is even. If a function has no constants and only odd exponents of \(x\), then it is odd. Now that we’ve covered everything and run through some examples, you should be pretty comfortable with identifying even and odd functions.
Is 0 neither odd nor even?
Zero is an even number. In other words, its parity—the quality of aninteger being even or odd—is even. The simplest way to prove that zero iseven is to check that it fits the definition of ‘even’: it is an integermultiple of 2, specifically 0 × 2.
Is 2.5 odd or even?
Standard Form –
- The standard form to represent the even number and odd numbers are as follows:
- Even Number = 2n
- Odd Number = 2n+1
- Where “n” can be any integer.
Zero is an even number because it obeys all the properties of the even number such as divisibility rule, and number line rule. The number 2.5 is neither even nor odd because it does not obey the property of even and odd numbers. If ” n” is an integer, the even numbers are represented in the form “2n”.
How do you identify odd numbers?
Odd Numbers (Definition, Chart, Properties & Solved Examples) Odd numbers are the numbers that cannot be divided by 2 evenly. It cannot be divided into two separate integers evenly. If we divide an odd number by 2, then it will leave a remainder. The examples of odd numbers are 1, 3, 5, 7, etc.
Is 67 odd or even?
67 (sixty-seven) is the natural number following 66 and preceding 68. It is an odd number.
What makes a function graph even?
A function is said to be an even function if its graph is symmetric with respect to the y-axis. For example, the function f graphed below is an even function. Verify this for yourself by dragging the point on the x-axis from right to left.
What makes a polynomial function even?
A polynomial is even if each term is an even function. A polynomial is odd if each term is an odd function. A polynomial is neither even nor odd if it is made up of both even and odd functions.
What makes a rational function even?
Options: If the signs all stay the same or all change, f(-x) = f(x), then you have even or y-axis symmetry. If either the numerator or the denominator changes signs completely, f(-x)= -f(x) then you have odd, or origin symmetry.
What makes a trig function even?
Key Concepts –
- The tangent of an angle is the ratio of the y -value to the x -value of the corresponding point on the unit circle.
- The secant, cotangent, and cosecant are all reciprocals of other functions. The secant is the reciprocal of the cosine function, the cotangent is the reciprocal of the tangent function, and the cosecant is the reciprocal of the sine function.
- The six trigonometric functions can be found from a point on the unit circle. See Example,
- Trigonometric functions can also be found from an angle. See Example,
- Trigonometric functions of angles outside the first quadrant can be determined using reference angles. See Example,
- A function is said to be even if \(f(−x)=f(x)\) and odd if \(f(−x)=−f(x)\).
- Cosine and secant are even; sine, tangent, cosecant, and cotangent are odd.
- Even and odd properties can be used to evaluate trigonometric functions. See Example,
- The Pythagorean Identity makes it possible to find a cosine from a sine or a sine from a cosine.
- Identities can be used to evaluate trigonometric functions. See Example and Example,
- Fundamental identities such as the Pythagorean Identity can be manipulated algebraically to produce new identities. See Example,
- The trigonometric functions repeat at regular intervals.
- The period \(P\) of a repeating function f f is the smallest interval such that \(f(x+P)=f(x)\) for any value of \(x\).
- The values of trigonometric functions of special angles can be found by mathematical analysis.
- To evaluate trigonometric functions of other angles, we can use a calculator or computer software. See Example,


We study the absolute Galois group by looking for invariants and orbits of its faithful action on Grothendieck’s dessins d’enfants. We deﬁne a class of functions called Belyi-extending maps, which we use to construct new Galois invariants of dessins from previously known invariants. Belyi-extending maps are the source of “new-type” relations on the injection of the absolute Galois group into the Grothendieck–Teichmüller group. We make explicit how to get from a general Belyi-extending map to formula for its associated invariant which can be implemented in a computer algebra package. We give an example of a new invariant differing on two dessins which have the same values for the other readily computable invariants.
Cite this article
Melanie Matchett Wood, Belyi-Extending Maps and the Galois Action on Dessins d’Enfants. Publ. Res. Inst. Math. Sci. 42 (2006), no. 3, pp. 721–737DOI 10.2977/PRIMS/1166642157


You have 15 sticks of length 1cm, 2cm, ..., 15cm (one of each length). How many triangles can you make by picking three sticks and joining their ends?
Note: Three sticks (eg 1, 2 and 3) lying on top of each other does not count as a triangle.
Note: Rotations and reflections are counted as the same triangle.
If you write out the numbers from 1 to 1000 (inclusive), how many times will you write the digit 1?
Not Roman numerals
The letters \(I\), \(V\) and \(X\) each represent a different digit from 1 to 9. If$$VI\times X=VVV,$$
what are \(I\), \(V\) and \(X\)?
The sequence of six numbers above has two properties:
- Each number is either 0, 1 or 2.
- Each pair of consecutive numbers adds to (strictly) less than 3.
Today's number is the number of sequences of six numbers with these two properties
In base 2, 1/24 is 0.0000101010101010101010101010...
In base 3, 1/24 is 0.0010101010101010101010101010...
In base 4, 1/24 is 0.0022222222222222222222222222...
In base 5, 1/24 is 0.0101010101010101010101010101...
In base 6, 1/24 is 0.013.
Therefore base 6 is the lowest base in which 1/24 has a finite number of digits.
Today's number is the smallest base in which 1/10890 has a finite number of digits.
Note: 1/24 always represents 1 divided by twenty-four (ie the 24 is written in decimal).
Put the digits 1 to 9 (using each digit exactly once) in the boxes so that the sums are correct. The sums should be read left to right and top to bottom ignoring the usual order of operations. For example, 4+3×2 is 14, not 10. Today's number is the smallest number you can make using the digits in the red boxes.
Today's number is the sum of all the numbers less than 40 that are not factors of 40.


...That's the goal: success! My goal is to provide you with the necessary tools to be successful. I understand that math is challenging.
Prospect Heights, ILView Tutor
...I strongly believe that students have the ability to succeed in any academic subject or standardized exams if they have the proper guidance and a willingness to put forth consistent effort in their work. As a tutor, I will do my best to help achieve mastery and success. If you are interested in...
Downers Grove, ILView Tutor
I am an educator who enjoys teaching and interacting with students. I have over 10 years of experience in the classroom as well as an administrator. I've taught 6th-8th grade math and I have expertise in Pre-Algebra, Algebra 1, Honors Algebra 1, Geometry and Honors Geometry.
Homewood, ILView Tutor
...Know that I am very much looking forward to meeting you! Please let me know if you have additional questions, and I will be sure to promptly answer them. I have grown up my entire life playing, coaching, or watching football.
Chicago, ILView Tutor
...As a substitute teacher in two different school districts working in one for six years and one for two years and being a recently certified K-9 teacher I always enjoy teaching Geometry. It is the one Math subject where you get to use three dimensional shapes, work with lies and shapes and triang...
Bolingbrook, ILView Tutor


ESTIMATES OF THE BERGMAN KERNEL FUNCTION ON PSEUDOCONVEX DOMAINS WITH COMPARABLE LEVI FORM Cho, Sang-Hyun;
Let be a smoothly bounded pseudoconvex domain in and let b a point of finite type. We also assume that the Levi form of b is comparable in a neighborhood of . Then we get precise estimates of the Bergman kernel function, (z, w), and its derivatives in a neighborhood of . .


The indicated function y1(x) is a solution of the given differential equation.
Use reduction of order or formula (5) in Section 4.2,
y2 = y1(x) e−∫P(x) dx y 2 1 (x) dx (5)
as instructed, to find a second solution y2(x). y'' + 100y = 0; y1 = cos 10x
I've gotten to the point all the way to where y2 = u y1, but my integral is wrong for some reason
This was my answer
y2= c1((sin(20x)+20x)cos10x)/40 + c2(cos(10x))
Get Answers For Free
Most questions answered within 1 hours.


Date of Award
Open Access Dissertation
College of Education
Doctorate of Education, Ed.D.
Belle B. Booker-Zorigian, Ph.D.
Joanna Gilmore, Ph.D.
Alecia C. Eubanks, Ph.D.
mindset, religiosity, achievement, math achievement, bioecological model
Growth mindset and religiosity as separate constructs have been shown to increase student achievement. This study sought to discover if a relationship existed between religiosity and mindset, as well as if mindset or religiosity could predict math achievement. A mixed methods study, guided by Brofenbrenner’s bioecological model, was conducted. This non-experimental quantitative study found a small statistically significant relationship between mindset and religiosity (p < .05). However, religiosity and mindset were not correlated with math achievement; therefore, these constructs could not be used to predict math achievement. Focus group interviews were used to further study the relationship between mindset and religiosity. Students were asked to describe how they developed both their mindset and religiosity beliefs, and then to discuss how these constructs work, both together and separately, to impact academic achievement. Through In Vivo and Process coding, two themes and one key assertion emerged from the interviews. Theme 1: Environmental factors impact religiosity and mindset. Theme 2: Religiosity and mindset impact academic success. Key Assertion: Religiosity and mindset are two distinct yet harmonious constructs within adolescents. Religiosity and mindset influence each other as students grow, develop, and achieve in school.
CU Commons Citation
Luebke, Kathryn, "Religiosity, Mindset, and Math Achievement" (2019). Ed.D. Dissertations. 305.


Math Interactive Notebook 6Th Grade. Interactive math notebook for second grade go math chapter 6. 6th grade math interactive notebook pdf.
Page 1 cornell notes for. Ad nurture your 6th grader's curiosity in math, english, science, and social studies. Hints for implementing math notebooks 5.
A Digital Interactive Notebook Allows You To Take Cut And Paste, Sorting, Or Matching Interactive Activities And Allow Them To Be Completed.
6th grade math interactive notebook. The interactive notebook is more than a notebook in which to take notes. This notebook is absolutely amazing!
Vocabulary For Every Sixth Grade Math Standard Is Covered.
Ad bring learning to life with thousands of worksheets, games, and more from education.com. History digital interactive notebook from teachingideas4u.com try free for 30 days. Notify me when this product is available:
Page 1 Cornell Notes For.
Sixth grade math interactive notebook bundle all. 6th grade math interactive notebook. This is a for my 6th grade math interactive notebook.
It Will Replace Your Math Textbook.
6th grade math interactive notebook from www.exploremathindemand.com this is a whole years worth of interactive Each page has the common core standard and activity that goes along with the standard. This is a whole years worth of interactive notebook for 6th grade math.
The First Page Is More Aimed Towards Direct Instruction / Notes.
Math notebook cover template 4. There are 5 units (6 units including unit 0). 6th grade math interactive notebook free.
Related Posts for Math Interactive Notebook 6Th Grade
- Create Your Own Culture Project
- Ode To Family Photographs Answer Key
- Oh Deer Door Decoration
- Lowercase C In Cursive
- Amoeba Sisters Meiosis Worksheet Answer Key
- Under The Sea Sign
- Cross Section Worksheet Form A Answer Key Pdf
- Biography Rubric 4Th Grade
- Weirdo Graphic Organizer Subjuntive
- Staar Review Algebra 1


Model reconstruction from temporal data for coupled oscillator networks.
In a complex system, the interactions between individual agents often lead to emergent collective behavior such as spontaneous synchronization, swarming, and pattern formation. Beyond the intrinsic properties of the agents, the topology of the network of interactions can have a dramatic influence over the dynamics. In many studies, researchers start with a specific model for both the intrinsic dynamics of each agent and the interaction network and attempt to learn about the dynamics of the model. Here, we consider the inverse problem: given data from a system, can one learn about the model and the underlying network? We investigate arbitrary networks of coupled phase oscillators that can exhibit both synchronous and asynchronous dynamics. We demonstrate that, given sufficient observational data on the transient evolution of each oscillator, machine learning can reconstruct the interaction network and identify the intrinsic dynamics.
Panaggio, MJ; Ciocanel, M-V; Lazarus, L; Topaz, CM; Xu, B
Volume / Issue
Start / End Page
Electronic International Standard Serial Number (EISSN)
International Standard Serial Number (ISSN)
Digital Object Identifier (DOI)


A motorcycle traveling at 30 m/s comes to a stop over a distance of 150 m. What was the motorcycle's acceleration?
The Attempt at a Solution
I tried plugging in what I know.
Then I divided 150 m and 900 by 150:
This yields an answer of -4. It doesn't seem right, but I can't place why. I think I may have needed to divide the v^2 by 150, but that's 0/150, which wouldn't make sense. Thanks in advance for a reply!


Design your own scoring system and play Trumps with these Olympic Sport cards.
Here is a version of the game 'Happy Families' for you to make and play.
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
Can you make the birds from the egg tangram?
Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?
Take it in turns to make a triangle on the pegboard. Can you block your opponent?
Have a go at this game which has been inspired by the Big Internet Math-Off 2019. Can you gain more columns of lily pads than your opponent?
Board Block game for two. Can you stop your partner from being able to make a shape on the board?
Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.
This article, the second in the series, looks at some different types of games and the sort of mathematical thinking they can develop.
This article supplies teachers with information that may be useful in better understanding the nature of games and their role in teaching and learning mathematics.
A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.
A game for two players on a large squared space.
An interactive activity for one to experiment with a tricky tessellation
The game uses a 3x3 square board. 2 players take turns to play, either placing a red on an empty square, or changing a red to orange, or orange to green. The player who forms 3 of 1 colour in a line. . . .
A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.
Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?
A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.
A Sudoku with clues given as sums of entries.
A game for 2 players. Take turns to place a counter so that it occupies one of the lowest possible positions in the grid. The first player to complete a line of 4 wins.
An old game but lots of arithmetic!
A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.
The computer starts with all the lights off, but then clicks 3, 4 or 5 times at random, leaving some lights on. Can you switch them off again?
Try this matching game which will help you recognise different ways of saying the same time interval.
In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?
How long does it take to brush your teeth? Can you find the matching length of time?
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?
Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?
Spiralling Decimals game for an adult and child. Can you get three decimals next to each other on the spiral before your partner?
Gillian Hatch analyses what goes on when mathematical games are used as a pedagogic device.
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
Here is a chance to play a version of the classic Countdown Game.
An extension of noughts and crosses in which the grid is enlarged and the length of the winning line can to altered to 3, 4 or 5.
Everthing you have always wanted to do with dominoes! Some of these games are good for practising your mental calculation skills, and some are good for your reasoning skills.
This is an adding game for two players.
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
A game for two players. You'll need some counters.
A fun game for two. You'll need some counters.
Board Block Challenge game for an adult and child. Can you prevent your partner from being able to make a shape?
In this article for teachers, Liz Woodham describes the criteria she uses to choose mathematical games for the classroom and shares some examples from NRICH.
Here are a collection of games from around the world to try during the holidays or the last few weeks of term.
You'll need two dice to play this game against a partner. Will Incey Wincey make it to the top of the drain pipe or the bottom of the drain pipe first?
Who said that adding couldn't be fun?
Can you work out how to win this game of Nim? Does it matter if you go first or second?
This challenge is a game for two players. Choose two of the numbers to multiply or divide, then mark your answer on the number line. Can you get four in a row?
We think this 3x3 version of the game is often harder than the 5x5 version. Do you agree? If so, why do you think that might be?
What might your first lesson with a new class look like? In this article, Cherri Moseley makes some suggestions for primary teachers.
Use the tangram pieces to make our pictures, or to design some of your own!
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.


Every Tuesday we send out an email to every employee with information from the district This email...
We are excited to announce three mathematics summer professional learning courses for 2019! Note that all locations will offer participants the chance to engage in either the elementary or secondary Mathematics for All Students course on Monday and Tuesday AND THEN the What the Tech? course on Wednesday and Thursday for a fluid four day run of fantastic mathematics-centric professional learning! See below for course details, dates, and locations.
Each course participant will receive the following:
Copy of MTSS in Mathematics Framework Triple EEE Framework Opportunity to collaborate with colleagues Opportunity to earn a $150 stipend via completion of a project related to the course (thanks to the STEM Action Center’s generous donation).
Sign up in MIDAS today using the course codes next to each course!
Elementary Mathematics For All Students (Course #50652):
Re-invigorate your math instruction by coming together to collaborate with teachers, engage with rich mathematics tasks, and apply key practices to your own math classroom. Leave with concrete strategies you can use to enhance your planning, instruction, and assessment to create an equitable learning environment that enables all of your students to succeed in mathematics.
Secondary Mathematics for All Students (Course #52312):
Participants will learn to apply the Utah Multi-Tiered System of Support (UMTSS) framework to increase student learning of mathematics and promote high expectations for each and every student. The sessions will focus on practical strategies to implement high quality math tasks in an accessible way, elicit student thinking, and support productive struggle. Discussions and activities will integrate and encompass the critical components of the UMTSS framework: High-quality Instruction, Team-based Problem Solving, and Data-based Decision Making.
What the Tech? Improving the Efficacy of Your Mathematics Classroom (Course #52275):
What the heck is “What the Tech”? In this course, mathematics plays the lead role with technology as the supporting actor. Come learn about what makes a mathematics classroom effective, how to incorporate technology into a mathematics classroom strategically and how to evaluate what’s working and what is not. Novice to expert tech users from grades K-12 will be engaged in the use of digital tools to provide opportunities for students to reason critically, communicate effectively, and model mathematical concepts using multiple representations. (Click on the link in the course title for an advertisement video.)
Each two-day course will cost $25 and will get participants lunch on both days, resources, and MIDAS credit.
Courses will run during the following dates and locations from 8:00 a.m. – 4:00 p.m. each day:
Mathematics for All Students: Monday and Tuesday (or Tuesday and Wednesday)
What the Tech?: Wednesday and Thursday (or Thursday and Friday)
- May 28-31, 2019 (Tuesday-Friday) Nebo School District
- June 3-6, 2019 (Monday – Thursday) Iron County
- June 3-6, 2019 (Monday – Thursday) Davis School District
- June 10-13, 2019 (Monday – Thursday) Washington County
- June 17-20, 2019 (Monday – Thursday) Cache County
- June 17-19, 2019 (Monday – Thursday) San Juan County
- June 24-27, 2019 (Monday – Thursday) Salt Lake
- June 24-27, 2019 (Monday – Thursday) Alpine
If you have any questions about these courses, please reach out to
Shannon Ference for Elementary Mathematics (email@example.com),
Joleigh Honey for Secondary Mathematics (firstname.lastname@example.org) and,
Nathan Auck for What the Tech? (email@example.com)


Actually my teaching method is step by step trying to teach the students and clearing their doubts , first every student should understand the topic/step .
I would prefer to teach students of 9,10,11 & 12 (science) i would love to teach them
I am an mechanical engg., I always loved maths from the beginning ,also i loved to teach maths to my friends ,till now i have not have any experience in teaching , but i would love teaching.
maths lessons closeby? Here's a selection of tutor listings that you can check out.
Superprof can also suggest algebra lessons to help you.
Learning isn't a problem, arithmetic lessons for all!
Taking geometry lessons has never been easier: you're going to learn new skills.
|at his home||at your home||By webcam|
|1 hour||Not available||Not available||RM34|


Its been a long time since I needed to understand algebra and when it came time to helping my son, I couldnt do it. Now, with your algebra software, we are both learning together. D.H., Tennessee
I do not have any issues. I just wanted to let you know that I am glad I purchased your product. I also appreciate the updates as they not only make for a better looking product, but things seem to be more user friendly now. Sonya Johnson, TX
What a great friendly interface, full of colors, witch make Algebra Buster software an easy program to work with, and also it's so easy to work on, u don't have to interrupt your thoughts stream every time u need to interact with the program. Christian Terry, ID.
I liked the detailed, clearly explained step by step process that Algebra Buster uses. I'm able to go into my class and follow along with the teacher; it's amazing! Carl J. Oldham, FL
Students struggling with all kinds of algebra problems find out that our software is a life-saver. Here are the search phrases that today's searchers used to find our site. Can you find yours among them?
Search phrases used on 2009-04-09 :
second order linear homogenous ODE solve
2nd order runge kutta matlab
7th grade sample slope intercept problems
technique in solving fractions
geometry cheat sheets
online division solver
elimination method rules-math
mcdougal littell geometry answers
how to make a factoring program on a graphing calculator


Math Magic Square Worksheet – Through the thousands of photographs on the web with regards to math magic square worksheet
, choices the top series with best quality exclusively for you all, and now this photos is usually one among pictures choices within our finest photographs gallery regarding Math Magic Square Worksheet. I really hope you’ll want it.
This particular impression (Math Magic Square Worksheet Lovely 7 Best Math Puzzle Boxes Images On Pinterest) previously mentioned can be classed having: math magic,math magic indesign,math magic sticks,math magician,math magician division,math magician multiplication,
placed through Layla with 2018-08-18 04:55:18. To discover all photos throughout Math Magic Square Worksheet pictures gallery you should adhere to that url.
The Most Elegant as well as Interesting math magic square worksheet
intended for Inspire The house Found Property|Inviting DesireHouse
Math Magic Square Worksheet Lovely 7 Best Math Puzzle Boxes Images On Pinterest Uploaded by Layla on Saturday, August 18th, 2018 in category Multiplication Worksheets Grade 5.
Here we have another image Math Magic Square Worksheet Awesome Magic Number Math Worksheet featured under Math Magic Square Worksheet Lovely 7 Best Math Puzzle Boxes Images On Pinterest. We hope you enjoyed it and if you want to download the pictures in high quality, simply right click the image and choose "Save As". Thanks for reading Math Magic Square Worksheet Lovely 7 Best Math Puzzle Boxes Images On Pinterest.


Now showing items 1-2 of 2
MLFMA solutions of transmission problems Involving realistic metamaterial walls
We present the solution of multilayer metamaterial (MM) structures containing large numbers of unit cells, such as split-ring resonators. Integral-equation formulations of scattering problems are solved iteratively by ...
Solutions of large integral-equation problems with preconditioned MLFMA
We report the solution of the largest integral-equation problems in computational electromagnetics. We consider matrix equations obtained from the discretization of the integral-equation formulations that are solved ...


It is a great idea to start introducing various concept to your child once they turns one. You can also point out simple objects or things they encounter in their daily lives. Here are some tips that will help you to teach preschoolers through a nice creative and educational exercise.
Toddlers and preschoolers only start associating objects with certain colors, sizes, and shapes. How to help them to develop logical thinking? With ‘Odd one out’ game – they can classify objects based on known concepts which depends upon visualization, comparison and discrimination.
An understanding of numbers helps children to learn, count and develop a basic sense of how numbers function. Understanding of numbers prepares preschoolers for the more complex mathematical tasks that they will face in their school years.


These fortune tellers are a fun way for students to practice basic multiplication facts. They can be sent home for students to practice with parents or friends, or can be laminated and used as a math center. Each page includes instructions for cutting and folding the fortune teller. I have used these with third, fourth, and fifth graders and all students have enjoyed using these fortune tellers to study.
Preview is of the 0's fortune teller that is available in my TpT store. This product is the 5's fortune teller.
Check out my other fortune tellers to help your students practice their multiplication facts!


Effective ways of studying algebra include reading the complete question, drawing diagrams, learning to use a calculator and starting over where necessary. When faced with a difficult problem when taking a practice test, continue with the test and return to the problem later.
First, reading math problems carefully and completely helps to give a clear idea of what is expected and the calculations required to arrive at an answer. Next, draw a diagram whenever possible. This helps to get a visual image of the problem and to see the problem objectively. This visual approach also adds auxiliary lines or labels for ideas on how to solve the problem.
Knowing how and when to use a calculator helps to get more accurate answers. It is a good idea to use the same calculator whenever possible. Read the instruction manual carefully to be conversant with the different applications.
Start a problem over again on a new sheet of paper when met with incorrect answers. Spending too much time attempting to find the error in the calculations is a time consuming process, risks overlooking the mistake and also takes the focus away from the question.
Lastly, keep the workspace and paper clean and easy to read. All work on the paper, including equations, diagrams, calculations and explanations should be written down clearly for the best result. Keeping organized also helps the student trace the correct line of thinking on the page when she finds the correct answer.


Published at Tuesday, August 18th 2020, 13:56:04 PM by Trinetta Klein. Kindergarten Worksheets. This sounds like an awful lot, does not it! A good set of preschool worksheets should cover all of this, and more. In the preschool years, repetition is the key to learning, but you should look for worksheets that teach the same skills in a variety of ways. This not only prevents boredom setting in, but also reinforces the concepts by encouraging understanding as well. The importance of reading to your child cannot be emphasised enough, and you should encourage them to read as much as possible too.
Published at Friday, August 21st 2020, 06:24:51 AM by Madelon Roche. Kindergarten Worksheets. Math is a basic subject and hence, it is included in the curriculum from the kindergarten level. However, doing math is not at all a good experience for all students. The subject needs more concentration and step-by-step understanding. Students cannot follow the same methodology for math preparation as they generally do for other subjects including geography, chemistry, physics and others. Math needs more practice and this is one of the subjects in which students can score well and improve their overall grades in exams. This subject has broad real life applications from purchasing groceries to maintaining bank transactions. We use math everywhere. We start learning math from our childhood days, for example counting flowers and birds with our parents. Moreover, some students face difficulties while solving math and to overcome these learning problems, some steps are discussed below.
Published at Sunday, August 23rd 2020, 11:58:35 AM. Kindergarten Worksheets By Voleta Leroy. There is one learning style that is absolutely essential if young children are to learn effectively. Children demonstrate their love of this approach on a daily basis often to the accompaniment of hair being torn out by frustrated parents. Young children are hands on learners. Nothing is usually too hot or too heavy. This tactile approach to life in general is their way of discovering and processing information about the world around them. "Children are born true scientists. They spontaneously experiment and experience and re-experience again. They select, combine, and test, seeking to find order in their experiences - "which is the moistest? which is the least-est? They smell, taste, bite, and touch-test for hardness, softness, springiness, roughness, smoothness, coldness, warmness: they heft, shake, punch, squeeze, push, crush, rub, and try to pull things apart."
Published at Sunday, August 23rd 2020, 11:57:37 AM. Kindergarten Worksheets By Harriett Leroux. Play is how children utilize this particular learning style. Play is one of the most powerful vehicles for facilitating learning. When you play with your child you are demonstrating how much you value them and enjoy their company. This helps build self-esteem and many studies now reveal that children with high emotional intelligence will outperform children with higher IQ but lower self esteem. In the UK questions are being asked regarding whether children are given enough time to simply play. The pattern seems to be that children are given more time to play during their early years in school but towards the middle years a more formal approach dominates their school day. Emeritus Professor Barbara argues that the tendency for state education to focus on a more formal, left-brain orientated approach to learning can have disastrous implications for a significant percentage of children, particularly boys, who tend to be predominantly tactile learners.
Published at Sunday, August 23rd 2020, 11:48:23 AM. Kindergarten Worksheets By Fantine Leduc. Once you have a scope and sequence book, make a list of each area in math that he needs to work on for the school year. For example for grades three and four, by the end of the year in subtraction, your child should be able to: Solve vertical and horizontal computation problems, Review subtraction of 2 numbers whose sums would be 18 or less, subtract 1- or 2-digit number from a 2-digit number with/without renaming, subtract 1-, 2-, or 3-digit numbers from 3- and 4-digit number with/without renaming, Subtract 1-, 2-, 3-, 4-, or 5-digit number from a 5-digit number. When you have this list, begin searching online for free math worksheets that fit your child has scope and sequence for the year and the goals you have set for your child.
Published at Sunday, August 23rd 2020, 11:45:32 AM. Kindergarten Worksheets By Laverna Lacombe. With adaptive learning programs, your child will not just play one level and complete the program. The games offer a comprehensive learning tool that works with kids from kindergarten through third grade. With hundreds of levels, different ways to play and constant interaction, the online games never lose their meaning. The same children can play the games but in different ways, since the programs are tailored toward the learning styles of each child. This is what makes adaptive learning an essential tool in classrooms as well. For 3rd grade math, you can expect a balance of fractions, graphs, money and multiplication that challenge the mind with each lesson. If you are unsure about investing in a particular program, try a program with a free trial. By implementing these valuable learning aids, you can help your child make the most of third grade.
Published at Sunday, August 23rd 2020, 11:45:14 AM. Kindergarten Worksheets By Nicolette Guillon. All my toys were one way or the other math related. I had puzzles, and tons of things Mom had me do as games on daily basis at home to get me ready for kindergarten! In fact, she continued guiding me towards being math friendly throughout kindergarten and first grade during which time 1st grade math worksheets was my constant companion.Practice surely makes perfect and I am very gratefully to Mom for taking her time to familiarize me with math even as a child. As a math tutor for 15 years, I have tutored hundreds of students from all the grade levels. I found most of the students were not comfortable with mathematics. More than 80% of them said, the mathematics is very hard. Why do most of the students find mathematics a hard subject and try to avoid it?
Published at Sunday, August 23rd 2020, 11:43:57 AM. Kindergarten Worksheets By Trinetta Klein. Patterns and sequencing and basic addition and subtraction should follow on from counting and number recognition. By the time your child is starting kindergarten or school, they should be able to count to 20 with ease, write numbers, do simple addition sums, and have some understanding of patterns and sequences. Even if they are attending preschool, extra practice at home will help them improve their math. A systematic set of mathematics worksheets will help you teach your child the basic principles of math and help them prepare for school. Worksheets can be used as the basis for counting and adding games and other activities. Teaching your child with worksheets also makes them more comfortable with doing worksheets - which will help them when they get to kindergarten and school, where worksheets are used every day.
Published at Sunday, August 23rd 2020, 11:40:15 AM. Kindergarten Worksheets By Fanetta Andre. A systematic set of mathematics worksheets will help you teach your child the basic principles of math and help them prepare for school. Worksheets can be used as the basis for counting and adding games and other activities. Teaching your child with worksheets also makes them more comfortable with doing worksheets - which will help them when they get to kindergarten and school, where worksheets are used every day.


BIOL398-03/S13:Class Journal Week 14
- Kevin McKay
- I feel that there is mathematics behind every phenomena in life that one could ever hope to study or understand, this obviously includes the science of life or biology. If one wishes to understand or make connections between data or observations of biology, a great way to analyse this data is with math. Using math in biological questions allows us to see the randomness and the orderliness of life.
- Looking back at the readings and the answers I gave to the questions for week 1, I have no new insights or answers to share. My answers remain the same, I still see myself as a biologist and a mathematician. Although over the past weeks in this class, my outlook on bio math has changed. I have gained a sense of the reality of biomath and the hard work that goes into it. I have gained an appreciation for how difficult this field of study really is. Analyzing biology with math seems to me a bit more complicated now as compared with analyzation of physical properties such as gravity. Biology is always changing, whereas gravity is a constant 9.81 Newtons per kilogram downwards. I have also learned that this type of work that involves this much use of computers is not really for me (although I did have an idea of this before the class).
Kevin Matthew McKay 15:28, 25 April 2013 (EDT)
James P. McDonald Week 14
- What is the value of combining biological and mathematical approaches to scientific questions?
- Combining biological and mathematical approaches gives multiple perspectives on a question and allows for a more complete solution to a scientific problem. A very important aspect of combining biological and mathematical approaches is that it allows for both qualitative and quantitative analysis and solutions. Math has the ability to take a biological observation or result and put it into a equation. A math equation can take a qualitative observation and make it into a quantitative explanation, which can easily be manipulated and analyzed to answer scientific questions. This can be very beneficial in doing research because you can make predictions and experiments can be reproduced with ease.
- Looking back on your reflections on the Janovy and Steward readings from the Week 1 Class Journal, do you have any further insights to share? Have your answers changed to those original reflection questions? Why or why not?
- When it comes to being a mathematician I now understand more of what Stewart was talking about. Stewart states that a mathematician more often sees the math that is taking place all the time around us. This class has shown me that math can be used, in addition to biology, to analyze and solve scientific questions. I originally would not have recognized the potential math that could be used in the biological processes we have looked at. In regards to the answers in my original reflection, my answer to the biologist question has not changed. I tend to thing of science in biological terms before anything else and this has not changed. But in regards to being a mathematician I am still not sure whether I would say I am one, but I have definitely seen the potential that mathematical approaches have. I have tried to learn to think more in mathematical terms and I think I will start to think more in terms of mathematical approaches in the future.
James P. McDonald 18:55, 25 April 2013 (EDT)