Researchers: Deniz Ustebay (Ph.D. Student), Boris Oreshkin (Ph.D. Student), Prof. Mark Coates & Prof. Mike Rabbat
Distributed consensus has been identified as a canonical problem in both the distributed signal processing and control communities. The prototypical example of a consensus problem is computation of the average consensus: in a network, initially each node has a scalar data value and the goal is to find a distributed algorithm that asymptotically computes the average at every node. Such an algorithm can further be used for computing linear functions of the data and can be generalized for averaging vectorial data.
In this study we propose a new randomized gossip algorithm, greedy gossip with eavesdropping (GGE), for the computation of average consensus. Unlike previous randomized gossip algorithms, which perform updates completely at random, GGE takes advantage of the broadcast nature of wireless communications and implements a greedy neighbor selection procedure. We assume a broadcast transmission model such that all neighbors within range of a transmitting node receive the message. Thereby, in addition to keeping track of its own value, each node tracks its neighbors values by eavesdropping on their transmissions. At each iteration, the activated node uses this information to greedily choose the neighbor with which it will gossip, selecting the neighbor whose value is most different from its own. Accelerating convergence in this myopic way does not bias computation and does not rely on geographic location information, which may change in networks of mobile nodes.
Although GGE is a powerful yet simple variation on gossip-style algorithms, analyzing its convergence behavior is non-trivial. The main reason is that each GGE update depends explicitly on the values at each node (via the greedy decision of with which neighbor to gossip). Thus, the standard approach to proving convergence to the average consensus solution (i.e., expressing updates in terms of a linear recursion and then imposing properties on this recursion) cannot be applied to guarantee convergence of GGE. To prove convergence, we demonstrate that GGE updates correspond to iterations of a distributed randomized incremental subgradient optimization algorithm. Similarly, analysis of the convergence rate of GGE requires a different approach than the standard approach of examining the mixing time of a related Markov chain. We develop a bound relating the rate of convergence of GGE to the rate of standard randomized gossip. The bound indicates that GGE always converges faster than randomized gossip, a finding supported by simulation results. We also provide a worst-case bound on the rate of convergence of GGE. For other gossip algorithms the rate of convergence is generally characterized as a function of the second largest eigenvalue of a related stochastic matrix. In the case of GGE, our worst-case bound characterizes the rate of convergence in terms of a constant that is completely determined by the network topology. We investigate the behavior of this constant empirically for random geometric graph topologies and derive lower bounds that provide some characterization of its scaling properties.
We also show that the improvement achieved using GGE over standard randomized gossip (i.e., exchanging information equally often with all neighbors) is proportional to the maximum node degree. Thus, for network topologies such as random geometric graphs, where node degree grows with the network size, the improvements of GGE scale with network size, but for grid-like topologies, where the node degree remains constant, GGE yields limited improvement. We propose an extension to GGE, which is called multi-hop GGE, that improves the rate of convergence for grid-like topologies. Multi-hop GGE relies on increasing artificially neighborhood size by performing greedy updates with nodes beyond one hop neighborhoods. We show that multi-hop GGE converges to the average consensus and illustrate via simulation that multi-hop GGE improves the performance of GGE for different network topologies.
D. Ustebay, B. Oreshkin, M.J. Coates and, M. Rabbat, Multi-hop Greedy Gossip with Eavesdropping, to appear, in Proc. Int. Conf. on Information Fusion, Seatle, WA, USA, July 2009.
D. Ustebay, B. Oreshkin, M.J. Coates and, M. Rabbat, Greedy Gossip with Eavesdropping, Technical Report, Department of Electrical and Computer Engineering, McGill University, Montreal, QC, Canada, 2009.
D. Ustebay, B. Oreshkin, M. Coates and, M. Rabbat, The Speed of Greed: Characterizing Myopic Gossip through Network Voracity, in Proc. of IEEE Int. Conf. on Acoustics, Speech, and Signal Processing (ICASSP), Taipei, Taiwan, April 2009.
D. Ustebay, B. Oreshkin, M. Coates and, M. Rabbat, Rates of Convergence for Greedy Gossip with Eavesdropping, in Proceedings of the Forty-Sixth Annual Allerton Conference on Communication, Control, and Computing, IL, USA, September 2008.
D. Ustebay, M. Coates and, M. Rabbat, Greedy Gossip with Eavesdropping, in Proceedings of the IEEE International Symposium on Wireless Pervasive Computing, Santorini, Greece, May 2008.


Nasah is a Postdoctoral Researcher in the Department of Applied and Computational Mathematics and Statistics (ACMS) and a research statistician at the Children's Environmental Health Initiative (CEHI) at the University of Notre Dame in South Bend, Indiana. He received his Ph.D. in Statistics in 2021 from Temple University in Philadelphia, Pennsylvania, and his M.S. in Mathematical Science in 2016 from East Tennessee State University in Johnson City, Tennessee. Prior to graduate school, he received his B.S. in Actuarial Science in 2012 from Kwame Nkrumah University of Science and Technology in Kumasi, Ghana.


For a freely propagating stable particle, the amplitude associated with an infinitesimal path segment dC — its end points given by the coordinates (x,y,z,t) and (x+dx,y+dy,z+dz,t+dt) — was found to be Z(dC) = [1: −b ds], with ds = √dt² − (dx² + dy² + dz²)/c². We know now that ds is an interval of (proper) time, so the physical dimension of the particle-specific constant b is that of a frequency. To convert it to energy units we have to divide it by ℏ, and to further convert it to its conventional mass units, we have to multiply it by c2. Once this is done, we use the letter m and write
(2.16.1) Z(dC) = [1: −(mc2/ℏ) ds].
(The famous formula E=mc2 is as unexciting as any conversion formula, for E and m are the same physical quantity, except that once it is measured in conventional units of energy and once in conventional units of mass.)
From particles as clocks to the principle of least action
Let us follow a particle as it travels from (A,tA) to (B,tB) along C, and let s stand for the proper time that has passed since its departure at (A,tA). As s increases, the complex number [1: −(mc2/ℏ) s] — an arrow of unit magnitude — rotates in the plane of complex number (the “complex plane,” for short). As suggested by Feynman, we may think of this rotating arrow as a clock. Though a feature of the quantum-mechanical probability calculus rather than a feature of the physical world, this clock reveals a deep connection between the quantum-mechanical probability calculus and the metric properties of the physical world. For what makes it possible to use a global system of spacetime units is the fact that the rates at which free particles “tick” in their momentary rest frames — which is to say, their masses — are constant. This is the reason why we can use meters and seconds everywhere and “everywhen,” secure in the knowledge that a second or meter here and now is equal to second or meter there and then.
A general way of accommodating influences on the behavior of a stable particle (albeit not the most general, as we shall see) is to modify the rate at which it “ticks.” It is customary to write the modified amplitude associated with an infinitesimal path segment dC in the form
(2.16.2) Z(dC) = [1:dS/ℏ],
where the infinitesimal increment dS of the so-called action S is a function of x, y, z, t, dx, dy, dz, and dt, which has to satisfy the following conditions:
- Like ds, dS must be invariant under Lorentz transformations. Otherwise it would not be the case that all inertial coordinate systems are “created equal”: the behavior of a particle (encapsulated by dS) would depend on the language (the inertial frame) we use to describe it.
- dS must be “homogeneous” in the following sense: multiplying by a factor u each of the infinitesimal coordinate intervals on which dS depends is equivalent to multiplying dS itself by u. This is a consequence of two facts: the multiplication of two complex numbers of unit magnitude is equivalent to the addition of their phases, and the amplitude associated with consecutive path segments is the product of the amplitudes of the individual segments.
With (2.16.2), the particle propagator takes the form
(2.16.3) <B,tB|A,tA> = ∫DC [1:∫C dS/ℏ].
One may be tempted to ask: what is the probability of finding that a particle with this propagator has traveled from (A,tA) to (B,tB) via a specific path C? Since the magnitude of the amplitude [1:∫C dS/ℏ] is the same for all paths (namely, 1), that probability seems to be the same for all paths. It is, however, strictly impossible to ascertain that a particle has traveled via a precise path. We obtain a more useful answer if we make the half realistic assumption that what can be ascertained is whether a particle has traveled from (A,tA) to (B,tB) inside a narrow bundle of paths.
Imagine a narrow “tube” T “filled” with paths whose endpoints are (A,tA) and (B,tB). The probability of finding that the particle has traveled inside T is (formally) given by the squared magnitude of
(2.16.4) ∫T DC [1:∫C dS/ℏ],
which sums the amplitudes of all paths contained in T. To make sure that a single path is obtained in the so-called classical limit, in which quantum physics degenerates into classical physics, we assume that there is a unique path G from (A,tA) to (B,tB) for which the action S(C) = ∫C dS is stationary: it does not change under infinitesimal deformations (“variations”) of G. We will consider two cases:
(1) G is contained in T. Because the action is stationary for G, T contains a large number of paths with almost equal amplitudes (think arrows in the complex plane). As a consequence, the magnitude of the sum of these arrows is almost as large as the sum of their magnitudes. This is illustrated by the almost straight chain of arrows in Fig. 2.16.1.
(2) G is not contained in T. In this case the arrows contributed by the paths in T are more or less equally distributed over all directions in the complex plane. As a result, the magnitude of the sum (2.16.4) is small by comparison. This is illustrated by the coiled chain of arrows in Fig. 2.16.2.
If we let ℏ go to zero (ℏ→0), the probability of finding that the particle has traveled inside T goes to 1 if G is contained in T, and it goes to 0 if G is not contained in T. Since we can make T as narrow as we wish, it is safe to assert that in this limit a particle traveling from (A,tA) to (B,tB) travels along G, as classical physics has it.
Because dS is homogeneous in the sense spelled out above, it defines a differential geometry — the kind of geometry appropriate for assigning lengths to paths on a warped surface, in a warped space, or in a warped spacetime. The next best thing to a straight line (which does not exist in a warped spacetime) is a geodesic: a path G that is either longer or shorter than all paths that have the same endpoints as G and lie in a sufficiently small neighborhood of G. What we just found is that classical particles follow the geodesics of the spacetime geometry defined by the action increment dS.
If we are dealing with a classical physical system that has N degrees of freedom, rather than just three (like a single particle), we can specify their values at any given time by a point in an N-dimensional “configuration space.” This system point, too, follows the geodesics of the geometry defined by the system’s action increment dS. Classical physics can therefore be encapsulated by the so-called principle of least action, although this is something of a misnomer, since what is actually required of a geodesic is that it either minimizes or maximizes the action when compared to the other paths in its neighborhood.


Anyway, a few comments: This will be used repeatedly in the remainder of this section. This means y depends on or is determined by x. Perhaps the data really is linear or near-linear is reality, but you could run non-linear analyses on the data.
An equation is a mathematical way of looking at the relationship between concepts or items.
For example click here to see special values for the sin, cos and tan functions. Also note that all we are really doing here is multiplying every term in the second polynomial by every term in the first polynomial. Symbols or Numbers in multiplication are called factors. Furthermore, their language is symmetric between input and output, i.
Are all of the middle term's 10m exponents to half of the power of one of the exponents on the outside terms? Each of the previous queries can be written by using implicit typing with varas shown in the following example: Click on any entry in the table for more information: Like the driveway into the house comes first.
This is probably best done with a couple of examples. Emil Kirkegaard A decent proxy for what I recommended to be done, thanks. Among other things, exponential notation for reciprocals is useful for seeing the connection between factoring and finding common denominators.
When x changes y also changes. The third expression demonstrates how to group results according to a key.
Hence, I guess you could say we have a good data point that race as social construct matters more than race as biological reality… …in Cape Verde anyway. The right side is considered to be simpler than the left side because a reciprocal on the left side is replaced by a negative on the right side.
Simplifications involving exponentials Simplify exponentials with bases or exponents of 0 or 1 Any exponential with base or exponent equal to 0 or 1 should be simplified as shown in this list: The first problem we will examine is below.
The following compositions of trig functions also simplify: Therefore this is a polynomial.
A monomial is an algebraic expression that is either a numeral, a variable, or the product of numerals and variables. Here are some examples of polynomials in two variables and their degrees.
And I will pay Perl another backhanded complement: All the exponents in the algebraic expression must be non-negative integers in order for the algebraic expression to be a polynomial.Ta-Nehisi has used an imagine of Walter White, the first African American head of the NAACP, to illustrate the pliability of the black kaleiseminari.com.
Algebra Expressions: Write an expression that has five terms, three of which are like terms and one term with a co-efficent of 1. kaleiseminari.com of the steps taken by Popes Paul 3rd and Paul 4th to reform the Catholic Chruch do you think were wise, which were unwise, Explain.
This polynomial has four terms, including a fifth-degree term, a third-degree term, a first-degree term, and a term containing no variable, which is the constant term.
The largest power on any variable is the 5 in the first term, which makes this a degree-five polynomial, with 2 x 5 being the leading term. For instance, the expression 3x + 2 has two terms: 3x and 2.
A term that has no variables is often called a constant because it never changes. Within each term, there can be two or more factors, the numbers and/or variables multiplied together. You can create a lambda expression that takes more than one parameter by surrounding the parameter list with parentheses and comma separate the parameters.
A polynomial is a monomial or the sum or difference of monomials, so the expression is a polynomial. The expression has two terms, so it is a binomial. 4t 5 + 3 t 2 + t.Download


To move the curves to the left 2 units, you want the sign of the term inside the math, help For the following set, which number has the largest absolute value? A 0 B 19 C D -1 wouldn't it be postive 20 but its not within the choices.
Since kf and kr are constants, the ratio of kf divided by kr must also be a constant. This ratio is the equilibrium constant for the reaction, Kc. The ratio of the concentrations of the reactants and products is known as the equilibrium constant expression.
No matter what combination of concentrations of reactants and products we start with, the reaction will reach equilibrium when the ratio of the concentrations defined by the equilibrium constant expression is equal to the equilibrium constant for the reaction.
When the reaction reaches equilibrium, the relationship between the concentrations of the reactants and products described by the equilibrium constant expression will always be the same. At 25oC, this reaction always reaches equilibrium when the ratio of these concentrations is 1.
The procedure used in this section to derive the equilibrium constant expression only works with reactions that occur in a single step, such as the transfer of a chlorine atom from ClNO2 to NO.
Many reactions take a number of steps to convert reactants into products. But any reaction that reaches equilibrium, no matter how simple or complex, has an equilibrium constant expression that satisfies the rules in the following section.
Rules for Writing Equilibrium Constant Expressions Even though chemical reactions that reach equilibrium occur in both directions, the reagents on the right side of the equation are assumed to be the "products" of the reaction and the reagents on the left side of the equation are assumed to be the "reactants.
The reactants are always written below the line in the denominator. For homogeneous systems, the equilibrium constant expression contains a term for every reactant and every product of the reaction. The numerator of the equilibrium constant expression is the product of the concentrations of the "products" of the reaction raised to a power equal to the coefficient for this component in the balanced equation for the reaction.
The denominator of the equilibrium constant expression is the product of the concentrations of the "reactants" raised to a power equal to the coefficient for this component in the balanced equation for the reaction.
Click here to check your answer to Practice Problem 1 Gas-phase reactions were chosen for this introduction to kinetics and equilibrium because they are among the simplest chemical reactions. Some might question, however, why the equilibrium constant expressions in the preceding exercise are expressed in terms of the concentrations of the gases in units of moles per liter.
Units of concentration were used to emphasize the relationship between chemical equilibria and the rates of chemical reactions, which are reported in terms of the concentrations of the reactants and products.
This choice of units is indicated by adding a subscript "c" to the symbols for the equilibrium constants, to show that they were calculated from the concentrations of the components of the reaction.
What happens to the magnitude of the equilibrium constant for a reaction when we turn the equation around? Consider the following reaction, for example.The value of such an equation is that it shows the reaction that actually occurs at the ionic level.
An example is the ionic equation representing the reaction of calcium (CaCl2) with potassium carbonate (K2CO3). Write state-variable equations for the mechanical system shown in Figure (a) and modeled in Example by Equation ().
Take the state variables to be the absolute displacements x 1 and x 2 and their derivatives v 1 and v benjaminpohle.come algebraic output equations for y 1, the viscous force of M 2 on M 1 (positive to the right), and y 2, the tensile force in spring K 2.
Split the redox equation into one half-equation representing the oxidation reaction and one half equation representing the reduction reaction 5. Balance the charges on each side of the half-equations by adding electrons, where suitable. The standard enthalpy of formation for an element in its standard state is zero.
have some unknown absolute enthalpy value (call it H 2) and the reactant(s) have another value (also unknown), Write the full chemical equation of formation for the substances in question 3.
Write a balanced thermochemical equation that expresses the enthalpy change for a given chemical reaction. Be sure to correctly specificy the physical state (and, if necessary, the concentration) of each component. Writing and Balancing Chemical Equations By the end of this section, you will be able to: Figure Regardless of the absolute number of molecules involved, The net ionic equation representing this reaction is: Pb2+(aq)+2I.


Repost: MonaVie’s Math Problem
Found this comment on the PurpleHorror web site:
MONAVIE’S MATH PROBLEM?
OK, so Açai extract has 32.5 g total fat per 100 g dry weight, according to Wikipedia. This equals 9.75 g per 30 g.
Someone who has Monavie can verify this, but let’s assume 30 ml of Monavie weighs about 30 g. (This is a fair approximation for juice.)
One serving of Monavie would have 9.75 g of total fat if it was pure Açaí extract.
In fact Monavie’s label states 0.5 g per serving.
Assume the extreme case where the rest of Monavie’s ingredients contribute 0 g of fat. (This is overly generous to Monavie’s defenders, but hey.)
(0.5 g from Acai – 0 g from other ingredients) / 9.75 g = 5.1% Açaí maximum in this overly generous scenario.
But, to be the first of 19 listed ingredients, you have to be #1 / 19 = 5.3% Açaí minimum.
Since I am being overly generous in assuming all the other ingredients of Monavie contribute 0 fat, I suspect that the labelling on Monavie is inaccurate AND Monavie has less Açaí than white grape juice (the second listed ingredient).
Additional evidence comes from this line of reasoning: The fourth listed ingredient, Acerola Cherries, has an insane amount of Vitamin C (2795% RDA per 100g, according to the website MonavieLand) and thus cannot contribute more than 3% of the total content of Monavie. Therefore the fifth through nineteen ingredients must at most be 3% each.
The top three ingredients must constitute at least 52% of the total for the labelling to be correct, which would be impossible given what was discussed above.
Posted by: B. Mull | June 21, 2009 2:16 AM


Hello and welcome to the Autodidactic podcast, season 2 episode 10. I wasn’t able to publish a podcast last week due to some time constraints. Hopefully this episode will have been worth the wait.
This week I’m going to be talking about a famous mathematician who was vital in the creation of the digital age. I’m going to be talking about George Boole, an English mathematician who helped establish modern symbolic logic and whose algebra of logic, now called Boolean algebra, is basic to the design of digital computer circuits.
George Boole approached logic in a new way reducing it to a simple algebra, incorporating logic into mathematics. He also worked on differential equations, the calculus of finite differences and general methods in probability.
He was born on the 2nd of November 1815 and died the 8th of December 1864.
George Boole’s parents were Mary Ann Joyce and John Boole. John made shoes but he was interested in science and in particular the application of mathematics to scientific instruments. Mary Ann was a lady’s maid and she married John on 14 September 1806. The family were not well off, partly because John’s love of science and mathematics meant that he did not devote the energy to developing his business in the way he might have done. George, their first child, was born after Mary Ann and John had been married for nine years. They had almost given up hope of having children after this time so it was an occasion for great rejoicing. They went on to have three more children, two boys and a girl.
George first attended a school in Lincoln for children of tradesmen run by when he was less than two years old. After a year he went to a commercial school run by a friend of John Boole, where he remained until he was seven. His early instruction in mathematics, however, was from his father.
When he was seven George attended a primary school and his interests turned to languages. His father arranged for him to receive instruction in Latin from a local bookseller. Having learnt Latin from a tutor, George went on to teach himself Greek. By the age of 14 he had become so skilled in Greek that it provoked an accusation of plagiarism after his father had one of his poems published.
At this time George was attending Bainbridge’s Commercial Academy in Lincoln. This school did not provide the type of education he would have wished but it was all his parents could afford. George was able to teach himself French and German studying and studying other academic subjects that a commercial school did not cover.
At 16, George started teaching as an assistant teacher in Doncaster after his father’s business collapsed and he found himself having to support financially his parents, brothers and sister. While he maintained his interest in languages, began to study mathematics seriously at this time. The first advanced mathematics book he read was Lacroix’s Differential and integral calculus. He was later to realise that he had wasted four years in trying to teach himself the subject instead of having a skilled teacher.
In 1834 he opened his own school in Lincoln although he was only 19 years old. Four years later Robert Hall, who had run Hall’s Academy in Waddington, died and Boole was invited to take over the school. His parents, brothers and sister moved to Waddington and together they ran the school which had both boarding and day pupils.
Boole was studying the works of Laplace and Lagrange and working on what would become is first mathmatics paper. He was encouraged by Duncan Gregory who was in Cambridge and was the editor of the Cambridge Mathematical Journal. Boole was unable to take up the offer to study at Cambridge as he needed the income from his school to look after his family. In the summer of 1840 he had opened a boarding school in Lincoln and again the whole family had moved with him. He began publishing regularly in the Cambridge Mathematical Journal.
Again encouraged by Duncan Gregory he began a serious study of Algebra. In 1844 he had a paper published called “On a general method of analysis; applying algebraic methods to the solution of differential equations” in the Transactions of the Royal Society. He received the Society’s Royal Medal in November 1844.
Boole was appointed to the chair of mathematics at Queens College, Cork in 1849. Boole was to become the first Professor of Mathematics at Queen’s College, Cork, and he took up the position in November. He taught there for the rest of his life, gaining a reputation as an outstanding and dedicated teacher.
In May of 1851 Boole was elected as Dean of Science, and he’d met his future wife Mary Everest (a niece of Sir George Everest, after whom the mountain is named) whose uncle was the professor of Greek at Cork and a friend of Boole.
July 1852 when Boole visited the Everest family in Wickwar, Gloucestershire, England. Boole began to give Mary informal mathematics lessons on the differential calculus. At this time he was 37 years old while Mary was only 20. In 1855 Mary’s father died leaving her without means of support and Boole proposed marriage. They married on 11 September 1855 at a small ceremony in Wickwar. It proved a very happy marriage with five daughters
It was in this period that Boole published his most important work. In 1854 he published An investigation into the Laws of Thought, on Which are founded the Mathematical Theories of Logic and Probabilities. Boole approached logic in a new way reducing it to a simple algebra, incorporating logic into mathematics. He pointed out the analogy between algebraic symbols and those that represent logical forms. It began the algebra of logic called Boolean algebra which now finds application in computer construction, switching circuits etc
Boole also worked on differential equations, the influential Treatise on Differential Equations appeared in 1859, the calculus of finite differences, Treatise on the Calculus of Finite Differences (1860), and general methods in probability. He published around 50 papers and was one of the first to investigate the basic properties of numbers, such as the distributive property, that underlie the subject of algebra.
Many honours were given to Boole as the genius in his work was recognised. He received honorary degrees from the universities of Dublin and Oxford and was elected a Fellow of the Royal Society (1857). However his career, which was started rather late, came to a tragic early end when he died at the age of 49.
One day in 1864 he walked from his residence to the College, a distance of two miles, in the drenching rain, and lectured in wet clothes. The result was a feverish cold which soon fell upon his lungs. Boole’s wife believed that a remedy should resemble the cause. She put Boole to bed and threw buckets of water over the bed since his illness had been caused by getting wet.
Boolean algebra has wide applications in telephone switching and the design of modern computers. Boole’s work has to be seen as a fundamental step in today’s computer revolution.
So what can we learn from Boole to use for ourselves as Autodidactics. Boole’s realisation that he had wasted time by not finding a teacher is a critical point.
As an autodidactic you may struggle to understand some concepts which you are learning. You should take some time to evaluate if you should look into getting a tutor to help you. Here are some tips to help you to evaluate.
- Is the work load taking you twice as long as you think it should? In subjects like math and science, concepts build on one another. Missing just one concept can have a snowball effect, and you may need some extra help.
- If you start needing more help than usual—and find your normal go-to people or places can’t help you—you might want to consider enlisting a tutor.
- If you are beginning to dislike the subject it might be a sign of frustration because you aren’t “getting it”.
- You’re putting in the effort, but not seeing the results you expect, then it’s time to pinpoint the problem and get some extra help.
- You are beginning to skip study times, or avoid the work. You’ve probably gotten frustrated to the point of quitting.
If you decide you need external assistance, then review your options. Would some kind of remote classroom or after work classes help? Do you need a lot of help on a particular subject, or is it just some concepts that you need to work on?
Here are some things to think about before going out to find someone.
- How much help do you need? A full course or just some help with a few key concepts?
- What is your budget for tutoring? Keep in mind a difficult subject will take longer to prepare, so expect to pay more for the extra preparation time. Cost varies greatly, depending on subject area, location, and the credentials of the tutor. Neighbors or friends may charge less, but remember, professional tutors charge professional rates.
- What hours do you expect to have available for tutoring?
- What references or qualifications do you want to see? You get references for electricians, doctors and dentists. Doesn’t it truly make sense to get a reference for a tutor?
How do you find a tutor? There are a number of places you can look and a lot depends on your location. Some places to start are:
- Local colleges or universities will often have a bulletin board or lists of tutors per subjects.
- Online websites like: https://www.personal-tutors.co.uk/, https://tutorful.co.uk/ or https://www.tutorhunt.com/
- Ask friends and family. If you’re learning music perhaps your neighbour knows someone?
Depending on what you’re learning the way to find a tutor or mentor will be different. But before paying anyone you should check credentials, and remember to be safe before allowing anyone inside your home.
Well that is all for this week.
If you enjoy the show, please give a rating on the platform you’re using to listen, and please share the podcast with friends and family who might be interested. Also, please feel free to email me at firstname.lastname@example.org, or leave feedback on the website autodidactic.info.


University of Michigan’s Science, Technology, Engineering, and Mathematics (STEM)-Africa Initiative, Third Biennial Conference, 2014
Effective U.S. Strategies for African STEM Collaborations, Capacity Building, and Diaspora Engagement
The conference brought together academic and policy experts from the U.S. and Africa, and to fulfill several objectives: (1) share some of the current scientific research happenings of significance to African contexts; (2) encourage and foster scientific research collaborations and educational infrastructure development with African partners; and (3) review the broad African Scientific Diaspora organizations in the US, and consider ways of advancing their involvement in African scientific development.
Science, Technology, Engineering, and Mathematics (STEM)-Africa sought to nurture early career scientists on the continent and advance research collaborations in STEM disciplines between the University of Michigan and partner institutions in Africa that extend scientific knowledge and yield solutions to global problems. U-M’s STEM-Africa Initiative is unique among peer institutions in the U.S. in its engagement of science as a trans-Atlantic affair, and its allocation of resources dedicated to developing the study of science, technology, engineering, and mathematics (STEM) in Africa.
Through STEM-Africa, ASC nurtures early-career scientists on the continent and advances research collaborations that extend scientific knowledge and yield solutions to global problems.
Panelists included administrators and faculty from universities in Ghana, Uganda, Cameroon, Kenya, Nigeria, Tunisia, Tanzania, Ethiopia, and South Africa
International partners and participating institutions:
· The African Union
· National Academy of Sciences
· Association of African Universities
· African Development Bank
· Constituency for Africa· African Virtual University· African Scientific Institute
· African Network of Science and Technology Institutes
· Next Einstein Initiative


For the second consecutive year, the Troy Mathletes Team from Troy Community School District 30-C’s Troy Middle School claimed 1st Place Overall at the Mid-High Math Competition. In addition, the Troy 8th grade team placed 1st in the category of Mental Math (solving problems without the use of a calculator or scratch paper), 2nd in Money Problem Division and 2nd in Motion Problem Division. Troy’s 7th graders placed 1st in Mental Math, 1st in Age Problem Division, 1st in Backwards Problem Division and 2nd in Classics Problem Division. First place individual awards in the Mental Math category were Troy Mathletes Josie Jarmuz, Angela Conde, Daniel Schalk and Sean Zarobsky. The meet was held at Joliet West High School and sponsored by the high school math honor society, Mu Alpha Theta.


Math is everywhere within our lives. For instance, taxes, loans, charge cards, purchases, budgeting and shopping. Parents should educate kids handle money wisely as he is small. All of this requires math understanding.
Today, we use math in each and every field, science field, technology field, production field,etc. Math might help us comprehend the world with large and small figures, statistics, probability and percents. We have to use math every single day. So you should educate kid’s math well as he is youthful.
A great way to educate kids math would be to provide encounters for ‘playing and living’ math. You’ll be amazed at how effective these activities have been in teaching math thinking. Many games are equipped for kids plus they can increase kids thinking skills. These games require kids to make use of their math skills, use strategies and involve logical thinking. Parents can enjoy these math games along with your kids. In this manner, you are able to instruct your children. And when he face trouble, you are able to provide him some hints too. You’ll have fun in this course.


Stephen Wolfram’s Mathematica is known around the world as the best computational software available today. It’s the only development platform fully integrating computation into complete workflows, moving you seamlessly from initial ideas all the way to deployed individual or enterprise solutions.
2. GNU Octave
This is a high-level interpreted language, primarily intended for numerical computations. It provides capabilities for the numerical solution of linear and nonlinear problems, and for performing other numerical experiments.
3. R (programming language)
R is a free software environment for statistical computing and graphics. The language can be run and compiled on a wide variety of Linux/Unix platforms, Windows and Apple’s MAC operating system.
Distributed under the CeCILL license, Scilab is widely used in higher and secondary education in order to teach languages like mathematics, automatic control engineering and many other subjects related to engineering services.
Sage is a free open-source mathematics software system licensed under the GPL. It builds on top of many existing open-source packages: NumPy, SciPy, matplotlib, Sympy, Maxima, GAP, FLINT, R and many more.
6. Microsoft Mathematics
Microsoft Mathematics provides a graphing calculator that plots in 2D and 3D, step-by-step equation solving, and useful tools to help students with studies in mathemtics and science.
7. SciPy & Numpy
SciPy (pronounced “Sigh Pie”) is a Python-based ecosystem of open-source software for mathematics, science, and engineering. It’s core packages include Numpy, Sympy, IPython, Pandas, SciPy Library and Matplotlib.
This is a document based interface for Maxima. It uses wxWidgets and runs natively on Windows, X11 and Mac OS X. In addition, wxMaxima provides menus and dialogs for many common Maxima commands, inline plots, autocompletion, and simple animations. It is distributed under the GPL licesnse.
This tool provides one of the best solutions. It brings one of the world’s most powerful computing engine side by side with an easy-to-use graphical user interface.


Scrabble & Words with Friends Word Unscrambler
Definition of Arctan
1 Definition of Arctan
The definition of arctan, the meaning of word Arctan
Is arctan a scrabble word? Yes!
- n.- the inverse function of the tangent; the angle that has a tangent equal to a given number
Arctan is worth 8 points in Words with Friends
There are 6 letters in arctan: A A C N R T


By Aníbal Moltó,José Orihuela,Stanimir Troyanski,Manuel Valdivia
Abstract topological instruments from generalized metric areas are utilized during this quantity to the development of in the community uniformly rotund norms on Banach areas. The e-book deals new strategies for renorming difficulties, them all in keeping with a community research for the topologies concerned contained in the problem.
Maps from a normed area X to a metric area Y, which supply in the community uniformly rotund renormings on X, are studied and a brand new body for the idea is bought, with interaction among practical research, optimization and topology utilizing subdifferentials of Lipschitz services and overlaying equipment of metrization concept. Any one-to-one operator T from a reflexive house X into c0 (T) satisfies the authors' stipulations, moving the norm to X. however the authors' maps will be faraway from linear, for example the duality map from X to X* offers a non-linear instance whilst the norm in X is Fréchet differentiable.
This quantity could be fascinating for the large spectrum of experts operating in Banach area thought, and for researchers in limitless dimensional sensible analysis.
Read or Download A Nonlinear Transfer Technique for Renorming (Lecture Notes in Mathematics) PDF
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The "extensions" of jewelry and modules have not begun to be explored in detail in a research monograph. This publication provides cutting-edge study and likewise stimulating new and additional examine. damaged into 3 parts, Part I begins with simple notions, terminology, definitions and an outline of the sessions of jewelry and modules.
This publication is dedicated to the topological fastened aspect conception of multivalued mappings together with functions to differential inclusions and mathematical economic climate. it's the first monograph facing the mounted element concept of multivalued mappings in metric ANR areas. even if the theoretical fabric was once tendentiously chosen with recognize to purposes, the textual content is self-contained.
This e-book contains new mathematical shape for Generalized Functions.
This quantity comprises contributions written via individuals of the 4th Workshop on Operator conception in Krein areas and functions, held on the TU Berlin, Germany, December 17 to 19, 2004. The workshop coated subject matters from spectral, perturbation, and extension conception of linear operators and kinfolk in internal product areas.
- Applied Optimization: Formulation and Algorithms for Engineering Systems
- The Infinite-Dimensional Topology of Function Spaces (North-Holland Mathematical Library)
- Spheroidal Wave Functions (Dover Books on Mathematics)
- Around the Research of Vladimir Maz'ya I: Function Spaces: 11 (International Mathematical Series)
- Wave Factorization of Elliptic Symbols: Theory and Applications: Introduction to the Theory of Boundary Value Problems in Non-Smooth Domains
- Integral Theorems for Functions and Differential Forms in C(m) (Chapman & Hall/CRC Research Notes in Mathematics Series)
Extra resources for A Nonlinear Transfer Technique for Renorming (Lecture Notes in Mathematics)
A Nonlinear Transfer Technique for Renorming (Lecture Notes in Mathematics) by Aníbal Moltó,José Orihuela,Stanimir Troyanski,Manuel Valdivia


Today, I would like to talk about the Ishango bone, or rather the first evidence of a calculator in the world. Named after the place where it was found in the Democratic Republic of Congo (DRC), the Ishango bone is what is called a bone tool or the craddle of mathematics. Dating as far back as 22000 years ago, in the Upper Paleolitic era, the Ishango bone is a dark brown bone which happens to be the fibula of a baboon, with a sharp piece of quartz affixed to one end for engraving. It is the oldest attestation of the practice of arithmetic in human history.
The Belgian geologist Jean de Heinzelin de Braucourt uncovered the bone buried in layers of volcanic ashes on the shores of Lake Edward in the Ishango region in DRC, near the border with Uganda. The Ishango bones are actually two (2) bones of baboon, 10 to 14 cm long, with several incisions on each faces. The smallest of the two bones was the first to be exposed at the Royal Belgian Institute of Natural Sciences in Brussels; it carries several incisions organized in groups of three columns.
The left column can be divided in 4 groups, with each group possessing 19, 17, 13, and 11 notches. The sum of these being 60. Those are the 4 successive prime numbers between 10 and 20. This constitutes a quad of prime numbers.
The central column is divided in groups of 8. By an approximate count, one can find (in the parenthesis, is the maximum number): 7 (8), 5 (7), 5 (9), 10, 8 (14), 4 (6), 6, 3. The minimal sum is 48, while the maximal sum is 63.
The right column is divided into 4 groups, where each group has 9, 19, 21, and 11 notches. The sum of these 4 numbers is 60.
The second bone has not been well-studied. However, we know that it is composed of 6 groups of 20, 6, 18, 6, 20, and 8 notches.
The first bone has been subject to a lot of interpretation. At first, it was thought to be just a tally stick with a series of tally marks, but scientists have demonstrated that the groupings of notches on the bone are indicative of a mathematical understanding which goes beyond simple counting. In fact, many believe that the notches follow a mathematical succession. The notches have been interpreted as a prehistoric calculator, or a lunar calendar, or a prehistoric barcode.
Jean de Heinzellin was the first to consider the bone as a vestige of interest in the history of mathematics. For instance, he noted that the numbers in the left column were compatible with a numeration system based on 10, since he saw that: 21 = 20 + 1, 19 = 20 – 1, 11 = 10 +1, and 9 = 10 -1. These numbers are also prime numbers between 10 and 20: 11, 13, 17, 19.
Some other scientists such as the Belgian physical engineer proposed that the bones were probably a slide rule. While Alexander Marshack has indicated that the bones could refer to the oldest lunar calendar on earth. Claudia Zaslavsky thinks that the author of the Ishango bone must have been a woman following the lunar phases to calculate her menstrual cycle. However, the second bone completely rules out the lunar calendar theory, and favors more the numeration system.
All said, it is amazing to realize that there were mathematicians 20,000 years ago on the African continent. It is so great to realize that my ancestors, on the shores of Lake Edouard, were actually brilliant scientists playing with prime numbers. Whether it was a woman calculating her menstrual cycle, or some brilliant tribe astronomer, it feels so good to know that the paleo-mathematicians of Ishango already knew prime numbers. They were a great civilization long before the pharaohs of Egypt. Thus, in reality, the Ishango bone is the oldest table of prime numbers in the world. To read more, check out Mathematicians of the African Diaspora,, the Prime Glossary, and Wolfram Mathworld.


Simple Algebra Worksheet Template Free and Effective to increase Score
One of the risks of being a math teacher is many students hate you. Truthfully, they do not hate you but the subject that creates this condition. A simple algebra worksheet template will save you from their inappropriate hatred. This modern tool frees printable and ready to help the students catching this lesson. If you never heard about this online worksheet, you might doubt it and feel inappropriate. The fact is the printable simple algebra worksheet template is a flexible tool. All education levels that teach algebra can use it anytime.
Let 14 Simple Algebra Worksheet Template Designs talk to you
Truthfully, this tool gives benefits for all that relates to the subjects. It eases the math’s teacher is preparing any place for the math practices. The template adds an idea to find the right practice questions according to the students’ levels. It is because this math worksheet frees editable easily and cuts your time from usual. You usually need three hours for each worksheet, now you can cut it into one hour. The editable or customizable change the making process that does not need from scratch.
Well, let the sample simple algebra worksheet template talk to you in 14 examples. Just see as well as pay attention to each number because they are different. It implies between one template and another have different types and function. Okay, let’s see it:
- Simple Algebra Worksheet Template Sample for Equation Questions
- Algebra Worksheet of Balancing Basic Equation with Addition and Subtraction in Simple PDF Template
- Sample Simple Worksheet Template Examples of Algebra for 7th Grade
- Worksheet Template for Simple Algebra Questions with Finding the Pattern
- Practice Problems Worksheet Template for Simple 7th Grade Algebra
- Simple Template of Algebra Problem
- Algebra Equation Worksheet Template Simple Design
- Printable Worksheet Template of Simple Algebra
- Simple Worksheet Template for Pre-Algebra Lesson
- Algebra Worksheet in Simple Template
- Worksheet Template for Basic Algebra Level
- Worksheet Template for Basic Algebraic Expression
- Simple Worksheet Template of Algebra for Beginners
Benefits of Using Simple Algebra Worksheet from These Templates
If you had ever used this kind of worksheet template and the come back again, you must know the benefits. It does not matter you come back and get a new template that simpler than the previous one. The prior worksheet template is not bad but the simple algebra worksheet template sample today is extraordinary. It is more helpful where a new beginner can understand algebra better and faster. Truthfully, this page has discussed briefly the benefits of using these free online worksheet. However, it will add some such as below:
- Easy to access and save a deal of energy and time.
- The templates are suitable for teachers, high school students, and college students as well.
- Quite use the same worksheet for each student in the class.
- Free and download anytime without thinking about additional expenses.
From now, do not be afraid if your student only respects in front of the class. They will not be afraid of you, hate you, and hate your math subject. The simple algebra worksheet template printable changes it easily in a short time. Their score will increase because this tool helps them with this subject effectively.
9+ Simple Algebra Worksheet Template Sample


As usual, what started out to be a simple activity quickly exploded into a whole collection of resources! I created the sorting activity as planned, but then I started thinking of other ways to use the Penguin Fraction Activity Cards. I ended up creating several variations and sizes of the cards, too, in both black and white and color. The color cards are especially helpful if you can afford the ink because all penguin fractions of the same color have the same denominator.
Equivalent Fraction Freebie
Would you like to try one of my Penguin Fraction lessons with your students? This Equivalent Fractions Sorting activity is a free sample lesson from Penguin Fractions: Exploring the Basics, and it comes with the penguin fraction activity cards and sorting mat you see here.
I love creating freebies for teachers, and this is just one of the many free resources I send to my email subscribers. If you'd like a copy, just click here to get Equivalent Fractions Sorting and to sign up for my newsletter all in one step!
If you already receive my newsletter, this freebie is located on the private, members-only page called Laura's Best Freebies along with more than 75 other free resources. If you can't find it, sign up here and I'll send this freebie right over!
Penguin Fraction Resources
So far I've completed about a half dozen separate products and several bundles in my Penguin Fractions series, and I've got more planned. All of the products are aligned with Common Core State Standards for 3rd and/or 4th grade, but they can also be used for review with older kids.
Tami Terry tried the activity with several of her classes and snapped a picture of these 4th graders testing out an early version of the benchmark sorting activity. The directions call for students to work with a partner and take turns sorting fractions into three groups: less than 1/2, equal to 1/2, or greater than 1/2. As the students work, they are encouraged to talk over the reasons for each fraction card placement. The kids loved it and it helped them understand the concept of comparing fractions to benchmarks. The final sorting board included in Penguin Fractions: Comparing and Ordering ended up looking like the one below.
Where to Find Penguin Fraction Resources
If you are creative and have time to make your own games, you can purchase the Fraction Activity Cards alone. If you would rather spend a few extra dollars and save yourself time, consider purchasing one of the ebooks or bundles which include the activity cards. Both ebooks include complete lessons as well as printable games and activities for practicing fraction skills. If you love the whole concept, you might want to purchase my Penguin Fraction Concepts Growing Bundle. I will be adding several more items to the bundle, and if you purchase it now, you'll get anything added to the bundle for free! You'll find links to all of these resources at the end of this post or by clicking the Penguin Fractions link in my TpT custom categories. Be sure to read the descriptions for each product before you make any purchase so you don't end up making duplicate purchases.
Years of Penguin Fraction Fun!
Yes, I know what you are thinking! Those penguin fraction cards are going to be a bit of work to print, laminate, and cut out. You want to print them in color, too, and color ink isn't cheap! Just remember that after you have them made, you'll be able to use them year after year. You'll be glad you invested the time and energy into creating these cards, because the penguin fraction activities will make fractions fun to teach and even more fun for your students to learn!


The Center for Combinatorics recruits about 20 postgraduates, mainly Ph. D students each year.
In addition to the general qualifications required for admission to the Graduate School of Nankai University,
applicants should have majored in Mathematics or related fields.
Candidates may enter themselves for the Graduation Entrance Test of Nankai University, or apply for admission without examination if they ranked top during their graduate education. All candidates are required to attend an interview, and they may choose pure mathematics or applied mathematics, or both as their main interest.
For international applicants, please click on the following link for further information: http://18.104.22.168/english/admissionanddegrees/admissionanddegrees.html


We DBA’s have all experienced query recompilation in our SQL Server environment. The entire journey of a query, right from inception till the formation of the Query Plan followed by execution is very interesting and involves a lot of internal processes. Recompilation is nothing but the re-initiation of compilation of a query when a certain compilation check fails. So what is the underlying algorithm or mathematics that the SQL server uses to decide whether to recompile or not. Here is how it works:
ABS( colmodctr(current) – colmodctr(snapshot)) ) >= RT
1) RT = Each column has a recompilation threshold (RT) associated with it. RT is a function of the number of rows in a table. We will discuss how RT is calculated later in this article.
2) colmodctr = This counter tracks the number of modifications that a table has undergone. The counter is not transactional in nature, which means if 1000 rows were inserted into the table and then rolled back then the counter value would not be rolled back.
3) colmodctr(current) is the current value of the counter and colmodctr(snapshot) is the value of the counter when the query plan was last compiled.
So when this absolute value crosses the RT, it is then that the query is recompiled. The next quetion is how does the engine decides or calculates the RT. Here is how it is done:
1) For permanent table:If n<=500 then RT = 500.If n>500 then RT = 500 + 0.20 * n.
2) For temporary table: If n<6 then RT = 6.If n between 6 and 500 then RT = 500. If n>500 then RT = 500 + 0.20*n
3) For Table variable: RT does not exist. They are not recompiled.
Here n stands for numbers of rows in the table.
I hope this concise article was helpful in understanding the decision making process for Recompilation.
Tagged: Microsoft SQL Server, Plan Cache, Query Re-compilation
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What is an Algorithm?
You’ve heard the word before, but do you actually know what an algorithm is? Algorithms can sound intense and complicated, but the actual concept of an algorithm is simple. Learn what algorithms are, how they function in your daily life without your notice, and why they’re important to digital marketing.
The Cambridge Dictionary defines algorithm as “a list of instructions for solving a problem”.
Merriam-Webster defines algorithm as “a step-by-step procedure for solving a problem or accomplishing some end.” They also define algorithm as, “a procedure for solving a mathematical problem in a finite number of steps that frequently involves repetition of an operation.”
The broadest definition of an algorithm is a set of rules, guidelines, or steps that produce a certain outcome or perform a specific task. While most people are scared off by the very technical sounding word, “algorithm”, at its root it is a simple concept.
The complex side of algorithms comes into play when there are many rules and factors included. Algorithms are commonly used to create complicated computer programs and solve intense mathematical equations.
What is an Algorithm, Really?
Algorithms really can be any set of steps that complete an action. An algorithm has a finite number of steps, and is meant to solve some problem or achieve a solution of some sort. They are commonly used for calculations, data processing, or other computer and math operations.
Algorithms can manipulate data in various ways, and they are designed to do so to complete a certain task or discover a desired result.
From an everyday standpoint, we all follow algorithms frequently – we just don’t think of them as such. A recipe to bake cookies is an algorithm: you follow steps to complete a goal. Map directions are an algorithm, a set of instructions to guide you to your location. Following any set of instructions is really just following an algorithm.
On the technical side of things, algorithms are more complex. You don’t have to know how every mathematical and computer algorithm works down to the details to understand the concept of algorithms, however. They simply create a set of rules to follow and complete that process to find a result.
There are endless types of algorithms, especially when you consider the fact that any set of instructions constitutes an algorithm. Most people think of intense code and programming when they hear the word algorithm, but there are simple algorithms as well. Here are the basics for the most common types of algorithms:
Algorithms are strongly associated with computer science, and rightly so. Computers run on algorithms to function, performing tasks based on inputs like keystrokes or clicks on specific buttons. For a computer program to work, programmers create algorithms that tell the computer exactly what to do given any specific input.
Just like with any problem in need of a solution, there are many different algorithms that can achieve a certain task. Technology has improved as programmers create more efficient algorithms to solve problems faster, with less computing power, or by taking up less space in terms of memory and storage.
Algorithms are also prevalent in mathematical equations. Since math is all about sets of rules, inputs, and answers, every math problem is essentially an algorithm.
Even when you learn basic math in elementary school, you are learning the rules to solve problems and the order that those rules must go in. You likely used algorithms without ever realizing it. Calculators use algorithms to compute answers for us, much like small computers.
Social Media Algorithms
Many people have probably heard of algorithms through discussion of social media algorithms. Social networking sites, like all websites, use algorithms to create their pages and also to display certain information to certain users. These algorithms take data from user experiences to determine what users are interested in.
The Instagram algorithm, for example, is designed to try to keep users on the platform for as long as possible. To accomplish this, their algorithm analyzes your behavior on the site – what kind of posts you like, whose posts you like and engage with, and other factors as well. The algorithm then takes that information and uses it to display content that it has determined to be most likely to interest you.
This algorithm based on your engagement and interests is why, now that Instagram’s feed is not chronological, you may notice that your friends’ posts or those of people that you like always appear higher in your feed.
Algorithms and Digital Marketing
Now that you have a better understanding of what an algorithm is and where it’s applied, you may wonder how it applies to digital marketing.
Since digital marketing is online, algorithms are really at the core of everything – the internet is essentially programmed through many algorithms, and computers are powered by them as well. Social media algorithms play heavily into digital marketing as well, since social media marketing is a huge and ever-growing field of marketing.
When it comes to SEO, algorithms are important to understand. Search engines run on algorithms to determine what results appear for what search queries, and search engines like Google have algorithms that are constantly changing and evolving.
Search Engine Algorithms
Learning how search engines work and how their algorithms display results in response to searches is vital to SEO. Since the point of SEO is optimizing websites for search engines, those algorithms affect the tactics used to get a website to rank in relevant search results.
In the earlier days of SEO, digital marketers used shady tactics, now called black hat SEO, to trick Google and other search engines into ranking their website for certain search terms.
Rather than creating a helpful, well-made website with relevant search engine-optimized content, they would just lace the page with the target keyword over and over, even where it didn’t make sense. This practice of keyword stuffing used to work, but now search engine algorithms have updated and become more complex to filter out spammy websites.
Search engine algorithms consider a wide variety of factors to produce the results that best answer the search query. SEO experts study this algorithm and learn what works through trial and error, and there are many tactics used to help a website perform better by conforming to the algorithms.
The concept of algorithms is simple, but many computer and search engine algorithms are much more complex when you get into the nitty gritty. Luckily, SEO professionals can handle the details of optimizing your website for search engine algorithms, so you can focus on your business. If you’re in need of digital marketing assistance or want to learn more, contact SEO Digital Group today.


Print out your own free printable division chart. I’ve included both a completed chart and one with missing dividends so that your child can practice all the division facts from 1÷1 up to 100÷10.
How to use your free printable division chart
This free printable division chart is an organized list of all of the division facts, from ÷1 up to ÷10. The answers are all lined up in order from 1 to 10 for each divisor, so it’s not very useful to give to a child to complete. After all, all he or she has to do is figure out the pattern and then blast through it. No thinking required!
But that doesn’t mean the division chart isn’t useful. You just have to use it a little differently than you use a multiplication chart. Here are 3 ways to put the division chart to good use and help your child master the division facts.
Look for patterns
Invite your child to look for patterns in the division chart. For example, if you look down the ÷3 column, what pattern do you see in the answers? Why?
Your child may also notice skip-counting patterns in the dividends (the first number in each equation), or she may notice the similarities between the ÷3, ÷6, and ÷9 charts.
Use the division chart as a checklist for oral drill
To use the division chart for oral practice, just read the problems aloud to your child. Go in random order (rather than down the columns) so that the practice is mixed. Check off the problems your child knows by heart, and leave the rest unchecked so that you know you need to go back and practice some more.
Complete the missing dividends
One simple twist makes the division chart more interesting. Instead of giving your child a division chart where the quotients are missing, give her one where the dividends are missing. (You’ll see an example below, and I’ve included a printable one in the link at the bottom of the article.) Completing the missing dividends in this type of table helps kids cement the connection between multiplication and division–which is key to mastering the division facts.


An overview of math biography and the role of johann carl friedrich gauss
In contrast, Gauss wrote a letter to Bolyai telling him that he had already discovered everything that Bolyai had just published.
On October 1, he published a result on the theory of solutions of polynomial equations.
Having suffered from shortness of breath and congestion in his last years, he was diagnosed as having an enlarged heart. Some have attributed this failure to his innate conservatismothers to his incessant inventiveness that always drew him on to the next new idea, still others to his failure to find a central idea that would govern geometry once Euclidean geometry was no longer unique.
He also made ths first systematic study of modular arithmetic - using integer division and the modulus - which now has applications in number theory, abstract algebra, computer science, cryptography, and even in visual and musical art.
For the entire content of the work Before she died, Sophie Germain was recommended by Gauss to receive her honorary degree. His personal diaries indicate that he had made several important mathematical discoveries years or decades before his contemporaries published them.
Carl friedrich gauss quotes
The prime number theorem, conjectured on May 31, gives a good understanding of how the prime numbers odd integers that are not divisible by any other integer except 1 are distributed among the integers. To visit Natalie's blog, go to. Mathematicians Are People, Too. The prime number theorem , conjectured on 31 May, gives a good understanding of how the prime numbers are distributed among the integers. All these explanations have some merit, though none has enough to be the whole explanation. Eugene immigrated to the United States about after a falling out with his father, eventually settling in St. The book presents a systematic analysis on the formation of images with a paraxial approximation. Gauss also had other unpublished insights into the nature of complex functions and their integrals , some of which he divulged to friends. Unwilling to court controversy, however, Gauss decided not to pursue or publish any of his avant-garde ideas in this area, leaving the field open to Bolyai and Lobachevsky , although he is still considered by some to be a pioneer of non-Euclidean geometry. While there he submitted a proof that every algebraic equation has at least one root or solution.
The book presents a systematic analysis on the formation of images with a paraxial approximation. Two individuals gave eulogies at his funeral, Gauss's son-in-law Heinrich Ewald, and Wolfgang Sartorius von Waltershausen, who was Gauss's close friend and biographer.
Gauss was pleased to accept and took personal charge of the survey, making measurements during the day and reducing them at night, using his extraordinary mental capacity for calculations. Research on these geometries led to, among other things, Einstein's theory of general relativity, which describes the universe as non-Euclidean.
Rather than publish such a description, Gauss confined himself to criticizing various a priori defenses of Euclidean geometry.
Carl friedrich gauss facts
Other mathematicians had tried to prove this before him, e. Though he did take in a few students, Gauss was known to dislike teaching it is said that he attended only a single scientific conference, which was in Berlin in Gauss supported the monarchy and opposed Napoleon , whom he saw as an outgrowth of revolution. For this work, he was awarded a medal by the Institute of France in for the most original astronomical observation. In recognition of his contributions to the theory of electromagnetism, the international unit of magnetic induction is known as the gauss. At the age of fourteen, Gauss was able to continue his education with the help of Carl Wilhelm Ferdinand, Duke of Brunswick. It took many years for Eugene's success to counteract his reputation among Gauss's friends and colleagues. Astronomical researches In that same year, Italian astronomer Giuseppe Piazzi discovered the planetoid Ceres, but could only watch it for a few days before it disappeared in the glare of the sun. This led him to question one of the central tenets of the whole of mathematics, Euclidean geometry, which was clearly premised on a flat, and not a curved, universe. Gauss used it to process data on astronomical positions. It is said that he attended only a single scientific conference, which was in Berlin in It is used to determine the most likely value of a parameter from a number of measurements that follow a statistical pattern of error. His another key work in mathematics was the development of number theory. From this he drew the trust, the confidence that our life course is not ended by death. In fact, Gauss often withheld publication of his discoveries.
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This calculator/utility allows the user to calculate TOD distance or decent rate needed to reach a target altitude in X distance based on relevant parameters such as current altitude, target altitude, ground speed, and descent rate or distance to target measurement (depending on what calculation mode is being used). Then calculates the result based on the selected calculation mode.
How to use:
- Open the TOD Calculator in your web browser.
- Select the desired calculation mode (TOD Distance by default).
- Select the desired measuring system with the "Units (Toggle Imperial/Metric)" button (Imperial by default).
- Enter the required values for the input fields.
- Click on the "Calculate" button to perform the calculation.
- See the calculation results, which are displayed below the input fields.
- Click the "Reset" button to reload the page and start again.
Now, you can use the TOD Calculator to determine the required TOD distance or descent rate for your aviation needs. Happy flying!


Court was concerned with a case where applications were invited for appointment to the post of Lecturer in MCA, from candidates holding a post graduate degree in the “relevant subject”. As a matter of fact, this Court found that candidates with Masters’ degree in Computer Applications were available, but a candidate with Masters’ degree in Mathematics was selected. This Court found fault with the decision of the Board of Appointment in selecting the candidate with a Master’s degree in Mathematics with a flawed reasoning that Mathematics is one of the subjects taught in MCA.
Ganapath Singh Gangaram Singh Rajput v. Gulbarga University, (2014) 3 SCC 767
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Credit: Carlos Muza
There are a number of budget forecasting methods to choose from. Knowing which one is right for you, and making it work, can be a confusing challenge. This article introduces and discusses three techniques used for budget forecasting.
What is Budget Forecasting?
Your budget is the lifeblood of your business. The circulation of your finances ensures continued operations to meet the needs of your clientele. Your budget details the flow of money in, out, and through your organization.
Forecasting is the prediction of the future, usually with a sensible rationale behind it. The budget forecasting definition, then, is the attempt to predict your future budget.
This can be tricky, though, because while many things about your budget are within your control, many are not. The most refined forms of budget forecasting seek to forecast these latter elements, to enable you to model the outcome of different choices your business can make.
Budget Forecasting Methods
There are lots of different methods used to forecast a budget. Generally speaking, the more powerful budget forecasting methods require more technical knowledge about statistics. While there are many more techniques than this, we will discuss the three most common ones.
This is perhaps the simplest method. A projection plots data from a budget element against time and uses a mathematical formula to extend the data into the future.
For instance, if you were doing a linear projection, you would calculate a line of best fit, and simply calculate the value of the budget element for a given point in time.
If the budget element you are looking at appears to follow a regular trend, whether it’s linear, exponential, etc. projection may be good enough. However, if the data doesn’t trend smoothly with time, a projection may be a poor way of predicting that budget element.
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What About Changes to the Status Quo?
Everything we are talking about here assumes things are more or less the same going forward. The more complex methods work to accommodate past changes into the future. But we also may have some inside knowledge that we can use to augment the math.
The math is still important, however, as it provides the formulas to show how we project further. We’ll use a combination of this inside knowledge on upcoming business events along with the formula to produce that projection into your business’ future!
One way to avoid problems with noisy data – that is, data that doesn’t trend smoothly – is to use a moving average. Moving averages take an average of a certain number of previous data points to plot a “smoothed” value of the data.
A moving average can be useful for smoothing out noisy data in order to do a projection. They can also be useful if your data is smooth, but appears to move in cycles (think seasonal fluctuations). In either case, moving averages are a rough way to capture the underlying trend.
The problem with projections and moving averages is that they presume that the only thing affecting your data is time. But as a business owner, you know that the choices and the conditions of the market impact the budget elements that are outside of your control.
A more advanced method of budget forecasting is regression. Regression analysis allows you to integrate other data that you believe impacts the budget elements you’re interested in forecasting.
|Read these other blogs about budgeting:
Single Linear Regression
With single linear regression, you are attempting to determine the impact of one factor on the budget element in question. For instance, how does your advertising spending impact your revenues?
A single linear regression will generate a formula for a line of best fit in the form Y=β0+β1X. A line of best fit minimizes the average squared vertical distance from the actual data points to the line itself. In other words, it ensures that the data points are on average as close to the line as possible.
The one pitfall to estimating a line of best fit is just because you can estimate such a line doesn’t mean that you should. If the relationship between your budget element and your other data does not look like a line, single linear regression would not be the way to go.
To provide some objective measures of the goodness of fit, statisticians consult the estimated t-scores, which indicate how well the β terms describe the relationship of the data, and the R2, which indicates the overall goodness of fit.
With the estimates for the β terms, you can plug in hypothetical values for X to generate projections for what your budget element Y might be.
Credit: Kelly Sikkema
Multiple Linear Regression
In all likelihood, you’re not going to be satisfied explaining your budget elements with just one other set of data. For this, budget forecasters use multiple regression analysis.
Like single linear regression, a multiple linear regression estimates a line of best fit for the data you plug in. Unlike single linear regression, the line of best fit is estimated over more than two dimensions.
The line of best fit for a multiple linear regression takes the form Y=β0+β1X1+β2X2+…+βnXn, where you have n causal factors that you are looking at.
Just like with single linear regression, you will need to check the t-scores for each coefficient β and the R2 to determine how good of a fit the line is. In addition, a statistician analyzing a multiple linear regression will look at the F-statistic, which checks whether all of the coefficients β are good estimates.
Multiple linear regression introduces several challenges. First, if the causal factors are correlated with each other, your regression analysis won’t be able to determine which is causing the budget element to change. This will require you to mathematically transform one of the factors.
Second, if there is a trend in how your data deviates from the line of best fit, it may indicate that a line is not the best form. This is also the case if there is a trend between one of your causal factors and the data deviations.
|Take the Guesswork Out of Budget Forecastingindinero’s experts rely on budget forecasting methods you can trust.
The Right Budget Forecasting Method
Choosing the right budget forecasting method isn’t easy. Whereas projection and moving average don’t give you much insight into what you do to impact your budget, regression analysis requires technical knowledge typically learned in a year long statistics course.
In the companies that have one, budget forecasting is something typically handled by the chief financial officer. A CFO can improve your business by giving you insights into how you can improve your financial operations to increase your bottom line.
Many business owners think that budget forecasting is too complicated, and that the professionals to do it for them are financially out of reach. However, with fractional CFO services, businesses of all sizes can enjoy all the benefits of a CFO at a fraction of the cost.
A fractional CFO is an outside consultant who works with your business part time. Because a fractional CFO works with many businesses, they will have insights and connections that most CFOs lack.
indinero offers CFO, controller, and tax preparation services for businesses just like yours. Our specialty is businesses at the level of Seed funding through Series B funding. To get started with indinero’s financial services, contact us today for a consultation.


For my Finite Math class I was to play a game called Master Mind and evaluate the logic of the game.
First I guessed all blue and nothing happened. For a moment I was confused by this games feedback, I didn’t see any but I realized they were all wrong. Then I did all green and all were wrong again. All brown, I messed up and didn’t notice one was right. All purple, all wrong. At this point I noticed a brown was right and so I choose one brown to test if it was the first position that was right, the rest red to see if there were any red.
I got lucky and that was the solution one brown, three red. So it took me 5 moves on my first game and I won. I have to say six colors seamed like a lot to me, I think I was expecting four.
As for calculating the number of possibilities, four sets each have six possibilities. I almost thought 4 x 6 but no, I think it’s 6 x 6 x 6 x 6, so 1,296. After arriving at this number I checked online and it seams to be accurate.
The way I used feedback in the game was that when I got one right I planned to mix my code and see where I got it right then to leave the right one there and work on finding others. When all brown came back with one right, I knew there was one brown somewhere. If it had said two right then I would have known there were two brown somewhere.


Whether you are beginning a business, organizing a report or analyzing the financial wellness of your company, business calculations are essential. Understanding the basic principles of how to execute these calculations can help you generate better decisions when running your company.
The break-even point is a point when your bills equal the sales. You can calculate the break-even point by using a formula that features your expense of goods sold and your adjustable costs. This will allow you to determine the number of products you need www.businessrating.pro/market-values-and-equity-values/ to sell to break even. It is important to know ways to calculate the cost of products sold, plus the amount of money you need to earn for your set costs.
Depending on type of organization you own, you may have to calculate earnings margin. Earnings margin certainly is the difference between the revenue price of any product as well as the costs you must pay to make it. This measurement will help you identify costs problems, and can be required to safeguarded financing.
Additionally , you may need to determine net income. Net income is the money left over after all expenses are paid. You can imagine this by simply subtracting the expenses out of your revenue. For instance , if your food handling business makes custom cakes, it’ll need to estimation how much it will cost you to create a wedding cake.
Your cost of goods purchased is a computation that takes into account your margin plus the trade low cost you receive. These kinds of factors permit you to determine how much it will cost to build up a new product, along with how much you will need to charge customers for it.


When it comes to fluid measurements, understanding the conversion between different units is crucial. One common question that often arises is, “How many ounces are in a gallon?” In this comprehensive guide, we will delve into the conversion factors, explore the relationship between ounces and gallons, and provide practical examples to make this conversion a breeze.
Understanding the Basics
Before we dive into the specifics, let’s establish the basic units of measurement. The ounce (oz) and the gallon are both units of volume. The ounce is a smaller unit, while the gallon is a larger one. To bridge the gap between these two units, we need to comprehend the conversion factors.
- The Fluid Ounce (fl oz):
- The fluid ounce is a standard unit of measurement for volume in the United States.
- 1 fluid ounce is equivalent to approximately 0.0078125 gallons.
- This conversion factor is crucial for understanding how many ounces make up a gallon.
- The Gallon (gal):
- The gallon is a larger unit commonly used in the United States for measuring liquids.
- 1 gallon is equivalent to 128 fluid ounces.
- Knowing this conversion factor is key to answering the question, “How many ounces in a gallon?”
Calculating the Conversion:
Now that we have the basic conversion factors, let’s put them into action:
- To find out how many ounces are in a gallon, multiply the number of gallons by the conversion factor (128 fl oz per gallon).
If you have 2 gallons, the calculation would be 2 gallons * 128 fl oz/gallon = 256 fluid ounces.
Understanding Practical Applications:
The conversion between ounces and gallons is not only a theoretical concept but also a practical one. It finds applications in various aspects of daily life, especially in cooking and understanding product quantities.
- Cooking Measurements:
- Recipes often specify ingredients in fluid ounces or gallons. Understanding this conversion helps ensure accurate measurements in the kitchen.
- Product Labels:
- Many beverages and liquid products have their volume indicated on the label. Being able to convert between ounces and gallons allows consumers to grasp the overall quantity of a product.
In conclusion, the conversion between ounces and gallons is a fundamental skill that proves useful in both everyday life and specific applications like cooking and product consumption. By understanding the basic conversion factors and applying them in practical scenarios, you can confidently answer the question, “How many ounces in a gallon?” This knowledge not only enhances your understanding of fluid measurements but also contributes to precision in various activities.


A negative sign in front of the absolute value
Unit #2 – Absolute Value – Google Sites
Apr 25, 2016 — Placing a minus sign outside absolute value bars gives you a negative result — for example, –|6| = –6, and –|–6| = –6. Sample questions. Negate …
Solving Equations Containing Absolute Value – Cliffs Notes
Solving Equations Containing Absolute Value
Absolute value cannot be negative – the output of absolute value is always positive or zero. However, we can use negative inputs for absolute value, …
To solve an equation containing absolute value, isolate the absolute value on one side of the equation. Then set its contents equal to both the positive and neg
What is the absolute value of 4 ? – Byju’s
As this illustrates, if you take the negative of an absolute value (that is, if you have a “minus” sign in front of the absolute-value bars), you will get a …
Solve for q |q-8|=14 – Mathway
Solve for q |q-8|=14 | Mathway
When we take the absolute value of a number, it is always either positive or zero. If the original value is already positive or zero, the absolute value is the …
Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.
Intro to absolute value inequalities (video) – Khan Academy
Intro to absolute value inequalities (video) | Khan Academy
Sammy,. If I read your question correctly, then here’s the scoop. The absolute value of either a positive or a negative …
Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.
Absolute Value Inequalities – Explanation & Examples
The absolute value inequalities are the expressions that contain both absolute functions and inequality signs. There are four different inequality signs.
Absolute Value – Math Skills Overview Guide
Absolute Value – Math Skills Overview Guide – Library Guides at Davenport University
Absolute Value Functions – Varsity Tutors
Absolute Value Functions
To divide by a fraction, multiply by the reciprocal of the fraction.
How to graph y=absolute value of x – YouTube
This is video 1 of 11 that shows students how to graph the absolute value parent function using “the dance” and using a table, connecting the appearance of t…
Learn how to use a table to graph the absolute value function – YouTube
👉 Learn about graphing absolute value equations. An absolute value equation is an equation having the absolute value sign and the value of the equation is a…
Keywords: a negative sign in front of the absolute value


The Form Element Math reCaptcha in Quix 4 can sometimes take up a significant amount of space, which may affect the layout and aesthetics of your form. In such cases, we recommend using a simple math captcha instead of the default math captcha to optimize the space. Follow the steps below to make this change:
- Edit the Form Element: Open the Quix 4 page builder and navigate to the page where the form element with the math captcha is located. Edit the form element to access its settings.
- Locate the Math reCaptcha Field: Within the form element settings, find the field related to the math captcha. It is usually labeled as "Math reCaptcha" or similar.
- Change to Simple Math reCaptcha: Look for an option or setting that allows you to switch the math captcha type from the default to a Simple Math reCaptcha. This option may vary depending on the specific version of Quix you are using. Refer to the documentation or support resources provided by Quix for precise instructions on finding this option. Simple Math reCaptcha option, save the changes made to the form element. Update or publish the page to apply the modifications to the live site.
You can reduce the amount of space the captcha element takes up in your form by switching to a straightforward math ReCaptcha. This optimization can help improve your form's overall layout and design while still providing a reliable anti-spam measure.


The Rise of What Is Standard in Math
The exponent equals the range of zeros in addition to the very first digit in the number collection. The write every potential book algorithm is all about as not-P as you are able to get. Another style of rendering a three-dimensional object is known as ray tracing.
The Benefits of What Is Standard in Math
Certainly not, and it ought not be tolerated in the arts. The Common Core State Standards Initiative is an attempt to be certain that all students in public schools in the united states acquire the abilities and knowledge they require to be able to be ready to attain success at college or in the workforce. In Life Science, they will show knowledge of the needs and characteristics of animals and the way they interact with their own distinct environments.
Numerical tests are made to look at the reach of skills and abilities required to perform most jobs. One of the most intriguing subjects, science is an essential part of every kid’s school curriculum. This is excellent practice for you.
New Ideas Into What Is Standard in Math Never Before Revealed
Also within this section you produce your own cheat sheet by utilizing these formulas. Color may look like something that’s unnecessary for a calculator, but it’s super nice when you have multiple lines on the exact graph. The digits must be written initially, followed by the right quantity of corresponding zeros so the number has the appropriate decimal point.
Getting the Best What Is Standard in Math
At times it’s wonderful to be aware of what your calculator is doing behind the scenes. These functions don’t have any buttons on the calculator. Even though the tape calculator function has improved, we’d recommend Digits if you want a tape calculator.
What Is Standard in Math – Is it a Scam?
The GRE Subject Tests are much like the SAT Subject Tests in they test your understanding of a specific subject like chemistry or literature. Students understand that computers are utilised to store personal info. Math can be a great deal of fun!
The What Is Standard in Math Cover Up
You may choose the maximum number and the range of problems to produce, or you can decide on the non repeating Kindergarten, 1st, or 2nd Grade set of special troubles. The particular standard kind of a term or equation is dependent on just what the subject is. The issue isn’t to determine which is which.
You will learn how to figure interest rates and you’ll develop a better knowledge of mortgages, charge cards, and other varieties of loans. You can be certain that anytime you need our writing service, we’ll be available to assist you process them. You will discover some rather interesting things about how calculators work, and then you are going to discover how best to find a handle on your earnings and expenses.
What Is Standard in Math Secrets
Unary minus If the very first character is a minus, the calculator will assume you wish to subtract from the prior outcome. Because both values can be exceedingly close, you drop a great deal of digits in precision when computing the difference. Last, utilize the third calculator to simplify a fraction, utilizing the best common component.
The process of locating the variance is extremely much like finding the MAD, mean absolute deviation. The intent of rounding is to earn a number simpler to work with. At the conclusion of Step 5 you have located a statistic known as the sample variance, denoted by s2.
The Ultimate What Is Standard in Math Trick
Thus are collinear and we’re done. It is just the exact same for a normal algorithm in math. It’s really crucial that you’re ready to work between the 3 distinct types of equations of lines.
Standard notation is normally utilized in everyday math. You may see the present math calculations in a more compact display that’s below the major display of the calculator. The maths calculator comprises virtually every calculator that’s employed in a daily life.
If your school isn’t currently recycling or might be in a position to do it better, you might have the students start by researching what the school recycles and what’s being put into the trash. These grade-based worksheets are designed bearing in mind the distinctive features of kids of different ages. Nim went into a supermarket to purchase some fruit.
But What About What Is Standard in Math?
The questions on such tests can be composed of the concepts in the normal numerical reasoning tests seen above. While a lot of these kinds of tests are fee-based, there are a number of no-cost on-line resources for assessments. These varieties of tests typically have a lot of components, including language, math and computer computer software skills, in addition to typing speed.
My initial interview was supposed to complete an application and take a typical math test. Answer the simple questions first, and return and answer the tougher ones when you have time remaining on that test. If you score a whole lot higher on a single test, select it.
Many different sources of data are typically distributed. Do not buy this software until you’re instructed to achieve that. You can also download ExamView software.
Since the training course is self-paced, you can finish the course in fewer than 16 weeks. The lessons which make up this course are full of practical exercises and information you can put to immediate use. Ask students to concentrate on using these words since they discuss the subject of the day.
What Is Standard in Math Features
From general math, nature and weather, company and accounting tools, and sometimes even percentage calculators, we’ve got every type you will need to finish your homework or job task. Byju’s classes unique means of solving the maths problem will force you to learn the method by which the equation was created, which is way superior than memorizing and applying the formula. One of the chief reasons this calculator is such a huge success is it is simple to use.
The Downside Risk of What Is Standard in Math
The standards draw on the main foreign models for mathematical practice, and research. You will find a handy way of converting one kind of measurement to another, and you’re going to be in a position to calculate areas correctly, and therefore you don’t overspend on your next home improvement project. As a consequence of this fact our understanding of the typical normal distribution can be utilized in a range of applications.
A Startling Fact about What Is Standard in Math Uncovered
Determine the total amount of time that has passed. We start by setting up coordinates. Quite simply, Standard form is a method of writing down an extremely large or very smaller numbers in the effortless way.


The Importance of STEM Today
Children today are being exposed to scientific and mathematical concepts starting at a young age, as careers in STEM (Science, Technology, Engineering and Math) are becoming increasingly important. It is evident, now more than ever, that jobs in STEM are needed to keep society advancing. By introducing children to STEM when they are young, they are gaining the confidence needed to excel in the field. However, the STEM education that most schools offer does not consider the fact that this subject is not one-size fits- all.