Beaver Ridge Elementary School was awarded a $2,000 grant to fully fund a new program called Mastering Math Skills Through Music.
The program concentrates on education through the arts, and it was pushed by early intervention teacher Kathy Boyer.
"It's like a high-energy, music-movement math skills program," said Boyer. She added that the fun program is geared more for third, fourth and fifth graders, but it has basic addition and subtraction activities that can be used with younger students.
She first heard about the program two years ago while attending the Georgia Council of Teachers of Mathematics conference. She went to a session headed by the author of the program, and she was hooked immediately.
"I had so much fun as an adult that I knew the kids would enjoy it," she said.
Boyer also noted that the school especially aims to use the program for at-risk students.
Backed by the Foresite Group, Advanced Disposal, the Norcross Cluster Schools Partnership and the Norcross Arts Alliance, the grant was awarded to the school Wednesday afternoon. The Foresite Group and Advanced Disposal helped fund the grant, and the Norcross Cluster Schools Partnership and the Norcross Arts Alliance also supported the grant since they have begun several programs to improve both education and art in local schools.
"I'm glad I did my part," said Norcross Arts Alliance board member Arlene Beckles, who was a major player in getting the grant fulfilled. When she first heard Boyer had submitted a grant request for the program, Beckles said, she got to work and twisted the arms of people whom she knew would want to support the school.
Members of the city council and representatives from the sponsors were present to award the check to the school Wednesday.


Agnes at Brown will be held October 26-28, 2012 at Brown University.
Funding is provided by the National Science Foundation and Brown University.
TITLES AND ABSTRACTS:
- Dmitry Arinkin (University of Wisconsin at Madison), Singular support of coherent sheaves: The notion of singular support plays an important role in the theory of constructible (and perverse) sheaves and holonomic D-modules. Informally, the singular support measures `non-smoothness' of the object. For instance, the singular support of a constructible sheaf is zero if and only if the sheaf is locally constant.
The goal of this talk is to sketch an analogous theory for coherent sheaves. It turns out that the singular support could be non-trivial only if the variety is singular. I will define singular support for coherent sheaves on a singular variety that is locally a complete intersection. The singular support measures `imperfection' of a coherent sheaf: it equals zero if and only if the coherent sheaf has finite Tor dimension (i.e., the sheaf is perfect).
- Frédéric Campana (Université Nancy), The geometry of orbifold pairs and birational classification: An obifold pair (X,D) consists of a complex projective variety together with an effective Q-divisor analogous to a ramification divisor. Orbifold pairs interpolate between projective and quasi-projective varieties, and naturally arise from multiple fibres of fibrations, which they permit to virtually eliminate by ramified base-change. Their geometry can be defined in complete analogy with the particular case of projective manifolds (ie: when D=0). Only in this enlarged category can arbitrary (quasi)-projective manifolds be decomposed in objects for which the canonical bundle is either ample, numerically trivial, or anti-ample.
- Melody Chan (Harvard University), From algebraic to tropical curves: I will give an expository talk introducing tropical geometry via the the study of tropical curves, and linear series on them, in relation to algebraic curves. In particular, I will highlight recent developments in the subject by O. Amini, M. Baker, L. Caporaso, and others.
- Daniel Huybrechts (Universität Bonn), Cycles on K3 surfaces: I will survey recent progress on the Chow group of K3 surfaces (due to O'Grady, Voisin, Kemeny and myself). On the one hand, we can now prove that symplectic automorphisms of finite order act trivially on the Chow group of degree zero cycles (as predicted by the Bloch-Beilinson philosophy) and on the other hand the role of the Beauville-Voisin ring has become clearer.
- Hee Oh (Brown University), Ergodic theory and rational points on homogeneous varieties
- Andrei Okounkov (Columbia University), The M-theory index
- Cathy O'Neil (New York), How math is used outside academia: We
will explore some common mathematical models, their use, their
transparency, and their impact in the fields of finance, economics,
medicine, education, and on the internet.
- Christian Schnell (Stony Brook University), From the generic vanishing theorem to D-modules: In the late 1980s, Green and Lazarsfeld studied the cohomology of topologically trivial line bundles on compact Kaehler manifolds. Among other things, they proved the "generic vanishing theorem": the cohomology of a generic such line bundle vanishes below a certain degree that only depends on the manifold. Recently, Mihnea Popa and I discovered that behind those results lies a certain class of D-modules on abelian varieties; in the talk, I am going to explain why.
- Angelo Vistoli (Scuola Normale Superiore, Pisa), The fundamental gerbe of a curve and the section conjecture: I will report on joint work with Niels Borne. I will explain how to formulate Grothendieck's section conjecture in terms of Deligne's relative fundamental groupoid of a curve. Then I'll discuss our work about the Nori fundamental gerbe, and show how this leads naturally to a formulation of the section conjecture in positive characteristic.


High fidelity simulation of corotational linear FEM for incompressible materials
High fidelity simulation of incompressible materials using corotational linear FEM
Mihai Francu, Arni Asgeirsson, and Kenny Erleben
We present a novel method of simulating incompressible materials undergoing large deformation without locking artifacts. We apply it for simulating silicone soft robots with a Poisson ratio close to 0.5. The new approach is based on the mixed finite element method (FEM) using a pressure-displacement formulation; the deviatoric deformation is still handled in a traditional fashion. We support large deformations without volume increase using the corotational formulation of linear elasticity. Stability is ensured by an implicit integration scheme which always reduces to a sparse linear system. For even more deformation accuracy we support higher-order simulation through the use of Bernstein-Bézier polynomials.


We investigated perimeter and area by thinking about objects in the classroom and then measuring their surfaces for perimeter. We then talked about area and what that represented in a 2-D shape and measured area of those classroom surfaces. Students began to understand that their completed teapot package would be a 3-D shape, and that we would measure the volume. Some students chose to measure rectangular objects like tables and cabinets. Keita and Haikal headed to the hallway to measure it in meters. Jesper and Caleb decided to find the area of a circular object and then work on volume of the box of tissues. They had to discover the formula for finding the area of a circle.
Students then drew out their ideas for the teapot package as a group. They measured their idea for a teapot package exactly, labeling dimensions with cm. For some, this meant connecting several pieces of paper together so that they could fit the entire package.
We then talked about scale or sizing the package so that it fit on a regular sheet of paper. Students used 1 cm graph paper to draw out a scaled version of their teapot. They chose the scale. For some, it was 2 cm, and for some it was 5 cm. Their new drawings reflected the scale.
One group, with a challenging design for their teapot package (a maple leaf) ran into problems trying to scale down their design. It wasn’t a rectangular prism or a trapezoid like some of the other shapes, and they couldn’t figure out how to scale it.
Even though they wanted to give up, through some collaboration, they began to figure it out. Yoshie said that she had to find the area of a complex shape in a past school but couldn’t quite figure out how to explain it. Eric came in and suggested dividing the shape into triangles and then finding the area of those triangles.
With some careful measurement, Yoshie, Eric and Kalea set to work trying to figure out the area of a variety of triangles: from acute triangles to right triangles. It’s taking a while, but they are engaged in the journey.
Others finished up their scaled drawings and set to work on designing their teapot package on Sketchup. There were some good engaging hours of Math this week.


Qaza umri namaz padhne ka tarikaArea between a curve and a line. Area between a curve and a line ... where s AC is the distance from A to the intersection point, C, along its line-of-sight, and s BC is the distance from B to C, along its line-of-sight. If either one of those distances is negative, the intersection point is behind the line-of-sight. That is, there is no real intersection in the direction of the bearing. Introduction: Root Locus Controller Design. In this tutorial, we will introduce the root locus, show how to create it using MATLAB, and demonstrate how to design feedback controllers that satisfy certain performance criteria through the use of the root locus. Geometry beyond the plane defined by this value is not rendered. The plane is perpendicular to the camera’s forward (Z) direction. See in Glossary will not be rendered. The diverging corner lines of the image along with the two clipping planes define a truncated pyramid - the view frustum.
(b) Find parametric equations for the line of intersection. To nd the equation of the line of intersection, we need a point on the line and a direction vector. Since the line lies in both planes, it is orthogonal to both N~ 1 and N~ 2. Thus, a direction vector for the line is N~ 1 N~ 2 = ~ i j ~k 4 2 1 2 1 4 = h7;18;8i: Introduction: Root Locus Controller Design. In this tutorial, we will introduce the root locus, show how to create it using MATLAB, and demonstrate how to design feedback controllers that satisfy certain performance criteria through the use of the root locus.
- Vintage jet ski for saleVenn diagrams. The union, intersection, difference and complement of sets can be depicted graphically by means of Venn diagrams. In a Venn diagram the universe U is represented by points within a rectangle and sets A, B, C, etc. are represented by points inside circles within the rectangle. Though the theme of this page is the points that lie on both of two surfaces, let us begin with only one, the contour x 2 z - xy 2 = 4 or essentially z = (xy 2 + 4)/x 2.Let us suppose that we want to find all the points on this surface at which a vector normal to the surface is parallel to the yz-plane.
- All bearings are measured in a horizontal plane. Example 10. State the bearing of the point P in each of the following diagrams: Solution: a. Mark the angle in a clockwise direction by indicating the turn between the north line and the line joining the centre of the compass to the point P. The bearing of point P is 048°. b. The calculation method uses the cross-product of two vectors to extract the apparent dip answer. The 1st vector is the pole to the vertical plane containing the apparent dip direction. The 2nd vector is the pole to the strike and dip plane. The intersection of the two planes perpindicular to these vectors will always yield the
- Baby chick swollen abdomenThe dial plate is the flat, horizontal surface that receives the shadow of both the style and the nodus. The plate is marked with lines that the shadows move across to indicate time of day and time of year. To create your own sundial use the hour line angle calculator at the top.
Conversely, every line is the set of all solutions of a linear equation. The phrase "linear equation" takes its origin in this correspondence between lines and equations: a linear equation in two variables is an equation whose solutions form a line. If b ≠ 0, the line is the graph of the function of x that has been defined in the preceding ... want to calculate the line of intersection between a geological horizon (i.e. bedrock, sandstone, etc) or the water table and the ground surface; or you might want to calculate the line of intersection between a surface based on airborne laser scanning data and a slightly inclined plane. Whatever data you have, want to calculate the line of intersection between a geological horizon (i.e. bedrock, sandstone, etc) or the water table and the ground surface; or you might want to calculate the line of intersection between a surface based on airborne laser scanning data and a slightly inclined plane. Whatever data you have,
Substituting λ = 1, μ = -3 into the equation of lines gives the point of intersection as being:x = 0, y = 4, z = -2.Therefore the lines meet at (0, 4, -2)The angle between the lines is the angle between the direction vectors, so using the scalar product we get,This gives us θ = 148.8o, but you must remember that when the two vectors ... Intersection of a line and a plane 1. Find the intersection of the line through the points (1, 3, 0) and (1, 2, 4) with the plane through the points (0, 0, 0), (1, 1, 0) and (0, 1, 1). Answer: This brings together a number of things we’ve learned. We must ﬁnd the equa tions of the line and the plane and then ﬁnd the intersection. Aio bot reviewLine plane intersection calculator Find the point of intersection of the lines given below and then find the plane determined by these lines. The point of intersection is . (Type an ordered triple.) A 78x- 104y + 18z= -91 B -78x + 104y- 18z = 91 C. - 39x + 26y+ 13z= 0 D.- 39x + 26y+ 13z- 91 Find the plane determined by the intersecting lines. The equation of the plane is . Apr 12, 2019 · Website project website project a plane is through the points 1 2 and perpendicular to 9 3 intersection of two planes a relative position la citadelle Website Project Website Project A Plane Is Through The Points 1 2 And Perpendicular To 9 3 Intersection Of Two Planes A Relative Position La Citadelle Line Of Intersection Two Planes In… Read More » Jul 28, 2013 · Would someone be kind enough to help me by showing (if possible) how to place the point of intersection (s1, s2, s3) between the plane and the line through the points (i) and (r), so that it lies on the line and not next to it. The coordinates seem to be calculated correctly, but the placement in the coordinate system turns out wrong:
Make your Flight Plan at SkyVector.com. SkyVector is a free online flight planner. Flight planning is easy on our large collection of Aeronautical Charts, including Sectional Charts, Approach Plates, IFR Enroute Charts, and Helicopter route charts. (b) Find parametric equations for the line of intersection. To nd the equation of the line of intersection, we need a point on the line and a direction vector. Since the line lies in both planes, it is orthogonal to both N~ 1 and N~ 2. Thus, a direction vector for the line is N~ 1 N~ 2 = ~ i j ~k 4 2 1 2 1 4 = h7;18;8i: 6. 7. 8. Angle between a Line and a Plane Point of Intersection of a Line and a Plane. Parametric Representation of a Curve. Exercises on Chapter XX. PAGE. 487. 488. 490. 494 CHAPTER XXI THE PLANE AND THE STRAIGHT LINE. ADVANCED METHODS 1. Linear Combination of Two Planes.. 2. Three Planes through a Line. Three Points on a Line 3. Line in a ...
The 3 terms are point, line, and plane . Do not be intimidated by the the phrase "undefined." You may already know a pretty good definition for these terms, especially the first two. NEW! For an exciting, interactive way to learn about the undefined terms in geometry, please take a look at our Geometer's Sketchpad Tutorial . (You will need ... BMI Calculator » Triangle Calculators » Length and Distance Conversions » SD SE Mean Median Variance » Blood Type Child Parental Calculator » Unicode, UTF8, Hexidecimal » RGB, Hex, HTML Color Conversion » G-Force RPM Calculator » Chemical Molecular Weight Calculator » Mole, Moles to Grams Calculator » R Plot PCH Symbols » Dilution ... If two planes intersect, they intersect in a straight line. This line divides each into two half-plane. Figure formed by two half-planes and the line is called a dihedral angle. In this straight - this is the edge angle, the half-plane - it faces the corner. Apr 15, 2020 · This perimeter can be drawn on the plan and. in Fig. 12/12, it is shown as the line marked 'SECT 2.12". Point 2 must lie on this line: it must also he on the line marked 6.2 and its exact position is the intersection of these two lines. Point 12' is the intersection of the same section line and the line marked 8.12. The most sophisticated and comprehensive graphing calculator online. Includes all the functions and options you might need. Easy to use and 100% Free! # PythonCaller Script Example (Python 2.7 only) # Create the intersection point between a plane containing the first three vertices # of 3D polygon and a straight line containing the first segment of 3D line. Question: Find The Angle Of Intersection Of The Plane -5x-5y+2z = -5 With The Plane 4x + 2y -1z = 4.Answer In Radians:and In Degrees:My Answer Is 2.82487299 Radiansand 161.8533 DegreesI Know The Formulas Is Cos Theta = A Dot B / Magnitude Of A Times Magnitude Of Bthus Theta = Arccos A Dot B / Magnitude Of A Times Magnitude Of BCan Some One Please Check My Answer ...
Plane is a surface containing completely each straight line, connecting its any points. The plane equation can be found in the next ways: If coordinates of three points A ( x 1, y 1, z 1 ), B ( x 2, y 2, z 2) and C ( x 3, y 3, z 3) lying on a plane are defined then the plane equation can be found using the following formula. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Understand that solutions to a system of two linear equations in two ... Liner graph calculators, help with algebra problem, FLORIDA SCHOOL GRADING SCALE IN DECIMAL FORM. Ks2algebra, ti calculator roms, root sums chart, algebra games for coordinate plane, Prentice hall physics answer sheet, can a TI 84 tell you asymptotes.
Line-Plane Intersection. The plane determined by the points , , and and the line passing through the points and intersect in a point which can be determined by solving the four simultaneous equations the line equation within that of the plane equation such that (a+λm)•n=k. Solve for the value of λand subsequently derive the common point of intersection through substitution of λinto the line equation. (iii) intersection between 2 planes: A. If one plane is presented in scalar product form and the other in parametric form, Example: 6 1 3 1 = An online calculator to find and graph the intersection of two lines. Calculator will generate a step-by-step explanation. Free Angle a Calculator - calculate angle between line inetersection a step by step. ... Plane Geometry ... line-intersection-calculator. en.
Line plane intersection calculator The difference quotient gives the precise slope of the tangent line by sliding the second point closer and closer to (7, 9) until its distance from (7, 9) is infinitely small. 10). Figure 10. Inequality solver that solves an inequality with the details of the calculation: linear Plane and line intersection calculator. The most fundamental aspects of the Geometry emerge from these concepts. Such lines show the relationship between the angles formed. Parallel Lines. Parallel lines are the lines in the same plane that, if extended to infinity, would never intersect. The angles formed by the intersection of a line with two parallel lines have some interesting ... Mathematical graph and charting software for geometry and statistics. The calculator can do statistics, best fits, function plotting, integration. It handles vectors, matrices, complex numbers , quaternions , coordinates , regular polygons and intersections. For point, line, plane, sphere, circle Calc 3D calculates distances, intersections, and ...
ACM SIGGRAPH is a thriving international organization. Everybody who shares ACM SIGGRAPH’s love for computer graphics and interactive techniques is warmly invited to join ACM SIGGRAPH and attend SIGGRAPH or SIGGRAPH Asia. Join Today! Pure Bending . Kinematics of pure bending: When a bar is subjected to a pure bending moment as shown in the figure it is observed that axial lines bend to form circumferential lines and transverse lines remain straight and become radial lines. In the process of bending there are axial line that do not extend or contract. The following three equations define three planes: Exercise a) Vary the sliders for the coefficient of the equations and watch the consequences. b) Adjust the sliders for the coefficients so that two planes are parallel, three planes are parallel, all three planes form a cluster of planes intersecting in one common line.


Posted on Apr 12, 2012 in Science & nature
Why do the sun and the moon both appear to be the same size? I know enough science to know they aren’t really the same size. But how does it work out that they look the same? Coincidence?
No, not really. But doesn’t it seem kind of convenient that the moon appears just large enough in the sky to cover the sun during a solar eclipse? How does that work? Isn’t the sun huge compared to the moon?
Here’s the deal: The moon has a diameter of about 3,476 km. The sun’s diameter is roughly 1,392,000 km. If you want to do the math yourself, you’re welcome to it, but that makes the sun roughly 400 times larger than the moon — 400.460 times, for you sticklers out there.
Here’s where things get fun. The sun is, on average, 149,597,870 km from Earth. The moon, on average, is about 384,400 km from Earth. Again, I’ll take care of the math here for you, so that makes the sun roughly 400 times as far from the Earth as the moon is — 389.172 times, using those mean distances.
Now, simple inference alone should be enough to tell you that makes both of those celestial bodies appear approximately the same size from Earth as a result, but if you really like math and science, then we can use a thing called angular diameter to show the apparent size of an object seen from a given position. So, using the formula:
…where 2.06 x 105 is the number of arc seconds in a radian, and make sure your distances are in the same units (i.e., km and km). This gives you an answer in arc seconds — simply divide by 60 to get an answer in arc minutes.
Now that your brain hurts, how about I just tell you that the angular diameter of the sun as seen from the Earth varies between 31.6 and 32.7 arc minutes, and the moon between 29.3 and 34.1 arc minutes.
So a lot of fancy math and words to tell you what I already told you in plain English.
Do keep in mind, the sun and moon are will rarely, if ever, appear the exact same size — due to the moon’s varying distance from the Earth and the Earth’s varying distance from the sun, their respective angular diameters won’t always sync up. But you have to admit, it’s close enough for government work.
>> What is a solar flare?
How fortunate to have this awesome combination of size and distance that allows us to have such spectacular things as solar eclipses both total and annular — an annular eclipse being that truly spectacular type where the moon appears just a bit smaller than the sun, leaving a brilliant ring. But… why?
According to astronomers, this phenomenon doesn’t occur anywhere else in our solar system. Does it occur in other solar systems? Maybe. We haven’t been there yet to take the measurements.
So the truth is, no one really knows what the odds are of this working out so wonderfully. Even a Vegas bookmaker would scratch his head at this one.
It’s worth mentioning, it hasn’t always been — and won’t always be — this way. The moon is moving away from the Earth by about 4 cm every year. This means that millions of years ago, there were no annular eclipses because the moon always appeared bigger than the sun. Also, this means that millions of years from now, there won’t be any total eclipses — they’ll all be annular — as the moon will always appear smaller than the sun.
Enjoy it while you can — your great grandchildren (times 100) will never know a total eclipse, except in pictures and stories.
Image above based on NASA educational drawing, showing the approximate relative size (not distance between) of the moon, the Earth and the sun. All three photos thanks to NASA and US taxpayers.
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Conditional Probabilities (CP) (P|A/B) and the Deductive Closure Principle (DCP) (If S knows P and P-> Q, P knows Q) are tightly knit concepts which is helpful for considering probabilities in axiomatic theories, especially in science and religion. Suppose that we evaluate the truth of some proposition P. Given axioms, say, A1…An, a person S believes P on the basis of the presumed axioms. In this case, with respect to conditional probabilities, P is probable—more probable than not, that is—given the axioms (and so S accepts P). Suppose, further, that P->Q (Q being a logical entailment of P). It is, then, appropriate to say that given the axioms, Q is more probable than not. I find that this is very significant for understanding many issues found in conceptual problems which arise in science. Here is an example from quantum physics:
- Jones, having reviewed the evidence for the Many Worlds Interpretation E1…En, believes that the Many Worlds Interpretation to Quantum Mechanics is true.
Jones, so far as we know, does not rely on any previous axioms in holding that the Many Worlds Interpretation is true. Indeed, Jones can be said to merely make his judgement on the evidence presented to him; however, this might become problematic when other factors come into consideration. For instance, suppose that the evidence in question was inconclusive, that is, didn’t amount to a proof and that, being persuaded by other considerations i.e., some other epistemological hypothesis, Jones decided that the epistemological hypothesis—since it was, let us say, inconsistent with the Many Worlds Interpretation—amounted to rejecting the Many Worlds Interpretation (since Jones had better grounds for thinking that the epistemological hypothesis was more probable than his evidence for the Many Worlds Interpretation. Jones has applied conditional probability in the following way: Suppose A is “Many Worlds Interpretation” and B “Epistemological Hypothesis”, it would mean that for Jones (P|A/B) = 0. Two inconsistent propositions have a 0 probability when taken conjunctively. (To see this consider the proposition “at some time T some object O exists and simultaneously does not exist”, a proposition with 0 probability since it is impossible—logically and metaphysically). So, since the evidence in favor or B is higher than A, he sees it as (P|A/B) < (P|not-A/B) (in the latter case, the probability amounts to 1. Inasmuch as Jones is not being ad hoc here (in denying A on the grounds that he does not like it (and so happens to accept B), Jones is perfectly rational in his conditional probability. Things are not much different when we consider the following case:
2. Sharon, a theist, believes that the Many Worlds Interpretation to Quantum Mechanics is false.
In a nutshell, Jones is pro-Many Worlds, and Sharon is against Many-Worlds. Let us apply CP and DCP here to see what is at work.
For Sharon, she believes that, where A is the proposition “that God exists” and B “the relevant evidence”, that (P|A/B) > .5. She, then, claims to know A (since, on conditional probability, B is more probable than not). But, since theism—some would argue (and I shall just presume it here)—that the Many Worlds Interpretation is logically inconsistent with A, it follows that A->Q (where Q is the proposition that “the Many Worlds Interpretation is false.” So, given the conditional probability of A on B, applying the DCP, Sharon reasonably believes that A and therefore that the Many Worlds Interpretation is false. The question now arises though: What is the conceptual difference between the case of Jones and the case of Sharon? My answer: nothing at all.
Whether it is a theological hypothesis or an epistemic one, it makes no difference regarding the probability of such statements. If S accepts P on the basis that it is more probable than not that P is true given Q, it does not matter if P is theological or epistemological. Even if one accepts P on the basis that they know some other proposition P* which implies P, if P* is a theological hypothesis or historical or scientific or whatever, it has no bearing on the truth of P itself. If one denies this, it can be for no other reason than begging the question (and I suspect that this goes on all the time).
 The latter half of this post could have been “Issues in Philosophy of Mind/Religion, Metaphysics, Logic” et cetera. I just used the quantum mechanical example as an example of a possible area that my speculations could have been relevant.


Squirrel AI Learning, a Shanghai-based online after-college tutoring company, plans to expand into foreign markets in two years by developing an English-language curriculum for mathematics as well as Mandarin lessons for non-native speakers.
“The reason mathematics and Chinese-language lessons there are so many foreigners who want to learn the Chinese language, and they do not have good options,” Joleen Liang, a companion at Squirrel AI Learning, stated in an interview last week in Hong Kong. “So, we’re going to expand our market in two years.”
Squirrel, whose formal name is Shanghai Yixue Education Technology Co., offers personalized lessons for students from elementary to high school through online courses and at brick-and-mortar learning centres.
Prospective students are first put through a diagnostic check to assess which areas in the subject they are weak. The AI algorithms will then cater the tutoring to focus on the areas of weakness, reducing the amount of time spent on unneeded coaching by 80%, according to Liang.
The firm’s adaptive learning methods claim to be able to recognize information gaps in real-time through the studying course of, then immediately fills them with tutorial content to close those gaps. The algorithms give each scholar a personalized learning plan and determine which areas the scholar is weak at, allowing human teachers to hone in on the weaknesses.
Squirrel fees decrease for its services in less well-off parts of China. It has also donated 1 million learning accounts value 10 million yuan (US$1.5 million) to underprivileged families in weak mountainous areas through the Qingxiyuanshan Educational Charity Foundation.
The company has so far raised US$150 million in three rounds of fundraising, giving it a valuation that exceeds US$1.1 billion and making it a so-called unicorn, according to an April statement.


Colloquium of the Central Academic Institution of Orientation and Undergraduate Studies
The 40th Colloquium of the Faculty of Basic Sciences will be held on Wednesday, 13. November 2019 starting at 17:00 in the auditorium in Flandernstrasse.
Math in Motion
PROF. DR. BURKHARD ALPERS
37. Mathematics competition with award ceremony
Here is the current mathematics competition.
PROF. DR. RER. NAT. JOACHIM GAUKEL
Optical vibration measurement
PROF. DR.-ING. DIPL.-ING JOACHIM BERKEMER
PROF. DR. RER. NAT. HANNO KÄSS
PROF. DR. MARCEL WIEDEMANN
Further information is available in our brochure.
List of colloquia since 2000
Interested? Apply! for the Wintersemester 2023/24
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The Department of Mathematical Sciences is pleased to invite you to the International Conference on Environmental Mathematics (ICE-MATH2016) to be held on November 14-16, 2016. The conference aims to bring together leading researchers and academic scientists to exchange ideas and to share their experiences and research results and findings about different topics related to environmental mathematics. The conference will be also an excellent opportunity for researchers, educators and decision makers to discuss results of conceptual, constructive, empirical, experimental, or theoretical work in all areas of Environmental Mathematics and the role of mathematics in solving certain environmental issues.
The conference will discuss the role of mathematics in the following environment related fields:
The conference will consist of three invited talks and several 20 minute talks by participants. The participants will be faculty members from local, regional and international educational and research institutions members of government and non-government organizations. Graduate students are welcome to present their work as well.


5th grade students are being introduced to ordered pair this week in Mrs. Jackson’s math class.
Category Archives: Math
Your child will be entering a new grade this August and it is required and expected by their classroom teacher, that they know their math facts at a quick pace. I have compiled a few math sites that will make their learning fun.
Clip art by http://phillipmartin.info
I have created a new category in our links section to the right to add new websites as I find them for your enjoyment and learning. Check back often for new activities. The new links are listed under A+ Summer Fun.


How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics
Math and Science Book Review
Eugenia Cheng takes on the ambitious task of trying to bring the excitement of math to the lay person through the study of category theory. This is a long shot that requires truckloads of metaphors. Luckily, she has a deft hand at metaphor and she does an admirable job of bringing her excitement about the subject matter to the page. She starts simple with, “Mathematics is the study of anything that obeys the rules of logic, using the rules of logic.” For you Vulcans out there, this means that math can study damn near anything, except for maybe teenage girls. One of the really cool aspects of math is that it is based on that very simple premise, math can take us to crazy new places. Another one of her great metaphors, “Do you know that feeling of climbing to the top of a hill, only to find that you can now see all the higher hills beyond it? Math is like that too. The more it progresses, the more things it comes up with to study.” This certainly brings to mind an internal exploration of logic and reason that can seem almost limitless in it’s scope and breadth. As long as you have the tools, there really are no limits to where math can take you and that really is exciting.
Two of the major tools to start this exploration are abstraction and generalization. Abstraction begs the budding mathematician to ignore some details so that the situation becomes easier to understand. In Cheng’s words, “Abstraction is like preparing to cook something and putting away the equipment and ingredients that you don’t need for this recipe, so that your kitchen is less cluttered. it is the process of putting away the ideas you don’t need for the present purposes, so that your brain is less cluttered.” She goes on to acknowledge that abstraction is also dangerous and where we lose a lot of people in the weeds. “Abstraction is the key to understanding what mathematics is. Abstraction is also at the heart of why mathematics can seem removed from ‘real life’. That detachment from reality is where math derives its strength, but also its limitations.” She emphasizes that one of the keys to the mathematical method is being very clear about your assumptions. This reminded me a lot of Nate Silver’s book, The Signal and The Noise, that dove deep into mathematical modeling. One of his major premises was that mathematical models need sunlight shone on their assumptions from the very beginning to be successful. You can tell that Cheng loves the process of abstraction because it opens up so many crazy doors, “Part of the process of abstraction is like using your imagination. Mathematical abstraction takes us into an imaginary world where anything is possible as long is it’s not contradictory. Can you imagine transparent Lego blocks?…Four dimensional Lego blocks? Invisible Lego blocks?”
Before she dives into generalization she spends some time on mathematical rigor. This is another area where I, as a physics major, always had a problem with math in school, mathematicians seemed to get all tied up in the minutia of the process which, in my mind, didn’t relate to the real world. Cheng poses that math really is all about the process and that’s what makes it interesting, “Math is a world in which the end does not justify the means: quite the reverse. The means justify the end; That’s the whole reason it’s there. It’s called mathematical proof,…” I’m starting to come around.
Generalization is the other major tool in a mathematicians toolbox. “This is the point of generalization in mathematics as well – you start with a familiar situation, and you modify it a bit so that it can become useful in more situations. It’s called generalization because it makes a concept more general, so that the notion of ‘cake’ can encompass some other things that aren’t exactly a cakes but are close.”
With these tools, imagination starts to become a mathematician’s friend. “The key in math is that things exist as soon as you imagine them, as long as they don’t cause a contradiction….Do you think it’s cheating to solve a problem by inventing a whole new concept and declaring it to be the answer? For me this is one of the most exciting aspects of math. As long as your new idea doesn’t cause a contradiction, you are free to invent it.” How many art majors would have become mathematicians with a teacher like Cheng? It’s a shame that we teach math in this painful, rote methodology that squeezes all of the excitement out of what rigor and logic have to offer. Math has been called a lot of things, but creative is rarely one of those things. How do we bring this excitement back to the classroom?
She never gets into the nitty gritty of category theory, but instead she alludes to it through many different examples. Here is one of them, “Whatever mathematics does to the world, category theory does for mathematics. It’s a sort of meta-mathematics like Lego Lego…Category theory is also an organizing principle, just one that operates inside the world of mathematics. It serves to organize mathematics.” I never truly understood category theory from the book, just that it is worth looking into in more detail.
I thoroughly enjoyed reading the book, especially the actually mathematical examples that took me out of my comfort zone. Those things that make you think beyond what you can see are what seem to bring true knowledge and this book is full of those things. Overall though, it’s her joy of the subject matter that makes the book work. It’s worth your while.


Aljabar linear elementer howard anton pdf. Constant exposure to high volumes can lead to hearing loss. I didn t even get a receipt confirmation from Ombudsman s office. Locking up the users in the PS3.
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Suryadi, Harini Machmudi. Teori dan Soal Pendahuluan Aljabar Linier. Jakarta: Graha Indonesia. Direktorat Pembinaan Sekolah Menengah Kejuruan. Friedberg, Stephen H. Linear Algebra. Prentice Hall. Mulyati, Yeti. Plomp, Tjeer. User Username Password Remember me. Notifications View Subscribe. Abstract This study aims to produce Linear Algebra module for mathematics education students.
Instruments used are in the form of validation sheet, test sheet and the questionnaire. The results showed that the Linear Algebra module that has been developed already met the aspects of good module quality, namely: the feasibility test module, Linear Algebra module that has been developed is valid based on the expert assessment; effectiveness test, where Linear Algebra module has an impact on the level of mastery and understanding of students on good criteria; test of practicality, where the result of questionnaire of practicality analysis shows that the module that has been developed can be implemented and used by the students.
Keywords plomp development model; linear algebra. Full Text: PDF. References Anton, Howard. Aljabar Linear Elementer. Ilham Anwar. Berbagai Pendekatan dalam Proses Belajar dan Mengajar. Jakarta: Bumi Aksara. Remember me.


CIMA P2: Learning Curves
It’s taken a while for me to get back on track with my CIMA P2 studies but here I am with an article on Learning Curves which is a feature of the CIMA P2 syllabus.
The Learning Curve
The learning curve relates to the observed tendency that workers become adept at a task, the more often they perform it. Hence the task will take less and less time the more often it is performed.
This is quite a simplistic way to look at the learning curve but there are many factors to consider when applying the learning curve and ultimately, understanding when and how to use it.
The official CIMA terminology for the learning curve can be found below:
Learning curve is the mathematical expression of the commonly observed effect that, as complex and labour-intensive procedures are repeated, unit labour times tend to decrease. The equation usually relates the average time taken per unit/batch to the cumulative number of units/batches produced.
– CIMA Terminology
History tells us that the “learning curve” was first observed during the construction of World War 2 aircraft. It was discovered, that, as workers gained more experience building complex aircraft it actually took less time to complete each. And not only that, but the rate at which learning took place was actually predictable.
In reality it was found that the cumulative average time per unit decreased by a fixed percentage each time the cumulative production doubled.
Learning Curve Example
The illustration below is using a learning rate of 80% and gives you a clear overview of the numbers involved.
Cumulative average time learning rate: 80%
|Batches||Cumulative average time per batch (hours)||Cumulative total (hours)|
Nevertheless, there is a more scientific way of generating this information above, in the form of an equation, which is expressed as The Learning Curve Formula.
And knowledge of how to use this formula is required for the P2 exam.
The Learning Curve Formula
The learning curve formula is simply expressed as y=ax^b
- y = cumulative average time taken per unit
- a = time taken for first unit
- x = total number of units
- b = the index of learning
- where b = the log of learning rate/ the log of 2
It’s a simple equation but perhaps the complex part is using the log tables when calculating the index of learning, as you may not be familiar with how to apply them on your calculator? I know it was relatively new to me.
While the formula itself gives you the answer for the Cumulative Average Time Taken Per Unit (Y), the CIMA P2 examiner might also ask you to calculate the Index of Learning (b). So it’s important to understand each element of the formula.
P2 Example Question on Learning Curves
So to see this formula in action let’s go through it step-by-step.
Q – Company B has a learning rate of 90% and the total time to make the first unit is 8 hours, use the learning curve formula to find out the average time per unit for 16 units
The above question gives us the following information:
a = 8 hours x = 16 units b = ?
- First of all we need to calculate (b) the index of learning by using log tables.
- So b = log of 90%/log of 2
- To calculate this on any scientific calculator you need to press the following:
- LOG, 0.9/LOG, 2 = -0.152
- Therefore, the index of learning (b) is -0.152
- Now we are in a position to complete the question.
- 8 x 16^-0.152 (8 hours multiply 16 units to the power of -0.152) = 5.25
- Therefore, the cumulative average time per unit (y) = 5.25 hours
- Finally, we need to multiply this by 16 units (16 x 5.25) = 84 hours.
Q – Calculate the index of learning when the learning rate is 80% and it takes 100 hours to produce 1 batch (I’ve used the table in the first illustration as a base for this question).
Here we know the learning curve formula is y=ax^b and b is the index of learning which can be calculated using log tables.
- b = log of 80%/log of 2
- Therefore, the index of learning b = -0.32192
- We can cross check this with the table in my first illustration to prove it’s the correct answer.
- So let’s use this data to calculate y based on 64 units.
- y = 100 (hours taken on first unit) x 64 (number of units) ^-0.321 (the index of learning). Remember the formula y=ax^b.
- Therefore, based on productions of 64 units, the cumulative time per unit (y) would be = 26.21 hours which is the same figure displayed in my original table.
- This confirms that the index of learning we calculated is correct.
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Washington State University Instructor of Mathematics and Statistics in Pullman, Washington
Summary of Duties
Washington State University, Tri-Cities campus, invites applications for a resident faculty position at the rank of Instructor in the Department of Mathematics and Statistics. Preference will be given to applicants with experience in teaching statistics. The successful candidate will be expected to utilize high impact, student centered pedagogical practices in all courses and be informed on current research-based practices in mathematics education used to foster student success.
The division of responsibilities in this mathematics faculty position will be 80% teaching (a respective teaching load of four courses per Fall and Spring semester) and 20% service. Service activities include mentoring undergraduate student research, participation in campus student recruitment, and/or participation in faculty governance committee work.
Duties and Responsibilities:
Teach undergraduate statistics and probability courses and one basic mathematics course The specific courses will include Basic Mathematics (MATH 100), Introduction to Statistical Methods (STAT 212); Probability and Statistics (MATH 360); Introductory Statistics for Engineers (STAT 370); Statistical Methods in Research (STAT 412)
Meet university service requirements through student mentoring, recruitment activities, and committee memberships
This faculty position is a 9-month, temporary, non-tenure track appointment made initially for one year. The position is available for the start of the Fall 2018 semester. Appointment will begin August 16, 2018 and end May 15, 2019. Position is 1.0 FTE and will be eligible for benefits. Salary is commensurate with training and experience.
Benefits Competitive benefits available hrs.wsu.edu/benefits
Earned doctorate in mathematics or related field involving significant quantitative skills
Record of teaching experience
Expertise in teaching statistics and basic math courses
Experience implementing high impact practices for teaching math courses
Experience with mentoring college students
Posting Detail Information
Special Instructions to Applicants
To apply visit www.wsujobs.com, position number 76668, and upload application materials. Applications must include a letter of application addressing qualifications and any additional requirements, a curriculum vitae, and reference contact information.
Review of application materials will begin immediately and continue until sufficient candidates are identified.
WASHINGTON STATE UNIVERSITY IS AN EQUAL OPPORTUNITY/AFFIRMATIVE ACTION EDUCATOR AND EMPLOYER. Members of ethnic minorities, women, special disabled veterans, veterans of the Vietnam-era, recently separated veterans, and other protected veterans, persons of disability and/or persons age 40 and over are encouraged to apply.
WSU is committed to excellence through diversity and faculty-friendly policy action, including partner accommodation and NSF ADVANCE Institutional Transformation programs (http://www.advance.wsu.edu/).
WSU employs only U.S. citizens and lawfully authorized non-U.S. citizens. All new employees must show employment eligibility verification as required by the U.S. Citizenship and Immigration Services.
WSU is committed to providing access and reasonable accommodation in its services, programs, activities, education and employment for individuals with disabilities. To request disability accommodation in the application process, contact Human Resource Services: 509-335-4521(v), Washington State TDD Relay Service: Voice Callers: 1-800-833-6384; TDD Callers: 1-800-833-6388, 509-335-1259(f), or firstname.lastname@example.org.
Employee Type: Faculty
Working Title: Instructor of Mathematics and Statistics
Position Number: 76668
College/Area: WSU Tri-Cities
Hiring Unit: College of Arts & Sciences
Department Link: WSU Tri-Cities Office of Academic Affairs College of Arts & Sciences
Work Location: Tri-Cities
Zip Code: 99354
Anticipated Start Date: 08/16/2018
Tenure Track: No
Full-Time/Part-Time: Full Time
Appointment Status: Temporary
Position Term in Months: 9
Monthly Salary: Salary is commensurate with training and experience.
Background Check: Yes
Type of Recruitment: Open Recruitment
Posting Open Date: 04/16/2018
Screening Begin Date: 04/24/2018
Open Until Filled (overrides close field): Yes
Posting Number: 20152371F


Train your brain in four key developmental areas by solving fun puzzles related to science, technology, engineering and mathematics.
Technology (Robot Transformer) - Convert the cube into a Robot, then figure out how to turn him back into a cube!
Engineering (Ball Bearing Test) - Can you work out how to make the ball bearings sit at opposite ends of the puzzle?
Mathematics (Number Challenge) - Can you make every row add up to 10? Arrange the numbers so every horizontal and vertical and the two corner to corner diagonal rows equal 10.
Science (Anti-Gravity Puzzle) - Break the Force of Nature! Place the rocket inside the cup, place on a flat surface, can you work out how to remove the rocket without moving or touching the cup?
Save 20% if you buy all four, choose the Full Set (four puzzles) option.
Solutions are included with each puzzle


When investfit projects future outcomes it uses a stochastic engine instead of a deterministic engine as in a spreadsheet model. The deterministic approach means the adviser or dealer group “determines” the investment market returns assumptions to forecast future outcomes. The problem with this approach is that these assumptions are static and this can lead to overly optimistic projections that underpin advice.
However a stochastic engine allows us to factor in the fact that markets go up and down and so market returns also go up and down. This gives us a far more robust projection and quality of advice. We can also measure how certain we can be of a particular outcome. Stochastic routines are used in many industries.


- What is this math symbol called?
- What does ∈ mean?
- Who is the father of math?
- Is God is a mathematician?
- Is 0 a real number?
- Is 0 an even number?
- How do you not cry in math?
- Who invented homework?
- Who found zero?
- Who is father of science?
- Is math man made?
- Who found zero in India?
- Is math discovered or invented?
- Who invented the mathematical signs?
What is this math symbol called?
Basic math symbolsSymbolSymbol NameMeaning / definition≠not equal signinequality≈approximately equalapproximation>strict inequalitygreater than.
What does ∈ mean?
set membership symbolThe symbol ∈ indicates set membership and means “is an element of” so that the statement x∈A means that x is an element of the set A. In other words, x is one of the objects in the collection of (possibly many) objects in the set A.
Who is the father of math?
ArchimedesArchimedes is known as the Father Of Mathematics. He lived between 287 BC – 212 BC. Syracuse, the Greek island of Sicily was his birthplace.
Is God is a mathematician?
Is God a Mathematician? investigates why mathematics is as powerful as it is. … Bestselling author and astrophysicist Mario Livio examines the lives and theories of history’s greatest mathematicians to ask how—if mathematics is an abstract construction of the human mind—it can so perfectly explain the physical world.
Is 0 a real number?
The number 0 is both real and imaginary. ): Includes real numbers, imaginary numbers, and sums and differences of real and imaginary numbers.
Is 0 an even number?
The use of the phrase “even number, or the number zero” implies that zero is not even. On the other hand, the mayor is lumping zero together with the even numbers, so he certainly doesn’t think it’s odd. So what is it – odd, even or neither? For mathematicians the answer is easy: zero is an even number.
How do you not cry in math?
Stopping Your Tears. Distract yourself. If you haven’t started crying yet, but think you might, try distracting yourself from your sad thoughts. Play a game on your phone, or try to joke around with a friend, or try engaging deeply in your math book, or listening carefully and fully to what your teacher is saying.
Who invented homework?
Horace MannInstead, it is believed that Horace Mann, an American 19th-century politician and educational reformer, invented the modern concept of homework and made it an educational essential in schools. He got the idea after traveling to Prussia and attending The Volksschulen (People’s Schools).
Who found zero?
MayansThe first recorded zero appeared in Mesopotamia around 3 B.C. The Mayans invented it independently circa 4 A.D. It was later devised in India in the mid-fifth century, spread to Cambodia near the end of the seventh century, and into China and the Islamic countries at the end of the eighth.
Who is father of science?
Galileo GalileiGalileo Galilei—The Father of Science.
Is math man made?
Their truth values are based on rules that humans created. Mathematics is thus an invented logic exercise, with no existence outside mankind’s conscious thought, a language of abstract relationships based on patterns discerned by brains, built to use those patterns to invent useful but artificial order from chaos.
Who found zero in India?
AryabhataWhat is widely found in textbooks in India is that a mathematician and astronomer, Aryabhata, in the 5th century used zero as a placeholder and in algorithms for finding square roots and cube roots in his Sanskrit treatises.
Is math discovered or invented?
2) Math is a human construct. Mathematics is not discovered, it is invented.
Who invented the mathematical signs?
This article contains Unicode mathematical symbols.SymbolNameFirst author to use·middle dot (for multiplication)Gottfried Leibniz⁄division slash (a.k.a. solidus)Thomas Twining≠inequality sign (not equal to)Leonhard Eulerx′prime symbol (for derivative)59 more rows


This set enables Primary 1 and 2 students to build and practise mathematical problem-solving competencies. Each set contains the LEGO® elements needed for twostudents. Building materials are contained in a storage bin with sorting tray, organisational stickers, base plates, brick separators and two LEGO® Minifigures, the problem-solvers Max and Mia.
• Use mathematical problem-solving competencies such as making sense of problems, reasoning, perseverance, precision, modeling and representation.
• Explore and practise Maths concepts such as numeracy, operations in base 10, algebraic thinking, measurement, data, geometry and spatial awareness
• Work collaboratively as well as individually
Piece count: 521


Friday, March 6, 2015
No, I'm NOT Smarter Than a 5th Grader!!
I spend a lot of time helping children with homework. Usually, it isn't a problem, because I am pretty smart, and they are all 12 and under.
Every week my 10 year old daughter gets a math packet that is about 40-50 problems. She does the packet on her own, skipping over the ones she needs help with. Most of the time she only has a few problems she needs help with. I can usually help her, but sometimes not. In which case I text people a picture of it, and if they don't know, I put it on Facebook.
For example these ones, from in the fall:
It's really not all that horrible since she only usually needs help with a few problems.
For a very long time, I didn't need to consult anyone if she needed help with a few problems here and there. I could always figure them out. Until a few weeks ago when she needed help with several questions.
It was late (like 11 PM late, too late to be thinking late). I was tired, and she hit's me with this one:
I was totally at a loss. I texted 3 sisters. No one could help me. I asked Facebook friends. No one replied. Then one of my sisters looked it up (thankd google) and texted me to figure out the whole square area, then subtract area the non shaded area for the answer. After that my daughter did it in two minutes, since she knew the formula to figure out area of a triangle ( I however, did not). I texted my sister that we got it and thanks.
When I was done, and was finally going to sit down my sister texted me about how I got the answer. Now, a math problem that didn't even belong to her kid was making her crazy. I tried to explain on text, but it wasn't working. An hour of texting later, she called me and I verbally explained. She understood and I got to finally sit down (AT 1215 AM)!!
Fast-forward to last Sunday. I get home from on overnight trip to see my sister and her band LOLAH play. It was a late night. I get two hours sleep. I drove 3 hours home had a bad headache and stomache ache (bar food, drinks, and little sleep anyone). My daughter informs me shortly after I walk through the door that she needs math help. Turns out, she needed help with 21 out of 45 problems! WTF??? Today this happens?? KILL ME NOW!
I was able to help her with most of them. Except these ones:
Ok, I will not tell you how these ended up being solved, because I really am not smart enough to explain it. See the 9 I wrote on the top one, I was wrong. Disregard that stupid 9. It should be an 8. See I can not do 5th grade math!
I spent 5 hours helping the girl with these 21 problems. The ones above I texted and posted to Facebook. Several people tried to help, but gave wrong solutions. Do you know how many people gave me correct solutions? ONE! Do you know who she is? A MATH teacher/tutor! She was the only person that know how to solve these.
These do not seem like 5th grade questions to me, or, apparently, any other adult I knew, since no one could do them!
I absolutely LOVE helping my kids with homework, I am good at it. But math at this age? No thanks! Anytime I hear my girl ask me sweetly for help with MATH, I start to sweat and my heart starts beating super fast! But who could say no to this face?
No really! Could you??? SUCH a cutie!
Needless to say, math is really not my favorite thing at this age. Before this, I had no problem helping her. My son, who is a 6th grader actually has easier math than she does. How is that even possible? I have no problem helping him. 5th grade math though? No Thanks!
I figure, I have 7 yrs of having school kids behind me and 12 yrs to go. I feel smarter already and I haven't even helped with high school homework yet! Just imagine how smart I will be twelve years from now!
How about you? Are YOU smarter than a 5th grader?


Fuzzy mathematics is traditionally done from the logical viewpoint, so the first step in introducing fuzzy metrics is often the transformation f(x,y) = exp(-d(x,y)).
Then we have the following correspondences:
d(x,y) = 0 if and only if f(x,y) = 1.
d(x,y) is plus infinity if and only if f(x,y) = 0.
d(x1, y1) < d(x2, y2) if and only if f(x1, y1) > f(x2, y2).
The axiom d(x,x) = 0 becomes f(x,x) = 1.
The axiom d(x,z) < d(x,y) + d(y,z) becomes f(x,y) * f(y,z) < f(x,z).
Non-expansive maps become maps which respect overlap by not letting it decrease.
However, this seems to be a rather superficial duality: basically two equivalent ways to write the same things using different notation.
The question is whether there is also a natural deeper duality here (of a contravariant nature, where function arrows would reverse direction when one switches between these two viewpoints).


One of the basic properties of numbers is that they may be expressed in exponential form. We are all familiar with the representation 1000 = 103 or 0.001 = 10-3. A more general way of stating this property is to say that any number (N) may be expressed as a base (B) raised to a power (x) or
In the examples above the formula the base is 10. Further examples using
base 10, base 2, and base e (where e = 2.718...) are given below in Table
The first four entries in the base-10 section look natural as do the entries in the base 2, but few students would immediately guess .301 as the appropriate exponent for 2 = 10x. Further, the natural base e (e = 2.71828..) probably seems at first an illogical base for representing numbers. As will be discussed below, exponential functions of the type y = aebx are very common in describing physical and chemical systems, and a basic understanding of this type of function is necessary.
The mathematical statement N = Bx serves as the basis for defining logarithms. The logarithm of a number (N) in base (B) is defined as (x).
logarithm(B)N = x
Two bases, 10 and e, are in common usage. The shorthand representations are:
base 10 logarithm10 N = log10 N = log NThus, the logarithm of a number is simply the power to which the base must be raised to give the number. Table 2 shows the log and ln of the numbers in Table 1.
There are a few basic rules for handling logarithms. Examples are given in base 10 but the rules are applicable to any base.
log (a x b) = log a + log b
log (2000) = log (2 x 1000) = log 2 + log 1000 = .301 + 3 = 3.301Rule 2: log (a/b) = log a - log b
log (2/4) = log 2 - log 4 = .301 - .602 = -.301Rule 3: log (a)b = b log a
log (4)3 = 3 log 4 = 3 x .602 = 1.806Rule 4: log (10)x = x
log 10-8 = -8If one has the logarithm of a number and wishes to find the number, one simply raises the base to the power of the logarithm. This is called taking the antilogarithm.
antilog .301 = 10.301 = 2Note: On most calculators, antilogarithms may be taken by
While logarithms are interesting and useful in their own right, they have greatest applicability for us in dealing with exponential functions.
One of the very common functional relationships appearing from experimental observations is that of an exponential increase or decrease. This takes the form of an expression as
y = ex and y = e-x
In the more general form this appears as
y = eax and y = e-ax
where a groups together any quantities that can be considered to be constant during the variation of x and y. When graphed, these functions appear as seen in Figure 1 (note that when x = 0, y becomes = 1). Base e logarithms can be converted to base 10 logarithms.
Figure 1. Exponential Functions
Since it is very difficult to obtain the exact form of the coefficient
a from graphs such as these, it becomes more convenient to apply logarithms
to functions in this form. Thus,
or 2.3 log y = ax. [Note that a' = a/2.3 ]
and a plot of ln (or log) y versus x will then give a straight line whose slope will be "a." The same considerations apply to these expressions when they are straight lines as to any straight line.
In a simple case, consider the data from Table 3 for the decomposition
of hydrogen peroxide. Two ways in which these data can be graphed are shown
below: (a) concentration against time on rectangular coordinates, (b) log
concentration against time on rectangular coordinates. These are illustrated
in Figures 2a - 2b.
Figure 2a. Decomposition of Hydrogen Peroxide
Figure 2b. Decomposition of Hydrogen Peroxide
Whether one uses the logarithmic or exponential form for such relationships depends on what is to be determined. Mathematically the exponential form has certain advantages while graphically the logarithmic form is more informative. Any functional relationship in this form has recognizable characteristics that are more obvious when one more symbol is included in the general expression. Thus,
y = yoe-ax
where yo is a constant determined by the fact that when x = 0, the value of e-ax = 1 and under these conditions, y = yo. The following examples illustrate the general characteristics of this type of function. The "a" is a specific constant in each example.
c = coe-at
where co is the concentration at time t = 0 (at the beginning of the experiment).
I = Ioe-al
where Io is the intensity of the incident radiation at l = 0, before it passes through the absorbing material.
P = Poe-ah
where Po is the pressure at h = 0, sea level.
y = mx + b
where m = slope and b = intercept of line with y axis (at x=0).
slope = m = rise/run = 2/3
Figure B. Negative slope
Calculate or read off the values for m and b, then insert the m and
b values into the equation y = mx + b. The result should be the equation
you're looking for. To double check your work, try some of the original
given values for x in your equation and see if y comes out as expected.
The equation of the line in Fig. A is y = 2x/3 + 5/3 and for Fig. B is
y = -x + 5 = 5 - x.
y = ae-b/T
where y is some property of the system, a and b are constants and T is the temperature in Kelvins. These functions are all linearized by taking the natural logarithym of the expression.
ln y = ln a - b/T. A plot of ln y vs 1/T will give a straight line with slope -b and intercept ln a.
|Ans||1. Plot the following
data in a graph of density versus temperature. Determine the relationship
between density and temperature from this graph. Write a mathematical expression
for this relationship, and from the graph evaluate all constants.
|Ans||2. Complete the
each of the following equations, indicate what type of scale should be
used on the y axis and the x axis to obtain a linear plot. Determine the
intercept and slope. Note that more than one approach is often possible.
(a) y = 3x2 + 4
D = -2.5 x 10-3 T + 13.60


Hlt-362v week 2 exercise 10 questions to be graded applied statistics for health care professionals - population and sampling distributions grand canyon university. Seven amazing facts about grand canyon national 7 amazing grand canyon facts by becky across at its widest, the gorge spans 18 miles (29 kilometers) on average, the canyon is only 10 . Explore grand canyon university reviews, rankings, and statistics is it the right college for you. Hlt-362v week 5 exercise 29 questions to be graded applied statistics for health care professionals - discovering relationships and building models grand canyon university.
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Welcome to MIIND: a population level simulator¶
MIIND is a simulator that allows the creation, simulation and analysis of large-scale neural networks. It does not model individual neurons, but models populations directly, similarly to a neural mass models, except that we use population density techniques. Population density techniques are based on point model neurons, such as leaky-integrate-and-fire (LIF), quadratic-integrate-and-fire neurons (QIF), or more complex ones, such as adaptive-exponential-integrate-and-fire (AdExp), Izhikevich, Fitzhugh-Nagumo (FN). MIIND is able to model populations of 1D neural models (like LIF, QIF), or 2D models (AdExp, Izhikevich, FN, others). It does so by using statistical techniques to answer the question: “If I’d run a NEST or BRIAN simulation (to name some point model-based simulators), where in state space would my neurons be?” We calculate this distribution in terms of a density function, and from this density function we can infer many properties of the population, including its own firing rate. By modeling large-scale networks as homogeneous populations that exchange firing rate statistics, rather than spikes, remarkable efficiency can be achieved, whilst retaining a connection to spiking neurons that is not present in neural mass models.


My understanding of...
Mean: Is were you have to add up all your numbers and you divide the final number with a number that is divisible by the group of data.
Median: Median is the number that is in the middle of the line or group, sometimes you might need to divide some numbers.
Mode: My understanding of mode is that mode is the number that you see the most, in the group of numbers.
Range: Is where you have to subtract the lowest and highest number to get your range.


Asheville Initiative for Mathematics Through UNC Asheville
The Asheville Initiative for Mathematics is a public outreach project run by the Math department. Our mission is to promote excellence in math education and universal math literacy. One step in that direction is to help people remember how much fun math can be – and how creative – and how beautiful. This is the motivation behind Project Snowflake. We hope you enjoy making paper snowflakes! And it’s even more fun with friends and family! Look for these snowflakes in the windows at local businesses, pictures of them on Facebook, and share pictures of your own! #avlsnowflake.
Why Math Literacy
Math literacy is more important than ever for the future of our nation, but our nation lags behind all other industrial countries in math education.
The national workforce of future years will surely have to handle quantitative concepts more fully and more deftly than at present. So will the citizens and policy leaders who deal with the public interest in positions of civic leadership. Sound education in mathematics across the population is a national interest. Final Report, President’s National Mathematics Advisory Council, 2008
There is much discussion about the achievement gap between racial groups. Though not as stark as the economic gap, racial gaps have not narrowed in the last few decades. However, a well-supported math education helps to eliminate both of these indicators.
Research suggests a strategy of supporting student’s math skills and preparing all students for upper-level math courses in high school. The ability to achieve such a goal is not far-fetched. We need to bring resources to bear on math literacy. However, teachers and school systems cannot address this issue alone. We must enlarge the conversation of improving math literacy to include teachers, students, parents, academic administrators, business leaders and community leaders to even have a chance at success.
The role of UNC Asheville as a public institution is to bring students, teachers and research to the table. By acting as a facilitator, UNC Asheville is well-positioned to impact math literacy locally and to act as a model for other communities to address this critical national issue.
The goal of public outreach is to reframe how we think of math. Math literacy includes the skills of arithmetic, mastery of basic statistical concepts, problem-solving skills, critical-thinking skills and the ability to communicate effectively in quantitative terms. These are essential skills in our current work force environment and will continue to grow in importance for personal economic success. These skills also allow us to adapt to a constantly shifting work arena.
- Mathematics is the study of relations between objects.
- Mathematics is fun and should be celebrated.
- Everyone can learn and enjoy mathematics.
- Mathematics connects to everyone’s everyday experience.
- There is no such dichotomy as “numbers people” and “words people.”
- Math literacy improves learning outcomes in math and science.
- Math literacy helps develop executive function, which in turn positively impacts every facet of a person’s life.
- Mathematics can positively transform both the individual and the community by opening doors to higher education, critical thinking, executive function, financial planning and self-esteem.
In Fall 2006, the UNC Asheville Math Department decided to extend our community outreach. But, we wanted to avoid a top-down approach, telling the community what they need. Instead we listened to community partners and identified needs and resources We formed an informal group of allies. Our conversations led to multiple activities including public outreach, professional development and tutor training. We are currently building a sustainable balance of outreach, student research and tutoring resources.
The Asheville Institute of Mathematics serves as conduit for faculty, students and ideas to reach out to the community and to identify and respond to needs in the community related to mathematics.
We currently sponsor an after-school program at the Pisgah View Apartments called “Marvelous Math Club.” Two UNC Asheville students are paid to spend every Monday afternoon with children who live in Pisgah View doing fun math activities, helping with homework, tutoring and generally building a positive attitude toward math with these young K-5 students. There are currently between 20 and 25 kids who regularly come to Math Club, and our intent is that next year, when those in the club graduate to 6th grade, they will come back and serve as tutors and mentors to the younger members. With appropriate funding, we would like to build on our success in Pisgah View and offer a Marvelous Math Club to every housing project in the city.


Maths Road Show Thursday 18 April
Number is an important part of our maths curriculum. To make number learning fun for our kids, we have arranged for the World of Maths Roadshow to visit our school. The World of Maths Roadshow is an opportunity for children to see how maths is applied to some real life situa-tions. More importantly, children will be engaged in hands-on activities, for all ability levels. This show will be lots of FUN! It will cost $1.00 per child.
WE NEED PARENTS TO COME TO HELP READ THE ACTIVITY CARDS TO THE CHILDREN. PLEASE LET YOUR TEACHER KNOW IF YOU CAN HELP!
(sorry but this will not be suitable for pre-schoolers to attend with parent helpers)


Math is always a fear for every student.
Because you are not properly approaching Math.
You should know what math is before you start learning it.
How does it function?
The relevance of arithmetic in everyday life.
Knowing math too well reduces your fear of math to nil.
In addition, practice makes perfect in math.
What is Math?
Math is the science of arrangements with the rationale of shape, amount, and plan.
Math is surrounding us, in all that we do.
It is the structure block for everything in our day-to-day routines, including cell phones, PCs, programming, design (antiquated and current), workmanship, cash, designing and even games.
Branches of Math
- Statistics & Probability
Is the branch of mathematics that helps in the representation of problems or situations in the forms of mathematical expression.
It involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression.
Is the branch of mathematics that studies sizes, shapes, positions, and angles.
And dimensions of things.
Flat shapes like squares, circles, and triangles are a part of flat geometry and are called 2D shapes.
These shapes have only 2 dimensions, the length and width.
Examples of 2D shapes in a flat geometry.
It is the mathematical study of change,
in the same way that geometry is the study of shapes and algebra is the study of operations and their application to solving equations.
Statistics & probability
These are two important concepts in Math.
Probability is all about chances.
Whereas statistics is more about how we are handling various data using different techniques.
It helps to represent complicated data in a very easy and understandable way.
It is the branch of mathematics concerned with specific functions of angles and their applications to calculations.
Importance of Math in day-to-day life
There is nothing without math in this world.
Math is always connected in our day to day life.
To calculate our daily life budget we need Math. Also in construction, when we do shopping.
In the hospital, the human body is completely connected with math.
In weather forecasting, we use math to know how the atmosphere makes differences.
Without math, we can’t make a new computer software.
Math always becomes the base of other subjects like chemistry, physics, and more.
We even need math to prepare food and way more.
Like these, math has a connection with our world.
Tips for Math Problem solving
- Practice, practice & more practice. It is impossible to study Math properly by just reading and listening
- Review errors
- Master the key concepts
- Understand your doubts
- Create a distract-free study environment
- Create a Mathematical dictionary
- Apply Math to real world problems
Practice, practice & more practice. It is impossible to study Math properly by just reading and listening
It is impossible to learn math by simply reading and hearing.
Math requires you to roll up your sleeves and solve some problems.
The more practice you have answering math questions, the better.
Each problem has unique properties, and it is critical to have solved it in multiple ways before taking the exam.
There is no getting around the fact that in order to do well in a Math exam, you must have done a LOT of mathematical problems beforehand.
It’s critical to work through the process for each solution when practicing with these problems.
If you made any mistakes, you should go over them to see where your problem-solving abilities failed you.
Understanding how you tackled the challenge and where you went wrong is a wonderful method to grow and prevent making the same mistakes again
Master the key concepts
Do not attempt to memorize the methods.
This is not productive. In the long run, it is far better and more gratifying to concentrate on comprehending the method and reasoning involved.
This will assist you in understanding how to handle similar challenges ahead.
Remember that math is a sequential discipline,
therefore it’s critical to have a good grasp on the main concepts that underpin a mathematical topic before moving on to work on other,
more sophisticated solutions that are predicated on comprehending the basics.
Understand your doubts
Sometimes you may become stuck when attempting to solve a portion of a math problem and find it difficult to progress to the next stage.
Many students will often skip this question and move on to the next.
You should avoid doing this and instead spend time attempting to comprehend the problem-solving process.
Once you’ve gotten an understanding of the initial dilemma, you can use it as a springboard to the rest of the question.
Create a distract-free study environment
Mathematics takes the most concentration of any subject.
When handling mathematical equations or problems in geometry, algebra, or trigonometry, a decent study atmosphere and a distraction-free location could be the deciding factor!
Music can help to create a soothing environment while also boosting the flow of information during studying.
Having appropriate background music might help to create a focused environment.
Apply Math to real world problems
When addressing arithmetic, try to apply as many real-world situations as possible.
Math can be quite abstract at times, but looking for a practical application might help you adjust your perspective and internalize information in a new way.
Probability, for example, can be utilized in everyday life to forecast the outcome of an event and decide whether or not to take a risk, such as purchasing a lottery ticket or gambling.
How and why Angle?
Angle one-to-one tuition is the best solution for all your worries about mathematics. In schools, there are various numbers of students.
Due to this overfilled class no teacher can concentrate on a single student, even though they have to.
Math becomes really complicated when you don’t take it seriously.
You need the right assistance to get them technically.
Angle’s expert tutors will assist you, only you.
That’s why we provide one-to-one tuition.
Through this method a teacher can put their effort into one student.
So the student can be more attentive in math.
One-to-one learning will set the student free to ask their doubts without being judged or hesitant.
Every student will be taught the fundamentals of mathematics by our teachers.
Math is constantly connected with previous year chapters, if you don’t know them you can’t move forward with new chapters and methods.
Our experts will check your knowledge in the basics of math, according to your level of knowledge in the base they will train you to be better.
Learning in the same pattern never works for mathematics.
Each problem has its own process.
Angle’s teacher will train a pupil using various techniques of learning while maintaining a warm and comfortable study environment.
When attempting to solve hard problems, it is a good idea to treat your teacher as a buddy with whom you may consult and bounce ideas.
In one-to-one learning, the teachers will look into them through some assessments to know their level.
After the inspection, the teacher can know the student’s level and they can choose the method for them.
If the pupil is unfamiliar with the fundamentals, they will begin there and work their way up via numerous phases.
There are less theory classes and up to 75-80 percent are practical to master Math.
In one-on-one learning, each student will have ample time to understand the topic, as well as additional tasks and repetitions.
Angle’s teachers often provide chapter-by-chapter assessments, allowing students to assess their own progress in mathematics.
Teachers will always be on the side of students who want to attain academic success.
Oh and don’t forget that it’s also important to have self-confidence in yourself and face the exam knowing that you have prepared properly!
Angle provides one to one interactive learning programs, personalized according to each student’s requirement.
Learn the fundamental concept from qualified tutors.


At present, the CA Lottery offers a wide variety of lottery games. There is the Draw game and the Scratchers Games. Under the Draw game they have the Mega Millions, SuperLotto Plus, Fantasy 5, Daily 4, Daily 3, and Daily Derby and Hot spot. These games allow you to choose winning number combinations from a range of numbers given depending on the type of draw game you want to play. For example, you can choose five numbers from 1 to56 and one MEGA number from 1 to 46 on a playslip or through Quick Pick to play their MEGA millions. Each specific draw games will be played on their respective appointed days. You can also play their Scratchers Games. You can freely choose to play $1, $2, $3, $5 and $10 Scratchers. It’s very simple. All you have to do is scratch the covered portion of the ticket to unravel the prices. Isn’t it the best way ever to win instant big prices? No sweat at all.
How to Win The CA Lottery – Tips & Strategies
Lottery may give us hopes on ending our financial difficulties. But let’s face the fact that this betting game more often threatens our saving than doing well. Winning the lottery is like finding a grain of rice among a file of gravel. The odd of winning is really slim. But just like any other phenomena in this world, lottery works in a system. In order to higher our chances of winning we have to decode this system. Sure, cracking the system is not an easy task. Here are some tips to help you with this endeavor.
The Odd-Even Number Strategy
For you to have 65% winning chances, you have to come up with an odd and even mixture of numbers. Having all your winning combination in all odd or even will only give you 6% winning chances. It is proven that most often the winning numbers in the lottery are most often a mixture of odd and even numbers. So if are thinking of having your combination all in odd or even numbers, then winning will surely remain as a dream for you.
High-Low Number Strategy
You may notice that in a lottery the winning numbers are scattered out on the entire number scheme. To get 68% chance of winning, try to cut the number field into half. For example, you are playing the MEGA Millions, divide the number range into two. Number 1 to 28 will be your lower numbers and 29 to 56 will be your higher half. If you choose all lower or higher number combination, then you only have 5% chance of winning. You are not only wasting your time but your money at the same time.
Lottery Group Strategies
Pay more attention to every draw. You will find out that one or more of the number groups is not represented. To better understand and appreciate this strategy keep tract on the winning combination in each draw. It will surely help you choose the best number combination.
Hot Number Secrets
Same as the Lottery Group Strategy, you need to list and track down the winning number combinations in each draw and from there gauge the hot numbers. Hot numbers are numbers that don’t frequently show up in every draw or those that have been losers for consecutive draws. They will account a higher chance of winning the next draw that follows.
The success of winning in the California Lottery will depend on how you used all these tips in choosing your lucky number combination. Remember that lottery is a system. This follows that Lottery is a diverse and complex phenomena so there is no better way than the other. And one more thing, be a responsible player. Don’t totally give in to the calling of pleasure from betting. Lottery is an alternative way to earn additional income. One should not solely depend with it for survival.I hope you enjoyed this article, and hopefully it will get you on your way to having a win. If you are looking for a complete lottery system with a money back guarantee and hundreds of happy customers since 1991 – It does actually exist! Click Here for details and see the hundreds of REAL testimonials.


Who knows how to quickly memorise Pi (not using imagination and words)?
'3.1415' '926' '535' '8' '979' '323'
It isn’t necessary to memorize Pi as in questions you usually round to 3.14 or just leave it as Pi. If you really want to memorize it, you can group digits. For example, you can write four digits as a group to help you memorize it. Words and imagination definitely help you to memorize it, but you can memorize it if you don’t want to use these two techniques. Again there is no need to memorize Pi for your study, you can just write Pi or round to 3.14. I hope this answer is helpful for you.
Get an answer in 5 minutes from expert tutors at Oxford, Cambridge, Imperial and more.


Twelve is a powerful number. It would have been wise to learn a base-12 number system rather than the common base-10. I understand that learning a base-10 system is logical because children have their fingers to learn with, but base-10 has more occurrences of fractional anomalies when written in point notation. While a base-12 number system is not new, I discovered it through my own experiments in number theory. I realized years ago that twelve was a powerful natural number because of its flexibility as being highly divisible. Twelve is also low enough to have a memorable and robust multiplication table. However, I have already learned the base-10 system and it’s difficult for me to work with current base-12 notation. There is a great deal of confusion when dealing with values written in dozenal point notation because the current dozenal progression is very similar to decimal progression. The value of
Fifty-six in decimal [(10×5) + 6 = 56]
Is represented the same as the value of
Sixty-six in dozenal [(12×5) + 6 = 56].
Do you see the predicament of a dozenal point system using symbols from an existing system? There’s no way to know which system you’re dealing with if there are no tens or elevens represented. For this reason, I’ve been working to create a new symbolic design for the dozenal point system. I’ve also been designing new words for each value. This will allow immediate recognition when you see or hear a value presented. Once I’ve learned the new symbolism and their spoken counterpart, I’ll be able to do many more experiments easily. Designing symbols for mathematical notation hasn’t been easy and I have alternates that I like, but it’s important to settle on a standard soon. I’ll release this work when I’ve finished.
The following is an excerpt from the Wikipedia page for “Duodecimal”:
The number twelve, a highly composite number, is the smallest number with four non-trivial factors (2, 3, 4, 6), and the smallest to include as factors all four numbers (1 to 4) within the subitizing range. As a result of this increased factorability of the radix and its divisibility by a wide range of the most elemental numbers, dozenal representations fit more easily than decimal ones into many common patterns, as evidenced by the higher regularity observable in the dozenal multiplication table. Of its factors, 2 and 3 are prime, which means the reciprocals of all 3-smooth numbers (such as 2, 3, 4, 6, 8, 9…) have a terminating representation in dozenal. In particular, the five most elementary fractions (1⁄2, 1⁄3, 2⁄3, 1⁄4, 3⁄4), all have a short terminating representation in dozenal (0.6, 0.4, 0.8, 0.3 and 0.9, respectively), and twelve is the smallest radix with this feature (since it is the least common multiple of 3 and 4). This makes it a more convenient number system for computing fractions than most other number systems in common use, such as the decimal, vigesimal, binary, octal, and hexadecimal systems. The sexagesimal system (where the reciprocals of all 5-smooth numbers terminate) does better in this respect (but at the cost of an unwieldy large multiplication table).
-Jeremy Edward Dion


The potential energy of anything falling from a height is given by U = mgh, where:
- U is the potential energy in joules
- m is the mass in kilograms
- h is the height in meters
Now, 1000 liters of water has a mass 1000 kg and the value of g is 9.8 m/s^2.
The amount of energy 1000 L of water would have after falling 20 m is,
U = 1000(20)9.8 = 196,000 J
Given 1000 L of water falls 20 m every hour the amount of power available is,
196,000/3600 = 54.444 W
There are 3600 seconds in an hour & watts is the joules per second.
Allowing for friction and efficiency of a turbine, say 20 percent of the available power is converted to electricity - turbine manufacturers will be able to give a more accurate number. The power generated would be,
Electrical power generated = 0.2(54.444) = 10.888 watts per hour.
Note watts, not kilowatts. If you want kilowatts then increase the height, the amount of water flowing and the flow rate.
From Móż's answer linked in comments, 90% efficiency from the turbine is possible, and 90% from the generator is also possible with large hydro stations(pdf) coming close to 90% overall efficiency(pdf) but in specific conditions that a small system won't be able to replicate, because for example they use large synchronous AC generators.
(via wikidot - relative efficiency of various turbines as flow rate varies as a proportion of rated)
With a very small system like the one asked about efficiency will be lower because water viscosity and edge effects play a larger role. However, since costs are irrelevant some normally ignored solutions become possible - a bucket chain, for example, scales better and could be more efficient for a system this small. But those can't scale up (100 cubic metres per second falling 100m... in buckets?!?)
Sorry, the only easy efficiency references were pdfs in glossy brochures