A photon (phonon, plasmon, etc) has a linear polarizability. To see this and to understand why this matters, it helps to set aside Maxwell's equations and quantum mechanics per se and start with the following basic physics. Suppose a rapidly oscillating wave field in a weakly inhomogeneous linear medium. Assuming the dispersion operator for the wave field is known, a reduced operator can be defined that governs just the wave envelope. Using the Weyl calculus, an asymptotic approximation of the reduced operator can then be constructed to any power n in the geometrical-optics (GO) parameter. The corresponding truncations yield GO (n = 0), extended GO (n = 1), and quasioptics (n = 2). Notably, an accurate formulation of the latter for inhomogeneous media has only been given recently [unpublished]. But there is even more to this approach. For waves propagating in modulated media (i.e., interacting with other waves), a reduced operator can be derived similarly for Floquet envelopes. The modulation-dependent term in this operator serves as the ponderomotive Hamiltonian of a wave, and its derivative with respect to the (loosely speaking) modulation intensity serves as the wave polarizability [Phys. Rev. A 95, 032114 (2017)]. When applied to charged particles treated as quantum waves, this gives the conventional particle polarizability. Conversely, when applied to classical waves, this defines an effective linear polarizability of a photon (phonon, plasmon, etc). Using this concept, one can interpret modulational dynamics (MD) of nonlinear electromagnetic waves as linear dispersive dynamics of a polarizable photon gas. This significantly simplifies calculations of MD and makes them less error-prone than the standard Maxwell--Vlasov approach [J. Plasma Phys. 83, 905830201 (2017)]. Even more generally, quasilinear MD of all wave ensembles are governed by Wigner--Moyal-type equations that are identical up to a (generally non-Hermitian) Hamiltonian. Then, for example, the modulational instability in the nonlinear Schrodinger equation, the zonostrophic instability of drift-wave turbulence, and the standard two-stream collisionless-plasma instability formally appear as essentially the same effect. In a broader context, elaborating on this approach seems promising for studying inhomogeneous wave turbulence.
Magneto-Fluid Dynamics Seminar, Courant Institute for Mathematical Sciences, New York U. Metriplectic dynamics -- a framework for plasma kinetic theory and numerics
In dissipationless systems, Hamiltonian mechanics, culminating in a Poisson bracket and a Hamiltonian, provides a convenient framework for both theoretical and numerical studies. In systems that obey both the First and the Second Law of Thermodynamics, the dissipationless dynamics can often be extended with a symmetric bracket and an entropy to account for the dissipation. The resulting, so-called metriplectic framework captures many interesting models, including the Navier-Stokes equations, non-isothermal kinetic polymer models, and the Vlasov-Maxwell-Landau model used in plasma physics. In this talk, we review the basic principles of metriplectic dynamics and discuss some prominent methods for time discretization. We focus on the Vlasov-Maxwell-Landau model and, especially, on the Landau collision operator for which a genuine metriplectic integrator is demonstrated. The gyrokinetic version of the Vlasov-Maxwell-Landau system is briefly visited.
ITER Organization Gyrokinetic Simulation of Pedestal and SOL Transport in Present Experiments and ITER


Concepts in math can be tough, and some little help can be of great importance. Teachers have guidelines that they find while teaching math. A personal tutor is vital for a student who is unable to understand some concepts in math. Many parents demand individual tutoring for their children who have math related problems. One on one discussion with a private tutor will help deal with math-related problems. Some concepts and principles in math are usually hard to understand, and a lot of practice should be done. Tutoring helps maintain regular study time and improve a student clear doubt in some ideas in math. The help of a parent when it comes to dealing with problems in math is highly recommended.
Learning through the internet is convenient and accessible. The help of a friend or a family member who has raised kids will go a long way in helping identify the best math help for your child. Online games capture the attention of kids and make math interesting. It is easy to learn and understand math if the concepts are made fun. Online learning has tools that help a student deal with math problems. The help of a professional will help one differentiate between games that are just for show and those that are essential for learning .
Math is a subject that requires the mastery of basic concepts to learn a new concept . Finding out information on sites that are reputable to offer math help is essential. A teacher help is essential when it comes to finding out math related issues in a child . Before hiring a tutor it is critical for a parent to explain in detail, the problems the child encounters in math. Meeting with a tutor will help one understand some of the values that a tutor possesses. The right qualifications are essential when it comes to dealing with a math tutor to ensure effectiveness and reliability.
It is important to note that almost all good jobs require the knowledge of necessary math skills. It is essential for parents to find help as soon as possible for her or his child. Practicing at home on simple addition and subtraction will help your child master other concepts gradually. The mastering of timetables is very important, and educationist, as well as teachers, should make it fun. Additional lessons should be short and helpful to ensure maximum help for a student. It is essential for a child to explore for additional minutes to help understand difficult concepts. A tutor should tackle different areas of math to enhance a student’s interest. When looking for a tutor, it is essential to consider one that is within your budget.
Cited reference: Learn More


|Advanced Audio Recording|
a digital sound generator
A digital sound generator can be built with some simple equations below. They are suitable for beeing used in a 8-bit microcontroller unit with assembler. lt produces a cosinus sine wave with 10% even and odd harmonics. It also can be transformed into a digital circuit.
This circuit uses an adder a multiplier and a substractor. It was tested in a Lattice PLD together with a programmable EEPROM for the multiplication. It can easily be changed to e.g. Verilog language or also VHDL (VLSI Hardware Description Language).
Conclusion and Summary
Simple equations can be used to produce sound in microprocessor applications and programmable logical devices.
|© 2001 - Dipl.-Ing. Jürgen Schuhmacher|


EUREKA — The Humboldt Math Festival invites student and teachers to submit works of art and posters for the annual Art and Poster Show as part of the April 9 math festival at the Bayshore Mall on April 9.
This year the mall is providing more space and display facilities for the show. Art pieces may include constructions like origami, kiragami, or other three-dimensional creations. Two-dimensional work may include tessellations, geometric designs, mandalas, tangram art, perspective drawings or other pieces that have a mathematical connection. Posters may include topics of mathematics, such as biographical posters of famous mathematicians, math explanations and mathematical proofs.
If the art piece or poster is at all related to math, then it is probably eligible for the show, according to the festival organizers.
A “People’s Choice Award” is presented each year. Festival organizers welcome other groups that might wish to recognize students’ work. The art and poster show is open to students of all ages, from kindergarten through college.
For more information, visit www.humboldtmathfestival.org or call 725-6980.


Here’s What I Know About Mathematics Signs
The One Thing to Do for Mathematics Signs
If you’re conscious of what they are, you will be in a position to catch a learning disorder early and quickly take steps to receive your child help. When solving math problems, they usually are expected to do the right steps in a specific order to achieve the correct answer. Fourth, the kid is equipped to follow and finish a work cycle.
Irrespective of whether your youngster’s problems are because of a learning disability, intervention is necessary. professional essay help You may experience some frustration attempting to work with your child, and it can appear to be an uphill battle if you don’t have the information which you need. When a solution pathway doesn’t make sense, search for one more pathway that does.
Details of Mathematics Signs
Like anything in life, there’ll be things you merely have to survive to attain the goals you’ve got for yourself. If you’re the kind of person who faces problems and welcomes challenges, always dancing on the time of your comfort zone, odds are that you’re fairly intelligent. Use the term parteto specify that it is a portion of a whole.
The notion that math ability is chiefly genetic is one dark facet of a bigger fallacy that intelligence https://samedayessay.me/ is largely genetic. As recently as two or three decades before, math held a position in our culture very similar to the one that music, for instance, holds today. The subtext, obviously, is that large quantities of American kids are just not born with the capacity to solve for x.
Every one of these skill areas depends on and influences the others. More than three-quarters of accidents happen as a result of a human error, states Ram Prasad, among the business’s co-founders. Not all intelligent people today are extremely productive, but nevertheless, it is sometimes a great indicator of higher intellect.
Mathematics Signs Explained
Please see the Assessment Process for information on how best to receive a thorough reading evaluation for your son or daughter. Sequence is provided incidentally in each one of the work. Math and Memory Memory may have an important effect on thinking with numbers.
Most Noticeable Mathematics Signs
Speaking of keeping busy, a fantastic indicator that you’re handling an extremely clever person is the simple fact they always have a couple projects they http://www.uoitc.edu.iq/images/documents/informatics-institute/Competitive_exam/Systemanalysisanddesign.pdf are working on. Worksheets may be used for random drilling after the first stage of structured drilling. After students are conversant with the procedure, I begin to give unique students different numbers, dependent on their degree of mathematical thinking.
By the conclusion of it you will have the ability to compose your own programs to carry out basic mathematical and scientific tasks. This information isn’t intended to diagnose or treat and should not take the area of private consultation, as appropriate, with an experienced healthcare professional. Experience a multi-step issue.
The teacher also needs to be able to observe the door from her or his desk. I would applaud somebody who is in a position to do that. Joe’s grandpa appears well.
Facts, Fiction and Mathematics Signs
Indeed, the majority of these notations are used unchanged in a number of other contexts. A vector may be used to spell out a translation. In this instance, the symbol is truly a lot like a function.
The Benefits of Mathematics Signs
Please be aware that students find it impossible to view their exams to find out what they missed. This may be the most crucial concept in all of Mathematics. Mathematics is a tool, not merely a notion.
Learning with understanding is important to allow students to address the new kinds of problems they’ll inevitably face later on. As a discipline it isn’t skill training for a specific vocation. Lessons must be shown in a number of ways.
Employing these easy rules you can readily simplify a number of signs. The usage of the minus sign isn’t a coincidence-in fact, subtraction isn’t anything more than addition involving a negative number! If a deal looks too fantastic to be true, it’s.
Random variable A randomvariable is a numerical quantity, the worth of which is dependent upon the results of a chance experiment. All variables should have a coefficient, a number that’s multiplied by the variable. The worth of each digit depends upon its place or position.
The folding line is known as the line of symmetry. It usually means there is an entire number included in the fraction. To add a way to combine numbers to form a larger number.
Things You Should Know About Mathematics Signs
There are a lot of other braille maths codes used from the other side of the world. Be sure the result has the right font and size. If you’ve taken Algebra I, you will likely recognize a number of these symbols.
Mathematics Signs and Mathematics Signs – The Perfect Combination
What they don’t see is that it took a reasonable amount of engineering ingenuity to achieve these tasks. Adding this text doesn’t have any influence on the behaviour of the program, but nevertheless, it can be helpful for every time a individual wants to read and understand the code at a subsequent date. They can use the worksheet, Investigating a Data Set as a step by step tool of how to calculate each analysis method.
What You Must Know About Mathematics Signs
Frequently used regions of the room and traffic lanes ought to be unobstructed and easily accessible. As one can see from prior discussions that the internal elements aren’t identical but represent various directions of the vector based on their place in the sequence. In a translation, an object is moved in a particular direction for a specific distance.
It’s the style in algebra to compose the numerical component to the left of the literal facets. All you have to know is basic arithmetic! For instance, the proposition might be identically true, regardless of what p and q are.
Mathematics Signs Features
See that the indication of the term isn’t separated from the term. Moreover, children have to be in a position to discriminate between the important info and the unnecessary data in word issues. Locating a respectable referral is critical.
What Is So Fascinating About Mathematics Signs?
At the top there are tabs for assorted pieces of the Toolbox. To be true, both parts would need to be true. Games must be won by at least two points.
The Key to Successful Mathematics Signs
For the question, you merely want to stick to the rules. On account of the wide variations, there’s no single symptom or profile that it is possible to look to as proof of an issue. The 2 numbers being multiplied are called factors, and the end result is known as the item.


Subjects required: Mathematics (general) Area of Study: Howrah, south kolkata. Grade: Bsc 1st year Details: I need msc teacher in mathematics who teach proper way of the maths.
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• Opportunities for manipulative play can be found in everything from a puzzle to a container full of different sized buttons.
Aside from the above, manipulative play helps children develop:
When children play with family figures in a miniature house, or create a city out of blocks, they are engaging in both manipulative and dramatic play.
Dramatic play is important because it helps develop social and language skills; allows the expression of positive and negative feelings; teaches children to negotiate, take turns and resolve conflict; and helps children make sense of the world.
When you read about manipulative play, you're likely to come across the term 'seriating'. To seriate means "to arrange in a series".
Some examples of seriation might be;
Putting together puzzles: jigsaws, inset boards, locks and latches, knobbed (for very young children)
Sorting and matching: buttons, bottle tops, shells, seeds, screws etc. (Some of these are choking hazards; make sure young children are supervised.)
Sorting shapes on a geometric shapes board
Performing seriation: sorting board (closed ring), graded stairs
Placing pegs in a peg board
Threading and lacing: beads, shoes
Playing 'Pound the Ball'
Manipulating clay or playdough
Connecting plastic nuts and bolts
Pushing the beads around a bead frame table
Constructing with Lego, Duplo, Mobilo or Stickle Bricks
Shifting the beads on an abacus
Playcentre recommends the following as a minimum for early learning centres:
Storage (as appropriate)
Working surface to accommodate four children
(a) Basic maths – raised whole pieces, different shapes or sizes, one colour only
(b) Fraction shapes board – raised pieces, one colour only
(c) Geometric puzzle, containing true maths shapes (e.g. square, triangle etc.)
(d) Graded size puzzle with pieces small to large
(e) Mosaic board
(f) Collection for colour/shape
(g) Collection for size
Seriating materials: for length, area and volume
Sorting and matching materials (a collection)
Peg board with suitably sized pegs
Screwing materials (a collection)
Threading materials (a collection)
The Playcentre basic equipment list
Here are some other resources for facilitating manipulative play:
For colour and/or shape matching: pebbles, leaves, shells
Posting boxes (make sure the shapes are not interchangeable in the holes)
Picture or shape dominoes
Stand up jigsaws
A set of special shapes (e.g. geometric or animal)
Hammer mosaic set with board
Geoboard with coloured elastic bands
Manipulative play relates particularly to Strand 5 of Te Whāriki, which is Exploration/Mana Aotūroa.
To learn more about Te Whāriki, visit the website.
Our thanks to the Auckland Playcentre Shop for permission to use this article. Great play starts here.


By default Texts stores inline math in “double dollar” style, which is compatible with GitHub Pages and other popular Markdown implementations.
Here is a famous formula: $$E=mc^2$$.
There is an option to store inline math in “single dollar” style, which has better support in Pandoc.
Here is a famous formula: $E=mc^2$.
Execute the following command in Terminal app.
defaults write io.texts.Texts TSInlineMathStyle single-dollar
Download and install the following file.
Please contact email@example.com if you have any questions.


intuitionism n : (philosophy) the doctrine that knowledge is acquired primarily by intuition
- This article is about Intuitionism in mathematics and philosophical logic. For other uses, see Ethical intuitionism.
In the philosophy of mathematics, intuitionism, or neointuitionism (opposed to preintuitionism), is an approach to mathematics as the constructive mental activity of humans. That is, mathematics does not consist of analytic activities wherein deep properties of existence are revealed and applied. Instead, logic and mathematics are the application of internally consistent methods to realize more complex mental constructs.
Truth and proof
The fundamental distinguishing characteristic of intuitionism is its interpretation of what it means for a mathematical statement to be true. As the name suggests, in Brouwer's original intuitionism, the truth of a statement is taken to be equivalent to the mathematician being able to intuit the statement. The vagueness of the intuitionistic notion of truth often leads to misinterpretations about its meaning. Kleene formally defined intuitionistic truth from a realist position, however Brouwer would likely reject this formalization as meaningless, given his rejection of the realist/Platonist position. Intuitionistic truth therefore remains somewhat ill defined. Regardless of how it is interpreted, intuitionism does not equate the truth of a mathematical statement with its provability. However, because the intuitionistic notion of truth is more restrictive than that of classical mathematics, the intuitionist must reject some assumptions of classical logic to ensure that everything he/she proves is in fact intuitionistically true. This gives rise to intuitionistic logic.
To claim an object with certain properties exists is, to an intuitionist, to claim to be able to construct a certain object with those properties. Any mathematical object is considered to be a product of a construction of a mind, and therefore, the existence of an object is equivalent to the possibility of its construction. This contrasts with the classical approach, which states that the existence of an entity can be proved by refuting its non-existence. For the intuitionist, this is not valid; the refutation of the non-existence does not mean that it is possible to find a constructive proof of existence. As such, intuitionism is a variety of mathematical constructivism; but it is not the only kind.
As well, to say A or B, to an intuitionist, is to claim that either A or B can be proved. In particular, the law of excluded middle, A or not A, is disallowed since one can construct, via Gödel's incompleteness theorems, a mathematical statement that can be neither proven nor disproved.
The interpretation of negation is also different. In classical logic, the negation of a statement asserts that the statement is false; to an intuitionist, it means the statement is refutable (i.e., that there is a proof that there is no proof of it). The asymmetry between a positive and negative statement becomes apparent. If a statement P is provable, then it is certainly impossible to prove that there is no proof of P; however, just because there is no proof that there is no proof of P, we cannot conclude from this absence that there is a proof of P. Thus P is a stronger statement than not-not-P.
Intuitionistic logic substitutes justification for truth in its logical calculus. The logical calculus preserves justification, rather than truth, across transformations yielding derived propositions. It has given philosophical support to several schools of philosophy, most notably the Anti-realism of Michael Dummett.
Intuitionism also rejects the abstraction of actual infinity; i.e., it does not consider as given objects infinite entities such as the set of all natural numbers or an arbitrary sequence of rational numbers. This requires the reconstruction of the foundations of set theory and calculus as constructivist set theory and constructivist analysis respectively.
History of IntuitionismIntuitionism's history can perhaps be traced to the nineteenth century. Cantor and his teacher Kronecker — a confirmed finitist — disagreed. Frege's effort to reduce all of mathematics to a logical formulation was a scientific breakthrough in the department of logic, and it greatly inspired the younger generation, including a youthful Bertrand Russell.
But Frege himself counted it as failure when a young Bertrand Russell sent Frege a letter about his hot-off-the-presses first volume, outlining the famous paradox now known as Russell's Paradox, that showed how one of Frege's rules of self-reference was self-contradictory. Frege, the story goes, plunged into depression and did not publish the second and third volumes of his work as he had planned. For more see Davis (2000) Chapters 3 and 4: Frege: From Breakthrough to Despair and Cantor: Detour through Infinity. See van Heijenoort for the original works and Heijenoort's commentary.
In the early twentieth century Brouwer represented the intuitionist position and Hilbert the formalist — see van Heijenoort. Kurt Gödel offered opinions referred to as Platonist. (see various sources re Gödel). Alan Turing considers: "non-constructive systems of logic with which not all the steps in a proof are mechanical, some being intuitive" (Turing (1939) Systems of Logic Based on Ordinals in Undecidable, p. 210) Later, Kleene brought forth a more rational consideration of intuitionism in his Introduction to Meta-mathematics (1952). For the view that there are no paradoxes in Cantorian set theory — thus calling into question the program of intuitionist mathematics, see Alejandro Garciadiego's now-classic Bertrand Russell and the Origins of the Set-Theoretic Paradoxes.
Branches of intuitionistic mathematics
- W. S. Anglin, Mathematics: A Concise history and Philosophy, Springer-Verlag, New York, 1994.
- Martin Davis (ed.) (1965), The Undecidable, Raven Press, Hewlett, NY. Compilation of original papers by Gödel, Church, Kleene, Turing, Rosser, and Post.
- Engines of Logic: Mathematicians and the origin of the Computer
- John W. Dawson Jr., Logical Dilemmas: The Life and Work of Kurt Gödel, A. K. Peters, Wellesley, MA, 1997.
- Less readable than Goldstein but, in Chapter III Excursis, Dawson gives an excellent "A Capsule History of the Development of Logic to 1928".
- Rebecca Goldstein, Incompleteness: The Proof and Paradox of Kurt Godel, Atlas Books, W.W. Norton, New York, 2005.
- In Chapter II Hilbert and the Formalists Goldstein gives further historical context. As a Platonist Gödel was reticent in the presence of the logical positivism of the Vienna Circle. She discusses Wittgenstein's impact and the impact of the formalists. Goldstein notes that the intuitionists were even more opposed to Platonism than Formalism.
- van Heijenoort, J., From Frege to Gödel, A Source Book in Mathematical Logic, 1879-1931, Harvard University Press, Cambridge, MA, 1967. Reprinted with corrections, 1977. The following papers appear in van Heijenoort:
- L.E.J. Brouwer, 1923, On the significance of the principle of excluded middle in mathematics, especially in function theory [reprinted with commentary, p. 334, van Heijenoort]
- Andrei Nikolaevich Kolmogorov, 1925, On the principle of excluded middle, [reprinted with commentary, p. 414, van Heijenoort]
- L.E.J. Brouwer, 1927, On the domains of definitions of functions, [reprinted with commentary, p. 446, van Heijenoort]
- Although not directly germane, in his (1923) Brouwer uses certain words defined in this paper.
- L.E.J. Brouwer, 1927(2), Intuitionistic reflections on formalism, [reprinted with commentary, p. 490, van Heijenoort]
- Jacques Herbrand, (1931b), "On the consistency of arithmetic", [reprinted with commentary, p. 618ff, van Heijenoort]
- From van Heijenoort's commentary it is unclear whether or not Herbrand was a true "intuitionist"; Gödel (1963) asserted that indeed "...Herbrand was an intuitionist". But van Heijenoort says Herbrand's conception was "on the whole much closer to that of Hilbert's word 'finitary' ('finit') that to "intuitionistic" as applied to Brouwer's doctrine".
- Gnomes in the Fog. The Reception of Brouwer's Intuitionism in the 1920s
- Arend Heyting: Intuitionism: An Introduction
- Introduction to Meta-Mathematics
- In Chapter III A Critique of Mathematic Reasoning, §11. The paradoxes, Kleene discusses Intuitionism and Formalism in depth. Throughout the rest of the book he treats, and compares, both Formalist (classical) and Intuitionist logics with an emphasis on the former. Extraordinary writing by an extraordinary mathematician.
- Constance Reid, Hilbert, Copernicus - Springer-Verlag, 1st edition 1970, 2nd edition 1996.
- Definitive biography of Hilbert places his "Program" in historical context together with the subsequent fighting, sometimes rancorous, between the Intuitionists and the Formalists.
- Paul Rosenbloom, The Elements of Mathematical Logic, Dover Publications Inc, Mineola, New York, 1950.
- In a style more of Principia Mathematica -- many symbols, some antique, some from German script. Very good discussions of intuitionism in the following locations: pages 51-58 in Section 4 Many Valued Logics, Modal Logics, Intuitionism; pages 69-73 Chapter III The Logic of Propostional Functions Section 1 Informal Introduction; and p. 146-151 Section 7 the Axiom of Choice.
- A. A. Markov (1954) Theory of algorithms. [Translated by Jacques J. Schorr-Kon and PST staff] Imprint Moscow, Academy of Sciences of the USSR, 1954 [i.e. Jerusalem, Israel Program for Scientific Translations, 1961; available from the Office of Technical Services, U.S. Dept. of Commerce, Washington] Description 444 p. 28 cm. Added t.p. in Russian Translation of Works of the Mathematical Institute, Academy of Sciences of the USSR, v. 42. Original title: Teoriya algorifmov. [QA248.M2943 Dartmouth College library. U.S. Dept. of Commerce, Office of Technical Services, number OTS 60-51085.]
- A secondary reference for specialists: Markov opined that "The entire significance for mathematics of rendering more precise the concept of algorithm emerges, however, in connection with the problem of a constructive foundation for mathematics....[p. 3, italics added.] Markov believed that further applications of his work "merit a special book, which the author hopes to write in the future" (p. 3). Sadly, said work apparently never appeared.
intuitionism in Czech: Intuicionistická logika
intuitionism in German: Intuitionismus
intuitionism in Spanish: Intuicionismo
intuitionism in Esperanto: Intuiciismo
intuitionism in Croatian: Intuicionizam
intuitionism in Italian: Intuizionismo
intuitionism in Dutch: Intuïtionisme
intuitionism in Japanese: 数学的直観主義
intuitionism in Polish: Intuicjonizm (matematyka)
intuitionism in Portuguese: Intuicionismo
intuitionism in Russian: Интуиционизм
intuitionism in Turkish: Sezgici Matematik
intuitionism in Chinese: 数学直觉主义


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Stanford stated Mirzakhani died Saturday. She had breast most cancers. The varsity did not point out the place she died.
Mirzakhani was born in Iran and joined Stanford as a arithmetic professor in 2008.
Stanford stated her work concerned the geometric and dynamic complexities of curved surfaces similar to spheres and doughnut shapes.
She acquired the Fields Medal in 2014. The award is taken into account the arithmetic equal of the Nobel Prize.
Stanford stated her work concerned the geometric and dynamic complexities of curved surfaces resembling spheres and doughnut shapes.
Stanford President Marc Tessier-Lavigne referred to as Mirzakhani an excellent theorist who made enduring contributions and impressed hundreds of girls to pursue math and science.
“Maryam is gone far too quickly, however her impression will stay on for the hundreds of girls she impressed to pursue math and science,” he stated in a press release to Stanford Information. She was “a humble one that accepted honors solely with the hope that it’d encourage others to comply with her path. Her contributions as each a scholar and a task mannequin are vital and enduring, and she or he shall be dearly missed right here at Stanford and around the globe.”
Mirzakhani is survived by her husband and a daughter.


Approachability with Constraints
Abstract. We study approachability in repeated games with vector payoffs, with the additional aspect that there are constraints. Namely, the goal of Player 1 is to approach a given set while ensuring that the realized average payoff in every given stage is not in a given set of payoff vectors that should be evaded. We characterize the pairs of sets (A,E) such that Player 1 can ensure that the long-run average payoff converges to A while evading E.


Check out Our Top 10 Hands-on Math Resources that will help your kids absorb math in ways worksheets just can’t!
I love to incorporate board games into our learning as often as I can, I have found that we can touch on just about every subject with games or other hands-on activities including the dreaded MATH. We cover everything from calendar skills to multiplication. Here are Our Top 10 Hands-on Math Resources!
Our Top 10 Hands-on Math Resources
- Math Dice- While this set comes with some instructions for activities we also use them for math bingo with a dry erase page and the kid’s race to fill up their squares first while doing whatever math skill they are working on, usually addition/subtraction and my son on multiplication. They are great for reinforcing basic math facts.
- The Allowance Game– Money money, something we have struggled with a bit here. But the game is more fun than sitting and doing worksheet after worksheet so the kids absorb more this way.
- Tri-Facta- Another fun way to practice addition facts that also tosses in some critical thinking skills practice.
- Planners- When Happy Planners came out with the kid’s version of their planners I couldn’t wait to get them in my kid’s hands. They came with stickers and fun things to decorate them with. We use them on Sunday evening or Monday morning and they open their planners while mom opens hers and we go over events for the week and/or a month together. This really helps the kids get a sense of time, as well as build planning and organizational skills.
- Power Pen- This is my alternative to drilling with flashcards or boring them with worksheets (which we regularly do both) Instead of flashcard repetition I hand them a small chunk of cards to practice and they love the interaction and self-correction from the pen buzzing or cheering to let them know if they answered correctly.
- Lego’s- My kids can get behind anything that involves LEGOs! We have used them to practice skip counting, addition, subtraction, multiplication, fractions, and just about everything you can imagine, they are the ultimate manipulative! Even if the kids have some in the bedroom I recommend a basic box just for your school room or school area.
- Math Box- We have several different topics in the Brain Box series and use the math one at least once a week. This quick and simple game is a great way to review basic math skills and get an introduction to some new ones.
- Sale ads- Plain and simple these are a great tool for comparing prices and budgeting. I am a big believer in teaching your kids these kinds of real-life math skills right from the get-go!
- Monopoly- While your kids may not get to practice coins they will be able to count up their money, pay rents, taxes, etc… They will learn to multiply when they have to figure out just how much those 3 houses on Park Place and Boardwalk will set them back.
- Yahtzee- I love when I can sneak in something of educational value and the kids just think it’s fun. Yahtzee is great for addition and even multiplication, my 7 and my 10-year-old are each able to practice current skills simply by having a family game night!
What is your favorite hands-on activity for teaching your kids math skills?


15 October 2020
New trials provided by Russian Foundation for Basic Research as part of the national subscription selection:
Journals on mathematics from the American Mathematical Society (AMS) and Society for Industrial and Applied Mathematics (SIAM)
28 September 2020
On this day, we clean the book stock from dust, carry out the minor repair of the equipment and undertake other urgent work. The Library is closed to the public from 10 a.m. to 9 p.m.
24 September 2020
The Office of Information Systems and Electronic Resources gives advisory classes on information search and use of the Library electronic resources


Nichrome is a solver for solving a system of mixed hard and soft constraints. Many inference tasks in diverse application domains such as machine learning, information retrieval, mathematical optimization, and many others require optimizing certain objectives in addition to satisfying soundness conditions. A natural specification for such tasks is a system of relational constraints with optional weights. Examples of such logics are MLNs (Markov Logic Networks) and PSLs (Probabilistic Soft Logic). The relational inference problem in such logics seeks a solution that satisfies all unweighted (“hard”) constraints while maximizing the sum of the weights of satisfied weighted (“soft”) constraints. Hard constraints thus enable to express soundness conditions while soft constraints allow to express the objectives to optimize.


Professor, Неаd of Сybersecurity Department, Institute of telecommunications and global information space, National Academy of Science of Ukraine
Serves as an editorial board member for several journals I’ve authored nearly 250 publications in peer-reviewed journals, 2 books, 3 monographs, h-index = 13 (Scopus); h-index = 21 (Google Scholar), Erdo's number – 2.
Fellowship of British Academy for Researchers at Risk 2022 (supported by University of London (Royal Holloway)).
SCOPUS ID: 16647651500
• 1993 – Dr. Sci. Mathematics (Habilitation), Kyiv State University, Department of Algebra and Mathematical Logic, Dissertation Title: Tits geometries. Association schemes and Permutation groups
• 1979 - PhD. Mathematics. Kyiv State University, Department of Algebra and Mathematical Logic Dissertation Title: Induced maximal permutation groups, Thesis Advisor: Professor Lev Kaluzhnin (Kiev)
• 1976 Master Diploma in Mathematics, Kiev University, Thesis title: Transitive extensions of permutation groups, Thesis Advisors: Professor Lev Kaluzhnin (Kyiv) (Thesis got a 1-st award •in the contest of Ministry of Education of Ukraine, 1976)
HISTORY OF EMPLOYMENT
• 2011 – date Head of Cybersecurity Department, Institute of telecommunications and Global Information Space (ITGIS), National Academy of Science of Ukraine, Kyiv, Ukraine, Member of Scientific Board.
• 2006 – 2011 Head Researcher of Cybersecurity Department, Institute of telecommunications and Global Information Space, National Academy of Science of Ukraine, Kyiv, Ukraine, Member of Scientific Board.
• 2003 – 2006 Professor of Department of Computer Science, National University of Kyiv Mohyla Academy, Ukraine, Member of University Senate.
• 1997 – 2002 Head of Department of Mathematics, National University of Kyiv Mohyla Academy, Ukraine, Member of University Senate.
• 1994 – 1997 Full Professor, Department of Algebra and Mathematical Logic, Kyiv State University (KSU), Ukraine.
• 1988 – 1994 Associate Professor, Department of Algebra and Mathematical Logic, Kiev State University, Ukraine.
• 1984 – 1984 Assistant Professor, Department of Algebra and Mathematical Logic, Kiev State University, Ukraine.
• 1980 – 1984 Seniour Researcher, Kiev State University, Ukraine, Supervisor of group of researchers working in Applications of Mathematics.
• 1979 – 1980 Junior Researcher, Kiev State University, Ukraine, Principal Investigator of joint project “Computer Algebra, Permutation groups and their applications” funded by KSU and Institute of Cybernetics and supervised by Prof. L. Kaluznin.
•1977 – 1979 Engeneer-Mathematician, Kiev Institute of Hydrodevices, Ukraine. Development of algorithms and software for Image Processing and Hydrolocation search.
RESEARCH EXPERTISE: Permutation groups, Algebraic Combinatorics, Multivariate cryptography, Noncommutative Cryptography, Coding Theory.
1. V. Ustimenko, On new symbolic key exchange protocols and cryptosystems based on hidden tame homomorphism, Dopovidi. NAS of Ukraine, 2018, n 10, pp. 26-36. DOI: 10.15407/dopovidi2018.10.026
2. V. Ustimenko, M. Klisowski, On Noncommutative Cryptography with cubical multivariate maps of predictable density, In “Intelligent Computing’’ , Proceedings of the 2019 Computing Conference, London, Volume 2, Part of Advances in Intelligent Systems and Computing (AISC, volume 99, pp, 654-674.DOI: 10.1007/978-3-030-22868-2_47
3. V. Ustimenko, U. Romanczuk-Polubiec, A. Wroblewska, M. Polak, E. Zhupa, On the constructions of new symmetric ciphers based on non-bijective multivariate maps of prescribed degree, Security and Communication Networks, Wiley-Hindavi, 2019 . Volume 2019, Article ID 2137561, 15 pages
4. V. Ustimenko, On small world non-Sunada twins and cellular Voronoi diagrams, Algebra and Discrete Mathematics, vol. 30, No1 (2020). Pp 118-142.DOI: 10.12958/adm1343
5. V. Ustimenko, On desynchronised multivariate algorithms of El Gamal type for stable semigroups of affine Cremona group, Theoretical and Applied Cybersecurity, National Technical University of Ukraine "Igor Sikorsky Kiev Polytechnic Institute", vol 1, 2019, pp. 22-30. DOI:10.20535/tacs.2664-29132019.1.169022
6. V.Ustimenko, On the usage of postquantum protocols defined in terms of transformation semi-groups and their homomorphisma, Theoretical and Applied Cybersecurity, National Technical University of Ukraine "Igor Sikorsky Kiev Polytechnic Institute", vol 2, 2020, pp. 32-44. DOI: 10.20535/tacs.2664-29132020.1.209435
7. O.Pustovit, V. Ustimenko, A new stream algovolrithms generating sensitive digests of digital documents, Mathematical modelling in economy, 2019, N3, P. 18-33.


Golden Ratio Defines New Class Of Variable Star
Using data from the Kepler Space Telescope (KST), and specially devised ‘model-independent nonlinear analysis’ techniques, a team from the University of Hawaii have discovered a new class of variable star that has unique fractal (strange) behaviour never-before-seen outside a laboratory environment.
Typically, variable stars (Cepheid/RR Lyrae) pulsate at a single frequency. However, light curves of the new class have been found to exhibit fluctuations at multiple frequencies approximate to the golden ratio, φ (where φ ≈ 1.62): ‘As the most irrational number, the golden ratio can have significant dynamical consequences,’ describe the team; ‘for example, by the KAM theorem dynamics with two frequencies in the golden ratio maximally resist perturbations. Furthermore, nonlinear systems driven by two incommensurate frequencies, forming an irrational ratio, and especially the golden ratio, exhibit distinctive dynamics that exist between order and chaos.’
‘A nonlinear dynamical system driven by an irrational ratio of frequencies generically exhibits a strange but nonchaotic attractor’, which has been found to exist in the RRc Lyrae star KIC 5520878, making it a model proto-type of the new class.
The team further expanded their non-linear technique to an additional five RR Lyrae KST objects: three exhibiting irrational, near golden ratio, pulsations and two with a rational ratio of 3/2; by comparing the two different classes, researchers found that only ‘golden stars’ displayed strange nonchaotic behaviour.
The team predict that the new discovery will help refine the classification of variable stars. A host of potential ‘golden’ objects have been isolated by the OGLE and ASAS sky surveys, which should help realise this prediction as well as updating current interior models: ‘The strange nonchaotic signatures of variable stars like KIC 5520878 may elucidate phenomena like the Eddington valve mechanism thought to underlie their pulsations: variations in the opacity of the star might quasiperiodically modulate the normal hydrostatic balance between pressure outward and gravity inward, thereby generating light curves somewhere between order and chaos that the best models will need to reproduce’, conclude researchers. ‘The pulsating star KIC 5520878 may be the first strange nonchaotic dynamical system observed in the wild.’
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- Reionization Zone Galaxy Reveals Highly Evolved Characteristics - March 21, 2015
- Golden Ratio Defines New Class Of Variable Star - March 14, 2015


Workplace Math 10 prepares students for the working world. The main concepts covered in this course involve a look at finance, measurements, scales and shapes. There are seven units: Probability, Graphs, Measurement Conversions, Trigonometry, Surface Area and Volume, Central Tendency and Financial Literacy. This course was specifically designed to break topics up into manageable sizes in order to help students of all ability levels and backgrounds be successful in secondary math. Online lessons are video-based, and students have complete control over the pace at which they learn—lessons can be paused, resumed and repeated. Examples have video, or step-by-step solutions.


Discovered by a chinese man in the mid 1200's, the triangle most popularly known as pascal's triangle has been the source of answers to many mathematical questions it is a simple triangle to create, made up of numbers rather than line segments. Any pages that are written for the more specialized audience will be clearly marked with these notes at the top of the page we have done our best to write the remaining pages assuming minimal background in mathematics so that they may be enjoyed by students, particularly those in liberal arts. Pascal's triangle is a triangle that works in the following way the sum of the numbers in each row is 2 to the nth power (remember, the first row is row zero) except for the first column, if one alternates the sum and difference (difference first), the value is always 0 for example. Pascal's triangle for expanding binomials how to use pascal's triangle to perform binomial expansions the formula for pascal's triangle comes from a relationship that you yourself might be able to see in the coefficients below.
In this example we will learn how to write a c++ program to print pascal's triangle as below subscribe to our newsletter and stay updated on the latest developments and special offers. Most of you know what is a pascal's triangle you add the two numbers above the number you are making to make the new number below i've figured that for every prime number row, all numbers on the row (except for the first and last numbers, which must be 1) are divisible by the row number. Now let's look at pascal's triangle algebraically in that case we again want to see why this is one of those places where lots of math comes together we have connected combinations with pascal's triangle and with binomial expansions, though at first blush these may not seem related.
Pascal's triangle is a geometric arrangement of binomial coefficients in a triangle even though other mathematicians studied these numbers before him, it was pascal who developed the uses for the triangle and arranged the numbers in this fashion. Pascal triangle 3 to show that the combinatorial coefficients are actually the entries of the triangle, we now need only to show that they start out right, for then the sum rule provides an inductive. To build the pascal triangle, start with 1 at the top, then continue placing numbers below it in a triangular pattern each number is build just sum of above two number, (except for the edge, which are all '1' and all numbers outside the triangle are figure: screen shot for pascal triangle c program.
This sequence has a difference of 3 between each number the pattern is continued by adding 3 to the last number each time, like this: this sequence has a difference of 5 between each number the pattern is continued by adding 5 to the last number each time, like this: this sequence starts at 10 and. Since pascal's triangle is infinite, there's no bottom row it just keeps going and going it just keeps going and going pascal's triangle is named for blaise pascal, a french mathematician who used the triangle as part of his studies in probability theory in the 17 th century. Pascal's triangle is a triangle which contains the values from the binomial expansion its various properties play a large role in combinatorics pascal's triangle is defined such that the number in row and column is.
Pascal's triangle is often presented in a symmetrical form, in which the columns and diagonals are both presented in a diagonal form: while this is a visually more appealing presentation, as well as being more intuitively clear, it can be argued that it is not as straightforward for investigating its properties as. Pascal's triangle is not just a mere array of numbers stacked in a triangular fashion, but there's a lot more to do with it firstly have a look at what he have so far been discussing then i shall explain to you in details. Pascal's triangle is an arithmetical triangle you can use for some neat things in mathematics here's how you construct it algebra let's say you have the polynomial x+1, and you want to raise it to some powers, like 1,2,3,4,5 if you make a chart of what you get when you do these power-raisings. To build a pascal triangle we start with a 1 at the top we then place numbers below each number in a triangular pattern: each number is the result of adding the two numbers directly for this challenge we will use a python script to output a pascal triangle after a fixed number of iterations (rows): eg. Pascal's triangle is a unique number pattern that has many different applications in mathematics use these multi-sensory games and activities to help students learn about pascal's triangle.
Pascal's triangle is a triangular array constructed by summing adjacent elements in preceding rows pascal's triangle contains the values of the binomial coefficient pascal's triangle can be used to visualize many properties of the binomial coefficient and the binomial theorem contents. It isn't like all those special triangles it consists of numbers that created by adding up two numbers on the top of it chinese mathematician jia xian devised a triangular representation for the coefficients in the 11th century his triangle was further studied and popularized by chinese mathematician yang. The pattern known as pascal's triangle is constructed by starting with the number one at the top or the high school students can also see that the numbers in pascal's triangle give the coefficients in a each week i send an email with fun and engaging math ideas, free resources and special offers. In mathematics, pascal's triangle is a triangular array of the binomial coefficientsin much of the western world, it is named after the french mathematician blaise pascal, although other mathematicians studied it centuries before him in india, persia (iran), china, germany, and italy.
1 generate the triangle using a formula apparently, there are a number of ways to do this the method below, takes the number of the rows to generate as a parameter and then outputs the number that make up the pascal triangle (although not in the triangular format. Why and when did pascal make the triangle what are some patterns in pascal's triangle(what is so important about what's in pascal's triangle) pascal didn't really make the triangle before he found out some discoveries inside it, and before it got changed to pascal's triangle, it was called.
The secret to pascal's triangle starts from where it comes from: expanding the powers of binomials this is pascals triangle pascal discovered that if we add two adjacent coefficients, this gives the number below the second coefficient for instance, adding 3 and 3 give the number below the. Pascal's triangle is a mathematical triangular array it is named after french mathematician blaise pascal, but it was used in china 3 centuries before his time. Pascal's triangle have you finished reading our web page no matter what, this fun and informative quiz will definately help you to learn not only about the mathematical principals of the pascal's triangle, but will also teach you about pascal and his life.


Students of America have celebrated Pi day on 14th March and it was mathematically known as 3-14. What makes this day so special is that “Albert Einstein” was born on this day.
Technically, Pi is supposed to be defined as a distance of circle or the circumferences or the Diameter. And, it is also used for determining calculation of the circle areas, spheres volumes and many others mathematical formulas supposed to be very important for science.
Unlike Math, Pi is very interesting and it is the reason that most of the Americans remember thousands of Pi numbers for various reasons. In 2009, the House of Representatives proposed that “14 March should be designated as national Pi day” and it is generally celebrated by a big number of people across the globe.
An Australian mathematician said that “Pi day is like Pie and you can celebrate it in way you like”. He further said if you are admitted to school, college or university, the math department might have prepared something special for u on this day.


Math problems like these1 skills such as solving quadratic equa- another to solve math problems that are embedded in the context of real life rather than. Resources for connecting math class to the real world active, but the archived questions remain a great source of real-life math problems. A list of math websites with real-life word problems, real-world math videos, multimedia, or lesson plans. Ted-ed lessons in the series math in real life ted-ed lessons grouped by series.
Math in the real world: 400 examples, lessons, & resources math in the real world lessons are aligned with the common core state standards (ccss) 8 steps to design problem-based learning in your classroom. Hilarious gifs to show your students next time they ask the dreaded question, when are we going to use this math in real life. Informal real-world mathematical problems are questions related to a concrete setting, such as adam has five. This is particularly true in the area of traditional math instruction if most of the time spent is focused on solving a set of problems in a textbook.
36-43 modelling of real-world problems is often the starting point for proof vimolan mudaly department of mathematics education, university of kwazulu- natal,. Mathability gives students the experience and ability to analyze and solve real- life mathematical problems, and explain their methods for arriving at the solution. Overview a rigorous math education includes an equal emphasis on procedural fluency, conceptual understanding, and applications real-world lessons from. Learn how to engage secondary math students in problem-based learning—with authentic problems from business, government, nonprofits,. Comparing those rates to the speed of the rescuers' and the boys' journeys a little geography of thailand and its place in the world is part of the whole picture.
Learn about the countless hidden uses and applications which mathematics has in everyday life: from weather prediction to medicine, video games and music. Real-world problems for secondary school mathematics students case studies edited by juergen maasz university of linz, austria john o'donoghue. Struggling students often become frustrated with complex math problems and quickly give in to the notion that they will never use math in real.
Many math problems in school involve prepackaged problems that aren't typical in the real world students are asked to solve the penultimate. 10 real world math problems in the style of dan meyer 3 acts math tasks shared by mathematics teachers and aligned with the ontario math curriculum. Mathematics can condition your life, specifically improve it if you are able to analysing problems and finding solutions with the available data,.
Buy math for real life for dummies on amazoncom ✓ free shipping on basic math and pre-algebra: 1,001 practice problems for dummies (+ free. Mathematics modeling is the process of translating real-world problems into quantitative terms for interpretation, suggestions of improvement.
Equip your students with skills needed to solve problems big and small real world math challenges students to analyze real-world data about global issues. Real-life math : everyday use of mathematical concepts / evan m glazer and work from textbooks that limit applications to age problems and mixtures of nuts. Bridging mathematics with real life problems in this research, we developed a word problem enrichment program (wpe) to encourage teachers to use. Solving real-world problems with high-level math dr jorge rebaza sees so much beauty in mathematics, it's only natural that he finds ways to connect math to.


Spring Term 2023
'Knights, Castles and Dragons!'
Shwmae! This term, we will be exploring conflict and co-operation during the iron age and Celts. We will have lots of fun learning about the Celt Warriors and recreate our own battles through expressive arts. We will discover the daily life of a Celt and learn how to create clothing using a loom.
In our writing journey, we will be learning how to write a poem, narrative and recount. In Mathematics, we will be learning how to find fractions of numbers and be learning all about angles. In science and technology, we will be learning about sound and applying all of our coding skills that we learnt last term.
Every pupil has access to a range of resources on Hwb. Use your login details to access them and to see any updates from your child’s teacher on teams.
Here are links to home learning tasks:
Free Math Learning Game for Kids | Prodigy Math Game | Prodigy Education (prodigygame.com)
www.oxfordowl.co.uk – Library of free e-books
ActiveLearn: Login (activelearnprimary.co.uk)
P.E. is every Thursday
Reading books to be brought in to school everyday.
Homework is set on prodigy and active learn weekly.
Summer Term 2022
The Great Outdoors
Our Autumn Term topic is;
We have lift off!
Croeso nol pawb/Welcome back everyone...


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At Northside Christian Academy, we strive to create a smooth transition from the concrete mathematics taught in elementary school to the more abstract algebraic concepts taught in later years. Beginning in Grade 6 and continuing through Grade 8, our experienced math educators work with students to introduce the fundamental concepts associated with algebra, while also honing students’ spatial reasoning skills, in a fresh new way.
However, our teachers still see many parents struggle to explain to their children why the math they used to find so fun is now so frustrating.
From integers to algebraic equations, help your child successfully navigate through middle school math (and perhaps even begin to enjoy it) with these clever tips from the staff at our private middle school in Charlotte, N.C.:
Don’t just provide the answer.
Because no parent wants to see their child frustrated and discouraged, it can be tempting to simply supply the correct answer to a difficult math problem. However, the path to math success doesn’t just mean having the right answers, but also understanding why and how to get there. By guiding your child through the problem, rather than providing a shortcut to get there, you are helping them formulate the connections they will need to understand not only what the question is asking, but also the best way to approach the solution.
Make use of your resources.
Taking notes in class and applying those notes to a given task is often a new concept for middle schoolers. Encourage your child to pull out their class notes, textbooks and any other resources they might need to complete a math problem. If stuck, they will likely be able to find a similar problem amongst these resources to help them move forward.
Pan out to the bigger picture.
Shifting your child’s focus from memorizing the steps of a mathematical procedure to understanding the “why” of the concept at hand will put both the question and its solution into perspective. While context is important in English and Language Arts, it’s a vital part of learning math concepts, too.
Highlight, underline, scribble…whatever works!
Encourage your child to do whatever it takes to make the question clearer. Create circles. Color code with a highlighter. Discover which math method works best for your student. This is a particularly handy technique with word or situational math problems. After all, knowing what to focus on in a word problem is often the first step towards the solution.
Take it to the teacher.
Middle school is filled with change and transition, and middle school math is no different. With that in mind, the teaching staff at our private middle school in Charlotte, N.C., offers face-to-face tutoring time with each student. Northside’s small class sizes make this one-on-one student-teacher time a promise, rather than a mere possibility.
School is almost back in session! If you are interested in learning about our private middle school in Charlotte, N.C., call Northside Christian Academy today at (704) 596-4074 or submit an online information request.


In second grade right now we are on our measuring unit. Today in Miss Steemken's class we measured our classroom. We used teamwork and used rulers to measure it. Once we found out it was 28 feet wide we did conversions on the board together to see how many inches our classroom was. We knew 12 inches was in one foot. With that information we worked together as a class to find out how many inches our classroom was. We found out that our class is 28 feet or 336 inches wide!
Learning about Feet and Inches in Grade Two
Wednesday, February 27, 2019


You’re not going to understand this unless you read Part I, and you probably won’t understand it even then. That’s a criticism of our ability to explain things, not your ability to absorb them.
Last week we tried to figure out what those measures of risk under a mutual fund’s chart mean. Here’s the chart for the Dodge & Cox stock fund, updated from last week. The numbers for the fund itself haven’t changed, as Yahoo! hasn’t recalculated them since September 29 (and we can’t be bothered to do it ourselves), but the numbers for the fund category itself have changed:
α and β we handled last time out. What about Mean Annual Return, R², standard deviation, and Sharpe and Treynor ratios? Let’s see if we can do this and still retain your interest.
Mean Annual Return. “Mean” means average, right? Yes, but there are different kinds of averages. Note the time period listed in boldface on the chart. This isn’t the standard (arithmetic) average, calculated by adding up the values of a bunch of items and then dividing by the number of items. This is geometric average. Replace “adding” with “multiplying” and “dividing by” with “taking the nᵗʰ root, where n is” in the previous sentence and you’ve got it.
Here’s the difference. For instance, what’s the average of 5, 6 and 7?
That’s the arithmetic average. (Ignore the vertical line down from and to the left of the 3, it’s just a typo.) Here’s the geometric average:
Not quite the same. Geometric average is necessary when calculating returns over a period of years. If you use arithmetic average it’s confusing and paints an inaccurate picture. Anyhow, by measuring the individual annual increases (or decreases) and calculating their geometric mean, we know that over the past 3 years the Dodge & Cox Stock fund has averaged a 1.46% gain, which beats the category.
Now onto R². It’s a measure of spread, which is contingent on mean (which, for our purposes, means mean annual return.) R² is supposed to separate how much of that return is attributable to the fund itself from how much is attributable to the underlying benchmark – here, the standard index. If DODGX is just riding the market’s coattails, we want to know about it. The lower R² is, the more the fund’s performance is its own doing, for better or worse. You calculate R² by graphing the performance of both entities, the fund and the index, over time. They won’t be identical, of course. You measure the difference between the fund and the index at different points, square the differences, and in this case discover that DODGX’s movements are explained almost entirely by the index. 96.5 on a scale from 0 to 100. Some if not most people prefer funds with high R², the argument being that a rising index lifts the boats that are most in sync with it.
Generally, R² of over 90 is considered high. R² of under 70 is considered low.
What about standard deviation? Like R², this is a general statistical term that applies to all sorts of sciences, not just finance. If you didn’t learn it in high school or college, here it is in its simplest form. Take 5, 6, and 7, the data points that served us so well in the previous example. Their (arithmetic) mean is 6, we know that. Just like the mean of -40, 27 and 31 is also 6. But obviously, the first set of values is a lot tighter than the second. In other words, their standard deviation is lower. You calculate standard deviation by
- Subtracting each term from the average.
- Squaring each of those differences.
- Adding them all together.
- Dividing by the number of items.
- Taking the square root of that.
Again, we don’t expect you to calculate this yourself. But we’re not just going to throw an unfamiliar term at you and explain it without going into details. We’re writing this in such a fashion that if you want to, you can reproduce the results yourself. Otherwise we’re not really explaining anything, we’re just listening to ourselves type.
Using the 5-step process above, the standard deviation of 5, 6 and 7 is .816. The standard deviation of -40, 27 and 31 is 32.568.
But how does this help us and what does it mean? What are the quantities, the data points we’re dealing with here?
Answer: Monthly total returns. Keep in mind that the table above shows results for only the last 3 years. So we take DODGX’s return in October of 2010, its return in November of 2010, etc., until we have all 36 monthly total returns. (Well, that’s not entirely true. We then annualize them, which is to say, we take each monthly total return to the 12ᵗʰ power.) DODGX’s standard deviation is 14.67, slightly higher than that for its category of funds. That number is a percentage, by the way. It means that assuming a normal distribution – a bell curve – DODGX’s returns will be within 1467 basis points of its average return 68% of the time. It’ll be within 2934 basis points – two standard deviations – of its average return 95% of the time. And it’ll be within 4401 basis points, or three standard deviations, 99.7% of the time. The 68%, 95% and 99.7% aren’t arbitrary, either. They’re natural constants. Well, they aren’t really, but they’re close enough that we can say they are without turning this into an introductory-level probability course.
Alright, it looks like we’re going to have to stretch this out to 3 parts. Friday, we’ll do Sharpe ratio, Treynor ratio, and give you our synopsis of what the point of all this is.


It involves predicting the outcome of a particular event or set of events, often based on the results of past events. Understanding the odds associated with Satta Matka Number is essential for successful gambling. The odds associated with Fix Fix Fix Satta Matka depend on the type of game being played.
Common odds associated with SattaMatka are fixed-odds betting, where the odds are predetermined and remain the same regardless of the outcome of the event; and parimutuel betting, where the odds fluctuate depending on the amount of money wagered. The odds of a particular game can also be influenced by the number of players involved and the amount of money bet. In this article, we will discuss the importance of understanding the odds in SattaMatka and how it can help you become a successful gambler.
Understanding the Odds:
The odds associated with fix fix fix satta nambar are determined by the probability of each outcome occurring. By understanding the odds, you can better predict the outcome of the game.
Knowing Your Chances:
Knowing your chances of winning is essential for successful gambling. By understanding the odds associated with SattaMatka, you can calculate your chances of success and make more informed decisions.
To calculate your chances of winning SattaMatka, you must first understand the game’s betting structure. SattaMatka is a lottery-style game in which players bet on the outcome of three numbers. Players select three different numbers from 0-9 and then place their bets. The winning number is then determined by a draw. The lower the three numbers add up to, the higher the prize.
To calculate your chances of winning, you must first know the odds associated with each number. The odds of winning a particular number in fix fix fix satta nambar 100 are calculated by dividing the number of possible outcomes by the number of possible combinations.
Maximizing Your Profits:
By understanding the odds associated with SattaMatka, you can maximize your profits by making more informed bets. By understanding the odds, you can choose bets that are more likely to be profitable and limit your losses. You can also take advantage of the various side bets offered by some fix fix fix satta nambar free websites. These side bets can provide you with additional chances to win and can also help you reduce your losses.
You should also consider taking advantage of the various bonuses and promotions offered by some SattaMatka websites. Bonuses and promotions can give you additional funds to use for your bets and can help you increase your chances of winning.
Avoiding Unnecessary Risk:
By understanding the odds associated with fix fix fix satta nambar trick, you can identify potential risks and avoid them. This will help you minimize your losses and increase your chances of success. It involves predicting the outcome of a lottery draw by selecting a certain set of numbers. The odds of correctly predicting the outcome of the lottery draw are based on the number of combinations available. Understanding the Variables:
The odds associated with SattaMatka are based on variables such as the number of players, the size of the bet, and the type of game. By understanding these variables, you can better predict the outcome of the game and make informed decisions. The house edge is the amount of money that the house takes from each bet placed. Generally speaking, the higher the house edge, the more likely the house is to win and the lower the payout for the player.
Improving Your Skills:
To understand the odds associated with fix fix fix satta guru nambar, it is important to understand the basic rules of the game. The game is played with two dice, each with six faces. The numbers on the faces of the dice are the numbers that will be used to determine the outcomes of the bets. The player who has the highest number on their dice will win the bet.
The odds of winning a SattaMatka bet depend on the number of players that are playing. Additionally, the type of bet that is being placed can also affect the odds. The two most popular bets are the Single Number and the Double Number bet. Both of these bets have different odds associated with them. For example, the Single Number bet has a higher chance of winning than the Double Number bet.
Knowing When to Quit:
By understanding the odds associated with SattaMatka, you can identify when it is time to quit and limit your losses. This will help you minimize your losses and increase your chances of success. Keeping Track of Your Wins:
By keeping track of your wins and losses, you can better understand the odds associated with SattaMatka and make more informed decisions. In addition, keeping track of your wins and losses will allow you to identify any patterns or trends in your SattaMatka play. This can help you identify when you are more likely to win or lose, allowing you to adjust your strategies accordingly. Furthermore, you can use this information to identify when you should take a break and when you should continue to play.
Utilizing Online Resources:
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Woensdag 18 Augustus
Good morning Krugersdorp Lions!
Lion Tammy is hosting a MATHS WORKSHOP for grade 12 pupils with the upcoming Prelims in mind!!
Friday 27 August 2010
2pm – 6pm
Krugersdorp High School at the Girls Hostel
Bring basic stationary (pen, pencil, paper) and calculator; and something to drink and snack on during breaks
PLEASE rsvp to Tammy on 082 786 8341, to let her know how many to prepare for
Please circulate this to ALL those who can benefit from this lovely service project!!
T 011 679 2863
F 011 679 2626
C 082 466 9336
Mathematician Algirdas Javtokas Takes Mathematics Into Conceptual Art
Algirdas Javtokas, a Lithuanian mathematician introduces mathematics which is no longer concerned with particular problems related to numbers, logic, space, transformations, etc. Instead Algirdas Javtokas gets beyond the limits of those traditional mathematical topics, and calls it existentialism mathematics.
Dr. Algirdas Javtokas
New York, NY (PRWEB) June 30, 2010
In his latest papers Lithuanian mathematician at Vilnius University Algirdas Javtokas puts mathematical truths into question by discovering existentialism mathematics. Dr. Javtokas defines existentialism mathematics as the study of the quantity, structure, space, and change through the individual person and their emotions, actions, responsibilities, and thoughts.
Read the full article here.


3 edition of Inhomogeneous Waves in Solids and Fluids (Series in Theoretical and Applied Mechanics) found in the catalog.
by World Scientific Pub Co Inc
Written in English
|The Physical Object|
|Number of Pages||150|
The authors review the concept of inhomogeneous waves and complete the work done by previous authors. By considering the propagation of an inhomogeneous wave they were able to derive a system of equations which couple Maxwell and potential equations in two different manners and show the importance of the telegrapher's equation with Heaviside's condition. The effect of horizontally inhomogeneous flows on internal wave propagation in a stratified ocean with a constant Brunt-Väisälä frequency is analysed. Dispersion characteristics of internal waves in a moving fluid and kinematics of wave packets in smoothly inhomogeneous flows are considered using wave-normal by:
Applied Wave Mathematics: Selected Topics in Solids, Fluids, and Mathematical Methods (55−81).. Heidelberg: Springer. /_5. Publikatsiooni tüüp. 1 longitudinal waves – the disturbance moves parallel to the direction of propagation. Examples: sound waves, compressional elastic waves (P-waves in geophysics); 2 transverse waves – the disturbance moves perpendicular to the direction of propagation. Examples: waves on a string or membrane, shear waves (S-waves in geophysics), water waves.
World Scientific has published a new book by Arkadi Berezovski, Jüri Engelbrecht and Gerard A. Maugin. NUMERICAL SIMULATION OF WAVES AND FRONTS IN INHOMOGENEOUS SOLIDS. This book shows the advances methods of numerical simulation of waves and fronts propagation in inhomogeneous solids and introduces related important ideas associated with tyhe application of numerical methods . In electromagnetism and applications, an inhomogeneous electromagnetic wave equation, or nonhomogeneous electromagnetic wave equation, is one of a set of wave equations describing the propagation of electromagnetic waves generated by nonzero source charges and source terms in the wave equations make the partial differential equations inhomogeneous, if the source .
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The book may be viewed as an introduction to time-harmonic waves in dissipative bodies, notably viscoelastic solids and fluids. The inhomogeneity of the waves, which is due to the fact that planes of constant phase are not parallel to planes of constant amplitude, is shown to be strictly related to the dissipativity of the medium.
The book may be viewed as an introduction to time-hadronic waves in dissipative bodies, notably viscoelastic solids and fluids. The inhomogeneity of the waves is shown to be strictly related to the dissipativity of the medium. The book may be viewed as an introduction to time-harmonic waves in dissipative bodies, notably viscoelastic solids and fluids.
The inhomogeneity of the waves, which is due to the fact that planes of constant phase are not parallel to planes of constant amplitude, is shown to be strictly related to the dissipativity of the by: The paper aims at presenting a numerical technique used in simulating the propagation of waves in inhomogeneous elastic solids.
The basic governing equations are solved by means of a finite-volume. Waves in Inhomogeneous Solids. Arkadi Berezovski, Mihhail Berezovski and Jüri Engelbrecht. Abstract. The paper aims at presenting a numerical technique used in simulating the propagation of waves in inhomogeneous elastic solids.
The basic governing equa-tions are solved by means of a ﬁnite-volume scheme that is faithful, accurate, and Cited by: 6. Inhomogeneous waves in porous piezo-thermoelastic solids. Inhomogeneous Waves in Solids and Fluids. Article. The book may be viewed as an introduction to time-hadronic waves in dissipative.
waves and fields in inhomogeneous media Download waves and fields in inhomogeneous media or read online books in PDF, EPUB, Tuebl, and Mobi Format. Click Download or Read Online button to get waves and fields in inhomogeneous media book now. This site is like a library, Use search box in the widget to get ebook that you want.
Get this from a library. Applied wave mathematics. II: selected topics in solids, fluids, and mathematical methods and complexity. [Arkadi Berezovski; Tarmo Soomere;] -- This book gathers contributions on various aspects of the theory and applications of linear and nonlinear waves and associated phenomena, as well as approaches developed in a global partnership of.
Table of Contents 1. Basic Equations for Wave Processes in Fluids and Solids.- Sound in Layered Fluids.- Derivation of Wave Equations.- Plane Waves and Spherical Waves.- Boundary Conditions.- Harmonic Waves.- Conditions at Infinity.- Waves with Harmonical Dependence on Horizontal Coordinates and Time.- Modified Wave Equations.- Elastic Price: $ Abstract.
The paper aims at presenting a numerical technique used in simulating the propagation of waves in inhomogeneous elastic solids.
The basic governing equations are solved by means of a finite-volume scheme that is faithful, accurate, and conservative. Wave Propagation in Solids and Fluids Softcover reprint of the original 1st ed. Edition water waves, and stress waves in solids.
Nonlinear effects and asymptotic phenomena will be discussed. Wave propagation in continuous media (solid, liquid, or gas) has as its foundation the three basic conservation laws of physics: conservation of Reviews: 2. The most valuable topic in this book would be the theory of aeroacoustics which is developed by the auther.
Everything is fundamental, but you can learn a great deal about waves which you cannot from other books. This book is a prerequisite to anyone who wants to talk about waves in by: Applied wave mathematics: selected topics in solids, fluids, and mathematical methods. The Perturbation Technique for Wave Interaction in Prestressed Material: o.- Waves in Inhomogeneous Solids: vski, vski, J.
Engelbrecht.- Part II. selected topics in solids, fluids, and mathematical methods\/span> \u00A0\u00A0. Inhomogeneous, plane, monochromatic waves travelling in viscoelastic media are considered. Through a description in terms of complex potentials, detailed expressions of phase speed and attenuation are derived by having recourse to thermodynamic restrictions and to the properties of the complex propagation vector under inversion of the by: PHYSICS LETTERS A 19 December Volumenumber 2 INHOMOGENEOUS WAVES AND SOUND ABSORPTION IN VISCOUS FLUIDS G.
CAVIGLIA Department of Mathematics, Via L.B. Alberti 4, Genoa, Italy and A. MORRO DIBE-University, Viale Ca Genoa, Italy Received 13 June ; revised manuscript received 20 September ; accepted for publication 12 October Cited by: 2. Selected Topics in Solids, Fluids, and Mathematical Methods.
Editors: Quak, Ewald, Soomere Waves in Inhomogeneous Solids. Pages Book Title Applied Wave Mathematics Book Subtitle Selected Topics in Solids, Fluids, and Mathematical Methods Editors. The example applications discussed include wave propagation in inhomogeneous solids, liquid crystals in mesoscopic physics, and long ship waves in shallow water bodies.
Other contributions focus on specific mathematical approaches, namely the pseudospectral method, the treatment of Maxwell equations, and scalar conservation laws.
At present there exist about ten thousand books and papers dealing with the subject of surface acoustic waves in solids first described by Rayleigh in , and it is impossible even to.
Seismic Waves in a Laterally Inhomogeneous Layered Medium, Part II: Analysis RuichongInhomogeneous waves in solids and fluids, World Scientific, Singapore.
Ishimaru, A.,Wave Propagation and Scattering in Random Media, Vols. 1 and 2, Academic Press, New Seismic Waves in a Laterally Inhomogeneous Layered Medium. I: Theory Cited by: 4. Numerical Simulation of Waves and Fronts in Inhomogeneous Solids. This book shows the advanced methods of numerical simulation of waves and fronts propagation in inhomogeneous solids and introduces related important ideas associated with the application of numerical methods for these problems.
Great care has been taken throughout the book. Waves in Inhomogeneous Solids: vski, vski, J. Engelbrecht.- Part II. Mesoscopic Theory.- Overview: k.- Dynamics of Internal Variables from the Mesoscopic Background for the Example of Liquid Crystals and Ferrofluids: uss.- Towards a Description of Twist Waves in Mesoscopic Continuum Physics: H.
Herrmann.- Part IIIWaves and Fields in Inhomogenous Media LA This comprehensive text thoroughly covers fundamental wave propagation behaviors and computational techniques for waves in inhomogeneous media. The author describes powerful and sophisticated analytic and numerical methods to solve electromagnetic problems for complex media and geometry as well.The emphasis is on developing the necessary mathematical techniques, and on showing how these mathematical concepts can be effective in unifying the physics of wave propagation in a variety of physical settings: sound and shock waves in gases, water waves, and stress waves in solids.
Nonlinear effects and asymptotic phenomena will be : Springer-Verlag New York.


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Engage your child in the exciting journey of learning numbers, mastering counting, and grasping the basics of addition and subtraction. This foundational math workbook is designed to support your child’s overall development.
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Melancholia Season 1 Episode 6 Added [Korean Drama] (Mp4 Download)
Download Melancholia Korean Drama Season 1 Episode 1-16 Completed MP4 HD Free Download with English Subtitle
Set at a corrupt private high school with preferential treatment, “Melancholia” will tell the beautiful story of a math teacher and a genius math student.
Ji Yoon Soo is a high school math teacher who appears good-natured on the outside but gets very tenacious and stubborn once she makes up her mind about something. Extremely passionate about math, she is a teacher who encourages her students to find their own answers.
Math genius Baek Seung Yoo is a guy of few words who is a voluntary outsider and enjoys taking photos with a DSLR camera. Although ranked last place at his high school, he actually dominated math Olympiads when he was younger, entered the Massachusetts Institute of Technology at age 10, and dropped out at age 12.
Original Network: tvN;
Director: Kim Sang Hyeob [김상협]
Genre: Drama; Romance; School;
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A dash of color, a dose of pattern and a burst of joie de vivre. A bright scarf is a way to push out of a uniform. Double-sided scarf designs that are lightweight and versatile.
When our son brought home his interest in irrational numbers and mathematical theorems, his excitement was contagious. His knowledge far outstrips mine, but I shared his fascination with Pi as a middle schooler. It is really fun to think of numbers unfurling in space, marching out beyond imagination and light. I also rediscovered e or Euler’s number while reading Margot Lee Shetterly’s Hidden Figures. In a scene in the celebrated movie, the protagonist Katherine Johnson used Euler’s number to calculate the trajectory of John Glenn’s space capsule on a blackboard. That moment inspired me to plot the numbers of e using a color algorithm – my own take on a color trajectory. I wanted to engage numbers in a new way and found there was an architecture, a different kind of reveal as I painted row after row of squares that looked like chiclets. I found cadence in irrationality and a new correspondence with color.
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Wells Fargo Asset Management’s Analytic Investors LLC, the Los Angeles-based quant shop that’s beaten the point spread in 10 of the last 14 Super Bowls, advises gamblers to take the New England Patriots over the Philadelphia Eagles.
Analytic Investors applies its predictive quant models to the game and it shows that the Patriots will beat the Eagles by at least five points, since the point spread on the game is 4 1/2 points.
“I know it’ll tick off a few of my Philly fan friends,” said Chris Lardieri, one of the study’s authors. “But the numbers don’t lie.”
Analytic predicted last season that the Falcons would beat the Patriots, which looked like a good forecast when the score was 28-3.
“The Falcons just had to run the clock out,” Lardieri said.“You can’t account for human error and questionable decisions.”


By Stefan Hougardy,Jens Vygen,Rabe von Randow
Algorithms play an more and more vital position in approximately all fields of arithmetic. This publication permits readers to strengthen easy mathematical talents, particularly these in regards to the layout and research of algorithms in addition to their implementation. It offers not just basic algorithms just like the sieve of Eratosthenes, the Euclidean set of rules, sorting algorithms, algorithms on graphs, and Gaussian removal, but additionally discusses undemanding information constructions, easy graph concept, and numerical questions. furthermore, it presents an creation to programming and demonstrates intimately tips on how to enforce algorithms in C++.
This textbook is acceptable for college students who're new to the topic and covers a simple mathematical lecture path, complementing conventional classes on research and linear algebra. either authors have given this "Algorithmic arithmetic" direction on the collage of Bonn a number of occasions in contemporary years.
Read or Download Algorithmic Mathematics PDF
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Extra resources for Algorithmic Mathematics


Stefan van der Lugt
I am a PhD student at the Mathematical Institute of Universiteit Leiden. My supervisor is Robin de Jong. My office number is 225.
E-mail address: click here to show
Things I wrote
- Tautological classes and forms on moduli spaces of curves - in the Algebra, Geometry and Number Theory seminar, September 2019, Universiteit Leiden
- The ring of tautological differential forms - at the DIAMANT symposium, April 2019, Veldhoven
- Riemannoppervlakken en overdekkingen - in the bachelor seminar Algebra, Geometry and Number Theory, Spring 2017, Universiteit Leiden.
- Selmer groups and Tate-Shafarevich groups - in the seminar Rational points on elliptic curves organized by Peter Bruin and Manolis Tzortzakis.
Seminars, conferences, summer schools, etc.
- DIAMANT Symposium, De Bilt, November 2019
- Masterclass: Elliptic Motives, Stockholm, May 2019
- DIAMANT Symposium, Veldhoven, April 2019
- DIAMANT Symposium, Veenendaal, November 2018
- Intercity Seminar on Arakelov Geometry, Copenhagen, September 2018
- Tropical Geometry Seminar, Leiden, Spring 2018
- DIAMANT Symposium, Breukelen, November 2017
- Algebraic Geometry with “Fancy” Coefficients, Caen, November 2017
- Néron models seminar, Leiden, Fall 2017
- IRTG 1800 Summer School, Texel, August 2017
- Arakelov geometry and diophantine applications, Grenoble, June 2017
- DIAMANT Symposium, Breukelen, May 2017
- Logarithmic Geometry, Leiden, Spring 2017
- DIAMANT Symposium, Soest, November 2016
- IRTG 1800 Student Conference, September 2016
- IRTG 1800 Summer School, Vlieland, August 2016
- Algebraization Theorems, Île de Tatihou (Normandy), July 2016
- Arakelov theory and automorphic forms, Berlin, June 2016
- DIAMANT Symposium, Veenendaal, May 2016
- Rational points on elliptic curves, Leiden, spring 2016
- DIAMANT Symposium, Lunteren, November 2015
- Étale cohomology seminar, Leiden, fall 2015 & spring 2016
- Moduli stack seminar, Leiden, fall 2015
- Algebraic Stacks and Related Topics, Mainz, September 2015