Science topics: Mathematics
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Mathematics - Science topic

Mathematics, Pure and Applied Math
Questions related to Mathematics
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In Mathematics, some proofs are not convincing since the assumption fails in the Proofs.
If equality is Changed to "approximately equal to" then the Proof becomes more Perfect. But Uniqueness cannot be guaranteed.
In Page number 291, Introduction to Real Analysis Fourth Edition authored by Bartle and Sherbert, the Proof of Uniqueness theorem is explained.
That Proof is not perfect.
Reason : Initially epsilon is assumed as positive and so not equal to zero. Before Conclusion of the Proof, epsilon is considered as zero and written as two limits are equal.
The equality cannot hold since epsilon is not zero. Only the possibility to write is Two limits are approximately equal.
Since Epsilon is arbitrary, never imply epsilon is zero.
I hope the authors and other mathematicians will notice this error and will change in new editions.
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The epsilon-delta arguments have a long history in mathematics based on the underlying concept of completeness. When an argument starts of "let epsilon >0 " what are we actually doing. Lets take an example namely the definition of the derivative. For a function of the appropriate conditions, f'(x)=limit as epsilon->0 of (f(x+epsilon)-f(x))/epsilon. Why when epsilon >0, because if epsilon equaled = 0 then the statement is undefined and makes on sense. However, no one questions what f'(x) is. It is the limit. In your example a similar argument shows that the two solutions are actually arbitrary close so in the limit since epsilon is arbitrary - they are equal. The use of this type of argument goes back to Cauchy who introduced it in 1823. The use of these types of arguments evolved over time. Since "infinitesimals" are part of the real number system dy/dx can not really be defined, the approach of "let epsilon >0" evolved to treat limits.
The proof in Bartle and Sherbert is fine.
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What research is there (if any), about gifted students frequently getting easy questions on academic tests/exams INCORRECT and harder more challenging ones CORRECT – particularly in mathematics? Does anyone have any empirical evidence as to why this might occur? Thank you.
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I agreed with You
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is there any literature available on a kinetic study on the working of RO membrane with any software or simple mathematical simulation?
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Now some especially on simulation. David Booth
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Every integer can be expressed as a sum of three triangular numbers.
Given two integers N=a+b+c and M=x+y+z , how to express the product N*M as a sum of three triangular numbers. Example:
11=0+1+10 and 13=0+3+10 ; the product 11*13=143=10+28+105
How to write the product N*M=F(a,b,c,x,y,z) +G(a,b,c,x,y,z) +H(a,b,c,x,y,z) as three triangular numbers?
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Abdolrahman Razani
The question is not clear.
Could you give an example?
Best regards
M.AZZEDINE
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I have digged into a theory established by D. Loeb from University of Bordeaux, and found an interesting way to represent the things you have (classical set) and the things you do not have and might need, want, be ready to acquire (new forms of set with negative number of elements)
This fits very well in the extension of the matrices of sets which I needed to develop, se why and how here (see references below).
I would be thrilled to know if you have use cases where this model of classical sets of what you have, and new negative sets of what you do not have, my help.
Please share your input!
REF:
[3] D. Loeb, Sets with a negative number of elements, Advances in Mathematics, 91 (1992), 64–74.https://core.ac.uk/download/pdf/82474206.pdf
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Thanks Peter Breuer , appreciated!
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In a mathematical analysis of piezoelectric models, we use the terms "the electrically open and short circuit case" for which we have some mathematical definition as well.
What is the physical significance of these boundary conditions in making sensors and other devices?
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Hi Sonal Nirwal,
The surface is metallized (short circuit (CC)): corresponds to the vanish of the electric potential.
The surface is non-metallized (open circuit (CO)): corresponds to the vanish of the surface charge density.
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It is well confirmed that the nonlinear evolution equation (NLEE) is widely used as a mathematical leading equation for describing the physical issues in many branches of physics. But it is very difficult to solve. Recently, many researchers have proposed various types of solution methods. Unfortunately, most of the solutions methods lead to additional free parameters. In my opinion, the solutions with additional free parameters of NLEEs are not useful for further verification in the laboratory. That is why my discussion topic is "What is the best solution method for nonlinear evolution equations?".
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Hi,
The short answer to your question is: there isn't one that can be applied in general. There may be only "satisficing" ones, for specific nonlinear (discrete or continuous), stable or unstable, equilibrium or non-equilibrium, single or multiple structural equilibria containing dynamical equations (problems) you either formulate yourself, or come across having been formulated by others.
There are significant methodological and epistemological questions involved in your question; as well as yet unsolved (possibly unresolvable) mathematical problems.
Good luck!
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Although Bashkar II, in his Siddhantha Shiromani, critisized a Buddhist school of astrology who held the Earth is moving, I have not seen any mention about texts on Buddhist astrological or mathematical tradition in recent studies. Vedic and Jain sources are well known.
Are there any primary textual resources on Buddhist astrology/mathematics?
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Japanese Buddhist Astrology and Astral Magic Mikkyō and Sukuyōdō
Kotyk, Jeffrey. Japanese Journal of Religious Studies; Nagoya Vol. 45, Iss. 1,  (2018): 37-86,214.
DOI:10.18874/jjrs.45.1.2018.37-86
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Dear experts and colleagues,
Hello, all! I recently received a reviewer's comment stating that the proposed network measures of graph theoretical analyses could be correlated by mathematical definition.
So I ran the correlational analyses and global efficiency, characteristic path length, mean clustering coefficient (global measures) showed correlated to each other.
I understand that Global efficiency is inversely related to characteristic path length, but I am quite confused about how characteristic path length is inversely correlated with mean clustering coefficient, while mean clustering coefficient is positively correlated with global efficiency.
Or does my data is wrongly suggested?
Briefly explaining my study, it is a neurological study using MR images (diffusion tensor imaging) to explore the structural networks.
Any feedback and discussion are welcomed here!
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Dear Yaeji Kim ,
Look the link, maybe useful.
Regards,
Shafagat
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hi, I have to get an inverse matrix of a square matrix (20*20) on excel , to make sure that calculation is right I Knew that multiplying the matrix with its inverse should yields a unity matrix which have a diagonal of ones and other cells are zeros but when i multiply the matrix with the inverse i got the result is a matrix with adiagonal of ones but not all other cells are zeros (some have values like 1,2,etc ... is this ok or what often is my mistake? thanks in advance
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To Manal Lotfy: I will suggest to try to solve your example in another program. For example, you may try Wolfram|Alpha (a computational knowledge engine):
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Need a journal published in German language in the fields of mathematics and programming indexed in scoups Q1?
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George Stoica
thank you very much i will follow your advice
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About two years ago, I have submitted a manuscript to a reputed journal. After a couple of months of the peer review process, the response was “major revision has been requested”. I made the necessary adjustments and resubmitted it again. The Journal's editor responded that my manuscript requires minor revision. Well, the decision was <<"Revise for Editor Only'' he claimed that revision should be quick and it will not undergo the entire review process>>. Again, I made the required edits in order to make the manuscript acceptable for publication. Afterward, I resubmitted it. It is the day 120 and the status is "With Editor". In fact, I did send two emails to the editorial team to update the status. Their response to both emails was the same, saying that they contacted the editor to accelerate the process.
Dear readers, I need to have a piece of advice: what to do as a next step?
Thank you in advance,
Bassam
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This kind of situation can be frustrating, however, I would encourage you to keep calm and focus on other things while awaiting the editor's decision. Sorry about this experience
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How to mathematically interpret the formula Kb=Kf (1−Rw)
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I am combining fish abundance and biomass data collected from five locations which have utilised different transect dimensions:
15 x 4 m (60 m2; from one location)
30 x 5 m (150 m2; from three locations)
50 x 4 m (200 m2; from one location)
When pooling data collected from transects of differing sizes, should you standardise your data down (to the smallest dimensions) or up (to the largest)? Or in this case, perhaps standardise according to the most commonly used dimensions (30 x 5 m/150 m2)?
To me it seems as though there would be no difference, but I was wondering if there was some sort of mathematical explanation for why one way might be preferable over the others?
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Hi Joseph,
Hope it's not too late to help.
Because there is a general trend of larger fish to move more, your chance of sampling larger individuals with larger transects is also higher.
If you scale down, you will be implicitly assuming that fish density wouldn't change, which may be inaccurate for very large and rare fishes, i.e., if you found 1 giant grouper on a 200m2 transect, would you really expect to find half a grouper on a 100m2 one?
Scaling up brings the same assumption of fish density not changing, but it may be more acceptable because smaller fish tend to move less and be more homogeneously distributed. You would still have bias for small and rare species, but because the contribution of these to biomass should be negligible, the problem would dissolve away.
Standardising to a mean dimension may bring both issues together, but may also mean that both of these biases are reduced.
At the end of the day, it's about what you're willing to assume about fish distributions. One way of dealing with this is rescaling your data down or to a mid-dimension by subsampling your community based on the density of specific phases/types of fish. That's what I do in this paper:
This, in essence, allows you to carry over uncertainty in density estimates to your further analyses, resulting in more 'messy' data, but in conservative estimates.
Cheers,
Renato
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the VPL formula can be given here as,
f(P)=sum((a+b*P+c*P^2)+abs(e*sin(f(Pmin-P))))
Can anyone please explain if the value from the term (Pmin-P) in the above formula is in degrees or radians?
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Thanks @Awniya kumar
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Hi everyone,
In engineering design, there are usually only a few data points or low order moments, so it is meaningful to fit a relatively accurate probability density function to guide engineering design. What are the methods of fitting probability density functions through small amounts of data or low order statistical moments?
Best regards
Tao Wang
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Good explanation is performed by Chao Dang,
Best regards
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Hello. I want to ask how can I translate weightages of "yes" or "no" of a criterion in terms of numbers in AHP calculations?
for examples, my goal is to select most suitable construction material vendor (Alternative) according to the set criteria including "ASTM Standards", with 4 other criteria.
This criterion means "Is the material vendor giving the material according to the Construction Standard ASTM, or not?" So the answer given to this by the alternative (vendor) would be a "Yes" or a "No", but not a value.
First, I've sent a questionnaire to the experts to give me pair wise comparison weightages for one criteria vs the other. And I've got great response with consistency of 0.9. Acceptable!
But when I ask the vendors to provide their responses, they put numerical values to the first four criteria, and I find the comparison matrix for these vendors (alternatives) for each criteria using simple maths division (value of one vendor divided by second vendor). It gives me the exact zero consistency, because I've found the alternatives weightages using exact math comparison. But I get numerical values of weightages to find ranks, so it works fine for me.
But when it comes to the 5th criterion (ASTM Standards), the responses are in "Yes" or "No" terms! My question is that what numerical value should I give to a Yes and a No so that I can get their comparison by dividing with each other?
for instance, if I use Yes =1 and No = 0, the system hangs because anything divided by zero gives an infinity answer, and it doesn't proceed further.
If I want to use a scale of 1 to 9, saying Yes = 9, and No = 1, it gives me good results. But I've no reason to use 1 or 9, for it could be any numerical value say 1000 for Yes, and 1 for No.
Please suggest me a reasonable value with a citation if possible.
Thanks in advance.
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Dear Usman
Very interesting your question. The problem lies in the fact that in AHP you determine artificial values, but if you use Yes or Nor, or 1 and 0, these are not only objective values but with only two possible answers
Coincidentally, less than a week ago, another colleague put the same question, something that I had not seen in years
This is one of the 'beauties' of AHP, so elemental a method, that does not allow for modelling frequently incidents like this.
In other systems, you simply put 1 and 0 respectively
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I want to learn fractal mathematics from scratch. What are the prerequisites and recommended resources for it?
Thanks and regards.
Nishanth
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Check the references from this resource:
Perhaps you may start with this masterpiece:
Mandelbrot, B. B. The Fractal Geometry of Nature. New York: W. H. Freeman, 1983.
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Sometimes , we use term of "zero time" in a formulation but are we sure it is really "0" ? maybe it is 0,000......1 and is there a "zero" time(can we stop the time?), or sometimes, we say v=0 are we sure?
On the other hand
1/0 = infinity. Well then, what's "infinity"? How does it work in all the other equations?
infinity - infinity = 0?
1 + infinity = infinity?
If we use closest number to zero-monad (basic thing that constitutes the universe-everything-)Gottfreid Leibniz, in his essayMonadology,” suggested that the fundamental unit of all things is the monad. He intended the monad to have some of the attributes of the atom, but with important differences. The monads Leibniz proposed are indivisible, indissoluble, and have no extension or shape, yet from them all things were made. He called them “the true atoms of nature.” At the same time, each monad mirrored the universe. If we use monad instead of zero, every equations work
I think Science says "Every Thing had originated from a basic thing"
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Real numbers can be positive or negative, and include the number zero. They are called real numbers because they are not imaginary, which is a different system of numbers. https://www.livescience.com/42619-real-numbers.html
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Boolean and ZFC logic are constructed from fundamentally different foundations. Modern (20th century) mathematics appears to be dominated by the ZFC approach. I am not sure it is understood the two approaches are incompatible. Is this incompatibility studied?
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Es posible debo seguir profundizando y actuálizando me en Matemáticas pero según lo que he estudiado lo métodos matemáticos no se contradicen por diversas vías si son correctas se llega a los mismos resultados
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I have done cropping attacks in visual (pictorial) form but, I want to do this test in mathematical form, i.e., I want to calculate values of cropping attack analysis in MATLAB.
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Puedes usar MATLAB, pero puedes indagar sobre otros métodos que podrían ayudarte con el objetivo que persigues
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Hi,
I am trying to write the motivation part for linearization of a non-linear mathematical formulation. I claim the mathematical model will be more simple and easier to solve. But, of course, I need a reference for that! Any suggested book chapters or articles that discuss this point please?
Thanks in advance...
Zak
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Linearization is one amongst most important problem solving methods, in science.
This link may help you?
Thanks
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STEM fue el tema principal de la conferencia internacional ASTE 2019, con al menos 8 pósteres, 27 presentaciones orales y 3 talleres que promovieron las aulas STEM, la instrucción/enseñanza STEM, las lecciones STEM, los campamentos de verano STEM, los clubes STEM y las escuelas STEM sin proporcionar una conceptualización o definición operativa de lo que es STEM. Algunas presentaciones defendían la integración de las disciplinas, pero el ejemplo proporcionado fue principalmente prácticas "indagatorias" y de "diseño de ingeniería" que de hecho no diferían del tipo de actividades en el aula hands-on/minds-off mal conceptualizadas y epistemológicamente incongruentes.
Por lo tanto, vale la pena considerar:
(1) ¿Por qué lo llamamos STEM si no difiere de las prácticas aplicadas durante décadas (por ejemplo, indagación, actividades hands-on)?
(2) ¿Qué beneficios (si los hubiere) puede aportar esta mentalidad/tendencia de STEMinificación a la educación científica y su investigación?
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1) Moda
2) Igualdad supuestamente.
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Dear colleagues, please tell me a link to materials about mathematics of Dropout regularization in ANN. I perfectly understand how this algorithm works in practice, but I don't quite understand the mathematics.
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Thank you, dear Muhammad Ali!
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I know that an infant's brain can repair itself when damaged but why doesn't the same happen in adults after stroke or brain injuries?
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With Regenerative Medicine, using stem cells, the ongoing Programs are doing it, with good results and promising expectations.
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Hello everyone
I would really appreciate it if anyone could give some idea of some mathematical techniques for developing correlation for a dependent variable, W which has to be defined as W=f(x,y,z) where the individual functions are in form of power-law, W=a(x^b), W=c(y^d) and W=e(z^f).
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The simplest advice via the remark:
Logarithm of the equations implies linear formulas for the dependence of log W on log x , log y and log z.x,
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In general in mathematics we work with groups that includ numbers, generally we work with constants.
So for exempel: For any x from R we can choose any element from R we will find it a constant, the same thing for any complex number, for any z from C we will find it a constant.
My question say: Can we find a group or groups that includ variabels not constants for exemple, we named G a group for any x from G we will find an x' it's not a constant it's another variabel ?
and if it exisit can you give me exempels ?
Thank you !
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While working in both the software, after loading the training and validation data for the prediction of a single output using several input variables (say 10), it skips some of the inputs and delivered an explicit mathematical equation for future prediction of the specific parameter but it skips some of the input variables (say 2 or 3 or maybe greater). What criteria are these software uses in the back for picking the most influential parameters while providing a mathematical predictive model?
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Look the link, maybe useful.
Regards,
Shafagat
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Hello
Can someone help me to solve this?
Because I really don't know about these problems and still can't solve it until now
But I am still curious about the solutions
Hopefully you can make all the solutions
Sincerely
Wesley
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Hi In what area was the issue raised? Euclidean space, Hilbert space, Banach space?
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Austrian-born mathematician, logician, and philosopher Kurt Gödel created in 1931 one of the most stunning intellectual achievements in history. His shocking incompleteness theorems, published when he was just 25, proved that within any axiomatic mathematical system there are propositions that cannot be proved or disproved from the axioms within the system. Such a system cannot be both complete and consistent.
The understanding of Gödel’s proof requires advanced knowledge of symbolic logic, as well as Hilbert and Peano mathematics. Hilbert’s Program was a proposal by German mathematician David Hilbert to ground all existing theories to a finite, complete set of axioms, and provide a proof that these axioms were consistent. Ultimately, the consistency of all of mathematics could be reduced to basic arithmetic. Gödel’s 1931 paper proved that Hilbert’s Program is unattainable.
The book Gödel’s Proof by Ernest Nagel and James Newman provides a readable and accessible explanation of the main ideas and broad implications of Gödel's discovery.
Mathematicians, scholars and non-specialist readers are invited to offer their interpretations of Gödel's theory.
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The idea is you have to go out of the system in order to prove some results.
Like the Fermat problem needed things like Eliptic curves also, foreign to just
plain integer arithmetic.
That is if you mix up a bunch of rules, there are also unexpected side effects which might be true, but cannot be proven. Some results are random (prime numbers)
Many other problems are still open.
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When I observed mathematics education in preservice teachers at my university, I found that What students learn in mathematics classes does not match what is needed in school mathematics classes. That led to my initiation to do design research, a Hypothetical Learning Trajectory that contains a sequence of learning processes related to elementary school mathematics learning. I consider starting with observations in elementary math class to identify misconceptions, then jointly reviewing issues on campus, conducting literature reviews, designing lessons to address identified problems, implementing them in class and evaluating the results. The final result is a Local Instructional Theory on Learning about Teaching Mathematics for prospective teachers to overcome misconceptions that occur in elementary mathematics classes. I need so many suggestions to do this research.
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From my experience your idea has been voiced by every teacher in every subject from the beginning of teaching. In addition, myself and very teacher wants a concept close to what you describe. So much so that they have refined it and set it in place as a curriculum goal at all levels of education.
And it usually fails in real-world classrooms. Especially teaching students from 5 to 18 years old. These are people in their early stages of developing skills to learn. And by their nature never at the same levels. To me those needs come first. You can be successful as a teacher and at same time put aside the obvious theory and hopeful goals.
Like someone else here suggested, spend a few years with the children you hope to help and find out what their needs are and those of their families and community VS what you think they are. First experience helping people to learn before you decide how they should learn and how to organize the curriculum.
Mathematical skills, concepts and facts - like anything else - are easily learned. With a big "if"...if the child likes to learn and has had people help them along the way.
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In 2010, Dr. Khmelnik has found the suitable method of resolving of the Navier-Stokes equations and published his results in a book. In 2021, already the sixth edition of his book was released that is attached to this question for downloading. Here it is worce to mention that the Clay Mathematics Institute has included this problem of resolving of the Navier-Stokes equations in the list of seven important millennium problems. Why the Navier-Stokes equations are very important?
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I finally could check the PDF, Prof. Aleksey Anatolievich Zakharenko
Dr. Khmelnik uses a variational principle to solve the NS equation, which is very powerful indeed.
He also discusses and gives examples & a reason for turbulence.
I know that the solution of NS is a non-linear problem that involves several modes and that it depends on the source.
However, my knowledge of the foundations of NS is very limited to a few linear/non-linear problems on non-equilibrium gas dynamics& MHD solved by the method, Prof. Miguel Hernando Ibanez had.
Thank you for sharing the link. I recovered my account.
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According to the resources; there is used to algorithm in HOMER sotware, grid search algorithm and derivative-free algorithm.
So how can I find the mathematical formulas of these algorithm ?
Please if you know the way or source help me
Thank you
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I am not sure yet whether the answer is included in the following HelpManual, I will search for that manual and please you search also. https://www.homerenergy.com/pdf/HOMER2_2.8_HelpManual.pdf
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Hello! I have an exercise to do and I am struggling with it for a week ago. I have a 2D flow with the initial velocity at the inlet=0.01m/s. And I want to calculate the numerical results of the velocity which is the function of x and y direction (U(x,y)) in the domain of the water flow. For example if I want to calculate the velocity at the distance x1 and x2 (as in the figure) in the function of x and y., how can I calculate it? Please note that it is incompressible flow. It is fully developed after it passed the entrance length. The height of the domain is 0.02 m and the length is 1 m. Please help me! You can see the following figure. Thank You in advance! I will appreciate your help !
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Finally, I did it after I know how to use 1st Simpson Rule to apply this problem!
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According to the resources; there is two algorithm used in HOMER sotware optimization process; grid search algorithm and derivative-free algorithm.
So how can I find the mathematical formulas of these algorithm ?
Please if you know the way or source help me
Thank you
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Table of Contents for a book suggested by David Eugene Booth is available at:
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I mean the mathematical component of said process.
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coupled eulerian lagrangian (cel in abaqus, ale in ls-dyna)
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Mathematical about the work-related with graphene or any other type of films/coatings.
Lubrication equations in solid films.
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The thesis "Aspects of Flow and Viscoelasticity in a Model Elastohydrodynamically Lubricated Contact"
by Ellen van Emden at UT Twente, might give you some ideas!
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The temptation in all the remodeling of the study plans to train teachers that I have experienced, faced with a new strong point of interest, has been to introduce a subject that caters for it. Thus, environmental education, for example, has been the curriculum of Spain for more than 25 years.
Now the SDGs are the focus of attention, and the university is committed to developing them. the challenge is to do it from the established curricular subjects
Educational mathematics is developed in three or four subjects of each training curriculum, and has to embrace achieving the teacher's competence development to teach school mathematics and also, the purpose of working on the SDG, how can we do it?
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What are the various fields
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Fractional Calculus especially Conformable Fractional derivatives. This area is still new but it will get popularity very soon.
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using BTE how do we get mobilities and conductivity ,more calculation(mathematics) oriented answers would be helpful.
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Found this useful,
Refer to chapter 1(Low field electron transport) of Rode's book 'semiconductor and semimetals' . It has a thorough explanation for mobility and conductivity calculations.
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In classical times there was a concept of pure science that was produced entirely in the intellect.
More recently sciences were developed by testing the intellectual product with empirical data. These sciences are not regarded as being pure.
Mathematics, often regarded as pure science, has for most of history been based on postulates of geometry that could not be proven. Then came relativity and other geometries. In the past century there was considerable effort to reformulate mathematics on a firmer basis of conditional sets. Math is now regarded as being somewhat more pure than before, while producing two generations of graduating students in some countries who are not able to do simple arithmetic.
Fortunately I had some excellent teachers who explained the two systems and why they were both needed. Other teachers displayed the Gödel's incompleteness theorems.
In academic settings there seems to be a difference of opinions about whether or not math is a science, and whether or not it is pure.
Is Mathematics A Science?
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I am interested in TPACK and mathematics education, can you share recent research articles on both topics here?
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Of course Yes, give me a little time
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Physical reality can be observed. At least part of the structure and behavior of physical reality is perceivable. Humans can communicate about these experiences. Curious humans want to comprehend these perceptions. Humans have designed linguistic tools to be able to communicate about the perceived structure and behavior of physical reality and with these tools, they have constructed structures and models of mechanisms that might explain the perceived structures and mechanisms that physical reality exposes. Some of these structures and models of mechanisms seem to be successful. People discuss the success of these approaches and call this activity exact science. Other humans discuss this activity and call themselves philosophers. Humans are interested in the structure and mechanisms of physical reality because this knowledge helps them survive as individuals and as communities. Part of the exact sciences is formed by mathematics. Mathematics contains structures and models of mechanisms that are not directly derived from perceptions of physical reality. These concepts are derived from abstract foundations. Examples are empty space and point-like objects. Scientists use these concepts to construct vector spaces, number systems, and coordinate systems. The scientists apply these higher-level concepts to construct a model of their living space. The philosophers will immediately indicate that it is impossible to prove that these models are correct. However, these models feature structure and behavior. If the structure and behavior of the models agree more with the perceived models and behavior, then there is a larger chance that the model fits reality. Since reality appears to be very complicated, little chance exists that good correspondence will ever end the dispute.
One of the aspects of the dispute concerns what the best inroad will be for comprehending most of the structure and the mechanisms of physical reality. That is the background of the posed question.
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The paper "Sticky Space Coverage" relies on the results of David Hilbert, John von Neumann, and Cantor. I consider them better and deeper-looking mathematicians than the EPR team. They all worked on set theory, vector spaces, and Hilbert spaces. Hilbert cooperated with Einstein on gravitation theory. The paper "The Standard Model of Elementary Fermions and the Hilbert Repository" ; https://vixra.org/abs/2106.0135 offers an explanation for the phenomenon of entanglement.
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US Fed's balanced sheet has recently doubled up from $4T to $8T (see the monthly chart) – not to mention it used to be $800B around 2008. It seems like to me, that is highly inflating the housing markets, pushing the housing prices higher as well as the inflation rates higher – regardless of taking economic productions much into consideration. Fed refers to the situation as "transitory".
I'm sure that there should be solid mathematical rations behind it. Does this parabolic Quantitative Easing approach a mathematically and/or economically sound strategy, considering the current economic situations? Any other alternative strategy? Any upsides and downsides?
Thank you!
---------
PS:
A bit outdated visual components of Fed's balanced sheet:
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From the perspective of monetary system stability it is ( ), so I'm supposing that provides a mathematical justification.
But that's not the only perspective to be looked at in my opinion. The question also needs to be asked where all that money went to. Since debt is bought on the financial markets by the central banks I'm supposing most of the money is going to investors and investment funds. How much of it is then used to contribute to something which is beneficial to our society? What are the effects on inequality?
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Dear colleagues, I would like to know if there is a mathematical equation or model to calculate the Soxhlet number of cycles by varying the following parameters:
- the type of solvent
- the volume of the extractor
- the temperature of the solvent heating
if yes how can we apply it? and how much uncertainty it has?
thank you so much
best regards
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Suggested reference: D.A. Ellis, "Prediction of multistage solvent extraction operation from limited data", Industrial and Engineering Chemistry, 52(3) March 1960, 251-252.
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I need mathematical formula to measure public service quality and organizational impact
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such as Fourier , Hilbert or Laplace transforms in order to analysis and studies in the field of music acoustics.
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You my see
1-Transform methods in applied mathematics: An introduction
Wiley-Interscience
Peter Lancaster, Kestutis Šalkauskas
Year:
1996
Language:
english
2-Integral transforms in applied mathematics
Cambridge University Press
John Miles
Year:
1971
Language:
english
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Please look at the mathematical construction of theta and zeta functions in the representation of a winding sphere. In this paper, based on the representation of the winding of a sphere, we construct a proof of the Riemann hypothesis of nontrivial zeros. Could you check this proof?
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Dear Bayak,
Your idea is certainly interesting, but unfortunately, I am not an expert on topolog,y. I strongly suggest you first meet a professor and talk to him on how you have tackled the problem. Then give him the paper to study. This procedure will make a good beginning. Also, you can start by giving seminars/ lectures on the proof. You will get suggestions for improvements ( if any) And then you get a few people to recommend your paper to a Journal.
Best of Luck and God Bless!
Regards
Dr Kumar Eswaran.
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Hi researchers,
I need to find a method of proving a mathematical equation that exist in attached file.
This mathematical equation is about Bessel function.
I will be thankful to hear your helps and advises.
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This link might be useful, have a look:
Kind Regards
Qamar Ul Islam
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Dimensional rules for Homogeneous Diophantine equations
A Diophantine equation is an algebraic equation with several unknowns and integer coefficients. Those are equations whose solutions must be whole numbers. The only solutions of interest are integers
In mathematics and physics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it or the minimum number of sides to build a physical area or volume.
To build a geometrical rectangle (square) we require 2 orthogonal sides (x, y are independent indeterminates) area = x*y (or area = x*x)
To compute a numerical square (square number) we require 2 numbers p and q coprime with gcd(p,q)=1 or independent numbers.
Let we introduce a dimension for nature of numbers like I (for integer), R (for real), C (for complex) and so on.
n^2 = p^2 +q^2 ; 5^2=3^2 +4^2
Dimensional analysis gives for n^2= p^2 +q^2
I*I =I*I +I*I ; The sum of square might be equal to a square in some conditions.
Then the equation n^2 = p^2 +q^2 may have integer solutions.
A dimension is anything we can independently adjust, it is based on some geometric or algebraic definition.
In any correct mathematical equation representing the relation between physical quantities or mathematical objects (length, area, volume,….,.simplex), the dimensions of all terms must be the same on both sides. Terms separated by ‘+’ or ‘–’ must have the same dimensions.
The degree of freedom is the number of free components : how many components need to be known before the « objects » is fully determined?.
For example:
- a point in the plane has two degrees of freedom : its two coordinates;
- a square has two degrees of freedom : its two sides ( length and breadth).
- A point in 3-dimensional space has three degrees of freedom because three coordinates are needed to determine the position of the point.
Law of Degree of Freedom
The degree of freedom of a Diophantine equation is the number of parameters of each side that may vary independently. The degree of freedom must be the same on both sides.
- The equation n^2= p^2 +q^2
LHS is a square number with two degrees of freedom (its two multipliers or components) .
RHS is a sum of two squares with two degrees of freedom p^2 and q^2 which vary independently.
The degree of freedom is defined as the dimension of a mathematical object. When the degree of freedom is used instead of dimension, this usually means that the object is only implicitly defined.
Attempt to answer to Hilbert 10th problem
Hilbert's Tenth Problem Given a Diophantine equation with any number of unknown quantities and with rational integral numerical coefficients: To devise a process according to which it can be determined in a finite number of operations whether the equation is solvable in rational integers.
The problem was solved in 1970 by Yuri Matiyasevichwho in his doctoral dissertation proved that a general algorithm for solving all Diophantine equations cannot exist.
I think the concept of dimensional analysis is an attempt to answer Hilbert 10th problem related to homogeneous Diophantine equations . It works very well and allows to know if a homogeneous Diophantine equation has integer solutions but it remains to calculate these solutions using modular arithmetic or algebraic method…. The most important thing is to answer Yes/No and affirm that the integer solutions exist or not.
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Hello A.H Sheikh,
The question is very clear. Can we use dimensional analysis for Diophantine equation?
1/x+1/y =1/z with x, y, z integers.
x^2 + y^2 =z^2 with x, y, z integers
1/x^2 + 1/y^2 = 1/z^2 with x, y, z integers
1/x +1/y =1/z (called optic equation) which has integer solutions (2,2,1), (4,4,2)…..
The physical interpretation shows this equation is used for distances in thin lens equation (1/d1 + 1/d2 = 1/f ) , (1/L + 1/L= 1/L dimensional equation is correct)
electrical engineering (1/R1 + 1/R2 =1/R3).(1/R + 1/R= 1/R dimensional equation is correct)
1/x^2 + 1/y^2 = 1/z^2 (in a right triangle) with x, y, z integers has integer solutions (15,20,12), (20,15,12) ,(80, 60, 48),….
In the right triangle we have the equality 1/a^2 + 1/b^2 =1/h^2 where a and b are the integer sides of the right triangle and h the integer altitude to the hypotenuse (geometric interpretation (1/L^2 + 1/L^2 =1/L^2 dimensional equation is correct)
If the dimensional equation is right, correct then the Diophantine equation has integer solutions.
Greetings
M.AZZEDINE
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Dear Community,
I want to center (subtract the mean) my data in order to lower my intercept (as close as possible to zero). However, as I have categorical data as well, which I don't know how I can possibly center, I can't seem to lower my intercept.
And the thing is that my dummy variable drive up the intercept... So I don't know to fix the issue.
When I enter only continuous variables that are centered, the intercept is close to zero.
I thank you in advance?
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Not sure why you want the intercept being zero, but one way you could easily achieve this is by first finding the (non-zero) intercept and the subtract this value from the response variable.
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Dear Colleagues!
I hope you are all doing well. I have a question to all of you. I love to teach and so far I have been teaching everything from international business, marketing, management to organisational psychology. I feel ambivalent towards this however.I love to teach and Im curious in my nature and what better way to learn new things than to teach? However I also feel that if I continue being a generalist It might also be bad since I risk loosing touch with my main specialisation.
What are your thoughts? Your experiences?
My speciality is this :
Best wishes Henrik and professor Hugo 3 months old who keeps me company when Im trying to work :-)
Ps stay safe.
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Teaching one subject is more scientific and it will give you more academic background.
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I have seen that some equation sets have an explicit way of defining the substrate consumption whereas others have an implicit way. I would like to know how to convert the former into the latter.
For instance, in the attached file, it can be seen that there are two ways to describe the growth of bacteria.
In the first (explicit), the presence of a half-saturation constant suggests that the model is a Michaelis-Menten case. The second is straight a logistic model.
I was wondering if I can convert the first into the second, that is explicit to implicit.
Considering that the Monod term says that
μ = μᵢ[S/(S + K)]
then I can write
Ṅ = μN * logistic term
My question is: Would this modification be mathematically and biologically sound?
If yes, how can I estimate the carrying capacity? For instance, if I know the amount of limiting substance, can I estimate the number of cells that a system can sustain?
Thank you
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You will be best judge I think . There are so many model papers of logistic regression on Michales Menten equation - https://www.youtube.com/watch?v=fv6OAVe2vQc
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I'm working on constructing a field based on finite undirected and unlabeled graphs. I've selected graph join and graph Cartesian product. But I'm trying to figure out if the latter distributes over the former (or simple graph union).
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I want to know how we can relate magnetostriction with Applied magnetic field mathematically? Or if there is any way to derive it using mechanical equations?
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There are some classic thermodynamic models to discuss the influence of an external magnetic field on magnetostriction. And we can discuss the influence of external magnetic field on magnetostriction in ferromagnetic materials with different initial stress states.
【1】Shi Pengpeng. One-dimensional magneto-mechanical model for anhysteretic magnetization and magnetostriction in ferromagnetic materials. Journal of Magnetism and Magnetic Materials 2021, 168212. https://doi.org/10.1016/j.jmmm.2021.168212
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Hi All,
Can anyone please tell me which mathematical equation can be used to normalize the single ion monitoring quantitation in GC-MS? Thanks in advance!
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Nice question
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The field equations originally starting as Maxwell distributions graphs configure a velocity variable. Understanding that in connection to wave theory requires a mathematical transformation of velocity variable into wave function parameter. This may help mathematically to define particle wave quantum relativity quantitatively. Legendre transform theoretically will have a way to provide link among functionality of parameter-variable systems.
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Dear
One paper for you
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There is a contradiction between the natural width of the energy transition, which is determined by the lifetime at the corresponding energy level and the spectral line width of the radiation line, which is determined by the duration of the wave train.
For example: For the Mössbauer transition, whose lifetime is of the order of 2 years, while the interaction time at the receiving end is about 10^(-10) sec.
Mathematically, this interaction is expressed by the Feynman diagram of the electron - electron interaction, which integrates over the internal photon line, which, together with the delta functions of the vertex parts, limits the photon spectrum.
By the way, the same paradox applies to any other type of collision.
So, is exist (really) the electromagnetic field?
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Dear Pratik,
dissatisfaction with quantum theory, among physicists, lies in the fact that it, like any statistical theory, does not allow describing the dynamic processes of individual physical objects. The only physical substantiation of quantum theory is that the exchange of energy between objects occurs (according to Max Planck) in portions of the integer Planck action per oscillatory cycle.
Thus, the phase space of coordinates / impulses (time / energy) is divided into cells, inside which any processes can occur without violating the Planck prohibition (the classical model of the hydrogen atom), and at the border between the cells, the Fourier transform degenerates to the zero component. The space of classical c-numbers is partitioned into symmetric and antisymmetric components. It is possible that this corresponds to splitting the wave functions into even and odd parts (fermions and bosons).
Thus, the task is to construct an internally consistent building of classical mechanics that is compatible with the quantum theory, taking into account the properties of symmetry and interaction parameters.
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When we derive the formula for length contraction, we use the direct Lorentz transformation. But for solving the formula for time dilation, we use the inverse transformation. Why is that so?
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A question from far away worlds...Life Sciences (cricket) and an hyperbolic function from history of mathematics are trivially juxtaposed to encourage whatever reply.
[The antennas of the cricket roughly complete the less frequently represented branches of the hyperbola in the photographed virtual third and fourth quadrant of the Cartesian coordinate system].
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Great correlation ! in picture . please go through one of the special aspects of compuational epidemology -https://www.researchgate.net/post/How_best_fit_regression_method_can_be_applied_to_model_SARS-COV-2_epidemology
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Here we discuss about one of the famous unsolved problems in mathematics, the Riemann hypothesis. We construct a vision from a student about this hypothesis, we ask a questions maybe it will give a help for researchers and scientist.
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They say -2, -4, -6,....are trivial zeros of the Riemann Zeta function.
Just what is the proof?
Introducing -2, I seem to get
1+4+9+..very far from zero.
1/(2^z) with z=-2 is 1/(1/4) =4??
Where is the mistake?
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They say the best educators are able to make a complex subject easily understood by a child. Perhaps this is a challenge to us all.
Quarternion mathematics can be quite complex to wrap your head around. For educators out there how are you explaining this to your students from high school.
Is a pictorial method the most appropriate under these circumstances.
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Hey Joseph,
In my opinion sticking with unit quaternions would be the way to go. At a high school level it may be a good idea to skip the complex math definitions and instead focus on the intuitive "definition" of a unit axis and a rotation about that axis. Depending on the context you could run through an animation/example in 2D or 3D to show how multiplication works, then give the multiplication rules as formulas -- the same way one might do for dot and cross products at the high school level.
I would guess another important question to answer is why a roboticist would use quaternions instead of other representation. Having a short discussion on gimbal lock could be a great motivator, especially if there audience is interested in aerospace applications or robotic arms.
Thanks,
Logan
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I have read that time is defined in terms of entropy (entropy of the universe maybe? I'm not sure). But entropy is a macroscopic quantity which makes time a macroscopic quantity. Yet time is a parameter in Schrodinger's equation. So we have a macroscopic quantity appearing in a microscopic equation. That makes me think that this microscopic equation is really a statistics equation. It produces deterministic solutions but maybe these deterministic solutions are just mathematical procedures for statistical calculations. That would be consistent with the fact that these solutions actually are used for statistics calculations. Does it makes sense for a macroscopic quantity (time) to appear in a microscopic equation, unless it is a statistics equation? Or, am I mistaken in calling time macroscopic? My primary question is whether Schrodinger's equation can be derived from some set of statistical postulates. The question is not whether the equation was historically obtained from statistical arguments (we already know it wasn't), the question is whether the same equation can be derived from statistical arguments. What Schrodinger was thinking at the time of producing his equation is not relevant to this question.
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Interesting, I still remember that my QM physics teacher in Moscow told us in a lecture that the SE came from a more general theory. I just found this on a Wikipedia commons article that remains me of what he said in 1990:
I always have been impressed more with the old quantum method of quantization that the same SE, systems such as superfluidity in He4 can be predicted by the old method quite nicely.
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Mathematics is the basis of exact sciences. The development of mathematics consists in the fact that, among others, new phenomena of the surrounding world, which until recently were only described in the humanistic perspective, are also interpreted in mathematical terms.
However, is it possible to write down the essence of artistic creativity in mathematical models and create a pattern model for creating works of art, creative solutions and innovative inventions? If that was possible, then artificial intelligence could be programmed to create works of art, creative solutions and innovative inventions. Will it be possible in the future?
Do you agree with my opinion on this matter?
In view of the above, I am asking you the following question:
Will mathematics help to improve artificial intelligence so that it will achieve human qualities of artistic creativity and innovation?
Please reply
I invite you to the discussion
Best wishes
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Dear Stan Sykora, Boris Pérez-Cañedo, Baidaa Mohammed Ahmed,
Thank you for answering the above question and participating in this discussion.
Regards,
Dariusz Prokopowicz
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what are other possible ways to convert a CW laser to a pulsed laser. Please give all the theoretical and mathematical details.
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Output optical power can be achived by optical phase shift in one arm of Mach Zehnder interferometer. π/2 phase shift will lead to destructive interference and lower values of output intencity.
If we consider integrated structure of silicon Mach Zehnder modulator, the phase shift is induced by changing electron and hole concentration along with the effective refractive index.
The attached picture represents output power equation of MZM with a phase shifter in one arm. Indices 1 and 2 corresponds to MZM arms with and without the phase shifter. Index 3 denotes the phase shifter itself. L - length, betta - propagation constant, alfa - absorption coefficient.
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More specifically I am looking to analyze and plot non-michaelian kinetics based on functional parameters from BRENDA or similar sites. I do not know how to find the mathematical function describing such kinetics and have not yet been able to find it in the literature.
I would greatly appreciate any help from the community!
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You might be able to find some useful equations for the situations that interest you in I. Segel's monumental book "Enzyme Kinetics: Behavior and Analysis of Rapid Equilibrium and Steady-State Enzyme Systems"
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Hello Experts,
I want to know that how to find theta maximum when i am using GPS and sphere and surface type distribution. and using cosine distribution.
then i want to know that is there any mathematical calculation to find theta maximum for biasing.
like in the Geant4/examples/advanced/radio-protection theta maximum is 0.003 deg. how they got this using the surface area of source or object. like how can i get for my object ?
any type of help will be appreciated.
Thanks in advance !
Best Regards
Priyanshu
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How to transfer the logical description of safe constraints to mathematical description?Any feasible idea?
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The following work maybe useful
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  • An understanding of theories about how people learn, and the ability to apply these theories in teaching mathematics; It is one of the primary requirements for effective teaching of mathematics, and a large number of scientists have studied mental development and the nature of learning in different ways, and this resulted in various theories of learning.
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I totally agree with Darren John Stevens, I consider that it is a precise and detailed reflection, as well as current and fundamental for the time that we are having to live! Many thanks.
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Question about the loss of hyperbolicity in nonlinear PDE: when complex eigenvalues appear, what is the effect on flow? I understand that we do not have general results on existence in this case, but is it only the mathematical tools that are lacking where can we show physical phenomena of instability?
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Different longitudinal studies, such as the Perry Preschool Project or the Abecedarian Project, have shown that early and effective exposure to different content in ECE students, as science or maths, cause positive effects in children later development not only in academical sphere, but also in personal, social and economic ambits.
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There is little interest in teaching children about science due to the many difficulties in this field. Among them
1- Indicators of learning difficulties related to language
The child's speech is delayed compared to his peers.
Limited vocabulary.
Problems with forming sentences, finding words, and using and using language appropriately.
2- Indicators of learning difficulties related to cognitive skills
Poor to follow directions or follow a daily routine.
Slowness in saving and retrieving information - when needed - such as memorizing colors and days of the week.
Forgetting thoughts while talking and not remembering the topic the child is talking about if someone interrupts it.
Problems with motor coordination (eg, jumping, undressing, buttoning, tying shoelaces).
Difficulty finding similarities and differences between different stimuli.
Problems with visual-motor coordination, represented by the child's inability to achieve coordination between hand and eye movement, and he cannot arrange beads, cut correctly, or follow a line while writing.
3- Indicators of learning difficulties related to attention
Moving from one activity to another without the child finishing his previous activity.
Having difficulty following the child to what he hears or sees.
Short attention span of the child, and distraction.
There is a problem with the child following the sequence of information or ideas.
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Hi all,
I attached an image file of excel data in which the problem is to predict the value of u by using any mathematical method.so, please share me the procedure or method to be followed to solve the problem.thank you in advance.
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You search data imputation in internet there are many tools to predict the missing values.
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Hi all, I am looking for a patterning assessment to use as a pre- and post-test alongside a patterning intervention in mathematics for 7 to 9 year old children.
I know of PASA by JT Mulligan, are there any others?
Thanks in advance for your help!
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I hope the following is useful !!
Assessment of Young Children from Culturally Diverse Backgrounds: A Journey in Progress
Notari-Syverson, A., Losardo, A., Young Sook Lim,
Journal:
Assessment for Effective Intervention