Mathematics - Science topic

Yes!

Refer to my book

Transport of information carriers in semiconductors and nano devices.

Chapter 7. Photon transport.

Aman Srivastava

The ways for measuring the trend are as follows. I Graphic Method or Freehand. (ii) Semi-Average Method. (iii) Moving Averages Method.

The Trend may be identified by looking at the months that have the same position in each set of three-period patterns. Month 1 is, for example, the first month in the pattern, as is month 4. Sales in month four are greater than in month one.

Respected sir,

My name is fawad nadeem belong to Pakistan. I am interested in bifurcation matlab code. Kindly provided me the bifurcation code.

Thank you so much to all of you for your detailed explanation and interest.

Prof. Maged, thank you so much for your reply. I will read carefully the articles you recommend to me. By the way, for some reason, I can't download the first article you recommended, do you have a pdf version? Many Thanks！@ Maged Gumaan Bin-Saad

Sikai

Zhwan

Please open the attached file

My an swers in red

In my view scientific research is about explaining or predicting phenomena. And that is impossible without the use of models, whether they are implicit, or explicit.

And the data are only "visible" by using , whether you are aware of that or not, models. And very often the language of mathematics is used to generate these models. In that sense we all are descendants of Isaac Newton.

Very often I do not see any explicit model, but instead a multitude of procedures in order to process raw data, and basically all is then a question of curve fitting, or one step ahead prediction, where the curve is not known, and the measure of goodness of fit is often not clear at all. And the scientists, that use these models very often do not have a clue about the relation between data and model.

And people from statistics or machine learning barely speak the language of each other. There is hard work to do in University, to redress this, and to partly destroy the Tower of Babel. But as long as we get our papers published , while nearly no one is reading them, the atomization of research will continue.

And that worries me!

You should check out seminal and fundamental work by Gregory Chaitin starting in 1965 when he was a student in CUNY (City Univ. of New York) and continuing through the 1970's.

I recommended the following books

1- FPGA Implementations of Neural Networks

Springer

Amos R. Omondi, Jagath C. Rajapakse

Year:

2006

Language:

English

2-Guide to FPGA Implementation of Arithmetic Functions

Springer Netherlands

Jean-Pierre Deschamps, Gustavo D. Sutter, Enrique Cantó (auth.)

Year:

2012

Language:

English

3-State Machines Using VHDL: FPGA Implementation of Serial Communication and Display Protocols

Springer International Publishing

Orhan Gazi, A.Çağrı Arlı

Year:

2020

Language:

English

In following link there is similar question :

Relationship of Laplace Transformations and Beta-Gamma F ( x ).

Dear Shuraik Kader,

Given Albert Einstein's theory of relativity, cosmology regarding the development of the universe, quantum mechanics, future technologies for building interplanetary spacecraft, etc., time travel is theoretically possible. But in practice the building of a time machine by humans is impossible. Even if a man would achieve the required technological development in the next several hundred years, unfortunately he would not have enough time for it. First of all, a person must first solve other global problems, such as the necessary one is urgent, i.e. in the perspective of the next max. 2-3 decades of time, stopping or significantly slowing down the progressing global warming process, achieving zero-emission economy and avoiding a global climate catastrophe, which may occur at the end of the current 21st century. In order for man to be able to create new technologies of the future, to be able to build interplanetary manned spacecraft, etc., he must first save the planet's climate, biosphere and biodiversity from the risk of almost total degradation.

Best regards,

Dariusz

maybe it will be more clear with an example: (categorical variable = fruit, categories =apple, orange, banana, continuous variable = shelf life in number of Days e.g. 8) I have already used ANOVA to test to see if there are differences between the fruit for shelf life. and have used post hoc tests to find which fruit combinations have different shelf lives (e.g. apples and oranges have different shelf lives)

i am wondering are there any other mathematical/computational methods I can use that will help me determine which fruit has the longest (maximises) shelf life

Peter Breuer Thank you for your kindly reply, Sir. Yes, that's the generating function that I mean. Do you have any references (papers or books) about this thing? Especially for a higher dimensional.

I appreciate any help you can provide.

What kind of statements are metamathematics: logical, mathematical, logical-mathematical, philosophical? In the case of Hilbert's claims, they were aimed at finding a secure foundation for mathematical theories, and he thought that this could be achieved if the consistency of arithmetic was established, but that is only an assumption as to "foundation" which, furthermore, results from assuming that logic (because consistency is a formal property studied by theories such as logic) is a kind of guarantee for human knowledge, but logical theories and have their own problems (such as the inapplicability of the principle from the excluded middle to quantum mechanics) and I believe that if the 20th century has taught us a lesson in terms of analytical philosophy and the "foundation of mathematics" it is that it is not even possible to find a deductive language -or an axiomatic system- that is perfect or basic, nor can logic be an unquestionable starting point.

Dear Bollapragada,

Please check out the following paper:

The same topic:

You have some question you want to answer. You choose a method that is capable of answering it . Then collect data and use the method. Answer the question and then write it up., Just like in science class. David Booth

Dear Umair Shahzad,

I suggest you see links on the topic.

Best regards

Dear Vishal Gavande,

PFA file FYR will help you to understand the calculation.

Apart from that,

In the Coulomb friction law, the critical shear stress is defined as τ = μp, where μ is the coefficient of friction and p is the contact pressure between the surfaces.

What is critical shear stress?

(solid-state physics) The shear stress needed to cause slip in a given direction along a given crystallographic plane of a single crystal.

I want analysis in the differential equation.

okey

Hi Mahdi Ebrahimnejad Shalmani

I understand that the 4DOF system for the washer can be quite lengthy. However, I'm unsure if your question is a control problem. If it is, and the 4DOF mathematical model can be expressed in such form:

x' = f(x) + g(x)·F_c(ω)

where

then I think it is possible to design the spin speed profile for the control input, ω, so that the desired responses of x can be achieved. If you want to design the profile, you need to at least understand the mathematical equation for F_c(ω). Do you want to regulate the spin speed at 300 rpm, 600 rpm, or 1200 rpm? Because I see only the signal oscillates within the dimensionless amplitudes ± 4×10^–3.

Hi Saeb AmirAhmadi Chomachar

I have plotted the signal according to your suggestion, and compared it with Mahdi's original signal. Note that if t₁ > 5/τ, then exp(–τ·θ(t – t₁)·t) ≈ 0 after t₁, because exp(–0.5·t) has decayed to almost zero.

Hi, I agree with Preston concerning the different methods used for planets detection. Now, concerning L1, L2 and L3, if you are talking about the Lagrange points of the Restricted Three-Body Problem. Their positions can be approximated by some simple computations. You can refer to existing literature, for e.g.:

Victor G. Szebehely and F. T. Geyling, "Theory of Orbits: The Restricted Problem of Three Bodies", 1967.

Dear Marco Ripà ,

I have done both. I cited my work in the sequences and the sequences in my work.

function f(x) works to do the prediction of accuracy to predict and built the next function of calculus.

read this link below:

https://opentextbc.ca/calculusv1openstax/chapter/the-limit-of-a-function/

@Knoll, I did it for my research paper. It was about mathematical formulas and equations on panel data econometric model. To open a pdf with MS word, you need to, at first, create a blank word file, then go to the option button on the left corner of the screen, there you will see the option "Open" along with options such as "Save". " Save as". Then click on "Open", then, select the specific pdf file, click on it, and it will be opened on MS word.

Dear Yahia

Please explain what your problem is.

Without it is impossible to help you since there are many problems in optimization

Yes, Björn, these phenomena of spontaneous synchronization of motions include the so-called nano-resonance or Egorov resonance, which explains, for example, the nature of the well-known narrow and intense optical J-band, where, under certain (resonant) conditions, the electronic motion and the motion of the nuclear reorganization of the environment are synchronized. There are good reasons to believe that nano-resonance plays an important role in the life of living organisms.

Actually Adobe Illustrator or even keynote

A first offhand very general remark: Market rules and habits infiltrated into sciences tend to deform scientific explorations and divert individual efforts to some sort of racing competitions...

After retracting my erroneous paper published in Turkish Journal of Computer and Mathematics Education, I have found a new proof and the preprint of my paper has been uploaded in ResearchGate, for public view and comments. The same is attached herewith

Thank you for your participation.

You may be too affirmative, since nobody ever checked that point (existence of aether) and a large part if the community thinks that it exists in some form or another, as explained in my text. My idea is that in absolute vacuum, matter transfer can be done at no expense (because the "effective mass" of nucleons is 0). The coefficient "1" in the RHS of Newton's law is artificial and corresponds to a choice of units for mass and force, related with our measures and experiments on earth. Maybe, in some distant regions of cosmos, it will be different (the "effective mass" becoming different for the same number of nucleons). This can also help to understand Zwicky's paradox (hidden mass problem).

Checking the existence of aether (or anything similar) would require very sophisticated experiments, maybe the most accessible way would be through the drag which should be perceivable by its action on moving matter, but if it exists it will be extremely weak, which makes the experimental protocol very delicate, cf. my other post https://www.researchgate.net/post/Any_idea_for_proving_or_disproving_the_existence_of_aether

Best wishes

Alain H.

@Jim Moore

Dear Jim,

To your first comment:

Of course no...You are welcome! This misunderstanding arose because you contacted me directly. This gave me the impression of criticism. I've been under all sorts of criticism for almost 2 years now. Accordingly, you could understand my response. In doing so, I have been asking you to "address your messages to EVERYONE". This happened when I began to understand that your messages are not directed entirely to criticism of my materials. [Although, I ask you to agree that it was also on your part...:)]

I ask you to forget this misunderstanding and move forward. I would be very interested in this!

I will reply to second comment later.

Sincerely,

Sergey

For classical MIMO detection, I recommend the paper "MIMO Detection Methods: How They Work" (https://www.diva-portal.org/smash/get/diva2:242286/FULLTEXT01.pdf)

For Massive MIMO, I recommend Chapter 4 in my book that you can download here: http://massivemimobook.com

Kindly viait..

Alain Didier Noutchegueme

Varun Varun

Euh...The closed L^2 unit ball is not totally bounded since it is closed but not compact. The open unit ball is not totally bounded either, since its closure is not compact.

I think Matlab is good

According to Web of Science, ESCI Journal can be included in Science Citation Index (SCI), Social Science Citation Index (SSCI), or Arts and Humanities Citation Index (AHCI), if they meet "Impact Criteria".

Accordingly, journals are included in Web of Science Core Collection (SCI, SSCI, AHCI, and ESCI) if they meet 2 criteria, namely; 1) Quality 2) Impact. The "Quality criteria" comprises 24 sub-criterion, while the "Impact criterion" consist of 4 sub-criteria.

Hence, any journal captured in ESCI have already meet the quality criteria , therefore the quality criteria is the only requirement for journal to be considered in ESCI. Similarly, any journal on ESCI must wait to meet the "Impact Criteria", which can take time, and may be impossible to be predicted. This is because the Impact Criteria is evaluated according to the number of citations the journal is receiving, the performance of authors who published in the journal before, and the number of cross-references between journals in web of science, etc. Waheed Ur Rehman .

American journal of mathematical and management sciences.

The application of jerk in physics have many instances and one of the example I can shot is simple that the jerk is nothing but it is all about the rate at which any objects acceleration changes with the time or with respect to time.

The answer is simply no. Additionally, considering "realist (platonic)" and "non-realist (non-platonic)" doesn't actually help with the answer I am going to provide, and the article also begs the question. It's like asking why you like music, is it because it sounds good, or is it because it makes you feel good? Well, that depends on what you mean! Equally, asking a working mathematician about the independence of math, or the construction of math will get you very confused looks. They way one treats math, is ever which is the most convenient, or the most sensible to the person. As such, the article in question does not particularly respect nor delineate the historical and functional differences between these two foundations of mathematics very well. Mathematics is a very broad, messy, overlapping subject. In fact, most of the math I regularly use does not really involve calculations, or functions per se. But, as the article is a pre-print, I assume it simply represents a scribbling of his thoughts.

In order to elucidate my answer better, some background in the cartography of mathematics is needed. There are many different universes (formal distinct foundations of mathematics as unique fields) of mathematics that have their own level of reasoning, and focuses. To name a few, category theory, abstract group theory, analysis, proof theory, many-valued logic, and the list just keeps going. All of which are employed at different levels to ascertain certain properties of math, or even to articulate certain questions. For instance, if one wants to study the different universes of mathematics, category theory is generally involved, and the object considered is called a topos. Or if one wishes to study how numbers work, one can employ number theory to study them as unique things, or you can employ analysis and study them as functions, or you can study them with group theory and consider them as action as well. In this view, no field of mathematics has a primacy over other mathematics, only advantages to the inquiries at hand.

Here is a simple question that I think illustrates the point I am making: is two an element of four, or not? That is to ask, in the construction of numbers, are they considered logically unique (aka type theory), or as informal primitives so that numbers are just simply numbers (set theory)? It is in fact this very question that helps separate type theory and set theory. This question, is akin to asking is meaning found in words or what the words represent? However both are true to a certain degree, and from different perspectives. If we are partial to the former, we are essentially asking, does the construction of words form the meaning they express? Yes, but only if we consider meaning as inherent to language alone (intensional). That is language makes meaning, not the world outside of our minds. If we are partial to the latter however, then words denote things, they are analogs to events, and point to common descriptions that we see (extensional). In the same manner, type theory considers numbers as things in themselves, to say "there are two dogs" is to say two dogs. Because the number two is different then dogs. Equally, computer scientists often employ type theory because it logically constructs things, whereas, mathematicians like set theory because its very good at describing things, and there relationships. It would be very burdensome for a mathematician if we had to logically construct everything from the bottom up. Instead of saying, let us consider a sequence of integers. The computer scientist would have to define every part of that sentence.

I hope this helps clarify the question.

read this research paper it will be useful

Dear Muhammad Ali

Indeed, that is a possibility. Perhaps what we call numbers are labels in a language, as a kind of names that do not really name anything that is literally beyond human language and representations, or that are a way of referring to systems, scales , etc. of which they are a part, mere nodes of a conceptual structure. Some authors have argued that numbers are only signs, signs that are part of representational and notational systems that have proven to be effective, useful instruments to be applied to parts of reality, which are improved and refined over time. However, I believe that it is necessary to take into account the fact that not every system, model or scale works, and this perhaps reveals that there are structural characteristics of the reality to which they are applied that are imposed as limits, that constrain what can be work and what doesn't, and this perhaps means that, although they do not literally describe abstract entities (numbers or geometric figures, for example) as we imagine them, mathematical systems and theories somehow express that which is beyond the representations themselves. You can't use just any geometry to build a house or to explain why Mercury "wobbles" when it's at perihelion, and that suggests that mathematical systems, mathematized theories and models are human creations but they could not be totally arbitrary, so that, even in a metaphorical or indirect way, it should not be ruled out that they represent structural characteristics of the world to which they are applied that is beyond human constructs. We must not forget that we humans perceive in three dimensions, we listen less than dogs, we believe that colors are in things and, to an important extent, we elaborate our theories and build our image of the world accordingly ("the human is the measure of all things" said Protagoras), but there seems to be more and more evidence that, at least the macroscopic physical world is not three-dimensional, so we may never really know what lies beyond us and our representations and to that mystery we must add that of why some models and mathematical theories work and others do not. Greetings.

Dear Parsa Sarosh

YOLO is a clever convolutional neural network (CNN) for doing object detection in real-time. With YOLO, a single CNN simultaneously predicts multiple bounding boxes and class probabilities for those boxes. YOLO trains on full images and directly optimizes detection performance. YOLO algorithm is an algorithm based on regression, instead of selecting the interesting part of an Image, it predicts classes and bounding boxes for the whole image in one run of the Algorithm. Ultimately, we aim to predict a class of an object and the bounding box specifying object location. Image segmentation is the task of clustering parts of an image together that belong to the same object class. This process is also called pixel-level classification. In other words, it involves partitioning images (or video frames) into multiple segments or objects.

Also, kindly check these papers:

Please see also the following useful RG link:

Kindly check also the following very good RG link:

Firstly you should calculate the equation at the centre of mass. And you can using reduction techniques in determinate system to reduce unknowns. exp: neglecting some parameters or some muscles.

Then using Newton laws to calculate forces and moment.

Consider summation of forces in the horizontal an vertical direction separately including GRF and external forces equal to m x a.

Finally consider summation of moments in centre of mass equal to mass moment of inertia x angular acceleration.

By solving these 3 equations by putting knowns, the unknown parameters are calculated.

جميل جدا

Neural Network Math by MICHAEL TAYLOR - https://www.google.com/search?sxsrf=AOaemvL2kwKXsOal_HZK72qNa68RRWndkw:1642256572635&q=The+Math+of+Neural+Networks&stick=H4sIAAAAAAAAAI1UO2jVUBhubmu9jbX0phX0ulyvCLWIN-_kuLT4QsGqaB2cws3Jq3mc3OTEPO4iFBR08gEKLoI4-NpcxEFEJx0cHHRRETdXQdBFvbbNCR0El5DvfP_3fef_c3LqG9qbO3aH4yzOzXUfcfxMbMIwCExkmEZLD0MPt6wwbiHzXNz1W0E3cczBYwni19SqEmJWBqzeL7HDAS4IRIJdALO-L4HXFN0JOqyogFQXS7KMJWJBdz0hT8tiTeEziZCWHAmqZKyREqdmAiDb4DKb1ZNB7PhfzOuBnCSRu1YLrT6fSxWHUk0SiQ9gOYVwCHscTqpuepKN5LSiNc_C_VLKaqCwCRdzTpBqRKoawICKXKUmKkQ-kfYlFJW1CPU83eKcai5xbjhF2Q0S5EyQWb2kdSVSsBirlRcQUNWOCJJqvz3WsEk7EZYzB9hWORYRiIJKXIteJOIMkpEqouVrASJYEryAE7MSD-ZtG65BsJFHMFcsnvAQ2FmaaBV2eQ5bKWla4QM36BG9o7lZEeTV7KFnCTgqyFACCWQCX2EFRzhVyUl0WMGzUjYqmxMg4nrVxxEh7vtEq_qRLkOW4Ajkej9TvlDXhzdNfv3xaap5afjao1fvqOVhemS_iRPmQo3edNpMFsOF0FiyCuY7xXyj6MljYYhNvzhl-t3ENBZDZg89egglS0nBjDdpur5yjmPX5qfp1ShP9qBjqL3J259vUMwDar3rLYq5-Z-uEtDxP1zPrDc9zBykxxbMQDdjfMJidtL0gdD3TZgshYjZ0pyiGx1IFjorf3174tTY3xA90aDwnKrtq83U2sODlzbitadvb7wZPdu4-_H378cnTs43d88y9Maj-FgIu37jPf1yy-XT9-dmp-j6YjcPURgUjWtHrno_lb1z7R1j2rbpoe8fPs81HjZ_nZ84Mzu_td6iZkY4Z9evuYtP2OezQ4OU5Wf3XoyO1KnJoX6tPjF-Z8P2RcdsLQyun1ZotY6v3kbHzSQLYw9fGaX-ALQqOu7JBAAA&sa=X&ved=2ahUKEwjE3ZC9-rP1AhWESWwGHRiOCRoQ-BZ6BAgKEBM

Check https://chem.libretexts.org/Bookshelves/General_Chemistry/Map%3A_Chemistry_-_The_Central_Science_(Brown_et_al.)/04._Reactions_in_Aqueous_Solution/4.5%3A_Concentration_of_Solutions

The components of random vector in your case are not independent, because they are connected with normalization condition. It means that you can calculate conditional expectations only. Say, M(X|Y) and M(Y|X) in 2D case. And the ME vector in this case consists of conditional components. You should verify, would it be unit vector or not. Concerning median I'm not sure. It is neccessary to think more. In any case it should be calculated using conditional probabilities.

Oblique assymptote rule for rational function - https://www.storyofmathematics.com/oblique-asymptote

Adrianna Kalinowska There is no special meaning of the value 1 for the khi-square... As a probability function, continuous, the probability of a random variable following a khi-square law to be exactly 1 is 0. As a distance between two contingency tables, it's not clear why 1 should be given a special consideration.

So, I don't really understand the context of your question. Please could you detail?

(By the way, I don"t understand either the origin of the original question and this debate around the value « 1 » in the khi-square…).

Hi Mohsin Ali Khan ,

First of all, was the fitness (error) zero (0) at the end of the evolution?

If yes, it means that the skipped variables are not important for the data being analyzed.

If not, it can either mean that some variables are not important or that the evolution is stuck in a local optimum.

Note, that for real-world data, it is unlikely to obtain fitness 0 because of noise or other imperfections (in data collection or measurement).

regards,

Mihai

Mathematics helps AI scientists to solve challenging deep abstract problems using traditional methods and techniques known for hundreds of years. Math is needed for AI because computers see the world differently from humans. Where humans see an image, a computer will see a 2D- or 3D-matrix. With the help of mathematics, we can input these dimensions into a computer, and linear algebra is about processing new data sets.

Here you can find good sources for this:

My intervention is limited to what Umberto Eco [who I met at the University of Urbino] thinks about Fermat's Theorem. Thank you Dear Dr. Mohamed Azzedine

Hi

(I haven’t looked at your xml as I doing this from my iPad).

i guess the answer is Yes and No.

Yes, we can use analytical and numerical models, or tests, to find, as best possible natural frequencies. To what effect may be worth pondering.

There are some problem with pipelines.

1) they tend to be very long. Infinite, may be a reasonable approx. Unbounded systems don’t not have modes, they have wave propagation. They can be approximated using modes but you need a lot of them and the modal summation doesn’t always converge as one would want it to.

2) every frequency is a natural frequency for an infinite system, ie you get lots of closely spaced modes, which in turn provides a high modal overlap situation (search RG, it has been discussed before).

3) I imagine that numerical solvers may have a problem with closely spaced modal systems.

4) pipelines tend to lie on something, ie the couple to terrain, again a large system.

So, chasing this problem using modes may not be your best bet.

Wave propagation for analytical models and direct numeric solution for FE probably is the better way to go.

Hope this helps

claes

Special functions approximations (Bessel Functions, Hypergeometric Functions, Confluent Hypergeometric Functions) can be applied to many practical applications of computer science, Physics and many industrial applications. See e.g., https://spie.org/Publications/Book/270709?SSO=1 and the attachment.

see

A SURVEY OF THE DIFFERENT TYPES OF VECTOR SPACE PARTITIONS

HEDEN, OLOF

Journal:

Discrete Mathematics Algorithms and Applications

Year:

2012

Before talking of fractional order models, it will be better to work on integer orders. After that you can work on fractional order problems easily. There are many references. You can check some of my papers in both fractional and integer forms!

I hope the following paper are interested to you

1-Computer Vision-Based, Noncontacting Deformation Measurements in Mechanics: A Generational Transformation

Sutton, Michael A.

Journal:

Applied Mechanics Reviews

Year:

2013

2-Vision-based detection of loosened bolts using the Hough transform and support vector machines

Cha, Young-Jin, You, Kisung, Choi, Wooram

Journal:

Automation in Construction

Year:

2016

Hi Solihu,

The orthometric height is hard to realize perfectly in practice because we need to know the exact path of the plumb line within the topography and the knowledge of gravity variations or mass-density distribution inside the topography at all points along the plumb line. So, the approximation (hypotheses) given by the Helmert (1890) orthometric heights is most used ( Heiskanen & Moritz, 1967, Chapter 4). Also, several refinements have been proposed to the Helmert method to improve models for the value of integral-mean gravity along the plumb line (Tenzer et al., 2005).

---------

Heiskanen, W.A. and Moritz, H. (1967) Physical Geodesy, WH Freeman & Co, San Francisco, USA, 364 pp.

Tenzer, R., Vaníček, P., Santos, M., Featherstone, W.E. and Kuhn, M. (2005) Rigorous determination of the orthometric height, Journal of Geodesy, vol. 79, nos 1-3, doi:10.1007/s00190-005-0445-2

Regards

Abdelrahim Ruby

see

Hi José de Jesús Camacho Medina

Unfortunately I missed your post. Possible implementation in Wolfram Mathematica is shown in the attached picture. Of course, Mathematica's native procedure Select looks much more elegant.

It seems the linearization is accomplished by replacing x1, for x1^2. And separately by replacing x2, for x2^2 & x2^4.

In this way, the surface function is linearized about the origin (0,0), it means we can find f1(x1,x2)=a*x1+b*x2, whilst a and b are calculable in terms of the algebraic parameters, k and c.

But my question transforms to another level. How, we can find a compact algebraic expression for f1(x1,x2), and f2(x1,x2), close enough to the origin. This algebraic expression, need NOT be necessarily linear (it could be a nonlinear function).

1--How to find another compact analytical expression equivalent to f1(x1,x2), f2(x1,x2)? (with fair accuracy)

2-- Is it possible to find an approximation near the origin (0,0), for f1(x1,x2), f2(x1,x2), as a function of only one of the two variables (either x1, or x2)?

Regarding the second synopsis, I am to cite another ResearchGate question linked below:

However, the gist of the idea in this link is not clear to me.

Nicolas Balacheff

Teachers may assist students achieve academic success by explicitly communicating positive expectations for each student, providing equal opportunity for students to engage in class discussions, and conveying to students that they are confidence in their capacity to succeed in their courses.

This is not something you learn when you first start learning arithmetic. However, this is a fundamental skill that every student should master since it allows them to develop critical thinking. Certain situations in life need you to be analytical, which is critical when making judgments.

Mathematics is the systematic application of matter. Mathematics organizes and prevents chaos in our lives. Mathematics fosters certain abilities such as reasoning ability, creativity, abstract or spatial thinking, critical thinking, problem-solving ability, and even excellent communication skills.