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Hello, Sharov, you wrote: S> Well physicists like to say that mathematics - physics with cheap experiments. Why not to turn out on the contrary? Because it simply idle talk from which it is not necessary to do far-reaching outputs.

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Hello, VladD2, you wrote: it is a lot of Answers, I hardly understand them. Would throw still at least pair of examples of tasks on a joint of mathematics and  is better.

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Hello, Khimik, you wrote: K> it is a lot of Answers, I hardly understand them. Would throw still at least pair of examples of tasks on a joint of mathematics and  is better. Many algorithms have been invented by mathematicians and adapted for a real life application by programmers. Well, and banal calculations of coordinates for a window is that other as mathematics. Various theories are used as models for type systems . Here misunderstanding of that than a science is faster differs from engineering. As not strange engineers create something new using results of a science, and scientists reveal laws existing in the nature, regularity and try to describe, systematize and explain them. Here the mathematics is a basic abstract science of this ordering. Applied sciences (physics, chemistry, computer science...) Study less abstract (more practical) knowledge domains. And programming - that engineering when any application-oriented tasks are solved. At the decision of application-oriented tasks in IT it is used  knowledge. Including knowledge specific to software development is computer science and other knowledge. Here the part from them it also is mathematics. Other knowledge (from physics, chemistry, jurisprudence and economy) is in the same way used also. The general at mathematics and programming is an abstraction. Both there, and there often there are models. Here there is an accurate joint.

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Hello, Khimik, you wrote: Pay attention that the main algorithms of IT have been developed in 60th years of the last century (Dijkstra, the Whip, Hoar, Virt etc.) simply did not come to to Great minds of mathematics of 17-19 centuries mind them not only to solve, but even to put. For example, sorting of Hoara. Really coryphaeuses of mathematics of 17-19 centuries could not invent it? I do not trust. They invented much more difficult things, such that and not any student understands them. And it is possible to explain sorting of Hoara to easy normal schoolboy. It would be necessary - somebody yes would invent. But it was simply unnecessary. There was no at them such task. I generally suspect that if the present mathematician to ask how to sort an array we can receive the answer:" Let's admit that the array is already sorted ". If to bother - we run into bewilderment. That for a problem - well select the least element, deliver on the first place, then following for Time of these swaps second etc. them not so excites. At them there any asymptotics, a logarithm to infinity aspires, whether so all is equal, how many it is necessary to rearrange time. In an asymptotic limit all the same all we rearrange

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Hello, Ikemefula, you wrote: I> Geometry it not only a ruler and a compasses, this distinct logical thinking. To fulfill such mechanics any more on what. I specially hardly inscribed here it more low:" As the tool which is working out ability to demonstrative thinking, the mathematics is, of course, invaluable ". But let's look that is meant mathematics while it is taught. Logical thinking? Partly yes, but it is strong indirectly. First of all it is skills (in particular, accounts) and devil's a great lot of determinations, statements and an other material which needs to be learned. The logic is given in very  a type. At the best elements of the theory of sets and boolean algebra. Even those to whom had the luck to take university course of mathematics, as a rule, not in course that such the big and small sendings, where in the expression , where a consequent. Word combinations" negation  "and" consequent acknowledgement "for them mean nothing. Such sensation that someone somewhere"above"considered that ability to logical thinking - too dangerous weapon and to start up it in the free reversal it is not necessary is better

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Hello, vdimas, you wrote: V> On sphere of activity depends. V> IT it is too wide. V> Someone writes warehouses with accounts departments on ready "engines", so there algebras for 5th class of high school for eyes. It is not necessary to forget that 99 % real  are that or warehouses with accounts departments on ready engines, or  sites, or everyone other  with whimsical API. V> And someone solves optimization tasks (the linear programming) either tasks on columns or handling of signals. Yes I also do not argue. Only these fine tasks all truly are laid down in the remained 1 %. V> in general, programming as a whole is an application-oriented part of mathematics. All our guilty world is an application-oriented part of mathematics Here I that I still noted. Yesterday the child stuck that at it does not turn out in any way  a problem on it . There it was necessary, having one given frequency curve of probabilities , to receive probability density of a given function from . Something at it all in any way did not converge with the answer. There was a serious suspicion that in a problem book a jamb (so happens). Told to me as it twisted these integrals. I naturally understood nothing (years  transited knowingly), but fast made hastily a label in , and by means of numerical methods, schedules and any mother  quitted on the answer a problem book. After that already, without distracting on doubts in correctness of the answer in a problem book, the child  the task the correct analytical method. It I to that programming gives us a tooling instead of fair a floor-mat. Analysts. The habit to work  well beats off skill of operation by a fret saw.

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Hello, Voblin, you wrote: V> Hello, Ikemefula, you wrote: I>> Geometry it not only a ruler and a compasses, this distinct logical thinking. To fulfill such mechanics any more on what. V> I specially hardly inscribed here it more low: "As the tool which is working out ability to demonstrative thinking, the mathematics is, of course, invaluable". V> But let's look that is meant mathematics while it is taught. Logical thinking? Partly yes, but it is strong indirectly. First of all it is skills (in particular, accounts) and devil's a great lot of determinations, statements and an other material which needs to be learned. It is impossible for abstraction '  ', they can be grown up only, long methodical application.> the logic is given in very  a type. It is not so important. The main thing that after the school program at you is more or less distinctly pumped over the abstract thinking and poorly poorly there are possibilities to apply it divergently.

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Hello, Khimik, you wrote: K> Hello, VladD2, you wrote: K> it is a lot of Answers, I hardly understand them. Would throw still at least pair of examples of tasks on a joint of mathematics and  is better. Well here I was engaged 15 years in designing of chips and printed-circuit boards. Simply to lead , vector algebra to the utmost. And then high frequencies went, and it became necessary to consider electrical transient phenomena. Here systems of the integro-differential equations of the big dimensionalities also got. Though, if someone only automates stalls, can to it and it is not necessary...

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Hello, Voblin, you wrote: V> Word combinations "negation " and "consequent acknowledgement" for them mean nothing. Yes in general also should not mean. On  this "condition" and "consequence".

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Hello, Khimik, you wrote: K> it is a lot of Answers, I hardly understand them. Would throw still at least pair of examples of tasks on a joint of mathematics and  is better. For example CAD, CAE, CAM - in Russian it is enveloped by the CAD term.

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Hello, alpha21264, you wrote: A> Word combinations "negation " and "consequent acknowledgement" for them mean nothing. A> yes in general also should not mean. On  this "condition" and "consequence". So too it is normal. "Condition negation" and "consequence acknowledgement". Two axiomatic logical errors.

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Hello, Pavel Dvorkin, you wrote: PD> I generally suspect that if the present mathematician to ask how to sort an array we can receive the answer: "we admit that the array is already sorted". If to bother - we run into bewilderment. That for a problem - well select the least element, deliver on the first place, then following on the second etc. PD> Time of these swaps not so excites them. At them there any asymptotics, a logarithm to infinity aspires, whether so all is equal, how many it is necessary to rearrange time. In an asymptotic limit all the same all we rearrange the Notation O-big by which complexity of algorithms is described is mathematics. At us on  on course  it was given.

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Hello, Voblin, you wrote: V> Here I that I still noted. Yesterday the child stuck that at it does not turn out in any way  a problem on it . There it was necessary, having one given frequency curve of probabilities , to receive probability density of a given function from . Something at it all in any way did not converge with the answer. There was a serious suspicion that in a problem book a jamb (so happens). Told to me as it twisted these integrals. I naturally understood nothing (years  transited knowingly), but fast made hastily a label in , and by means of numerical methods, schedules and any mother  quitted on the answer a problem book. After that already, without distracting on doubts in correctness of the answer in a problem book, the child  the task the correct analytical method. V> it I to that programming gives us a tooling instead of fair a floor-mat. Analysts. The habit to work  well beats off skill of operation by a fret saw. Not instead of, and together the Computing methods allowing approximately to solve any mathematical task is a part of mathematics.

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Hello, Pavel Dvorkin, you wrote: PD> Time of these swaps not so excites them. Excites including. Alexander Stepanov once made comments on this thesis (attempt to dissolve mathematics and computre science on the basis of interest to cost of operations) - 1:04:22 AM - https://youtu.be/Ih9gpJga4Vc? t=3862

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Hello, anton_t, you wrote: PD>> Time of these swaps not so excites them. At them there any asymptotics, a logarithm to infinity aspires, whether so all is equal, how many it is necessary to rearrange time. In an asymptotic limit all the same all we rearrange _> the Notation O-big by which complexity of algorithms is described is mathematics. At us on  on course  it was given. Count of an absolute amount of operations, comparing and minimization of absolute runtime is mathematicians all too. Moreover, these tasks have for a long time the methods worked out in the mathematician, approaches and tools for the decision/research. For some reason permanently there are attempts to tear off pieces, and even the whole areas of programming from mathematics. The vivid example is announcements about  the functional programming and not  imperative, based only on that that some code on  is close to any known for it from school of the mathematical notation. Though both , and  are is exceptional strict systems with is rigid-logical rules - and consequently including are mathematics.

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Hello, Evgeny. Panasyuk, you wrote: EP> For some reason permanently there are attempts to tear off pieces, and even the whole areas of programming from mathematics. Hardly in I will shift. , , ballistics... It too mathematics?... <<RSDN@Home 1.2.0 alpha 5 rev. 1495>>

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Hello, pagid, you wrote: EP>> For some reason permanently there are attempts to tear off pieces, and even the whole areas of programming from mathematics. P> hardly in I will shift. , , ballistics... It too mathematics? About  and ballistics I will tell nothing, and here resistance of materials it as a matter of fact applied mathematics - on the basis of hypotheses and assumptions (a hypothesis of plane sections, a principle of Saint-Venant, etc.) is under construction a mathematical model and is researched by mathematical methods ( given functions, Slough, derivative lines  beam axes, integrals on sections, tensors of pressure etc., etc.), further mathematical methods estimate applicability of this model to real systems on the basis of experiments.

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Hello, Evgeny. Panasyuk, you wrote: EP> About  and ballistics I will tell nothing, and here resistance of materials it as a matter of fact applied mathematics - on the basis of hypotheses and assumptions (a hypothesis of plane sections, a principle of Saint-Venant, etc.) is under construction a mathematical model and is researched by mathematical methods ( given functions, Slough, derivative lines  beam axes, integrals on sections, tensors of pressure etc., etc.), further mathematical methods estimate applicability of this model to real systems on the basis of experiments. Then also to the physicist and . it is necessary to consider too .... <<RSDN@Home 1.2.0 alpha 5 rev. 1495>>

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Hello, pagid, you wrote: EP>> About  and ballistics I will tell nothing, and here resistance of materials it as a matter of fact applied mathematics - on the basis of hypotheses and assumptions (a hypothesis of plane sections, a principle of Saint-Venant, etc.) is under construction a mathematical model and is researched by mathematical methods ( given functions, Slough, derivative lines  beam axes, integrals on sections, tensors of pressure etc., etc.) Further mathematical methods estimate applicability of this model to real systems on the basis of experiments. P> then also to the physicist and . it is necessary to consider too . Why it "is necessary"? The applied mathematics in the pure state also is. Arithmetics applied daily for count of the prices it is conclusive consider as mathematics - than . is worse? Historically it is one of the first areas of application of mathematics, and it is reverse - one of areas from which mathematics grew. Certainly it is possible to argue/philosophize on that how much these application-oriented disciplines were isolated, and whether there is any edge of isolation crossing which discipline ceases to be mathematics is a question of terminology. But I anyway resolutely do not understand those who for some reason names  mathematics, but does not award this honor . Or for example considers that in algorithms of the mathematician appears only when to them the asymptotic analysis of complexity is applied, but thus do not consider as mathematics the analysis of an absolute amount of operations and their cost, not to mention  the internal device of algorithms. That is here or then all it to consider as mathematics, or anything (with what I do not agree, but it at least internally a consistent position).

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Hello, Evgeny. Panasyuk, you wrote: EP> Why it "is necessary"? The Applied mathematics in the pure state also is. EP> arithmetics applied daily for count of the prices it is conclusive consider as mathematics - than . is worse? Is worse nothing. But then all life - mathematics. And actually it . Used in many sciences, application-oriented disciplines and activity types.... <<RSDN@Home 1.2.0 alpha 5 rev. 1495>>

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Hello, Evgeny. Panasyuk, you wrote: EP> Suddenly etymology of a word of the mathematician approximately so it is wide and it is decrypted: Simply it is not necessary to confuse "uses" and "is". And yes, if the bookkeeper, the physicist or the programmer doing any calculations or mathematical calculations I tells "now I am engaged in mathematics", it will be right, only here from it ., physics or programming by mathematics do not become.... <<RSDN@Home 1.2.0 alpha 5 rev. 1495>>

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Hello, pagid, you wrote: EP>> Suddenly etymology of a word of the mathematician approximately so it is wide and it is decrypted: P> Simply it is not necessary to confuse "uses" and "is". I do not confuse. P> and yes if the bookkeeper, the physicist or the programmer doing any calculations or mathematical calculations I tells "now I am engaged in mathematics", it will be right, only here from it ., physics or programming by mathematics do not become. Programming is mathematics because the code is mathematical abstraction, even imperative, data structures - too mathematics, process of creation of the code,  its properties (let and not absolutely strictly) - mathematical activity. And at all only because somewhere in the code there is any "calculation" a-lja x*2. If it it is not visible, look such abstract mathematical pieces as the machine of Turing, the formal grammar, the graph, Hoare logic etc., etc.

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Hello, Evgeny. Panasyuk, you wrote: EP> I do not confuse. EP> programming is mathematics because the code is mathematical abstraction, even imperative, data structures - too mathematics, process of creation of the code,  its properties (let and not absolutely strictly) - mathematical activity. And at all only because somewhere in the code there is any "calculation" a-lja x*2. If it it is not visible, look such abstract mathematical pieces as the machine of Turing, the formal grammar, the graph, Hoare logic etc., etc. Then we begin on-new In all already mentioned sciences, disciplines and spheres of activity not less abstract mathematical pieces are used. In everything, since physics and to .. They mathematics are not, but its methods use. Why for programming the exception should be made and it is necessary to consider it as mathematics absolutely not clearly.... <<RSDN@Home 1.2.0 alpha 5 rev. 1495>>

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Hello, pagid, you wrote: P> Then we begin on-new In all already mentioned sciences, disciplines and spheres of activity not less abstract mathematical pieces are used. In everything, since physics and to .. They mathematics are not, but its methods use. Why for programming the exception should be made and it is necessary to consider it as mathematics absolutely not clearly. I like accurately told that I consider also physics and . as applied mathematics P>> Then also to the physicist and . it is necessary to consider too . EP> Why it "is necessary"? The applied mathematics in the pure state also is.