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dRic2

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thanks

Ric

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- #1

dRic2

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thanks

Ric

- #2

phyzguy

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- #3

dRic2

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I have been using Matlab (similar to Mathematica, but the Android app is free) since a long time while doing my studies. Though it's not permitted in my institution, I feel it is very necessary for learning purposes. I have used it mostly for graphing. Equation solving is another great utility that I have been using.

Now, why and where should you use Matlab/Mathematica?

- While solving a problem, if you find that you have encountered some calculations that are lengthy,
**but you know how to solve them**, then go for such software, as it saves time. But sometimes do the calculations on pen and paper as well so as to keep practice. - If you encounter
**something that you do not know**how to solve on pen and paper, but you know how to do it in software, go ahead and use the software for the time being, but make sure to learn the process later.

Graphing is of vital importance as it helps you to visualise what you are doing. In most institutions, during practical classes, you have to plot the data points on graph paper by hand, then draw the best fit line, and do further calculations. But things become simpler and more accurate when you perform a linear regression on the data points using software.

What I wanted to say is, in short, it is not wrong to use Mathematica for problem-solving. However, for examinations, you need to prepare yourself such that when you will not be allowed to use the software, you can still do your work. If you get into research fields, however, no such limitations will exist.

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gleem

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Here one can learn something even when he/she is making his/her work easy. For example, while searching for functions that do some specific job in matlab, I have learnt quite an amount of maths.

The reason is similar to why one would use a high level language like java instead of assembly language or machine language.

- #7

dRic2

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Two days ago I calculated a Fourier Transform but I spent 1 hour trying to simplify the result according to the book. Yesterday I was doing a recap exercise on electric dipoles and, at I certain point, I just had to brutally integrate a function over and over... It took me 4 min with Mathematica and 30 min with pen and paper an a huge amount of mistakes due to distraction while integrating.

I'll be using mathematica mostly in similar occasions. I think this can be very helpful, but I'm asking to hear different opinions. The problem, to me, arise when you're facing something that you can do with pen and paper in a few minutes and decide to go for Mathematica because you are lazy: that's risky, but I hope I can manage it.

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Dr Transport

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- #9

dRic2

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I know. That is why I use it only for exercises that I find on my own in textbooks, not for the ones assigned by professors

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phyzguy

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So do I understand from your comment that when doing problems, you re-derive every result from first principles, and calculate all needed functions (logs, sines, cosines, etc.) with pencil and paper? It obviously wouldn't be fair to use a calculator, because that would be the equivalent of copying from the people that wrote the software for the calculator, right?

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FactChecker

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gleem

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So do I understand from your comment that when doing problems, you re-derive every result from first principles, and calculate all needed functions (logs, sines, cosines, etc.) with pencil and paper? It obviously wouldn't be fair to use a calculator, because that would be the equivalent of copying from the people that wrote the software for the calculator, right?

I figured someone would jump on my post. I'm disappointing that you had to go to manual calculations to make your point. I figured that the use of a book of integrals would have been brought up as an example not a calculator. But anyway do we not still teach children to calculate with pencil and paper before letting them use a calculator?

It is not reasonable to compare arithmetic to symbolic manipulation. When you have performed one addition you know (theoretically at least ) how to perform any addition it is just a matter of inculcating the process, So when can/should you move on to "better" methods? That is an interesting question especially for activities that have benefits. There is more to "learn" when working through problems in their entirety than just getting the answer. I believe that whole process contribute to the building of a sound mental infrastructure resulting in the promotion of creativity , expanding a repertoire of processes and developing an insight that would be of value in the solution of other problems. @dRic2 you say you use Mathematica primarily for working on your own problems which obviously is very useful and expedient how else could you even consider working extra problems considering the time involved.

I am not against computer algebra systems or whatever technology that can facilitate our efforts per se but their use and when is the question which we as individuals must answer.

My post is an opinion based on my experience and observations and offered for thoughtful consideration.

In the future as technology progresses will it be reasonable to eventually introduce such a convenience into elementary schools? Will we need to teach math as it is currently taught if at all?

Anecdote: As an undergraduate (pre-calculator era) we where encouraged to perform integrations unassisted. One never knew when she needed to integrate without a table of integrals.

"Accept the challenges so that you can feel the exhilaration of victory", George S. Patton

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symbolipoint

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symbolipoint

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Yes, and by the time this person has reached the need to handle that "consolidating the summation of several polynomials", he has achieved a large amount of learning, and is now in need to do some work.

- #16

vela

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It really depends on the point of the exercise you're working on and how you use it. For example, if you're a student taking basic algebra and learning to find roots of quadratics, then using Mathematica to "do" homework problems misses the whole point of the homework. On the other hand, if you're a physics undergrad who needs to solve the same quadratic equation to diagonalize a matrix, Mathematica can be a time-saving tool.

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A lot of physics is intuition on when to do something. Algebraic systems can take that away if you depend on them too much.

What I do is: Derive the general equation by hand. Do problems by hand, and then check with an algebraic system. This allows me to get the best of both worlds: I learn how to do it by hand, but also learn how to build it up in mathematica/matlab/python. To be a well rounded scientist in this day and age, you need to know computational methods, simple as that. If you don't practice them at every chance, you will miss out on crucial skills.

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2. At the advanced undergraduate level, say an undergraduate course in E&M, finding solutions to differential equations, etc. is actually part of the learning process. You may have studied those things in math, but you haven't seen it applied and solved in physics. You have to actually grind through it to find the intricate detail of the problem and to get a feel for how something like that is solved. So working through it is part of the learning process. And again, I do not know of schools that allow students to use such devices in exams.

3. I've used MathCad, Mathematica, etc. to do class projects, especially at the graduate level. Here, students are already expected to have grind their way already and have an intimate knowledge of how to solve various problem. Then the target here is no longer about the problem-solving process, but to actually find the solution to a task or problem via whatever means possible. So this is where one encounters differential equations etc. that can't be solved analytically, or one ends up with a transcendental equation that requires numerical means to find the solutions. No one is arguing that computers should not be used here. In fact, that's why many schools have classes in computational physics, so that students are equipped to be able to solve these numerical problems.

4. How many schools actually let a students use Mathematica, etc. during their qualifying exams?

So why do you want to depend on a crutch that you can't use when it matters the most?

Zz.

- #20

dRic2

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Moreover, I think that most of the time it is faster to solve problems by hand than with Mathematica.

I think it is pointless to specify exactly in what scenarios I'll be using Mathematica because everyone seems to have his##^{**}## own point of view on the subject. I really appreciate the discussion and to hear from you all, but, in the end, I realized it is a very "personal" question. The real advise that all of us seem to be sure about is the following:

##^{**}## Just a curiosity: (...) everyone seems to have

- #21

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I don't want to sound harsh but It seems to me (maybe I'm getting the wrong idea though) that some of you are taking this on a "philosophical" level, also implying that I'll be cheating if I relay on a tool to solve my homework even though I clearly specified that I would use Mathematica only for my own business and not to solve school problems.

Wait, what? This was your FIRST POST:

Hi, I was wondering if you suggest to use such softwares tohandle complicated calculations during your studying. Generally the exercise given by my professors can be handled with pen and paper, but I often run into "complicated" problems in textbooks that require some heavy calculations.For example, when you solve a differential equation or an integral you may have to spend a great amount of time to make the solution "nice and beautiful" so that you can deduce physical insights on the problem more easily. It is not that I'm lazy (because up until now I did everything I can on paper), but, sometimes, a little help with the math could save me a lot of time (and stress! ). Again, I like math, it is just to speed things up a little.

Is this another case of "english mistakes"? Where is the "mistake" here?

Furthermore, if this has nothing to do with school work, then it doesn't belong in a forum called "Academic Guidance"!

Zz.

- #22

dRic2

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Maybe I did not express myself correctly. When I'm facing a problem given by a professor of mine I do NOT use Mathematica. But when I study something ON MY OWN (not for the university) if I run into complicated problems (in textbooks) I use Mathematica to speed things up.

Sorry if it wasn't clear.

PS:

I didn't say that the "exercises in textbooks" are the one assigned by professors. In fact I didn't even said the subject is the same: usually I study stuff that are not related with my degree.

I thought it was clear, but I'm sorry if it was not. I really didn't want to be mean to you, but I suppose it came out wrong.

Sorry if it wasn't clear.

PS:

dRic2 said:but I often run into "complicated" problemsGenerally the exercise given by my professors can be handled with pen and paper,in textbooksthat require some heavy calculations.

I didn't say that the "exercises in textbooks" are the one assigned by professors. In fact I didn't even said the subject is the same: usually I study stuff that are not related with my degree.

I thought it was clear, but I'm sorry if it was not. I really didn't want to be mean to you, but I suppose it came out wrong.

Last edited:

- #23

FactChecker

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My experience is that doing it by hand is faster 90% of the time. But the exceptions are real horror stories where Mathematica/Maple saved the day.Moreover, I think that most of the time it is faster to solve problems by hand than with Mathematica.

Right. I am too old to have faced a moral dilemma regarding homework since there was no computer solution when I was taking classes. But many of us have made their decision long ago and have paid the price. You just have to suit yourself.everyone seems to have his##^{**}## own point of view on the subject. I really appreciate the discussion and to hear from you all, but, in the end, I realized it is a very "personal" question.

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That might be a sign that the exam system is out of date. If you are a research physicist or indeed in the non academic world you can use whatever technology is available. That in my view enhances someone's ability to do a job or solve a problem. It's important, of course, to understand what you are doing. Also it could give exam setters more scope to set conceptually more challenging problems as the grunt work of algebra and integrals can be done by computer.

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That might be a sign that the exam system is out of date. If you are a research physicist or indeed in the non academic world you can use whatever technology is available. That in my view enhances someone's ability to do a job or solve a problem. It's important, of course, to understand what you are doing. Also it could give exam setters more scope to set conceptually more challenging problems as the grunt work of algebra and integrals can be done by computer.

This is utter fantasy. It is as if I can ask a question that requires that you solve a differential equation, and then, voila! Using some software package, you get an answer by hitting a button! What fantasy research world is this?

Use any finite-element package, such a FEMlab. How long do you think it takes to set up not only the problem that one wish to solve, but also to verify that one is getting the right answer? How long does it take to bench mark a code or routine that has been set up? And you think this is a valid thing to do in an in-class exam that is trying to evaluate the knowledge and ability of a student? Maybe if the exam runs for days continuously.

In advanced undergraduate physics, the ability for the student to work out the mathematics is often PART of the course objective!

Zz.

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