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## Five good reasons to teach with Mathcad

Chris Hartman, the Education Program Manager for Mathcad here at PTC, outlined five benefits of teaching with Mathcad.

1. Mathcad is Easy To Use - An intuitive, live math environment with notational and unit-handling capabilities that reduce errors and miscalculations
2. Mathcad offers Powerful Tools - Excellent CAS, graphics, text, and programming capabilities
3. Mathcad enables student thinking - Documentation and communication capabilities leave creative thinking in plain sight
4. Mathcad supports instructional excellence - A useful curriculum development environment for text, graphics, images and animations
5. Mathcad develops 4G Skills - Enables students to acquire the computational thinking strategies required for success in today’s workforce

The full blog can be found here.

What are some other good reasons for using Mathcad or any technology as a learning tool?

1 ACCEPTED SOLUTION

Accepted Solutions
1-Newbie
(To:DanMarotta)

Dan, here are some more reasons:

Mathcad Enhances the STEM Curriculum at Every Educational Level

A STEM professional typically has studied algebra and trigonometry, the calculus sequence, and differential equations. Engineering and math students might also study linear (matrix) algebra; a more advanced course in differential equations (ordinary and partial); probability and statistics (possibly including Design of Experiments). A course in advanced calculus for applications might survey some or all of the post-calculus areas mentioned.

Pick up a textbook on any of these math subjects, and Mathcad works well as a supplement. Mathcad can literally make the equations and graphs in the book "come alive." Plus, Mathcad has programming, the value of which cannot be overestimated.

Mathcad actually facilitates two kinds of math: symbolics and numerics. In symbolics, one simplifies and/or solves equations and systems of equations. The solutions are expressed with symbols, and not numbers per se. In numerics, one assigns numerical values to the symbols up front, and wants the results to have numerical values. Mathcad experts tend to favor one or the other: symbolics or numerics. I associate symbolics with "classical" mathematics. Classical mathematics is what is typically taught in schools, colleges and universities these days. Success leads to neat, though possibly quite complicated solutions: expansions in terms of circular or special functions, Fourier analysis, etc.

There are areas of STEM that do not admit "tidy" analytical solutions, areas that suggest problems which we can only investigate and solve using computers and numerics. One such area is nonlinear systems. Research in nonlinear systems typically involves setting up and solving systems of nonlinear differential equations. Here are just two examples.

The Newtonian N-body Problem for N >= 3. Even for N = 3 (three gravitating Newtonian particles), no purely analytical solution to the associated system of eighteen first-order, ordinary differential equations is possible. But we can investigate the numerical behavior with Mathcad. Mathcad's powerful numerical integrators make this kind of nonlinear math relatively easy to investigate.

Chemical Kinetics. Do a Google search for YouTube videos on the Belousov-Zhabotinsky (BZ) reaction, a chemical reaction in which the quantities of reactants and products actually oscillate as the reaction proceeds. This leads, for example, to solutions that change color, back and forth over spectrum of colors, as the concentrations of the chemical species oscillate. Want to know more about chemical kinetics? PlanetPTC has a forum on this! Viktor Korobov and Valery Ochkov will be publishing in spring 2011 a book that uses Mathcad to quantify, for example, what happens in a BZ reaction.

To sum up: any high school student who is so fortunate as to be taught Mathcad by STEM professionals (the ones whom we know as high school science and math teachers!) will be well-positioned for success in his or her college and post-academic STEM career.

19 REPLIES 19
1-Newbie
(To:DanMarotta)

Dan, here are some more reasons:

Mathcad Enhances the STEM Curriculum at Every Educational Level

A STEM professional typically has studied algebra and trigonometry, the calculus sequence, and differential equations. Engineering and math students might also study linear (matrix) algebra; a more advanced course in differential equations (ordinary and partial); probability and statistics (possibly including Design of Experiments). A course in advanced calculus for applications might survey some or all of the post-calculus areas mentioned.

Pick up a textbook on any of these math subjects, and Mathcad works well as a supplement. Mathcad can literally make the equations and graphs in the book "come alive." Plus, Mathcad has programming, the value of which cannot be overestimated.

Mathcad actually facilitates two kinds of math: symbolics and numerics. In symbolics, one simplifies and/or solves equations and systems of equations. The solutions are expressed with symbols, and not numbers per se. In numerics, one assigns numerical values to the symbols up front, and wants the results to have numerical values. Mathcad experts tend to favor one or the other: symbolics or numerics. I associate symbolics with "classical" mathematics. Classical mathematics is what is typically taught in schools, colleges and universities these days. Success leads to neat, though possibly quite complicated solutions: expansions in terms of circular or special functions, Fourier analysis, etc.

There are areas of STEM that do not admit "tidy" analytical solutions, areas that suggest problems which we can only investigate and solve using computers and numerics. One such area is nonlinear systems. Research in nonlinear systems typically involves setting up and solving systems of nonlinear differential equations. Here are just two examples.

The Newtonian N-body Problem for N >= 3. Even for N = 3 (three gravitating Newtonian particles), no purely analytical solution to the associated system of eighteen first-order, ordinary differential equations is possible. But we can investigate the numerical behavior with Mathcad. Mathcad's powerful numerical integrators make this kind of nonlinear math relatively easy to investigate.

Chemical Kinetics. Do a Google search for YouTube videos on the Belousov-Zhabotinsky (BZ) reaction, a chemical reaction in which the quantities of reactants and products actually oscillate as the reaction proceeds. This leads, for example, to solutions that change color, back and forth over spectrum of colors, as the concentrations of the chemical species oscillate. Want to know more about chemical kinetics? PlanetPTC has a forum on this! Viktor Korobov and Valery Ochkov will be publishing in spring 2011 a book that uses Mathcad to quantify, for example, what happens in a BZ reaction.

To sum up: any high school student who is so fortunate as to be taught Mathcad by STEM professionals (the ones whom we know as high school science and math teachers!) will be well-positioned for success in his or her college and post-academic STEM career.

24-Ruby IV
(To:RogerMansfield)

Around the world (here in Russia in particular), students study math by help textbooks written in... XVIII century.
Mathcad (Maple, Mathematica etc) can help us to write modern textbooks on mathematics (hard book + site on Internet). Natalia Sliina and me are starting in 2011 a project of writing such textbook. My animations on this forum is a part of this tutorial. See first Russian book on this subject here (Mathcad: Mathematics workshop for engineers and economists). I have a dream to write this book (hard book + site on Internet) in English too. Help us!

But I know that many teachers of mathematics are against this idea. They believe that such textbooks are a profanation of (Classical) Mathematics.

PS

Roger! Thanks for good words about our book on Chemical Kinetic.

PPS

One joke about an American mathematician.
What is one typical American university? This is the place where former Soviet Jews are taught mathematics to Chinese students. By help textbooks written in... XVIII century

Careful, there ... some of my very best friends are Jewish 🙂

I think we do agree that Mathcad (and Maple, Matlab, Mathematica) need to be more closely integrated into the STEM curriculum. I focus only on Mathcad partly because I don't have the time (nor money) to install, use, and maintain all four. (I determined a long time ago that Mathcad, for me, was the best choice of the four, since I had to pick just one.)

It is a real educational marketing challenge to get more educational institutions to incorporate Mathcad into the academic curriculum. The two biggest obstacles that I see and care about have to do with software bugs and licensing issues. (I'll just address bugs for now.)

Having spent more than two decades working large software development projects, I know how hard it is to release bug-free software (actually, it is impossible).

From my past experience as a Mathcad tester, I would say that the biggest and worst post-major-release bugs have had to do with the Windows API - Mathcad interface.

PTC and other major software developers have to spend a lot of money just to keep up with Microsoft's ever-changing Windows API. New software releases would be necessary from time to time, to keep up with the ever-changing Windows API, even if no new AP features were ever introduced.

When, on account of inadequate testing, PTC ships buggy software, it hurts the standing of the marketers, administrators, and teachers who promoted Mathcad, not to mention it hurts the students who are using Mathcad.

So we can come up with a lot of good reasons to teach with Mathcad, and we can feel a glow about "how great Mathcad is for STEM." But in doing so, we are trusting that Mathcad will always work well with the latest version of Windows, and will not ship with any egregious bugs.

In particular, we trust that this will be the case going forward, starting with Mathcad Prime 1.0.

 RogerL.Mansfield wrote:It is a real educational marketing challenge to get more educational institutions to incorporate Mathcad into the academic curriculum. The two biggest obstacles that I see and care about have to do with software bugs and licensing issues. (I'll just address bugs for now.)

I work for a large Aerospace company. The company provided (after I lobbied hard) Mathcad as an installed software tool, enterprise installation with licenses "checked out" for anyone who wanted it. They had been doing the same with MatLab; they were surprised at the bargain Mathcad is per seat. But they've just let the maintenance agreement lapse, which means that Mathcad 15 won't happne here. Why? In the last year Mathcad useage was almost non-existent. With 3000 engineers working, the maximum number of Mathcad seats in use at one time was three (3). (I have one of two stand-alone versions and don't get counted, so add two more. Compared with MatLab, no-one is using Mathcad.

Why? The incoming new-hires have used MatLab, many of them quite extensively, in school. They know how to use it; many of them walk in the door with a library of utilities they have written for their own use. Student versions of MatLab are quite cheap--and I suspect (without verification) that schools can get MatLab very cheaply too. So a professor has MatLab and teaches MatLab. (It's a great product; I happen to like Mathcad better.) The student learns and uses MatLab, then gets a job. The new engineer is given a calculation to perform, he wants to use the tool he's used to, so his boss authorises a seat for him. The administrator asks if he can use Mathcad instead, it's less expensive. The boss and engineer don't want the time and expense of learning a new software package, and MatLab has triumphed again.

I'd add another obstacle: Mathcad is not being supplied to the educators and students actractively. PTC needs to take a lesson from Shick: Give the razor away! The profit is in selling the blades.

24-Ruby IV
(To:f.kohlhepp)
 f.kohlhepp wrote:I'd add another obstacle: Mathcad is not being supplied to the educators and students actractively. PTC needs to take a lesson from Shick: Give the razor away! The profit is in selling the blades.

Give Mathcad away! The profit is in selling Pro/E.

24-Ruby IV
(To:f.kohlhepp)

Do you know the price of Mathcad Prime !?

 Valery Ochkov wrote:Do you know the price of Mathcad Prime !?

That's not the point (and no, I don't know.)

By the time you sell it to my company at whatever the cost, my colleagues won't use it because they don't want to spend the time to learn it; they already know how to get the answer with MatLab because they learned MatLab in school. At that point you could give away Mathcad and it still wouldn't be used because they would have to invest time to learn how to use it--time they either don't have or don't want to spend. We have 25 seats in Mathcad (not counting mine.) The attached file is the utilization plot for the year; we never had four sessions in use at once. A Mathcad seat is about a fourth the cost of a MatLab seat, but we constantly have people complaining because all 100 licenses are in use and they can't check one out.

F

24-Ruby IV
(To:f.kohlhepp)

Sorry, but

Matlab (Matrix Laboratory) is a programming language for technical calculation. As C, C++ etc. If I well know C, C++ etc I can find job faster...

It is not quit correct to compare Mathcad and Matlab.

 Valery Ochkov wrote:Sorry, butMathcad (Math CAD) is an Engineering calculatorMatlab (Matrix Laboratory) is a programming language for technical calculation. As C, C++ etc. If I well know C, C++ etc I can find job faster...It is not quit correct to compare Mathcad and Matlab.

The reason I prefer Mathcad over MatLab precisely because it's been a long time since I tried to write programs; although I have looked at MatLab and it's easier than FORTRAN or BASIC. (I've tried to learn C, not enough motivation to endure the pain!) I can, however, manipulate data, run Fourier transforms, track units (something my MatLab compatriots don't do), and do most of the other calculations they do in MatLab. That is the comparison I'm making.

Fred

5-Regular Member
(To:f.kohlhepp)

I have spoken to PTC on a number of occasions about advertising Mathcad to Universities. I can't understand why haven't been doing this before.

Mike

6-Contributor
(To:MikeArmstrong)

In Denmark some use Mathcad in Primary and lower secondary schools... and this have been going on since 1996

5-Regular Member
(To:SteenGroðe)
 In Denmark some use Mathcad in Primary and lower secondary schools... and this have been going on since 1996

That's good to hear.

I commence my studies this month with a University in Scotland, I am intrigued to see what software they use.

Mike

5-Regular Member
(To:f.kohlhepp)
 Compared with MatLab, no-one is using Mathcad.Why? The incoming new-hires have used MatLab, many of them quite extensively, in school. They know how to use it; many of them walk in the door with a library of utilities they have written for their own use. Student versions of MatLab are quite cheap--and I suspect (without verification) that schools can get MatLab very cheaply too.

I agree with this. I went to University in the UK and this is the tool they used.

 The new engineer is given a calculation to perform, he wants to use the tool he's used to, so his boss authorises a seat for him. The administrator asks if he can use Mathcad instead, it's less expensive. The boss and engineer don't want the time and expense of learning a new software package, and MatLab has triumphed again.

Not my boss. I had to leanr Mathcad from scratch....Never looked back, I think!!!!!!

Mike

1-Newbie
(To:f.kohlhepp)

I'm in aerospace, too (actually, more on the space side). I conducted a workshop, "Doing Orbital Mechanics with Mathcad," at the AAS/AIAA conference in Sedona, AZ in January 2007. Later in 2007, Mona Zeftel sponsored a PTC Express article on my presentation. The workshop was for younger engineers, but most of the attendees were senior engineers (and all very accomplished). All were proficient in Matlab. I didn't get much traction for Mathcad. I think the reasons were: (a) attendees too vested in Matlab, and (b) attendees didn't really get, and would not concede, the fundamental advantages of Mathcad over Matlab (although the advantages were the whole point of my workshop). So I, too, have found it to be an uphill struggle to get aerospace engineering departments and aerospace companies to adopt, and then follow through with Mathcad. The biggest reason, I have concluded, is Matlab got there first.

5-Regular Member
(To:DanMarotta)

I'll give you one........

1. BECAUSE YOU CAN THEN CONTRIBUTE TO THIS FORUM

Mike

24-Ruby IV
(To:MikeArmstrong)

I have heard:
1. Mathcad is Matlab for the lazy (but lazy people are the main driving force of progress).
2. MathWorks (Matlab) introduced agents (bugs) in MathSoft/PTC and they work very well.
3. More a lot same things...

24-Ruby IV
(To:ValeryOchkov)
While we argue that it is better Mathcad or Matlab, SMath and SciLab go on stage...
5-Regular Member
(To:ValeryOchkov)
 While we argue that it is better Mathcad or Matlab, SMath and SciLab go on stage...

Which is the best in your opinion.

Mike

24-Ruby IV
(To:MikeArmstrong)
 Mike Armstrong wrote:While we argue that it is better Mathcad or Matlab, SMath and SciLab go on stage... Which is the best in your opinion.Mike

SMath and SciLab is free of charge projects!

It is difficult to compare Mathcad or Matlab at one hand and SMath and SciLab at others hand.

But we can try...

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