Math Is needed!

11/21/2010 11:33 PM EST

Jack, as a technology journalist who got his bachelor of science degree in journalism (but minors in mathematics, physics and electrical engineering) I enthusiastically agree with you about S.T.E. M.
Mathematics, especially as related to statistics and probabilities, has been enormously useful to me, given 1) how abysmally bad humans are at calculating probabilities, and 2) how prevalent the deceptive use, abuse and misuse of statistics and probabilities is in ordinary life.
Ditto on calculus. It is not that in every day life we sit down and work out the calculus of things. It is that in addition to their professional use in engineering and science, mathematics - be it calculus, statistics, set theory, etc. - math gives me a sense of the “pattern of things” that allows me 1) to make off the cuff but informed evaluations of things, 2) determine when “common sense” does not make sense, and 3) to get a sense of when I am being fed a line of BS by some self-proclaimed expert, talking head personality on TV, or politician. (Bernard Cole, EET/Embedded.com Editor)

11/22/2010 11:23 AM EST

Hmmm... This is a tough one! I struggled mightily with math back in jr. high and high school, and came away with a profound distaste for math, to the point that I gave up on the idea of an engineering career. Many years later, however, I actually taught (or re-taught) myself much of the algebra I had failed in school, to the point that I took classes in math at a local college. I got A's in my calculus classes, but in the intervening years, I have never needed to use those skills, and now I don't think I could do ANY differentiation or integration without having to do a lot of review. The fact is that virtually all of the math I use is "canned" - someone else, a long time ago, figured out a formula for whatever, and I just plug my data in and use that. I do believe that those who work more in the R&D realm probably actually USE what they learned far more than those who don't. The point, however, is well made that learning math helps teach a person to think and reason a way to solve problems, and that is, in the long run, probably much more important than being able to remember how to calculate the volume of a sphere from memory.

11/22/2010 12:48 PM EST

"the rate at which the fluid level in a martini glass will go down"

One of the exercises I did back in chemistry class was to try to calculate how deep a mole of moles would cover the Earth. This didn't take much calculus, if any, and I had to make a number of assumptions such as the specific species and the average volume of said mole. If I remember correctly, the volume could be estimated without calculus. I don't recall my answer. I might have to dust off a lot of brain cob webs and try to re-do the calculation sometime.

Exercises like the martini glass and a mole of moles just make the study of math more fun. Neither are particularly relevant to the real world, but they give a creative mind something to hang on to. If that makes math more interesting, then it's a good thing.

I did lousy in calculus, but I loved it none the less. It gives you a new way of thinking and a new way of looking at the world. That's where I found and still find the most value. With math, even if we don't use the calculations, we can start to see beneath things. We look at inter-relationships, logic, cause and effect - all from a different and more enlightened perspective.

All that and you can figure out if you get more by getting one large pizza vs two mediums. That's important.

11/23/2010 4:40 PM EST

You miss the point of calculus in engineering. It is true that I rarely have the need for an integral, although sometimes a derivative pops up.

However, the real benefit to an engineer is the fundamental association of a thing, its rate of change, and acceleration of that rate. Because you can write i=c*dv/dt, you can visualize that capacitor filling up with those little electrons. Because you can say "the first derivative is continuous", you can appreciate the smooth increase of current through an inductor. And because this tends to be a EE blog, it is easy to overlook that our brother mechanical engineers are routinely called upon to integrate the cross sections of funny-shaped beams. Simply knowing that quite often allows you to see the flaws in the articles (sometimes in these very pages) written by incompetent tech-writers or marketing weenies.

It is a credit to those that preceded us that computer programs now predict field densities and complex circuit behavior. Maxwell had no computer, but could in a few short sentences convey all that is necessary to realize those solutions. He _knew_ he had the right answer, he knew it was beautiful, and he did that with neither pizza nor martini.

11/23/2010 5:14 PM EST

Can't you both be right?

Math has very little day-to-day relevance for most people (as does history, poetry and politics).

Math is however very relevant to certain groups of people: engineers, scientists and the like.

I do agree with the professor that there is no need to teach the masses to a high level of mathematical proficiency - it is just a waste and frustration for most.

So how do you go about teaching math to the get those that need it college ready? I propose that this is achieved by running "pre-engineering" streams at school so that kids can spend their last two or three years at school dumping history etc and focusing on those areas needed for engineering: math, physics and the like.

Some educators suggest that most children only achieve readiness to really cope well with math once the get to around 14 or so. Before that anything more than the basics is generally wasted. In fact it is destructive because kids learn that they're bad at math and learn to hate it. How many potential engineers gave up before they even started?

We have home schooled our kids which has given us some flexibility to explore education differently than what schools do. Both of our kids really only got heavily engaged with math at around 14. Our 14 year old started out approx 1 year behind his age group a year back and is now about 2 years ahead of his age group (ie. he has done 4 years of school math in one year).

So while I do believe we need to see quality math education, I do think we need to re-think how we teach it.

11/23/2010 7:30 PM EST

@Nevada_Dave, I share some of your experience, but have kept the math active by exercises and study. Anytime my everyday electronic design labwork throws up a problem that needs a little research I find I need math techniques, resources and visualisation. So I think maths can be learned late on, although you need to catch the geniuses young so that they can use their teenage years getting to the boundaries of their chosen field, ready to advance the subject while still in their 20s.

11/23/2010 9:25 PM EST

I have used some algebra in my computer programs over the years and lost an interview because I forgot how to do matrices. The concept I think that is missing is the idea that the journey may be more important than the destination. Mathematics teaches how to systematically reach an answer, much like an algorithm in a computer program. I have found many similarities between mathematical problem solving and computer programing (i.e. long division and multiplication on paper). Even though we may rarely use mathematics in our job, the processes of logical thinking that comes with math stay with us in engineering. Most if not all students need to learn math if for that reason only.

11/24/2010 11:21 AM EST

You cannot do signal processing without calculus! At least if you wan't to understand what's happening

11/25/2010 12:32 AM EST

I think that math is important, even if we don't use the more advanced math that much in our daily work.

Interestingly, there is a current discussion going on among educators about how US students do less well mathematically than the students in many other countries.

Part of the problem is the lack of qualified teachers. I have a friend with an mechanical engineering degree who recently passed both the math and phyics tests required to qualify for a teaching position in the state of Florida. He pointed out that many secondary education math majors struggle to pass these tests. This suggests that we are not attracting those who both love and can actually do math to teach math to our students. Of course, anyone who is good at math can make more money doing something besides teaching, which doesn't pay that much relatively speaking.

The other thing that is clear to me is that being really good at math is a special talent that not every one has. This is an even better reason to find and train the mathematically talented to teach math.

11/25/2010 12:41 AM EST

Sadly, the state of our economy leaves me focused on the overriding concept that it matters little how much math you know, or how beautiful your equations and algorithms and designs are, when you know you've either been laid off or are subject to be so by a manager who controls your fate who barely got through business arithmetic himself (and is totally incapable of and uninterested in all this "elegance"), all because some little cell in a spreadsheet changed color at a certain time! And you'll probably think even less of me when I declare that this whole STEM notion is coldly calculated to make certain the extreme oversupply of engineering talent in this country persists and even expands! (And sadly I AM one of the few holders of a US software patent on a DSP algorithm so I know whereof I speak!) Sorry, life is tough and getting even tougher, get over it!!

11/25/2010 1:02 AM EST

Maths teaching should be done on a needs basis i.e. you learn a Maths topic when you are about to need it for a useful purpose. For most people, basic arithmetic is enough. For Engineers on the other hand, Maths is key. But even in Engineering, Maths should be taught gradually in my opinion, rather than lamped in few modules in the early years of University stufy. Maths should be embedded in modules that make use of them, that's the best way to make students appreciate the need for Maths.

11/25/2010 1:54 AM EST

Everyone is so fervent about this subject judging by the number of comments. I loved math and eventually physics in college. However, being a firmware engineer, I rarely used anything but basic math. Now, I lament not retaining or being able to use those skills in my jobs. What a waste. I think you are much sharper and see the world a little differently when you actively use those skills. Although seen as primarily "left brain" skills, I believe they actually help the "right brain" be more creative...And thats what we need in the U.S. to ultimately be more competitive.

11/25/2010 1:58 AM EST

Jack,
I am an admirer, and hold your views in high regard. In this case You AND Prof. Ramanathan are both right! It’s a simple case of viewing the same problem from two different angles. Or in mathematical terms, the intersection of a cone and a plane could be a parabola or an elliptic or a circle, depending on how the plane intersects the cone.
You ARE of course right! There can be no two ways about the case you have made out for math. However, I do respectfully disagree with your interpretation of Prof. Ramanathans statements, though I do not blame you. Prof. Ramanathan is correct in making out a case for the way society at large gives importance to and indeed sometimes judges the individual worth of a human being on his/her ability to do math. A kid in school who is say more artistically inclined, should his/her performance in that subject be a measure of intelligence?
I rather got the impression that Prof. Ramanathan is only objecting to the way we go about promulgating math. Perhaps what he is trying to say is ... "hey guys this is not the way to go about taking math to a wider audience, if that is what is intended". Perhaps we should give more importance to what he has left unsaid.
I live in India. I mention with no disrespect to anyone, recently the local newspapers reported a spate of suicides - by kids in the age group of 12 - 18yrs. On closer examination it emerged that the cause of suicides in all cases was more or less the same - the unrealistically high expectations placed by the parents. Perhaps if Prof. Ramanathan is trying to make a point that discourages placing such unrealistic expectations, then I think his efforts are laudable. Yes, the Indian society in general places a high premium on acquiring mathematical ability, almost to the exclusion of all other abilities, however, if I may suggest that American Society could take a leaf from India and perhaps take course corrective action, I think the lessons learnt by India may not be in vain.
Regds

11/25/2010 4:59 AM EST

Without math, you can't even correctly rewrite a data from a log-scale-graph in a datasheet to a table. If you work on an original design, then math may be essential.

11/25/2010 8:22 AM EST

It is my opinion that in school, engineering
or otherwise, students should be taught about
twice the math they will need.
I found that I forgot about half the math I learned in engineering school, so retained about
the amount that I need from time to time in my
work and daily life.
What you are supposed to come away with from the stuff you may forget, is the general idea of it, not the functional aspects.
Fourier analysis, for instance, I've long forgotten, but it gave me a very good gut feel for many aspects of RF, noise, etc.
Also calculus is required, not from a computational view, but a basic understanding to
have any success with control systems and stability.
Also, maybe it's just a geek thing, but I am
constantly hearing statistics that scream -
"how can people be so gullable."
One recent example was in an EE trade magazine.
The article was about the "Smart Grid" and how much energy could be saved with this technology.
There was a statement of the amount of energy that could be saved that seemed to be at least an order of magnitude higher than logic dictated.
I wrote the author and was told that he took it
directly from a white paper done by a group contracted by the gov't. I could find no names or any references used to compute the ridiculous number they used. Seems they just made it up.

11/25/2010 10:28 AM EST

I've been an Electrical Engineer for nearly 30 years earning a BS and 2 MS degrees. I agree with Prof G.V. Ramanathan, but teach through basic Algebra. In less than 5 years there will be no more technical jobs in the U.S. Why waste time teaching a subject that will be obsolete in this country. I believe advanced math courses should be available for students who wish to take the courses. However, it is very likely less than 1/10 of 1 percent of the working population will need more than basic arithmetic to succeed in their career (if you can call it a career anymore).

11/25/2010 10:40 AM EST

"How often do we EEs use calculus?"
As a control systems EE, all the time! The "s", or in the UK the "p", variable - the complex number (a+jw) - is derived from Heaviside's operational calculus. Analog signal processing uses it all the time; digital SP has it's own, related mathematics. To paraphrase the film subtitle it's "How I stopped worrying and came to love the... calculus". Stay numerate, everyone!
Cheers,
Roger

11/25/2010 11:35 AM EST

Having always considered Maths as a permanent member of the knowledge set, this idea of simply shunning study of the subject sounds refreshing. Mathematics upto a certain level is essential, upto another level is enjoyable, upto yet another level is challenging and then it is plainly too abstract to be thought about, except for by a very small fraction of students. It does not help with the practical aspects of life or personality!

11/26/2010 6:48 PM EST

I am a little surprised by the negativity about higher math. I had several insights studying engineering-physics in college that have stuck with me for 30 years. It has been mentioned that differential equations are behind the behavior of every analog component. How exactly can you understand capacitance and inductance without them? At a deeper level, a single partial differential equation (Laplace's equation) gives you electric potential, temperature profile and heat flow, diffusion rate, and mechanical deformation of a membrane. How beautiful and unifying is that? But it's more than beautiful, it means someone who understands Laplace's equation can detect nonsense in four seemingly disparate field of endeavor. And of course Laplace's equation plus a 2nd order time derivative gives the wave equation. I think electrical engineers have some interest in waves??

11/27/2010 12:44 AM EST

It is amazing that so many people are saying that advanced math is not needed!!! I think the professor's comments was w.r.t. advanced math for general population but it is amazing that so many people think even EEs do not need it!

*Firstly, to the folks saying all high tech jobs will be gone, no business can function without calculus. Operations research, finance and marketing all require use of calculus and probability distributions. Everyone needs to know what a normal distribution is and all businesses require statistical analysis

* Secondly, for EEs the use of advanced maths is prevalent right from signal processing, communications, IC design (power analysis/ statistical timing), image processing, control systems etc etc. In fact I can not think of any EE stuff that does not require maths.

* Thirdly, as others have mentioned (in slightly different words) the purpose of the education is to provide you with tools to navigate different aspects of life. Maths is a very powerful tool and helps you understand beyond the obvious in lots of cases. I read a lot of subjects in Engineering school that I rarely use in my day-to-day work but every now and then some concept from those helps understand something or provide fresh approach to a problem. enginneering without maths is inconceivable.

11/27/2010 11:50 AM EST

I love applied mathematics too. However, in general datasheets/magazines/literaure - like EETimes, EDN and others - they provide very little of mathematical derivation and calculation. Exceptions are ANs by Jim Williams, Bob Pease and others. One AN of interest was explaination and understaning of dB by Rhodes and Shwartz. When you read IEEE Transactions, you do get them lot.

I stronlgy request EETimes to cover more technical article with lots of mathematics to make engineer better understand the concept. They may start tutorial article in maths as related to EE.

11/27/2010 2:53 PM EST

I think we all agree that math is needed to help develop analytical thinking skills for engineers and others in science professions. But what about a different skill that is still taught in school today, cursive writing. How often do you use that particular skill?

11/27/2010 7:23 PM EST

A compromise is needed here. Most kids have no idea what they want to do in life. So they need a good grounding in just about everything before they get chucked out into the hard cold world. So that incudes Math, and History, and English, and Geography, and lots more besides, until they're at LEAST 16.

When I was that age, we had to specialise thereafter, in either "Arts" or "Science" subjects. I was always mad keen on electronics, so chose Math, Physics and Chemistry, and was just about bored to tears. I really wanted to do Math, English and French but I couldn't.

University or college is where you should specialise, but before that I think you need to do as diverse a grounding as you can. I've always regretted my lack of knowledge in Latin, History, Art.... although it wouldn't have helped me directly in an electronics career.

I recently tried to brush up my calculus....not easy when you're 53 and last did it at 17..... but at least I have some basis to build on.

11/27/2010 10:52 PM EST

David Ashton: I think you are assuming that education ends when you leave school. That's a bit limiting as a world view.

I am more interested now in history than I was at school and now devour history books.

Regretting your knowledge of Latin, History and Art is pointless. There is nothing stopping you studying this stuff **now** - either formally or informally.

Most professionals learn their whole life. I know a person that learned embedded programming when in his 70s. I intend to learn until the day I die.
As a hone educator, I am little interested in what kids learn. I am more interested in them learning how to learn. It is often said that History is useful because it teaches research skills. Well my kids spent a lot of time playing war games - spending days reading rule books making up armies. That needed all the research skills you could ever need.

11/28/2010 9:48 PM EST

I am largely self educated electronics dude and a lover of mathematics (group rocks!). I think science and engineering education might be well served by a historical context approach. Seeing and experiencing how mathematics has informed science and engineering (and vice versa) might go a long way to help bridge contentious gap between theory and practice.

Education is a lifelong adventure/endeavor.

11/29/2010 3:05 AM EST

This whole subject is related to something I've always believed in. There should be a standardized set of tests for any possible degree. We should all be able to get a degree by traditional school attendance, by testing at any standardized testing centers, or by any combination of both. Why hasn't the standardized testing become a possibility by now so that we aren't all forced to go to formal, expensive, restrictive, brick and mortar schools to prove we can learn or know something? Education options need to be taken to the next level before we fall even further behind other countries.

11/29/2010 7:06 AM EST

All: I read the professor's comments, and was disturbed by them. There is some grain of truth there, but it is far too easy to twist that into a lazy rejection of the need for math.

What, for example, constitutes "the basics"? Most folks would agree that addition, subtraction, multiplication, division, fractions, decimals, etc., are necessary parts of adult life. There is, however, something unnamed that's missing from all that, and that's this: Above everything else, the person learning the language and methods of mathematics has to learn how to APPLY it to the problems of everyday life, or it just becomes a useless exercise. This is, I believe, a huge gap, and the gap that allows the professor to make his comments without being considered an idiot.

Every new part of mathematics that is introduced (from the "basics" named above through algebra, geometry, trigonometry, calculus, differential equations, complex variables, matrix algebra, probability and statistics, etc., etc., etc.), should be taught from that standpoint: We're going to introduce this new "tool" to you so you can add it to your existing bag of tools, and then we're going to drill you on it so that you know how to apply it in your daily life.

The true practice of mathematics is not in solving equations; it is in WRITING THEM TO FIT THE PROBLEM TO BE SOLVED.

11/29/2010 9:30 AM EST

For a few years I tried NJ's "Alternate Route" program to become a high school teacher; it was a natural fit with my CS/EE background to aim for high school math. Even seventh-grade students questioned why they would ever use any of this stuff - after all, said one, he would go into his father's driveway paving business and never use it. Of course you'll use algebra, I said; how will you calculate the amount of blacktop for a project, and figure the pricing? No problem; he'd just look it up on the chart. (sigh) So I tried the example of how he, a football player, lifted weights to build muscle "in abstract" even though lifting metal blocks isn't the primary purpose of most sports, and the idea that algebra is similar training for the brain in organizing and solving problems. But this kid didn't have any problems that needed solving, because the charts covered them. (deeper sigh) And who makes the charts? How do you know they're right, and current? What if you have a situation not on the charts? The blacktop vendors, and they cover everything. (deepest sigh)

It's no wonder the public is so easy to mislead.

11/29/2010 9:43 AM EST

Depends upon what type of work that you are doing: an RF microwave engineer has to know a great deal of electromagnetic theory, a DSP programmer today almost has to have a PhD in math,physics,electronics. That being said I'll paraphrase a famous American woman who married an English King a few years ago:"You can never be rich or thin enough, or know too much math."

11/29/2010 12:58 PM EST

Professor Ramanthan makes valid points about the marketing of math education and the lack of effectiveness of government spending directed at math education over the last 25 years.

Although math scores for high school students have been relatively flat during that time, the professor notes that "Those who do love math and science have been doing very well. Our graduate schools are the best in the world. This "nation at risk" has produced about 140 Nobel laureates since 1983 (about as many as before 1983)."

This seems to be stating the obvious -- that not everyone needs to become proficient in advanced mathematics, just as most people would agree that not everyone needs to be an expert on English literature or biochemistry or any other field of study you can name. Advanced education is not what the U.S. high school curriculum was designed to provide -- that is what universities are for.

For those that do require advanced knowledge of mathematics...or English literature or biochemistry...our university system provides excellent educational resources and opportunities to study.

11/29/2010 1:50 PM EST

Calculus IS fun! Just ask the students of a M.E. professor when they were asked to perform a stress analysis of a strapless evening gown.

I must admit however that my actual use of higher mathematics in my daily work and life is rather minimal. But I am not a bit sorry that my E.E. curriculum required so much of it. One course in probability was all it took to keep me out of casinos.

11/29/2010 3:15 PM EST

I wholeheartedly that math education is a must. Personally, I wish that it was always taught along with practical applications--but that's my personal bias.

The following exchange by Theodore Gray, a co-founder of Wolfram Research of Mathematica fame, is telling on why the nitty-gritty details may not be necessary for everyone.

"Brain Rot"
http://theodoregray.com/BrainRot/index.html

Here's another fun take, courtesy of Isaac Asimov, on the power of the math-capable over the rest of the planet.

"The Feeling of Power"
http://downlode.org/Etext/power.html

11/29/2010 4:40 PM EST

Wow. Just wow. Remind me to never send my kids to U of I / Chicago. Shameful.

In my work (firmware development & embedded electonics), I use so many different types of math: calculus, probability, statistics, graph theory, differential equations, linear systems, set theory, algebra... I could go on & on.

I had great math teachers through high school (university was less "teaching" - pretty much sink-or-swim). I hope that my kids are fortunate enough to be taught by teachers like I had, as opposed to this doorknob. Regardless, I'll take an active role in the education & inquisitiveness of my kids.

11/29/2010 4:53 PM EST

A mathematics education is absolutely required to appreciate mathematically derived comedy.

Tom Lehrer: New Math
http://www.youtube.com/watch?v=DfCJgC2zezw

Tom Lehrer: That's Mathematics
http://www.youtube.com/watch?v=zRRXiAzC5Wg

Tom Lehrer: Lobachevsky
http://www.youtube.com/watch?v=UQHaGhC7C2E

... and his immitators

I Will Derive!
http://www.youtube.com/watch?v=P9dpTTpjymE

Even Hollywood used to be in on the act.

Abbott & Costello: 13 x 7 is 28
http://www.youtube.com/watch?v=Lo4NCXOX0p8

Ma & Pa Kettle: The Old New Math
http://www.youtube.com/watch?v=MRiTzrIS5fo

Abbott & Costello: Numbers Game
http://www.youtube.com/watch?v=4xpTjMhdIA0

or, the subprime mortgage crisis explained by Abbott & Costello
http://www.youtube.com/watch?v=f7pMYHn-1yA

Math is also necessary to watch "The Big Bang Theory"
"I Never Joke About Math or Sex" (rated PG-13 or TV-14)
http://www.youtube.com/watch?v=7IKFS7ZHqXo

11/29/2010 5:33 PM EST

If you slack off on math, then you should be very very careful around computers.

Without math, we'd never figure out the infamous Pentium division bug.

I once had an application that wasn't returning expected results. I isolated it down to an math function in an API - it was returning incorrect numbers!

Too many people take applications like Excel or Spice for granted. Without a math background you have no way of knowing if those Excel functions are returning correct numbers. Without a math background you would never know if a Spice component model is accurate - and after the real circuit fails, your design skills would be questioned!

You'd better believe that math is important in my work.

11/29/2010 6:05 PM EST

Someone should have taught probability to the idiots in front of me at the gas station buying lottery tickets.

11/30/2010 6:00 PM EST

The awful truth about math at work is that real-world problems neither know nor care what your math skills are. A problem may present as a simple linear function, (lovely, y=mx+c...) or as a complex hyperbolic function (..er, I'll need to look that up). The crunch is that PROBLEMS ARE NOT LABELLED WITH THE FUNCTION NEEDED TO MODEL THEM. So when stuck with a problem, you have nowhere to go, and no-one to ask, except to appeal to someone with a higher level of math skill and hope that they recognise the math function most likely to model the problem. Finally (and you can hear the gods laughing), there MAY NOT EVEN BE A SOLUTION (YET), and only a Cambridge, Oxford or other world-class education will help you out there on the bleeding edge, because you will need to get down to first principles, on your own.
Cutely, this can happen to anyone, anywhere, in any job where something unexpected happens and you (or your boss) care about understanding WHY.
I have seen very little taught about how to sleuth your way into finding out which math you will need to crack a given set of problem behaviours; only experience, intuition and LUCK will get you anywhere, so you have to be taught basic methodology to stop you going round in circles.
But wow, it is thrilling out there!

12/1/2010 12:40 PM EST

We should give up on math.
We had to give up converting to the Metric system since most in this country couldn't handle it.

12/2/2010 9:53 AM EST

If I've said it once I've said it 100 times: an engineer is a scientist with math phobia.

12/2/2010 12:24 PM EST

"Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable subhuman who has learned to wear shoes, bathe, and not make messes in the house."

From 'The Notebooks of Lazarus Long' (1978), Robert Heinlein.

12/3/2010 7:10 PM EST

It is quite a discussion here, that is for certain.It is also true that there are some math teachers who are not very skilled at presenting the reality that we do need to understand the principles explained by higher mathematics. Field theory, both electrical and magnetic, are some sort of magic until you are able to use math to understand the relationships, and actually come up with answers without building hundreds of prototypes. HYdraulic and fluidic systems need math to be understood, although some people seem to have a natural insight about how they work. But even a good general understanding is seldom adequate when you need precise results the first time. Now just look at the new thing: mechatronics, which is built on evaluating systems by means of mathematical models. These models require a bit of understanding to create, so there is one more reason why we need to learn math.
Note that all of my explanations have ignored the basic beauty of the calculus, which is a serious challenge for many to see.

12/3/2010 8:03 PM EST

During our time, advanced maths for electrical enginnering was core course. We did study many new interesting things and was quite rewarding for research work that time. However, after few years, we forgot most of it and only remember few names and their maain appplications. How can we prolong the life our aquired knowledge? What can be soluion for this?

12/4/2010 2:38 AM EST

I think math just makes coming to a solution quicker and with less work.

Tesla said it best when he talked about how Edison worked so hard to find a solution when he could have done it much quicker and easier with a little math.

12/4/2010 10:42 AM EST

As a retired US EE who loves mathematics I am quite disappointed in several of the comments. How can we build superior cost effective machines without understanding the physics involved? And the physics understanding does not come about without mathematics. Is the US engineering community satisfied with simply shuffling application notes generated by a few "superior" people. (That was deliberately insulting hoping to motivate.) Think about sonograms, gps, etc.... . Even when you are just trying to build better and less expensive equipment; understanding the physics and the ability to actually work through the detailed quantitative analysis seems essential.
Working by trial and error without insight will surely leave the US a second rate country. Typically management types don't care how something is done; but dearly love better performance, less cost, and a market edge; those are things that can be sold.
As far as the statements and statistics promulgated by news networks goes; your a fool if you don't quantitatively evaluate what is said for yourself. Even people I agree with seem incapable of presenting quantitative information and statistics accurately.

12/4/2010 2:36 PM EST

I've found my physics degree and maths invaluable to my 40+ year engineering career. Only last year a colleague came to me about a patent application problem. I solved the problem in five minutes with some high-school calculus and was paid as a co-patentor as result. There are a legion of other examples throughout my career, and also in my hobbies.

12/5/2010 4:28 PM EST

Like the headline of the story, most of the comments continue to be orthogonal (oops, a math word!) to the points professor Ramanathan made in the article -- either that, or many of the commenters feel it is somehow wrong for students to choose non-technical career paths that do not require the level of mathematics education each of us experienced and enjoyed.

As a taxpayer who helps fund education, I'm encouraged that future policemen, bus drivers, restaurant workers and even business managers are not expected to learn, or experience the failure to learn, how to solve calculus problems as part of obtaining a basic education. From a societal perspective, it would be a poor investment.

As an engineer, I'm discouraged to learn from some of these comments that there is still some truth to the old stereotype that engineers are lacking critical skills in the analysis and critcism of written arguments.

Rather than worry about the level of advanced mathematics education that the average citizen receives, perhaps we should be more concerned about the level of liberal arts education that the average engineer or scientist receives.

Many times in my career I have found that the ability to express complex technical arguments in layman's terms that business people can understand was at least as important as my ability to analyze technical problems and formulate those technical arguments in the first place. Rather than view it as "he should speak my engineering language", I always viewed those situations as "I should speak his business language."

If you ever made a Powerpoint presentation that included equations to a group of non-engineers and watched their eyes glaze over, you probably understand what I mean.

12/6/2010 11:38 AM EST

My 2¢: Math is useful to learn even if you will never use it directly. It teaches the brain how to solve problems by breaking them down and following the rules to the solution. I lament the fact that too often, math is taught by rote memorization; memorize this equation and plug the numbers in. In my old job I often had a problem with no equation to follow. So I collected data, found relationships and made my own formulas to tweak the processes. That said, I do wish they would teach more applications for math in school. Students are more inspired to learn when they see a use for the knowledge. How about teaching finances in high school? That is one application for math - and heaven knows we need to be smarter about our money!

12/6/2010 2:46 PM EST

Does anyone remember the 1958 R.A. Heinlein juvenile science fiction novel "Have Space Suit - Will Travel"? The first three chapters were the main character learning and applying high-school (and beyond) math, then math is regularly presented throughout the rest of the plot.

In re-read retrospect this was a subtle way to get teenagers to appreciate math and engineering. Several other social commentaries (such as quality of education) are presented as well.

12/14/2010 5:48 PM EST

So, it seems we need a reason to justify teaching and studying math? Well, how about this for a reason: survival of human society as we now know it. Is there any need for further "motivation"? To demonstrate, please consider this scenario:

Let's say that humanity discovers a non-renewable resource, of which there is only 10,000 (ten-thousand) tonnes available globally, and which quickly becomes an important part of the world's economy and lifestyle. It becomes so important, in fact, that we decide to ration its use: we start off by using it at the rate of just 1 tonne per year, and at that rate it will last humanity 10,000 years (of course).

But, we humans being what we are, we want to use more of it. So, the politicians, under pressure from the big-business lobbyists, and of course wanting to get voted in at the next election, decide to allow the use to increase by a very modest 10% per year, which sounds perfectly reasonable. So, we use 1 tonne during year 1, then 1.1 tonnes during year 2, and so on. Surely at that modest rate of growth it will still last humanity for thousands of years, and hundreds of generations, right?

Do you agree? How long will the non-renewable resource last? I am after your first reaction, your "gut feel" response. Ask your colleagues, ask people across a range of careers: from the technically based engineers and technicians, to the more liberal-arts based accountants, lawyers, and importantly politicians and business people. You will be amazed at the range of answers; I have found that they vary by a ratio of over 500 to 1! Please, don't apply a brute-force spreadsheet to calculate the answer, I will post the answer later for sure, I am just trying to prove a point here: Do we, as a society, as a species, understand the power of the exponential function? We ignore its power at our own peril.