Algebra -- Don't Knock It -- The Beauty and Usefulness of Math

I am sure that many of you read the Op-Ed piece in yesterday's New York Times that is creating, if not a furor, then, at least, a lot of discussion not only in scientific and engineering circles, but also in business ones.

The Op-Ed piece, Is Algebra Necessary?, was written by a retired political science professor, Andrew Hacker,  and argued that requiring algebra is not necessary.

Just read the following from his Op-Ed:

Mathematics is used as a hoop, a badge, a totem to impress outsiders and elevate a profession’s status. 

Sorry, the above statement is arrogant, and just promulgates math phobias.

I also strongly  differ from his conclusions: Think of math as a huge boulder we make everyone pull, without assessing what all this pain achieves. So why require it, without alternatives or exceptions? Thus far I haven’t found a compelling answer.

I do agree, however, with  the following comments by Hacker:

Peter Braunfeld of the University of Illinois tells his students, “Our civilization would collapse without mathematics.” He’s absolutely right. 

Algebraic algorithms underpin animated movies, investment strategies and airline ticket prices. And we need people to understand how those things work and to advance our frontiers. 

Quantitative literacy clearly is useful in weighing all manner of public policies, from the Affordable Care Act, to the costs and benefits of environmental regulation, to the impact of climate change. Being able to detect and identify ideology at work behind the numbers is of obvious use. Ours is fast becoming a statistical age, which raises the bar for informed citizenship. What is needed is not textbook formulas but greater understanding of where various numbers come from, and what they actually convey.

I use algebra every day in my work and I love what I do -- expressing network problems with a wide-range of fascinating applications from congested urban transportation networks to blood supply chains  through mathematics. Then I go about solving the mathematical models, with may be either optimization models or game theory models, and which are expressed through mathematical symbols.  I implement algorithms in software in order to make sense of a complex world and to suggest real-world solutions. Such research and teaching related courses never, ever bores me. And, I might add, my undergrad  students, whether in operations management, management science, or operations research, typically, get terrific jobs in industry and my doctoral students become professors at business schools (although several of my PhD students are in industry -- high tech and financial services).

Yes, algebra can be viewed as another language, and, indeed, that is the power of it -- the communication of relationships and  ideas in science, engineering  and business.

If so many can tweet and text with abbreviations that have entered the lexicon from LOL to Thnx (pick your favorite), why can't we make algebra understandable and accessible for all high school students in the United States of America?

The report of the National Mathematics Advisory Panel, which has a nice summary and discussion of algebra in Chapter 4, can be accessed here.  Dr. Schmid, who was one of the co-authors of this report, and is a Harvard University Professor of Mathematics, further explicates what algebra is and why it is important here. I especially liked his eloquent description:

Algebra involves three main circles of ideas, symbolic computation, the notion of function, and the process of translating problems into equations that then can be solved. Our list of major topics of algebra is an elaboration of these circles of ideas. The idea that one can compute with symbols as if they were numbers-provided one uses the rules that apply to computations with numbers-is absolutely crucial to algebra and all the mathematics that comes after algebra.

Expressing problems through mathematical symbols helps to move our civilization forward. Shouldn't everyone have an opportunity to be challenged and have jobs or opportunities within their reach?

If we were to teach math through applications, starting in high school, and this is something that operations research excels at, I believe that we would captivate more students, who would eagerly want to learn not only algebra 1 and 2, but linear algebra, and then calculus.

We need more problem solvers and they and we need algebra. 

Just look at the Forbes list of best-paying  jobs for women (brought to my attention by fellow blogger, Dr. Laura McLay).

Clearly, if you want to be paid well, algebra can help you. Why limit our children?

Crisis Management and Resilient Leaders

People are starting to take notice.

It is hard not to -- with record-breaking temperatures in the United States this summer, severe drought enveloping many states, including some of our major grain and corn states, which will surely drive prices up for food products, extreme weather events and storms happening with increasing frequency, plus climate change even affecting our infrastructure -- from our roads to our electric power networks.

There is even a blood shortage this summer -- the worst in 15 years -- being reported by the Red Cross, partially attributed to the storms and heat this summer.

We have been researching fragile critical infrastructure networks and even wrote the book, Fragile Networks, in which we defined terms such as robustness and quantified synergies associated with network integration, through the prism of supply chains, since, truly, it is supply chains that link our economic activities together through production, transportation, storage, and ultimate distribution. I spoke on Building Resiliency in Washington DC on a special Transportation Research Board panel.

Our world is changing and  leaders must become aware of crisis management.


We are in need of Resilient Leaders.

The Isenberg School of Management at UMass Amherst has on its homepage the following:

Resilient Leadership for an Evolving Business Climate

and it is great to see new courses being taught around this theme and new initiatives.

There is a feature news article, Students Learn Crisis Management in Innovative Isenberg Course,  on the new course in Humanitarian Logistics and Healthcare  that I taught in Spring 2012. In the course, we had speakers from the National Guard, the Red Cross, the UMass emergency preparedness group, and even a disaster communication expert and a former student of mine from the profit sector, who has worked in healthcare. Nice to see my students quoted in the article.

Yes, even the army has realized the importance of location theory in determining where its critical supplies should be stored since it expects a greater role in humanitarian crises and evacuation management -- topics that we studied in my course and timely response and deliveries can save lives in crises.

Our research from blood supply chains to supply chain metrics in the case of disasters can be accessed on the Virtual Center for Supernetworks website.

Best of Luck to the Olympians and What They Teach Us

The day has arrived and the opening ceremonies for the 2012 Summer Olympic Games will be taking place tonight in London, England. I hope to catch the parade, although I will be watching from the US and not from Europe.

The excitement is palpable not only because of the venue but the scale of these games.

What fascinates me, besides the athletes, their hard work, and the support from their coaches, family members, and friends (plus all the individual stories and journeys taken to reach this point), is the logistics behind the games and the transportation impacts.

I purchased the above official 2012 Summer Olympic t-shirt, which I am displaying in honor of all the athletes, in London Heathrow Airport, when I was waiting for my connecting flight back to Boston last March, after my stay at the University of Gothenburg in Sweden. 

I also spent the full month of June in Gothenburg, and met another Visiting Professor, Dr. Michael Browne, who is from the United Kingdom. He is a transportation and logistics expert, and was involved in transportation planning for these Olympic Games! How exciting is this?! There has been a lot of discussion in the news about the possible impacts on transportation and congestion (and I don't just mean the lost bus-driver who took Olympic athletes on an extended bus journey because he could not find his way to the Olympic Village).

What I especially appreciate about the athletes is their focus, hard work and dedication, plus that they follow their dreams. In times of impatience, restlessness, numerous distractions,  and pressure from all sorts of different constituents, we can all learn from these Olympic athletes.

And for those who almost made their country's Olympic team, but, not quite (as one of my neighbors in Amherst almost did, but got injured during the diving  finals), you are already great successes.

Now, for a nice writeup on our sports management program at the Isenberg School of Management at UMass Amherst and our graduates who are contributing to the games, in auxiliary ways, see this article.

And, thanks to my fellow blogger, Dr. Laura McLay, for even identifying an Olympic athlete with a degree in Operations Research!

For photos of the 2010 Winter Olympic Games in Vancouver, Canada, provided by our friends, the Wassermans, whom we met while we were living in Stockholm, Sweden,  see this blogpost.

Always Great to Hear from Former Students

The summer is more than half over and, before we know it, it will be September, and students will be converging from different parts of the globe to institutions of higher education in the United States

It has been a very intense summer, since I spent all of June at the University of Gothenburg in Sweden, and have been working on some big writing projects.

Various campuses in Amherst, Massachusetts from UMass Amherst to Amherst College and Hampshire College are different in the summer than during the academic year, with special programs and activities, and relative peace and quiet.

It is always great to hear from former students and this summer has been no exception.

I have had the pleasure of a visit from a former MBA student of mine, who is now an executive in the automobile industry, who even treated my family to dinner but, most importantly, the face-to face conversations and the laughter, I will long remember.

Plus, I have received many emails from former undergrad students asking whether I could get together for coffee  with them (they will do the traveling) since they are seeking some advice as to graduate school options and/or just want to share their experiences in industry with me.

Others have simply reconnected and updated me as to their professional successes.

Prospective students have also been in touch so I enjoy discussing the strengths of and opportunities at the Isenberg School of Management and, of course, the programs that are especially dear to me -- from our undergraduate Operations Management program, which has recently been renamed "Operations and Information Management," to the doctoral program in Management Science.

A former doctoral student, who is now a "Dr.", having received her PhD, has, in turn, flown off to the West Coast to assume her new position as an Assistant Professor and it is great to hear from her as she settles in to her new life in a great location.


Nothing gives a professor greater satisfaction than seeing her former students achieve and do so well!

When the Most Recent Time Feels as Good as the First Time -- Getting a Paper Accepted and Published

I recently received an email message from a former doctoral student of mine that is the kind of message that is a keep-sake. It highlighted milestones in an academic career.


The message included the following, which had been copied to several former and present doctoral students of mine.

When I received your phone calls in my dorm at China, I didn't realize that's one of the biggest decisions in one's life. From the first day at UMASS, the first presentation at Professor's 821 class, the first homework that I ever graded, the first paper, the first conference, the first job interview, the first job offer,...until now the tenure and promotion, every step in my growth records Professor Nagurney's effort. I can't thank you enough, Professor!

I met my best friends in the supernetwork lab which is really like a family. Thank you all for friendship and support, which is my lifelong asset!~~~

This got me thinking -- I hope that, as an academic, one never loses that sense of wonder and, indeed, happiness, at getting another paper accepted for publication and then seeing it in a journal.


Do you recall the time that you received the good news of the acceptance of your first journal article?


My first three journal articles were co-authored with my doctoral dissertation advisor at Brown University, Professor Stella Dafermos, the second female in the world to receive a PhD in Operations Research. We actually had, as our first set of joint publications,  a series of three papers, published, in Mathematical Programming, Transportation Research B, and in Operations Research.

That same year (and only a year after receiving my PhD), I then had a single-authored paper (another first) published in Transportation Research B.

Last week, we heard the good news that a paper that I had written with the other Dr. Nagurney, who is educated in physics, had been accepted for publication. The effort in understanding the scope of the medical nuclear supply chain network problem and issues, which are affecting medical diagnostics, and even security, along with acquiring the data for the problem, had been intense, and, after two revisions, we had done it. The paper integrates operations research and physics for a supply chain network application.

The good news of the paper acceptance made our day and the warm feeling continues and makes the hard work worth it.


I hope that I never lose that feeling -- and wish you all the same.

An Operations Researcher to the Rescue as the Interim Dean of the School of Engineering at Columbia

This past year, there has been major national coverage of various administrative academic dramas in the media, from the resignation and, subsequent reinstatement, of Dr. Sullivan as the President of the University of Virginia (which I was following in Sweden in June) to the resignation of Dr. Pena-Mora, the Dean of Engineering at Columbia University, and the appointment of an operations researcher, Dr. Don Goldfarb, that many of us know professionally, as the Interim Dean. Don, if I may, had been helping out Pena-Mora, according to the Columbia Spectator, as the Executive Vice Dean.

The New York Times has been covering the discord at Columbia and even posted a letter from the senior faculty in Engineering  to the Provost, which notes some of the reasons for the faculty dissension.

Recently, there have been discussions as to how some top administrators are viewed as moving too fast, and some, as not fast enough, in making changes.

Given Pena-Mora's academic background, which includes two graduate degrees, including the PhD, from MIT, in civil engineering, and his productivity, as well as appointments at the University of Illinois, I am rather surprised at the outcome of events. He was born in the Dominican Republic.

According to The New York Times, a demonstration is planned, complete with Al Sharpton, sometime n September, to support Pena-Mora, since some view this as an issue at Columbia with administrators who are minorities (3 such top level ones were appointed by the President, two have left, and now Pena-Mora has resigned).

The posted letter on the link above does provide information, which would be troublesome to many faculty members.

Nice to see an INFORMS member and well-known scholar coming to the rescue of Engineering at Columbia.


In September 2006, I gave a seminar on Dynamic Networks  in the  Industrial Engineering and Operations Research and Decision Science, Risk and Operations Series at Columbia University. My hosts were wonderful and I wish the school well.

No 4th of July Parade in Our Small Town -- How Sad

For a decade now we have all come to enjoy what has become a tradition -- the 4th of July parade in our small town of Amherst, Massachusetts.

Over the years, we have gathered with neighbors, friends, and even families of my doctoral students, who come from many different countries to celebrate Independence Day, which would begin with the parade from Amherst College to UMass Amherst at around 3PM.

This year, because of "funding woes," as reported on masslive.com, there will be no parade, which we have enjoyed immensely -- from the bagpipers, to the women doing something like square dancing on a moving truck, to the veterans, police and fire trucks from different communities, and even dancing horses. There were never many floats but who would not enjoy candy thrown out for the children and, sometimes, even apples distributed by Atkins Farms.

The parade marked a time when we came out as a community and one of my favorite comments was from a mother of one of my students, who had just received his PhD, Dr. Patrick Qiang,  and his wife had borne a son the day after his graduation from UMass Amherst. The "grandma" had traveled from China to help take care of the infant, who had been born in May, 2009. They all joined us for the 4th of July parade that year in Amherst, and, despite the blaring horns and sirens, the baby slept through it all. The grandma said that the police in the US, that she saw marching, were so much handsomer than those in China!

At least we have the memories of previous parades and you can see photos of them from last year here, from 2010 here, and from 2009 here.

Amherst somehow managed to mark its 250th anniversary with a parade, also back in 2009, although it rained on that parade. 

Our neighboring town of Hadley, Massachusetts put on a spectacular 350th anniversary parade in 2009 and photos can be viewed here.

Let's hope that the forecast does not knock out the fireworks tonight in our area!