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Child doing advanced math

A quiet but animated discussion is underway among many Information Sciences and Technology (IST) faculty. The discussion involves what mathematics should be required of, or taught to, our IST undergraduate students.

Because only a limited number of courses can be required of students in order for them to graduate in a reasonable amount of time, a tradeoff exists between background and enrichment courses involving general education, intellectual and cultural diversity, foundational courses in mathematics, and courses focused specifically on the information sciences.

Some argue that the number of courses specific to IST must continue to expand as we seek to address rapid changes in technology and the need for specific skills in programming, database, system design, and related areas.

The discussion also involves the role and level of mathematics required to understand areas such as data structures, discrete computing, estimation, encryption, optimization, numerical applications, and even artificial intelligence.

The list of potentially applicable mathematics is nearly boundless, and includes discrete mathematics, logic, calculus, matrix algebra, differential equations, probability and statistics, set theory, and many others. However, the level of mathematical background that is actually needed, and deemed feasible, is debatable. We must also recognize that mathematical needs may differ significantly based upon a student’s major (IST vs. SRA) and the specific track within a major.

On one side of the debate are those who push for an increasingly strong background and additional required courses. On the other side are those who worry that excessive mathematics requirements, especially courses such as calculus, are not necessary and would discourage those seeking to major in IST or SRA who could perform perfectly well without such mathematics.

I must confess that while I try not to influence this discussion in one direction or the other, I am clearly not an unbiased observer.  When I went to undergraduate school majoring primarily in physics, I found myself taking an increasing number of math courses in order to better understand physics. I ended up with more credits in math than in physics, and inadvertently achieved a double major. The trend continued in graduate school. At one point, I briefly entertained the idea of obtaining a Ph.D. in mathematics until a graduate course in topology convinced me otherwise. Let’s just say I didn’t do very well in that course, and we won’t discuss it in analysis.

Regardless of where one stands in the debate on mathematics, most agree that an understanding of statistics is very important. Beyond the classrooms of IST, all citizens need a fundamental grasp of statistics to make sense of the big data and statistical “results” they are being presented with in nearly every news story in the media.

Two recent books lend interesting perspectives to this discussion. Naked Statistics: Stripping the Dread from the Data, by Charles Wheelan, is a very readable treatise on the fundamentals of statistics, including statistical inferences, correlation, regression analysis, and other standard topics. Wheelan provides everyday examples to explain these concepts, such as how Netflix determines what movies you’ll like and why you should choose the other door on a game show (the Monty Hall problem).

A second book, The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century, by David Salsburg, traces the history of statistical thought in the twentieth century and describes how it revolutionized many aspects of science and society. Both of these books are fun to read and very understandable, providing insight into statistics and why an understanding is increasingly important.

The larger debate on mathematics in IST, however, will continue as we strive to provide students with the background they need to stay abreast of rapid developments in information technology.  I doubt if there is a simple, “one size fits all” solution.  Instead we may need to develop at least an introductory course, perhaps an “Introduction to Mathematics for the Information Sciences,” which will then funnel into additional tracks of mathematics courses depending upon a student’s major and option within IST. We are fortunate in IST to have a number of very talented faculty who can develop and teach such courses.

Regardless of the outcome of the debate and our resulting implementation, the need for statistical training is clear – over 70 % (nearly half!) of people don’t understand statistics.

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3 thoughts on “The Debate on Math: A 70% Solution

  1. Dean Hall,

    10 years after graduating from IST, here is my perspective: I wish that I had had an introduction to lambda calculus, matrix algebra, and set theory (I did get a little bit of set theory). My perspective comes from a decade in information systems development in the defense industry, and I don’t claim it as an absolute answer to your quandary – merely a perspective.

    More and more, the data sets that I work with are directed acyclic graphs, which can more or less be represented as a sparse matrix. It wasn’t until a few years ago that I even knew those terms, which is why I would call for at least a survey-like introduction to these topics to be mandatory.

    Whether or not full courses on these topics should be a mandatory part of the IST curriculum, I cannot say, but I would guess that the answer is probably: no.

    Opinions are worth what you pay for them… and I’m offering this one for nothing.

    • John,

      Thanks for your perspective. I certainly hope others will also come forward with their perspectives on math that they wish they had been familiar with.

      In my old graduate physics days, we had a course titled, “Mathematical Methods of Physics,” a two-semester course that provided a brief introduction to a wide variety of math methods used in graduate physics. Of course these evolved over time as topics such as quantum mechanics became more common. In information sciences, a challenge is how to; i) determine which methods are of potential use, ii) how these topics might change depending upon the specific area within information science that one is focused on (e.g., cyber-security, versus system design and development, versus applications of IST in different areas, etc.), and iii) how to fit such courses into the already filled curriculum. Certainly techniques such as graph-based methods, including “dirty graphs,” uncertainty representation, classic and fuzzy logic, optimization techniques, and others may be of use.

      A number of years ago in the College of Engineering, the aerospace department offered a series of one-credit courses to introduce math topics such as asymptotic series, estimation, special topics in partial differential equations, etc. In our evolving concept of math for IST, we may look to novel techniques such as this to create and offer courses for those interested in details of particular methods.

      Best regards,

      Dave Hall

  2. Very interesting perspectives, and interesting comment from John. I agree with all of the above – an introductory math course for “real life math” would be perfect. However, a deeper dive is required depending on the anticipated course in life after college. While John and others went on to development roles, requiring much more in-depth knowledge of key mathematical subjects, I and others went on to more business oriented roles, where we require the ability to understand what a typical MBA would learn when it comes to math. Simple math, but in a business-world context.

    As you mentioned in your post, there may not be a “one size fits all” solution, but this certainly would be a starting point, with options (or even a requirement) for the students to take additional math courses (i.e. IST230). As usual, food for thought. Great topic though!

    -Paul

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