WHY IS MATHEMATICS IMPORTANT?
In this note we excerpt some of the highlights of Professor Arnold's May 2003 commencement address, titled "Doing the Math and Making an Impact", and given by him for the mathematics and statistics graduation at the University of Illinois in Urbana-Champaign. Professor Arnold is the Director of the Institute for Mathematics and its Applications which is associated with our department. The full text of this interesting and inspiring talk is online at
http://www.ima.umn.edu/newsltrs/updates/summer03Asking "What makes the math sciences so central?", he answers by quoting Galileo: "The great book of nature can be read only by those who know the language in which it was written. And that language is mathematics.", adding "Math is the way to understand all sorts of things in the world around us." To elaborate on this point he gives some well-chosen examples, beginning with some insightful comments on the Swiss victory in the 2003 America's Cup. "...you know that Switzerland is a small, mountainous, land-locked country. So how did the Swiss pull this upset off?" While acknowledging that a number of diverse factors had to come together, he makes his point: " Well Switzerland may not have a great sailing tradition (at least until now!) but it does have a very strong tradition in mathematics--Euler's picture appeared on a Swiss 10 franc note--and the Swiss team wisely brought this strength in math to bear on the America's Cup challenge. They enlisted a group of mathematicians specializing in mathematical modeling and numerical computation led by Professor Alfio Quarteroni at the national polytechnical university in Lausanne.
The mathematicians used partial differential equations to model the flow of the sea around the hull, the dynamics of the air and the sails, and the turbulent interaction of the ocean, wind, and boat. They then applied advanced numerical algorithms to solve these equations on high performance computers. This allowed them to optimize such things as hull and keel design, sail geometry and placement, and so forth. Their work was essential to the design of the Alinghi, and so to the Swiss victory. They did the math and made a big impact." ("Alinghi" was the name of the Swiss boat.)On the increasing role of mathematics in biological sciences he comments as follows: "Increasingly math is making an impact in the life sciences as well, prompting biologist Rita Colwell, director of the National Science Foundation, to observe that "mathematics is biology's next microscope--only better." In their recent bio textbook Keener and Sneyd wrote that "teaching physiology without a mathematical description of the underlying dynamical processes is like teaching planetary motion to physicists without mentioning...Kepler's laws;" He then mentions still other areas of applications: "And math increasingly reaches outside the sciences, to economics, sociology, and business for example. ...Illinois's new Applied Mathematics Program ...involves no less than 22 departments from bioengineering to linguistics. ...Problems which need mathematics for their solution also arise throughout industry."To underline how seriously this is taken worldwide, he cites a strategic plan published by the British government in 2003, seeking to exploit mathematical research to improve the competitiveness of industry in the UK: ""Mathematics is the most versatile of all the sciences. It is uniquely well placed to respond to the demands of a rapidly changing economic landscape...Mathematics now has the opportunity more than ever before to under-pin quantitative understanding of industrial strategy and processes across all sectors of business. Companies that take best advantage of this opportunity will gain a significant competitive advantage: mathematics truly gives industry the edge." He also notes that British government policy in dealing with the hoof-and-mouth disease outbreak a few years ago relied heavily on studies based on mathematical epidemiology.
Importance of Mathematics for a Future Career
1. How important is mathematics as an entrance requirement to university programs?
Students who choose to ignore Mathematics, or not take it seriously in High School, forfeit many future career opportunities that they could have. They essentially turn their backs on more than half the job market (see the areas listed below). The vast majority of university degrees require Mathematics. The importance of Mathematics for potential future careers cannot be more emphasized.
For example, degrees in the following areas require good knowledge of Mathematics and Statistics:
the physical sciences (like Chemistry, Physics, Engineering),
the life and health sciences (like Biology, Psychology, Pharmacy, Nursing, Optometry),
the social sciences (including Anthropology, Communications, Economics, Linguistics, Education, Geography)
the tech sciences (like Computer Science, Networking, Software development),
Business and Commerce,
Actuarial science (used by insurance companies)
Medicine
2. That marks are important and have a strong bearing on, not only entrance to university, but also success upon their arrival in their first year.
Yes, students would be wise to enter university with a good background in Mathematics. Experience has shown that students who come to university with a poor grade in Math (or who choose to skip Math in high school) have a difficult time progressing in the disciplines they have chosen to major in. So we strongly recommend students take Mathematics seriously during their high school years and score at least a B to be able to do reasonably well in university Mathematics. This is in the student's best interest. Nevertheless, the Mathematics Department at UNBC offers MATH 115 for students who did not take MATH 12, to help such students bridge their transition to university life.
3. The challenges that face first year students. (Work load, Math topics covered, how students cope with the transition from high school.)
Indeed, there are cultural differences and challenges. In the university setting students are treated as adults who are responsible for their own welfare and course work. Normally, students take 5 courses per semester so as to complete the degree requirements in 4 years (which are normally 120 credits, though some degrees have more). However, help is available in terms of tutorials, support from the Learning Skills Center, office hours, and collaboration with fellow students. Our faculty have a proven record of being helpful and supportive of their students (something which we often hear rumored by our students). 4. The many uses of mathematics in the university setting.
The answer to question 1 shows just how pervasive Mathematics is in the university and in the many other degrees that UNBC offers. Mathematics courses are required for students who want to major in the following areas: Business, Marketing, Finance, Commerce, Biology, Economics, Chemistry, Computer Science, Physics, Environmental Engineering, Forestry, Psychology, Nursing, Health and Human Sciences.
5. Your experiences with mathematics as it is used in a variety of career areas.
Every area of Mathematics has its own unique applications to the different career options. For example, Algebra is very important for computer science, cryptology, networking, study of symmetry in Chemistry and Physics. Calculus (including differential equations) is used in Chemistry, Biology, Physics, Engineering, the motion of water (hydrodynamics), rocket science, molecular structure, option price modeling in Business and Economics models, etc.
6. Any other motivational topic that will help students understand the competative nature of the working world and the importance of being successful in math.
Students are encouraged to give serious attention to their future. The career world is competitive. The competition and the opportunities in the career world become a serious problem for students if they do not do well in Mathematics, because then they are excluding themselves from the many career paths that need Mathematics. We therefore exhort all our high school students to take matters in their own hands, to study hard, achieve a level of excellence, and take such a fundamental discipline like Mathematics seriously if they think they may go into any of the Physical, Social, Health Sciences, Business, Medicine, or related areas.
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