What can I do with mathematics?

Simulating Galaxies

Galaxies can be more than 100,000 light years across, consisting of hundreds of billions of celestial bodies, and with a mass more than a trillion times that of our sun. Modeling such huge, complex systems, in which many of the stars have chaotic orbits, requires new computational techniques.Advances in the speed and memory of computers have improved models, as has parallel computing, but advances in algorithms—the way the mathematics of a problem is converted into steps a computer can perform—are indispensable in developing accurate galaxy models.

The complexity of simulating the behavior of a galaxy is not limited to the galaxy itself. Since a galaxy is usually part of a cluster or supercluster of galaxies, the external forces exerted by these larger agglomerations on the galaxy must also be accounted for.Thus, models must be accurate across many scales of distance. Instead of numerically solving the equations of the model uniformly across all sectors, researchers employ multi-scale algorithms that do more calculations in sectors determined to be more significant.This kind of technique uses computing power more efficiently, giving us a glimpse of the underlying structure of the universe.

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While the main motivation to choose math as a major should stem from a combination of keen interest and high ability in math, students are naturally concerned about the opportunities available to a mathematics major or a mathematics teaching major after graduation. At this time, the math major appears to be in a better position than many other majors for employment in business, industry, government agencies, and teaching. The prospects are also good for well-qualified students to obtain support for graduate studies in either mathematics or mathematics education. Also a major in mathematics is excellent preparation for further study in many other fields.

In order to help you clarify your thoughts on what you want to get out of your collegiate experience as a math major, here are some questions to ask yourself:

  • Why do I like mathematics? What is it about math that attracts me to majoring in mathematics?
  • What type of mathematics do I like? Do I like the computational aspect? The rigor and logic? The problem solving experience? The theoretical aspect? Which content areas interest me?
  • What do I want to do for a career? Do I want to teach, or do I want pursue other avenues? If you want to teach, then:
    • what age group(s) do you want to teach? PreK, 1-6, 6-9, 9-12, college?
    • do you want to teach just mathematics, or do you want to have the flexibility to teach other fields as well?
  • If you are not interested in a career in teaching, then: are you interested in a career in business, industry, government, nonprofits, other alternatives?
  • How much education do I want to complete? Bachelors, Masters, or Ph.D.? Do I want to enter the work force right after graduation with the option to pursue graduate work later?
  • What do I need to do in order to further my career prospects?
  • What should I be doing academically to further my goals? Should I pick up a minor in another area? Should I try to double major?
  • What extracurriculars should I become involved in to further my goals? For example, should I get involved with the math club? Should I participate in the MCM Modeling Competition?
  • What types of work experience should I try to get to further my goals? Should I consider volunteer work experiences such as tutoring? Should I consider internships?
  • What organizations should I become involved in? What conferences or meetings might it be helpful to attend?


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