What can I do with mathematics?

Topology is useful in distinguishing between distinct types of a given disease and is important in the operation of wireless sensor networks.

Analyzing Data

Much of modern research—from genome sequencing to digital surveys of outer space—generates tremendous amounts of multi-dimensional data. Unfortunately, visualizing dimensions higher than three is not easy, which makes analyzing and understanding the data difficult. Topology, a branch of mathematics concerned with the properties of geometrical structures, helps make sense of large data sets by providing a way of classifying the shapes of these sets. It’s especially useful for locating groups of similar points called “clusters”, which can, for example, distinguish between distinct types of a given disease, each requiring its own treatment.

Topology (specifically algebraic topology) is also important in the operation of wireless sensor networks, which are used in applications as diverse as monitoring automobile traffic and controlling irrigation. Combined with numerical integration, results from algebraic topology provide the complete picture based on strictly local data. The advantage is that such sensor networks, maintained without GPS or other distance measures, are generally much cheaper to operate. So, in the case of irrigation, mathematical discoveries made almost a century before the advent of today’s technology save money while helping us use precious water wisely. In topological terms, just like the Möbius strip: What goes around, comes around.

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“Topology and Data”, Gunnar Carlson, Bulletin of the American Mathematical Society (Vol. 46, No. 2), April 2009.

Article © AMS Mathematical Moments program

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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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