What can I do with mathematics?

Mathematicians' study of network properties has significance for applications from the microscopic to the worldwide.

Making Connections

People in a society, neurons in the brain, andpages on the Web, along with their connections, are all examples of networks. Mathematicians study characteristics of networks, such as the number and distribution of connections, to discover what such attributes may reveal about the intrinsic nature of a network. For example, the colors in the picture below indicate how disruptive deleting a node would be to the network, in this case a living cell. The discovery and verification of network properties such as this has significance for applications ranging from the microscopic to the worldwide, including the protection of both computers and humans against viruses.

The study of networks spawned the phrase “six degrees of separation”, the theme of a game involving actors’ connections via common film appearances. In an experiment done in the 1960s, over 100 randomly chosen people in the Midwest were found to be connected to a Massachusetts stockbroker (by a friend of a friend of a friend, and so on) in an average of just six steps. That people halfway across the country could be so closely connected was quite a revelation and proved that even a large network could be a “small world”. Today, researchers use parameters from graph theory and probability in analyzing networks to determine whether an elaborate network, be it a power grid or actors connecting to Kevin Bacon, is indeed a small world after all.

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“Scale-Free Networks”, by Albert-LÁszlÓ BarabÁsi and Eric Bonabeau, Scientific American, May 2003

Article © AMS Mathematical Moments program

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WHAT CAN I DO WITH A MATHEMATICS MAJOR?

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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