What can I do with mathematics?

Getting Results on
the Web

Imagine trying to find the right information quickly in a library where billions of pages are randomly piled in a heap, instead of being in books shelved in order. That's what Web search engines do, millions of times a day. First-generation search engines often found usefulpages, but thosepages may have been too far down the list to be of any practical use. Current search engines rankpages by using mathematics— probability, graph theory, and linear algebra—so that sites most relevant to a query are listed at the top, where the user can most easily see them.

The vast number ofpages and links on the Web can be represented as a graph in which the nodes are Webpages and the directed edges are links.Today's search engines determine the relevance of a page to a query by incorporating the importance ofpages pointing to and from that page.Thus, when it comes to a search, a page’s links can be just as important as its content.The final ranking comes from techniques in linear algebra and probability that help formulate and solve equations which, according to the founders of one search engine, involve millions of variables and billions of terms. In the future, search engines may use artificial intelligence and information on past searches to discern the actual intent of a query.

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David Voss,“Better Searching Through Science,”
Science, 14 Sept. 2001

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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