What can I do with mathematics?

Solving Sudoku

Sudoku puzzles involve a lot of mathematics. Of course, the puzzles are filled with numbers, but the solution process would be the same regardless of the symbols used. More interesting is the logic behind the solution process, which can provide extra satisfaction upon solving a puzzle (with a lot less erasing). In addition, the puzzles are examples of Latin squares—important in abstract algebra and in statistics, in experimental design.

Two Sudoku counting problems are: What is the fewest number of filled-in squares possible for a puzzle, and how many different puzzles are there? There are Sudoku puzzles with 17 numbers that have only one solution, but no one knows if there are puzzles with only 16 numbers that have a unique solution. As for the second question, there are more than five billion different puzzles. For counting purposes, puzzles that can be transformed by processes such as interchanging numbers or the top two rows are not considered different. This result depends on group theory and symmetry, crucial for much of modern physics and chemistry.

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"Sudoku Squares and Chromatic Polynomials," Agnes M. Herzberg and M. Ram Murty, Notices of the American Mathematical Society, June–July, 2007.

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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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