Goals for Math Majors

What should a Mathematics major know, be able to do, and/or have achieved when s/he graduates?

*** Downloadable PDF of Goals for Math Majors ***

Develop Mathematical Maturity

  • Feel comfortable finding sources
  • Take initiative to find out things on own
  • Intellectual independence
  • Read proofs critically (question, understand, verify)
    • Don’t take anyone’s word for it.
  • Move from concrete to abstract thinking and back with facility
    • Understand something well enough to create your own examples
  • Analyze: what is given?  what is known?  what is unknown?
  • Understand the value of a community of learners
    • Value and take advantage of group study as a tool
    • Participate in (and create) a math community (people and ideas)
    • Develop an advisor/advisee relationship
    • Connect with past, present, future peers
    • Engage each other mathematically
  • Recognize patterns and connections between other subjects and mathematics
  • Recognize patterns and connections between areas within mathematics
  • Synthesize ideas across math courses
  • Read and understand symbolic language
  • Develop symbiotic facility with symbolic and verbal/written language

Logical Thinking

  • Demonstrate the process, not just the answer
  • Provide evidence to support arguments
  • Organize and construct a logical argument
  • Develop problem solving “skills”

Communicate Effectively in All Forms (written, oral, etc.)

  • Clear, precise, thorough
  • Understand and write for an audience
  • Articulate arguments clearly and succinctly
  • Speak about math before a variety of audiences (students, faculty, professionals) in a way they can understand
  • Writing
    • Develop a voice
    • Write works that are interesting to read
    • Eliminate assumptions (writing should stand alone)
    • Use appropriate mechanics

Intellectual Development

  • Develop self-critical skills (know what you don’t know and how to address it)
  • Risk failure for the opportunity to succeed
  • Know how to access knowledge (learn how to learn)
  • Develop mathematical and intellectual confidence

The Basics

  • Exposure to a wide variety of concepts
  • Enjoy mathematics
  • Preparation for a variety of challenging careers
  • Computational ability (with use of software such as MATLAB)
  • Math typesetting software (such as LaTeX)