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According to Vault, mathematics and physics research can be divided into the following areas:

Applied Mathematics

Applied mathematicians “use mathematical theories and principles to address real-world problems. They might create mathematical models to calculate the characteristics of new products, systems, or population trends.”

Theoretical Mathematics

Theoretical mathematicians work with pure and abstract mathematical concepts to expand and define the scope of mathematical knowledge.”

Experimental Physics

Experimental physics uses experiments to gather information.

Theoretical Physics

Theoretical physics constructs theories to explain experimental results.

To explore specific careers see, as well as options other than research for mathematics and physics majors see:

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• Visit government laboratories or research centers to learn more about opportunities in the field. Schedule informational interviews to learn about the profession and specific career paths.
• Join relevant professional associations. Attend meetings and stay up-to-date on research/publications.
• Stay informed of new developments and current trends in the field.
• Participate in summer research institutes. Submit research to local poster competitions or research symposiums.
• A willingness to relocate is helpful due to limited opportunities in specialized areas.

• Oral and written communication and interpersonal skills for sharing findings and collaborating with interdisciplinary teams
• Computer skills and the ability to use scientific instruments and equipment
• Critical thinking
• Problem diagnosis and solving