Learning Goals for Mathematics Majors

By the time of graduation, majors should have acquired the following knowledge and skills:

Analytical skills

Graduates of our program should understand:

  • The role of axioms and assumptions in the formulation of mathematical definitions and theorems.
  • The basic rules of logic and have acquired the ability to follow the logical flow of proofs.
  • How to distinguish a coherent mathematical argument from a fallacious one.
  • The core concepts of analysis and algebra (for graduates in the Mathematical options), or key techniques of applied mathematics and the ability to analyze mathematical models (for graduates in Mathematical Sciences option).

Problem-solving and modeling skills (important for all, but especially for majors in Mathematical Sciences)

Students should be able to:

  • Recognize which real-world problems are subject to mathematical reasoning.
  • Make vague ideas precise by representing them in mathematical notation, when appropriate.
  • Use a variety of techniques for solving problems expressed in mathematical notation.

Communication skills

Graduates should have the ability to:

  • Formulate a mathematical statement precisely.
  • Develop and write a coherent proof using proper sentence structure and grammar.
  • Present a mathematical argument verbally.
  • Understand and explain mathematical arguments derived from a variety of sources including textbooks, research papers, and research presentations.

Reading and research skills

Students should have:

  • Sufficient experience in mathematical language and foundational material to be well-prepared to extend ones mathematical knowledge further through independent reading.
  • Exposure to and successful experience in solving mathematical problems presenting substantial intellectual challenge.


Department of Mathematics

75 Shannon Street
Middlebury College
Middlebury, VT 05753