By the time of graduation, students should have acquired the following skills:

• Proficiency in basic computational methods in calculus, algebra, and differential equations.
• Facility with computer-aided computations.
• Understanding of the basic rules of logic and proficiency in using them.
• The ability to derive general principles from examples.
• The ability to formulate mathematical conjectures and to test them.
• The ability to complete mathematical proofs.
• The ability to relate mathematical concepts to problems arising in other disciplines.
• The ability to represent problems and ideas precisely in mathematical terms.
• The ability to identify facts and techniques relevant to a given problem, and proficiency in using them to solve the problem.
• Comprehension of the general framework of mathematical research; an understanding of the role of axioms, assumptions, theorems, proofs, and conjectures.
• The ability to present mathematical concepts, statements, and arguments clearly.