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Learning Goals
Students who major in mathematics can expect to achieve the following learning goals:
Be able to use the techniques of calculus to:
Compute a derivative
Compute an integral
Establish the convergence of an infinite series, and find its sum in certain common cases
Be able to solve a variety of kinds of equations, as well as practical problems whose solutions lead to them:
A polynomial, or algebraic equation
A system of linear equations
A separable differential equation
Be able to further solve a variety of practical problems, using an appropriate mathematical model:
Simple or constrained optimization
A kinematic problem involving rates and displacements
A geometrical problem involving spatial relationships
A problem involving area, length, or volume measure
Decide questions related to abstract algebra or number theory
Decide questions related to topology, continuity, or convergence
Apply deductive logic
Assess the probability of a random event, and to interpret the result of a statistical study
Assess the validity of a mathematical argument
Solve mathematical problems using technology (e.g. a spreadsheet, a CAS, or an Integrated Development
Environment)
Be able to give proofs of a variety of results, such as:
A trigonometric identity
A set-theoretic result
A result in group theory (e.g. the order of a subgroup H of G divides the order of G)