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)