 # Mathematics 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)