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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)