Math 201: Objectives for Final Exam
Mathematical Writing
- Follow "Chapter 0" guidelines for use of symbols.
- Use displays for important formulas and long expressions and calculations.
- Use effective transition phrases to connect the stages of a proof.
Relations and Functions
- State the Definitions; use them in proofs
- Relation; composition of relations, inverse relation
- Function; domain, codomain, image, range
- One-to-one function; onto function; bijective function; identity function
- Permutation
- State the Theorems; use them in proofs
- One-to-one or onto functions between finite sets of the same cardinality.
- Composition of one-to-one functions; composition of onto functions.
- Associative property of function composition.
- Criterion for the inverse of a function to be a function.
Limits of Sequences; Sums of Infinite Series
- State the Definitions; use them in proofs
- Sequence; convergent sequence; divergent sequence; limit of a sequence.
- Series; partial sum of a series; convergent series; divergent series; sum of a series.
- State the Theorems; use them in proofs
- Divergence of the harmonic series.
- Criterion for convergence of geometric series; sum of a geometric series.
Limits of Functions on R; Continuity; the Derivative
- State the Definitions; use them in proofs
- Deleted neighborhood of a point.
- Limit of a function.
- Continuity of a function.
- Derivative of a function.
- State the Theorems; use them in proofs
- Limit of a constant; limit of the identity function.
- Limits of sums, products and quotients.
- Characterization of differentiability.
- Differentiable implies continuous.
- Derivatives of constant functions; derivative of the identity function.
- Linearity of the derivative.
- Derivatives of products and quotients.
- The Chain Rule for derivatives.
