This page collects together all of the “outcomes” associated with individual modules. Outcomes identify what students will know and be able to do if they master the material.

- Use truth tables and logical operators to solve problems.
- Translate between narrative arguments and propositional logic.
- Prove logical equivalency, contingency, tautology, and contradictions.

*Referencing modules:*
Propositional Logic

- Translate between narrative arguments and predicate logic.
- Identify valid, satisfiable, and unsatisfiable assertions.
- Apply inference rules to solve problems.
- Prove or disprove assertions using predicate logic.

*Referencing modules:*
Predicate Logic

- Determine union, difference, and intersection of sets.
- Express sets in set-builder and tabular form.
- Prove properties of sets both with and without Venn diagrams.
- Prove logical equivalency, contingency, tautology, and contradictions.

*Referencing modules:*
Sets

- Specify function injections and surjections.
- Prove that sets are countably finite or infinite.
- Solve equations using exponentiation and logarithms.

*Referencing modules:*
Functions

- Compute matrix addition and multiplication.
- Invert matrices.
- Evaluate determinants.

*Referencing modules:*
Linear algebra

- Enumerate terms of a finite or infinite sequence.
- Derive closed formulas for series.

*Referencing modules:*
Sequences, series, summations

- Convert between decimal, binary, octal, and hexidecimal notations.
- Represent numbers using signed, unsigned, two’s complement, and floating point representations.

*Referencing modules:*
Data representations

- Use Big O notation to characterize complexity of algorithms.
- Represent an algorithm using pseudocode.
- Use the greedy algorithm to solve problems such as the coin change problem.

*Referencing modules:*
Algorithms

- Compute the least common multiple and greatest common divisor.
- Apply Euclid’s algorithm
- Solve congruence systems using back substitution.

*Referencing modules:*
Number theory

- Give inductive definitions for sets such as palindromes, unsigned integers, etc.
- Prove properties using induction.
- Write recursive algorithms to solve problems.

*Referencing modules:*
Induction and recursion

- Use combinatoric methods to solve “number of” and “how many ways” problems.
- Write pseudocode to generate permutations and combinations.

*Referencing modules:*
Counting

- Determine probability of outcomes (such as coin flipping).
- Determine prior and posterior probabilities.
- Determine the expected value and variance for outcomes of procedures.

*Referencing modules:*
Discrete probability