Learning Outcomes

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 propositional logic to solve problems.

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

Use predicate logic to solve problems.

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

Use set theory to solve problems.

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

Use functions to solve problems.

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

Referencing modules: Functions

Use linear algebra to solve problems.

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

Referencing modules: Linear algebra

Use sequences to solve problems.

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

Referencing modules: Sequences, series, summations

Understand how numbers and characters are represented.

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 algorithm principles to characterize and solve problems.

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

Use number theory to solve problems.

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

Referencing modules: Number theory

Use induction and recursion to solve problems.

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 counting techniques to solve problems.

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

Referencing modules: Counting

Use discrete probability techniques to solve problems.

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