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Experiential Learning in module order

This page collects together all of the “experiences” associated with individual modules.

In this site, experiences represent “active” learning opportunities, as opposed to readings, which represent “passive” learning opportunities. In many courses, readings and experiences together constitute the “assignments”.

Module: Boolean Algebra

Boolean functions

Truth tables (Rosen Section 12.1)

Problems

Boolean functions

Truth tables (Rosen Section 12.1)

Solutions

Representing boolean functions

Boolean products, sum of products (Rosen Section 12.2)

Problems

Representing boolean functions

Boolean products, sum of products (Rosen Section 12.2)

Solutions

Logic gates

Outputs of circuits (Rosen Section 12.3)

Problems

Logic gates

Outputs of circuits (Rosen Section 12.3)

Solutions

Module: Models of computation

Languages and grammars

Phrase-structure grammars, derivation trees, production rules (Rosen Section 13.1)

Problems

Languages and grammars

Phrase-structure grammars, derivation trees, production rules (Rosen Section 13.1)

Solutions

Finite-state machines with output

State diagrams, state tables, state machine design (Rosen Section 13.2)

Problems

Finite-state machines with output

State diagrams, state tables, state machine design (Rosen Section 13.2)

Solutions

Finite-state machines with no output

Deterministic finite-state automatons, language recognition (Rosen Section 13.3)

Problems

Finite-state machines with no output

Deterministic finite-state automatons, language recognition (Rosen Section 13.3)

Solutions

Language recognition

Regular expressions, regular grammars, (Rosen Section 13.4)

Problems

Language recognition

Regular expressions, regular grammars, (Rosen Section 13.4)

Solutions

Turing machines

Turing machine execution, construction (Rosen Section 13.5)

Problems

Turing machines

Turing machine execution, construction (Rosen Section 13.5)

Solutions

Module: Relations

Relations and their properties

Reflexive, symmetric, antisymmetric, transitive properties (Rosen Section 9.1)

Problems

Relations and their properties

Reflexive, symmetric, antisymmetric, transitive properties (Rosen Section 9.1)

Solutions

n-ary relations

n-ary relations, primary keys, composite keys, selection, projection, join (Rosen Section 9.2)

Problems

n-ary relations

n-ary relations, primary keys, composite keys, selection, projection, join (Rosen Section 9.2)

Solutions

Representing relations

Matrix representation, directed graphs, digraphs (Rosen Section 9.3)

Problems

Representing relations

Matrix representation, directed graphs, digraphs (Rosen Section 9.3)

Solutions

Closure of relations

Reflexive, symmetric, and transitive closures, Warshall’s algorithm (Rosen Section 9.4)

Problems

Closure of relations

Reflexive, symmetric, and transitive closures, Warshall’s algorithm (Rosen Section 9.4)

Solutions

Equivalence relations

Determining equivalence relations, partitions (Rosen Section 9.5)

Problems

Equivalence relations

Determining equivalence relations, partitions (Rosen Section 9.5)

Solutions

Partial Orderings

Determine partial orderings, posets, lexicographic orderings, Hasse diagrams, lattices (Rosen Section 9.6)

Problems

Partial Orderings

Determine partial orderings, posets, lexicographic orderings, Hasse diagrams, lattices (Rosen Section 9.6)

Solutions

Module: Graphs

Graphs and graph models

Niche overlap graphs, influence graphs (Rosen Section 10.1)

Problems

Graphs and graph models

Niche overlap graphs, influence graphs (Rosen Section 10.1)

Solutions

Graph terminology

Vertices, edges, degree, neighborhood, bipartite, union (Rosen Section 10.2)

Problems

Graph terminology

Vertices, edges, degree, neighborhood, bipartite, union (Rosen Section 10.2)

Solutions

Representing graphs and graph isomorphism

Adjacency lists, adjacency matrices, undirected graphs, incidence matrices, isomorphism (Rosen Section 10.3)

Problems

Representing graphs and graph isomorphism

Adjacency lists, adjacency matrices, undirected graphs, incidence matrices, isomorphism (Rosen Section 10.3)

Solutions

Graph connectivity

Simple paths, circuits, lengths, strongly and weakly connected graphs and components (Rosen Section 10.4)

Problems

Graph connectivity

Simple paths, circuits, lengths, strongly and weakly connected graphs and components (Rosen Section 10.4)

Solutions

Euler and Hamilton paths

Determining Euler and Hamilton circuits, Dirac’s theorem, Ore’s theorem (Rosen Section 10.5)

Problems

Euler and Hamilton paths

Determining Euler and Hamilton circuits, Dirac’s theorem, Ore’s theorem (Rosen Section 10.5)

Solutions

Shortest path

Finding lengths and shortest paths (Rosen Section 10.6)

Problems

Shortest path

Finding lengths and shortest paths (Rosen Section 10.6)

Solutions

Planar graphs

Recognizing and manipulating planar graphs (Rosen Section 10.7)

Problems

Planar graphs

Recognizing and manipulating planar graphs (Rosen Section 10.7)

Solutions

Graph coloring

Constructing dual graphs, finding chromatic numbers (Rosen Section 10.8)

Problems

Graph coloring

Constructing dual graphs, finding chromatic numbers (Rosen Section 10.8)

Solutions

Module: Trees

Introduction to trees

Identifying trees, roots, leaves, vertices, edges (Rosen Section 11.1).

Problems

Introduction to trees

Identifying trees, roots, leaves, vertices, edges (Rosen Section 11.1).

Solutions

Applications of trees

Binary search trees, Huffman coding (Rosen Section 11.2).

Problems

Applications of trees

Binary search trees, Huffman coding (Rosen Section 11.2).

Solutions

Tree traversal

Universal address system, preorder, inorder, postorder traversal, prefix, postfix, infix notation (Rosen Section 11.3).

Problems

Tree traversal

Universal address system, preorder, inorder, postorder traversal, prefix, postfix, infix notation (Rosen Section 11.3).

Solutions

Spanning trees

Spanning trees, depth-first and breadth-first search (Rosen Section 11.4).

Problems

Spanning trees

Spanning trees, depth-first and breadth-first search (Rosen Section 11.4).

Solutions

Minimum spanning trees

Prim’s algorithm, Kruskal’s algorithm (Rosen Section 11.5).

Problems

Minimum spanning trees

Prim’s algorithm, Kruskal’s algorithm (Rosen Section 11.5).

Solutions

Module: Advanced counting techniques

Applications of recurrence relations

Creating recurrence relations, initial conditions (Rosen Section 8.1)

Problems

Applications of recurrence relations

Creating recurrence relations, initial conditions (Rosen Section 8.1)

Solutions

Solving linear recurrence relations

Determining linear homogeneous recurrence relations and their degree, solving recurrence relations (Rosen Section 8.2)

Problems

Solving linear recurrence relations

Determining linear homogeneous recurrence relations and their degree, solving recurrence relations (Rosen Section 8.2)

Solutions

Divide-and-conquer algorithms

Providing Big-O estimates, designing divide-and-conquer algorithms, using the master theorem (Rosen Section 8.3)

Problems

Divide-and-conquer algorithms

Providing Big-O estimates, designing divide-and-conquer algorithms, using the master theorem (Rosen Section 8.3)

Solutions

Inclusion-exclusion

Using the inclusion-exclusion principle (Rosen Section 8.5)

Problems

Inclusion-exclusion

Using the inclusion-exclusion principle (Rosen Section 8.5)

Solutions

Inclusion-exclusion applications

More applications of the inclusion-exclusion principle (Rosen Section 8.6)

Problems

Inclusion-exclusion applications

More applications of the inclusion-exclusion principle (Rosen Section 8.6)

Solutions

Module: Verification

Program correctness

Prove program segment properties (Rosen Section 5.5)

Problems

Program correctness

Prove program segment properties (Rosen Section 5.5)

Solutions