CpSc 311 Section 01 August 26, 2013 Course Outline



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CpSc 311 Section 01 August 26, 2013

Course Outline


  1. Introduction

    1. Explain basic terminology

                  1. Sets

                  2. Relations

                  3. Functions

                  4. Trees

                  5. Graphs

    2. Applicability to computing

                  1. Functions

                  2. Relations - Equivalence relations, closures

                  3. Sets - Finite, countably infinite, uncountably infinite sets

                  4. Trees

    3. Using structure in programs

                  1. Functions

                  2. Relations

                  3. Sets

                  4. Trees

  2. Formal Methodology

    1. Binary operators

    2. Symbolic logic

    3. DeMorgan’s laws

  3. Proof techniques

    1. Proof by induction

    2. Using proofs to solve problems such as puzzles

  4. Demonstrate basic counting principles

    1. Diagonalization

    2. pigeonhole principle

  5. Relate the ideas of mathematical induction to recursion

  6. Computing and analysis (3 hours)

    1. permutations of a set

    2. combinations of a set

    3. evaluate the run-time performance of alternative algorithms

  7. Probabilities (3 hours)

    1. Discrete probabilities

    2. Distributions

    3. Monte Carlo method

  8. Apply the tools of probability to solve problems

    1. the average case analysis of algorithms

    2. hashing

  9. Computational Complexity

    1. Asymptotic analysis of bounds

    2. Big-O, little-O

    3. Worst-case

    4. Best Case

    5. Average case

    6. Time-Space trade-offs

    7. Recurrence relations

  10. Introduction to Graphs and Trees

    1. Binary Search Tree

    2. Spanning Trees

    3. Shortest Path

    4. Undirected graphs

    5. Directed graphs

  11. Graphs

    1. Cycles

    2. Traversability

    3. Connectedness

    4. Distance

  12. Traversal methods

    1. Demonstrate and implement tree traversals

    2. Demonstrate and implement graph traversals

  13. Model problems in computing

    1. Graphs

    2. trees

    3. Markov chains

  14. Data structures and algorithms for graphs and trees

    1. Enumeration

    2. practical instantiation

    3. Producing a random graph, tree, and table

Computer Science Department


Course Competency Plan

COURSE: CpSc 311 - Discrete of Computational Structures



Catalog Description: Introduces computational implementations of the mathematical structures most frequently used in computing including sets, equivalence relations, functions, graphs, trees and standard logic. Also introduces automata, formal languages, countability, decidability and computational complexity, Markov and stochastic processes. The course will stress traditional programming and mathematical approaches to these structures such as the use of recursion, elementary data structures, and proof techniques to instantiate, parse, traverse, demonstrate correctness, or use these computational objects. (Prereq: CpSc140, Math 120)

Course Outcomes: This course and its outcomes support the Information Technology Learning Outcome of Problem Solving and Critical Thinking (PS&CT) . This Information Technology Learning Outcomes is tied directly to the University Wide Outcome of Critical Thinking and Problem Solving.

Program Objectives Assessed in CpSc 427

Degree

Program Objective

Assessed Course Objective

IT

I.a. Apply programming and system management techniques to address information technology problems

1. Build programs and prove theorems concerning fundamental structures of discrete mathematics.

 

Additional Course Objectives include:

The student will be able to:

1. Define basic computational terms and perform computational operations associated with sets, functions, relations, trees, and graphs.

2.Apply formal methods of symbolic logic and proof techniques used to solve traditional computing problems.

3.Apply the tools of probability to solve problems.

4. Evaluate the run-time performance of alternative algorithms.

5. Model problems in computing using graphs, trees and Markov chains.



6. Relate graphs and trees to data structures, algorithms and counting.

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