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Official Course
Description: MCCCD Approval: 6-27-1995 |
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MAT227 2007 Summer I – 2011 Sumer II |
LEC 3.0 Credit(s) 3.0 Period(s) 3.0 Load Acad |
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Discrete
Mathematical Structures |
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Introduction
to lattices, graphs, Boolean algebras, and groups. Emphasis on topics
relevant to computer science. Prerequisites: Grade of "C" or
better in CSC100 and (MAT220, or MAT221, or equivalent) or permission of
Instructor. |
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Go to Competencies Go to Outline
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MCCCD
Official Course Competencies: |
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MAT227 2007
Summer I – 2011 Sumer II |
Discrete Mathematical Structures |
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1.
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Solve problems using sets, subsets, denumerable sets and find
direct products of these sets. (I) |
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2.
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Determine paths, cycles, connectivity, and trees given a
graph. (I) |
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3.
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Represent a graph with its incidence matrix. (I) |
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4.
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Create proofs using relations, order relations, and equivalence
relations. (I) |
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5.
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Identify domain and range of a mapping and find its
inverse. (I) |
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6.
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Calculate permutations and combinations of sets. (I) |
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7.
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Solve problems by using the definitions of groups, fields,
lattices and transformations of these. (II) |
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8.
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Use the axioms of Boolean Algebra to evaluate
propositional functions by assigning truth values and using truth tables.
(III) |
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9.
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Analyze a
switching circuit by denoting it using a Boolean function and simplifying
that function into conjunctive and disjunctive normal forms. (III) |
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10.
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Apply Boolean
Algebra to other computer science topics including decision tables,
determination of minimal paths, and coding theory. (III) |
Go to Description Go to top of
Competencies
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MCCCD
Official Course Outline: |
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MAT227 2007
Summer I – 2011 Sumer II |
Discrete Mathematical Structures |
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I. Foundations of Discrete
Math A. Sets 1. Direct Products 2. Finite and Denumerable
Sets 3. Finite Sets and Their
Subsets B. Graphs 1. Paths 2. Cycles 3. Connectivity 4. Trees 5. Adjacency and the
Incidence Matrix C. Relations 1. Order Relations 2. Equivalence Relations a. Equivalence Classes b. Partition of Sets c. Congruences
D. Mappings 1. Domains 2. Ranges 3. Inverse Mappings 4. Preservation of
Relations Under Mappings E. Combinatorial Concepts 1. Permutations 2. Combinations II. Basic Algebraic
Structures A. Algebraic Structures as
Sets with Particular Functions and Relations Defined on Them B. Groups 1. Subgroup 2. Cyclic Groups C. The Concept of Hemomorphism and Isomorphism on a set with Operations D. Semigroups
and Semigroups with Transformations E. Structures with Several
Operations 1. Fields 2. Lattices III. Boolean Algebra and
Propositional Logic A. Theory: The Axioms of
Set Algebra 1. Axiomatic Definition of
Boolean Algebras as Algebraic Structures with Two Operations 2. Basic Facts About Boolean
Functions 3. Propositions and
Propositional Functions 4. Logical Connectives 5. Truth Values and Truth
Tables 6. The Algebra of
Propositional Functions 7. The Boolean Algebra
Truth Values 8. Conjunctive and
Disjunctive Normal Forms B. Applications: Boolean
Algebra and Switching Circuits 1. Basic Computer
Components 2. Decision Tables 3. Graph Examples in Coding
Theory 4. Algorithms for
Determined Cycles in Minimal Paths 5. Basic Elements of List
Structures 6. Accessing Problems 7. Graphs of a Game 8. Matching Algorithms |