MATH 2200  Discrete Mathematics Credit Hours: 4.00 Prerequisites: MATH 1760 with grade C or better; or an equivalent college course; or an acceptable score on a placement or prerequisite exam
MATH 2200 is an introduction to logic, circuits, graphs, trees, matrices, algorithms, combinatorics and relations within the context of applications to computer science.
Billable Contact Hours: 4
Search for Sections OUTCOMES AND OBJECTIVES Outcome 1: Upon completion of this course, the student will build the truth table for a complex Boolean expression and draw the corresponding circuit diagram.Objectives:  Translate English statements into logical expressions using propositions and connectives.
 Translate English statements into symbolic expressions involving predicates and quantifiers.
 Translate a symbolic logical expression into English.
 Construct truth tables for compound proposition.
 Demonstrate two expressions are logically equivalent using truth tables.
 Show that two expressions are logically equivalent using laws of logic.
 Determine the truthvalue of an expression involving quantifiers.
 Construct truth tables for Boolean functions.
 Construct a logic circuit corresponding to a Boolean function.
 Determine the output from a logic circuit.
Outcome 2: Upon completion of this course, the student will perform basic set operations. Objectives:  Use set builder notation.
 Work with subsets.
 Find combinations of sets involving unions, intersections, compliments and Cartesian products.
 Show that two sets are equal by: showing that they are subsets of each other, using laws of set operations, using membership tables, and using Venn diagrams.
 Determine the cardinality of a set using the principle in inclusionexclusion.
 Determine if a relation is a function.
 Determine whether a function is a bijection.
Outcome 3: Upon completion of this course, the student will draw and explain the significance of graphs and trees. Objectives:  Recognize the difference between a simple graph, a multigraph, and a psuedograph.
 Construct an adjacency matrix for graph.
 Construct a graph from its adjacency matrix.
 Use the adjacency matrix to determine the number of paths of a fixed length from one vertex to another.
 Determine the degrees of the vertices of a graph.
 Determine if a graph is bipartite.
 Determine if a graph has an Euler cycle.
 Construct an incidence matrix for a graph.
 Determine if two graphs are isomorphic and verify the result.
 Use a digraph to represent a relation.
 Determine if the relation is an equivalence relation.
 Determine if a graph is a tree.
 Determine if a tree is balanced.
 Work with the relationship between the number of vertices, internal vertices, and leaves for a full mary tree.
Outcome 4: Upon completion of this course, the student will calculate permutations and combinations. Objectives:  Determine the cardinality of a set using the multiplication principle.
 Count the number of possible outcomes using the sum rule.
 Work with the pigeonhole principle.
 Count the number of possible outcomes using permutations.
 Count the number of possible outcomes using combinations.
 Use the binomial theorem to expand a binomial.
 Use the above counting techniques to determine the probability of an event.
Outcome 5: Upon completion of this course, the student will identify and analyze recurrence relations. Objectives:  Provide a simple formula for geometric and arithmetic sequences.
 Compute the first 5 terms of sequence defined recursively.
 Prove a result using mathematical induction.
 Find the solution of a simple recurrence formula using an iterative approach.
 Solve a linear homogeneous recurrence relation with constant coefficients using the characteristic polynomial.
 Construct a simple algorithm using psuedocode.
 Measure the complexity of a program in psuedocode using bigo and bigtheta measurements.
 Work with the division algorithm and modular arithmetic.
 Convert numbers from one base to another with emphasis on binary, octal, and hexadecimal number systems.
 Use the Euclidean algorithm.
COMMON DEGREE OUTCOMES (CDO) • Communication: The graduate can communicate effectively for the intended purpose and audience. • Critical Thinking: The graduate can make informed decisions after analyzing information or evidence related to the issue. • Global Literacy: The graduate can analyze human behavior or experiences through cultural, social, political, or economic perspectives. • Information Literacy: The graduate can responsibly use information gathered from a variety of formats in order to complete a task. • Quantitative Reasoning: The graduate can apply quantitative methods or evidence to solve problems or make judgments. • Scientific Literacy: The graduate can produce or interpret scientific information presented in a variety of formats.
CDO marked YES apply to this course: Critical Thinking: YES Quantitative Reasoning: YES COURSE CONTENT OUTLINE  Logic
 Propositional calculus
 Language of propositions
 Symbolic representation
 Truth tables
 Laws of logic
 Logical equivalence
 Predicate calculus
 Symbolic representation
 Quantifiers
 Language of quantifiers
 Symbolic representation
 The truthvalue of a logical expression using predicates and quantifiers
 Nested quantifiers
 Boolean Algebra
 Boolean arithmetic
 Boolean functions
 Logic Circuits
 Sets
 Set operations: unions, intersections, complements, and Cartesian products
 Relations and functions
 Images
 Properties of functions: injection, surjection, and bijection
 Inverse functions
 Algorithms
 Search algorithms
 Linear
 Binary
 Sorting algorithms
 Bubble sort
 Insert sort
 BigO, BigOmega, BigTheta
 Complexity of algorithms
 Integers
 Prime numbers and composite numbers
 Division algorithm
 Modular arithmetic
 Other bases
 Euclidian algorithm
 Sequences
 Summation
 Finite geometric series
 Mathematical induction
 Counting
 Product rule
 Sum rule
 The Pigeonhole Principle
 Permutations
 Combinations
 Binomial coefficients
 Binomial theorem
 Finite probability
 Modeling with recurrence relations
 Solving homogeneous recurrence relations with constant coefficients
 Graph theory
 Types of graphs
 Graph terminology
 Paths and cycles
 Degree of a vertex
 Euler Cycles
 Matrix representations of graphs
 Isomorphic of graphs
 Trees
 Tree terminology
 Properties of trees
Primary Faculty Williams, Paul Secondary Faculty Halfaf, Matt Associate Dean McMillen, Lisa Dean Pritchett, Marie
Official Course Syllabus  Macomb Community College, 14500 E 12 Mile Road, Warren, MI 48088
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