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Mar 29, 2024
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MA 2310 - Discrete Mathematics I3 lecture hours 0 lab hours 3 credits Course Description This course provides an introduction to discrete mathematics as it applies to computer science. Topics include sets, logic, relations, functions, recursion, Boolean algebra, and graph theory. (prereq: MA 127 or equivalent, sophomore standing) Course Learning Outcomes Upon successful completion of this course, the student will be able to:
- Illustrate by examples the basic terminology of functions, relations, and sets
- Illustrate by examples, both discrete and continuous, the operations associated with sets, functions, and relations
- Apply functions and relations to problems in computer science
- Manipulate formal methods of symbolic propositional and predicate logic
- Demonstrate knowledge of formal logic proofs and logical reasoning through solving problems
- Illustrate by example the basic terminology of graph theory
- Apply logic to determine the validity of a formal argument
- Identify a relation; specifically, a partial order, equivalence relation, or total order
- Identify a function; specifically, surjective, injective, and bijective functions
- Illustrate by examples tracing Euler and Hamiltonian paths
- Construct minimum spanning trees and adjacency matrices for graphs
Prerequisites by Topic
- Basic concepts of college algebra
- Basic concepts of set theory
Course Topics
- Course introduction
- Propositional logic: normal forms (conjunctive and disjunctive)
- Propositional logic: Validity
- Fundamental structures: Functions (surjections, injections, inverses, composition)
- Fundamental structures: Relations (reflexivity, symmetry, transitivity, equivalence relations
- Fundamental structures: Discrete versus continuous functions and relations
- Fundamental structures: Sets (Venn diagrams, complements, Cartesian products, power sets)
- Fundamental structures: Cardinality and countability
- Boolean algebra: Boolean values, standard operations, de Morgan’s laws
- Predicate logic: Universal and existential quantification
- Predicate logic: Modus ponens and modus tollens
- Predicate logic: Limitations of predicate logic
- Recurrence relations: Basic formulae
- Recurrence relations: Elementary solution techniques
- Graphs: Fundamental definitions
- Graphs: Directed and undirected graphs
- Graphs: Spanning trees
- Graphs: Shortest path
- Graphs: Euler and Hamiltonian cycles
- Graphs: Traversal strategies
Coordinator Chunping Xie
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