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Sep 12, 2024
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MTH 2310 - Discrete Mathematics3 lecture hours 0 lab hours 3 credits Course Description This course covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include logic, proofs, sets, functions, modular arithmetic, induction, recursion, counting, relations, graphs, and trees. Prereq: MTH 1110 or sophomore standing (quarter system prereq: MA 137 or sophomore standing) Note: None This course meets the following Raider Core CLO Requirement: Think Critically Course Learning Outcomes Upon successful completion of this course, the student will be able to:
- Convert logical statements from informal language to propositional and predicate logic expressions
- Apply formal methods of symbolic propositional and predicate logic, such as calculating validity of formulae
- Use the rules of inference to construct proofs in propositional and predicate logic
- Use propositional and predicate logic to model, analyze, and interpret real-life situations
- Outline the basic structure of direct proof and proof by contradiction
- Apply direct proof or proof by contradiction, where appropriate, in the construction of a sound argument
- Use the basic terminology of sets, functions, and relations
- Perform common operations associated with sets, functions, and relations
- Use sets, functions, and relations to model, analyze, and interpret real-life situations
- Recognize and construct arithmetic and geometric progressions
- Perform computations involving modular arithmetic, including solving linear congruences
- Construct proofs using weak and strong induction
- Solve a variety of basic recurrence relations
- Analyze a problem to determine an underlying recurrence relation
- Apply counting arguments, including sum and product rules, inclusion-exclusion principle, and the pigeonhole principle.
- Compute permutations and combinations of a set, and interpret the meaning in the context of the particular application
- Identify whether a relation is reflexive, symmetric, antisymmetric, or transitive and if it is an equivalence relation
- Use basic terminology of graph theory
- Identify the type and special properties of a graph
- Demonstrate different traversal methods for trees and graphs, including pre-, post-, and in-order traversal of trees
Prerequisites by Topic Course Topics
- Propositional logic
- Predicate logic
- Universal and existential quantifiers
- Modus ponens and modus tollens
- Direct proofs
- Proof by contradiction
- Sets
- Functions
- Arithmetic and geometric progressions
- Cardinality, countability, and inclusion-exclusion principle
- Basic modular arithmetic
- Greatest common divisor and Euclidean algorithm (time permitting)
- The Chinese Remainder Theorem
- Mathematical induction and well ordering principle
- Recursive definition
- Sum and product rules
- The pigeonhole principle
- Permutations and combinations
- The binomial theorem
- Recurrence relations
- Solving recurrence relations
- Relations (reflexivity, symmetry, antisymmetry, transitivity)
- Equivalence relations and partial ordering
- Fundamental terminology of graphs
- Directed, undirected, and weighted graphs
- Graph isomorphism (time permitting)
- Trees, traversal strategies
Coordinator Dr. Chunping Xie
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