## MAT 2570 Discrete Mathematics

A course in Discrete Mathematics for students interested in information technology, computer science, and related fields. Topics include logic, proof techniques, set theory, functions and relations, counting, elementary number theory, graphs and tree theory, base-n arithmetic, and Boolean Algebra.

Division: Science, Mathematics and Engineering
Department: Mathematics
Repeatable Credit: No
Offered Online: Yes

Prereqs: MAT 1460 OR MAT 1470 OR MAT 1580

#### Outcomes

• Demonstrate the proper use of set notation, set operations, counting principles, graphs, trees, and a knowledge of the associated terminology.
• Define and apply inductive/deductive reasoning; identify logical statements and connectives; identify faulty reasoning and construct truth tables. Construct direct proofs, proofs by contradiction, by contraposition, or by induction.
• Identify Boolean algebras, prove their properties, convert between logic networks and Boolean expressions and truth functions, and minimize the canonical sum-of-products form for a truth function.
• Determine the domain, codomain, and range of discrete functions. Identify injections, surjections, and bijections. Identify the Big-O estimate for basic functions.
• Convert between various base-n systems. Perform arithmetic in various base-n systems. Represent signed binary numbers with 1s and 2s complements. State and use the Division and Euclidean Algorithms. Perform modular Arithmetic.

#### Credit Hours: 4

Classroom Hours: 4