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# University Catalog

### MATH 171. Fundamentals of Mathematics

Credits: 3
 Department: Mathematics Description: Mathematics as a problem solving tool. Concepts of sets, logic, induction, combinatorics, numeration, recursion, trees, graph theory, and matrices. Prerequisites: MATH 072, or high school advanced algebra with satisfactory math placement score Semester Offered: DEMAND Grading Method: ABCDF

#### Student Learning Outcomes

 1 Generate a truth table for at least 5 different sets of propositional statements (and, or, not, if-then, if-and-only-if). 2 Convert informal English expressions to and from formal quantified logical expressions. 3 Discriminate between valid and invalid arguments. 4 Identify the union, intersection, and complements of at least 3 simple sets. 5 Prove that one set is a subset of, or is equal to, another set. 6 Prove a stated algebraic relation using any of the following techniques, with 100% accuracy: direct proof, indirect proof, contradiction, mathematical induction. 7 Identify different components of a graph (e.g. vertex, edge, loop, parallel edges, isolated vertex). 8 Determine when two graphs are isomorphic. 9 Create and apply algorithms to solve Euler path and circuit problems, shortest-path problems, and minimal spanning tree problems. 10 Describe the historical development of discrete mathematics including contributions from diverse cultures.

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