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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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