# MA 320 Standards

Foundations of Math - 2019 Fall

Following are a list of topics included in the Content Mastery grade specification for this course.

• 1. Guidelines for Good Mathematical Writing. Read and understand these guidelines.
• 2. Statements. Be able to identify whether a sentence is a statement or not.
• 3. Denials of Compound and Conditional Statements. Be able to write the denial of an English compound or conditional statement.
• 4. Denials of Universal and Existential Qualifiers. Be able to write the denial of an English statement involving a universal or existanetial qualifier.
• 5. Conditionals, Converses, Inverses, and Contrapositives. Be able to rewrite a conditional as its converse, inverse, and contrapositive, and analyze each statement.
• 6. Proving tautologies by truth tables. Be able to prove a tautology by generating its truth table.
• 7. Direct, indirect, and contrapositive proofs Be able to identify whether a proof is direct, indirect, or contrapositive.
• 8. Set operations Be able to compute and illustrate a combination of set operations, including intersections, unions, complements, subtractions, power sets, and cardinalities.
• 9. Valid and Invalid Proofs Be able to identify a proof as valid or invalid, and give a reason why.
• 10. Equivalence Relations Given a non-equivalence relation and three elements, explain which pairs are related, and explain why the relation is not an equivalence relation based on those elements.
• 11. Functions Be able to analyze a given function, including computing things such as pre-images, and identifying functions as onto or one-to-one.
• 12. Binary Operations Be able to compute a given binary operation and identify it as commutative or associative.
• 13. Finite Sums Be able to compute finite sums and express them in sigma notation.
• 14. Upper and Lower Bounds Be able to identify upper and lower bounds for sets of real numbers, including least upper bounds and greatest lower bounds.