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.