\( \newcommand{\sech}{\operatorname{sech}} \) \( \newcommand{\inverse}[1]{#1^\leftarrow} \) \( \newcommand{\<}{\langle} \) \( \newcommand{\>}{\rangle} \) \( \newcommand{\vect}{\mathbf} \) \( \newcommand{\veci}{\mathbf{\hat ı}} \) \( \newcommand{\vecj}{\mathbf{\hat ȷ}} \) \( \newcommand{\veck}{\mathbf{\hat k}} \) \( \newcommand{\curl}{\operatorname{curl}\,} \) \( \newcommand{\dv}{\operatorname{div}\,} \) \( \newcommand{\detThree}[9]{ \operatorname{det}\left( \begin{array}{c c c} #1 & #2 & #3 \\ #4 & #5 & #6 \\ #7 & #8 & #9 \end{array} \right) } \) \( \newcommand{\detTwo}[4]{ \operatorname{det}\left( \begin{array}{c c} #1 & #2 \\ #3 & #4 \end{array} \right) } \)

MA 320 Standards

Foundations of Math - 2019 Fall
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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.