\section{Appendix B: MTH 225 Learning Targets} \label{sec:learning-targets} \begin{subsubsection}{Module 1: Computer Arithmetic} \begin{description} \tightlist \item[CA.1] \textbf{(CORE)} \ I can represent an integer in base 2, 8, 10, and 16 and represent a negative integer in base 2 using two's complement notation. \item[CA.2] I can perform addition, subtraction, multiplication, and division in binary. \end{description} \subsubsection{Module 2: Logic} \begin{description} \tightlist \item[L.1] \textbf{(CORE)} \ I can identify the parts of a conditional statement and write the negation, converse, and contrapositive of a conditional statement. \item[L.2] I can construct truth tables for propositions involving two or three variables and use truth tables to determine if two propositions are logically equivalent. \item[L.3] I can identify the truth value of a predicate, determine whether a quantified predicate is true or false, and state the negation of a quantified statement. \end{description} \subsubsection{Module 3: Sets and Functions} \begin{description} \tightlist \item[SF.1] \textbf{(CORE)} \ I can represent a set in roster notation and set-builder notation; determine if an object is an element of a set; and determine set relationships (equality, subset). \item[SF.2] I can perform operations on sets (intersection, union, complement, Cartesian product), determine the cardinality of a set, and write the power set of a finite set. \item[SF.3] \textbf{(CORE)} \ I can determine whether or not a given relation is a function; determine the domain, range, and codomain of a function; and find the image and preimage of a point using a function. \item[SF.4] I can determine whether a function is injective, surjective, or bijective. \item[SF.5] I can evaluate special computer science functions: floor, ceiling, factorial, \texttt{DIV}, and \texttt{MOD} (\texttt{\%}). \end{description} \subsubsection{Module 4: Combinatorics} \begin{description} \tightlist \item[C.1] \textbf{(CORE)} \ I can use the additive and multiplicative principles and the Principle of Inclusion and Exclusion to formulate and solve counting problems. \item[C.2] \textbf{(CORE)} \ I can calculate a binomial coefficient and correctly apply the binomial coefficient to formulate and solve counting problems. \item[C.3] I can count the number of permutations of a group of objects and the number of $k$-permutations from a set of $n$ objects. \item[C.4] I can use the "stars and bars" method to count the number of ways to distribute objects among a group. \end{description} \subsubsection{Module 5: Recursion and Induction} \begin{description} \tightlist \item[RI.1] \textbf{(CORE)} \ I can generate several values in a sequence defined using a closed-form expression or using recursion. \item[RI.2] I can use sigma notation to rewrite a sum and determine the sum of an expression given in sigma notation. \item[RI.3] I can find closed-form and recursive expressions for arithmetic and geometric sequences. \item[RI.4] \textbf{(CORE)} \ I can determine a recurrence relation for a given recursive sequence and check whether a proposed solution to a recurrence relation is valid. \item[RI.5] I can solve a second-order linear homogeneous recurrence relation using the characteristic root method. \item[RI.6] \textbf{(CORE)} \ Given a statement to be proven by mathematical induction, I can state and prove the base case, state the inductive hypothesis, and outline the proof. \end{description}