--- tags: mth225, learning-targets --- # MTH 225 Fall 2021 Learning Targets ## Module 1: Computer Arithmetic * CA.1 (**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. * CA.2 I can perform addition, subtraction, multiplication, and division in binary. ## Module 2: Logic * L.1 (**CORE**) I can identify the parts of a conditional statement and write the negation, converse, and contrapositive of a conditional statement. * 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. * 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. ## Module 3: Sets and Functions * SF.1 (**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). * 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. * SF.3 (**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. * SF.4 I can determine whether a function is injective, surjective, or bijective. * SF.5 I can evaluate special computer science functions: floor, ceiling, factorial, DIV, and MOD (`%`). ## Module 4: Combinatorics * C.1 (**CORE**) I can use the additive and multiplicative principles and the Principle of Inclusion and Exclusion to formulate and solve counting problems. * C.2 (**CORE**) I can calculate a binomial coefficient and correctly apply the binomial coefficient to formulate and solve counting problems. * 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. * C.4 I can use the "stars and bars" method to count the number of ways to distribute objects among a group. ## Module 5: Recursion and Induction * RI.1 (**CORE**) I can generate several values in a sequence defined using a closed-form expression or using recursion. * RI.2 I can use sigma notation to rewrite a sum and determine the sum of an expression given in sigma notation. * RI.3 I can find closed-form and recursive expressions for arithmetic and geometric sequences. * RI.4 I can determine a recurrence relation for a given recursive sequence and check whether a proposed solution to a recurrence relation is valid. * RI.5 I can solve a second-order linear homogeneous recurrence relation using the characteristic root method. * RI.6 (**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.