SLO+Chart+MAT+167

**NOTE: ** This table describes the alignment of the course description and student learning outcomes with the module objectives and assessments.
 * Student Learning Objectives Chart MAT 167 **

Sets and Counting || **Module 1 Assessments ** || **Module 1 Assignment Description ** || Upon completion, students should be able to demonstrate competence in the topics covered. || Upon successful completion of this course, the student will have:
 * **Combined Course Library Description ** || **Course Outcomes ** || **Module Objectives ** || **Module Assessments ** || **Assignments Description ** ||
 * **Combined Course Library Description ** || **Course Outcomes ** || **Module 1 Objectives **
 * <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">This course is a study of discrete mathematics with emphasis on applications. Topics include number systems, combinations/permutations, mathematical logic/proofs, sets/counting, Boolean algebra, mathematical induction, trees/graphs, and algorithms.
 * 1) <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Identified and applied the <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt;">basic terminologies of functions, relations and sets.
 * 2) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Calculated permutations and combinations of sets and interpreted the meaning.
 * 3) <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">A <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt;">pplied formal logic proofs and logical reasoning to solve problems.
 * 4) <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Constructed <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt;">logic statements with proper quantifiers.
 * 5) <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Applied counting principles including the pigeonhole principle.
 * 6) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Proven or disproven statements in elementary number theory using direct and indirect proof methods.
 * 7) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 12pt;">Identified and constructed various graphs and trees.
 * 8) <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Applied the basic concepts of Boolean algebra. || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Upon successful completion of this module, you will have:
 * 9) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Evaluated various set operations such as union, intersection, complement.
 * 10) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 6pt;">Constructed Venn Diagrams based on various set operations.
 * 11) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 6pt;">Evaluated truth tables and proposition statements.
 * 12) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 6pt;">Classify reflexive, symmetric, antisymmetric and transitive relations. || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt;">The student’s work will be assessed with: || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 6pt;">(1-2) Discussion forum: Identify two sets you are a member of and two sets you are not a member of.

<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 6pt;"> (1) Writing Assignment 1: Define an equivalence relation and provide an example. <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 0pt;">(2) Writing Assignment 2: Construct your own Venn Diagram using two sets, A and B, applying at least two different set operations. <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 0pt;">(3) Writing Assignment 3: Construct a truth table using r, s and t with at least three operations. <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 0pt;">(4) Writing Assignment 4: Describe one of the following and provide an example: reflexive, symmetric or transitive function. <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 0pt;">(1-4) Module Homework: Students will complete a variety of homework exercises to practice modular concepts. || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">(1-4) Module Quiz: Ten question quiz including multiple choice and true/false. **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt;">Discussion Forum: Sets **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt;">requires the student to share sets they are members of and why. **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt;">Writing Assignment 1: Equivalence Relation **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt;"> requires the student to define equivalence relations and provide a personal example. **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt;">W ****<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt;">riting Assignment 2: Venn Diagram **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt;">requires the student to use set operations to construct their own Venn Diagram using two sets and at least two different operations with those sets. **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt;">Writing Assignment 3: Truth Table **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt;">requires the student to construct their own truth table with three variables and three operations with those variables. **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt;">Writing Assignment 4: Choose a Function **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt;">requires the student to choose between three types of functions, describe the characteristics of this type and provide an example. || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Mathematical Logic and Proofs || **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Module 2 Assessments ** || **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Module 2 Assignment Description ** || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Upon completion, students should be able to demonstrate competence in the topics covered. || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt;">Upon successful completion of this course, the student will have:
 * <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt;">The student will complete these assignments:
 * **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Combined Course Library Description ** || **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Course Outcomes ** || **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Module 2 Objectives **
 * <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">This course is a study of discrete mathematics with emphasis on applications. Topics include number systems, combinations/permutations, mathematical logic/proofs, sets/counting, Boolean algebra, mathematical induction, trees/graphs, and algorithms.
 * 1) <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Identified and applied the <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt;">basic terminologies of functions, relations and sets.
 * 2) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Calculated permutations and combinations of sets and interpreted the meaning.
 * 3) <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">A <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt;">pplied formal logic proofs and logical reasoning to solve problems.
 * 4) <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Constructed <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt;"> logic statements with proper quantifiers.
 * 5) <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Applied counting principles including the pigeonhole principle.
 * 6) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 12pt;">Proven or disproven statements in elementary number theory using direct and indirect proof methods.
 * 7) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 12pt;">Identified and constructed various graphs and trees.
 * 8) <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Applied the basic concepts of Boolean algebra. || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 0pt;">Upon successful completion of this module, the student will have.
 * 9) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt 0.5in; text-indent: -0.25in;">Defined a proposition and constructed truth values for the propositions.
 * 10) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt 0.5in; text-indent: -0.25in;">Used truth table to show to two propositions are logically equivalent.
 * 11) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt 0.5in; text-indent: -0.25in;">Translated statements into logical expressions using predicates, quantifiers and logical connectives.
 * 12) Used direct, indirect and contra positive proof strategies to prove a mathematical statement. || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 0pt;">Student work will be assessed with:

<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 6pt;">(4) Discussion forum: Describe the difference between indirect and contra positive proof strategies. Give an example of a use of each.

<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 6pt;">(1) Writing Assignment 1: Define a proposition and construct a truth table.

<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 0pt;">(2) Writing Assignment 2: Use a truth table to show two propositions are logically equivalent.

<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 0pt;">(3) Writing Assignment 3: Prove that two compound propositions are logically equivalent using truth tables.

<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 0pt;">(4) Writing Assignment 4: Construct a direct proof.

(1-3) Module Quiz || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt;">The student will complete these assignments:

<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 6pt;">**Discussion forum**: **Proof Strategies** requires the student to describe the difference between indirect and contra positive proof strategies and give an example of the use of each.


 * <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 6pt;">Writing Assignment 1: Define a proposition **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 6pt;"> requires the student to define a proposition and construct a truth table for the proposition.


 * <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 0pt;">Writing Assignment 2: Use a truth table **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 6pt;"> requires the student to use a truth table to show two propositions are logically equivalent.

requires the student to prove that two compound propositions are logically equivalent by constructing truth tables.
 * <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 0pt;">Writing Assignment 3: Logic**


 * <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 0pt;">Writing Assignment 4:Proofs **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 0pt;">requires the student to construct a direct proof.

<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 0pt;">(1-4) Module Homework: Students will complete a variety of homework exercises to practice modular concepts. || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Algorithms and Number Theory || **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Module 3 Assessments ** || **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Module 3 Assignment Description ** || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Upon completion, students should be able to demonstrate competence in the topics covered. || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt;">Upon successful completion of this course, the student will have: <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt 0.5in; text-indent: -0.25in;">1. Determined the properties of an algorithm.
 * **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Combined Course Library Description ** || **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Course Outcomes ** || **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Module 3 Objectives **
 * <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">This course is a study of discrete mathematics with emphasis on applications. Topics include number systems, combinations/permutations, mathematical logic/proofs, sets/counting, Boolean algebra, mathematical induction, trees/graphs, and algorithms.
 * 1) <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Identified and applied the <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt;">basic terminologies of functions, relations and sets.
 * 2) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Calculated permutations and combinations of sets and interpreted the meaning.
 * 3) <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">A <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt;">pplied formal logic proofs and logical reasoning to solve problems.
 * 4) <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Constructed <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt;"> logic statements with proper quantifiers.
 * 5) <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Applied counting principles including the pigeonhole principle.
 * 6) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 12pt;">Proven or disproven statements in elementary number theory using direct and indirect proof methods.
 * 7) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 12pt;">Identified and constructed various graphs and trees.
 * 8) <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Applied the basic concepts of Boolean algebra. || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 0pt;">Upon successful completion of this module, the student will have:

<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt 0.5in; text-indent: -0.25in;">2. Applied the properties of number theory to prove modular congurency.

<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt 0.5in; text-indent: -0.25in;">3. Used the prime number theorem to determine the greatest common factors of a set of numbers.

<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt 0.5in; text-indent: -0.25in;">4.Determine the solution to a system of congruences. || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 0pt;">Student’s work will be assessed with:

<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 6pt;">(1) Discussion forum: Describe which properties of an algorithm are present in making a long distance call, which properties are lacking?

<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 0pt;">(2) Writing Assignment 1: Show that a **mod** m = b **mod** m if a__=__ b (mod m)

(3) Writing Assignment 2: Show that if 2^n-1 is prime then n is prime.

(4) Writing Assignment 3: Solve a a system on congruences || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt;">The student will complete these assignments:

<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 0pt;">(1-4) Module Homework: Students will complete a variety of homework exercises to practice modular concepts. || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Induction and Recursion || **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Module 4 Assessments ** || **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Module 4 Assignment Description ** || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Upon completion, students should be able to demonstrate competence in the topics covered. || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt;">Upon successful completion of this course, the student will have:
 * **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Combined Course Library Description ** || **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Course Outcomes ** || **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Module 4 Objectives **
 * <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">This course is a study of discrete mathematics with emphasis on applications. Topics include number systems, combinations/permutations, mathematical logic/proofs, sets/counting, Boolean algebra, mathematical induction, trees/graphs, and algorithms.
 * 1) <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Identified and applied the <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt;">basic terminologies of functions, relations and sets.
 * 2) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Calculated permutations and combinations of sets and interpreted the meaning.
 * 3) <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">A <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt;">pplied formal logic proofs and logical reasoning to solve problems.
 * 4) <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Constructed <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt;"> logic statements with proper quantifiers.
 * 5) <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Applied counting principles including the pigeonhole principle.
 * 6) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 12pt;">Proven or disproven statements in elementary number theory using direct and indirect proof methods.
 * 7) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 12pt;">Identified and constructed various graphs and trees.
 * 8) <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Applied the basic concepts of Boolean algebra. || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 0pt;">Upon successful completion of this module, the student will have:
 * 9) Used mathematical induction to prove summation formula.
 * 10) Used strong induction to prove mathematical statements as true.
 * 11) Determined if a proposed definition is a valid recursive definition.
 * 12) Devised a recursive algorithm. || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 0pt;">The student’s work will be assessed with:

<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 6pt;">(4) Discussion forum:

<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 6pt;">(1) Writing Assignment 1: Prove a summation formula

<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 0pt;">(2) Writing Assignment 2: Use strong induction in a proof.

<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 0pt;">(3) Writing Assignment 3: Determine if a definition is recursive.

<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 0pt;">(4) Writing Assignment 4: Devise a recursive algorithm.

(1-4) Module Quiz || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt;">The student will complete these assignments:

<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 0pt;">(1-4) Module Homework: Students will complete a variety of homework exercises to practice modular concepts. || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Advanced Counting || **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Module 5 Assessments ** || **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Module 5 Assignment Description ** || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Upon completion, students should be able to demonstrate competence in the topics covered. || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt;">Upon successful completion of this course, the student will have: <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 12pt 0.5in; text-indent: -0.25in;">1. Performed calculations using the multiplication rule, combinations and permutations. <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 12pt 0.5in; text-indent: -0.25in;">2. Calculated various probabilities. <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt 0.5in; text-indent: -0.25in;">3. Applied the Pigeonhole Principle. || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 0pt;">The student’s work will be assessed with: <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 12pt;">(2) Discussion forum: Describe your personal probability of completing your educational goals within four years. <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 12pt;">(1-3) Module quiz: Ten question quiz including multiple choice and true/false. <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 12pt;">(3) Writing assignment: Describe the Pigeonhole Principle and provide two uses of it. || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt;">The student will complete these assignments: **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt;">Discussion Forum: What’s Your Probability? **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt;">requires the student to discuss a personal probability of completing their educational goals within four years. **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt;">Module Quiz: **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt;">requires the student to complete a ten question quiz including definitions and calculations of modular objective concepts. **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt;">W ****<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt;">riting Assignment: Pigeonhole Principle **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt;">requires the student to use describe the Pigeonhole Principle and provide two detailed uses of it. || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Graphs || **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Module 6 Assessments ** || **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Module 6 Assignment Description ** || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Upon completion, students should be able to demonstrate competence in the topics covered. || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt;">Upon successful completion of this course, the student will have: <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt;">(2-3) Discussion forum <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt;">(1-3) Module quiz <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt;">(2) Writing assignment || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt;">The student will complete these assignments: || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Trees || **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Module 7 Assessments ** || **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Module 7 Assignment Description ** || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Upon completion, students should be able to demonstrate competence in the topics covered. || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt;">Upon successful completion of this course, the student will have: <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt 0.5in; text-indent: -0.25in;">1. First module objective. <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt 0.5in; text-indent: -0.25in;">2. Second module objective. <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt 0.5in; text-indent: -0.25in;">3. Etc. || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 0pt;">The student’s work will be assessed with: <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt;">(2-3) Discussion forum <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt;">(1-3) Module quiz <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt;">(2) Writing assignment || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt;">The student will complete these assignments: || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Boolean Algebra || **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Module 8 Assessments ** || **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Module 8 ** **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Assignment Description ** || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Upon completion, students should be able to demonstrate competence in the topics covered. || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt;">Upon successful completion of this course, the student will have:
 * **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Combined Course Library Description ** || **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Course Outcomes ** || **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Module 5 Objectives **
 * <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">This course is a study of discrete mathematics with emphasis on applications. Topics include number systems, combinations/permutations, mathematical logic/proofs, sets/counting, Boolean algebra, mathematical induction, trees/graphs, and algorithms.
 * 1) <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Identified and applied the <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt;">basic terminologies of functions, relations and sets.
 * 2) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Calculated permutations and combinations of sets and interpreted the meaning.
 * 3) <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">A <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt;">pplied formal logic proofs and logical reasoning to solve problems.
 * 4) <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Constructed <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt;"> logic statements with proper quantifiers.
 * 5) <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Applied counting principles including the pigeonhole principle.
 * 6) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 12pt;">Proven or disproven statements in elementary number theory using direct and indirect proof methods.
 * 7) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 12pt;">Identified and constructed various graphs and trees.
 * 8) <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 12pt;">Applied the basic concepts of Boolean algebra. || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 0pt;">Upon successful completion of this module, the student will have:
 * **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Combined Course Library Description ** || **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Course Outcomes ** || **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Module 6 Objectives **
 * <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">This course is a study of discrete mathematics with emphasis on applications. Topics include number systems, combinations/permutations, mathematical logic/proofs, sets/counting, Boolean algebra, mathematical induction, trees/graphs, and algorithms.
 * 1) <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Identified and applied the <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt;">basic terminologies of functions, relations and sets.
 * 2) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Calculated permutations and combinations of sets and interpreted the meaning.
 * 3) <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">A <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt;">pplied formal logic proofs and logical reasoning to solve problems.
 * 4) <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Constructed <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt;"> logic statements with proper quantifiers.
 * 5) <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Applied counting principles including the pigeonhole principle.
 * 6) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 12pt;">Proven or disproven statements in elementary number theory using direct and indirect proof methods.
 * 7) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 12pt;">Identified and constructed various graphs and trees.
 * 8) <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Applied the basic concepts of Boolean algebra. || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 0pt;">Upon successful completion of this module, the student will have:
 * 9) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Label graphs, paths and cycles.
 * 10) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Identify isomorphic and planar graphs. || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 0pt;">The student’s work will be assessed with:
 * **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Combined Course Library Description ** || **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Course Outcomes ** || **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Module 7 Objectives **
 * <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">This course is a study of discrete mathematics with emphasis on applications. Topics include number systems, combinations/permutations, mathematical logic/proofs, sets/counting, Boolean algebra, mathematical induction, trees/graphs, and algorithms.
 * 1) <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Identified and applied the <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt;">basic terminologies of functions, relations and sets.
 * 2) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Calculated permutations and combinations of sets and interpreted the meaning.
 * 3) <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">A <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt;">pplied formal logic proofs and logical reasoning to solve problems.
 * 4) <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Constructed <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt;"> logic statements with proper quantifiers.
 * 5) <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Applied counting principles including the pigeonhole principle.
 * 6) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 12pt;">Proven or disproven statements in elementary number theory using direct and indirect proof methods.
 * 7) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 12pt;">Identified and constructed various graphs and trees.
 * 8) <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Applied the basic concepts of Boolean algebra. || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 0pt;">Upon successful completion of this module, the student will have:
 * **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Combined Course Library Description ** || **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Course Outcomes ** || **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Module 8 Objectives **
 * <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">This course is a study of discrete mathematics with emphasis on applications. Topics include number systems, combinations/permutations, mathematical logic/proofs, sets/counting, Boolean algebra, mathematical induction, trees/graphs, and algorithms.
 * 1) <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Identified and applied the <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt;">basic terminologies of functions, relations and sets.
 * 2) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Calculated permutations and combinations of sets and interpreted the meaning.
 * 3) <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">A <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt;">pplied formal logic proofs and logical reasoning to solve problems.
 * 4) <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Constructed <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt;"> logic statements with proper quantifiers.
 * 5) <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Applied counting principles including the pigeonhole principle.
 * 6) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 12pt;">Proven or dis-proven statements in elementary number theory using direct and indirect proof methods.
 * 7) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 12pt;">Identified and constructed various graphs and trees.
 * 8) <span style="color: windowtext; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">Applied the basic concepts of Boolean algebra. || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 0pt;">Upon successful completion of this module, the student will have:

1. Verified properties and laws in Boolean algebra.

2. Constructed the sum-of-products expansion of Boolean functions.

3. Used a K-map to find a minimal expansion as a Boolean sum of Boolean products of functions. || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 0pt;">The student’s work will be assessed with: <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt;">(2-3) Discussion forum <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt;">(1-3) Module quiz <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt;">(2) Writing assignment || <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 9.5pt; line-height: normal; margin: 0in 0in 10pt;">The student will complete these assignments:

<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 0pt;">(1-4) Module Homework: Students will complete a variety of homework exercises to practice modular concepts. ||