This course introduces the concepts of finite mathematical structures. Topics
        include set theory, logic, proof techniques, functions and relations, graphs,
        trees, and combinatorics.

As a result of completing this course, the student will be able to do the following:
        1. Use critical thinking skills to solve problems by modeling the problem as an
                instance of the finite mathematical structures studied in the course;
        2. Demonstrate understanding of the concept of a finite mathematical structure
                based on experience with various examples of mathematical structures,
                especially those with application to computer science;
        3. Construct and understand proofs based on direct or indirect reasoning,
                mathematical induction, or the pigeonhole principle;
        4. Apply the basic operations for sets, namely, union, intersection, complement,
                and subset formation;
        5. Construct, interpret, and evaluate logical statements involving and, or,
                negation, and implication;
        6. Describe similarities and differences in the mathematical structures of sets
                and logical statements in terms of properties for the basic operations in each;
        7. Classify a relation as one-to-one, onto, or functional;
        8. Determine if a relation is an equivalence relation, a partial order, a permutation,
                or a tree;
        9. Given a finite relation, construct its incidence matrix, graph/digraph, and inverse;
        10. Compose two sets given as ordered pairs, incidence matrices, or graphs;
        11. Determine if a partial order is a Boolean algebra;
        12. Represent a Boolean function as a circuit;
        13. Traverse a tree in preorder, inorder, or postorder;
        14. Describe the language of a phrase structure grammar;
        15. Classify a grammar as Type 0, 1, 2 (context-free), or 3 (regular);
        16. Represent a context-free or regular grammar with syntax diagrams or in BNF notation.

I.      This course addresses the general education outcome relating to communication by providing
        additional support as follows:
        A. Students develop their listening skills through lecture and through group problem solving.
        B. Students develop their reading comprehension skills by reading the text and by reading
                the instructions for text exercises, problems on tests, or on projects. Reading
                mathematics text requires recognizing symbolic notation as well as analyzing problems
                written in prose.
        C. Students develop their writing skills through the use of problems that require written
                explanations of concepts.
II.     This course addresses the general education outcome of demonstrating effective individual
        and group problem-solving and critical-thinking skills as follows:
        A. Students must apply mathematical concepts previously mastered to new problems and situations.
        B. In applications, students must analyze problems and describe problems through pictures,
                diagrams, or graphs, then determine the appropriate strategy for solving the problem.
III.    This course addresses the general education outcome of using mathematical concepts to
        interpret, understand, and communicate quantitative data as follows:
        A. Students must demonstrate proficiency in problem-solving skills including applications of
                finite mathematical structures, functions and relations, graphs, combinatorics and logic.
        B. Students must write functions to describe real-world situations and interpret information
                from both the function (relation) rule and the graph of the function (relation).
        C. Students must solve problems in combinatorics, graph theory and logic that often arise in
                modeling numerical relationships.

  1.      Sets and Logic
        2.      Proof Techniques
        3.      Relations and Functions
        4.      Combinatorics
        5.      Graphs and Trees


ENTRY LEVEL COMPETENCIES
Upon entering this course the student should be able to do the following:
        1.      Analyze problems using critical thinking skills.
        2.      Use algebraic symbols to make a meaningful statements.
        3.      Identify a function.
        4.      Compose two functions.
        5.      State the domain and range of a function.
        6.      Sketch and identify a one-to-one function and its inverse.
        7.      Find the inverse of a linear function.

I.      COURSE GRADE
        Exams, assignments, and a final exam prepared by individual instructors will be used
        to determine the course grade.

II.     DEPARTMENTAL ASSESSMENT
        This course will be assessed every five years. The assessment instrument will consist
        of a set of free response questions that will be included as a portion of the final
        exam for all students taking the course.

        A committee appointed by the Executive Committee of the Mathematics Academic Group
        will grade the assessment instrument.

III.    USE OF ASSESSMENT FINDINGS
        The Math 2420 Committee, or a special assessment committee appointed by the Executive
        Committee of the Mathematics Academic Group, will analyze the results of the assessment
        and determine implications for curriculum changes. The committee will prepare a report
        for the Academic Group summarizing its finding.


EFFECTIVE DATE: August 2004                     APPROVED DATE: April 2004