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MAT 117

I.  TITLE:   Mathematical Concepts

II. CATALOG DESCRIPTION:  Provides students with skills and literacy related to the mathematics which is commonly encountered in our society.  Topics include descriptive statistics, analysis and problem solving, growth patterns with an emphasis on social choice, management science, and probability.  This course is especially appropriate for students whose degree programs do not otherwise require a course in mathematics.

III. PURPOSE:  This course is designed to give students a view of Mathematics broader than that they received from their high school experience.  That is, a view of Mathematics as a mode of thought rather than as a discipline comprised only of algebra and other computational skills.  To this end, students are introduced to problems of fairness, decision making, planning, and data interpretation in the social sciences, business, personal finance, and organizational management. There is a wide array of problems, ranging from those problems which they likely did not know existed to those with which they are familiar from every day life, to those which they would have never expected involved Mathematics at all.  In this way, students not only are shown the relevance and surprising versatility of Mathematics, but also are introduced to some important concerns of society.  Through the discussion of these problems, the students can gain insight into why each problem is important, why its solution is non-trivial, and why Mathematicians address each problem in the way they do.  In addition, by instructor requirements that student work (exams, projects, presentations) be composed with precision appropriate to the task, students better understand the precision necessary within Mathematics and can perhaps express themselves more effectively as well.  Chapters addressing statistics, opinion polls, social choice, and some associated pitfalls, help students learn to be better voters and more critical listeners to public discourse.  Chapters addressing probability, arithmetic growth, and geometric growth help students become more discerning individuals, consumers, and investors.  Finally, chapters on topics in management science teach students how to follow basic algorithms and help students understand how industry works toward optimal results by appropriate planning.

IV. COURSE OBJECTIVES: By the end of the semester, students should
    A)   be able to identify potential bias in surveys;
    B)   know the difference between a survey and an experiment;
    C)   be able to identify confounding in experiments;
    D)   understand the placebo effect;
    E)   know the meaning and purpose of measures of central tendency such as the mean and median, and measures of
          dispersion such as standard deviation and quartiles.
    F)   know how to interpret statistical information;
    G)   be able to read statistics (and charts) critically;
    H)   be able to collect data appropriately and then be able to illustrate characteristics of the data using (as pertinent)
           histograms, charts, the mean, median, five-number summaries, variance, and standard deviation;
    I)    have an basic understanding of probability;
    J)    know the implications when data is normally distributed;
    K)  be able to interpret the margin-of-error of a poll;
    L)   understand strategic voting;
    M)  understand that the outcome of an election or vote may depend upon the method of voting employed for the election;
    N)  be aware that the mathematical search for a good voting method began with the task of precisely defining the term
          'good voting method'
    O)   have an idea of what an impossibility theorem is;
    P)   understand the difference between geometric growth and arithmetic growth;
    Q)   be able to use compound interest and annuity formulae
    R)   be able to organize information within an appropriate framework (whether this framework is a graph, a matrix, or  a
           mixture chart);
    S)   be able to carefully follow an algorithm or a basic method of solving a problem and then be able to interpret the results;
    T)   have some grasp and personal glimpse of the idea that Mathematics is what one does when one takes a puzzle,
          identifies and discards all extraneous information, finds some underlying structure to what remains, logically puts these
          remaining pieces of the puzzle together according to this structure, and then interprets the result.

V. CONTENT OUTLINE:
    1) The Science of Data
     a)  Sampling
     b)  Experimentation
     c)  Measures of central tendency and measures of dispersion
     d)  Normal Distributions
     e)  Perils of Data Analysis
    2) Decision Making
     a)  Voting methods, strategic voting
     b)  Arrow’s Impossibility Theorem
     c)  Fair division and Apportionment
     d)  Game Theory and Matrices
    3) Growth
     a)  Arithmetic growth
     b)  Geometric growth
     c)  Applications to biological models
     d)  Applications to financial models
    4) Management Science
     a)  Graphs (or networks)
     b)  Minimum cost spanning trees
     c)  Critical Path Analysis
     d)  Linear Programming

VI.  INSTRUCTIONAL ACTIVITIES:  Class time may be spent on class discussions, group work on written projects or simulations, student presentations of the results of projects and simulations, teacher presentation of new topics, or on student solution of example exercises (with instructor guidance, as necessary).

VII.  FIELD AND CLINICAL EXPERIENCES:  While there is not a laboratory for this course, there may be in-class projects and/or simulations.

VIII.  RESOURCES:  Besides the textbook (listed below), on file in the Science Resource Center is a set of videos which accompany the entire text.  In addition, many instructors use current newspapers to accompany sections on voting, opinion polls, and finance. In addition, there are the office hours of the instructor.

IX.  GRADING PROCEDURE:   The course grade will be based on quizzes (5-15%), project grades (10-15%), regular hour exam grades (50-70%) and a comprehensive final exam (20-30%).  Short quizzes may be given as often as daily, and they may address anything from a topic in a reading assignment or group project, to skill exercises similar to those already assigned.  Projects are typically in-class group activities which are extensions of a concept or an application of current interest.  The group report for the project (sometimes oral and sometimes written) is evaluated on the basis of clarity, and completeness; later, a quiz may be given which asks each member of the class a question relevant to the project completed by their group.  Project grades for an individual may be based on these two results.  The regular hour exams test how well the student has assimilated concepts and skills discussed since the previous exam.  The final exam is a comprehensive survey of topics covered that semester.  Due to the objectives of the course, the core concepts and core skills receive roughly equal emphasis.  The level of expertise expected is consistent with the course objectives.  The grading scale for the course is:

     90 < A < 100%
     80 < B < 90%
     70 < C < 80%
     60 < D < 70%
       0 < E < 60%

X.  ATTENDANCE POLICY:   Attendance will be noted each class period.  Typically, a penalty (which may vary with instructors) is imposed for missing more than 10% of the classes.

XI.  ACADEMIC HONESTY POLICY:  Cheating and plagiarism (submitting another person's material as one's own, or doing work for another person which will receive academic credit) are not permitted. This includes 1) the use of unauthorized notes on an exam,   2) looking at the exam of another or allowing another to look at your exam,  3) taking an exam for another or having another take an exam for you, 4) telling others the contents of an exam they have not yet taken or soliciting from others the contents of an exam which you have not taken, and 5) copying the contents of another's take-home assignment or allowing another to copy the contents of your take-home assignment (this does not include working together, with mutual understanding, on a take-home assignment or group project).  The result of non-premeditated cheating will be a zero for that assignment.  The result of premeditated, an ‘E’ for the course.  Repeated offenses might result in expulsion from Murray State University.

XII.  TEXT AND REFERENCES:  Current

XIII.  PREREQUISITES:   ACT Mathematics standard score of at least 20, or MAT 105.

Last updated February 14, 2000. Designed and maintained by Kyosung Koo