Summer 2008   Blackboard Vista Online Course
CCA’s Summer Online Courses start on
Monday, June 2^nd, 2008.

COURSE SYLLABUS

Community College of Aurora

Mathematics for Liberal Arts

SECTION I: COURSE IDENTIFICATION

COURSE TITLE: MATHEMATICS FOR LIBERAL ARTS

COURSE DESCRIPTION:

Prerequisite: Successful completion Math 090 (grade C or better) or assessment.

This course develops mathematical and problem-solving skills.  Appropriate technological skills are included.  Content is selected to highlight connections between mathematics and the society in which we live.  Topics include set theory and logic, mathematical modeling, probability and statistical methods, and consumer mathematics.  Additional content will include one topic in geometry, numeration systems, decision making.

COURSE MATERIALS:

REQUIRED TEXTS: Mathematics In Our World, Allan G. Bluman

REQUIRED MATERIALS: Scientific calculator. TI-83 recommended.

OPTIONAL MATERIALS: Student’s Solutions Manual

Other

CCA will provide accommodations for qualified students with disabilities. To request an accommodation, contact the Accessibility Services Coordinator, Reniece Jones, at your earliest convenience.  The Accessibility Services office is located in the Learning Resource Center (LRC) in the Student Centre building on the Centre Tech campus.  Arrangements may also be made at the Lowry Campus.  You may contact Reniece at (303)361-7395 V/TDD or e-mail:  Reniece.Jones@ccaurora.edu.

SECTION II STUDENT OUTCOMES AND COURSE OUTLINE

INSTRUCTIONAL GOALS

 The Instructional Unit has identified the following lifelong/workplace skills that are the foundation for your course of study at CCA: Communication, Critical Inquiry, Intra/Interpersonal Responsibility, Quantitative Reasoning, Technology, and Aesthetic Perception. Of these skills, this course will focus on:  calculating loans, annuities, organizing and visualizing data and other skills.

GENERAL LEARNING OUTCOMES OF THE COMMUNITY COLLEGE OF AURORA

Successful students will have shown through in-class exercises and specific course assignments the ability to pursue and retain knowledge, comprehend the various significant levels of acquired knowledge (analyzing and identifying their various components), evaluate the significance of that knowledge, synthesize ideas from multiple sources, and apply what is learned to work and life situations.

GENERAL  OUTCOMES

Successful occupational and technical students will be able to:

1.    Perform tasks related to specific jobs or cluster of jobs.

2.    Understand the conceptual framework underlying the acquired technical skills.

3.     Demonstrate an understanding of personal and work characteristics that contribute to

      effective job performance.

SPECIFIC COURSE OUTCOMES

The student will be given the opportunity to:

Course Competencies:

I.          Solve problems involving principles of set theory and logic.

II.         Solve problems involving mathematical modeling. 

III.       Solve problems involving probability.

IV.       Solve problems involving statistics .

V.        Solve problems involving consumer mathematics

VI.    One of the following competencies is also required.

    1.         Solve problems involving Euclidean geometry.

    2.         Solve problems involving varying numeration systems. 

    3.         Solve problems involving mathematics of social choice.

    4.         Solve problems involving management science.

Topical Outline:

I.          Solve problems involving principles of set theory and logic. 

            A.        Describe well-defined sets using set theory notation and terminology.

            B.         Determine subsets of sets.

            C.        Find the union, intersection, and complement of sets using Venn diagrams.

D.        Find combinations of unions, intersections and complements of sets using Venn diagrams.

E.         Solve applications involving overlapping sets of data using Venn diagrams.

F.         Distinguish between inductive and deductive reasoning.

G.        Write statement in symbolic form using the connectives for conjunction, disjunction, and negation.

H.        Relate conjunction, disjunction, and negation to the set operations of intersection, union, and complementation.

I.          Write conditional and biconditional sentences using symbols of logic.

J.          Write converses, inverses, and contrapositives of given statements using logic notation.

K.        Construct truth tables to write arguments symbolically.

L.         Construct truth tables to determine validity of reasoning by converse, inverse, or contrapositive.

M.        Construct truth tables to determine whether or not pairs of statements are logically equivalent.

II.         Solve problems involving mathematical modeling.

            A.        Explain the meaning of a function, its domain and range.

            B.         Test whether or not a relationship between two variables is a function.

C.        Identify and plot the graphs of linear functions.

D.        Solve applications involving linear functions.

E.         Solve linear inequalities in one variable.

            Solve applications involving linear programming.

F.         Identify and plot the graphs of quadratic functions.

G.        Solve applied problems involving quadratic functions.

H.        Identify and plot the graphs of exponential functions.

I.          Solve applications involving exponential functions.

J.          (Optional)  Identify and plot the graphs of logarithmic functions.

            (Optional)  Solve applied problems involving logarithmic functions.

III.       Solve problems involving probability. 

            A.        Describe the sample spaces of experiments.

            B.         Apply basic probability rules.

C.        Identify theoretical and experimental approaches to assigning probabilities.

D.        Determine the possible number of outcomes using the multiplication rule.

E.         Calculate permutations and combinations.

F.         Solve applications involving basic counting rules.

G.        Evaluate probabilities involving the union and/or intersection of events.

H.        Calculate probabilities involving conditional, dependent, independent and mutually exclusive events.

I.          Calculate odds.

J.          Calculate expected values.

IV.       Solve problems involving statistics. 

            A.        Explain the difference between descriptive and inferential statistics.

            B.         Create various graphical presentations of data.

            C.        Interpret varying graphical representations of data.

D.        Identify populations and samples.

E.         Calculate the mean, median and mode of sets of data given numerically or pictorially.

F.         Evaluate and interpret the range, variance and standard deviation of ungrouped data.

G.        Identify normal distribution curves.

H.        Calculate z-values.

I.          Calculate probabilities/percentages in applications using z-values.

V.        Solve problems involving consumer mathematics. 

A.        Calculate simple interest, or amount, principal, simple interest rate or time given the other three.

B.         (Optional)  Calculate credit card finance charges given a monthly or periodic rate.

C.        Calculate compound amount, present value, annual interest rate, and periods of compounding using the formula for compound interest.

D.        Calculate effective rates.

E.         Describe the effect of inflation.

F.         Calculate the time for money to double at a fixed rate with compound interest and the rate needed for money to double in a fixed amount of time.

G.        Describe the major types of annuities.

H.        Calculate the future value of an annuity using a formula.

I.          Calculate the present value of an annuity using a formula.

J.          Find the size of payment necessary to pay off a loan.

K.        Construct an amortization schedule.

“ONE” OF THE FOLLOWING TOPICS (VI – IX) IS ALSO REQUIRED.

1.         Solve problems involving Euclidean geometry. 

a.         Define and identify points, lines and planes, and determine relationships among them.

b.         Define and recognize the basic types of angles and the special angle relationships resulting from two parallel lines cut by a transversal.

c.         Define and distinguish among varying types of polygons, including triangles and quadrilaterals.

d.         Describe what the Fibonacci sequence is and determine the first terms of the sequence.

e.         Give examples of where the Fibonacci sequence occurs in architecture, nature or the human body.

f.          Describe what the Golden ratio is and give examples of where it is found in architecture, art or nature.

(Choose one of the following two topics.)

g.         Fractal Geometry

            1.         Describe what a fractal is.

            2.         Give examples of fractals that occur in nature.

3.         Continue a fractal construction given a description of a fractal and the first few steps in its construction.

h.         Tessalations.

            1.         Explain what a tessalation is.

            2.         Depict the three regular polygons that tessalate a plane.

3.         Tessalate a small area using translation and/or reflection principles on one of these three regular polygons.

4.         Give examples of where tesselations are found in our environment.

2.         Solve problems involving varying numeration systems. 

            a.         Symbolize counting numbers from different cultures.

            b.         Convert numerals from one system to another.

c.         Perform addition and subtraction with numerals from other numeration systems.

d.         Describe the origin of our own system of numeration.

e.         Convert between differing number bases.

f.          Perform simple computations involving previous calculating devices, i.e., abacus, Napier’s bones, slide rule, etc.

g.         Relate the binary system to modern-day calculating devices, such as computers and calculators.

3.         Solve problems involving mathematics of social choice. 

            a.         Describe the most common and popular voting systems.

            b.         Use different voting methods to determine election results.

c.         Use criteria that society believes to be rational and reasonable to judge whether a voting system is always fair and sensible.

d.         Give examples of where weighted voting systems are used in the world of business and politics.

e.         Use the Banzhaf Power Index to determine relative voting power.

f.          Use different apportionment methods to determine fair shares.

g.         Identify various flaws and paradoxes of apportionment methods.

4.         Solve problems involving management sciences. 

            a.         Determine whether or not a graph has an Euler circuit.

            b.         Use an algorithm to find at least one Euler circuit if the graph has one.

c.         Determine whether or not a graph has a Hamiltonian cycle and find one if it does.

d.         Use a heuristic algorithm to find Traveling Salesman Problem (TSP) routes and evaluate the efficiency of the routes.

e.         Give examples of where alternate interpretations of the Traveling Salesman Problem might be applied to networking applications in the real world.

f.          Use an algorithm to find a minimum spanning tree for a graph.

g.         Determine the shortest network linking more than three points.

h.         Design a flowchart (network) for a project with multiple stages or tasks.

i.          Determine the condition under which a project remains on schedule and the conditions under which it falls behind.

SECTION III: EVALUATION PROCEDURES

OVERALL STRATEGIES

This course will cover selected chapters (1,2,3,5,7,8,9,10,12) of the book and additional selected information. Student progress may be based on a combination of activities such as homework, quizzes, handouts, papers, tests, and participation. Each student will be responsible for all assignments required whether listed in the syllabus or assigned by email without prior notice. Timely completion of assignments, participation, and the tested ability to apply learned knowledge to common-life experiences will weigh toward the grade.

CLASS POLICIES:  This course is broken into nine distinct chapters.  You will not want to fall behind and then try to play catch-up.  By communicating with your instructor regularly and doing your assignments nightly, you will be successful in this course.  Calculators will be needed in this course, and are not supplied by the instructor.  A scientific calculator will be sufficient.  Grades will be based on participation, homework/quiz assignments (MathZone), and one Final exam, ( available from the last two weeks of November-2007, you can take it in the Tutoring Lab on Tue. or Thurs. 12:30-3:30pm with me or in the Testing Center *.  Extra credit may be given during the semester and within the assignments. 

The Community College of Aurora Math Department web page provides other important information that the student may need.  This site contains information such as course prerequisites, syllabus, contact numbers, tutoring, course assessment, and other important information.  The student may also check  the Learning Research Center (LRC) website for any other resources. (Testing Center)*(S202;  phone: 303-360-4736)

ASSIGNMENTS: All assignments from MathZone will be taken online. 

They are due by May 12/08. Please do them regularly throughout the semester, the date and time you do it will be recorded, extra credit could be assigned if you do the work every week. Remember your course code in MathZone is: AFA-FA-648

Please go to Announcements in your course home page to see instructions to log in MathZone.

PARTICIPATION:  There are a few links within this web site where the student can obtain participation points.  The student can also obtain participation points by communicating and visit (C-101. Tutoring Lab Tue. and Thurs. 12:30-3:30pm) with the instructor regularly and accessing and working on the website. (MathZone) 

IMPORTANT DATES:  The student should be aware of all the important dates for the college semester.  Please check the college website for important dates such as withdrawal dates and holidays.  Although holidays are enforced in campus, the online course calendar for this class is continuous. .