VIRGINIA HIGHLANDS COMMUNITY COLLEGE

SYLLABUS

 

COURSE NUMBER AND TITLE

MTH 151 - Mathematics For The Liberal Arts I (Fall, 1998)

COURSE DESCRIPTION

This course is intended for students in a liberal arts curriculum that are not planning to major in math or science field. Topics presented include sets, logic, numeration systems, geometric systems, and elementary computer concepts. Lecture 3 hours per week. Prerequisites: a placement recommendation for MTH 151 and Algebra I, Algebra II, and Geometry, or equivalent.

BROAD GOALS OF COURSE

(Communication/ (1) To help students develop the ability to read, understand, interpret,

Learning Skills) and write about mathematics.

(Interpersonal Skills & (2) To develop responsibility for regular attendance and completion

Human Relations) of work in a timely fashion as would be expected by an employer.

(Computational & (3) To develop skill in using a graphing calculator or computer as a

Computer Skills) problem-solving tool.

(Understanding Science (4) To provide an understanding of the development of mathematics

and Technology) and its application to the world around us by exploring different branches of mathematics.

(Critical Thinking) (5) To apply mathematics to solve problems.

UNITS TO BE COVERED

Chapter 1 - Sets and Problem Solving

Chapter 2 - Logic

Chapter 3 - Numeration Systems

Chapter 7 - Geometry

Chapter 8 - Mathematical Systems and Matrices

Chapter 12 - Your Money and Your Math (Optional)

SPECIFIC OBJECTIVES

Are given in each chapter in the textbook.

Chapter 1 - Sets and Problem Solving

  1. To describe what problem solving is and what it is not.

    2. 2. To identify the mathematician George Polya with problem solving and to describe Polya=s heuristic/algorithim.

  2. To describe what an algorithm is and to give an example of one.

    3. 4. To use some common strategies for problem solving.

  3. To describe the mathematical modeling process.

    4. 6. To use some mathematical models.

  4. To decide which among several mathematical models is most appropriate.

    5. Chapter 2 - Logic
  5. To give a description of the historical development of the subject of logic, including some approximate dates, the names of some people involved, and some important concepts that have developed.

    6. 2. To understand and use the notation and terminology associated with symbolic logic.

    3. To consider conjunction, disjunction, and negation as operations on statements, and to relate these operations to the set operations of intersection, union, and complementation.

    4. To construct truth tables for compound statements.

  6. To work with conditional and biconditional statements.

    7. 6. To know the relations among a statement, its converse, its inverse, and its contrapositive.

  7. To analyze arguments and discuss their validity.

    8. 8. To determine when statements are equivalent.

  8. To use DeMorgan=s Laws and other known information to write a statement in an alternate form.

    9. Chapter 3 - Numeration Systems
  9. Develop an understanding of our numeration system by studying several ancient systems.

    10. 2. Convert between number bases.

  10. To describe the historical development of fractions and decimals.

    11. 4. To do arithmetic with fractions including unit fractions, comparison, and converting between fractions and decimals.

  11. To describe a need for and the origin of integers and to review arithmetic involving negative integers.

    12. 6. To find check digits for numbers by three different schemes

    Chapter 4 - Geometry

    1. To outline briefly the origins of geometry.

    2. To know properties of points, lines, planes, rays, segments, half-lines, half-planes, and angles.

  12. To solve problems involving supplementary and complementary angles.
  13. To solve problems involving parallel and perpendicular lines.
  14. To use terms applying to polygons in general and to triangles and quadrilaterals in particular.
  15. To know and use the Pythagorean theorem and to work with Pythagorean triples.
  16. To work with similar triangles.
  17. Find perimeter, area and circumference of common plane figures.
  18. Briefly examine topics from non-Euclidean geometry, topology, and graph theory.

    19. Chapter 5 - Mathematical Systems and Matrices
  19. Lise matrices to solve systems of equations.

    20. 2. Use clock and modular arithmetic to solve problems.

  20. Recognize an abstract mathematical systems as a group or field.

    21. 4. Apply game theory to business problems, games of chance, and military science.

    Chapter 6 - Your Money and Your Math
  21. Solve verbal problems concerning interest, taxes, discounts, credit cards, consumer credit, annual percentage rate, and buying a house.

GRADING CRITERIA

There will be five (six, if time allows) and a final exam. No make-up tests will be given. If one test is missed, the final exam will substitute for that test grade. A test may be taken early (before the scheduled time) if discussed with professor in advance. The final grade will be the average of four (five) test scores and a final exam (equal weight). A student with a 90% test average may be exempt from the final exam. If a student takes all five (six) chapter tests, the lowest of the first four (five) grades will be dropped.

Letter grades for the course will be assigned as follows:

 

Average

Grade

90-100

80-89

67-79

50-66

Below 50

A

B

C

D

F

Cheating is unacceptable and will be handled in accordance with the VHCC Honor System.

INSTRUCTIONAL MATERIALS

Textbook - Topics in Contemporary Mathematics, by Ignacio Bello and Jack R. Britton, Houghton Mifflin Company, Boston, 1997.

Calculators are acceptable for use in this course. TI-85 calculators will be provided for classroom use when needed. Four of these calculators are available for student use in the library.