FUNDAMENTALS OF MATH, MATH 102

1. Catalogue Description

Students seeking a general knowledge of mathematics should take this course. Topics included are: set theory, mathematical logic, number theory, number systems, algebra and geometry.

Prerequisite: Ma 098 Algebra for College or equivalent in high school

(3 credits)

2. Goals

A. To provide insight into what mathematics is, what it accomplishes, and how it is pursued as a human enterprise.

B. To provide experience with a variety of problem solving techniques and strategies.

C. To provide experience with the different areas of mathematics and how each is applied to a variety of disciplines.

D. To create opportunities for the successful study of mathematics.

E. To acquire the ability to think critically and analyze information displayed graphically.

F. Students will acquire the ability to read, write, and communicate mathematically.

3. Procedures

A. Reading of the text and written homework exercises

B. Lecture/Discussion

C. One or more projects in which students may use a variety of materials such as computers, artistic presentations, film or research skills to elaborate upon one of the topics of the course.

D. Computer tutorials which accompany the text.

4. Course Content

A. Critical Thinking Skills

1. Inductive Reasoning

2. Estimation

3. Problem Solving

B. Set Theory

1. Introduction

2. The Different Kinds of Sets

3. Subsets and Set Operations

4. Using Venn Diagrams to Understand Sets

5. Applications of Sets

6. Infinite Sets

7. Summary

C. Logic

1. Inductive and Deductive Reasoning

2. Nature and Patterns of Inductive Logic

3. Using Venn Diagrams to Test Validity

4. Applications to Arguments

5. Application to Switching Circuits (Optional)

D. Different Number Systems

1. Base 10 Number System

2. Other Bases

3. Converting From Other Bases to Base 10

4. Converting From Base 10 to Other Bases

5. Applications to the Computer (Optional)

6. Applications to the Game of NIM (Optional)

7. Some Interesting Numbers (Optional)

8. Prime Numbers and Prime Factorization

9. Large and Small Numbers - Scientific Notation

10. Metric System

E. Real Number System

1. Natural, Whole Numbers, and Integers

2. Divisibility

3. Rational Numbers

4. Irrational Numbers

F. Geometry

1. Similar and Congruent Triangles

2. Euclidean Geometry

3. Non Euclidean Geometry

4. The Konigsberg Bridge Problem

5. The Mobius Strip

G. Probability

1. Nature of Probability

2. Theoretical Probability

3. Odds

4. Tree Diagrams

5. "Or" and "And" Problems

6. Conditional Probability

7. The Counting Principle and Permutations

8. Combinations

H. Statistics

1. Sampling Techniques

2. The Misuses of Statistics

3. Frequency Distributions

4. Statistical Graphs

5. Measures of Central Tendency

6. Measures of Dispersion

7. The Normal Curve

5. Evaluation Methods

a. In-class tests. Questioning formats will vary depending on the topic. Some will be multiple choice, some fill in the blank, some short essay and others will require some mathematical processes to identify the correct result. (25%-60%)

b. Periodic quizzes may be given on a frequent basis to motivate the students. (10% of grade)

c. Students’ ability to communicate mathematically, orally and in writing, will be assessed. Weekly written explanations (prepared outside of class and 1 page typed) are required. (10%-25% of grade)

d. One or more projects or papers. Papers will be 5 typewritten pages medium. The project must include a bibliography and be presented in the standard format for term projects. (10% of grade)

e. Final Exam. A comprehensive final exam will be administered. Questions will be in a variety of formats. (20%-30% of grade)

6. Bibliography

a. Required Text

Angel, Allen R and Porter, Stuart R., A Survey of Mathematics with Applications, 4th Ed., Addison-Wesley Publishing, New York, 1993.

Setlek, William M., Fundamentals of Mathematics, 5th Ed., MacMillan Publishing Co., New York, 1991.

Smith, Karl J., The Nature of Mathematics, 7th Ed., Brooks/Cole Publishing, Pacific Grove, Calif., 1995.

b. Supporting Bibliography

Ascher, Marcia, Ethnomathematics: A Multicultural View of Mathematical Ideas, Brooks/Cole Publishing, Pacific Grove, Calif., 1991.

Britton, Jack and Bello, Ignacio, Topics in Contemporary Mathematics:, 3rd Ed., Harper & Row Publishing, New York, 1990.

Garfunkel, Solomon, Director, Consortium for Mathematics and Its Applications (COMAP), For All Practical Purposes: Introduction to Contemporary Mathematics, W.H. Freeman & Co., New York, 1988.

Gudder, Stanley, A Mathematical Journey, 2nd Ed., McGraw Hill, New York, 1994.

Meserve, Bruce E., Sobel, Max A. and Dossey, John A., Contemporary Mathematics, 4th Ed., Prentice Hall, Englewood Cliffs, N.J., 1987.

Newmark, Joseph and Lake, Frances, Mathematics as a Second Language, 4th Ed., Addison-Wesley Publishing, 1988.

Smith, Karl J., Mathematics: Its Power and Utility, Brooks/Cole Publishing, Monterey, Calif., 1983.

Staszkow, Ronald, Bradshaw, Robert, The Mathematical Palette, 2nd Ed., Saunders College Publishing, Orlando, Fla., 1995.

Wheeler, Ruric E., Modern Mathematics, 8th Ed., Brooks/Cole Publishing, Pacific Grove, Calif., 1992.