Catalog Description

MATH 124 INTRODUCTION TO MATHEMATICAL THOUGHT (4-0-4)(F,S)(Area III). Emphasis is on the nature of mathematical knowledge, its meaning, methodology and use. Usually topics are selected from elementary materials in set theory, logic, number theory, algebra, geometry, probability, statistics, graph theory. PREREQ: MATH 25 or satisfactory score on mathematics placement examination.

Prerequisites

MATH 25 or satisfactory score on mathematics placement examination.

Jurisdiction

This course is overseen by a departmental committee. The choice of a text book, if any, as well as the administration of examinations and the choice grading system are left to the instructor.

Learning Objectives

As a course in Mathematics, the objectives of MATH 124 include that students be able to:

1. describe the cultural role of mathematics in civilization;
2. explain the significance of a few important mathematical results;
3. solve some problems from elementary mathematics.

Upon completion of this course, students should be able to:

1. explain the significance of at least four important mathematical results;

2. use these mathematical results to solve related mathematical problems;

3. give a brief biographical description of at least one famous mathematician;

Assessment of Learning Objectives

Students will be assessed by evaluating their ability to meet the learning objectives. The assessments may occur in several contexts:

• Periodic problem sets for homework serve both as learning and as assessment tools. Classroom activities may vary depending on students' outcomes on homework assignments.

• Questions given on take-home exams are designed to evaluate a student's ability to solve more complicated and time consuming problems.

• Problems given on in-class exams are designed to give students the opportunity to demonstrate their ability to work simpler and less time consuming problems.

• Some instructors also have students complete either group or individual projects which are graded.

Core Outcomes

After successfully completing MATH 124, students will be able to demonstrate the following competencies in order to fulfill specific requirements set by the Core Philosophy and Goals statement.

1. Critical Thinking/Problem Solving Skills

   Clearly identify and analyze a problem, identify possible solutions and give the rationale for a preferred solution.

   Students will be asked to identify, analyze, solve and justify their solutions to problems as a normal part of the work assigned in this course.

2. Communication Skills

   Employ speaking, listening, and interpersonal communication skills appropriate to various rhetorical situations.

   Students are expected to participate in classroom discussions regarding the cultural impact of mathematical ideas. Students are also expected to use correct mathematical notation and grammar when writing up their solutions to problems.

3. Cultural Perspective

   Make meaningful comparisons between the creative accomplishments of their own and other cultures.

   Students in MATH 124 learn more about the historical development of mathematics and the cultural influences than they do in any other mathematics course. Students are expected to recall this information and to write about the influence of mathematics in human society.

4. Breadth of Knowledge and Intellectual Perspective

   Apply appropriate critical thinking/problem solving skills and communication skills in discipline-specific contexts.

   Students are given many opportunities to develop and use their problem solving skills and to communicate their solutions throughout the course. Their individual problem solving skills are assessed during exams and other individual work.

Topics and Approximate Timeline

The following table is based on a typical semester schedule-60 class meetings of 50 minutes each. The list below gives a selection of topics that have been covered in MATH 124. The actual selection of topics and the amount of time spent on each selected topic varies from semester to semester and instructor to instructor. It has happened that a single topic was covered in great depth per semester, or several topics were covered with more emphasis on breadth.

In light of this variation, no time allocation is set for the topics.

• Elementary Set Theory
• Relations; Functions (including exponential and logarithmic functions and their applications)
• Mathematics and Art
• Elementary Logic
• Elementary Number Theory (included: Cryptography)
• Elementary Modern Algebra
• The Axiomatic Method (included: Euclidean and Non-Euclidean Geometries)
• Map Coloring
• Elementary Graph Theory

Text

There is no single prescribed or required text for the course. Several textbooks have been published for this course in recent years; here is a sample list of such textbooks:

A Mathematics Sampler: Topics for the Liberal Arts, Berlinghoff and Grant, Ardsley House.
A Mathematical Journey, Stanley Gudder, McGraw-Hill,Inc., 1994.
Fundamentals of Mathematics, William M. Setek,Jr., Prentice-Hall (1996)
Excursions in Modern Mathematics, P. Tannenbaum and R. Arnold, Prentice-Hall (1998)
For all practical purposes, COMAP Inc., W.H. Freeman and Company (1997)
Mathematics: One of the liberal arts, T.J. Miles and D.W. Nance, Brooks/Cole Publishing Company (1997)

Format, Student Activities, and Grades

Class meetings involve a combination of lecture, questions and discussion, and sometimes small group activity or special projects; the instructor chooses the appropriate mix. The computer algebra system, Maple, is sometimes used for laboratory activities and homework. Homework is an important part of the course. Exams may be take-home or in-class. The instructor chooses the exact grading scheme, but a typical distribution might be: