Standard Course Syllabus

MAT 101

Survey of Mathematics 1

COURSE NUMBER:MAT-101

COURSE TITLE:Survey of Mathematics 1

DEPARTMENT:Mathematics and Computer Science

CREDITS:3

PREQUISITES:MAT 050 (Grade C or better) or placement by exam

COREQUISITES:none

COURSE DESCRIPTION:

Intended to meet minimum college requirements in mathematics. Explore the role of mathematics in modern culture, emphasizing techniques and applications in the social, natural, and management sciences, as well as those in technological fields. Topics studied may include: problem solving, real numbers, number theory, set theory, logic, consumer math, geometry, probability, and statistics.

NOTE: TOPICS COVERED, AND THEREFORE, GOALS AND OBJECTIVES, WILL INCLUDE A CHOICE OF SEVERAL OF THOSE OUTLINED BELOW.

COURSE GOALS:

  1. Engage in both inductive and deductive reasoning.
  2. Explore set theory and apply the concepts to solve counting problems.
  3. Be introduced to symbolic logic and apply the concepts to analyze arguments.
  4. Study statistics as the science of data.
  5. Study the real number system and its algebraic properties.

STUDENT LEARNING OBJECTIVES or OUTCOMES:

Upon successful completion of this course, students will be able to:

Goal 1:

  1. Identify when inductive or deductive reasoning has been used.
  2. Use inductive reasoning to formulate a conjecture.
  3. State the difference between a conjecture and a mathematical theorem.
  4. Use reasoning to formulate the problem solving strategies.

Goal 2:

  1. Use listing or set-builder notation to designate a variety of sets.
  2. List subsets of a given set and give the cardinal number of each subset.
  3. Compute with set operations such as complement, union, difference and intersection.
  4. Construct accurate Venn diagrams.
  5. Use Venn diagrams to solve counting problems.

Goal 3:

  1. Identify a well-defined statement and write out its negation.
  2. Symbolize compound statements using symbolic logic notation.
  3. Construct a truth table for a given compound statement.
  4. Decide if two compound statements are equivalent.
  5. Use a truth table to decide whether an argument is valid or invalid.
  6. Use an Euler diagram to decide whether an argument, which involves quantifiers, is valid or invalid.

Goal 4:

  1. Recognize standard sampling methods and evaluate the quality of the design of an experiment.
  2. Evaluate distributions using the median, mean, five-number summary, standard deviation and regression lines.
  3. Define probability and calculate probabilities involving equally likely outcomes.
  4. Find the mean of a random phenomenon.
  5. Recognize normal distributions, apply the 68-95-99.7 rule, and apply the Central Limit Theorem.
  6. Estimate a population proportion and calculate confidence intervals.

Goal 5:

  1. Identify a real number and classify it as natural or irrational.
  2. Use properties of and operations with real numbers to simplify numerical expressions.
  3. Identify a real number written in decimal notation as rational or irrational.
  4. Convert fractions to decimals and vice-versa.
  5. Solve problems involving decimals and percents.

SEQUENCE of TOPICS:

The instructor will cover a choice of several of the topics outlined:

  1. Reasoning and Problem Solving
  2. Sets
  3. Logic
  4. Probability and Statistics
  5. The Real Number System
  6. Number Theory
  7. Consumer Mathematics
  8. Graph Theory

ASSESSMENT and GRADING:

A comprehensive Final Exam must be given.

The instructor my select from the following assessment tools:

  1. In-class exams and/or quizzes.
  2. Graded paper-and-pencil homework problem sets.
  3. Individual and/or group projects, demonstrations, or presentations.

TEXT:Mathematical Ideas, 13th Edition. By Charles D. Miller, Vern E. Heeren, John Hornsby, and Christopher Heeren, Pearson Publishers.

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