Course Outline for Mathematics 47
Mathematics for Liberal Arts

Effective: Fall 2020
SLO Rev: 10/19/2017
Catalog Description:

MTH 47 - Mathematics for Liberal Arts

3.00 Units

An introductory study of mathematical topics, emphasizing real life applications. Topics may include problem solving, geometry, statistics, probability, finance, graph theory, and history and culture of mathematics. Emphasis on real life applications.
Prerequisite: MTH 53 or MTH 53B or MTH 55 or MTH 55B or an appropriate skill level demonstrated through the mathematics assessment process.
1701.00 - Mathematics, General
Letter Grade Only
Type Units Inside of Class Hours Outside of Class Hours Total Student Learning Hours
Lecture 3.00 54.00 108.00 162.00
Laboratory 0.00 18.00 0.00 18.00
Total 3.00 72.00 108.00 180.00
Measurable Objectives:
Upon completion of this course, the student should be able to:
  1. solve applied problems involving annuities, sinking funds and amortization;
  2. compare the future value for simple interest and compound interest, including different compounding periods;
  3. determine which method of computing financial charges minimizes the total financial charges on a particular loan and/or credit card;
  4. determine the probability that a specified event will occur;
  5. find the conditional probability of an event;
  6. use expected values to solve application problems;
  7. describe a distribution using measures of central tendency and measures of variations; and
  8. solve an applied problem that has a normal distribution.
Course Content:
Instructors will include problem solving techniques and 4 additional topics selected from the list below.
  1. Problem Solving
    1. Percents
    2. Dimensional analysis
    3. Geometric Proportions
    4. Estimating
  2. Descriptive Statistics
    1. Tables, charts and graphs
    2. Measures of central tendency
    3. Measures of variation
    4. Normal distribution
    5. Applications
  3. Simulation-Based Inferential Statistics
    1. Sampling distribution
    2. Bootstrap distribution
    3. Confidence intervals for one proportion
    4. Hypothesis testing for one proportion
    5. P-value
    6. Central Limit Theorem
  4. Geometry
    1. Lines, angles, and properties of parallel lines
    2. Circles
    3. Polygons
    4. Perimeter and area
    5. Volume and surface area
    6. Additional topics may be chosen from non-Euclidean geometry, conic sections, fractal geometry, polyhedra, symmetry and tesselations. 
  5. Finance
    1. Simple Interest and Compound Interest
    2. Future Value and Present Value
    3. Annuities, Sinking Funds and Amortization 
    4. Applications
      1. Credit Card Statements
      2. Consumer Loans
  6. Graph Theory
    1. Basic Concepts
      1. Walks, paths, circuits
      2. Complete graphs
      3. Connected graphs
    2. Special Graphs
      1. Euler circuits
      2. Hamilton circuits
      3. Trees
    3. Graph Algorithms
      1. Fleury
      2. Nearest Neighbor
      3. Brute Force
      4. Kruskal
    4. Applications
      1. Traveling Salesman Problem
      2. Scheduling
  7. Probability
    1. Basics of probability
    2. Conditional probility
    3. Expected Value
    4. Applications
  8. History and Culture of Mathematics
    1. Overview of the historical development of mathematics
    2. Role of theorem and proof in mathematical thought
    3. Significant mathematifcal results and mathematicians
Methods of Instruction:
  1. Lecture/Discussion
  2. Problem Solving
  3. Presentation of audio-visual materials
  4. Group Activities
  5. Class and group discussions
  6. Distance Education
Assignments and Methods of Evaluating Student Progress:
  1. Collaborative group assignment such as: determine how much 5 pounds of $5 bills is worth.
  2. Exercises from the textbook such as the following: Suppose state A has a population of 935,000 and five representatives, whereas state B has a population of 2,343,000 and 11 representatives. Determine which state is poorly represented, and calculate the absolute unfairness for this assignment of representatives. Determine the relative unfairness for this apportionment.
  3. Exercises from the textbook such as the following: The heights of 5-year old girls in the U.S. are normally distributed with a mean of 42.56 inches and a standard deviation of 1.573 inches. 68.27% of 5-year old girls have heights between ______ inches and ______ inches.
  1. Homework
  2. Quizzes
  3. Class Participation
  4. Exams/Tests
  5. Final Examination
  6. Projects
Upon the completion of this course, the student should be able to:
  1. Analyze mathematical problems critically using a logical methodology.
  2. Communicate mathematical ideas, understand definitions, and interpret concepts.
  3. Increase confidence in understanding mathematical concepts, communicating ideas and thinking analytically.
Textbooks (Typical):
  1. Lippman, David (2017). Math in Society Creative Commons Attributions.
  • Graphing/Scientific calculator
Abbreviated Class Schedule Description:
An introductory study of several mathematical topics. Emphasis is placed on the use of mathematics to make informed decisions in different areas of daily life. Recommended for liberal arts students.
Prerequisite: MTH 53 or MTH 53B or MTH 55 or MTH 55B or an appropriate skill level demonstrated through the mathematics assessment process.
Discipline:
Mathematics*