### Math 1050: Quantitative Reasoning

#### Course Description

Promotes mathematical literacy among students. This course will cover important mathematical ideas and problem solving skills in the context of science, technology, and/or society. Topics may include logic and critical thinking, Venn Diagrams, problem solving, sets, units of measure, percentages and ratios, counting and probability, exponential growth and decay, linear and exponential models. Quantitative Reasoning is designed to stimulate interest in and appreciation of mathematics and quantitative reasoning as valuable tools for comprehending the world in which we live.

This course does not satisfy the prerequisite of any other math course.

#### Textbook and Course Materials:

• MML AUTOACCESS – Required
• COURSE WORKBOOK – Custom Edition - Required – A manual containing an outline of class notes.
• TEXTBOOK – Recommended - Using & Understanding Mathematics: A Quantitative Reasoning Approach (7th Edition) by Bennett and Briggs.

#### Sections Covered

• Chapter 2-Approaches to Problem Solving
• 2A  Understand, Solve, and Explain
• Learn a general problem-solving process, along with the basic principles of unit analysis that can be very useful to this approach.
• 2B  Extending Unit Analysis
• Review standardized units, and apply unit analysis to problems involving energy, density, and concentration.
• 2C  Problem-Solving Hints
• Explore a general set of hints for effective problem solving.

• Chapter 3-Numbers in the Real World
• Review  Percentages and Ratios
• 3A  Uses and Abuses of Percentages
• Become familiar with subtle uses and abuses of percentages.
• 3B  Putting Numbers in Perspective
• Develop techniques for giving perspective to many large and small numbers we encounter in daily life.
• 3C  Dealing with Uncertainty (Significant Errors, Random and Systematics Error, Absolute and Relative Error)
• Understand the types of errors that affect measured numbers and explore ways of dealing with the inevitable uncertainty of numbers in the daily life.
• 3D  Index Numbers: The CPI and Beyond
• Study the role of index numbers, particularly the Consumer Price Index (CPI), in modern life.
• 3E  How Numbers Can Deceive: Polygraphs, Mammograms, and More
• Explore how numbers can be deceiving unless we interpret them carefully.

• Chapter 4 - Managing Money
• Review  Powers and Roots
• 4A  Taking Control of Your Finances
• Review the basics of personal budgeting.
• 4B  The Power of Compounding
• Explore the basic principles of compound interest.
• 4C  Savings Plans and Investments (Savings Plan Formula, Total and Annual Return, Stocks and Bonds)
• Calculate the future value of savings plans and study investments in stocks and bonds.
• 4D  Loan Payments, Credit Cards, and Mortgages
• Understand the mathematics of loan payments, including those for student loans, credit cards, and mortgages.
• 4E  Income Taxes
• Explore the mathematics of income taxes and the political issues that surround them.

•  Chapter 5 - Statistical Reasoning
• 5A  Fundamental of Statistics
• Understand how statistical studies are conducted, with emphasis on the importance of sampling.
• 5B Should You Believe in a Statistical Study?
• Be familiar with eight useful guidelines for evaluating statistical claims.
• 5C Statistical Tables and Graphs
• Interpret and create basic tables and graphs, including frequency tables, bar graphs, pie charts, histograms, and line charts.
• 5D Graphics in the Media
• Interpret and explore common types of media graphics.
• 5E Correlation and Causality
• Investigate correlations and learn how to decide whether a correlation is the result of causality.

• Chapter 6 - Putting Statistics to Work
• 6A Characterizing Data
• Investigate ways of describing data by their average value – including mean, median, and mode – and their distribution.
• 6B Measures of Variation
• Explore common measures of variation, or spread, in a data set: the range, the five-number summary, and the standard deviation.
• 6C The Normal Distribution
• Study the characteristics of the normal distribution, or bell-shaped curve, and learn why it is so important.
• 6D Statistical Inference
• Explore three crucial ideas used when inferring a conclusion about a population from results for a sample: statistical significance, the margin of error, and hypothesis testing.

• Chapter 7-Probability
• 7A  Fundamentals of Probability (Theoretical, Frequency, and Subjective Probability, Distributions)
• Explore basic concepts of probability and learn three methods for determining probabilities: theoretical, relative frequency, and subjective.
• Review  The Multiplication Principle
• 7B  Combining Probabilities (And vs Either/Or, At Least Once Rule)
• Learn basic rules for adding and multiplying probabilities.
• Review  Factorials
• 7E  Counting and Probability (Arrangements, Permutations, Combinations)
• Learn about permutations and combinations and apply them to probability and to exploring coincidences.

• Chapter 8-Exponential Growth and Decay
• 8A  Growth: Linear vs Exponential
• Distinguish between linear growth and exponential growth, and explore the remarkable effects of the repeated doublings that characterize exponential growth.
• 8B  Doubling Time and Half-life (Approximate Doubling Time and Half-life Formula, Exact Formulas)
• Find and understand the doubling time for exponential growth and the half-life for exponential decay.

• Chapter 1 - Thinking Critically
• 1A  Living in the Media Age
• Explore common fallacies, or deceptive arguments, and learn how to avoid them.
• 1B  Propositions and Truth Values (Negation, Logical Connectors)
• Study basic components of logic, including propositions, truth-values, truth tables, and the logical connectors and, or, and if…then.
• 1C  Sets and Venn Diagrams
• Understand sets, and use Venn diagrams to visualize relationships among sets.
• 1D  Analyzing Arguments (Inductive and Deductive)
• Learn to distinguish and evaluate basic inductive and deductive arguments.
• 1E      Critical Thinking in Everyday Life
• Apply logic to common situations in everyday life.