M123 Quantitative Reasoning
Catalog Description
MATH 123 QUANTITATIVE REASONING (3-0-3)(F, S)(DLM). Survey of quantitative reasoning skills
including deductive and inductive reasoning, benchmarks, and sense of scale, applied in a conceptual
way to interpretation of graphical displays, descriptive and inferential statistics, elementary probability,
and exponential growth. PREREQ: MATH 25 or satisfactory placement score.
Prerequisites
MATH 25 or satisfactory placement score.
Syllabus Statement
Boise State's Foundational Studies Program provides undergraduates with a broad-based education
that spans the entire university experience. MATH 123 Quantitative Reasoning satisfies three credits of
the Foundational Studies Program's Disciplinary Lens-Mathematics (DL-M) requirement. It supports
the following University Learning Outcomes, along with a variety of other course-specific goals:
7. Apply knowledge and the methods of reasoning characteristic of mathematics, statistics, and
other formal systems to solve complex problems.
MATH 123: Quantitative Reasoning is designed to introduce students to the methods of reasoning used
in science and mathematics. This course helps to achieve the goals of the Foundational Studies
Program by focusing on the following course learning outcomes. After successful completion of this
course, you will be able to:
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Assess data for reasonableness
Create and interpret graphical information
Appreciate the statistical techniques used in studies and experiments
Recognize the characteristics of exponential growth
Topics covered
Methods of reasoning
Inductive
Deductive
Retroductive (Abductive or Bayesian)
Number Sense or Attention to numbers
Sense of scale
Reasonableness and benchmark figures (numbers that experts use to judge reasonableness)
Source of numbers
Relationship between a thousand, million, billion, trillion
Proportional reasoning
Understanding Percentages
Per hundred
Techniques for calculator free approximations
Using proportional reasoning to find approximations for non-linear behavior
error issues with linearizing
Non linear functions
Compound interest as a introduction to exponential growth
How the components of compound interest formula affect total interest earned
How to make compounding you earn work for you. (You must reinvest the interest and/or dividend.)
Simplifying assumptions when using financial formulas
How the duration of a loan affects payment size and total interest paid
Change in Area and Volume vs. change in linear dimensions
Understanding Risk (Hope to Certitude)
Relative frequency
Absolute frequency
High-risk and low-risk in context "Is one in ten thousand good or bad?" (Airplane crashes,
misreading medical test result)
Conditional probability
Specificity vs. positive predictive value
How prevalence affects positive predictive value
Elementary Probability
Expected value
Normal Distribution
Using observations
How, why, and by whom was the data collected
Communicating data graphically
Association (correlation) vs. causation
Avoid being misled
Ethics