Mathematics for Liberal Arts

At the conclusion of this course students will be able to:

• identify and discuss at least three common misconceptions about mathematics
• understand and explain the importance of mathematical literacy in modern society
• reflect on the role that mathematics plays in their own lives

• recognize and analyze fallacies in given arguments
• use appropriate logic notation and simple truth tables to analyze the truth values of propositions   involving negation, conjunctions, disjunctions, conditionals
• distinguish between inclusive and exclusive uses of the word “or”
• given a conditional, write its converse, its inverse and its contrapositive
• illustrate relationships between sets using Venn diagrams
• solve problems using Venn diagrams to organize information
• use Venn diagrams to test the validity of arguments
• distinguish between inductive and deductive arguments
• apply critical thinking strategies to analyze arguments

• know standard metric units of measurement
• perform unit conversions
• apply problem solving strategies to solve word problems
• solve percentage problems
• calculate absolute and relative change
• identify common abuses of percentages
• write and interpret numbers in scientific notation
• demonstrate number sense through estimation, comparison and scaling
• understand and give examples of Simpson’s Paradox

• understand and interpret the 5 basic steps in a statistical study
• describe simple random sampling, systematic sampling, convenience sampling and stratified sampling
• distinguish between observational studies and experiments
• describe the placebo effect and the importance of blinding in experiments
• determine a confidence interval from a margin of error
• understand and apply guidelines for evaluating a statistical study
• interpret and create frequency tables, bar graphs, pie charts, histograms and line charts
• interpret graphs that relay statistical information
• distinguish between causation and correlation
• describe possible explanations for correlation
• understand and apply guidelines for recognizing causality

• explain the difference between linear and exponential growth
• calculate the doubling-time or half-life in given situations
• contrast exponential growth and logistic growth
• understand factors affecting carrying capacity
• understand and use the Richter scale, decibel scale, and pH scale

• understand the concept of a mathematical function
• given a real-life functional situation, identify dependent and independent variables, domain and range
• represent functions with tables, graphs and equations
• use functions given in the form of tables, graphs or equations to answer questions about real-life quantities

Depending on the sections covered by the instructor the students will also be able to:

ACCURACY AND PRECISION

• distinguish significant digits from non-significant zeros
• identify and distinguish between random and systematic errors
• calculate absolute and relative error
• distinguish between accuracy and precision
• apply rounding rules for combining approximate numbers

PROBABILITY AND COUNTING

• distinguish between theoretical, empirical and subjective probabilities
• calculate simple probabilities
• make a probability distribution
• calculate probabilities of the conjunction of independent and dependent events
• calculate probabilities of the disjunction of mutually exclusive and non-mutually exclusive events
• understand and apply the law of large numbers
• calculate and interpret expected values
• measure risk in terms of accident or death rates
• understand and interpret vital statistics and life expectancy
• calculate permutations and combinations
• determine the probability of winning a lottery

MORE ADVANCED LINEAR AND EXPONENTIAL MODELS

• calculate the slope of a linear function
• determine the equation of a line
• determine the equation of an exponential function

MATH IN MUSIC

• understand how a plucked string produces sound
• measure frequency and find harmonics of the frequency
• understand the musical scale and the ratios of frequencies among musical notes
• understand how the frequencies of a scale exhibit exponential growth
• explain the difference between analog and digital representations of music

MATH IN ART

• understand the use of perspective in painting
• find symmetries in paintings and tilings
• create tilings with regular or irregular polygons
• name several places that the golden ratio occurs in art and nature

MATH IN FINANCIAL MANAGEMENT

• know when and how to apply formulas for simple interest, compound interest and continuously compounded interest
• understand investment types:  stocks, bonds, cash
• read financial tables for stocks, bonds and mutual funds
• use formulas appropriately to calculate total and annual returns
• understand the uses and dangers of credit cards
• understand considerations in choosing a mortgage
• use the loan payment formula to calculate payments
• calculate the total cost of a loan

MATH IN THE SPORTS SCIENCE CLASSROOM

• solve problems involving energy and power units
• understand and apply the concept of concentration (e.g. blood alcohol content)
• understand  statistics, charts and tables related to health and wellness studies
• apply the mathematics learned in this course to a number of problems relevant to the sports science educators including:
• scheduling tournaments
• calculations of calories burned, percentage body-fat
• performance monitoring
• spreadsheets and student grades