A College Level Liberal Arts Mathematics Text.
1: Statistics - Part 1
1.1: Statistical Basics 1.2: Random Sampling 1.3: Clinical Studies 1.4: Should You Believe a Statistical Study? 1.5: Graphs 1.6: Graphics in the Media 1.7: Exercises
2: Statistics - Part 2
2.1: Proportion 2.2: Location of Center 2.3: Measures of Spread 2.4: The Normal Distribution 2.5: Correlation and Causation, Scatter Plots 2.6: Exercises
3.1: Basic Probabilities and Probability Distributions; Three Ways to Define Probabilities 3.2: Combining Probabilities with “And” and “Or” 3.3: Conditional Probabilities 3.4: Expected Value and Law of Large Numbers 3.5: Counting Methods 3.6: Exercises
4: GrowthPopulation growth is a current topic in the media today. The world population is growing by over 70 million people every year. Predicting populations in the future can have an impact on how countries plan to manage resources for more people. The tools needed to help make predictions about future populations are growth models like the exponential function. This chapter will discuss real world phenomena, like population growth and radioactive decay, using three different growth models.
4.1: Linear Growth 4.2: Exponential Growth 4.3: Special Cases- Doubling Time and Half-Life 4.4: Natural Growth and Logistic Growth 4.5: Exercises
5.1: Basic Budgeting 5.2: Simple Interest 5.3: Compound Interest 5.4: Savings Plans 5.5: Loans 5.6: Exercises
6: Graph TheoryGraph theory deals with routing and network problems and if it is possible to find a “best” route, whether that means the least expensive, least amount of time or the least distance. Some examples of routing problems are routes covered by postal workers, UPS drivers, police officers, garbage disposal personnel, water meter readers, census takers, tour buses, etc. Some examples of network problems are telephone networks, railway systems, canals, roads, pipelines, and computer chips.
6.1: Graph Theory 6.2: Networks 6.3: Euler Circuits 6.4: Hamiltonian Circuits 6.5: Exercises
7: Voting Systems
7.1: Voting Methods 7.2: Weighted Voting 7.3: Exercises
8: Fair Division
8.1: Basic Concepts of Fair Division 8.02: Continuous Methods 1 - Divider 8.2: Continuous Methods 1 - Divider/Chooser and Lone Divider Methods 8.3: Continuous Methods 2 - Lone Chooser and Last Diminisher Methods 8.4: Discrete Methods - Sealed Bids and Markers 8.5: Exercises
9: ApportionmentApportionment involves dividing something up, just like fair division. In fair division we are dividing objects among people while in apportionment we are dividing people among places. Also like fair division, the apportionment processes that are widely used do not always give the best answer, and apportionment is still an open field of mathematics.
9.1: Apportionment - Jefferson’s, Adam’s, and Webster’s Methods 9.2: Apportionment - Jefferson’s, Adams’s, and Webster’s Methods 9.3: Apportionment Paradoxes 9.4: Exercises
10: Geometric Symmetry and the Golden RatioPatterns and geometry occur in nature and humans have been noticing these patterns since the dawn of humanity. In this chapter, topics in geometry will be examined. These topics include transformation and symmetry of geometric shapes, similar figures, gnomons, Fibonacci numbers, and the Golden Ratio.
10.1: Transformations Using Rigid Motions 10.2: Connecting Transformations and Symmetry 10.3: Transformations that Change Size and Similar Figures 10.4: Fibonacci Numbers and the Golden Ratio 10.5: Exercises