A MATHEMATICAL VIEW OF OUR WORLD helps students understand and harness the power of mathematics in their present studies and future careers. Designed for a liberal arts mathematics course that has a strong focus on applications, this student-friendly textbook helps students see the beauty and power of mathematics as it is applied to the world around them. Recognizing that quantitative literacy is essential in an increasing number of professional fields as well as in the daily decision-making and communication of informed citizens, the book develops students' mathematical self-confidence and prepares them to use mathematics in the future. In writing the book, the authors endeavored to be faithful to the recommendations of such professional mathematics associations as the MAA, AMATYC, and NCTM. Overall, students will recognize the connections, patterns, and significance of the mathematics they study, and see that mathematics has a meaningful place in their lives.
Key Features :
Table of Contents :
1. NUMBERS IN OUR LIVES.
Identification Numbers and Check Digits. Modular Arithmetic and Check Digit Schemes. Encoding Data.
2. SHAPES IN OUR LIVES.
Tilings. Symmetry, Rigid Motions, and Escher Patters. Fibonacci Numbers and the Golden Mean - Shapes in Nature.
3. VOTING AND ELECTIONS.
Voting Systems. Flaws of the Voting Systems. Weighted Voting Systems.
4. FAIR DIVISION.
Divide and Choose Methods. Discrete and Mixed Division Problems. Envy-Free Division.
The Apportionment Problem - Quota Methods. The Apportionment Problem - Divisor Methods. Flaws of the Apportionment Methods.
6. ROUTES AND NETWORKS.
Routing Problems. Network Problems. The Traveling Salesperson Problem.
Basic Concepts of Scheduling. The List-Processing Algorithm and the Decreasing-Time Algorithm. The Critical-Path Algorithm.
8. DESCRIPTIVE STATISTICS - DATA AND PATTERNS.
Organizing and Picturing Data. Comparisons. Enhancement, Distraction, and Distortion.
9. COLLECTING AND INTERPRETING DATA.
Populations, Samples, and Data. Survey Sampling Methods. Measures of Central Tendency and Variability.
Computing Probabilities in Simple Experiments. Computing Probabilities in Multistage Experiments. Conditional Probability, Expected Value, and Odds.
11. INFERENTIAL STATISTICS.
Normal Distributions. Applications of Normal Distributions. Confidence Intervals and Reliable Estimation.
12. GROWTH AND DECAY.
Malthusian Population Growth. Population Decrease, Radioactive Decay. Logistic Population Models.
13. CONSUMER MATHEMATICS—BUYING AND SAVING.
Simple and Compound Interest. Loans. Buying a House.