Excursions in Modern Mathematics 10th Edition By Peter Tannenbaum
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- Education
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- eBook[PDF]
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About this ebook
The Excursions in Modern Mathematics (10th Edition) by Peter Tannenbaum is organized into 17 chapters across 5 distinct thematic parts, which cover accessible, real-world applications of math for liberal arts students. [1, 2]
Part I: The Mathematics of Social Choice
- The Mathematics of Voting: Explores the paradoxes of democracy, preference ballots, preference schedules, the plurality method, the Borda count method, instant runoff voting (plurality-with-elimination), and pairwise comparisons. [1, 2]
- Weighted Voting Systems: Covers power dynamics in voting, coalitions, and calculating voting power using indices like the Banzhaf or Shapley-Shubik power indexes. [1, 2]
- Fair Division: Analyzes the mathematics of sharing assets, inheritance, or estate division using continuous and discrete fair-division methods. [1, 2]
- The Mathematics of Apportionment: Investigates how legislative seats or resources are distributed fairly using methods like Hamilton, Jefferson, Webster, and the Huntington-Hill rules. [1, 2]
Part II: Management Science
- Euler Circuits: Covers graph theory optimization applied to routing problems like garbage collection, postal routes, and urban navigation.
- The Traveling-Salesman Problem: Discusses Hamilton circuits and paths used to optimize complex logistics, touring, and travel itineraries.
- The Mathematics of Networks: Focuses on the minimum cost of connecting nodes using trees, networks, and Kruskal’s algorithm.
- Scheduling: Evaluates how to sequence complex projects using architectural networks, critical paths, and the priority-list algorithm. [1, 2, 3, 4]
Part III: Growth & Financial Mathematics
- Population Growth Models: Compares different models of change including linear, exponential, and logistic growth dynamics.
- Financial Mathematics: Delves into percentages, simple interest, compound interest, managing retirement savings, and understanding consumer debt. [1, 2, 3]
Part IV: Shape and Form
- The Mathematics of Symmetry: Discusses rigid motions, geometric reflections, rotations, translations, glide reflections, and symmetry patterns.
- Fractal Geometry: Explores the structures of nature using self-similarity, the Koch Snowflake, the Sierpinski Gasket, and the Mandelbrot Set.
- Fibonacci Numbers and the Golden Ratio: Studies the recursive relationships of Fibonacci numbers, gnomons, and spiral growth formations in the natural world. [1]
Part V: Statistics
- Data Collection: Investigates censuses, population sampling methods, clinical studies, and the mechanics of modern opinion polling.
- Descriptive Statistics: Teaches data organization through graphs, charts, and numeric measurements like the mean, median, and standard deviation.
- Probability: Covers basic probability concepts, calculation of odds, and expected values.
- Normal Distributions: Explores the properties of normal curves, standard scores (z-scores), and the central limit theorem. [1, 2, 3, 4]
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