Number-Crunching

Synopsis

More stimulating mathematics puzzles from bestselling author Paul Nahin

How do technicians repair broken communications cables at the bottom of the ocean without actually seeing them? What's the likelihood of plucking a needle out of a haystack the size of the Earth? And is it possible to use computers to create a universal library of everything ever written or every photo ever taken? These are just some of the intriguing questions that best-selling popular math writer Paul Nahin tackles in Number-Crunching. Through brilliant math ideas and entertaining stories, Nahin demonstrates how odd and unusual math problems can be solved by bringing together basic physics ideas and today's powerful computers. Some of the outcomes discussed are so counterintuitive they will leave readers astonished.

Nahin looks at how the art of number-crunching has changed since the advent of computers, and how high-speed technology helps to solve fascinating conundrums such as the three-body, Monte Carlo, leapfrog, and gambler's ruin problems. Along the way, Nahin traverses topics that include algebra, trigonometry, geometry, calculus, number theory, differential equations, Fourier series, electronics, and computers in science fiction. He gives historical background for the problems presented, offers many examples and numerous challenges, supplies MATLAB codes for all the theories discussed, and includes detailed and complete solutions.

Exploring the intimate relationship between mathematics, physics, and the tremendous power of modern computers, Number-Crunching will appeal to anyone interested in understanding how these three important fields join forces to solve today's thorniest puzzles.

Summary

Chapter 1: The Power of Numbers

* Numbers can be used to describe and understand the world around us.
* Data can be collected, analyzed, and used to make informed decisions.
* Examples:
* A company uses data to track sales and identify trends.
* A scientist uses data to test hypotheses and develop theories.

Chapter 2: Collecting and Analyzing Data

* There are different types of data, including qualitative and quantitative data.
* Data can be collected through surveys, experiments, or observations.
* Statistical analysis can be used to summarize and analyze data.
* Examples:
* A survey is conducted to collect data on consumer preferences.
* A statistical model is used to analyze data from an experiment to determine the effectiveness of a new drug.

Chapter 3: Displaying Data

* Data can be displayed using tables, graphs, and charts.
* Different types of displays are suited for different types of data.
* Examples:
* A bar chart is used to display the number of students in each grade level at a school.
* A pie chart is used to display the proportion of students who prefer different subjects.

Chapter 4: Describing Data

* Data can be described using measures of central tendency (e.g., mean, median, mode) and measures of variability (e.g., range, standard deviation).
* These measures can help us understand the overall distribution of data.
* Examples:
* The mean income of a population can be used to describe the average income level.
* The standard deviation of test scores can be used to describe the spread of scores.

Chapter 5: Making Inferences from Data

* Statistical inference allows us to make generalizations about a population based on a sample.
* This can be done using sampling techniques and hypothesis testing.
* Examples:
* A company uses a sample of customers to estimate the average satisfaction level of their overall customer base.
* A researcher conducts a hypothesis test to determine if a new teaching method is more effective than the current method.

Chapter 6: Using Numbers in Decision Making

* Numbers can be used to support decision making by providing evidence and insights.
* Numerical analysis and forecasting can be used to make predictions and assess risks.
* Examples:
* A business uses historical sales data to forecast future sales and make decisions about inventory levels.
* A government uses economic data to make decisions about tax policies and interest rates.

Chapter 7: The Ethics of Number-Crunching

* It is important to use numbers ethically and responsibly.
* This includes being transparent about data sources, avoiding bias, and considering the implications of using numbers to make decisions.
* Examples:
* A politician uses misleading statistics to support their claims.
* A company manipulates data to inflate its financial performance.