Latin America is richly endowed with natural resources, fertile land, and vibrant cultures. Yet the region remains much poorer than its neighbors to the north. Most Latin American countries have not achieved standards of living and stable institutions comparable to those found in developed countries, have experienced repeated boom-bust cycles, and remain heavily reliant on primary commodities.

Proof is the primary vehicle for knowledge generation in mathematics. In computer science, proof has found an additional use: verifying that a particular system (or component, or algorithm) has certain desirable properties. This book teaches students how to read and write proofs using Athena, a freely downloadable computer language. Athena proofs are machine-checkable and written in an intuitive natural-deduction style. The book contains more than 300 exercises, most with full solutions.

Algorithms are what we do in order not to have to do something. Algorithms consist of instructions to carry out tasks—usually dull, repetitive ones. Starting from simple building blocks, computer algorithms enable machines to recognize and produce speech, translate texts, categorize and summarize documents, describe images, and predict the weather. A task that would take hours can be completed in virtually no time by using a few lines of code in a modern scripting program. This book offers an introduction to algorithms through the real-world problems they solve.

The study of industrial organization (IO)—the analysis of the way firms compete with one another—has become a key component of economics and of such related disciplines as finance, strategy, and marketing. This book provides an issue-driven introduction to industrial organization. Although formal in its approach, it is written in a way that requires only basic mathematical training. It includes a vast array of examples, from both within and outside the United States. This second edition has been thoroughly updated and revised.