Final answer:
The U.S. military strategy during the Mexican-American War aimed to capture northern Mexico, seize California, and take Mexico City. The strategic execution and conquests led to the Treaty of Guadalupe Hidalgo and significant territorial gains for the United States.
Step-by-step explanation:
The U.S. military strategy for the war with Mexico included several key objectives to secure victory and territorial expansion. Firstly, the strategy aimed to take control of northern Mexico, including New Mexico, which was assigned to General Zachary Taylor and his Army of the Center. They used superior weapons to capture Monterrey and maintain presence in the north.
Another objective was the seizure of California. A naval fleet was positioned off the coast of California, and a small group of American settlers peacefully took the garrison at Sonoma, leading to the short-lived California Republic, which was soon replaced by U.S. control under John Frémont. The final strategic aim was to capture Mexico City, which fell into the hands of the Army of Occupation under General Winfield Scott following an amphibious assault on Veracruz. Scott's campaign took advantage of the political chaos in Mexico, with interrupted leadership and the eventual return of Santa Anna to presidency just as the U.S. closed in on Veracruz.
The outcome of the strategy was a significant territorial acquisition for the United States, with Mexico ceding lands that would become California, Arizona, New Mexico, Nevada, Colorado, Utah, and part of Wyoming under the Treaty of Guadalupe Hidalgo. The war also had significant military and political implications, including increased respect for American military training, but it also fueled sectional tensions within the U.S. over the issue of slavery.