Practice solving systems of two linear equations by graphing the corresponding lines and looking for the intersection point. Discover that there are three possible outcomes: no solution, infinitely many solutions, and exactly one solution.

In examining the diverse functions and types of portraits, study the important elements of facial presentation and the subject's position and gaze with relation to the viewer and the pictorial space. See how Rembrandt added dramatic power to his group "corporation" portraits, and how David carefully rendered Napoleon in symbolic terms.

The Old Testament is one of the foundational documents of Western civilization. In this course, viewers will study a selection of the major books of the Old Testament, probing their meaning and relevance. Among these, viewers will explore the prophets, the wisdom literature, and the apocalyptic literature, finding their deeper historical and religious import, as well as their sublime literary treasures.

Religious pilgrimage was a central feature of medieval life. First, visualize pilgrimage to the Holy Land through the writings of the Spanish pilgrim Egeria. Note how travel to venerate holy relics was a major lure for the faithful. Witness spiritual pilgrimage in Asia, in Japan through the diaries of Abutsu and Lady Nijo, and in the Muslim world with Ibn Battuta, Islam's most iconic traveler.

Trace the effects on warfare of gunpowder, first developed by the Chinese. See how gunpowder weapons spread to the Islamic world, and to Europe in the Hundred Years' War between England and France. Visualize the new armies and military strategy, using cannon, guns, and longbows, and the decline of mounted knights. Witness these currents of events in the extraordinary story of Joan of Arc.

Shift gears away from polynomials to focus on expressions involving roots, including square roots, cube roots, and roots of higher degrees (all known as radical expressions). Practice multiplying, dividing, adding, and subtracting a wide variety of radical expressions.

After a short introduction to probability, celebrate your completion of the series with a deck of cards. Can you use the principles of probability, permutations, and combinations to calculate the probability of being dealt different hands? As with the rest of algebra, once you know the rules, it's simplicity itself!

Today, legislative and judicial oversight of the presidency are a permanent part of American government and critical to limiting and restraining the possibility of executive abuse. In this episode, learn how our system of checks and balances came to exist - with, among other things, a close look at the landmark judicial review case, Marbury v. Madison.

Why is life expectancy in the United States decreasing and infant mortality so high compared to other industrialized nations? Take a captivating look behind the scenes at the debate between scientists fighting for their individual points of view. Does the media explain the statistics behind their competing theories? If not, who suffers from the oversimplification of a "clickbait" headline?

This course explores the history of religious violence, its multiple manifestations, its scriptural justifications, and how its perpetrators perceive the world. Ony by understanding the roots, causes, and circumstance of religious violence can we grapple with it intellectually and practically. These lectures treat the topic not as something resistant to analysis, but as a recurrent religious impulse that can be decoded, interpreted, and understood...