Algebra is the language of modern mathematics. This course introduces students to that language through a study of groups, group actions, vector spaces, linear algebra, and the theory of fields.
Some of the topics that this book addresses are: Vector spaces; finite-dimensional vector spaces; differential calculus; compactness and completeness; scalar product space; differential equations; multilenear functionals; integration; differentiable manifolds; integral calculus on manifolds; exterior calculus.
Note: this is a 57 MB PDF Document.
Modern China presents a dual image: a society transforming itself through economic development and social revolution; and the world’s largest and oldest bureaucratic state, coping with longstanding problems of economic and political management. Both images bear the indelible imprint of China’s historical experience, of its patterns of philosophy and religion, and of its social and political thought.
In this free Chinese studies online course, these themes are discussed to understand China in the modern world and as a great world civilization that developed along lines different from those of the Mediterranean.
The true “hero” of this ancient Greek literature course is the logos, or word, of logical reasoning, as activated by Socratic dialogue. The logos of dialogue requires careful thinking, realized in close reading and reflective writing. The last “word” read in the course comes from Plato’s memories of the last days of Socrates. These memories depend on a thorough understanding of concepts of the hero in all their varieties throughout the history of Greek civilization and beyond. This course is driven by a sequence of dialogues that lead to such an understanding, guiding the attentive reader through some of the major works of the ancient Greek classics, from Homer to Plato.
This online math course develops the mathematics needed to formulate and analyze probability models for idealized situations drawn from everyday life. Topics include elementary set theory, techniques for systematic counting, axioms for probability, conditional probability, discrete random variables, infinite geometric series, and random walks. Applications to card games like bridge and poker, to gambling, to sports, to election results, and to inference in fields like history and genealogy, national security, and theology. The emphasis is on careful application of basic principles rather than on memorizing and using formulas.