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Advanced Calculus
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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.

Subject:
Calculus
Mathematics
Material Type:
Textbook
Provider:
Harvard University
Provider Set:
Individual Authors
Author:
Sternberg Shlomo and Lynn Loomis
Date Added:
02/16/2011
Gödel, Escher, Bach
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CC BY-NC-SA
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How are math, art, music, and language intertwined? How does intelligent behavior arise from its component parts? Can computers think? Can brains compute? Douglas Hofstadter probes very cleverly at these questions and more in his Pulitzer Prize winning book, "Gödel, Escher, Bach". In this seminar, we will read and discuss the book in depth, taking the time to solve its puzzles, appreciate the Bach pieces that inspired its dialogues, and discover its hidden tricks along the way.

Subject:
Applied Science
Arts and Humanities
Composition and Rhetoric
Computer Science
Engineering
English Language Arts
Life Science
Literature
Philosophy
Physical Science
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Speer, Robert
Date Added:
02/01/2007
Modal Logic
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Modal logic is the logic of necessity and possibility, and by extension of analogously paired notions like validity and consistency, obligation and permission, the known and the not-ruled-out. This a first course in the area. A solid background in first-order logic is essential. Topics to be covered include (some or all of) the main systems of propositional modal logic, Kripkean "possible world" semantics, strict implication, contingent identity, intensional objects, counterpart theory, the logic of actuality, and deontic and / or epistemic logic. The emphasis will be more on technical methods and results than philosophical applications.

Subject:
Arts and Humanities
Linguistics
Philosophy
Social Science
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Yablo, Stephen
Date Added:
02/01/2015