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1,2,3, .. infinity. Mathematical Induction

Explain the Method of Mathematical Induction. Francesco Maurolico, Pascal and John Wallis. Applying the method of Induction to prove the sum of odd numbers is a more


5.33 Advanced Chemical Experimentation and Instrumentation (MIT)

5.33 focuses on advanced experimentation, with particular emphasis on chemical synthesis and the fundamentals of quantum chemistry, illustrated through molecular spectroscopy. The more


12.490 Advanced Igneous Petrology (MIT)

Advanced Igneous Petrology covers the history of and recent developments in the study of igneous rocks. Students review the chemistry and structure of igneous rock-forming minerals more


18.306 Advanced Partial Differential Equations with Applications (MIT)

The focus of the course is the concepts and techniques for solving the partial differential equations (PDE) that permeate various scientific disciplines. The emphasis is on more


12.491 Advanced Seminar in Geology and Geochemistry: Organic Geochemistry (MIT)

12.491 is a seminar focusing on problems of current interest in geology and geochemistry. For Fall 2005, the topic is organic geochemistry. Lectures and readings cover recent more


18.701 Algebra I (MIT)

This undergraduate level Algebra I course covers groups, vector spaces, linear transformations, symmetry groups, bilinear forms, and linear more


18.702 Algebra II (MIT)

This undergraduate level course follows Algebra I. Topics include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic more


18.725 Algebraic Geometry (MIT)

This course covers the fundamental notions and results about algebraic varieties over an algebraically closed field. It also analyzes the relations between complex algebraic more


18.906 Algebraic Topology II (MIT)

In this second term of Algebraic Topology, the topics covered include fibrations, homotopy groups, the Hurewicz theorem, vector bundles, characteristic classes, cobordism, and more


18.905 Algebraic Topology (MIT)

This course is a first course in algebraic topology. The emphasis is on homology and cohomology theory, including cup products, Kunneth formulas, intersection pairings, and the more


18.101 Analysis II (MIT)

This course continues from Analysis I (18.100B), in the direction of manifolds and global analysis. The first half of the course covers multivariable calculus. The rest of the more


12.119 Analytical Techniques for Studying Environmental and Geologic Samples (MIT)

This is a laboratory course supplemented by lectures that focus on selected analytical facilities that are commonly used to determine the mineralogy, elemental abundance and more


12.005 Applications of Continuum Mechanics to Earth, Atmospheric, and Planetary Sciences (MIT)

This course focuses on the practical applications of the continuum concept for deformation of solids and fluids, emphasizing force balance. Topics include stress tensor, more


8.901 Astrophysics I (MIT)

This course provides a graduate-level introduction to stellar astrophysics. It covers a variety of topics, ranging from stellar structure and evolution to galactic dynamics and dark more


12.003 Atmosphere, Ocean and Climate Dynamics (MIT)

This undergraduate class is designed to introduce students to the physics that govern the circulation of the ocean and atmosphere. The focus of the course is on the processes that more

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