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MATH 6130: Modern Algebra
3.00 Credits
University of Colorado Boulder
Studies groups, rings, and ideals. Prereq., MATH 3140. Undergraduates need instructor consent.
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MATH 6130 - Modern Algebra
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MATH 6140: Modern Algebra
3.00 Credits
University of Colorado Boulder
Studies modules, fields, polynomials, and Galois theory. Prereq., MATH 6130. Undergraduates need instructor consent.
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MATH 6140 - Modern Algebra
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MATH 6150: Commutative Algebra
3.00 Credits
University of Colorado Boulder
Introduces topics used in number theory and algebraic geometry, including radicals of ideals, exact sequences of modules, tensor products, Ext, Tor, localization, primary decomposition of ideals, and Noetherian rings. Prereq., MATH 6140. Undergraduates must have approval of the instructor.
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MATH 6150 - Commutative Algebra
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MATH 6170: Algebraic Geometry
3.00 Credits
University of Colorado Boulder
Introduces algebraic geometry, including affine and projective varieties, rational maps and morphisms, and differentials and divisors. Additional topics might include Bezout's Theorem, the Riemann-Roch Theorem, elliptic curves, and sheaves and schemes. Prereq., MATH 6140. Undergraduates must have approval of the instructor.
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MATH 6170 - Algebraic Geometry
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MATH 6180: Algebraic Number Theory
3.00 Credits
University of Colorado Boulder
Introduces number fields and completions, norms, discriminants and differents, finiteness of the ideal class group, Dirichlet's unit theorem, decomposition of prime ideals in extension fields, decomposition, and ramification groups. Prereqs., MATH 6110 and 6140. Undergraduates must have approval of the instructor.
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MATH 6180 - Algebraic Number Theory
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MATH 6190: Analytic Number Theory
3.00 Credits
University of Colorado Boulder
Acquaints students with the Riemann Zeta-function and its meromorphic continuation, characters and Dirichlet series, Dirichlet's theorem on primes in arithmetic progressions, zero-free regions of the zeta function, and the prime number theorem. Prereqs., MATH 6110 and 6350. Undergraduates must have approval of the instructor.
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MATH 6190 - Analytic Number Theory
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MATH 6210: Introduction to Topology
3.00 Credits
University of Colorado Boulder
Introduces elements of general topology, algebraic topology, and differentiable manifolds. See also MATH 6220. Prereqs., MATH 3130, 3140, 4310, and 4320. Undergraduates must have approval of the instructor.
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MATH 6210 - Introduction to Topology
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MATH 6220: Introduction to Topology
3.00 Credits
University of Colorado Boulder
Introduces elements of general topology, algebraic topology, and differentiable manifolds. See also MATH 6210. Prereq., MATH 6210. Undergraduates must have approval of the instructor.
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MATH 6220 - Introduction to Topology
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MATH 6230: Introduction to Differential Geometry
3.00 Credits
University of Colorado Boulder
Instructs students on fundamental concepts such as manifolds, differential forms, de Rham cohomology, Riemannian metrics, connections and curvatures, fiber bundles, complex manifolds, characteristic classes, and applications to physics. Prereqs., MATH 3130 and 4320. Undergraduates must have instructor consent.
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MATH 6230 - Introduction to Differential Geometry
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MATH 6240: Introduction to Differential Geometry
3.00 Credits
University of Colorado Boulder
Continuation of MATH 6230. Undergraduates must have instructor consent.
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MATH 6240 - Introduction to Differential Geometry
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