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AS 110.304: Elementary Number Theory
4.00 Credits
Johns Hopkins University
Not Available
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AS 110.304 - Elementary Number Theory
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AS 110.328: Non-Euclidean Geometry
4.00 Credits
Johns Hopkins University
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AS 110.328 - Non-Euclidean Geometry
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AS 110.401: Advanced Algebra I
4.00 Credits
Johns Hopkins University
Prereq: Linear Algebra An introduction to the basic notions of modern algebra. Elements of group theory: groups, subgroups, normal subgroups, quotients, homomorphisms. Generators and relations, free groups, products, commutative (Abelian) groups, finite groups. Groups acting on sets, the Sylow theorems. Definition and examples of rings and ideals. Introduction to field theory. Linear algebra over a field. Field extensions, constructible polygons, non-trisectability.
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AS 110.401 - Advanced Algebra I
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AS 110.402: Advanced Algebra II
4.00 Credits
Johns Hopkins University
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AS 110.402 - Advanced Algebra II
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AS 110.405: Analysis I
4.00 Credits
Johns Hopkins University
This course is designed to give a firm grounding in the basic tools of analysis. It is recommended as preparation (but may not be a prerequisite) for other advanced analysis courses. Real and complex number systems, topology of metric spaces, limits, continuity, infinite sequences and series, differentiation, Riemann-Stieltjes integration.
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AS 110.405 - Analysis I
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AS 110.406: Analysis II
4.00 Credits
Johns Hopkins University
This course continues 110.405 with an emphasis on the fundamental notions of modern analysis. Sequences and series of functions, Fourier series, equicontinuity and the Arzela-Ascoli theorem, the Stone-Weierstrass theorem, functions of several variables, the inverse and implicit function theorems, introduction to the Lebesgue integral.
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AS 110.406 - Analysis II
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AS 110.413: Intro to Topology
4.00 Credits
Johns Hopkins University
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AS 110.413 - Intro to Topology
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AS 110.416: Honors Analysis II
4.00 Credits
Johns Hopkins University
Prerequisite: 110.415, or 110.405 and permission of the instructor Continuation of 110.415, introduction to real analysis. Lebesgue integration and differentiation. Elementary Hilbert and Banach space theory. Baire category theorem.
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AS 110.416 - Honors Analysis II
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AS 110.417: Partial Diff Equations
4.00 Credits
Johns Hopkins University
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AS 110.417 - Partial Diff Equations
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AS 110.421: Dynamical Systems
4.00 Credits
Johns Hopkins University
Prereqs: Calculus III, Linear Algebra, ODEs. This is a course in the modern theory of Dynamical Systems. Topic include existence and uniqueness of general ODEs, nonlinear analysis and stability, including bifurcation theory and stable and center manifolds, smooth flows, limit sets, Hamiltonian mechanics, perturbation theory and structural stability.
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AS 110.421 - Dynamical Systems
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