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Math 113 Summer 2014.
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DateLecture
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Group Theory
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Week 16/23/2014Examples.
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6/24/2014Basic arithmetic properties of Z. Equivalence relations.
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6/25/2014Definitions: group, subgroups, order.
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6/26/2014Homomorphisms, kernel, image. Isomorphisms. Cosets.
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Week 26/30/2014Lagrange's Theorem. Applications: groups of prime order. Cyclic Groups.
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7/1/2014Group actions. Orbits, stabilisers. Orbit partition. Normalisers, centralisers. .
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7/2/2014Conjugacy. Symmetric groups. Cayley's Theorem.
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7/3/2014Orbit-Stabliser Theorem. Actions of p-groups.
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Week 37/7/2014Sylow's Theorems
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7/8/2014Normal subgroups. Quotients. First Isomorphism Theorem.
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7/9/2014Finite abelian groups (+ products)
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7/10/2014Structure of p-groups. Subgroups of p-groups, Hall polynomial.
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Week 47/14/2014Structure theorem of finitely generated abelian groups.
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7/15/2014Classifying small groups. Simple groups OR Finite subgroups of rotations of the plane and sphere. (NON-EXAMINABLE)
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7/16/2014Exam Review.
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7/17/2014Exam 1 (in class)
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Ring Theory
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Week 57/21/2014Examples. Basic Definitions
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7/22/2014More on rings. Homomorphisms.
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7/23/2014Kernels, ideals.
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7/24/2014Quotient rings. Examples.
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Week 67/28/2014Isomorphisms. Isomorphism Theorem.
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7/29/2014Types of Rings: ED, PID
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7/30/2014Division algorithm in ED
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7/31/2014Relations between various rings
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Week 78/4/2014Prime, maximal ideals
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8/5/2014Fields. Examples.
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8/6/2014Field of fractions of domain.
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8/7/2014Finite fields. Examples.
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Week 88/11/2014Field extensions.
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8/12/2014Minimal polynomials etc
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8/13/2014Review
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8/14/2014Exam 2 (in class)
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