SYLLABUS
Math 31 Homepage General Information Homework Assignments Exam related and Announcements
This
is a tentative course syllabus and it will be updated irregularly. The Homework
Assignments page will be updated every lecture..
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Lectures |
Sections in Text |
Brief Description |
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Day 1: 1/5 |
Chapter 0 |
Properties of integers; Euclidean
algorithm, Modular arithmetic |
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Day 2: 1/7 |
Chapters 0 and 1 |
Mathematical Induction,
Equivalence Relations, Properties of Functions, First Examples of groups |
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Day 3: 1/8 x-hour instead of Saturday 1/10 |
Chapter 2 |
Binary operations,
Definition and further examples of groups. |
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Day 4: 1/9 |
Chapter 2, and 3 |
Elementary properties of
groups, Finite groups, Subgroups. |
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Day 5: 1/12 |
Chapter 3 |
Subgroups, Subgroup tests. |
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Day 6: 1/14 |
Chapter 3 and start Chapter
4 |
Center of a group,
Centralizer of an element. Cyclic groups: definitions and examples |
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1/15 optional x-hour problem solving session and
preparation for the quiz |
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Day 7: 1/16 |
Chapter 4 |
Properties of cyclic groups
and start classification of subgroups of cyclic groups. |
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1/19 Martin Luther King Jr. Day No class |
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Day 8: 1/21 1st 30
minute quiz |
Chapter 4 |
Classification of subgroups
of cyclic groups. |
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Day 9: 1/22 x-hour instead of the class
on 1/19 |
Chapter 5 |
Permutations; Cycle
notation and Properties |
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Day 10: 1/23 |
Chapter 5 |
Properties of permutations |
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Day 11: 1/26 |
Chapter 6 |
Group isomorphism; Examples |
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Day 12: 1/28 |
Chapter 6 |
Properties of an
isomorphism; Automorphisms |
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1/29 optional x-hour problem solving session and
preparation for the Midterm exam |
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Day 13: 1/30 |
Chapter 7 |
Cosets; Lagrange's theorem; Arithmetical corollaries |
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Day 14: 2/2 Midterm exam |
Chapter 7 |
Fermat's little theorem;
Orbits and stabilizers; |
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Day 15: 2/4 |
Chapter 8 |
External Direct Product of
Groups |
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Day 16: 2/6 |
Chapter 9 |
Normal subgroups, Factor
Groups, Hölder's theorem |
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Day 17: 2/9 |
Chapter 9 |
More comments on normal
subgroups, Application of Factor Groups, Internal Direct Product |
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Day 18: 2/11 |
Chapter 10 |
Group Homomorphisms,
properties of subgroups under homormorphisms |
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Day 19: 2/12 x-hour instead of the class
on 2/13 |
Chapter 10 |
Normal subgroups and
kernels, First Isomorphism Theorem |
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2/13 Winter
Carnival No class J |
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Day 20: 2/16 The
date of 2nd 30 minute quiz is changed to 2/18 following students
wishes |
Chapters 10 |
Applications and Examples |
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Day 21: 2/18 2nd 30
minute quiz |
Chapters 12 |
Rings and examples of rings |
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Day 22: 2/20 |
Chapters 12 and 13 |
Subrings, and Integral Domains |
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Day 23: 2/23 |
Chapter 13 |
Fields, Characteristic of a
Ring with Unity |
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Day 24: 2/25 |
Chapter 14 |
Ideals and Factor Rings,
prime and maximal ideals |
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2/26 optional x-hour problem solving and
preparation for the quiz |
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Day 25: 2/27 |
Chapter 15 |
Ring Homomorphisms,
properties, ideals are kernels |
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Day 26: 3/1 3rd 30
minute quiz |
Chapter 15 |
Finish Ring Homomorphisms |
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Day 27: 3/3 |
Chapter 16 |
Polynomial rings, division
of polynomials |
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Day 28: 3/5 |
Chapter 17 |
Factorization of
Polynomials, Irreducible polynomials |
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Day 29: 3/8 |
Chapter 19, 20, 21 |
Vector spaces and their
dimensions (briefly). Extensions and algebraic extensions of fields. |