Skip to main content
Contents
Embed
Dark Mode Prev Up Next
\(\require{mathtools}\require{color} \setcounter{MaxMatrixCols}{15}
\newcommand{\mbu}[1]{\mathbf{\mathrm{#1}}}
\newcommand{\N}{\mathbb N}
\newcommand{\Z}{\mathbb Z}
\newcommand{\Q}{\mathbb Q}
\newcommand{\R}{\mathbb R}
\newcommand{\cC}{\mathcal{C}}
\newcommand{\F}{\mathbb{F}}
\newcommand{\GF}{\mathrm{GF}}
\DeclareMathOperator{\Span}{Span}
\DeclareMathOperator{\rank}{rank}
\DeclareMathOperator{\lcm}{lcm}
\DeclareMathOperator{\rk}{rk}
\DeclareMathOperator{\wt}{wt}
\DeclareMathOperator{\im}{im}
\makeatletter
\@ifundefined{char}{
\DeclareMathOperator{\char}{char}
}{}
\makeatother
\DeclareMathOperator{\GRS}{GRS}
\DeclareMathOperator{\RS}{RS}
\DeclareMathOperator{\BCH}{BCH}
\newcommand{\transpose}[1]{#1^{\top}}
\newcommand{\by}{\mathbf{y}}
\newcommand{\bc}{\mathbf{c}}
\newcommand{\bx}{\mathbf{x}}
\newcommand{\bm}{\mathbf{m}}
\newcommand{\bs}{\mathbf{s}}
\newcommand{\be}{\mathbf{e}}
\newcommand{\bu}{\mathbf{u}}
\newcommand{\bv}{\mathbf{v}}
\newcommand{\bh}{\mathbf{h}}
\newcommand{\br}{\mathbf{r}}
\newcommand{\bzero}{\mathbf{0}}
\newcommand{\balpha}{\boldsymbol{\alpha}}
\newcommand{\subgroup}[1]{\langle{#1}\rangle}
\newcommand{\isom}{\cong}
\DeclareMathOperator\Aut{Aut}
\DeclareMathOperator\Char{char}
\DeclareMathOperator\cl{cl}
\DeclareMathOperator\Conj{Conj}
\DeclareMathOperator\Inn{Inn}
\DeclareMathOperator\Gal{Gal}
\DeclareMathOperator\Out{Out}
\DeclareMathOperator\orb{orb}
\DeclareMathOperator\Orb{Orb}
\DeclareMathOperator\Perm{Perm}
\DeclareMathOperator\stab{stab}
\DeclareMathOperator\Stab{Stab}
\DeclareMathOperator\fix{fix}
\DeclareMathOperator\Fix{Fix}
\DeclareMathOperator\Syl{Syl}
\DeclareMathOperator\Sym{Sym}
\DeclareMathOperator\soc{soc}
\DeclareMathOperator{\nil}{nil}
\DeclareMathOperator{\Nil}{Nil}
\DeclareMathOperator\jac{jac}
\DeclareMathOperator\Jac{Jac}
\DeclareMathOperator\Eq{Eq}
\DeclareMathOperator\Hol{Hol}
\DeclareMathOperator\Frac{Frac}
\DeclareMathOperator\GL{GL}
\DeclareMathOperator\SL{SL}
\DeclareMathOperator\So{SO}
\DeclareMathOperator\SU{SU}
\DeclareMathOperator\PGL{PGL}
\DeclareMathOperator\PSL{PSL}
\DeclareMathOperator\PSU{PSU}
\DeclareMathOperator\PSP{PsP}
\DeclareMathOperator\AGL{AGL}
\DeclareMathOperator\Heis{Heis}
\DeclareMathOperator\Dic{Dic}
\DeclareMathOperator\SA{SA}
\DeclareMathOperator\SD{SD}
\DeclareMathOperator\Fr{Fr}
\DeclareMathOperator\Mod{Mod}
\DeclareMathOperator\DQ{DQ}
\DeclareMathOperator\QD{QD}
\DeclareMathOperator\OD{OD}
\DeclareMathOperator\Cl{Cl}
\DeclareMathOperator\BinTet{2T}
\DeclareMathOperator\BinOct{2O}
\DeclareMathOperator\BinIcos{2I}
\DeclareMathOperator\Aff{Aff}
\DeclareMathOperator\BS{BS}
\newcommand{\normal}{\lhd}
\newcommand{\normaleq}{\unlhd}
\newcommand{\nnormal}{\ntriangleleft}
\newcommand{\nnormaleq}{\ntrianglelefteq}
\def\longto{\longrightarrow}
\def\into{\hookrightarrow}
\def\longinto{\longhookrightarrow}
\def\onto{\twoheadrightarrow}
\DeclareRobustCommand\longonto{\relbar\joinrel\twoheadrightarrow}
\DeclareMathOperator{\Image}{Im}
\DeclareMathOperator\Ker{Ker}
\DeclareMathOperator{\Id}{Id}
\newcommand{\ceil}[1] {\left\lceil #1 \right\rceil}
\newcommand{\floor}[1] {\left\lfloor #1 \right\rfloor}
\definecolor{xRed}{RGB}{229, 31, 58}
\definecolor{xBlue}{RGB}{68, 119, 170}
\definecolor{xGreen}{RGB}{33, 135, 51}
\definecolor{xPurple}{RGB}{170, 51, 119}
\definecolor{xOrange}{RGB}{ 197, 83, 17}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\newcommand{\fillinmath}[1]{\mathchoice{\underline{\displaystyle \phantom{\ \,#1\ \,}}}{\underline{\textstyle \phantom{\ \,#1\ \,}}}{\underline{\scriptstyle \phantom{\ \,#1\ \,}}}{\underline{\scriptscriptstyle\phantom{\ \,#1\ \,}}}}
\)
Section Course Calendar
The following is a tentative calendar for the course. Changes may be made as the semester progresses. Any changes will be announced in class and posted on the course website.
Table 2. Tentative Calendar
Week 1
May 19
Course Introduction, Symmetries, Cayley Graphs
Daily Prep 1
Chapters 1-2
May 21
Groups & Subgroups
Daily Prep 2
Startup, Modular Arithmetic Review
Chapters 2-3
Friday May 22 is drop deadline without a W
Week 2
May 26
Cyclic Groups
Daily Prep 3
Weekly Practice 1, Proof Review
Chapter 4
May 28
Permutation Groups
Daily Prep 4
Chapter 5
Week 3
June 2
Isomorphisms & Cosets
Daily Prep 5
Weekly Practice 2, Problem Set 1
Chapters 6-7
June 4
Cosets & Lagrange’s Theorem
Daily Prep 6
Exam 1
Chapter 7
Week 4
June 9
Products
Daily Prep 7
Weekly Practice 3, Video Project Group Selection
Chapter 8
June 11
Normal Subgroups
Daily Prep 8
Chapter 9
Week 5
June 16
Quotients & Homomorphisms
Daily Prep 9
Exam 1 Reattempt
Chapter 9 & 10
June 18
Homomorphism Theorems
Daily Prep 10
Weekly Practice 4, Video Project Topic Selection & Contract
Chapter 10
Week 6
June 23
Group Actions & Counting
Daily Prep 11
Weekly Practice 5, Problem Set 2
Chapter 7 & 29
June 25
Sylow’s Theorems
Daily Prep 12
Exam 2
Chapter 24
Week 7
June 30
Rings
Daily Prep 13
Weekly Practice 6
Chapter 12
July 2
No class - Independence Day Break
Sunday July 5 is the last day to withdraw with a W
Week 8
July 7
Domains
Daily Prep 14
Exam 2 Reattempt, Video Project Report
Chapter 13
July 9
Ideals & Quotients
Daily Prep 15
Weekly Practice 7
Chapter 14
Week 9
July 14
Ring Homomorphisms
Daily Prep 16
Problem Set 3
Chapter 15
July 16
Polynomial Rings
Daily Prep 17
Weekly Practice 8, Exam 3
Chapter 16
Week 10
July 21
Factorization & Divisibility
Daily Prep 18
Weekly Practice 9
Chapter 17, 18
July 23
Divisibility & Field Extensions
Daily Prep 19
Exam 3 Reattempt
Chapter 18, 20
Week 11
July 28
Finite Fields
Daily Prep 20
Problem Set 4, Weekly Practice 10, Video Project
Chapter 22
July 30
No class - Reading Day
Week 12
August 5
Final Exam: 8:00 - 10:50 AM
Exam 4: Week 9-11, Connections Exam