Instructor: Foster Tom

Course on canvas.dartmouth.edu ⇗

Syllabus

Date Topic Homework/Exams Other notes
F Jun 26 Introduction, definition of a group, examples
S Jun 27 9:20am Basic properties of groups, division algorithm

Special day of classes

Math31MultiplicationTableForD6.pdfDownload Math31MultiplicationTableForD6.pdf

Math31BasicPropertiesofGroups.pdfDownload Math31BasicPropertiesofGroups.pdf
M Jun 29 Euclidean algorithm, Bezout theorem

Homework 1: 

Math31HW1.pdfDownload Math31HW1.pdf
W Jul 1 Modular arithmetic, cyclic groups, multiplicative groups of integers
F Jul 3

 

 Holiday - no class
M Jul 6 Permutation groups

Homework 2:

Math31HW2.pdfDownload Math31HW2.pdf
W Jul 8

Cycle notation, sign of a permutation
F Jul 10 Dihedral groups, generators and relations
M Jul 13 Homomorphisms, isomorphisms, subgroups

Homework 3
W Jul 15

Cauchy's theorem, Cayley's theorem
F Jul 17 Cosets, Lagrange's theorem
M Jul 20 Normal subgroups, quotients

Homework 4

 
W Jul 22

Midterm 1

 
F Jul 24 Isomorphism theorems
M Jul 27 Group actions

Homework 5
W Jul 29 Orbits, stabilizers, Burnside's theorem
F Jul 31 Conjugacy classes, class equation
M Aug 3 Sylow theorems

Homework 6
W Aug 5 Finite abelian groups
F Aug 7 Definition of a ring, examples, subrings
M Aug 10 Ideals, quotients

 

Homework 7
W Aug 12

Midterm 2

 
F Aug 14 Prime and maximal ideals
M Aug 17 Principal ideal domains, unique factorization domains

 

Homework 8
W Aug 19 Euclidean domains
F Aug 21 Modules
M Aug 24 TBD

Homework 9
W Aug 26 Further topics not to be tested: Introduction to Galois theory Last day of classes
Su Aug 30 11:30 am Final exam