Sophie Marques

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MATH-UA.343.001:
Algebra 1

Contents

  • Set theory
    • Fixing notation
    • Equivalence classes
  • Integers
    • Some algebra on the sets of the integers
    • Order on Z
    • Induction
    • Finite sets
    • Arithmetic in the integers Z
    • Divisibility in the system of integers
    • Prime factorization in Z
    • Modular arithmetic
    • The rational numbers
  • Group theory
    • Groups
    • Homomorphism
    • Generated subgroups
    • Cosets and quotient groups
    • Basic counting principles in group theory
    • Automorphisms and Inner Automorphisms
  • Transformation Groups
    • Actions of a Group G on a Space X
    • Transitive Group Actions
    • Applications of the Conjugacy Class Equation
  • Permutation Groups
    • The Structure of a Permutation
    • Parity of a Permutation
    • The Significance of the Simple Groups
    • Conjugacy Classes in Sn
    • More about the Alternating Group An
    • The Structure of S3 and S4
  • Product Structure in Groups
    • Direct products of groups
    • Direct Products and the Chinese Remainder Theorem
    • Semi direct product
    • Group Extensions
    • The Sylow theorems
    • Abelian Groups and the Sylow Theorems
    • More on Non-Abelian G
    • Types of Groups: Simple, Solvable, Nilpotent

Schedule:

TR 11:00AM- 12:15PM for MATH-UA.343.001
TR 12:30PM - 1:45PM for MATH-UA.343.005

Location:

CIWW 317 for MATH-UA.343.005
CIWW 517 for MATH-UA.343.001

Office hours:

Thursday 2:00-3:00pm MATH-UA.343.005
Thursday 3:00-4:00pm MATH-UA.343.001
or by appointment.

Grading:

  • Homework: 15%
  • Quizzes: 20%
  • Midterm : 25%
  • Final : 40%

Recommended book:

I.N. Herstein- Topics in Algebra, 2nd edition, 1975

Notes for the course by Frederick Greenleaf:

Slides.pdf (Extract from the notes more details are in the notes, do not contain solution of exercises and proofs done in class.)

-->For a better class.pdf

Syllabus

Syllabus MATH-UA.343.005
Syllabus MATH-UA.343.001


Having trouble with writting a good proof, logic (Set theory)?

Knowing how to prove is essential for this course, it will affect a lot your grade if your proof is incomplete or not well structure. If needed, we have gone over the basics of logics and proof techniques in the following page:
Logic and proofs page

Lost after chapter 2 ?

If Chapter 2 on Integers Goes too fast, find a slower overview in section 1, 2, 3, 4, 6, 7, 8 in my number theory class notes (you can also find more problem sets):
Number theory page

Having trouble with complex variables?

If your complex variables knowledge is a bit rusty see Greenleaf Complex variable chapter 1:
Complexvariable.pdf

Not remembering your linear algebra?

If your linear algebra knowledge is a bit rusty see my linear algebra page:
Linear algebra page

Homeworks

Past Quizzes

Midterm for this semester 21 March.

Past Midterm/Help for Midterm

  • Mains definitions, results you need to know for the midterm and advises :Help.pdf

Past Final