Kurdistan Algebra Project · 2026 edition

A foundation
in algebra.

2026 course archive · Salahaddin University-Erbil

2026 delivery updates
Module 4 was taught online. Modules 5 and 6 were cancelled. Their originally planned dates, lecturers and topics are retained below for reference.

Course information

Study & teaching

The course was scheduled for six hours of lectures per week at the College of Science, Salahaddin University-Erbil. Module 4 was taught online; modules 5 and 6 were cancelled.

For further information, contact Dr. Andam Mustafa Ali.

Reading & resources

Algebra I: Online Notes by Peter Stevenhagen, translated by Reinie Erné (2025).

Further reading: Abstract Algebra, 3rd edition, David S. Dummit and Richard M. Foote. ISBN 978-0-471-43334-7.

Local textbook copy · PARI/GP

Course programme

Select a module title to explore its topics.

Module 01

11 Jan – 22 Jan

Peter Stevenhagen

What Is Algebra?
  • Groups, Rings, and Fields
  • Symmetries of the Rhombus
  • Arithmetic Modulo 8
  • Symmetries of the Square
  • Permutations of Four Elements
  • Spatial Symmetries
  • The Group Axioms
  • Orders of Groups and Elements
  • Permutation Groups
  • Cycle Notation
  • Subgroups, Cyclic Groups
  • The Sign Map
Module 02

25 Jan – 5 Feb

Ahmad El-Guindy

Plane Symmetries and Homomorphisms
  • Plane Geometry
  • Isometries
  • The Orthogonal Group
  • Plane Symmetry Groups
  • Sign of an Isometry
  • Geometry with Complex Numbers
  • Plane Transformation Groups
  • Exercises
  • Homomorphisms, Isomorphisms, Automorphisms
  • Additive Notation
  • Kernel and Image
  • Injectivity
  • Cosets
  • The Isomorphism Theorem
  • Normal Subgroups
  • Quotient Groups
Module 03

8 Feb – 19 Feb

Daniele Angella

Group Actions
  • Cubic and Tetrahedral Groups
  • Orbit, Stabilizer, Fixed Point
  • Orbit Decomposition Formula
  • Combinatorial Applications
  • Regular Action
  • Conjugation Action
  • Cauchy’s Theorem
  • Integers
  • Division with Remainder
  • GCD and LCM
  • Prime Numbers
  • Unique Prime Factorization
  • Rings
  • The ring Z/nZ
  • Arithmetic Modulo n
  • Euler’s Theorem and Fermat’s Little Theorem
Midterm exam
Module 04

5 Apr – 16 Apr

Laura Geatti (Lea Terracini)

Taught online

Factorization and Cryptography
  • Primality of Large Numbers
  • Large Number Factorization
  • Cryptography
  • The RSA Cryptosystem
  • Digital Signatures
  • Safety of RSA
  • Discrete Logarithms
  • Diffie–Hellman protocol

Module 4 teaching materials →

Module 05

19 Apr – 30 Apr

Rahim Zaare-Nahandi (Rashid Zaare-Nahandi)

Cancelled
Originally planned module · Not delivered

Quotients, Products and Abelian Groups
  • Subgroups under Quotient Maps
  • Homomorphism Theorem
  • Commutator Subgroup
  • Direct Product
  • Semi-direct Product
  • Exact Sequences
  • Splitting Exact Sequences
  • Free Abelian Groups
  • Structure Theorem
  • The Group (Z/nZ)∗
Module 06

3 May – 14 May

Francesco Pappalardi (Michel Waldschmidt)

Cancelled
Originally planned module · Not delivered

Finite Groups
  • Non-abelian Exact Sequences
  • Classification for Simple Group Orders
  • Sylow p-Subgroups
  • Construction of Normal Subgroups
  • Solvable Groups
  • Simple Groups
  • Further topics
  • Preparation to final Exam

Exams & solutions