Math 3360

• Classes start Mon Aug 28th, 9:00--9:50.
• Location: Math 110
  
• Office Hours: Mon, Wed, Fri; 11:00--12:00.
• Homework: Set periodically and posted to this website.
  
• Exams:
• The first midterm exam will be on Friday the 13th of October.
• The second midterm exam will be on Monday the 27th of November.
• The final exam will be on Wednesday the 13th of December from 7:30am to 10:00 am.
• Syllabus:
• Textbook: Algebra Pure and Applied. By Papantonopoulou.
  
• Outline: The course will cover some basic topics from an area of abstract algebra known as Group Theory. Group Theory provides a way to encode the symmetry of mathematical objects. The topics from the book that I intend to cover are:
• 0.3 Properties of the integers
• 1.1 Examples and Basic Concepts
• 1.2 Subgroups
• 1.3 Cyclic Groups
• 1.4 Permutations
• 2.1 Cosets and Lagrange's Theorem
• 2.2 Homomorphisms
• 2.3 Normal Subgroups
• 2.4 Quotient Groups
• 2.5 Automorphisms
• 3.1 Examples and Definitions
• 3.2 Computing Orders
• 3.3 Direct Sums
• 3.4 Fundamental Theorem of Finite Abelian Groups
• 4.1 Group Actions and Cayley's Theorem
• 4.2 Stabilizers and Orbits in a Group Action
• 4.3 Burnside's Theorem and Applications
• 4.4 Conjugacy Classes and the Class Equation
• 4.5 Conjugacy in the Symmetric Groups and Simplicity of the Alternating Groups.
• Note: This syllabus may be subject to modest alterations in content as the semester progresses.
  
• Assessment:
• Homework assignments will contribute to 10% of your grade. It is important that you hand them in on time.
• There will be two midterm exams, worth 25% each.
  
• There will be a final exam, which will be worth 40%.