# 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%.

 Homework Date due Sec 0.3: Q2, 3, 4. Fri 8th September. Sec 0.3: Q16, 17, 18, 23. Fri 15th September. Sec 0.3: Q24, 29, 32, 35. Fri 22nd September. Sec 1.1: Q1, 11, 14, 16, 18, 25, 26. Fri 29th September. Sec 1.2: Q2, 6, 11, 20, 22, 25. Fri 6th October. Sec 1.3: Q4, 19; Sec 1.4: Q28, 32. Fri 27th October. Sec 2.1: Q4, 5, 9, 16, 17, 21, 25. Fri 3rd November. Sec 2.2: Q2, 3, 6, 16, 33, 38, 41. Fri 10th November. Sec 2.3: Q8, 13, 14, 15, 16, 18, 26. Fri 17th November. Sec 2.4: Q19, 20, 22, 23; Sec 3.1: Q5, 8. Fri 1st December.
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