MATH 451 – Abstract Algebra 2

Syllabus

Certainly, here’s a sample syllabus for an Abstract Algebra 2 course, which typically covers more advanced topics in abstract algebra. Please note that this is a general example, and you should adapt it to meet the specific requirements and standards of your educational institution:

Course Title: Abstract Algebra 2

Course Description: Abstract Algebra 2 is an advanced course that explores deeper and more abstract concepts in algebraic structures. This course covers topics such as module theory, field extensions, and advanced group theory.

Course Objectives: By the end of this course, students should be able to:

  1. Understand and apply advanced concepts in abstract algebra.
  2. Work with algebraic structures such as modules, fields, and field extensions.
  3. Prove advanced algebraic theorems and properties rigorously.
  4. Solve mathematical problems using abstract algebraic techniques at an advanced level.
  5. Develop strong mathematical reasoning and problem-solving skills in abstract algebra.

Textbook:

  • [Insert Abstract Algebra 2 Textbook Title and Author(s)]

Materials:

  • Notebook or binder for class notes and assignments.
  • Graphing calculator (if required by the school or teacher).
  • Pencils, erasers, and a ruler.

Grading:

  • Homework and Class Participation: XX%
  • Quizzes and Assignments: XX%
  • Midterm Examinations: XX%
  • Final Examination: XX%

Course Outline:

Unit 1: Module Theory

  • Definitions and properties of modules.
  • Submodules, quotient modules, and module homomorphisms.
  • Free modules and projective modules.

Unit 2: Field Extensions

  • Field extensions and algebraic extensions.
  • Minimal polynomials and splitting fields.
  • Algebraic and transcendental elements.
  • Finite fields and field automorphisms.

Unit 3: Galois Theory

  • Galois extensions and Galois groups.
  • Fundamental theorem of Galois theory.
  • Solvability of polynomial equations by radicals.

Unit 4: Group Cohomology (Optional)

  • Introduction to group cohomology.
  • Cohomology of cyclic groups.
  • Applications of group cohomology.

Unit 5: Review and Final Exam Preparation

Note: This is a general example of a syllabus for an advanced Abstract Algebra 2 course. It’s essential to adapt it to meet the specific needs and standards of your educational institution. The percentages for grading, the textbook, and materials may vary. Additionally, consult with your institution’s curriculum guidelines and any state or district standards that may apply. Abstract Algebra 2 is typically a college-level course, and the level of rigor and depth may vary based on the institution’s curriculum.

Free Textbooks

Finding a completely free textbook for an advanced course like Abstract Algebra 2 can be challenging. However, there are some open educational resources (OER) and freely available online textbooks that cover advanced abstract algebra topics. Here are a few options:

  1. “Abstract Algebra: Theory and Applications” by Thomas W. Judson:
    • This free online textbook covers abstract algebra topics beyond the basics, including advanced group theory, ring theory, and field theory.
    • Website: https://abstract.ups.edu/aata/
  2. “Abstract Algebra: A First Course” by Dan Saracino:
  3. “A Course in Universal Algebra” by Stanley N. Burris and H.P. Sankappanavar:
  4. MIT OpenCourseWare (OCW):
    • MIT OCW offers free access to course materials from Massachusetts Institute of Technology (MIT) courses, including advanced abstract algebra. You can find lecture notes, assignments, and exams related to the subject.
    • Website: https://ocw.mit.edu/index.htm
  5. “Topics in Algebra” by I.N. Herstein:
    • While not entirely free, some universities provide online access to this textbook. Check if your institution has access through its library or website.

Please note that the availability of free online textbooks may vary depending on your institution’s resources and access to digital libraries. Additionally, some textbooks, like “Abstract Algebra: A First Course” and “A Course in Universal Algebra,” are freely accessible online. Be sure to explore these options and choose the one that aligns with your course’s curriculum and your learning style.

Free MOOCs

As of my last knowledge update in January 2022, finding a completely free Massive Open Online Course (MOOC) specifically focused on Abstract Algebra 2 can be challenging due to the advanced nature of the subject. However, you can explore MOOC platforms for related courses in advanced mathematics and abstract algebra. These courses may cover topics that align with the curriculum of an Abstract Algebra 2 course. Keep in mind that while auditing is often free, fees may apply if you want certificates or additional features. Here are some platforms where you can explore relevant courses:

  1. Coursera:
    • Coursera offers advanced mathematics courses, including abstract algebra. While auditing is often free, fees may apply for certificates.
    • Website: https://www.coursera.org/
  2. edX:
    • edX provides courses in advanced mathematics and algebraic structures. You can audit many of these courses for free, but fees may apply for certificates.
    • Website: https://www.edx.org/
  3. MIT OpenCourseWare (OCW):
    • MIT OCW offers free access to course materials from Massachusetts Institute of Technology (MIT) courses, including abstract algebra. You can find lecture notes, assignments, and exams related to the subject.
    • Website: https://ocw.mit.edu/index.htm
  4. Khan Academy:
    • Khan Academy offers a wide range of free math courses and tutorials that cover advanced topics, including abstract algebra.
    • Website: https://www.khanacademy.org/
  5. YouTube:
    • Some educators and institutions upload abstract algebra lectures and courses to YouTube for free. You can search for specific topics or courses on the platform.

While these courses may not be specifically tailored to Abstract Algebra 2, they cover advanced mathematical topics that are relevant to the subject. Be sure to explore the course descriptions and offerings on each platform to find courses that align with your learning objectives. Additionally, verify the availability of free auditing options for the courses you are interested in.

Leave a Comment

This site uses Akismet to reduce spam. Learn how your comment data is processed.