MATH 351 – Abstract Algebra 1

Syllabus

Certainly, here’s a sample syllabus for an Abstract Algebra 1 course. 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 1

Course Description: Abstract Algebra 1 is an introductory course that explores the fundamental concepts and structures in algebraic systems, including groups, rings, and fields. This course lays the foundation for advanced algebraic studies.

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

  1. Understand and apply the basic principles of abstract algebra.
  2. Work with algebraic structures such as groups, rings, and fields.
  3. Prove algebraic theorems and properties rigorously.
  4. Solve mathematical problems using abstract algebraic techniques.
  5. Develop strong mathematical reasoning and problem-solving skills.

Textbook:

  • [Insert Abstract Algebra 1 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: Introduction to Abstract Algebra

  • Historical overview of abstract algebra.
  • Sets, relations, and operations.
  • Group theory: definitions, examples, and basic properties.

Unit 2: Group Theory

  • Subgroups, cyclic groups, and permutation groups.
  • Group homomorphisms and isomorphisms.
  • Cosets and Lagrange’s theorem.

Unit 3: Rings and Integral Domains

  • Ring definitions and examples.
  • Integral domains, fields, and subrings.
  • Ring homomorphisms and ideals.

Unit 4: Polynomials and Factorization

  • Polynomial rings and their properties.
  • Factorization in polynomial rings.
  • Unique factorization domains and Euclidean domains.

Unit 5: Review and Final Exam Preparation

Note: This is a general example of a syllabus for an introductory Abstract Algebra 1 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 1 is typically a college-level course, so the level of rigor and depth may vary based on the institution’s curriculum.

Free Textbooks


You can find several free textbooks and open educational resources (OER) for studying Abstract Algebra 1. Here are a few options:

  1. “Abstract Algebra: Theory and Applications” by Thomas W. Judson:
    • This textbook is available for free online and covers the fundamental concepts of abstract algebra, including groups, rings, and fields.
    • Website: https://abstract.ups.edu/aata/
  2. “A First Course in Abstract Algebra” by John B. Fraleigh:
    • While not entirely free, some universities provide online access to this textbook. Check if your institution has access through its library or website.
  3. “Abstract Algebra” by Dummit and Foote:
    • “Abstract Algebra” by Dummit and Foote is a widely used textbook in abstract algebra. Some universities provide free online access to this book through their libraries or websites.
  4. “OpenStax Abstract Algebra”:
  5. MIT OpenCourseWare (OCW):
    • MIT OCW provides 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
  6. Abstract Algebra Online:
    • This website offers free lecture notes and resources for abstract algebra. While not a traditional textbook, it provides valuable content for self-study.
    • Website: http://abstract.ups.edu/

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 Dummit and Foote, may have limited free online access through specific universities or libraries. Be sure to explore the 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 1 can be challenging. However, you can explore MOOC platforms for related courses in abstract algebra and advanced mathematics. While these courses may not cover the entire Abstract Algebra 1 curriculum, they can still provide valuable insights into the subject. 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 and algebraic structures. While auditing is often free, fees may apply for certificates.
    • Website: https://www.coursera.org/
  2. edX:
    • edX provides courses in mathematics and related fields. 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 algebraic concepts, including abstract algebra topics.
    • Website: https://www.khanacademy.org/
  5. Harvard Online Learning – Abstract Algebra Course:
  6. 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 tailored to Abstract Algebra 1, 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.

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