Abstract Algebra II's Full Profile
This course is a continuation of Abstract Algebra I: we will revisit structures like groups, rings, and fields as well as mappings like homomorphisms and isomorphisms. We will also take a look at ring factorization, which will lead us to a discussion of the solutions of polynomials over abstracted structures instead of numbers sets. We will end the section on rings with a discussion of general lattices, which have both set and logical properties, and a special type of lattice known as Boolean algebra, which plays an important role in probability. We will also visit an important topic in mathematics that you have likely encountered already: vector spaces. Vector spaces are central to the study of linear algebra, but because they are extended groups, group theory and geometric methods can be used to study them.Later in this course, we will take a look at more advanced topics and consider several useful theorems and counting methods. We will end the course by studying Galois theory—one of the most important theories in algebra, but one that requires a thorough understanding of much of the content we will study beforehand.
Days of the Week:
Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday
- Level of Difficulty: Intermediate
- Size: One-on-One
- Cost: Free
- Institution: Saylor
- Topics: Algebra, General Mathematics, Linear Algebra, Probability
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