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torquerotates
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Which one should I take first? Does it help to take one before the other?
Depends on your interests.torquerotates said:Which one should I take first?
The two subject matters are largely unrelated. As long as you are comfortable with logical thinking and proofs as in the normal upper division linear algebra you should be fine.Does it help to take one before the other?
Depends on your interests.
Have you developed any interests yet?
torquerotates said:Also, do I need to know anything for real analysis or algebra besides proof skills? I know that my school has prereqs, but sometimes not everything is used.
jbunniii said:I studied algebra after analysis, so had built some mathematical maturity by then. I found a lot of the introductory algebra books to be boring and not very challenging, e.g. Gallian. The course I took nominally used Dummit and Foote, but the professor followed his own notes and I hardly ever looked at the book as it seemed very longwinded and dry. I read part of Herstein's "Topics in Algebra" instead, and really liked it, particularly the group theory parts. That book would be my first recommendation to anyone new to the subject but not new to proof-oriented mathematics in general.
Abstract Algebra is a branch of mathematics that studies algebraic structures such as groups, rings, and fields. It focuses on the properties and operations of these structures, rather than specific numbers or objects. Real Analysis, on the other hand, is a branch of mathematics that studies the properties of real numbers and functions. It involves the use of calculus and other mathematical tools to analyze continuous functions.
Abstract Algebra has many applications in fields such as cryptography, coding theory, and computer science. It is also used in physics, chemistry, and engineering to model and understand complex systems. For example, group theory is used to study crystal structures in chemistry, while ring theory is used in coding theory to design error-correcting codes.
Like any branch of mathematics, Abstract Algebra can be challenging to learn due to its abstract nature and the use of rigorous proofs. However, with dedication and practice, it can be a rewarding and interesting subject to study. It is recommended to have a strong foundation in algebra and calculus before delving into Abstract Algebra.
Real Analysis is a fundamental subject in advanced mathematics and is used in many areas such as differential equations, functional analysis, and topology. It provides the tools and techniques needed to rigorously prove theorems and solve complex problems in these fields. It is also a prerequisite for many graduate-level mathematics courses.
One example of a problem that can be solved using Abstract Algebra is the Rubik's Cube. The Rubik's Cube is a 3D puzzle with 6 colors on each of its 6 faces. The goal is to solve the puzzle by making all 6 faces have the same color. Group theory, a branch of Abstract Algebra, is used to study the different possible moves and positions of the cube, leading to a solution that can be applied to any scrambled cube.