Abstract Algebra Proof Concerns

In summary: It is recommended to go through each proof in Gallians Contemporary Abstract Algebra, starting with a quick glance and potentially practicing with shorter proofs before diving into more complex ones. Revisiting proofs at a later time may only require skimming.
  • #1
kvkenyon
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Hello. I started Gallians Contemporary Abstract Algebra today. Is it wise to go through each of the given proofs for all of the theorems. For example I just studied the proof for division algorithm. Took Quite some time. I don't know if I could have produced this proof without peeking at the proof that was given. Although I do understand how it works. I guess I'm curious how one of you tackles such a book.

-kevin
 
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  • #2
kvkenyon said:
Hello. I started Gallians Contemporary Abstract Algebra today. Is it wise to go through each of the given proofs for all of the theorems. For example I just studied the proof for division algorithm. Took Quite some time. I don't know if I could have produced this proof without peeking at the proof that was given. Although I do understand how it works. I guess I'm curious how one of you tackles such a book.

-kevin

I usually glance at the textbook's proof first. If it seems short/simple, I prove it myself as an exercise. If it seems long and convoluted, I read through the book's arguments with extreme detail. I only do this the first time I'm reading the text. If I come back to it a long time later, I might only skim the proof, since I know I have gone through its details already.

BiP
 

1. What is Abstract Algebra?

Abstract Algebra is a branch of mathematics that studies algebraic structures such as groups, rings, and fields. It deals with abstract objects and their operations, rather than specific numbers or variables.

2. What is a proof in Abstract Algebra?

A proof in Abstract Algebra is a logical argument that uses axioms, definitions, and previously proven theorems to demonstrate the truth of a statement. It is a way to rigorously verify the validity of a mathematical claim.

3. How do I construct a proof in Abstract Algebra?

To construct a proof in Abstract Algebra, you must first clearly state the theorem or proposition you are trying to prove. Then, use the axioms and definitions of the algebraic structure to logically deduce the truth of the statement. Remember to clearly explain each step and use proper mathematical notation.

4. What are some common techniques used in Abstract Algebra proofs?

Some common techniques used in Abstract Algebra proofs include direct proof, proof by contradiction, proof by induction, and proof by cases. These techniques involve using logical reasoning and mathematical properties to show the validity of a statement.

5. How can I improve my skills in writing Abstract Algebra proofs?

To improve your skills in writing Abstract Algebra proofs, practice regularly and seek feedback from others on your proofs. Additionally, familiarize yourself with common proof techniques and study a variety of proofs to enhance your understanding of the subject.

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