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Linear and Abstract Algebra Forum

Join experts in discussing linear and abstract algebra topics. This includes vector spaces and linear transformations. Also groups and other algebraic structures along with Number Theory.

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Is Induction or Contradiction Better for Proving 2n+1 < 2^n When n > 3?

Sep 30, 2003 · Replies 6 · Oct 20, 2003

Replies: 6

Views: 5K

Divisibility of c by a and b but not ab .

Oct 1, 2003 · Replies 3 · Oct 17, 2003

Replies: 3

Views: 12K

Has the Prime Number Distribution Conjecture Been Cracked?

Sep 30, 2003 · Replies 6 · Oct 16, 2003

Replies: 6

Views: 6K

How is division defined in mathematics?

Sep 28, 2003 · Replies 6 · Oct 15, 2003

Replies: 6

Views: 9K

Understanding the Euclidean Algorithm: Solving for Relatively Prime Numbers

Sep 25, 2003 · Replies 2 · Oct 3, 2003

Replies: 2

Views: 5K

What is the relationship between the magenta and cyan areas?

Sep 30, 2003 · Replies 3 · Oct 2, 2003

Replies: 3

Views: 10K

Proving Divisibility: A Corrected Proof and Tips for Improvement

Sep 30, 2003 · Replies 2 · Sep 30, 2003

Replies: 2

Views: 5K

Is 1ln(5)/2πi Equal to 5 in Complex Number Exponentiation?

Sep 23, 2003 · Replies 9 · Sep 24, 2003

Replies: 9

Views: 5K

Proof of (m+n*)* = m* + n* in Modern Abstract Algebra

Sep 23, 2003 · Replies 2 · Sep 24, 2003

Replies: 2

Views: 4K

Guide to Constructing a Proof by Induction for Natural Numbers

Sep 23, 2003 · Replies 7 · Sep 23, 2003

Replies: 7

Views: 6K

Understanding Fermat's Last Theorem: A General Overview

Sep 18, 2003 · Replies 10 · Sep 22, 2003

Replies: 10

Views: 7K

What is Abstract Algebra and why is it important?

Jul 5, 2003 · Replies 3 · Jul 5, 2003

Replies: 3

Views: 4K

Linear and Abstract Algebra

Linear and abstract algebra are branches of mathematics that deal with algebraic structures and their properties.

Linear algebra primarily focuses on vector spaces, linear transformations, and systems of linear equations. It provides essential tools for understanding geometric concepts, solving linear equations, and working with matrices. Abstract algebra, on the other hand, is a more generalized study that investigates algebraic structures such as groups, rings, and fields. It delves into the properties and relationships of algebraic systems, aiming to identify common structures and abstract patterns.

Both linear and abstract algebra are foundational areas of mathematics with applications spanning diverse fields, from physics and computer science to cryptography and optimization.

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