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Gauss's lemma (polynomials)
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Rings and Fields: Principal Ideals and Ring Homomorphisms
Covers principal ideals, ring homomorphisms, and more in commutative rings and fields.
Polynomial Factorization: Field Approach
Covers the factorization of polynomials over a field, including division with remainder and common divisors.
Rational Numbers Construction
Explores the construction of rational numbers, irreducible fractions, equivalence, and simplification rules.
Polynomial Root Finding
Explores polynomial root finding methods based on evaluating potential roots from divisors of the constant term.
Finite Fields and Group Theory
Explores solutions of the 2018 exam, finite fields, group theory, congruences, and polynomial irreducibility in Q[X].
Decimal Numbers
Explains the conversion process from fractions to decimal numbers and vice versa.
Berlekamp's Algorithm: Polynomial Factorization
Explores Berlekamp's algorithm for efficient polynomial factorization.
Real Numbers: Properties and Operations
Covers the properties and operations of real numbers, including divisibility rules and the concept of irreducible fractions.
Factoring Polynomials: Complexity and Algorithms
Delves into the complexity of factoring polynomials and the implications for security.
Rational Numbers: Amplification and Simplification
Covers rational numbers, amplifying and simplifying fractions, and calculating values.