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Related lectures (31)

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Polynomials: Definition and Operations

Covers polynomials, their operations, division theorem, and provides illustrative examples.

Cyclic Groups: Structure and Applications

Explores cyclic groups, generators, isomorphisms, and the discrete logarithm problem in depth, highlighting their importance and applications.

Polynomials: Theory and Operations

Covers the theory and operations related to polynomials, including ideals, minimal polynomials, irreducibility, and factorization.

Euclidean Algorithm

Explains the Euclidean algorithm for polynomials over a field K, illustrating its application with examples.

Taylor Series: Finding Remainders

Covers Taylor series, remainder order, limits, and convergence criteria in approximating functions.

Homomorphisms and Isomorphisms

Explores homomorphisms, isomorphisms, group properties, and their applications through examples and exercises.

Frobenius Theorems in Number Theory

Explores Frobenius theorems in number theory, ideal class groups, norm properties, and geometry of numbers.

Projective Plane Curves

Introduces projective plane curves, degrees, components, multiplicities, intersection numbers, tangents, and multiple points, culminating in the statement of Bézout's theorem and its consequences.

Number Theory: Division

Explores the concept of division in number theory, including properties, algorithms, and examples.

Diffie-Hellman and ElGamal Cryptosystems

Explores Diffie-Hellman key exchange, ElGamal cryptosystem, and their security applications in cryptography.