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Lecture
Algebraic Functions: Two Gendarmes
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Related lectures (34)
Integration by Recurrence
MOOC: Analysis I
MOOC: Analysis I (part 7) : Indefinite and definite integrals, integration (selected chapters)
Explores integration by recurrence method with examples of square roots and polynomials.
Algebraic Identities and Trigonometry
Covers algebraic identities, trigonometry, and real functions, including injective, surjective, bijective, and reciprocal functions.
Integration: Simple Elements
MOOC: Analysis I
MOOC: Analysis I (part 7) : Indefinite and definite integrals, integration (selected chapters)
Covers the integration of simple elements using various techniques to solve integration problems.
Complex Roots: Conjugate Pairs and Quadratic Equations
Explores complex roots, conjugate pairs, and quadratic equations solving strategies.
Terminologie conventions
MOOC: Analysis I
MOOC: Analysis I (part 4) : Limit of a function, continuous functions
Covers the terminology and conventions related to the limit of a function and introduces algebraic and transcendental functions.
Attack on RSA using LLL
Covers Coppersmith's method for attacking RSA encryption by efficiently finding small roots of polynomials modulo N.
Second Degree Trinomial: Roots and Formulas
Covers second degree trinomials, discriminants, Viète's formulas, and root calculations.
Limits in Function Analysis
Introduces the concept of limits in function analysis and demonstrates their application through various examples.
Complex Numbers: Roots and Polynomials
Covers the properties of complex numbers, including finding roots and factorizing polynomials.
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Continuous Functions: Examples and Properties
Explores examples and properties of continuous functions, including limits and continuity.
Polynomials, Division, and Ideals
Explores polynomials, their operations, and the concept of ideals in polynomial rings.
Discrete Log Problem: Index Calculus
Explores the discrete log problem and index calculus method in cryptography.
Coppersmith's Method: Small Roots of Polynomials Mod N
Covers Coppersmith's method for finding small roots of polynomials modulo N efficiently.
Reed Solomon Codes: Basics and Applications
Introduces Reed Solomon Codes, their applications, polynomial definitions, interpolation, roots, and the Fundamental Theorem of Algebra.
Complex Roots and Polynomials
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Explores complex roots, polynomials, and factorizations, including roots of unity and the fundamental theorem of algebra.
Functions Composition: Continuity & Elements
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Covers the composition of functions, continuity, and elementary functions, explaining the concept of continuity and the construction of elementary functions.
Polynomials: Definitions and Operations
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Covers the definition and operations of polynomials, including addition and multiplication, degree, coefficients, and their role in algebraic systems.
Linear Combinations and Vector Spaces
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Introduces linear combinations in vector spaces, operations, and polynomials of degree 2.
Weil Conjectures: Rationality and Function Equation
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Covers the Weil conjectures on rationality, functional equation, and the Riemann hypothesis, exploring properties of varieties in algebraic geometry.
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