Lectures related to Solving the Quintic: Dominant Balance Analysis

Solving the Quintic: Dominant Balance

Explores dominant balance analysis in solving the quintic polynomial, with a focus on non-dimensionalization and series expansions.

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Covers data manipulation and exploration using Python with a focus on visualization techniques.

Complex Polynomials and Factorization

Explores complex polynomials, factorization, roots of equations, equilateral triangles, and infinite sums in sequences.

Laurent Series and Convergence: Complex Analysis Fundamentals

Introduces Laurent series in complex analysis, focusing on convergence and analytic functions.

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Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

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Provides an overview of analysis and algebra courses, focusing on real numbers, limits, functions, and exams.

Polynomial Roots: Finding Solutions and Division

Explains how to find solutions for polynomial equations and perform polynomial division.

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Offers a comprehensive introduction to Data Science, covering Python, Numpy, Pandas, Matplotlib, and Scikit-learn, with a focus on practical exercises and collaborative work.

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Covers various methods for solving polynomial equations through examples.

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Explores the intuition behind transforms of the place and addresses audience questions on integral calculations and function choices.

Complex Numbers: Operations and Applications

Explores complex number properties, roots, and polynomial equations in the complex plane.

Fourier Series: Understanding Periodicity and Coefficients

Explores t-periodic functions in Fourier series, discussing intervals, propositions, and variable changes for coefficient calculation and series convergence.

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Explores complex roots, conjugate pairs, and quadratic equations solving strategies.

Taylor Polynomials: Calculating Limits and Derivatives

Covers the calculation of Taylor polynomials and their applications in limits and derivatives of functions from R² to R.

Complex Roots and Polynomials

Explores complex roots, polynomials, and factorizations, including roots of unity and the fundamental theorem of algebra.

Taylor Series: Convergence and Applications

Explores Taylor series convergence and applications in approximating functions and solving mathematical problems.

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Explains the integration of Taylor series for CnR class functions.

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Covers the basics of numerical analysis and computational methods using Python, focusing on algorithms and practical applications in mathematics.

Attack on RSA using LLL

Covers Coppersmith's method for attacking RSA encryption by efficiently finding small roots of polynomials modulo N.

Approximation of Functions by Taylor Polynomials

Explores the theory and application of Taylor polynomials for function approximation and limit calculations.