Category: Mathematics
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Why are there no general equations for polynomials with degrees 5 or above? – A Study with Galois Theory
Galois Theory reveals the insolvability of quintic polynomials via radicals. Its elegance illuminates algebra’s limits and the profound complexity of higher-degree equations, shaping modern mathematical inquiry.
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The Method of Scientific Thinking – On E. Wigner’s Thesis of Mathematics’ Effectiveness
Eugene Wigner’s essay delves into the surprising link between mathematics and the natural world, showcasing its unpredictable influence on science and technology.
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Feynman’s Trick to Integration
The content describes Feynman’s trick: differentiating under the integral sign, to simplify and solve complex integrals – an often overlooked yet powerful mathematical method.
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Fractional Calculus – A Study of Differintegrals with Fractional Orders
The historical development and mathematical complexities of working with fractional derivatives.
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Bayesian Probability – A Conundrum of the Ages
Bayesian probability offers a dynamic, adaptable framework for decision-making, challenging traditional intuition by integrating new information and evolving beliefs.
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An Introduction to Calculus – Integration and Applications
Exploring integration as a tool for finding areas, accumulation, and continuous change, and usages in practical applications of real-world problems.
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An Introduction to Calculus – Differentiation Properties and Rules
The article offers deeper insights into calculus, focusing particularly on the principles, properties, and rules of differentiation, including the power, product, quotient, and chain rule.
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An Introduction to Calculus – Limits and Differentiation
The content covers calculus basics, especially limits and differentiation, their significance, and real-world problems solving using these concepts.
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Complex Numbers and Applications
How were they invented and what effect does it have on the modern world?