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所在平台: Udemy |
课程主页: https://www.udemy.com/course/complex-numbers-polynomials-basic-advanced/
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**课程总结：复数与多项式——基础与进阶** 本课程深入探讨了复数及其在数学领域中的核心地位。课程认为，正如原子构成了物质世界，复数构成了数学世界。本课程旨在帮助学习者理解复数如何统一并扩展我们所熟知的实数概念，以及如何通过引入虚数部分来解决实数范围内看似无解的数学问题，例如多项式方程的根。 课程强调，复数的引入是数学发展中的一个重要突破，它保证了任何函数至少有一个解，解决了实数范围内“方程无解”的尴尬局面。即使某些方程的解是复数形式（包含虚部），这也为数学研究开辟了新的、令人兴奋的探索方向。 学习完本课程，您将能够解决涉及复数（包括虚数）及其运算的各类问题，甚至探索虚数幂运算可能产生的实数结果。课程将带领您全面深入地理解复数及其在多项式理论中的广泛应用。
Just like everything in this universe is made up of atoms which in turn is made up of sub-atomic structures like electrons, protons and neutrons, everything in the mathematical universe is made up of complex numbers. In that sense, complex numbers are the most fundamental elements of the mathematical universe. Everything we know of numbers since elementary school also applies to complex numbers. But everything we know of complex numbers doesn't apply to real numbers. This is because, complex numbers consists of imaginary numbers (that we do not know of) in addition to real numbers (that we know everything of). So, learning complex numbers is fun. We revisit everything we know of and generalize the result and understanding so that it applies all the numbers i.e. real and imaginary.Any given function has at least a solution. This is a mathematical way of saying that the graph of the function cuts the X-axis at least once. A simple way to put it is 'the number of times a function cuts the X-axis, the same number of Xs will satisfy the given equation. When a given X satisfies a given equation, it is called the root of the equation. But it turns out that there are functions which do not seem to cut X-axis for any value of X. So for those functions we do not have a root or solution. It was insulting for the mathematicians to know that a function may not have a solution. To get around this, they invented complex numbers. Now with the introduction of complex numbers, even those functions which had no solution, seem to have a solution. But this solution is called a complex solution because it is in the form of a complex number (which consists of real and imaginary parts). Although a complex number consists of imaginary part (and therefore not only real part), the notion that there is a complex solution is actually contributing to newer real avenues of discovery and research. This is the beauty of complex number.After the completion of the course, you will also see and do problems involving how an imaginary number raised to a power of another imaginary number also might lead to a real number.If you want to know the fact of this matter, please enroll in the course where we have covered everything there is to know on the topic.
