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所在平台: Udemy |
课程主页: https://www.udemy.com/course/numbertheory/
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课程名称：掌握数论2020：数字的秘密 课程概述：数千年来，数学家们一直对数字充满好奇。它们从何而来？它们具有什么属性？事实上，只有通过学习数论，你才能揭开数字的秘密，而参与此课程所需的只是一个好奇的头脑（此课程没有先决条件！）。历史上最大的问题之一是：如何将一个数字分解为质因数？例如，26=13*2，但试着分解1432479，难度就大了。如果我问你，1432479之后的下一个质数是什么？这些都是很有挑战性的问题，答案涉及一种不同类型的数学，但你不需要微积分的知识，而需要大量的好奇心。 在本课程中，你将探索整数的秘密及其所拥有的许多属性。尽管此课程属于高级数学课程，但理解这些内容并不需要微积分或任何高级数学知识。课程内容将主要围绕证明展开，而不是“求解...”问题。它是纯数学的良好入门，涵盖现代许多教授研究的主题。 你将学习并掌握： - 算术、质数与因数分解 - 解决丢番图方程 - 二次互反律与勒让德符号 - 连分数与原根 - 扩展欧几里得算法 - 现代因数分解的高级知识 - 质数的代数 - 毕达哥拉斯三元组 - 现代数学的代数 这不仅仅是一个基础数学课程。课程提供超过7小时的内容，内容的深度远超过大多数大学的数论课程。我们深入探讨每一个主题，提供清晰的例子帮助你理解。例如，威尔逊定理的证明，我们将以不同方式证明三次，而这只是课程中的一个定理。 那么，你还在等什么？
For thousands of years, mathematicians have been curious about numbers. Where did they come from? What properties do they have? The truth is that you will never learn the secrets of numbers until you take Number Theory, and all you need is a curious mind to understand (no prerequisites to this course!). One of the biggest problems in history has been: how do you factor a number into prime factors? Well, 26=13*2, but try factoring 1432479.Not so easy now? What if I asked what the next prime number was after 1432479 is? These are tough questions and their answers involve a different type of math - one that you don't need calculus for - but you need a lot of curiosity.In this course, you will look into the secrets of the integers and the many properties that they hold. You do not need Calculus or any advanced mathematics to understand this course, however this is an advanced mathematics course. The material will not involve "solve for..." problems. This course is designed to prove things, and so most of the lectures will cover proofs, and not problem solving. This is a great introduction to what pure mathematics actually deals with, and what many modern professors research.Learn and Master Arithmetic, Prime Numbers and Factorization Solving Diophantine EquationsQuadratic Reciprocity Theorems and Legendre SymbolContinued FractionsPrimitive RootsExtended Euclidean AlgorithmAdvanced Modern FactorizationAlgebra of Prime NumbersPythagorean TriplesSee the Algebra of Modern MathematicsThis is not just a basic math course. This course offers over 7 hours of content that will blow your mind. You will learn more material than most Universities offer in their own Number Theory courses. We go into depth on everything with clear examples that helps you understand.How in depth do we go? Take for example the proof of Wilson's Theorem. We will prove it Once, Twice, Three times each in a different way. And that's just one theorem in this course.So what are you waiting for?
