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所在平台: Udemy |
课程主页: https://www.udemy.com/course/math_olympiads_for_beginners/
课程评论：没有评论
课程名称：数学竞赛问题解决入门 课程概述：该课程旨在使初学者能够接触奥林匹克数学的众多主题，分为三个主要部分：三角学、几何与问题解决。课程包含20节视频讲座，课程理论和应用均有详细讲解，并且每个部分都有相应的作业，作业中包含来自各类奥林匹克竞赛的问题。在剩余的20节讲座中，我们将讨论超过125个问题，并解释其思想。 课程内容涉及多个高级主题，包括：函数、极值、 不等式、三角学、三角几何、集合与划分、函数方程、极值原理、数列与级数、高级不等式、解析几何（包括圆锥曲线）、曲线家族、数学归纳法、复数及其性质、递归序列与周期序列、构造法、组合数学、包含与排除原理、递归计数、数论、同余、丢番图方程、多项式及其根等。 该课程还涵盖了大量的奥林匹克代数主题，分为五个部分，每部分也包含多个理论和应用的视频讲解，以及相应的作业。一些高级主题包括：二次函数的代数、高级不等式、复数及其性质、代数表达式的极值、代数恒等式（包括拉格朗日恒等式和索非亚·热尔曼恒等式）、多项式、自反多项式与多项式的根、不可约性。 针对不同水平的学生，作业题目设计从初级到高级。如果学生在完成作业过程中遇到困难，可以联系讲师提供更多帮助（视频解答）以澄清问题。如果你在任何奥林匹克数学上下文中遇到特定的想法或定理，这门课程可能都涵盖了它！祝学习愉快，问题解决顺利！
The course covers a lot of the Olympiad topics making them accessible for beginners. The entire course is divided into 3 sections - Trigonometry, Geometry and Problem-Solving. Each section has multiple videos which cover the theory and applications. Most sections also have assignment with problems from various Olympiads. The theory for the course is covered in a total of 20 video lectures. We then discuss hundreds of problems (>125) in the remaining 20 or so lectures while explaining the ideas.Some of the advanced topics covered in the course include - Functions, Maxima/Minima, Inequalities, Trigonometry, Triangle Geometry, Sets and Partitions, Functional Equations, The extreme principle, Sequences and Series, Advanced Inequalities, Analytic Geometry including Conic Sections, Families of Curves, Mathematical Induction, Complex Numbers and their properties, Recursive and Periodic Sequences, The Construction Method, Combinatorics, Principle of Inclusion and Exclusion, Recursive counting, Number Theory, Congruences, Diophantine Equations, Polynomials, Roots of Polynomials. The course covers a lot of topics in Olympiad Algebra. The entire course is divided into 5 sections. Each section has multiple videos which cover the theory and applications. Most sections also have assignment with problems from various Olympiads. Some of the advanced topics covered in the course include - Algebra of Quadratic functions, Advanced Inequalities, Complex Numbers and their properties, extrema of algebraic expressions, Algebraic identities including Lagrange's identity and Sophie Germain identities, Polynomials, self-reciprocal polynomials and Roots of Polynomials, Irreducibility. The assignment problems have been specially designed to go from beginner to advanced levels. Any students who face difficulties with the assignments can reach out to the instructor and I shall try and provide more content (video solutions) to help clarify your issues.If you have come across a particular idea or theorem in any Olympiad Maths context, we have probably covered it in this course! Happy learning and have fun problem-solving!
