描述
课程须知
1. 一对一定制辅导:个性定制,专属辅导,弹性时间,高效高质
2. 3-6人小班辅导:小组教学,针对辅导,及时反馈,性价比高
3. 线上辅导班:克服地域,网络授课,节约时间,课程回放
4. 线下授课地址:上海市长宁区镇宁路525号3楼
参赛须知
ARML 区域竞赛内容包括几何,代数,组合数学,概率,不等式等,简答为主,以6 人制团队形式参赛,更加注重数学的趣味性、跨学科运用的综合性以及同学们团队协作能力。ARML晋级挑战赛仅邀请在ARML区域赛中获得优异成绩团队参赛,以团队形式参赛,题型全部为证明题。晋级挑战赛非常新颖,通常是以某热门社会话题、议题为切入点,让团队用数学的方法解决问题,非常强调数学的应用性。
比赛语言:英文
ARML中国赛区区域挑战报名截止时间:2023年4月12日
ARML中国赛区区域挑战时间:2023年4月23日(周六),下午13:00-15:40(160分钟)
第一轮比赛日期:2023年10月28日(星期六)14:00-14:45(考试时间:45分钟)
ARML当地日期:2024年4月21日(星期日)14:00-16:50
考试地点: 考点学校(建议考点学校的同学选择本校考试,非考点学校的同学可以联系本校相关负责老师申请成为考点组织考试)
参赛资格:高中各个年级学生,6人组队参赛
课程大纲
Number Theory | Prime factorization; Number of divisors, Sum of divisors, Product of divisors; LCM and GCD |
Euclidean Algorithm and Bezout's Theorem | |
Congruence and Divisibility | |
Chinese remainder theorem(CRT), Fermat’s little theorem, Euler’s function and theorem, Wilson's Theorem | |
Diophantine Equations | |
Algebra | Algebraic identities and Algebraic manipulations |
Function Composition and Functional Equations (Induction and iteration Method) | |
Polynomials and Vieta's Theorem; Newton's Sum; | |
Fundamental inequalities, Cauchy inequality, other advanced inequalities | |
Rescursive Sequence; Characteristic Equation | |
Geometry | Basics in Geometry( Polygon; Area Method; The law of Cosine and the law of Sine) |
Triangles, Centers of triangle; Menelaus's theorem, Ceva's theorem, Stewart Theorem | |
Circles; Cyclic Quadrilateral;Power of Point Theorem: Ptolemy's theorem; Radical Axis; | |
Probability and Statistic | Counting Principles (Sum Rules, Product Rules, Permutation and Combinations) |
Geometric probability; Conditional Probability; Bayes Theorem | |
Logic reasoning (Pigeon Hole's Principle; Winning Strategy; Prove by contradiction; Principles of Inclusion and Exclusion) | |
Elementary Graph Theory; Coloring Problem and Labelling Method | |
College Topics | Limit, Differentiation, and simple Integration, |
Simple Series and convergency test | |
Simple Group Theory |