美国区域数学联赛 (ARML) 全称是 The American Regions Mathematics League ，也叫美国地区数学联盟或者全美高中数学竞赛，是全美历史悠久、影响力非凡的团体赛制国际数学竞赛之一。是具有一定难度和挑战性的数学活动，美国学校通常通过AMC选拔优秀选手参加ARML。
ARML 主要包括区域赛(Local)、晋级挑战赛(power contest) 与国际赛(international)。区域赛在各个城市由各个学校组织，所有对数学感兴趣的学生都可以参加。晋级挑战赛邀请在区域赛中成绩优异的团队参加。国际赛主要在美国宾夕法尼亚大学、佐治亚州立大学、爱荷华州立大学和位于拉斯维加斯的内华达州立大学四所大学同时举办。
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;Powerof 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
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