Product Details
參賽須知
ARML 區域學術活動內容包括幾何，代數，組合數學，概率，不等式等，簡答為主，以6 人制團隊形式參賽，更加注重數學的趣味性、跨學科運用的綜合性以及同學們團隊協作能力。ARML晉級挑戰賽僅邀請在ARML區域賽中獲得優異成績團隊參賽，以團隊形式參賽，題型全部為證明題。晉級挑戰賽非常新穎，通常是以某熱門社會話題、議題為切入點，讓團隊用數學的方法解決問題，非常強調數學的應用性。
比賽語言：英文
考試地點： 考點學校（建議考點學校的同學選擇本校考試，非考點學校的同學可以聯系本校相關負責老師申請成為考點組織考試）
參賽資格：高中各個年級學生，6人組隊參賽
課程大綱
| 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 |
