2023 ARML美國區(qū)域數(shù)學(xué)聯(lián)賽沖刺班
翰林的ARML美國區(qū)域數(shù)學(xué)聯(lián)賽沖刺班是為想要參加ARML比賽的學(xué)生提供。翰林的課程內(nèi)容包括廣泛的數(shù)學(xué)知識和技巧，包括數(shù)論、代數(shù)、幾何和組合數(shù)學(xué)。翰林的課程目標(biāo)是為學(xué)生提高數(shù)學(xué)競賽水平，讓他們有更好的競爭力。翰林提供高質(zhì)量的學(xué)習(xí)材料和團(tuán)隊競賽模擬考試，幫助學(xué)生更好地準(zhǔn)備比賽。
- 課時：30課時/10次課
Product Details
參賽須知
ARML 區(qū)域?qū)W術(shù)活動內(nèi)容包括幾何，代數(shù)，組合數(shù)學(xué)，概率，不等式等，簡答為主，以6 人制團(tuán)隊形式參賽，更加注重數(shù)學(xué)的趣味性、跨學(xué)科運(yùn)用的綜合性以及同學(xué)們團(tuán)隊協(xié)作能力。ARML晉級挑戰(zhàn)賽僅邀請在ARML區(qū)域賽中獲得優(yōu)異成績團(tuán)隊參賽，以團(tuán)隊形式參賽，題型全部為證明題。晉級挑戰(zhàn)賽非常新穎，通常是以某熱門社會話題、議題為切入點，讓團(tuán)隊用數(shù)學(xué)的方法解決問題，非常強(qiáng)調(diào)數(shù)學(xué)的應(yīng)用性。
比賽語言：英文
考試地點： 考點學(xué)校（建議考點學(xué)校的同學(xué)選擇本校考試，非考點學(xué)校的同學(xué)可以聯(lián)系本校相關(guān)負(fù)責(zé)老師申請成為考點組織考試）
參賽資格：高中各個年級學(xué)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 |
