2023年AIME全程班
AIME全程班是為備戰(zhàn)AIME競(jìng)賽而設(shè)計(jì)的一門數(shù)學(xué)課程。該課程主要涵蓋數(shù)學(xué)基礎(chǔ)知識(shí)、題目解析以及解題技巧等內(nèi)容，旨在提高學(xué)生的數(shù)學(xué)水平和應(yīng)試能力，以便更好地應(yīng)對(duì)AIME數(shù)學(xué)競(jìng)賽的挑戰(zhàn)。
Product Details
學(xué)員須知:
受不同學(xué)校開(kāi)學(xué)時(shí)間影響，班課具體開(kāi)學(xué)時(shí)間可能會(huì)有微調(diào)，具體時(shí)間以班課學(xué)員為主
班課時(shí)間一經(jīng)確認(rèn)不再變更，開(kāi)課后每課若有超半數(shù)學(xué)員按時(shí)出席，則當(dāng)天正常上課，如有特殊情況請(qǐng)?zhí)崆案嬷獏f(xié)調(diào)
課程大綱
| Essential?Topics | Extended?Details?(Divison?A?and?Beyond) | |
| Number?Theory | Prime?factorization | Number?of?factors |
| Sum/Product?of?factors | ||
| LCM?and?GCD | ||
| Euclidean?Algorithm?and?Bézout's?Theorem | ||
| Congruence?and?Modular?Algebra | Chinese?Remainder?Theorem(CRT) | |
| Euler’s?Theorem/Fermat's?Little?Theorem | ||
| Wilson's?Theorem | ||
| Diphantine?Equations | Estimation?and?Molular?Metthod | |
| Algebra | Resursive?Sequences | Characteristic?Equation?Method |
| Conjecture?and?Mathematical?Induction?Proof | ||
| Functions?and?Equations | Gaussian/Floor?function | |
| *Functional?Equations | ||
| Inequalities?and?Extreme?Value?Problems | Cauchy?inequality | |
| Jensen's?inequality | ||
| Weighted?AM-GM?Inequality | ||
| Rearrangement?Inequality?and?Chebyshev?Inequality | ||
| Polynomials | Fundamental?Theorem?of?Algebra?(Polynomial?Factorization) | |
| Generalized?Remainder's?Theorem | ||
| Rational?Root?Theorem | ||
| Vieta's?Theorem?and?Newton's?Sums | ||
| Complex?numbers | De?Moivre's?Theorem?and?Roots?of?unity | |
| Rotation,?Translation?and?Complex?Vector?Method | ||
| Geometry | Basic?Geometry?(Triangles?and?Polygons) | The?Law?of?Sines,?The?Law?of?Cosines |
| Area?Method?and?Heron's?formula | ||
| Centers?of?triangle | ||
| Menelaus's?theorem,?Ceva's?theorem,?Stewart?Theorem | ||
| Circles | Inscribed?and?circumscribed?polygon/Circle,?Cyclic?Quadrilateral | |
| Ptolemy's?theorem,?*Butterfly?Theorem | ||
| Basic?Analytic?Geometry | Ellipse,?*Parabola?and?Hyperbola | |
| Basic?Solid?Geometry | *Euler's?Polyhedron?Formula | |
| Combinatorics | Basic?Counting?Principle | Sum?Rules?and?Product?Rules |
| Permutations?and?Combinations | Advanced?problems?in?combinatorics | |
| Logic?reasoning | Pigeonhole?principle |
