Product Details
學員須知:
受不同學校開學時間影響，班課具體開學時間可能會有微調，具體時間以班課學員為主
班課時間一經確認不再變更，開課后每課若有超半數學員按時出席，則當天正常上課，如有特殊情況請提前告知協調
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 |
