At 6/17/11 10:32 PM, i-am-ghey wrote:
that's interesting.
i never realise there is such a HUGE difference in terms of syllabus. even ordinary differential equations are not included in HKALE pure math, let alone partial differential equation. we never learn anything about multivariable calculus until year one in undergraduate studies. do you guys need to know hyperbolic sines and cosines and stuff like that as well?
I'm always confused when people talk abu-out graduate/undergraduate/...
Math curriculum from the age of 13:
13-14-> Elements of calculations (PEMDAS), handling expressions with abstract letters, planar geometry with area of circle and so on.
14-15-> linear equations, goniometry, basic graphs
15-16-> geometry of similarity and congruence, full trigonometry, quadratic equations, geometry of circle
16-17-> systems of linear equations, continuity, limits, logic, logarithms
17-18-> differentiation/integration, elements of affine geometry, conic sections, probability theory/ statistics (also, some elements of mathematical reasoning, like induction)
University: things have changed, but this is how I've done it.
Year 1
Analysis: rigorous integration and differential equations, limits and Cauchy sequences, theory of differentiation and integration, multivariate functions (differentiation and continuity), metric spaces, introduction of special functions (goniometric, goniometric hyperbolic, exponential function, Gamma/Beta function)
Linear Algebra: Introduction of vectorspaces, matrices and notions of inproduct spaces
Geometry: Affine Geometry and theory of curves (Frenet frame)
Logic/Algebraic structures: Elements of logic languages and integer moduli spaces
Year 2:
Statistics and probability theory: A global overiew of probability theory (Bayes and such) and manipulation of statistic distributions and estimators
Algebra: Theory of groups, rings and algebras (isomorphism theories, normal subgroups and ideals, UFD, PID) , theory of diagonalisation theorems for normal operators, Gauss-Jordan theory
Analysis: Lebesgues integration, Cauchy theorem for complex functions, elements of Banach spaces.
Geometry: Projective spaces, theory of algebraic curves, surfaces in Euclidean space
Topology: (never took this course) Open sets, closed sets, continuous functions, connected and compact sets,...
Year 3 and year 4 (I've taken this within the new system, so i just run down the courses I've picked)
Differential Geometry: theory of surfaces more in depth (theorema egregium, differential frames, Hopf theorem,..)
Riemannian Geometry: expansion of the above-> Riemann curvature tensor, Desch symmetric spaces, Schur theorem,...
Submanifolds: Theory of submanifolds in standard spaces, in spheres and Kahler geometry
Advanced geometry: Quantification, Fedosov and Hodge cohomology and *-products, geometry of fibre bundles.
Differential Topology: Brouwer degree, winding number, theorem of Gauss-Bonnet
Algebra: Theory of Gallois, Multinomial rings (Groebner basis), Hilbert's Nullstellenszatz on algebraic curves.
Algebraic geometry: Algebraic curves and surfaces with a stress on the interaction of algebra and algebraic maps
Operator theory: Hilbert spaces and operators on it, theory of Gelfand, theorem of Stone, study of spectra.
Functional analysis: traceclass operators, theory of Banach/Hilbert spaces, topologies, theorem of Krein-Milman, Hahn-Banach theorem
Algebraic topology: Homotopy fundamental groups, Homology and cohomology theory
but of course the exam questions in hong kong is less standard and much harder. needs more problem solving skills than knowledge.
Chinese students here, stand out a lot. Other students are out there partying and having fun in their time off, however Chinese students usually just keep on going and you rarely ever see a Chinese student not busy studying. There seems to be a very heavy responsibility on performing and obtaining the best possible grades where you come from.
We have pretty high standards when it comes to exams, as I've heard stories comparing with other universities. But it will never rival the demands made in a few Asian universities. I'm pretty confident that some high level American university would be a cake walk to you.