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Stage 1 Introductory Calculus

Introductory Calculus:
As you may have seen, calculus is crucial. It is not only important in advanced mathematics but also can be applied to many other fields. If you learn first year calculus in a college, your suggested text is probably J. Stewart's Calculus. This is a standard modern text, it is colorful and quite detailed. If you prefer it, that's fine. This book is thick, you would like to leave a few section, say vector calculus, double, triple, line and surface integrals, to the next stage. I would suggest a few non-standard texts and notes.

The first thing we need to fix up is the definition of limit, learn the epsilon and delta proof. Other key concepts are the mean value theorem, fundamental theorem of calculus, logarithm and exponential functions, inverse trigonometric functions, hyperbolic functions, basic differential equations, limit of sequences, indeterminate form, infinite series, basic idea of several variables.

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Stage 1 Introductory Algebra

Introductory Algebra:
Complex number, polynomials, matrix, system of equation, Gaussian elimination, vector space, linear transformation, etc. T.M. Aposotol's Calculus Vol. 1 in the calculus sections also introduce topics that is relevant to this area.

A few Americans (exchanged to Sydney) in my third year abstract algebra class told us they couldn't follow because they haven't learnt much complex number. In order to have fun with linear algebra and complex variables in stage 2, it's better to learn complex number now.

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Stage 1 Introductory Discrete Mathematics

Introductory Discrete Mathematics:
You will study logic and set theory in an introductory discrete mathematics. The concepts you learnt here will play a key role in your later studies and improve your thinking skill. You will also study proofs, functions (injective, surjective, bijective inverse), introductory graph theory and number theory, Euclid's algorithm, discrete probability (counting, nCr, nPr) etc in this course.

Only for Proof, Logic and Set Theory:

In general:

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Stage 1 Elementary Stuff

Elementary Stuff:
Here is a list that helps you to refresh and enrich your high school mathematics.

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Stage 1

For many reasons, high school mathematics is taught in an informal way, we'll fix things up here. The first stage contains the basic material that is required for most scientists and engineers, discrete mathematics is particularly meant for computer scientists.
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