heres a cool trick i learnt regarding infinite decimal numbers - 
ie
3.711711711711711711.....

let S = 3.711711711...
S= 3 + 711/1000 + 711/1000^2 + 711/1000^3....

see the pattern - the "ratio" is 1:1000 each time, each element in the series.

therefore 1000.S = 3711 + 711/1000 + 711/1000^2 + 711/1000^3....
1000.S - S = 3711- 3    (the infinite recurring decimals subtract and are removed from the picture)

999 S = 3708

S = 3708/999 or 412/111

pretty nifty !

second semesters exams just around the corner ! : O
this had been a really tough semester ! the work isn't too hard - but there is so much of it.

The math has been really fun.
Project/Team Management not so much since my team are a bunch of lazy ass teenagers...sheesh...

Statistics...its ok.

Here's a breakdown of the Maths we've covered.

* Proof of Pythagoras
* Trig ratios
* Natural Numbers, integers, Rational Numbers
* Proof root(2) is not a fraction
* Real Numbers as infinite decimals

* Intervals, closed and open notation
* Domain and range of a function
* Inverse trig functions
* The unit circle
* Elementary trig properties
* Periodicity of sin cos and tan

* Graphing of Functions
* Slope of a line between two points
* Average velocity for positions given in terms of time
* Instantaneous velocity defined as a limit.
* Derivatives, elementary calculus
* Polar coordinates
* Addition formulae for angles, double and half angle formulae

* Addition of two wave functions
* Modulus
* The Product Rule for differentiation of two functions
* The Chain Rule for Differentiation
* Trig identities and Simplifications
* Polynomials / RemainderTheorem
* Factorisation of Polynomials
* Completion of the square

* Leibniz Notation
* Implicit differentiation
* Differentiation of sin(x) and thus other trig ratios including powers and multiple angles
* Complex numbers, modulus of and argument of.
* Properties of modulus and complex conjugate of a complex number
* De Moivere's Theorem
* Square and Cube roots of complex numbers
* Relation to factoring polynomial functions


* Simple harmonic Motion

* Defn of natural log as the area under the graph of 1/x for x> 0

* graphing Exponential functions
* Decay / Half life

* Complex exponentials and their relation to trig functions

* Hyperbolic functions

* Derivatives of the inverse trig functions

* Local and Global maxima and minima, how to find them if they exist

* Vectors in R2 and R3 from both geometric POV and algebraic POV
* Length and dot product of vectors

* Angle between vectors, Orthogonality

* Parallel and perpendicular vectors

* Vector Cross Product

* Equations of lines and planes in R3

* Find a plane through 3 given non collinear points

* Row operations and simultaneous Equations

* Continuity on a point and on an interval.

* Max and min for continuous functions on closed bounding intervals

* Mean Value theorem, and consequence of a positive derivative 

* Rolle's Theorem as a special case

* Verbally posed max min problems

* Snell's Law

* Intermediate Value Theorem

* Approximate Solutions by repeated bi-sections

* Distance between two parallel lines.

* Indefinite integration - example of falling body under constant gravity

* Differential eqn's for Projectiles

* Geometric Sequence and its limit

* Summation

* Parametric curves in the plane

* Slope and equation of the tangent line

* Power Series

* Gregory Series

* Maclaurin Series

* Binomial Series

* Escape Velocity under the inverse square law of attraction