
MSC Classification: msc# (mscname) 
Prerequisites: Algebra
Getting Oriented
Rough Guides to Analysis 
Calculus  
Real Analysis  
Complex Analysis 
This guide will discuss vectors and mathematical objects in 3dimensional space. Vectors provide a significant portion of the language of multivariable calculus, and must be understood before adequately broaching that subject.
In early mathematics courses, one usually sees functions of one variable only. For example, the function f(x)=x^{2} represents a function that takes in any number x and returns the number x*x. General functions, on the other hand, might have several input (independent) variables and several output (dependent) variables. For example, your position in space might be a function of time, and at least three numbers are required to specify the position exactly. The bodymass index is a function with two independent variables, weight and height, and a single dependent variable.
In order to study these kinds of functions, one needs to understand how they are typically represented mathematically. The purpose of this guide is to move beyond the Euclidean plane, and beyond representing points in space by pairs of values (x,y).
The Basics
3Dimensional Space
Vectors
Vector Functions
Functions of Two Variables
Implicit Functions and Surfaces
Vector Fields
Going Further
 functions with more than two/three inputs and outputs
The Road Ahead
References
 Reference