Fundamentals of Modern Mathematics

Fundamentals of modern mathematics (FoMM) includes all the fundamentals of modern mathematics.  We study a variety of foundational topics such as algebra and precalculus as well as the fundamental elements of proof in the following pages.  Many people mistakes mathematics for calculations.  They are related, but they are not the same.  Proof is the ability to demonstrate a statement is true given some assumptions (called axioms) and the rules of logic.  Calculations are an underpinning of mathematics in the way that a particular alphabet is an underpinning of a language.  You can speak Japanese- even read and write Japanese to a large extent without knowing any Kanji.  Mathematics is much broader than calculation.  

Modern math is based upon certain kinds of calculations and we will study these because they have been fruitful.  I also want to make the point that mathematics is difficult.  It is precisely very difficult right up until the moment that it becomes easy.  With sufficient tenacity and practice every new area of mathematics you encounter will become easy.  Almost everything you have studied up through most of this course is expressible in terms of addition.  For the first time in many of your mathematical careers we will, however, move substantially beyond addition and begin to reach into the realms of modern mathematics!

Arithmetic

Sets

Coordinate Systems

Functions

Transformations of Functions

Polynomials and the Fundamental Theorem of Algebra

Trigonometric Functions

Implicit Functions

Vectors and Polar Coordinates

Parametric Equations

Limits