# 'Mathematics' series

These books attempt to give a formal education on various fields of advanced mathematics, supplying fundamental results and intuitions that are essential for research in modern mathematics.

## Prerequisites
All of these books have the 'elementary mathematics' series of books I have written as prerequisites. In addition to this, some books in the series have other books as prerequisites; this will be discussed in the introduction of each book.

Since the first step to understanding more advanced mathematics is to get familiar with foundational mathematics and constructing valid proofs in mathematics, the following books have no other prerequisite structure:
- set-theory (fundamentals)
- mathematical-logic (fundamentals)

## Structure of books
These books are split into 3 parts
- Fundamentals; introduction to the rudiements of the field (assumed knowledge varies)
- Advanced; more advanced techniques and concepts frequently employed in the field (fundamentals is assumed knowledge)
- Miscellaneous; rather specific subfields of the field that are not fundamental nor frequently encountered (assumed knowledge varies)





definition; a mathematical description for an object or property
proposition; these are mathematical results
lemma; these are propositions used in propounding a specific theorem or set of theorems, or otherwise called a lemma for historical purposes
theorem; these are 'big' propositions
conjecture; these are propositions that are unproven
example; these are concrete demonstrations of mathematical results working

## References
Countless works have been used in the creation of these books; although they are not referenced yet, I plan to eventually make a reference section in each book.