Introduction of Set theory

a set is a collection of objects (called members or elements) that is regarded as being a single object. To indicate that an object x is a member of a set A one writes x ∊ A, while x ∉ A indicates that x is not a member of A.

  • A ∪ B—read “A union B” or “the union of A and B
  • A ∩ B—read “A intersection B” or “the intersection of A and B
  • U is called the universal set
  • A′ or U − A is called as complement of A
  • Cartesian product: Let A and B be two sets. Cartesian product of A and B is denoted by A × B, is the set of all ordered pairs (a,b), where a belong to A and B belong to B.

A × B = {(a, b) | a ∈ A ∧ b ∈ B}

  • if every element in A is also in B and every element in B is in A; symbolically, x ∊ A implies x ∊ B and vice versa.

Resources for Learning Mathematics

Since I had decided to start my buttoms up approach for learning data science, I decided to start by refreshing and learning mathematics. I tried to search for some books from which I can learn, but found some really interesting and god MOOC Course and free ebooks (all legal).

 

MIT Open Sourceware

  1. Linear Algebra

eBooks

Getting Started with Mathematics – Again

We all know mathematics ( Well I mean, you know there is something called as mathematics, you or rather most are not aware of mathematics). This is a quick refresher and a handy reference for Mathematics.

What is Math?

Well, we all know what is math. It deals with numbers and only some of us seems to know it and most of us hate it. So we will know what math is, however, its difficult to define it and define scope of mathematics.

The Merriam-Webster dictionary defines mathematics as “the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations.” Well, the defination makes it more complex.

We will leave mathematics definition to experts and we will look at what constituents mathematics.

Major Division of Mathematics

There are various ways of classifying different sub-streams of mathematics, some varies a lot and some have similarity. Mathematics is still heavily researched areas and who knows, there will be another sub-stream of mathematics.

  • Pure Mathematics
    • Arithmetic
      • Number Theory
    • Algebra
      • Elementary Algebra
      • Linear, Multilinear Algebra
      • Order Theory
      • Field Theory
    • Geometry
      • Discrete Geometry
      • Algebric Geometry
      • Trignometry
      • Differencial Geometry
      • Finite Geometry
      • Topology
    • Combinatorics
    • Calculas
      • Differential Equation
      • Numerical Analysis
      • Functional Analysis
  • Applied mathematics
    • Probability
    • Mathematics Statistics
    • Computational Science
    • Mathematical Physics
    • Game Theory
    • Information Theory

Some of these sections can be debated as whether they are mathematics or physics etc, however, I have kept them as per my understanding. I will keep reviewing this list as and when my understanding matures.

It is practically impossible to create blog for these topics as each of them are huge topic and more and more dept is being uncovered everyday. I will try to create some notes which will be handy.

Thanks