Parity and Counting Arguments Two very powerful elements of the proof-making arsenal: Parity – a way of referring to the result of an even/odd calculation Counting arguments – most often in the form of

Counting Many questions in Mathematics are related to the question: “How many … “? How many subsets does a finite set have? How many handshakes will transpire when n people first meet? How many functions

Document your progress and share as you go so that others can learn along with you. source 5. Tell Good Stories Work doesn’t speak for itself Art forgery is a strange phenomenon. Accordingly, when shown

The C Programming Language C is a general-purpose programming language, closely associated with the UNIX systems since most of the programs and even the UNIX systems itself are written in C. Interestingly,

“For artists, the great problem to solve is how to get oneself notice.” source 1. You don’t have to be a genius Be an amateur The best way to flourish is to retain an amateur’s spirit and embrace uncertainty

There are a great many functions that fail the horizontal line test (HLT) which nevertheless have an inverse function. fails HLT but is a pretty reasonable inverse for it (just be careful with the negative

The most useful abstractions in mathematics is the concept of function, which can be further abstracted. Another mathematical object that acts like functions is an operator, an entity that devours functions

Ordering Relations The prototypical symbol for ordering relations is , another example of ordering relation is . Note, however, that they are different in two aspects: first is that one doesn’t contain

Equivalence relations The idea of equivalence relation is not limited to equality (" = "), another interesting equivalence relation is “equivalence mod m” which we will denote using Equivalence

Equivalence and Ordering relation There are two classes of relations we are going to cover in the coming posts namely: equivalence relations and ordering relations. These relations have salient properties

What is a mathematical relation? It’s a mathematical symbol you can place between two numbers/variables to create a logical statement (or an open sentence). The importance of "relation" is its

The Strong form of mathematical induction The strong form of mathematical induction is so called because the hypotheses one uses are stronger. It comes in various names, strong induction is also called

In the previous post, long time ago, we talked about an application of the principle of mathematical induction in proving statements, for instance, sums and product rules. In this section, we will explore

There is this old tale about a child who found a formula for summing the first 100 natural numbers. The kid is no other than Gauss. He developed a clever method for justifying it, and he was only 7 at

The Principle of Mathematical Induction (PMI) may be the least intuitive proof method available to us. Despite the indisputable fact that proofs by PMI often feels like magic, we need to convince you of

source: pixabay As a physics student, it is natural for me to describe and analyze complex phenomena in terms of its fundamental elements. This approach to thinking, done by reducing a complex system into

1:03 AM The silence of the early morning made me hear natural sounds of the surrounding at this hour of the day. I can hear the faucet dripping. I can hear the fan rotating as it tries to distribute the

Disclaimer: this is a summary of section 4.5 from the book A Gentle Introduction to the Art of Mathematics: by Joe Fields, the content apart from rephrasing is identical, most of the equations are screenshots

The discussion of set theory would not be complete without the inclusion of a useful tool known as Venn diagram. Venn diagram is useful in visualizing set operations, in which logical sets are presented

Disclaimer: this is a summary of section 4.3 from the book A Gentle Introduction to the Art of Mathematics: by Joe Fields, the content apart from rephrasing is identical, most of the equations are screenshots