A board overview of the subject, intended primarily for liberal arts students. What do mathematicians do, and why do they do it? We will examine the art of proving theorems,form the both the philosophical and aesthetic points of view, using examples such as non Eucliden geometrics, prime numbers, abstract groups and uncountable sets. Emphasis will be placed on appreciating the beauty and variety of mathematical ideas. The course will include a survey of important results and unsolved problems that motivate mathematical research. In AISS mathematics department was started in June2015. We had conducted inaugural function in Sep '2016 in that function we have chosen some students as a chairman, vice chairman and secretary. We proudly say we have conducted Rama Expo'2017 in Jan 7th 2017 as a remembrance of Ramanujam's birth In semester exams our students got Centum in Calculus and Theory of Equation in the year 2015 - 2016 and recently one student got centum in Arithmetic Ability in the year 2016 - 2017. In our department around 80 students are pursuing their under graduation programme.