Padmal's BLOG

What is Big O ??? Big O notation is a technique used to describe the complexity of an algorithm. It is very useful when evaluating performance wise of different algorithms doing the same task. In this post, I'm not going deep into the programming side but let's take a code snippet as an example. In this code, we are trying to add up all the natural numbers up to 100. There are two algorithms doing the same job but they perform differently. #***********************# # Method 1 n = 100 sum = 0 for i in range ( 0 , n + 1 ): sum = sum + int (i) print sum #***********************# # Method 2 print str (n * (n + 1 ) / 2 ) #***********************#

What is Taylor Series ??? Taylor Series in simple terms, is a way of finding the value of a function at any point. To calculate and formulate the answer, all we need is the function value at a single point and the values of all its derivatives at that point . The general expression for Taylor Series is expressed as follows. $$f(x) = \sum_{k = 0}^{\infty}\frac{1}{k!}(x - a)^kf^k(a)$$ Note that we need to know what the function values are at $f(a)$, $f'(a)$, $f''(a)$, ...

Python Programming Assignments This is the second set of python assignments I found.

1 ♦ 0 = 0.a 0.a = 0.a 0.a = (0 + 0 ).a [ Since 0 is the additive identity ] 0.a = 0.a + 0.a [ Distributive Axiom ] -0.a + 0.a = -0.a + 0.a + 0.a [ Adding (-0.a) to both sides, the additive inverse of 0.a ] 0 = ( -0.a + 0.a ) + 0.a [ Associative Axiom ] 0 = 0 + 0.a 0 = 0.a [ Since 0 is the additive identity ] ♠ 2 ♦ -a = -1(a) (-a) = (-a) (-a) = (-a) + 0 [ Additive Identity ] (-a) = (-a) + 0.a [ Since 0 = 0.a (By above theorem (1)) ] (-a) = (-a) + ( 1 + (-1) ) a [ Additive Inverse of 1 ] (-a) = (-a) + ( 1.a + (-1)a ) [ Distributive Axiom ] (-a) = (-a) + ( a + (-1)a ) [ Multiplicative Identity ] (-a) = ( (-a) + a ) + (-1)a [ Associative Axiom ] (-a) = 0 + (-1)a [ Additive Identity ] (-a) = (-1)a [ Additive Identity ] ♠ 3 ♦ -(a + b) = (-a) + (-b) -(a + b) = -(a + b) –(a + b) = (-1)( a + b ) [ By above theorem (2) ] (-1)(a + b) = (-1)(a) + (-1)(b) [ Distributive Axiom ] -(a + b) = (-a) + (-b) [ By above theorem

L1_2.2 Python Programs Step 1: Type the Python program using a text editor such as gedit or vi or emacs or Kwrite and save as test1.py ( $ gedit test1.py ) Step 3: Modify the above program to display the source code. # Step 1 # ******** # # display Hello World print "Hello world !\n" # Step 3 # ******** # print "# display Hello World\n" print "print \"Hello world !\\n\"\n"

Definition Let A and B be two subsets of ℝ A relation from A to B is a rule which assigns a member of B to each member of A. Definition Let A and B are two subsets of ℝ A function from A to B is a rule which assigns a unique member of B of each number of A.

This is my very first blog. Learning and implementing about blogging and discovering it's trends, basically this blog will help anyone out with Mathematics, Python Programming Fundamentals at the university level. Mathematics will cover Logic and Set Theory [Propositions, Quantifiers, Techniques of Proof, Sets, Relations, Functions], Real Analysis [Intervals, Supremum and Infemum, Completeness Axiom, Limit of a Function, Differentiability, Rolle’s Theorem, L’ Hospital’s Rule, Sequences, Convergence of Series: Ratio Test, Comparisons Test, Limit Comparison Test, Maclaurine’s Integral Test; Taylor’s Series, Integration of Continuous Functions, Definite and Indefinite Integrals], Complex Numbers, Vectors, and Matrices [Algebra of Complex Numbers, De Moriver’s Theorem, Argand Diagram, Vector Algebra, Scalar Triple Product, Vector Triple Product, Line and Plane, Matrix Algebra, Echelon Forms, Rank, Determinants, Eigen Values, Spectral Radius, Matrix Norms: Maximum Row Sum, M