  One of the great triumphs in the history of numerical methods was the
discovery of the Conjugate Gradient (CG) algorithm. It could solve a symmetric
positive-definite system of linear equations of dimension N in exactly N steps.
As many practical problems at that time belonged to this category, CG algorithm
became rapidly popular. It remains popular even today due to its immense
computational power. But despite its amazing computational ability, mathematics
of this algorithm is not easy to learn. Lengthy derivations, redundant
notations, and over-emphasis on formal presentation make it much difficult for
a beginner to master this algorithm. This paper aims to serve as a starting
point for such readers. It provides a curt, easy-to-follow but minimalist
derivation of the algorithm by keeping the sufficient steps only, maintaining a
uniform notation, and focusing entirely on the ease of reader.
