Engineering Mathematics Formula Sheet

A formula and reference sheet for the Engineering Mathematics part of the GATE CS 2027 syllabus, in four parts. Part A, Discrete Mathematics: propositional and first-order logic; sets, relations and functions with their counts; partial orders, lattices, monoids and groups; graph theory; combinatorics, recurrences and generating functions. Part B, Linear Algebra, over three pages: matrix algebra and determinants; rank, systems of equations and LU decomposition; eigenvalues and eigenvectors. Part C, Calculus: limits, continuity, differentiability, mean value theorems, maxima and minima, and integration. Part D, Probability and Statistics: the laws of probability, conditional probability and Bayes' theorem, random variables, expectation and variance, the uniform, binomial, Poisson, exponential and normal distributions, and mean, median, mode and standard deviation. Each card states the relation, what every symbol means, the conditions under which it holds and the mistake students make with it. The linear algebra and probability parts carry the most worked examples: rank and solution type, a full 3 x 3 eigen computation, two LU factorisations, Bayes with a rare condition, expectation and variance by the shortcut, and a table of the named distributions with mean, variance and memorylessness. A final page collects the pairs students confuse and a Last-Minute Recall list. Every worked number on the sheet was recomputed by a script. It is a revision aid for students who have already studied the topics; it does not replace a textbook or a course.