Syllabus Mathematics for Computer Engineering - (2113111/2013111/2023111/2123111/2163111/2173111/2153111/2453111) Theory Term work Pract / Oral Total Internal Assessment End Sem Exam Exam Duration (in Hrs) Test 1 Test 2 Total 20 20 40 60 2 25 - 125 Sr. No. Name of Module Detailed Content I. Linear Algebra (Theory of Matrices) 1. Characteristic Equation, Eigenvalues and Eigenvectors, and properties (without proof). 2. Cayley-Hamilton Theorem (without proof), verification and reduction of higher degree polynomials 3. Similarity of matrices, diagonalizable and non - diagonalizable matrices. (Chapter - 1) II. Linear and Non-Linear Programming Problems 1. Types of solutions, Standard and Canonical of LPP, Basic and Feasible solutions, slack variables, surplus variables, Simplex method. 2. NLPP with one and two equality constraint (two or three variables) using the method of Lagrangeās multipliers. (Chapter - 2) III. Modular Arithmetic 1. Introduction to Congruence, Linear congruence, reminder theorem, solving polynomials, system of linear congruence. 2. Eulerās theorem, Fermatās little theorem, Application of congruence-RSA algorithm. (Chapter - 3) IV. Fourier Series 1. Dirichletās conditions, Fourier series of periodic function with period 2Ļ and 2l. 2. Fourier series of even and odd functions. (Chapter - 4) V. Statistical Techniques 1. Karl Pearsonās coefficient of correlation (r). 2. Spearmanās Rank correlation coefficient (R) (with repeated and non-repeated ranks). 3. Lines of regression, fitting of first-degree curves. (Chapter - 5) VI. Probability 1. Moment generating function, Raw moments. 2. Poisson Distribution, Normal Distribution (Chapter - 6)
