Discrete Mathematics and Engineering Mathematics:Syllabus
Propositional and first order logic. Sets, relations, functions, partial orders and lattices. Groups. Graphs: connectivity, matching, coloring. Combinatorics: counting, recurrence relations, generating functions.
Linear Algebra: Matrices, determinants, system of linear equations, eigenvalues and eigenvectors, LU decomposition.
Calculus: Limits, continuity and differentiability. Maxima and minima. Mean value theorem. Integration.
Probability: Random variables. Uniform, normal, exponential, poisson and binomial distributions. Mean, median, mode and standard deviation. Conditional probability and Bayes theorem.1. What Books to read :
1 Kenneth H Rosen 7 th Ed. - Chapter 1,2 and 6 , 8, 9 , 10 ( 10.4, 10.5, 10.8)
2 Susanna S Epp - Discrete Mathematics with Applications : Chapter 2 , 3, 6, 7, 8 , 9
3 Erwin Kryszig - 9th edition Chapter 7.1 to 7.7 , 8.1 to 8.3 , 20.2
4 Narsingh Deo - Chapter 2-5, 2-6, 4-5, 8-1, 8-2, 8-4, 8-6
5 Sheldon Ross - Chapter 1,2,3, 4 [exclude 4.8] ,5 [ exclude 5.6 ]
6 Kolman-Busby-Ross - Group and Semigroup - 9.1 to 9.5
7 Ralph P Grimaldi - Discrete & Combinatorial Math - Ring : 14.1 and 14.2 "
Video : IITM Discrete - https://www.youtube.com/playlist?list=PL0862D1A947252D20
LU Decomposition - https://www.youtube.com/watch?v=gA7m5lttIcU , this is the first video which need to be watched then shortcut ,finally system of equations video have to watch.
LA and calculus - video - https://www.youtube.com/playlist?list=PLx5CT0AzDJCmqjbTWbWCwzanbZwWQ_b182. Topics for that subject to read along with Chapter Subparts :
Propositional and first order logic - Rosen Chapter 1 - 1.1 to 1.6
Propositional Logic - Page 1 to 12. page 16 and 17
Propositional Equivalences - Page 25 to 31
Predicates and Quantifiers - page 37 to 49
Nested Quantifiers - page 57 to 63
Rules of Inference - page 69 to 78
Sets - Rosen Chapter 2 : 2.1 , 2.2
relations - Rosen Chapter 9 , 9.1 to 9.5
functions - Rosen Chapter 2.3
partial orders and lattices - Rosen Chapter 9.6
Groups : GROUP, Abelian Group, SEMIGROUP, MONOID, RING, INTEGRAL DOMAIN, FIELD from IITM Kamala Madam video lectures 35, 36, 37
Graphs : connectivity, matching, coloring is there in syllabus
From Rosen - connectivity, euler and hamilton paths , coloring is in chapter 10 - 10.4, 10.5, 10.8
From narsingh deo Chapter no 2 - 2-5, 2-6, Chapter no 4 - 4-5 [ connectivity] , Chapter no 8 - 8-1, 8-2, 8-4, 8-6 , so 4 color theorem , Independent set is imp from graph coloring.
Counting, recurrence relations, generating functions - Rosen Chapter 6 and Chapter 8
Linear Algebra : Erwin Kryszig - 9th edition Chapter 7.1 to 7.7 , 8.1 to 8.3 , video - https://www.youtube.com/playlist?list=PLx5CT0AzDJCmqjbTWbWCwzanbZwWQ_b18
Calculus : mean value theorem page 402 Kreyszig , and also from above video link
Probability : A first course in probability ~ Sheldon Ross,8th edition, chapter 1,2,3, 4 [exclude 4.8] ,5 [ exclude 5.6 ]3. Types of problems from where questions came previous years : Simple problems on logic.
Sets Related Questions. Properties of relation, function. Partial and Total Ordering.
Hasse Diagrams, Group Theory.
Different types of graph and there properties : vertex and edge connectivity , separable graph , k-connected graph , connected component, matching , graph coloring ( 4 color theorem ) ,
Euler and Hamiltonian Graphs , konigsberg Bridge problem, Independent set of vertices , chromatic number are important .
Tricky Problems on Permutations and Combinations. Pigeonhole principle.
LA : Eigen values and eigen vectors question. Simple questions related to matrix.
LA : Finding Values of variable with some properties of linear equations like infinite no of solutions or unique solution.
Calculus : Finding Maxima and Minima. Properties of limit, Continuity and differentiability. Finding values by Mean Value Theorem. Integration.
For probability questions You need to practice Bays theorem, Normal and poisson distribution, mean and variance of different distributions , standard deviaton .