Basic Structures:
Sets: Principle of Inclusion, Exclusion and Pigeonhole principle (6.2, 8.5, 8.6); Functions; and Matrices: Eigenvalues and Eigenvectors.
Mathematical Logic
Propositional Logic, Applications of Propositional Logic, Propositional Equivalences Predicates and Quantifiers, Nested Quantifiers, Rules of Inference Introduction to Proofs
Relations
Relations and Their Properties, n-ary Relations and Their Application, Representing Relations, Closures of Relations, Equivalence Relations, Partial Orderings
Random variable and probability distribution
Concept of random variable, discrete probability distributions, continuous probability distributions, Mean, variance and co-variance and co-variance of random variables. Binomial and normal distribution, Exponential and normal distribution with mean and variables and problems
Graph Theory
Graphs and Graphs models, Graph Terminology and Special Types of Graphs, Representing Graphs and Graph Isomorphism, Connectivity, Euler and Hamilton Paths, Shortest-Path Problems, Planar Graphs, Graph Coloring
Assessment Details (both CIE and SEE)
The weightage of Continuous Internal Evaluation (CIE) is 50% and for Semester End Exam (SEE) is 50%.
The minimum passing mark for the CIE is 50% of the maximum marks.
Minimum passing marks in SEE is 40% of the maximum marks of SEE.
A student shall be deemed to have satisfied the academic requirements and earned the credits allotted to each subject/ course if the student secures not less than 50% (50 marks out of 100) in the sum total of the CIE (Continuous Internal Evaluation) and SEE (Semester End Examination) taken together.
Continuous Internal Evaluation:
1. Three Unit Tests each of 20 Marks
2. Two assignments each of 20 Marks or one Skill Development Activity of 40 marks to attain the COs and POs The sum of three tests, two assignments/skill Development Activities, will be scaled down to 50 marks CIE methods /question paper is designed to attain the different levels of Bloom’s taxonomy as per the outcome defined for the course.
Semester End Examination:
1. The SEE question paper will be set for 100 marks and the marks scored will be proportionately reduced to 50.
2. The question paper will have ten full questions carrying equal marks.
3. Each full question is for 20 marks. There will be two full questions (with a maximum of four sub-questions) from each module.
4. Each full question will have a sub-question covering all the topics under a module.
5. The students will have to answer five full questions, selecting one full question from each module.
Suggested Learning Resources:
Text Books
1. Kenneth H Rosen, “Discrete Mathematics and its Applications”, McGraw Hill publications, 7th edition.
2. Wolpole Myers Ye “Probability and Statistics for engineers and Scientist” Pearson Education, 8th edition.
References Books
1. Richard A Johnson and C.B Gupta “Probability and statistics for engineers” Pearson Education.
2. J.K Sharma “Discrete Mathematics”, Mac Millian Publishers India, 3rd edition,2011.
Skill Development Activities Suggested
Course outcome (Course Skill Set)
At the end of the course the student will be able to :
CO1 Apply the fundamentals of set theory and matrices for the given problem.
CO2 Apply the types of distribution, evaluate the mean and variance for the given case study/ problem.
CO3 Solve the given problem by applying the Mathematical logic concepts.
CO4 Model the given problem by applying the concepts of graph theory.
CO5 Design strategy using gaming theory concepts for the given problem.
CO6 Identify and list the different applications of discrete mathematical concepts in computer science.
Program Outcome of this course
1 Engineering knowledge: Apply the knowledge of mathematics, science, engineering fundamentals, and computer science and business systems to the solution of complex engineering and societal problems.
2 Problem analysis: Identify, formulate, review research literature, and analyze complex engineering and business problems reaching substantiated conclusions using first principles of mathematics, natural sciences, and engineering sciences.
3 Design/development of solutions: Design solutions for complex engineering problems and design system components or processes that meet the specified needs with appropriate consideration for the public health and safety, and the cultural, societal, and environmental considerations.
4 Conduct investigations of complex problems: Use research-based knowledge and research methods including design of experiments, analysis and interpretation of data, and synthesis of the information to provide valid conclusions.
5 Modern tool usage: Create, select, and apply appropriate techniques, resources, and modern engineering and IT tools including prediction and modeling to complex engineering activities with an understanding of the limitations
6 The engineer and society: Apply reasoning informed by the contextual knowledge to assess societal, health, safety, legal and cultural issues and the consequent responsibilities relevant to the professional engineering and business practices.
7 Environment and sustainability: Understand the impact of the professional engineering solutions in business societal and environmental contexts, and demonstrate the knowledge of, and need for sustainable development.
8 Ethics: Apply ethical principles and commit to professional ethics and responsibilities and norms of the engineering and business practices.
9 Individual and team work: Function effectively as an individual, and as a member or leader in diverse teams, and in multidisciplinary settings.
10 Communication: Communicate effectively on complex engineering activities with the engineering community and with society at large, such as, being able to comprehend and write effective reports and design documentation, make effective presentations, and give and receive clear instructions.
11 Project management and finance: Demonstrate knowledge and understanding of the engineering, business and management principles and apply these to one‟s own work, as a member and leader in a team, to manage projects and in multidisciplinary environments.
12 Life-long learning: Recognize the need for, and have the preparation and ability to engage in independent and life-long learning in the broadest context of technological change.