[vc_row el_class=”inner-body-content” css=”.vc_custom_1667212280779{padding-top: 30px !important;padding-bottom: 20px !important;}”][vc_column][vc_custom_heading text=”Pre-requisite(s)” font_container=”tag:h2|font_size:20px|text_align:left” use_theme_fonts=”yes” css=”.vc_custom_1667212267735{margin-top: 0px !important;}”][vc_column_text]None[/vc_column_text][vc_custom_heading text=”Recommended Book(s)” font_container=”tag:h2|font_size:20px|text_align:left” use_theme_fonts=”yes”][vc_column_text]Discrete Mathematics And Its Applications With Combinatorics And Graph Theory, 6th Edition; By Rosen; McGraw-Hill.[/vc_column_text][vc_custom_heading text=”Reference Book(s)” font_container=”tag:h2|font_size:20px|text_align:left” use_theme_fonts=”yes”][vc_column_text]Essentials Of Discrete Mathematics David J. Hunter (Reference Book)
Invitation To Discrete Mathematics (2nd Edition), By Matousek And Nevestril.
Discrete Mathematics Elementary & Beyond, By Lovasz, Pelikan And Vesztergombi[/vc_column_text][vc_custom_heading text=”COURSE OBJECTIVES” use_theme_fonts=”yes”][vc_column_text]
This course will lay the foundations for theoretical computer science. Basic mathematical concepts generally required for most computer science courses will be covered in the course. The course aims at developing precise and formal reasoning skills in students. Different ways of mathematical thinking will be explored i.e. Logical thinking, Relational thinking, Recursive thinking, Quantitative thinking and Analytical thinking.
[/vc_column_text][vc_custom_heading text=”COURSE LEARNING OUTCOMES (CLO)” font_container=”tag:h3|text_align:left” use_theme_fonts=”yes”][vc_column_text]Course Objectives[/vc_column_text][vc_custom_heading text=”COURSE CONTENTS” use_theme_fonts=”yes”][vc_custom_heading text=”Basics” font_container=”tag:h3|text_align:left” use_theme_fonts=”yes”][vc_column_text]Sets and their properties, Sequences, Summations[/vc_column_text][vc_custom_heading text=”Logical Thinking” font_container=”tag:h3|text_align:left” use_theme_fonts=”yes”][vc_column_text]
- Propositional and Predicate Logic (5 lectures)
- Truth Tables, Quantifiers, Implications, Logical fallacies
- Proof Techniques (7 lectures)
- Direct, Contradiction, Contra-positive, Induction
[/vc_column_text][vc_custom_heading text=” Recursive Thinking” font_container=”tag:h3|text_align:left” use_theme_fonts=”yes”][vc_column_text]
- Recursion, Recursive Definitions and induction (1 lecture)
[/vc_column_text][vc_custom_heading text=”Relational Thinking” font_container=”tag:h3|text_align:left” use_theme_fonts=”yes”][vc_column_text]
-
- Functions, Relations, Closures, Equivalences (3 lectures)
-
- Graphs (3 lectures)
- Subgraphs, Graph Isomorphism, Degree sequences
- Connectivity
- Eulerian graphs, Hamilton graphs
- Shortest paths
- Trees ( 3 lecture)
- Basic Properties
- Application
- Tree traversal
- Spanning trees/MST
- Graphs (3 lectures)
[/vc_column_text][vc_custom_heading text=” Quantitative Thinking” font_container=”tag:h3|text_align:left” use_theme_fonts=”yes”][vc_column_text]
- Number Theory (3 lectures):
- Division algorithm, GCD, LCM (Homework)
- Prime numbers, Fundamental theorem, Co-prime numbers, congruences
- Combinatorics (4 lectures)
- Permutations, Combinations, Binomial Coefficients
- Inclusion-Exclusion
- Pigeonhole principle
[/vc_column_text][vc_custom_heading text=”Analytic Thinking” font_container=”tag:h3|text_align:left” use_theme_fonts=”yes”][vc_column_text]
- Algorithms, Complexity (2 Lectures)
[/vc_column_text][vc_custom_heading text=”MAPPING OF CLOs TO ASSESSMENT MODULES” font_container=”tag:h2|font_size:20px|text_align:left” use_theme_fonts=”yes”][vc_column_text css=”.vc_custom_1667212244282{margin-bottom: 0px !important;}”]Quizzes
Assignments
Midterm/s
Final
[/vc_column_text][/vc_column][/vc_row]