Course Info

Course Category

Computer Science/Information Technology

Course Level

Graduate

Credit Hours

3

Prerequisites

N/A

Instructor

Dr. N. A. Zafar Ph.D Computer Science Kyushu University, Japan


Course Contents

Introduction,
Mathematical Tools,
Logic and Proving Techniques,
Proofs, Validation, Verification,
Strong Math. Induction,
Fibonacci Sequences,
Recurrence Relations: Mathematical Models, Analysis Techniques,
Recurrence Relations: Algorithms Design and Analysis Techniques,
Further Techniques Solving Recurrence Relations,
Time Complexity Measuring Notations,
Relations over Asymptotic Notations,
Brute Force Approach: Introduction, Starting with Primality, Sorting sequence of numbers,
Designing Algorithms using Brute Force and Divide & Conquer Approaches,
Designing Algorithms using Divide & Conquer Approaches,
Dynamic Programming for Solving Optimization Problems: Chain Matrix Multiplication Problem,
Chain Matrix Multiplication Problem using Dynamic Programming,
AssemblyLine Scheduling Problem,
2Line Assembly Scheduling Problem, nLine Assembly Scheduling Problem,
01 Knapsack Problem's Algorithm using Dynamic Programming, Optimal Weight Triangulation,
Optimal Weight Triangulation using Dynamic Programming,
Longest Common Subsequence, Optimal Binary Search Trees,
Dynamic Programming: Optimal Binary Search Trees, Greedy Algorithms,
Greedy Algorithms: Activity Selection Algorithm, Fractional Knapsack, Coin Change Making,
Greedy Algorithms: Huffman Coding,
Huffman Coding Problem, Road Trip Problem, Graph Theoretic Concepts,
Breadth First Search: Shortest Paths,
Proof of Breadth First Search Algorithm, Depth First Search,
Proof of White Path Theorem, Applications of Depth First Search,
Backtracking, Branch & Bound Algorithms,
Minimal Spanning Tree Problem, Kruskal's Algorithm, Prim's Algorithm,
Road Map Problem, Paths and Shortest Paths, BellmanFord Algorithm,
Proof: Bellman Ford Algorithm, Shortest Paths in Directed Acyclic Graphs,
Dijkstra's Algorithm: Problem Statement, Analysis, Correctness,
AllPairs Shortest Paths, Shortest Paths and Matrix Multiplication,
The FloydWarshall Algorithm, Johnson's Algorithm,
Number Theoretic Algorithms: Definitions and Some Important Results,
Number Theoretic Algorithms: GCD, Euclid's Algorithm, Groups and Rings,
Groups and Rings, Chinese Remainder Theorem, RSA Cryptosystem,
Fermat Theorem, Euler's Theorem, RSA Cryptosystem, String Matching Problem,
String Matching: Naive Algorithm, RabinKarp Algorithm, String Match. with Finite Automata,
Polynomials and Fast Fourier Transform: Representation of Polynomials, The DFT and FFT,
NP Completeness: Circuit Satisfiability; Proof: Formula Satisfiability, 3CNF; Clique


