Course Info
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Course Category
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Computer Science/Information Technology
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Course Level
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Graduate
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Credit Hours
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3
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Pre-requisites
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N/A
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Instructor
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Dr. N. A. Zafar
Ph.D Computer Science
Kyushu University, Japan
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Course Contents
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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,
Assembly-Line Scheduling Problem,
2-Line Assembly Scheduling Problem, n-Line Assembly Scheduling Problem,
0-1 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, Bellman-Ford Algorithm,
Proof: Bellman Ford Algorithm, Shortest Paths in Directed Acyclic Graphs,
Dijkstra's Algorithm: Problem Statement, Analysis, Correctness,
All-Pairs Shortest Paths, Shortest Paths and Matrix Multiplication,
The Floyd-Warshall 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, Rabin-Karp 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, 3-CNF; Clique
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