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What are the limits of computation? Are there problems that cannot be solved by computer? Which problems can solve quickly and efficiently and which problems cannot be solved quickly? The [course_title] course answers all these questions and shows you power and limitations of algorithms.

You will learn the nuts and bolts of algorithms that help you to create tools that make the computer smarter, faster and safer.

Upon completion, you will gain a solid understanding of the tools and techniques for dealing with the real-world problems.

Assessment

This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.

Certification

Edukite courses are free to study. To successfully complete a course you must submit all the assignment of the course as part of assessment. Upon successful completion of a course, you can choose to make your achievement formal by obtaining your Certificate at a cost of £49.

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Course Credit: Georgia Institute of Technology and Georgia Tech Online Master of Science in Computer Science

Course Curriculum

Languages & Countability
Introduction – Georgia Tech – Computability, Complexity, Theory: Algorithms L12 00:01:00
Functions – Georgia Tech – Computability, Complexity, Theory: Computability 00:02:00
Rules of the Game – Georgia Tech – Computability, Complexity, Theory: Computability 00:03:00
Operations on Languages 00:04:00
Countability – Georgia Tech – Computability, Complexity, Theory: Computability 00:03:00
Countability 2 – Georgia Tech – Computability, Complexity, Theory: Computability 00:04:00
Languages Are Uncountable – Georgia Tech – Computability, Complexity, Theory: Computability 00:02:00
Consequences – Georgia Tech – Computability, Complexity, Theory: Computability 00:02:00
Conclusion – Georgia Tech – Computability, Complexity, Theory: Computability (1) 00:01:00
Turing Machines
Motivation – Georgia Tech – Computability, Complexity, Theory: Computability 00:01:00
Introduction – Georgia Tech – Computability, Complexity, Theory: Computability – L2 00:04:00
Notation – Georgia Tech – Computability, Complexity, Theory: Computability 00:03:00
Testing Oddness 00:02:00
Configuration Sequences – Georgia Tech – Computability, Complexity, Theory: Computability 00:02:00
The Value of Practice – Georgia Tech – Computability, Complexity, Theory: Computability 00:01:00
Equality Testing – Georgia Tech – Computability, Complexity, Theory: Computability 00:04:00
Language Deciders – Georgia Tech – Computability, Complexity, Theory: Computability 00:01:00
Turing Machines Conclusion – Georgia Tech – Computability, Complexity, Theory: Computability – L2 00:01:00
Church-Turing Thesis
Introduction – Georgia Tech – Computability, Complexity, Theory: Computability L3 00:02:00
Simulating Machines – Georgia Tech – Computability, Complexity, Theory: Computability 00:02:00
Multitape Turing Machines – Georgia Tech – Computability, Complexity, Theory: Computability 00:01:00
Duplicate the Input – Georgia Tech – Computability, Complexity, Theory: Computability 00:02:00
Multitape SingleTape Equivalence – Georgia Tech – Computability, Complexity, Theory: Computability 00:03:00
RAM Model – Georgia Tech – Computability, Complexity, Theory: Computability 00:04:00
Equivalence of RAM and Turing Machines – GT – Computability, Complexity, Theory: Computability 00:03:00
Conclusion – L3 00:01:00
Universality
Introduction – Georgia Tech – Computability, Complexity, Theory: Computability L-4 00:01:00
Encoding a Turing Machine – Georgia Tech – Computability, Complexity, Theory: Computability 00:04:00
Building a Universal Turing Machine 00:02:00
Abstraction – Georgia Tech – Computability, Complexity, Theory: Computability 00:01:00
Language Recognizers 00:03:00
Recognizability and Decidability – Georgia Tech – Computability, Complexity, Theory: Computability 00:02:00
Alternating Machines – Georgia Tech – Computability, Complexity, Theory: Computability 00:01:00
Dovetailing – Georgia Tech – Computability, Complexity, Theory: Computability 00:02:00
Universality Conclusion – Georgia Tech – Computability, Complexity, Theory: Computability – L4 00:01:00
Undecidability
Introduction – Georgia Tech – Computability, Complexity, Theory: Computability L5 00:01:00
Diagonalization – Georgia Tech – Computability, Complexity, Theory: Computability 00:04:00
An Undecidable Language – Georgia Tech – Computability, Complexity, Theory: Computability 00:02:00
Mapping Reductions – Georgia Tech – Computability, Complexity, Theory: Computability 00:01:00
Some Trivial Reductions – Georgia Tech – Computability, Complexity, Theory: Computability 00:01:00
Reductions and (Un)decidability – Georgia Tech – Computability, Complexity, Theory: Computability 00:03:00
A Simple Reduction – Georgia Tech – Computability, Complexity, Theory: Computability 00:02:00
The Halting Problem – Georgia Tech – Computability, Complexity, Theory: Computability 00:03:00
Filtering – Georgia Tech – Computability, Complexity, Theory: Computability 00:02:00
Rice’s Theorem – Georgia Tech – Computability, Complexity, Theory: Computability L5 00:04:00
Conclusion – Georgia Tech – Computability, Complexity, Theory: Computability – L5 00:01:00
P and NP
Introduction – Georgia Tech – Computability, Complexity, Theory: Complexity – L6 00:01:00
Friends or Enemies – Georgia Tech – Computability, Complexity, Theory: Complexity 00:01:00
P and NP – Georgia Tech – Computability, Complexity, Theory: Complexity 00:02:00
Delicacy of Tractability – Georgia Tech – Computability, Complexity, Theory: Complexity 00:03:00
Running Time Analysis – Georgia Tech – Computability, Complexity, Theory: Complexity 00:02:00
Asymptotic Analysis – Georgia Tech – Computability, Complexity, Theory: Complexity 00:02:00
The Class P – Georgia Tech – Computability, Complexity, Theory: Complexity 00:02:00
Problems and Encodings – Georgia Tech – Computability, Complexity, Theory: Complexity 00:02:00
Nondeterministic TMs – Georgia Tech – Computability, Complexity, Theory: Complexity 00:03:00
Composite Numbers – Georgia Tech – Computability, Complexity, Theory: Complexity 00:03:00
The Class NP – Georgia Tech – Computability, Complexity, Theory: Complexity 00:01:00
NP Equals Verifiability Intuition – Georgia Tech – Computability, Complexity, Theory: Complexity 00:01:00
P and NP Conclusion – Georgia Tech – Computability, Complexity, Theory: Complexity – L6 00:01:00
NP - Completeness
Introduction – Georgia Tech – Computability, Complexity, Theory: Complexity – L7 00:01:00
The Hardest Problems in NP – Georgia Tech – Computability, Complexity, Theory: Complexity 00:03:00
Polynomial Reductions Part 2 – Georgia Tech – Computability, Complexity, Theory: Complexity 00:01:00
Independent Set – Georgia Tech – Computability, Complexity, Theory: Complexity 00:02:00
Vertex Cover – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:01:00
Vertex Cover = Ind Set – Georgia Tech – Computability, Complexity, Theory: Complexity 00:02:00
NP Completeness – Georgia Tech – Computability, Complexity, Theory: Complexity 00:02:00
CNF Satisfiability – Georgia Tech – Computability, Complexity, Theory: Complexity 00:02:00
Cook Levin – Georgia Tech – Computability, Complexity, Theory: Complexity 00:02:00
The Variables – Georgia Tech – Computability, Complexity, Theory: Complexity 00:02:00
Configuration Clauses – Georgia Tech – Computability, Complexity, Theory: Complexity 00:02:00
Transition Clauses Cont – Georgia Tech – Computability, Complexity, Theory: Complexity 00:01:00
Transition Clauses Cont – Georgia Tech – Computability, Complexity, Theory: Complexity 00:01:00
Cook Levin Summary – Georgia Tech – Computability, Complexity, Theory: Complexity 00:04:00
Conclusion – Georgia Tech – Computability, Complexity, Theory: Complexity – L7 00:02:00
NPC Problems
Introduction – Georgia Tech – Computability, Complexity, Theory: Complexity L8 00:01:00
Basic Problems – Georgia Tech – Computability, Complexity, Theory: Complexity 00:01:00
Strategy and Warm up – Georgia Tech – Computability, Complexity, Theory: Complexity 00:02:00
Transforming One Clause – Georgia Tech – Computability, Complexity, Theory: Complexity 00:04:00
CNF SAT – Georgia Tech – Computability, Complexity, Theory: Complexity 00:02:00
3CNF INDSET – Georgia Tech – Computability, Complexity, Theory: Complexity 00:01:00
Proof that 3CNF INDSET – Georgia Tech – Computability, Complexity, Theory: Complexity 00:02:00
Subset Sum – Georgia Tech – Computability, Complexity, Theory: Complexity 00:02:00
3 CNF Subset Sum – Georgia Tech – Computability, Complexity, Theory: Complexity 00:03:00
Proof that 3CNF SUBSET SUM – GT – Computability, Complexity, Theory: Complexity 00:01:00
NPC Conclusion – Georgia Tech – Computability, Complexity, Theory: Complexity 00:02:00
Dynamic Programming
Intro to Algorithms – Georgia Tech – Computability, Complexity, Theory: Algorithms 14 00:02:00
Introduction – Georgia Tech – Computability, Complexity, Theory: Algorithms – L9 00:01:00
Lesson Plan – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:02:00
Optimal Similar Substructure – GT- Computability, Complexity, Theory: Algorithms 00:04:00
Prefix Substructure – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:02:00
Sequence Alignment Algorithm – GT – Computability, Complexity, Theory: Algorithms 00:01:00
Sequence Alignment Summary – GT – Computability, Complexity, Theory: Algorithms 00:01:00
Chain Matrix Multiplication – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:02:00
Subchain Substructure – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:02:00
CMM Algorithm – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:02:00
CMM Summary – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:01:00
All Pairs Shortest Path – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:03:00
Shortest Path Substructure – GT – Computability, Complexity, Theory: Algorithms 00:04:00
The Floyd-Warshall Algorithm – GT – Computability, Complexity, Theory: Algorithms 00:02:00
All Pairs Summary – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:01:00
Transitive Closure – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:02:00
Dynamic Programming Conclusion – GT – Computability, Complexity, Theory: Algorithms 00:01:00
FFT
Introduction – Georgia Tech – Computability, Complexity, Theory: Algorithms L10 00:01:00
Prerequisites – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:01:00
Convolution – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:03:00
Representations of Polynomials – GT – Computability, Complexity, Theory: Algorithms 00:02:00
Multiplying Polynomials – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:01:00
Multiplying Polynomials Continued – GT – Computability, Complexity, Theory: Algorithms 00:02:00
Divide and Conquer Inspiration – GT – Computability, Complexity, Theory: Algorithms 00:03:00
Roots of Unity – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:05:00
FFT Example – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:01:00
FFT Algorithm – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:02:00
Butterfly Network – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:03:00
Recap of Progress – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:01:00
Vandermonde at Roots of Unity – GT – Computability, Complexity, Theory: Algorithms 00:03:00
Inverse FFT – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:01:00
FTT Conclusion – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:02:00
Maximum Flow
Introduction – Georgia Tech – Computability, Complexity, Theory: Algorithms L11 00:02:00
Lesson Plan – Georgia Tech – Computability, Complexity, Theory: Algorithms 00 00:01:00
Flow Networks – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:02:00
Tricks of the Trade – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:02:00
Residual Networks – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:03:00
Augmentations – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:01:00
The Ford-Fulkerson Algorithm – GT – Computability, Complexity, Theory: Algorithms 00:04:00
Flows and Cuts – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:02:00
Flows and Cuts – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:02:00
Cut Basics – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:02:00
Cut Capacity – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:01:00
Cut Capacity Continued – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:01:00
The Max-Flow Min-Cut Theorem -GT – Computability, Complexity, Theory: Algorithms 00:02:00
Better Augumentations – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:01:00
Scaling Algorithm – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:02:00
Analysis of Scaling – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:04:00
The Edmonds-Karp Algorithm – GT – Computability, Complexity, Theory: Algorithms 00:01:00
Analysis of Edmonds-Karp – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:00:00
Dinic’s Algorithm – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:02:00
Analysis of Dinic’s Algorithm – GT – Computability, Complexity, Theory: Algorithms 00:02:00
Maximum Flow Conclusion – Georgia Tech – Computability, Complexity, Theory: Algorithms – L 11 00:01:00
BP Matching
Introduction – Georgia Tech – Computability, Complexity, Theory: Algorithms L12 00:01:00
Bipartite Graphs – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:02:00
Matching – Georgia Tech – Computability, Complexity, Theory: Algorithms L12 00:01:00
Reduction to Max Flow – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:02:00
Reduction Correctness – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:02:00
Deeper Understanding – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:01:00
Augmenting Paths – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:04:00
Vertex Cover – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:01:00
Max Matching Min Vertex Cover – GT – Computability, Complexity, Theory: Algorithms 00:04:00
The Frobenius-Hall Theorem – GT – Computability, Complexity, Theory: Algorithms 00:03:00
Toward a Better Algorithm – GT – Computability, Complexity, Theory: Algorithms 00:01:00
The Hopcroft-Karp Algorithm – GT – Computability, Complexity, Theory: Algorithms 00:03:00
Shortest Augmenting Paths – GT – Computability, Complexity, Theory: Algorithms 00:03:00
Analysis of a Phase – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:01:00
Number of Phases – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:03:00
BP Matching Conclusion – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:02:00
Linear Programming
Introduction – Georgia Tech – Computability, Complexity, Theory: Algorithms L-13 00:01:00
Preliminaries – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:02:00
HS Linear Programming – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:05:00
To n Dimensions – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:02:00
Favored Forms – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:03:00
Basic Solutions and Feasibility – GT – Computability, Complexity, Theory: Algorithms 00:03:00
Fundamental Theorem of LP – GT – Computability, Complexity, Theory: Algorithms 00:05:00
Simplex Equations – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:03:00
Simplex Summary – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:01:00
Simplex Example – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:03:00
Simplex Correctness – Georgia Tech – Computability, Complexity, Theory: Algorithms 00:04:00
Getting Started – Georgia Tech – Computability, Complexity, Theory: Algorithms L-13 00:01:00
Conclusion L-13 00:02:00
Duality
Intro to Algorithms – Georgia Tech – Computability, Complexity, Theory: Algorithms 14 00:02:00
Dual Programs – Georgia Tech – Computability, Complexity, Theory: Computability 00:02:00
Duality Theorem – Georgia Tech – Computability, Complexity, Theory: Computability 00:03:00
Duality of Max Matching – Georgia Tech – Computability, Complexity, Theory: Computability 00:03:00
Duality of Max Flow – Georgia Tech – Computability, Complexity, Theory: Computability 00:02:00
Duality Conclusion – Georgia Tech – Computability, Complexity, Theory: Computability 00:01:00
Approximation Algorithms
Introduction – L 15 00:01:00
An Approximation for Min Vertex Cover 00:03:00
Lower Bounding the Optimum 00:01:00
Optimization 00:02:00
Approximation Algorithms 00:01:00
An FPTAS for Subset Sum 00:02:00
Traveling Salesman Problem 00:02:00
Hardness of Approximation for TSP 00:02:00
Summary – L15 00:01:00
Metric TSP 00:02:00
Correctness of Factor 2 TSP Approx 00:02:00
Conclusion – L15 00:01:00
Randomized Algorithms
Introduction – L16 00:01:00
Verifying Polynomial Identities 00:02:00
Discrete Probability Spaces 00:03:00
Repeated Trials 00:04:00
Independence and Conditional Probability 00:02:00
Monte Carlo and Las Vegas 00:03:00
Random Variables 123 00:01:00
Expectation 00:02:00
Quicksort 00:03:00
Analysis of Quicksort 00:04:00
A Minimum Cut Algorithm 00:02:00
Analysis of Min Cut 00:04:00
Max 3 SAT 00:02:00
Approx Max 3 SAT 00:04:00
PCP Theorem 00:04:00
Conclusion – L16 00:01:00
Assessment
Submit Your Assignment 00:00:00
Certification 00:00:00

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