Introduction to Graduate Algorithms from Udacity

What's inside

Syllabus

Overview of main topics covered, course webpage available at: https://gt-algorithms.com

Dynamic programming: Toy problem (Fibonacci numbers), Longest Increasing Subsequence (LIS), and Longest Common Subsequence (LCS).

Dynamic programming: Knapsack, and Chain Matrix Multiplication.

Dynamic programming algorithms for solving various shortest path problems on graphs.

Modular Arithmetic: Fast Modular Exponentiation and Multiplicative Inverses.

RSA Cryptosystem: Fermat's Little Theorem, RSA Protocol, and Primality Testing.

Lecture about Hashing: Toy problem of Balls into Bins, Traditional Chain Hashing, and Bloom Filters.

Faster Divide-and-Conquer Algorithm for Multiplying Large Integers.

Linear-time Divide-and-Conquer Algorithm for Finding the Median from an unsorted list.

Refresher Lecture about Solving Recurrences.

High-level approach for polynomial multiplication and FFT (Fast Fourier Transform). Primer on complex numbers, including complex roots of unity.

FFT and polynomial multiplication algorithms, and inverse FFT.

Connectivity: Connected components of undirected graphs, Topological sorting of a DAG, and strongly connected components of general directed graphs.

Polynomial-time algorithm for 2-SAT, using the SCC algorithm.

Minimum Spanning Tree (MST): Cut Property for MST's, and Kruskal's MST algorithm.

Introduction to Markov Chains, and an exposition of the PageRank algorithm.

Max-flow: Problem statement, residual network, and Ford-Fulkerson algorithm.

Max-Flow Min-Cut Theorem: Statement and Proof, and proof of correctness of Ford-Fulkerson and Edmonds-Karp augmenting path algorithms.

Max-flow: Application to Image Segmentation problem.

Max-flow: Edmonds-Karp augmenting path algorithm.

Max-flow: Generalization allowing demand constraints.

Linear Programming: Basics, Standard Form, and Simplex Algorithm Overview

Geometry of Linear Programs: Feasible Region, Infeasible LP's, and Unbounded LP's.

Dual of a Linear Program; Converting an LP problem to its Dual; Weak and Strong Duality.

Maximum Satisfiability Problem; Approximate Solutions; Integer Programming; Calculus.

NP: Definition of a Search Problem and Computational Complexity Classes P and NP; Proving a Problem is in NP; Reductions; and the notion of NP-Completeness

3-SAT Problem is NP-Complete

NP-Completeness of Graph Problems: Independent Sets, Clique, and Vertex Cover

Knapsack and Subset Sum Problems are NP-Complete

Halting Problem is Undecidable

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Develops advanced algorithmic techniques for solving hard computational problems, which is highly relevant in academia and industry

Taught by Eric Vigoda and Arpan Chakraborty, who are recognized for their work in algorithms and computational complexity

Covers a wide range of topics, including dynamic programming, graph algorithms, number theory, and linear programming

Designed to build a strong foundation for students interested in pursuing graduate studies in algorithms or computer science

Provides interactive materials and exercises to enhance understanding

Assumes a basic understanding of algorithms and data structures

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Introduction to Graduate Algorithms with these activities:

Read 'Introduction to Algorithms' by Cormen, Leiserson, Rivest, and Stein

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Supplement your learning with a classic textbook that provides a comprehensive foundation in algorithms.

View Introduction to Algorithms, fourth edition on Amazon

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Purchase or borrow a copy of the book
Read the relevant chapters that align with the course topics
Take notes and highlight important concepts
Complete the practice exercises at the end of each chapter

Follow online tutorials on graph algorithms

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Supplement your learning by exploring additional resources that provide visual explanations and interactive exercises.

Browse courses on Graph Algorithms

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Search for online tutorials on specific graph algorithms
Watch the tutorials and take notes on key concepts
Try out the interactive exercises and test your understanding
Refer back to the tutorials as needed to reinforce your learning

Join a study group

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Collaborate with peers to discuss concepts, solve problems, and reinforce your learning.

Browse courses on Algorithms

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Find a study group or create your own with classmates
Meet regularly to discuss course topics and work on assignments
Take turns presenting concepts to the group
Work together to solve challenging problems

Five other activities

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Practice coding challenges on Leetcode

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Challenge yourself with a variety of coding problems to strengthen your understanding of the algorithms covered in the course.

Browse courses on Dynamic programming

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Create a Leetcode account
Choose a problem that corresponds with a topic you are studying in the course
Attempt to solve the problem on your own
If you get stuck, refer to the discussion forums or tutorials for guidance
Submit your solution and review the feedback

Attend a workshop on advanced graph algorithms

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Engage with experts in the field and gain exposure to cutting-edge research and applications.

Browse courses on Graph Algorithms

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Research and find a workshop on advanced graph algorithms
Register for the workshop and attend all sessions
Take notes and ask questions during the workshop
Follow up with the speakers or organizers to clarify any concepts

Write a blog post explaining an algorithm

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Enhance your understanding by teaching others. Choose an algorithm and break it down in a clear and concise manner.

Browse courses on Dynamic programming

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Select an algorithm that you feel comfortable explaining
Research the topic to ensure your understanding is correct
Write a blog post that includes a step-by-step explanation, examples, and diagrams (if necessary)
Share your blog post with others and invite feedback

Develop a data visualization for a graph algorithm

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Enhance your problem-solving skills by applying your knowledge to visualize the results of graph algorithms.

Browse courses on Graph Algorithms

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Choose a graph algorithm and a dataset to work with
Design a data visualization that effectively represents the results of the algorithm
Use a data visualization tool to create the visualization
Present your visualization and explain how it enhances the understanding of the algorithm

Contribute to an open-source graph library

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Reinforce your understanding by contributing to real-world projects and collaborating with other developers in the field.

Browse courses on Graph Algorithms

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Find an open-source graph library that aligns with your interests
Review the documentation and familiarize yourself with the codebase
Identify an area where you can contribute, such as fixing bugs or adding new features
Submit a pull request with your changes and provide clear documentation
Collaborate with other contributors to improve the library

Career center

Learners who complete Introduction to Graduate Algorithms will develop knowledge and skills that may be useful to these careers:

Algorithm Engineer

An Algorithm Engineer develops and analyzes algorithms to solve complex computational problems. This course would be highly useful for this role, as it covers advanced techniques for designing algorithms and applying them to hard computational problems. The course also provides a strong foundation in dynamic programming, divide-and-conquer algorithms, and graph algorithms, which are all essential skills for an Algorithm Engineer.

See salaries and explore the career path for Algorithm Engineer

Machine Learning Engineer

A Machine Learning Engineer develops and deploys machine learning models. This course would be moderately useful for this role, as it covers techniques for designing and analyzing algorithms, which are essential skills for a Machine Learning Engineer. The course also provides a strong foundation in dynamic programming, divide-and-conquer algorithms, and graph algorithms, which are all useful for machine learning.

See salaries and explore the career path for Machine Learning Engineer

Operations Research Analyst

An Operations Research Analyst uses mathematical and analytical techniques to improve the efficiency of organizations. This course would be moderately useful for this role, as it covers techniques for designing and analyzing algorithms, which are essential skills for an Operations Research Analyst. The course also provides a strong foundation in dynamic programming, divide-and-conquer algorithms, and graph algorithms, which are all useful for operations research.

See salaries and explore the career path for Operations Research Analyst

Software Engineer

A Software Engineer designs, develops, and maintains software systems. This course would be moderately useful for this role, as it covers techniques for designing and analyzing algorithms, which are essential skills for a Software Engineer. The course also provides a strong foundation in dynamic programming, divide-and-conquer algorithms, and graph algorithms, which are all useful for software development.

See salaries and explore the career path for Software Engineer

Database Administrator

A Database Administrator designs, builds, and maintains databases. This course would be moderately useful for this role, as it covers techniques for designing and analyzing algorithms, which are essential skills for a Database Administrator. The course also provides a strong foundation in dynamic programming, divide-and-conquer algorithms, and graph algorithms, which are all useful for database administration.

See salaries and explore the career path for Database Administrator

Information Security Analyst

An Information Security Analyst protects an organization's computer systems and networks from cyberattacks. This course would be moderately useful for this role, as it covers techniques for designing and analyzing algorithms, which are essential skills for an Information Security Analyst. The course also provides a strong foundation in dynamic programming, divide-and-conquer algorithms, and graph algorithms, which are all useful for information security.

See salaries and explore the career path for Information Security Analyst

Data Scientist

A Data Scientist uses data to solve business problems. This course would be moderately useful for this role, as it covers techniques for designing and analyzing algorithms, which are essential skills for a Data Scientist. The course also provides a strong foundation in dynamic programming, divide-and-conquer algorithms, and graph algorithms, which are all useful for data analysis.

See salaries and explore the career path for Data Scientist

Software Architect

A Software Architect designs and develops the overall architecture of a software system. This course would be moderately useful for this role, as it covers techniques for designing and analyzing algorithms, which are essential skills for a Software Architect. The course also provides a strong foundation in dynamic programming, divide-and-conquer algorithms, and graph algorithms, which are all useful for software architecture.

See salaries and explore the career path for Software Architect

Cryptographer

A Cryptographer develops and analyzes cryptographic algorithms to protect information. This course would be moderately useful for this role, as it covers techniques for designing and analyzing algorithms, which are essential skills for a Cryptographer. The course also provides a strong foundation in dynamic programming, divide-and-conquer algorithms, and graph algorithms, which are all useful for cryptography.

See salaries and explore the career path for Cryptographer

Quantitative Analyst

A Quantitative Analyst uses mathematical and statistical models to analyze financial data. This course would be moderately useful for this role, as it covers techniques for designing and analyzing algorithms, which are essential skills for a Quantitative Analyst. The course also provides a strong foundation in dynamic programming, divide-and-conquer algorithms, and graph algorithms, which are all useful for financial analysis.

See salaries and explore the career path for Quantitative Analyst

Computer Scientist

A Computer Scientist researches and develops new computing technologies. This course would be moderately useful for this role, as it covers techniques for designing and analyzing algorithms, which are essential skills for a Computer Scientist. The course also provides a strong foundation in dynamic programming, divide-and-conquer algorithms, and graph algorithms, which are all useful for computer science research.

See salaries and explore the career path for Computer Scientist

Network Engineer

A Network Engineer designs, builds, and maintains computer networks. This course would be moderately useful for this role, as it covers techniques for designing and analyzing algorithms, which are essential skills for a Network Engineer. The course also provides a strong foundation in dynamic programming, divide-and-conquer algorithms, and graph algorithms, which are all useful for network engineering.

See salaries and explore the career path for Network Engineer

Systems Analyst

A Systems Analyst analyzes and designs business systems. This course would be moderately useful for this role, as it covers techniques for designing and analyzing algorithms, which are essential skills for a Systems Analyst. The course also provides a strong foundation in dynamic programming, divide-and-conquer algorithms, and graph algorithms, which are all useful for systems analysis.

See salaries and explore the career path for Systems Analyst

Product Manager

A Product Manager manages the development and launch of new products. This course may be useful for this role, as it covers techniques for designing and analyzing algorithms, which can be useful for product development. The course also provides a strong foundation in dynamic programming, divide-and-conquer algorithms, and graph algorithms, which can all be useful for product management.

See salaries and explore the career path for Product Manager

Business Analyst

A Business Analyst analyzes and solves business problems. This course may be useful for this role, as it covers techniques for designing and analyzing algorithms, which can be useful for solving business problems. The course also provides a strong foundation in dynamic programming, divide-and-conquer algorithms, and graph algorithms, which can all be useful for business analysis.

See salaries and explore the career path for Business Analyst