LAFF – On Programming for Correctness from edX

Is my program correct? Will it give the right output for all possible permitted inputs? Computers are now essential in everyday life. Incorrect programs lead to frustration in the best case and disaster in the worst. Thus, knowing how to construct correct programs is a skill that all who program computers must strive to master.

In this computer science course, we will present "goal oriented programming" the way Edsger Dijkstra, one of the most influential computer scientists, intended. You will learn how to derive programs hand-in-hand with their proofs of correctness. The course presents a methodology that illustrates goal-oriented programming, starting with the formalization of what is to be computed, and then growing the program hand-in-hand with its proof of correctness. The methodology demonstrates that, for a broad class of matrix operations, the development, implementation, and establishment of correctness of a program can be made systematic.

Since this technique focuses on program specifications, it often leads to clearer, correct programs in less time. The approach rapidly yields a family of algorithms from which you can then pick the algorithm that has desirable properties, such as attaining better performance on a given architecture.

The audience of this MOOC extends beyond students and scholars interested in the domains of linear algebra algorithms and scientific computing. This course shows how to make the formal derivation of algorithms practical and will leave you pondering how our results might extend to other domains.

As a result of support from MathWorks, learners will be granted access to MATLAB for the duration of the course.

What's inside

Learning objectives

Develop assertions describing states in a program.
Prove programs correct using logic.

Build algorithms using goal-oriented programming techniques.
“slice and dice” to discover families of loop-based algorithms for matrix computations.

Develop assertions describing states in a program.
Prove programs correct using logic.
Build algorithms using goal-oriented programming techniques.
“slice and dice” to discover families of loop-based algorithms for matrix computations.

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Designed for those interested in matrix operations, linear algebra algorithms, and scientific computing

Covers how to make the derivation of algorithms practical

Led by instructors Maggie Myers, Robert van de Geijn, and Devangi Parikh

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 LAFF – On Programming for Correctness with these activities:

Gather Resources on Matrix Decompositions

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Compile a collection of resources, such as articles, videos, and online tutorials, that provide a comprehensive overview of matrix decompositions.

Browse courses on Matrix Decompositions

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Conduct research to identify relevant resources on matrix decompositions.
Organize and categorize the resources based on topic or level of difficulty.

Review Eigenvalues and Eigenvectors

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Refresh your knowledge of eigenvalues and eigenvectors to ensure a smooth transition into the course.

Browse courses on Eigenvalues

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Review the concepts of eigenvalues and eigenvectors.
Solve problems involving finding eigenvalues and eigenvectors of matrices.

Explore MATLAB Tutorials

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Utilize the provided MATLAB access to enhance your understanding of matrix operations and algorithm implementation.

Browse courses on MATLAB

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Find tutorials on MATLAB basics and matrix operations.
Follow along with the tutorials, practicing the concepts.

Five other activities

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Create a Summary of Algorithms

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Create a summary of the algorithms covered in the matrix operations section of the course, including the methodology for deriving and proving their correctness.

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Identify the key algorithms and their derivations.
Summarize the steps and properties of each algorithm.
Include examples and illustrations to clarify the concepts.

Participate in a Study Group

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Join a study group to discuss course concepts, solve problems together, and clarify misunderstandings.

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Find or form a study group with other students in the course.
Meet regularly to discuss the course material and work on assignments together.

Solve Matrix Operation Problems

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Engage in targeted practice by solving a variety of matrix operation problems to enhance your problem-solving skills in this domain.

Browse courses on Matrix Operations

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Find problem sets or online resources with matrix operation problems.
Attempt to solve the problems independently.
Review your solutions and identify areas for improvement.

Develop a Matrix Calculator

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Build a comprehensive matrix calculator that can perform various operations, such as matrix addition, subtraction, multiplication, and finding eigenvalues.

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Design the calculator's interface and functionality.
Implement the matrix operations using appropriate algorithms.
Test and debug the calculator to ensure accuracy.

Attend a Workshop on Goal-Oriented Programming

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Enroll in a workshop that delves into the principles of goal-oriented programming, providing practical guidance and hands-on experience.

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Research and find a workshop on goal-oriented programming.
Attend the workshop and actively participate in the exercises and discussions.

Career center

Learners who complete LAFF – On Programming for Correctness will develop knowledge and skills that may be useful to these careers:

Algorithm Researcher

An Algorithm Researcher develops and analyzes algorithms to solve computational problems. The LAFF - On Programming for Correctness course may be useful in this field by helping you build a foundation in developing correct programs using logic and proof techniques. This is a valuable skill for Algorithm Researchers as it enables them to create algorithms that are efficient and reliable.

See salaries and explore the career path for Algorithm Researcher

Computer Architecture Researcher

A Computer Architecture Researcher designs and analyzes computer hardware and software systems. The LAFF - On Programming for Correctness course may be useful in this field by helping you build a foundation in developing correct programs using logic and proof techniques. This is a valuable skill for Computer Architecture Researchers as it enables them to create computer systems that are reliable and efficient.

See salaries and explore the career path for Computer Architecture Researcher

Software Architect

A Software Architect designs and oversees the development of software systems. The LAFF - On Programming for Correctness course may be useful in this field by helping you build a foundation in developing correct programs using logic and proof techniques. This is a valuable skill for Software Architects as it enables them to create software systems that are reliable and efficient.

See salaries and explore the career path for Software Architect

Database Administrator

A Database Administrator designs and maintains databases to ensure that data is accurate and accessible. The LAFF - On Programming for Correctness course may be useful in this field by helping you build a foundation in developing correct programs using logic and proof techniques. This is a valuable skill for Database Administrators as it enables them to create databases that are reliable and efficient.

See salaries and explore the career path for Database Administrator

Computer Scientist

A Computer Scientist conducts research and develops new computing technologies. The LAFF - On Programming for Correctness course may be useful in this field by helping you build a foundation in developing correct programs using logic and proof techniques. This is a valuable skill for Computer Scientists as it enables them to create new technologies that are reliable and efficient.

See salaries and explore the career path for Computer Scientist

Software Quality Assurance Engineer

A Software Quality Assurance Engineer tests and evaluates software to ensure that it meets quality standards. The LAFF - On Programming for Correctness course may be useful in this field by helping you build a foundation in developing correct programs using logic and proof techniques. This is a valuable skill for Software Quality Assurance Engineers as it enables them to identify and fix bugs in software.

See salaries and explore the career path for Software Quality Assurance Engineer

Scientific Programmer

A Scientific Programmer develops and maintains software for scientific research. The LAFF - On Programming for Correctness course may be useful in this field by helping you build a foundation in developing correct programs using logic and proof techniques. This is a valuable skill for Scientific Programmers as it enables them to create software that is reliable and accurate.

See salaries and explore the career path for Scientific Programmer

Information Security Analyst

An Information Security Analyst protects an organization's computer systems and data from unauthorized access. The LAFF - On Programming for Correctness course may be useful in this field by helping you build a foundation in developing correct programs using logic and proof techniques. This is a valuable skill for Information Security Analysts as it enables them to create security systems that are reliable and effective.

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Systems Analyst

A Systems Analyst analyzes and designs computer systems to meet business needs. The LAFF - On Programming for Correctness course may be useful in this field by helping you build a foundation in developing correct programs using logic and proof techniques. This is a valuable skill for Systems Analysts as it enables them to create computer systems that are reliable and efficient.

See salaries and explore the career path for Systems Analyst

Computational Scientist

A Computational Scientist uses computers to solve scientific problems. The LAFF - On Programming for Correctness course may be useful in this field by helping you build a foundation in developing correct programs using logic and proof techniques. This is a valuable skill for Computational Scientists as it enables them to create scientific simulations and models that are reliable and accurate.

See salaries and explore the career path for Computational Scientist

Computer Programmer

A Computer Programmer writes and maintains code for software applications. The LAFF - On Programming for Correctness course may be useful in this field by helping you build a foundation in developing correct programs using logic and proof techniques. This is a valuable skill for Computer Programmers as it enables them to create software that is reliable and efficient.

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Software Test Engineer

A Software Test Engineer develops and executes test plans to ensure that software meets requirements. The LAFF - On Programming for Correctness course may be useful in this field by helping you build a foundation in developing correct programs using logic and proof techniques. This is a valuable skill for Software Test Engineers as it enables them to create test cases that are effective and efficient.

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Software Developer

A Software Developer designs, builds, and deploys software systems that power many facets of modern life. The LAFF - On Programming for Correctness course may be useful in this field by helping you build a foundation in developing correct programs using logic and proof techniques. This is a valuable skill for Software Developers as it enables them to create software that is reliable and meets specific requirements.

See salaries and explore the career path for Software Developer

Software Engineer

A Software Engineer applies engineering principles to the design, development, deployment, and maintenance of software systems. The LAFF - On Programming for Correctness course may be useful in this field by helping you build a foundation in developing correct programs using logic and proof techniques. This is a valuable skill for Software Engineers as it enables them to create software that is reliable and meets specific requirements.

See salaries and explore the career path for Software Engineer

Data Scientist

A Data Scientist uses data to extract insights and knowledge that can be used to make informed decisions. The LAFF - On Programming for Correctness course may be useful in this field by helping you build a foundation in developing correct programs using logic and proof techniques. This is a valuable skill for Data Scientists as it enables them to create data-driven insights that are reliable and accurate.

See salaries and explore the career path for Data Scientist