In computability theory and computational complexity theory, a reduction is an algorithm for transforming one problem into another problem. A sufficiently efficient reduction from one problem to another may be used to show that the second problem is at least as difficult as the first. Intuitively, problem A is reducible to problem B, if an algorithm for solving problem B efficiently (if it existed) could also be used as a subroutine to solve problem A efficiently. When this is true, solving A cannot be harder than solving B. "Harder" means having a higher estimate of the required computational resources in a given context (e.g., higher time complexity, greater memory requirement, expensive need for extra hardware processor cores for a parallel solution compared to a single-threaded solution, etc.). The existence of a reduction from A to B, can be written in the shorthand notation A ≤m B, usually with a subscript on the ≤ to indicate the type of reduction being used (m : mapping reduction, p : polynomial reduction). The mathematical structure generated on a set of problems by the reductions of a particular type generally forms a preorder, whose equivalence classes may be used to define degrees of unsolvability and complexity classes. (Wikipedia).
Reduction of Order - Linear Second Order Homogeneous Differential Equations Part 1
This video explains how to apply the method of reduction of order to solve a linear second order homogeneous differential equations. Site: http://mathispower4u
From playlist Second Order Differential Equations: Reduction of Order
Reduction of Order - Linear Second Order Homogeneous Differential Equations Part 2
This video explains how to apply the method of reduction of order to solve a linear second order homogeneous differential equations. Site: http://mathispower4u
From playlist Second Order Differential Equations: Reduction of Order
Solve a System of Equations Using Elimination with Fractions
👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e
From playlist Solve a System of Equations Using Elimination | Hard
There are two different types of reductionism. One is called methodological reductionism, the other one theory reductionism. Methodological reductionism is about the properties of the real world. It’s about taking things apart into smaller things and finding that the smaller things determ
From playlist Philosophy of Science
Solve a System of Equations with Elimination when Your Solutions are Fractions
👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e
From playlist Solve a System of Equations Using Elimination | Hard
Using Multipliers to Solve a System of Equations Using Elimination
👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e
From playlist Solve a System of Equations Using Elimination | Hard
Solve a System of Equations Using Elimination
👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e
From playlist Solve a System of Equations Using Elimination | Hard
Learn the Basics for Solving a System of Equations by Elimination
👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e
From playlist Solve a System of Equations Using Elimination | Medium
Graphing a System of Equations by Eliminating the Fractions
👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e
From playlist Solve a System of Equations Using Elimination | Hard
(May 19, 2010) Professor Robert Sapolsky gives what he calls "one of the most difficult lectures of the course" about chaos and reductionism. He references a book that he assigned to his students. This lecture focuses on reduction science and breaking things down to their component parts i
From playlist Lecture Collection | Human Behavioral Biology
Organometallic Reactions Part 3: Reductive Elimination
With oxidative addition understood, let's check the precise reverse process, reductive elimination. This is way for two ligands to be removed from a transition metal complex. What is the mechanism for this, and how can it be used in tandem with oxidative addition to replace ligands on coor
From playlist Inorganic/Organometallic Chemistry
MIT 7.05 General Biochemistry, Spring 2020 Instructor: Matthew Vander Heiden View the complete course: https://ocw.mit.edu/7-05S20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62wNcIMfinU64CAfreShjpt In this lecture, Professor Vander Heiden introduces oxidative phosp
From playlist (Selected Lectures) MIT 7.05 General Biochemistry, Spring 2020
Abhishek Rathod (7/27/70): Hardness results in discrete Morse theory for 2-complexes
Title: Hardness results in discrete Morse theory for 2-complexes Abstract: In this talk, we will discuss the problem of minimizing the number of critical simplices (Min-Morse Matching) from the point of view of inapproximability and parameterized complexity. Letting n denote the size of a
From playlist ATMCS/AATRN 2020
Synthesis Workshop: A Logic to Redox-Neutral C-C Bond Formation with Dr. Terry McCallum (Episode 43)
In this Research Spotlight episode, we are joined by Dr. Terry McCallum, who shares with us his work in the area of redox-neutral radical chemistry. References (in order of appearance): Angew. Chem. Int. Ed. Engl. 1983, 22, 753 For Polar Effects in Radical Addition Reactions: J. Org. Che
From playlist Special Topics: Organometallics
The Minimum Formula Size Problem is (ETH) Hard - Rahul Ilango
Computer Science/Discrete Mathematics Seminar I Topic: The Minimum Formula Size Problem is (ETH) Hard Speaker: Rahul Ilango Affiliation: Massachusetts Institute of Technology Date: March 7, 2022 Understanding the complexity of the Minimum Circuit Size Problem (MCSP) is a longstanding mys
From playlist Mathematics
26. Oxidative Phosphorylation/Photosynthesis I
MIT 7.05 General Biochemistry, Spring 2020 Instructor: Matthew Vander Heiden View the complete course: https://ocw.mit.edu/7-05S20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62wNcIMfinU64CAfreShjpt Professor Vander Heiden continues the discussion of topics related
From playlist (Selected Lectures) MIT 7.05 General Biochemistry, Spring 2020
Bruno Escoffier : Et si SAT était vraiment difficile? Quelques conséquences des hypothèses ETH et...
CONFERENCE Recording during the thematic meeting : « ALEA Days» the March 16, 2023 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker : Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathemat
From playlist Mathematical Aspects of Computer Science
Lecture 4: The Connes operator on HH
Correction: The formula we give for the Connes operator B is slightly wrong, there needs to be a '+' instead of a '-' in between the two summands. In this video, we discuss the Connes operator on Hochschild homology. Feel free to post comments and questions at our public forum at https:
From playlist Topological Cyclic Homology
Solving a system of equations with infinite many solutions
👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e
From playlist Solve a System of Equations Using Elimination | Medium
Michal Pilipczuk: Introduction to parameterized algorithms, lecture I
The mini-course will provide a gentle introduction to the area of parameterized complexity, with a particular focus on methods connected to (integer) linear programming. We will start with basic techniques for the design of parameterized algorithms, such as branching, color coding, kerneli
From playlist Summer School on modern directions in discrete optimization