A familiar use of modular arithmetic is in the 12-hour clock, in which the day is divided into two 12-hour periods. If the time is 7:00 now, then 8 hours later it will be 3:00. Usual addition would suggest that the later time should be 7 + 8 = 15, but this is not the answer because clock time "wraps around" every 12 hours; in 12-hour time, there is no "15 o'clock". Likewise, if the clock starts at 12:00 (noon) and 21 hours elapse, then the time will be 9:00 the next day, rather than 33:00. Because the hour number starts over after it reaches 12, this is arithmetic modulo 12. According to the definition below, 12 is congruent not only to 12 itself, but also to 0, so the time called "12:00" could also be called "0:00", since 12 is congruent to 0 modulo 12.
What is Modular Arithmetic - Introduction to Modular Arithmetic - Cryptography - Lesson 2
Modular Arithmetic is a fundamental component of cryptography. In this video, I explain the basics of modular arithmetic with a few simple examples.
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published: 25 Jul 2014
Modular Arithmetic (Part 1)
Network Security: Modular Arithmetic (Part 1)
Topics discussed:
1) Introduction to modular arithmetic with a real-time example.
2) Clock analogy for understanding the concept of modulus.
3) Usage of congruence in cryptography.
4) Explanation on the usage of congruence instead of equality in cryptography.
5) Identification of a few valid and invalid congruence with suitable explanations.
Follow Neso Academy on Instagram: @nesoacademy (https://bit.ly/2XP63OE)
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published: 08 Sep 2021
What does a ≡ b (mod n) mean? Basic Modular Arithmetic, Congruence
Basic congruence introduction in modular arithmetic. We will go over 3 ways to interpret a ≡ b (mod n), and you will see this in a number theory or a discrete math class. Learn how to solve congruence, subscribe to @blackpenredpen
💪 Support this channel, https://www.patreon.com/blackpenredpen
published: 23 Apr 2018
This completely changed the way I see numbers | Modular Arithmetic Visually Explained
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published: 27 Aug 2019
Basics of Modular Arithmetic
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EXPLORE 😎:
A rational equation. A challenge in algebra: https://youtu.be/XUq96gvZ_vA
Finding the area of a weird region in a quarter circle: https://youtu.be/1Ckw39vxETM
Solving an exponential equation: https://youtu.be/in8dH2LQaSY
PLAYLISTS 🎵 :
Number Theory Problems: https://www.youtube.com/playlist?list=PLvPOIUdohGFBjmKtCL0LXGPBxr7CVyjJV
Challenging Math Problems: ht...
published: 03 May 2021
Congruences & Modular Arithmetic ← Number Theory
𝙎𝙞𝙜𝙣 𝙪𝙥 for Number Theory course (coming soon) on our website:
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Numbers can be grouped into congruence classes based on remainders when divided by a positive integer (modulus). Congruences are represented with the symbol "≡," and two numbers are considered congruent if their difference is a multiple of the modulus.
In this video, we provide examples of congruences, both true and false, and show how to check them using the subtraction and division method. We also introduces the concept of modular arithmetic (explained visually with "clock arithmetic," and the notation for congruences, such as "A ≡ B mod n."
If you enjoy what we do, please consider supporting us on Patreon so we can continue making educational videos that help you Learn More...
published: 06 Feb 2024
■ What is Modular Arithmetic? | An introduction to the strange world of mathematical time-telling
What is modular arithmetic? In this video I'll introduce you to the strange world of mathematical time-telling that is modular arithmetic!
What is the final digit of 7 to the power of 100? Can 4003 be written as the sum of two squares? Is 1,200,304,501 divisible by 3? All these are questions that are made much simpler by using modular arithmetic!
In this video we'll go over the basics of what modular arithmetic is, and how to answer different questions when working in different modulos. I'll also explain the applications of modular arithmetic and why it's so important!
Modular arithmetic is a fantastic tool for answering funky questions about numbers - and thus a great tool to add to your mathematics tool kit :)
Here is the modular arithmetic hand-out which contains the formal defin...
published: 02 Oct 2020
MODULAR ARITHMETIC | INTRODUCTION
published: 16 Nov 2020
Don't fall and break your Sudoku Bone!
BremSter solves "Anklebones" by FullDeck and Missing a Few Cards.
This Sudoku uses the Modular Lines and Cages constraints.
Solve in Sven's SudokuPad WebApp: https://sudokupad.app/6zrib0785f
This puzzle has been published on Logic Masters Germany: https://logic-masters.de/Raetselportal/Raetsel/zeigen.php?id=000KST
Check out more of FullDeck and Missing a Few Cards' puzzles at: https://missingdeck.net/
📋 Puzzle Rules:
• Normal Sudoku rules apply. The digits 1 through 9 appear in every row, column, and box.
• Modular lines: Any set of three adjacent digits along a modular line has three different remainders when divided by 3.
• Cages: Digits in cages cannot repeat and must sum to the value shown in the upper left corner of the cage.
----------------------------------------
Check out t...
published: 18 Dec 2024
[Discrete Mathematics] Modular Arithmetic
We introduce modular arithmetic, the function that outputs remainders and separates them into equivalence classes.
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Modular Arithmetic is a fundamental component of cryptography. In this video, I explain the basics of modular arithmetic with a few simple examples.
Join this ...
Modular Arithmetic is a fundamental component of cryptography. In this video, I explain the basics of modular arithmetic with a few simple examples.
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Modular Arithmetic is a fundamental component of cryptography. In this video, I explain the basics of modular arithmetic with a few simple examples.
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Network Security: Modular Arithmetic (Part 1)
Topics discussed:
1) Introduction to modular arithmetic with a real-time example.
2) Clock analogy for understandi...
Network Security: Modular Arithmetic (Part 1)
Topics discussed:
1) Introduction to modular arithmetic with a real-time example.
2) Clock analogy for understanding the concept of modulus.
3) Usage of congruence in cryptography.
4) Explanation on the usage of congruence instead of equality in cryptography.
5) Identification of a few valid and invalid congruence with suitable explanations.
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#NetworkSecurityByNeso #Cryptography #NetworkSecurity #ModularArithmetic
Network Security: Modular Arithmetic (Part 1)
Topics discussed:
1) Introduction to modular arithmetic with a real-time example.
2) Clock analogy for understanding the concept of modulus.
3) Usage of congruence in cryptography.
4) Explanation on the usage of congruence instead of equality in cryptography.
5) Identification of a few valid and invalid congruence with suitable explanations.
Follow Neso Academy on Instagram: @nesoacademy (https://bit.ly/2XP63OE)
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Music:
Axol x Alex Skrindo - You [NCS Release]
#NetworkSecurityByNeso #Cryptography #NetworkSecurity #ModularArithmetic
Basic congruence introduction in modular arithmetic. We will go over 3 ways to interpret a ≡ b (mod n), and you will see this in a number theory or a discrete m...
Basic congruence introduction in modular arithmetic. We will go over 3 ways to interpret a ≡ b (mod n), and you will see this in a number theory or a discrete math class. Learn how to solve congruence, subscribe to @blackpenredpen
💪 Support this channel, https://www.patreon.com/blackpenredpen
Basic congruence introduction in modular arithmetic. We will go over 3 ways to interpret a ≡ b (mod n), and you will see this in a number theory or a discrete math class. Learn how to solve congruence, subscribe to @blackpenredpen
💪 Support this channel, https://www.patreon.com/blackpenredpen
Sign up with brilliant and get 20% off your annual subscription: https://brilliant.org/MajorPrep/
STEMerch Store: https://stemerch.com/
Support the Channel: htt...
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#NumberTheoryTopics #ModularArithmetic
EXPLORE 😎:
A rational equation. A challenge in algebra: https://youtu.be/XUq96gvZ_vA
Finding the area of a weird region in a quarter circle: https://youtu.be/1Ckw39vxETM
Solving an exponential equation: https://youtu.be/in8dH2LQaSY
PLAYLISTS 🎵 :
Number Theory Problems: https://www.youtube.com/playlist?list=PLvPOIUdohGFBjmKtCL0LXGPBxr7CVyjJV
Challenging Math Problems: https://www.youtube.com/playlist?list=PLvPOIUdohGFDy3byhJ1wBQPVFwu9ZlM-7
Trigonometry Problems: https://www.youtube.com/playlist?list=PLvPOIUdohGFAbHlGlzKTHpOzDh2cQCN56
Diophantine Equations and Systems: https://www.youtube.com/playlist?list=PLvPOIUdohGFBTgY5FKFfalwTFtNieOY5I
Calculus: https://www.youtube.com/playlist?list=PLvPOIUdohGFAmPjF08A7llzsa4qtIAa_K
ADDITIONAL TOPICS:
Chinese Remainder Theorem
Fermat’s Little Theorem
Euler’s Theorem
Primitive Roots and Power Residues
Hensel’s Lemma
Quadratic Residues and Quadratic Reciprocity
RESOURCES:
https://en.wikipedia.org/wiki/Modular_arithmetic
https://www.britannica.com/science/modular-arithmetic
https://www.geeksforgeeks.org/modular-arithmetic/
https://crypto.stanford.edu/pbc/notes/numbertheory/arith.html
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If you need to post a picture of your solution or idea:
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#NumberTheoryTopics #ModularArithmetic
EXPLORE 😎:
A rational equation. A challenge in algebra: https://youtu.be/XUq96gvZ_vA
Finding the area of a weird region in a quarter circle: https://youtu.be/1Ckw39vxETM
Solving an exponential equation: https://youtu.be/in8dH2LQaSY
PLAYLISTS 🎵 :
Number Theory Problems: https://www.youtube.com/playlist?list=PLvPOIUdohGFBjmKtCL0LXGPBxr7CVyjJV
Challenging Math Problems: https://www.youtube.com/playlist?list=PLvPOIUdohGFDy3byhJ1wBQPVFwu9ZlM-7
Trigonometry Problems: https://www.youtube.com/playlist?list=PLvPOIUdohGFAbHlGlzKTHpOzDh2cQCN56
Diophantine Equations and Systems: https://www.youtube.com/playlist?list=PLvPOIUdohGFBTgY5FKFfalwTFtNieOY5I
Calculus: https://www.youtube.com/playlist?list=PLvPOIUdohGFAmPjF08A7llzsa4qtIAa_K
ADDITIONAL TOPICS:
Chinese Remainder Theorem
Fermat’s Little Theorem
Euler’s Theorem
Primitive Roots and Power Residues
Hensel’s Lemma
Quadratic Residues and Quadratic Reciprocity
RESOURCES:
https://en.wikipedia.org/wiki/Modular_arithmetic
https://www.britannica.com/science/modular-arithmetic
https://www.geeksforgeeks.org/modular-arithmetic/
https://crypto.stanford.edu/pbc/notes/numbertheory/arith.html
𝙎𝙞𝙜𝙣 𝙪𝙥 for Number Theory course (coming soon) on our website:
https://www.socratica.com/courses/number-theory
Numbers can be grouped into congruence classes b...
𝙎𝙞𝙜𝙣 𝙪𝙥 for Number Theory course (coming soon) on our website:
https://www.socratica.com/courses/number-theory
Numbers can be grouped into congruence classes based on remainders when divided by a positive integer (modulus). Congruences are represented with the symbol "≡," and two numbers are considered congruent if their difference is a multiple of the modulus.
In this video, we provide examples of congruences, both true and false, and show how to check them using the subtraction and division method. We also introduces the concept of modular arithmetic (explained visually with "clock arithmetic," and the notation for congruences, such as "A ≡ B mod n."
If you enjoy what we do, please consider supporting us on Patreon so we can continue making educational videos that help you Learn More:
https://www.patreon.com/socratica
Thank you to our VIP Patreon Members who helped make this video possible!
José Juan Francisco Castillo Rivera
KW
M Andrews
Jim Woodworth
Marcos Silveira
Christopher Kemsley
Eric Eccleston
Jeremy Shimanek
Michael Shebanow
Alvin Khaled
Kevin B
John Krawiec
Umar Khan
Tracy Karin Prell
— Thank you kind friends! 💜🦉
✷✷✷
Written & Produced by Michael Harrison
Edited by Megi Shuke
About our Instructor:
Michael earned his BS in Math from Caltech, and did his graduate work in Math at UC Berkeley and University of Washington, specializing in Number Theory. A self-taught programmer, Michael taught both Math and Computer Programming at the college level. He applied this knowledge as a financial analyst (quant) and as a programmer at Google.
#congruences
#numbertheory
#socratica
𝙎𝙞𝙜𝙣 𝙪𝙥 for Number Theory course (coming soon) on our website:
https://www.socratica.com/courses/number-theory
Numbers can be grouped into congruence classes based on remainders when divided by a positive integer (modulus). Congruences are represented with the symbol "≡," and two numbers are considered congruent if their difference is a multiple of the modulus.
In this video, we provide examples of congruences, both true and false, and show how to check them using the subtraction and division method. We also introduces the concept of modular arithmetic (explained visually with "clock arithmetic," and the notation for congruences, such as "A ≡ B mod n."
If you enjoy what we do, please consider supporting us on Patreon so we can continue making educational videos that help you Learn More:
https://www.patreon.com/socratica
Thank you to our VIP Patreon Members who helped make this video possible!
José Juan Francisco Castillo Rivera
KW
M Andrews
Jim Woodworth
Marcos Silveira
Christopher Kemsley
Eric Eccleston
Jeremy Shimanek
Michael Shebanow
Alvin Khaled
Kevin B
John Krawiec
Umar Khan
Tracy Karin Prell
— Thank you kind friends! 💜🦉
✷✷✷
Written & Produced by Michael Harrison
Edited by Megi Shuke
About our Instructor:
Michael earned his BS in Math from Caltech, and did his graduate work in Math at UC Berkeley and University of Washington, specializing in Number Theory. A self-taught programmer, Michael taught both Math and Computer Programming at the college level. He applied this knowledge as a financial analyst (quant) and as a programmer at Google.
#congruences
#numbertheory
#socratica
What is modular arithmetic? In this video I'll introduce you to the strange world of mathematical time-telling that is modular arithmetic!
What is the final d...
What is modular arithmetic? In this video I'll introduce you to the strange world of mathematical time-telling that is modular arithmetic!
What is the final digit of 7 to the power of 100? Can 4003 be written as the sum of two squares? Is 1,200,304,501 divisible by 3? All these are questions that are made much simpler by using modular arithmetic!
In this video we'll go over the basics of what modular arithmetic is, and how to answer different questions when working in different modulos. I'll also explain the applications of modular arithmetic and why it's so important!
Modular arithmetic is a fantastic tool for answering funky questions about numbers - and thus a great tool to add to your mathematics tool kit :)
Here is the modular arithmetic hand-out which contains the formal definition of when two numbers are congruent to each other, as well as proofs of the addition and multiplication theorem: https://www.dropbox.com/s/3sn5p55sm0p3m5m/ModularArithmetic_MathsUnboxed_Handout.pdf?dl=0
Click here for a mini-series of videos on how to solve a variety of modular arithmetic questions:
https://www.youtube.com/playlist?list=PLpw5dUNGvQBoG0t1Tnf_gYlWTn62XtuPW
------------
Subscribe to my youtube channel: https://youtube.com/mathsunboxed?sub_confirmation=1
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What is modular arithmetic? In this video I'll introduce you to the strange world of mathematical time-telling that is modular arithmetic!
What is the final digit of 7 to the power of 100? Can 4003 be written as the sum of two squares? Is 1,200,304,501 divisible by 3? All these are questions that are made much simpler by using modular arithmetic!
In this video we'll go over the basics of what modular arithmetic is, and how to answer different questions when working in different modulos. I'll also explain the applications of modular arithmetic and why it's so important!
Modular arithmetic is a fantastic tool for answering funky questions about numbers - and thus a great tool to add to your mathematics tool kit :)
Here is the modular arithmetic hand-out which contains the formal definition of when two numbers are congruent to each other, as well as proofs of the addition and multiplication theorem: https://www.dropbox.com/s/3sn5p55sm0p3m5m/ModularArithmetic_MathsUnboxed_Handout.pdf?dl=0
Click here for a mini-series of videos on how to solve a variety of modular arithmetic questions:
https://www.youtube.com/playlist?list=PLpw5dUNGvQBoG0t1Tnf_gYlWTn62XtuPW
------------
Subscribe to my youtube channel: https://youtube.com/mathsunboxed?sub_confirmation=1
Follow me on instagram: https://instagram.com/maths_unboxed
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BremSter solves "Anklebones" by FullDeck and Missing a Few Cards.
This Sudoku uses the Modular Lines and Cages constraints.
Solve in Sven's SudokuPad WebApp: ht...
BremSter solves "Anklebones" by FullDeck and Missing a Few Cards.
This Sudoku uses the Modular Lines and Cages constraints.
Solve in Sven's SudokuPad WebApp: https://sudokupad.app/6zrib0785f
This puzzle has been published on Logic Masters Germany: https://logic-masters.de/Raetselportal/Raetsel/zeigen.php?id=000KST
Check out more of FullDeck and Missing a Few Cards' puzzles at: https://missingdeck.net/
📋 Puzzle Rules:
• Normal Sudoku rules apply. The digits 1 through 9 appear in every row, column, and box.
• Modular lines: Any set of three adjacent digits along a modular line has three different remainders when divided by 3.
• Cages: Digits in cages cannot repeat and must sum to the value shown in the upper left corner of the cage.
----------------------------------------
Check out the BremSter Games YouTube Channel
https://youtube.com/@BremSterGames
Come join my Patreon, either as a Free Member, or you may support if you wish to.
https://www.patreon.com/bremster
If you would like to submit a puzzle for me to cover, you can find my submission guidelines on the following post or described in detail in the following video.
https://www.patreon.com/posts/66467875
https://youtu.be/KDsIP36nds0
You can see a catalogue of Free Sudoku Puzzle Packs at the following links:
https://www.patreon.com/collection/110878
https://tinyurl.com/FreeSkunkworksPacks
You can Join as a channel member on YouTube to get early access to videos.
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Check out other content on the channel by visiting the Playlists Page:
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Find the details of all the puzzles posted on my channel on the following tracking sheet: https://tinyurl.com/BremSterVidsv1
If you would like to reach out to me you can.
I am BremSter on discord, or you can email [email protected]
#sudoku #sudokusolver
BremSter solves "Anklebones" by FullDeck and Missing a Few Cards.
This Sudoku uses the Modular Lines and Cages constraints.
Solve in Sven's SudokuPad WebApp: https://sudokupad.app/6zrib0785f
This puzzle has been published on Logic Masters Germany: https://logic-masters.de/Raetselportal/Raetsel/zeigen.php?id=000KST
Check out more of FullDeck and Missing a Few Cards' puzzles at: https://missingdeck.net/
📋 Puzzle Rules:
• Normal Sudoku rules apply. The digits 1 through 9 appear in every row, column, and box.
• Modular lines: Any set of three adjacent digits along a modular line has three different remainders when divided by 3.
• Cages: Digits in cages cannot repeat and must sum to the value shown in the upper left corner of the cage.
----------------------------------------
Check out the BremSter Games YouTube Channel
https://youtube.com/@BremSterGames
Come join my Patreon, either as a Free Member, or you may support if you wish to.
https://www.patreon.com/bremster
If you would like to submit a puzzle for me to cover, you can find my submission guidelines on the following post or described in detail in the following video.
https://www.patreon.com/posts/66467875
https://youtu.be/KDsIP36nds0
You can see a catalogue of Free Sudoku Puzzle Packs at the following links:
https://www.patreon.com/collection/110878
https://tinyurl.com/FreeSkunkworksPacks
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#sudoku #sudokusolver
We introduce modular arithmetic, the function that outputs remainders and separates them into equivalence classes.
Visit our website: http://bit.ly/1zBPlvm
Sub...
We introduce modular arithmetic, the function that outputs remainders and separates them into equivalence classes.
Visit our website: http://bit.ly/1zBPlvm
Subscribe on YouTube: http://bit.ly/1vWiRxW
*--Playlists--*
Discrete Mathematics 1: https://www.youtube.com/playlist?list=PLDDGPdw7e6Ag1EIznZ-m-qXu4XX3A0cIz
Discrete Mathematics 2: https://www.youtube.com/playlist?list=PLDDGPdw7e6Aj0amDsYInT_8p6xTSTGEi2
*--Recommended Textbooks--*
Discrete and Combinatorial Mathematics (Grimaldi): https://amzn.to/2T0iC53
Discrete Mathematics (Johnsonbaugh): https://amzn.to/2Hh7H41
Discrete Mathematics and Its Applications (Rosen): https://amzn.to/3lUgrMI
Book of Proof (Hammack): https://amzn.to/35eEbVg
Like us on Facebook: http://on.fb.me/1vWwDRc
Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any questions, leave them below. I try to answer as many questions as possible. If something isn't quite clear or needs more explanation, I can easily make additional videos to satisfy your need for knowledge and understanding.
We introduce modular arithmetic, the function that outputs remainders and separates them into equivalence classes.
Visit our website: http://bit.ly/1zBPlvm
Subscribe on YouTube: http://bit.ly/1vWiRxW
*--Playlists--*
Discrete Mathematics 1: https://www.youtube.com/playlist?list=PLDDGPdw7e6Ag1EIznZ-m-qXu4XX3A0cIz
Discrete Mathematics 2: https://www.youtube.com/playlist?list=PLDDGPdw7e6Aj0amDsYInT_8p6xTSTGEi2
*--Recommended Textbooks--*
Discrete and Combinatorial Mathematics (Grimaldi): https://amzn.to/2T0iC53
Discrete Mathematics (Johnsonbaugh): https://amzn.to/2Hh7H41
Discrete Mathematics and Its Applications (Rosen): https://amzn.to/3lUgrMI
Book of Proof (Hammack): https://amzn.to/35eEbVg
Like us on Facebook: http://on.fb.me/1vWwDRc
Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any questions, leave them below. I try to answer as many questions as possible. If something isn't quite clear or needs more explanation, I can easily make additional videos to satisfy your need for knowledge and understanding.
Modular Arithmetic is a fundamental component of cryptography. In this video, I explain the basics of modular arithmetic with a few simple examples.
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Network Security: Modular Arithmetic (Part 1)
Topics discussed:
1) Introduction to modular arithmetic with a real-time example.
2) Clock analogy for understanding the concept of modulus.
3) Usage of congruence in cryptography.
4) Explanation on the usage of congruence instead of equality in cryptography.
5) Identification of a few valid and invalid congruence with suitable explanations.
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#NetworkSecurityByNeso #Cryptography #NetworkSecurity #ModularArithmetic
Basic congruence introduction in modular arithmetic. We will go over 3 ways to interpret a ≡ b (mod n), and you will see this in a number theory or a discrete math class. Learn how to solve congruence, subscribe to @blackpenredpen
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#NumberTheoryTopics #ModularArithmetic
EXPLORE 😎:
A rational equation. A challenge in algebra: https://youtu.be/XUq96gvZ_vA
Finding the area of a weird region in a quarter circle: https://youtu.be/1Ckw39vxETM
Solving an exponential equation: https://youtu.be/in8dH2LQaSY
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Challenging Math Problems: https://www.youtube.com/playlist?list=PLvPOIUdohGFDy3byhJ1wBQPVFwu9ZlM-7
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Diophantine Equations and Systems: https://www.youtube.com/playlist?list=PLvPOIUdohGFBTgY5FKFfalwTFtNieOY5I
Calculus: https://www.youtube.com/playlist?list=PLvPOIUdohGFAmPjF08A7llzsa4qtIAa_K
ADDITIONAL TOPICS:
Chinese Remainder Theorem
Fermat’s Little Theorem
Euler’s Theorem
Primitive Roots and Power Residues
Hensel’s Lemma
Quadratic Residues and Quadratic Reciprocity
RESOURCES:
https://en.wikipedia.org/wiki/Modular_arithmetic
https://www.britannica.com/science/modular-arithmetic
https://www.geeksforgeeks.org/modular-arithmetic/
https://crypto.stanford.edu/pbc/notes/numbertheory/arith.html
𝙎𝙞𝙜𝙣 𝙪𝙥 for Number Theory course (coming soon) on our website:
https://www.socratica.com/courses/number-theory
Numbers can be grouped into congruence classes based on remainders when divided by a positive integer (modulus). Congruences are represented with the symbol "≡," and two numbers are considered congruent if their difference is a multiple of the modulus.
In this video, we provide examples of congruences, both true and false, and show how to check them using the subtraction and division method. We also introduces the concept of modular arithmetic (explained visually with "clock arithmetic," and the notation for congruences, such as "A ≡ B mod n."
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Written & Produced by Michael Harrison
Edited by Megi Shuke
About our Instructor:
Michael earned his BS in Math from Caltech, and did his graduate work in Math at UC Berkeley and University of Washington, specializing in Number Theory. A self-taught programmer, Michael taught both Math and Computer Programming at the college level. He applied this knowledge as a financial analyst (quant) and as a programmer at Google.
#congruences
#numbertheory
#socratica
What is modular arithmetic? In this video I'll introduce you to the strange world of mathematical time-telling that is modular arithmetic!
What is the final digit of 7 to the power of 100? Can 4003 be written as the sum of two squares? Is 1,200,304,501 divisible by 3? All these are questions that are made much simpler by using modular arithmetic!
In this video we'll go over the basics of what modular arithmetic is, and how to answer different questions when working in different modulos. I'll also explain the applications of modular arithmetic and why it's so important!
Modular arithmetic is a fantastic tool for answering funky questions about numbers - and thus a great tool to add to your mathematics tool kit :)
Here is the modular arithmetic hand-out which contains the formal definition of when two numbers are congruent to each other, as well as proofs of the addition and multiplication theorem: https://www.dropbox.com/s/3sn5p55sm0p3m5m/ModularArithmetic_MathsUnboxed_Handout.pdf?dl=0
Click here for a mini-series of videos on how to solve a variety of modular arithmetic questions:
https://www.youtube.com/playlist?list=PLpw5dUNGvQBoG0t1Tnf_gYlWTn62XtuPW
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BremSter solves "Anklebones" by FullDeck and Missing a Few Cards.
This Sudoku uses the Modular Lines and Cages constraints.
Solve in Sven's SudokuPad WebApp: https://sudokupad.app/6zrib0785f
This puzzle has been published on Logic Masters Germany: https://logic-masters.de/Raetselportal/Raetsel/zeigen.php?id=000KST
Check out more of FullDeck and Missing a Few Cards' puzzles at: https://missingdeck.net/
📋 Puzzle Rules:
• Normal Sudoku rules apply. The digits 1 through 9 appear in every row, column, and box.
• Modular lines: Any set of three adjacent digits along a modular line has three different remainders when divided by 3.
• Cages: Digits in cages cannot repeat and must sum to the value shown in the upper left corner of the cage.
----------------------------------------
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If you would like to reach out to me you can.
I am BremSter on discord, or you can email [email protected]
#sudoku #sudokusolver
We introduce modular arithmetic, the function that outputs remainders and separates them into equivalence classes.
Visit our website: http://bit.ly/1zBPlvm
Subscribe on YouTube: http://bit.ly/1vWiRxW
*--Playlists--*
Discrete Mathematics 1: https://www.youtube.com/playlist?list=PLDDGPdw7e6Ag1EIznZ-m-qXu4XX3A0cIz
Discrete Mathematics 2: https://www.youtube.com/playlist?list=PLDDGPdw7e6Aj0amDsYInT_8p6xTSTGEi2
*--Recommended Textbooks--*
Discrete and Combinatorial Mathematics (Grimaldi): https://amzn.to/2T0iC53
Discrete Mathematics (Johnsonbaugh): https://amzn.to/2Hh7H41
Discrete Mathematics and Its Applications (Rosen): https://amzn.to/3lUgrMI
Book of Proof (Hammack): https://amzn.to/35eEbVg
Like us on Facebook: http://on.fb.me/1vWwDRc
Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any questions, leave them below. I try to answer as many questions as possible. If something isn't quite clear or needs more explanation, I can easily make additional videos to satisfy your need for knowledge and understanding.
A familiar use of modular arithmetic is in the 12-hour clock, in which the day is divided into two 12-hour periods. If the time is 7:00 now, then 8 hours later it will be 3:00. Usual addition would suggest that the later time should be 7 + 8 = 15, but this is not the answer because clock time "wraps around" every 12 hours; in 12-hour time, there is no "15 o'clock". Likewise, if the clock starts at 12:00 (noon) and 21 hours elapse, then the time will be 9:00 the next day, rather than 33:00. Because the hour number starts over after it reaches 12, this is arithmetic modulo 12. According to the definition below, 12 is congruent not only to 12 itself, but also to 0, so the time called "12:00" could also be called "0:00", since 12 is congruent to 0 modulo 12.
What Is Ethereum’s ‘The Splurge’? ...EOF lays the groundwork for further upgrades like the EVMModularArithmeticExtensions (EVM-MAX) and the integration of Single-Instruction-Multiple-Data (SIMD) capabilities ... .
... number systems, the ‘learning with errors’ math problem, public key encryptions, prime modular arithmetic and high-dimensional vector spaces – not really great topics for polite company.
These algorithms, such as the linear congruential generator or Mersenne Twister, use principles from number theory and modular arithmetic to generate sequences of numbers that, over a sufficient ...
At the center of the debate is SFUSD... Her program, Black MathGenius, began in the 1990s as a curriculum guide designed for students in grades K-8 that covers modular arithmetic, problem solving, introductory calculus and even cryptocurrency ... ....
Cryptography helps the world build trust ... The discrete logarithm problem involves modular arithmetic (numbers wrap around, as in a clock, where hours run from 0 to 11 and back to 0 again – this is written as “mod 12”) ... Quantum-resistant algorithms ... .
In a new study, researchers explore one such perturbation method to obtain non-converging outputs with long periods and analyze these periods using modular arithmetic, obtaining a complete list of parameter values for optimal perturbations.
and professor and chair of mathematics. These algorithms serve two main functions ... Thus, he decided to replace the modular arithmetic that these systems used with calculations on an elliptic curve, which simplified the algorithmic computations ... Email.