Experimental mathematics
Experimental mathematics
  • Видео 777
  • Просмотров 412 298
effectively multiplication and division free residue number systems 1080p
Date: April 25, 2024
Speaker: Eugene Zima, Wilfrid Laurier University
Title: Effectively multiplication- and division-free residue number systems
Abstract: Several methods of selection of moduli in modular arithmetic are considered. With the proposed choice of moduli both modular reduction of an integer and reconstruction from modular images are accelerated. Special attention is paid to the moduli of the forms 2n ± 1 and 2n ± 2k ± 1. Different schemes of choice of these types of moduli and algorithms for conversion of arbitrary precision integers into the modular representation and back are considered. Results of experimental implementation of a two-layer modular arithmetic in GMP system are...
Просмотров: 70

Видео

Eric Angelini's Comma Sequence Part 2
Просмотров 36Месяц назад
Natalya Ter-Saakov speaks to the Experimental Mathematics Seminar. Abstract: At the beginning of the semester, Neil Sloane introduced the comma sequence (introduced to him by Eric Angelini) that works as follows. Choose your favorite number in your favorite base. Now we'll build a sequence from it with the following rule: the difference between consecutive terms is equal to the concatenation of...
Reinforcement learning and pattern finding in combinatorics 1080p
Просмотров 1242 месяца назад
Adam Zsolt Wagner speaks to the Experimental Mathematics Seminar. Abstract: We will look at two ways we can use tools from machine learning to help us with research in combinatorics. First we discuss reinforcement learning, a method that gives us a way to check conjectures for counterexamples efficiently. While it usually does not perform as well as other simpler methods, there have been severa...
bilateral rational ramanujan series and their p-adic mates
Просмотров 462 месяца назад
Jesús Guillera speaks the the Experimental Mathematics Seminar. Abstract: We conjecture p-adic identities associated to bilateral rational Ramanujan-like series. Then, we show how to recover the rational Ramanujan series from their p-adic mates.
Studying the area under generalized dyck paths 720p
Просмотров 522 месяца назад
AJ Bu speaks to the Experimental Mathematics Seminar. Abstract: I will be presenting my work (along with some joint work with Doron Zeilberger) on how to use symbolic computation to study the area under generalized Dyck paths (i.e. paths in the xy-plane from the origin to (n,0) with an arbitrary set of atomic steps and that never go below the x-axis).
Allen tannenbaum and computer vision
Просмотров 843 месяца назад
Peter Olver speaks to the Experimental Mathematics Seminar. Abstract: I will present some of the late Allen Tannenbaum's fundamental contributions to image processing and computer vision, concentrating on our collaborative research. Topics include use of symmetry groups and nonlinear partial differential equations, image denoising and segmentation, and differential invariant signatures for obje...
counting maximal seat assignments that obey social distancing
Просмотров 333 месяца назад
George Spahn speaks to the Experimental Mathematics Seminar. Abstract: If I'm proctoring an exam and write on the board that students may not sit adjacent to another student, what should I expect the density of students to be in the seats? We analyze this question by counting maximal arrangements and then show how to generalize the method to answer other related questions. (Joint work with Doro...
Eric angelini's comma sequence
Просмотров 2424 месяца назад
Neil Sloane speaks to the Experimental Mathematics Seminar. Abstract: The Comma Transform of a sequence replaces each comma between the terms by the number formed by concatenating the single digits to the left and right of the comma. (E.g., the Comma Transform of the even numbers is 2, 24, 46, 68, 81, 1, ....) The remarkable "comma sequence" is defined by the property that it starts with 1 and ...
Nontrivial Zeros of the Riemann Zeta Function Know a lot
Просмотров 1,6 тыс.5 месяцев назад
Yuri Matiyasevich speaks to the Experimental Mathematics Seminar. Abstract: Bernhard Riemann gave an exact formula for the number of primes below given bound via a particular sum over the zeros of zeta function. In the course of large scale computer calculations the speaker discovered new relationships between these zeros and prime numbers. See: logic.pdmi.ras.ru/~yumat/personaljournal/finitedi...
sphere packings, singularities, and statistical mechanics
Просмотров 2056 месяцев назад
Miranda Holmes-Cerfon speaks to the Experimental Mathematics Seminar. Abstract: What are all the ways to arrange N hard spheres into a rigid packing? And what can the solution tell us about how materials crystallize? I will introduce an algorithm to enumerate rigid sphere packings (clusters) and describe some of the data it produces, which include many clusters with geometrically unusual proper...
Hardinian Arrays
Просмотров 1136 месяцев назад
Robert Dougherty-Bliss speaks to the Experimental Mathematics Seminar. Abstract: Kauers and Koutschan recently performed an automated search of sequences in the OEIS that might satisfy previously unknown recurrences. Among many promising hits was a 2014 sequence about king-moves on an array submitted by R.H. Hardin. I will show how to confirm and extend the conjectured recurrence using determin...
gambler's ruin with k gamblers
Просмотров 1237 месяцев назад
Persi Diaconis speaks to the Experimental Mathematics Seminar. Abstract: Consider (say) three gamblers with initial capital A, B , C. Each time a pair of gamblers are picked (uniformly at random), a fair coin is flipped and $1 is transfered. Eventually, one of the gamblers goes broke and the other two continue with the usual coin tossing until one is left with all A B C. Of interest: how long d...
The Ramanujan Machine 2
Просмотров 6508 месяцев назад
The Ramanujan Machine 2.0: algorithm-assisted discovery of an intrinsic order among mathematical constants Ido Kaminer speaks to the Experimental Mathematics Seminar. Abstract: Recent years have shown a rise in the number of discoveries in fields of mathematics that are being assisted by computer algorithms, primarily for exploring large parameter spaces that humans would take too long to inves...
New gilbreath conjectures, sum and erase, dissecting polygons, and other new sequences
Просмотров 2448 месяцев назад
Neil Sloane speaks to the Experimental Mathematics Seminar. Abstract: Topics to be discussed: Scott Shannon's Circle Counting Problems, Dissecting Polygons into Rectangles (with Gavin Theobald), New Gilbreath Conjectures, Eric Angelini's Sum and Erase Sequence, and a Report on Status of OEIS.
experimental mathematics techniques for boolean functions and combinatorial games
Просмотров 1569 месяцев назад
PhD defense
Partitioning a square into similar rectangles
Просмотров 202Год назад
Partitioning a square into similar rectangles
Solving the race in backgammon
Просмотров 922Год назад
Solving the race in backgammon
Noncommutative generalized-catalan numbers and their generating functions
Просмотров 157Год назад
Noncommutative generalized-catalan numbers and their generating functions
Gosper's Algorithm and Bell Numbers
Просмотров 245Год назад
Gosper's Algorithm and Bell Numbers
Thresholds by Jinyoung Park
Просмотров 196Год назад
Thresholds by Jinyoung Park
Continued Fractions And The 4-Color Theorem
Просмотров 203Год назад
Continued Fractions And The 4-Color Theorem
Unification Of Set Partitions
Просмотров 115Год назад
Unification Of Set Partitions
The KRR via a Composition Lemma Part 1
Просмотров 146Год назад
The KRR via a Composition Lemma Part 1
The KRR via a Composition Lemma Part 2
Просмотров 64Год назад
The KRR via a Composition Lemma Part 2
The KRR via a Composition Lemma Part 3
Просмотров 78Год назад
The KRR via a Composition Lemma Part 3
The KRR via a Composition Lemma Part 4
Просмотров 77Год назад
The KRR via a Composition Lemma Part 4
Hitting a prime in 2.43 dice rolls on average and on round robin tournaments
Просмотров 73Год назад
Hitting a prime in 2.43 dice rolls on average and on round robin tournaments
The arithmetic periodicity of the game cut
Просмотров 33Год назад
The arithmetic periodicity of the game cut
Enumerative combinatorics and coding theory
Просмотров 223Год назад
Enumerative combinatorics and coding theory
sorting probability for young diagrams
Просмотров 92Год назад
sorting probability for young diagrams

Комментарии

  • @alexandermedina9445
    @alexandermedina9445 7 дней назад

    This video came up right after watching Archaix's video "Incredible Giza Code." (13:34 hrs, Thursday, June 18fh, 2024)

  • @popnsons5144
    @popnsons5144 8 дней назад

    Channel owner: "Who the hell is this Archaix and why is his community spamming my comment section?" 😂😂😂

  • @floressonia55
    @floressonia55 8 дней назад

    Had to see this...came up kn my feed. Hello Archaix familia ❤

  • @dm78_87
    @dm78_87 10 дней назад

    People praising archaix = fools.

  • @scooter183
    @scooter183 11 дней назад

    2178 is divisible by 138, which is the Pheonix Cataclysm Protocol through history, also all linear and rectilinear measurements in the Great Pyramid, measured by Sir Flinders Pertee

  • @cathyrenick8562
    @cathyrenick8562 12 дней назад

    Wouldnt it be 2178?

  • @fractalofathena2178
    @fractalofathena2178 12 дней назад

    1089 x 2=2189 🤷🏼‍♀️

  • @fractalofathena2178
    @fractalofathena2178 12 дней назад

    Ah , this is where the Errants are gathering! 😜🔥❤️🔥

  • @jc3dynamic949
    @jc3dynamic949 14 дней назад

    and just like that, RUclips shows us 2178 videos. errants arise 😎

  • @ErrantCrow
    @ErrantCrow Месяц назад

    I, Also, Am An ARCHAIX Errant Who Found Herself Curious (or Whatever...) To See What This Video Was Laying Down,Concerning 2178,An Obviously [ERRANT]Number Here Inside This Construct.... And LOOK! ARCHAIX FOLLOWERS!! Whoop Whoop !!!!!!!!! I'd Be WILLING To Bet On The Fact That Jasons ARCHAIX Channel Has W A Y More Subs Than What The Sold Out Fuck-tards Over At Google Claims He Has. I Think They Say 157,000. I Believe It Would Truthfully Be Closer To 250,000. !! E. A. S. I L. Y. !! Kinda Random, But Accurate!! ❤

  • @wolf2164
    @wolf2164 Месяц назад

    The end of the beginning, ARCHAIX 2106

  • @errantprotocol8044
    @errantprotocol8044 Месяц назад

    2178 is the non-ending loop. Much love to all errants.

  • @SS-ty4el
    @SS-ty4el Месяц назад

    Archaix rocks!!!

  • @benjaminhildebrand2220
    @benjaminhildebrand2220 Месяц назад

    The algorithm

  • @rachelkeefer5030
    @rachelkeefer5030 Месяц назад

    Yep 👍🏻

  • @Unalienable-Arrant
    @Unalienable-Arrant Месяц назад

    2178 had to click it.. whats up my errant family ...

  • @SammSimm-md5rs
    @SammSimm-md5rs Месяц назад

    I can give you n biger than 2^100000-1 and i can difind steps to 1

  • @paladinrpg
    @paladinrpg Месяц назад

    If a truth is visible somewhere, it must be true everywhere.

  • @StevoRicho
    @StevoRicho Месяц назад

    Just came up in my feed 🤯 ,hi to all the errants ❤❤

  • @Kma060582
    @Kma060582 Месяц назад

    Euler….euler……euler

  • @Kma060582
    @Kma060582 Месяц назад

    lol archaix people found this….

  • @Bd-ox4mi
    @Bd-ox4mi Месяц назад

    End of the world

  • @FlatEarther319
    @FlatEarther319 Месяц назад

    2178? There's a tater in them onions!!

  • @j13more38
    @j13more38 Месяц назад

    EPIC WORK .... JASON BRESHEIRS FROM ARCHAIX SPEAKS OF THIS TOO ... INTERESTING CONCEPTS THAT HAVE TRUTH N FACTS MAKES YA REALIZE THIS MAY BE A MISSING LINK OF SOME SORT ...HHMMMM TIME WILL TELL IM SURE ... STAY SAFE N STAY BLESSED YALL

  • @MyHappyPlaceGarden
    @MyHappyPlaceGarden Месяц назад

    This just came up in my feed! Hello Archaix family 🩷

    • @Ya_Love
      @Ya_Love Месяц назад

      just showed-up on my feed, too. I noticed that Jason left a comment under the second part of this video-sequence two weeks ago already. WOW! How interesting that this shows-up in people's feed that watch a lot of Jason's videos. Algorithm? 😉

    • @bradhamilton432
      @bradhamilton432 Месяц назад

      Same!🙌🕺

    • @j13more38
      @j13more38 Месяц назад

      Interesting ... Great mind do think alike

    • @globetardnation
      @globetardnation Месяц назад

      Hola 👋 🎉😂 crazy eh

    • @lidiejennifer6645
      @lidiejennifer6645 Месяц назад

      idem apparu aujourd'hui dans mon fil d'actualité. et je regarde la chaine de Jason. je trouve cela bizarre.

  • @pattyek3556
    @pattyek3556 Месяц назад

    And interesting that in your 1089 exercise, 9801-1089= 8712 (2178). Or did you already see that? Also, if 2178 is placed on a linear 0-9 line, if traced it makes an infinite path, a figure 8. Same as 1089 but more elongated and not as balanced. Many dimensions…

  • @Bambabah
    @Bambabah Месяц назад

    The Archaix Paradox 😀

  • @Archaix138
    @Archaix138 2 месяца назад

    Your refusal to remove the integers forces the formula to operate in the abstract. Remove the integers and 2178 reveals itself to be the only immortal numbers, with all other numbers in existence collapsing into zero. I demonstrate this on my channel. It can only be true if we exist inside a holographic structuring and out arithmetic is actually the photo-negative of a REAL mathematical structure beyond the looping of 2178/8712. I've published charts making this easy to comprehend.

    • @brentabel724
      @brentabel724 Месяц назад

      If the following statement is the generally accepted reasoning of constants ... "in the same way the Golden ratio governs how things grow, the Fine-structure constant governs how things stick together, while Pi seems to control the space between." Is the immortal number's sole (edit: soul) purpose to demonstrate the broken/impossible/illogical nature of our reality? Or alternatively the infinite/eternal looping nature of reality? Or does it represent something else?

    • @OttoChenault
      @OttoChenault Месяц назад

      Wondered if you had seen this!😂✌🏻

    • @Livin_LettinLive
      @Livin_LettinLive 11 дней назад

      @Archaix138 | 👋🏼 Hi JB, To My Total Surprise Earlier TODAY (Sun., 9 June '24) Part 1 Of This Title And Its Content ( 3k Views - As Published A Full Decade Ago ) Was Queued For Viewing By you.T Immediately After Watching YOUR Very Fine Presentation: "St Paul's Cathedral Phoenix Prophecy In Stone." Obviously, Got My Undivided Attention Because Of YOUR Year-2178 "INFINITY-Related" Demonstrations/Contributions Of Record, And Continually Being Added To The Record ... This Being Pt. 2 (439 Views) It Was Likewise Queued-Up For Viewing After The First. Glad No Need To Bring This Presentation To Your Attention. I Do Wish That The Good Professor Would Have Extended The Courtesy Of Reply To You Before Now, One Month After You Commented. Perhaps A Reply From Him Is Forthcoming? Perhaps, He Has A Conversation In Mind ... Kind Regards Out Of The "Far East" 🙂

  • @imrematajz1624
    @imrematajz1624 3 месяца назад

    The presenter got himself into a pickle at 21.55 when he starts explaining the strata of the Homotopic Universe. The Universe is not the starting point. Type is. Type that contains its closed paths as a point or points. Elements are the maps, or functions within a Type. Points are identities with a path connecting a point to itself. If the Theory is not explained from the bottom up, it becomes extremely difficult to divorce the classical SET theory from this new notion of foundation which is the Homotopy Type Theory. No wonder the person who asked the question is confused and finds it counterintuitive.

    • @merbst
      @merbst 2 месяца назад

      Thank you for making clear his mistake!

  • @testingapps2145
    @testingapps2145 5 месяцев назад

    Does anyone understand what hes speaking? which language is that? i know Rutgers university is in US and it supposed to be English.

  • @omargaber3122
    @omargaber3122 5 месяцев назад

    Amazing❤

  • @ardahankonk5275
    @ardahankonk5275 5 месяцев назад

    1:49 for the person making eating sounds: common man, this is the reason I quit this video.

  • @JJ-fr2ki
    @JJ-fr2ki 6 месяцев назад

    15:28 Witt. means that a calculation could lead to a conceptual discovery including a discovery that the rules for the calculation are vague. There are now many cases of this found in the history of math. Sorry had to stop Could not take casual pace and presentation.Of course I studied Witt and logic in detail through Gödel and other foundational work and set theory debates.

  • @rbnootan101
    @rbnootan101 8 месяцев назад

    Great lecture

  • @JC-sg1do
    @JC-sg1do 9 месяцев назад

    It is an interesting video.. I know a better solution, there is someone has found the solution for the integer partition problem. please check these links: ruclips.net/video/8YIslPFOB84/видео.html ijcionline.com/paper/12/12423ijci06.pdf

  • @user-ir5dj6ut6w
    @user-ir5dj6ut6w 9 месяцев назад

    1.對於任意正整數 只要會收斂到1 就逃不出4->2->1的循環 所以只需證明收斂到1即可 2.所有正偶數必定收斂成正奇數 所以只需證明所有正奇數會收斂到1 3.(3x+1)必為偶數且必定小於等於4x 此處初始值x為任意正奇數 所以迭代函數對奇數的放大率至少是3/2=1.5且必定小於等於2 而此迭代函數對於偶數的收斂率卻是2的次冪永遠大於等於2 所以不論輸入的初始常數多大 最終迭代函數必定會出現收斂到1的情況 詳細的證明過程網路上找得到 說完了

  • @virtualvessel0
    @virtualvessel0 9 месяцев назад

    So. Fundamentally, is the question and proof, "why does ever decreasing numbers occur, and not ever increasing numbers??"

  • @an337
    @an337 9 месяцев назад

    Hello, I'm trying to prove “3n+1”. ruclips.net/video/UNvG7IJlHQ8/видео.html ruclips.net/video/OFJAJ1jZqmM/видео.html ruclips.net/video/cJdsEmD1lhw/видео.html ruclips.net/video/EMDaWwYovH8/видео.html

  • @jamestagge3429
    @jamestagge3429 10 месяцев назад

    So, it is obvious that if any odd number is multiplied by 3, the result will also be odd, e.g., 3 x 3 = 9 and 3 x 9 = 27, etc. This is simply because the last digit in the multiplication which is odd, multiplied by an odd number, structurally cannot be but odd. It follows then, logically that the addition of 1 will make it even, i.e., it changes the last digit (or the only digit if a one digit number) to an even number. Then the division by 2 will always be possible because the number being divided, as per the above, is always going to be even. The problem then arises when dividing an even number which can result in two odd numbers of equal value such as in 10/2 = 5. If then there is a particular structure in the application of this process, it should be predictable. Note an example of a structure…….in each column the black numbers are increments of 10 as would be expected. The red numbers in the columns are separated each by 30. The columns of black numbers each of which is the product of halving the even numbers are separated each by 5. The red numbers in rows are separated by 6. The black numbers in rows, the divided product of the numbers above are separated by 1. I believe that given this structure, it should be understood that the progression would have to always come back down to 1 and loop. 1 2 3 4 5 6 7 8 9 10 4 1 10 2 16 3 22 4 28 5 11 12 13 14 15 16 17 18 19 20 34 6 40 7 46 8 52 9 58 10 21 22 23 24 25 26 27 28 29 30 64 11 70 12 76 13 82 14 88 15 31 32 33 34 35 36 37 38 39 40 94 16 100 17 106 18 112 19 118 20 41 42 43 44 45 46 47 48 49 50 124 21 130 22 136 23 142 24 148 25 51 52 53 54 55 56 57 58 59 60 154 26 160 27 166 28 17 29 178 30 31 32 33 34 35 36 37 38 39 40 94 16 100 17 106 18 112 19 118 20 41 42 43 44 45 46 47 48 49 50 124 21 130 22 136 23 142 24 148 25

    • @eon2330
      @eon2330 4 месяца назад

      Repeating 9s is the closest we have to breaking this. AS multiplying LARGE #s by 3 +1, ends up netting more than dividing by 3. 999999s are uniform and go to X plus 9s plus 8 at the end, then divide by 2, 9998 divided by 2 is 4999. 4999X 3 plus 14,998. 7,499 x3+1. is 22498. 22498. Etc. It starts breaking down when the 9s start flowing backwards. But with enough 9s would it loop? I keep having it fluctuate. As long as the 9s keep coming back, its actually kinda cool. But yeah. Eventually it seems like, even with a rediculously LARGE number, it would loop back to 1. 9s looping is kinda the best example, it goes above and below its self, but it ALWAYS increases when the 9 is the last number, and a 9 is infront. It slowly works its way back down. From right to left. So even with 9s, yes after like billions of spaces and commas etc, it would take a VERY VERY large number of moves, but i am pretty certain it would loop back around. And its because odd by odd is odd, +1 is even. Divide by 2 is now even or odd. If even keep dividing. If odd, make it even. If even divide, if odd, make it even. etc. Probably not. So you would need to math.

    • @jamestagge3429
      @jamestagge3429 4 месяца назад

      @@eon2330 thanks for responding. very cool stuff. Though i have no illusions about being able to solve this, it is fund to play with.

  • @jofel131
    @jofel131 Год назад

    I feel a bit frightened.

  • @tikgamerz8098
    @tikgamerz8098 Год назад

    Ramanuj

  • @gytoser801
    @gytoser801 Год назад

    Assumptions are dead, long Live the Logic

  • @hayalgeta6024
    @hayalgeta6024 Год назад

    Perfectly explained professor 🐕🙏🙏🙏🙏🙏🌺🌺🌺🌺🌺🌺🌺🌺🌺🌺🌺🌺🌺🥀🥀🥀🥀

  • @williejohnson5172
    @williejohnson5172 Год назад

    Yes. They iterate to 1.

    • @robheusd
      @robheusd Год назад

      Have you checked for googolplex+1?

  • @samro7890
    @samro7890 Год назад

    super pleased to hear the reference of Hobson's book on Trigonometry. I had used that in high school, and that is a superb text!

  • @yetanotherjohn
    @yetanotherjohn Год назад

    3n+1 reminds me of the Mersenne Primes, a function that bumps the system over by one unit and gets an amazing result.

  • @youknowitistrue
    @youknowitistrue Год назад

    Amazing Lecture. I wish this kind of simplified motivation is given for all advanced topics.

  • @patrickwithee7625
    @patrickwithee7625 Год назад

    The Liar’s Paradox is both true and false, which indicates that some forms of self reference are self-defeating. This is similar to the set of all sets that don’t contain themselves. There just are not valid propositions of the form “this sentence is false” or something like that. A similar example is that 1/0 looks like it is a valid expression in terms of just using numbers and division, but clearly division by zero is invalid.

  • @7177YT
    @7177YT Год назад

    Awesome!

  • @7177YT
    @7177YT Год назад

    Subscriiibed!