William Rose
William Rose
  • 717
  • 375 322
Logic - Dedekind Cuts are Closed Under Addition
Logic - MBHS - Blair - Rose - 12/04/2024
Here's a proof that Dedekind Cuts are closed under addition. We review what a Dedekind Cut is, mention all its defining properties, propose a definition/construction of the sum of two Dedekind Cuts, and prove that under this definition of addition, the resulting set of rationals is indeed a Dedekind Cut (by showing it has all the defining properties).
Переглядів: 199

Відео

MCTM Presentation: Rediscovering Formulas Through Examples
Переглядів 1162 місяці тому
Presentation by Will Rose at the 2024 MCTM (Maryland Council of Teachers of Mathematics) Annual Conference on 10/19/2024; Title: Rediscovering Formulas Through Examples We talk about FORMULAS, where they come from, how to prove them, and how to help students think about them and care about them.
Building the Poincaré Disc Model & Poincaré Half-Plane Models in GeoGebra
Переглядів 1162 місяці тому
Logic - Rose - MBHS - Blair - Building the Poincaré Disc Model & Poincaré Half-Plane Models in GeoGebra - 10/16/2024 We use Geogebra and various theorems and constructions from Euclidean geometry to create the Poincare Disc and Poincare Half-plane Model (both originally discovered and published by Eugenio Beltrami). Brief detour into Circle Inversion.
Logic - Euclid Book I, Props 17-21
Переглядів 1643 місяці тому
Logic - Euclid Book I, Props 17-21
Walking from P9 to Room 309 at Montgomery Blair High School
Переглядів 1,1 тис.4 місяці тому
Can a person walk from P9 (the farthest portable) into Blair, up two flights of stairs and all the way to room 309 (the farthest opposite point) in under 6 minutes?!? Only one way to find out.
Introduction to Curve Sketching
Переглядів 2388 місяців тому
Using the first and second derivative to sketch functions by hand. By considering domain, range, end behavior, sign charts, and the sign of the first and second derivative, we can produce a graph of any function that is accurate with respect to relative extrema and points of inflection. Analysis 1A - Rose - Blair - MBHS - 04/19/2024 Asynchronous Learning Monday 4/22/24
Logic - Introduction to ZFC Axioms
Переглядів 40811 місяців тому
Logic - Rose - Blair - MBHS - Introduction to the Axioms of ZFC - Axiomatization of Set Theory - 01/19/2024
Conic Sections in Polar Coordinates
Переглядів 14711 місяців тому
Rose - MBHS - Blair - Introduction to Conic Sections in Polar Coordinates - 01/19/2024
Advanced Geometry - Miquel Points - Recap of Section 3.3 of Coxeter's Geometry Revisited
Переглядів 180Рік тому
Advanced Geometry - MBHS - Rose - Blair - A recap and clarification of several small subtleties from the past two week of Advanced Geometry class, including a thorough review of Section 3.3 of Geometry Revisited - Miquel Points, Complete Quadrilaterals, Pedal Triangles, Simson Lines, Oblique Pedal Triangles, Oblique Simson Lines, Inner and Outer Napoleon Triangles - 11/14/2023
Occupancy Problems - Short Review
Переглядів 413Рік тому
Discrete Math - Rose - MBHS - Blair - Combinatorics - Partition Numbers - Sterling Numbers of the Second Kind - 05/11/2023
sin(A+B+C)
Переглядів 1812 роки тому
A geometric proof of the formula for the sine of the sum of three angles. Made with Geogebra. Jazzy Frenchy by Benjamin Tissot on www.bensound.com/
Precalc C - Partial Fractions with Repeated Linear Factors
Переглядів 2342 роки тому
Precalc C - Rose - MBHS - Blair - Partial Fractions - This video explains how to treat partial fractions problems with repeated linear factors & why - 10/28/2022
Precalc C - Complex Roots Packet #1
Переглядів 2342 роки тому
Precalc C - Blair - MBHS - Rose - Complex roots come in conjugate pairs - Using knowledge of complex roots and the factor theorem to write formulas for polynomials - 10/03/2022
Logic - Propositions 16 - 31 of Book I of Euclid
Переглядів 2132 роки тому
Logic - Blair - MBHS - Rose - Euclidean Geometry - Book I of Euclid's Elements - Proofs of Propositions 16 to 31 - Exterior Angle Theorem, Ordering Theorem, Triangle Inequality, Hinge Theorem, & the Parallel Postulate - 09/28/2022 [Battery died on video camera with 20 minutes to go, oh well]
sin(α+β) and cos(α+β)
Переглядів 2502 роки тому
Proofs of the formulas for sine of a sum and cosine of a sum, using transformational reasoning. Made with GeoGebra. Jazz Comedy by Benjamin Tissot on www.bensound.com
Logic - Introduction to Ordinals
Переглядів 4772 роки тому
Logic - Introduction to Ordinals
Analysis 1A - Going over the HW on Calculus of Parametric Curves
Переглядів 4102 роки тому
Analysis 1A - Going over the HW on Calculus of Parametric Curves
Analysis 1A - Using the MVT to Find Extrema (Asynchronous Learning)
Переглядів 2682 роки тому
Analysis 1A - Using the MVT to Find Extrema (Asynchronous Learning)
Analysis 1A - Implicit Differentiation
Переглядів 2062 роки тому
Analysis 1A - Implicit Differentiation
Logic - Introduction to Descartes
Переглядів 6342 роки тому
Logic - Introduction to Descartes
Analysis 1A - Introduction to the ε-δ Definition of a Limit
Переглядів 5572 роки тому
Analysis 1A - Introduction to the ε-δ Definition of a Limit
Precalc C - Introduction to Counting
Переглядів 3823 роки тому
Precalc C - Introduction to Counting
Parametric Equations Example
Переглядів 1883 роки тому
Parametric Equations Example
Graphing Rational Functions Example
Переглядів 1973 роки тому
Graphing Rational Functions Example
The Rational Root Theorem
Переглядів 4713 роки тому
The Rational Root Theorem
Discrete Math - Proof of Uniqueness of Prime Factorization
Переглядів 3,9 тис.3 роки тому
Discrete Math - Proof of Uniqueness of Prime Factorization
Analysis 1A - Method of Washers
Переглядів 1303 роки тому
Analysis 1A - Method of Washers
Discrete Math - Going over the 10.5 HW on Graph Theory
Переглядів 4163 роки тому
Discrete Math - Going over the 10.5 HW on Graph Theory
Discrete Math - Going over the 10.3 HW on Graph Theory
Переглядів 3803 роки тому
Discrete Math - Going over the 10.3 HW on Graph Theory
Discrete Math - Going over the 10.4 HW on Graph Theory
Переглядів 4183 роки тому
Discrete Math - Going over the 10.4 HW on Graph Theory

КОМЕНТАРІ

  • @raxirex6443
    @raxirex6443 9 годин тому

    Hi! In your last tweet you mentioned no one explaining the Pascal Triangle as paths of probability. Actually I have learned it that way from the Feynman lectures, Lecture 6 Probability.

  • @Pyross
    @Pyross 7 днів тому

    Great explanation !!

  • @robertrussell7241
    @robertrussell7241 10 днів тому

    I'm lost on 10:26 If you square both sides, given that (√x)² = X, anything under the radical should just be itself. So where does the -20 come from as well as duplicating (4-x)²+y? (10-√(4-x)²+y²)² You'd distribute the square therefore squaring 10 and squaring √(4-x)²+y² leaving 100-(4-x)²+y² Please explain what I missed

    • @robertrussell7241
      @robertrussell7241 10 днів тому

      Never mind. I was seeing multiplication between 10 and a -√ rather than subtraction. That means (a-b)². All is well now.

  • @ling-feitsao
    @ling-feitsao 17 днів тому

    Well done

  • @dylanchong3346
    @dylanchong3346 22 дні тому

    man I wish I found these videos before I took my symbolic logic final exam 2 days ago. everything makes so much more sense now. 😭

  • @innerproductspace
    @innerproductspace 26 днів тому

    it's almost midnight and tmr i have an exam on fol, propositional logic, truth tables and fitch proofs. i know everything besides the last topic so i will see much i can learn by watching as many videos of yours as i can before the exam

    • @dodecahedra
      @dodecahedra 26 днів тому

      @innerproductspace Be sure to get some sleep!

  • @ЛачинАлиев-о4х
    @ЛачинАлиев-о4х 26 днів тому

    Watching in 2024 button _____>

  • @arthurhill5567
    @arthurhill5567 26 днів тому

    Would this proof work for problem 24? (By-the-way, I'm very impressed with your grasp of the topic and your ability to communicate how to understand the inticacies of complex Formal Logic proofs.) 1 ¬(P ∨ Q) 2 ¬(¬P ∧ ¬Q) 3 P 4 P ∨ Q ∨I 3 5 ⊥ ⊥I 1, 4 6 ¬P ¬I 3-5 7 Q 8 P ∨ Q ∨I 7 × 9 ⊥ ⊥I 1, 8 10 ¬Q ¬I 7-9 11 ¬P ∧ ¬Q ∧I 6, 10 12 ⊥ ⊥I 2, 11 13 ¬¬(¬P ∧ ¬Q) ¬I 2-12 14 ¬P ∧ ¬Q DNE 13

  • @snowflakeman6000
    @snowflakeman6000 29 днів тому

    which uni do you teach at?? I wanna study there

    • @dodecahedra
      @dodecahedra 29 днів тому

      @@snowflakeman6000 I teach high school. So this is a class for 17-year-olds. Enjoy on the Internet for free. Find some rich person to give me tons of money and I'll quit my job and make more videos.

    • @snowflakeman6000
      @snowflakeman6000 29 днів тому

      @ Really!? this is the exact same thing as one of my university modules! Maybe you should take tuitions on the side or start a patreon! You should legit be a Uni prof not a High-school teacher. I’m literally trying to understand hoare logic which is the next step from this for uni. If you do take tuitions plz lmk 🙏

  • @arthurhill5567
    @arthurhill5567 29 днів тому

    I think I have a better proof for Problem 16: 1 P ∨ Q Prem 2 ¬P Prem 3 ¬Q Supp 4 P Supp 5 ¬P R 2 6 ⊥ ¬E 4, 5 7 Q Supp 8 ¬Q R 3 9 ⊥ ¬E 7, 8 10 ⊥ ∨E 1, 4-6, 7-9 11 ¬¬Q ¬I 3-10 12 Q DNE 11

  • @snowflakeman6000
    @snowflakeman6000 Місяць тому

    Which uni do you teach at? I wanna study from profs like you!

  • @samueldeandrade8535
    @samueldeandrade8535 Місяць тому

    Dedekind cuts are such a nice construction.

  • @lazaredurand6675
    @lazaredurand6675 Місяць тому

    In Proof # 12 you can also prove that Q is false with the same method. So it lead to an other contradiction.

    • @lazaredurand6675
      @lazaredurand6675 Місяць тому

      I mean, If you assume that Q is true Instead of false, you can prove that it is false.

  • @dariusztomaszewski-guerrer7874
    @dariusztomaszewski-guerrer7874 Місяць тому

    proof - rlly helped me understand this proof thank u !!!

  • @jeromeglick
    @jeromeglick 2 місяці тому

    Why?

    • @dodecahedra
      @dodecahedra 2 місяці тому

      @@jeromeglick old digital video camera technology would auto truncate the video files at 33 minutes and I was too old, dumb, lazy to do any editing, so I just put the videos up in parts.

  • @jeromeglick
    @jeromeglick 2 місяці тому

    15:27 Oh man, those old TVs... high-tech '90s technology, with TI-83 displays invoking warm fuzzy nostalgic feelings These lectures go underappreciated as usual. Rivals Netflix, actually. At least we can rest assured in their (relatively) eternal preservation.

  • @jeromeglick
    @jeromeglick 2 місяці тому

    Why am I watching this?! LMAO 🤣

  • @asepulven2768
    @asepulven2768 2 місяці тому

    Blessed!

  • @tamerali7631
    @tamerali7631 2 місяці тому

    Great videos. Thanks a bunch!

  • @toshivharidra6407
    @toshivharidra6407 2 місяці тому

    thanks a lot. I was doing this for my math competition, and I needed some basic practice problems to get the gist of it :)

  • @Soft-e6f
    @Soft-e6f 2 місяці тому

    Great!!

  • @asokannaidoo9574
    @asokannaidoo9574 2 місяці тому

    your explanations are brilliant! Thank you so much for these videos!

  • @semihaturkoglu
    @semihaturkoglu 2 місяці тому

    😪

  • @andredejager3637
    @andredejager3637 2 місяці тому

    "The destiny of any negation is to be used in a contradiction" :)

  • @andredejager3637
    @andredejager3637 2 місяці тому

    Thanks Mr Rose, I was up Schitz Creek

  • @nn-kk4du
    @nn-kk4du 2 місяці тому

    Great work

  • @joshual5597
    @joshual5597 2 місяці тому

    In the proof you assumed the negation of (B & C). My question is, why can't we use disjunctive syllogism on lines 1 & 4 to get B & C for line 5 instead of assuming the negation? Then we can simplify line #5 B & C to get line #6 B and line #7 C. Then we can use addition (or) on line #6 to get line #8 (A or B ) . Then modus ponens on line #3, #8 to get line #9 (D or E). Then use disjuntive syllogism on line #2, #9 to get line #10 D. Then using conjunction from line#7 ,#10 to get line #11 C & D? is my reasoning correct or no? thanks!

  • @SpicyKroket
    @SpicyKroket 2 місяці тому

    Great video, thank you!

  • @Legotyres
    @Legotyres 3 місяці тому

    Is there any way of getting a measurement between point P and E? If the semi major is 5 and the semi minor is 3 as in your illustration?

    • @dodecahedra
      @dodecahedra 3 місяці тому

      @@Legotyres P is arbitrary with coordinates (x,y), so PE = √(x²+y²). But not sure how that helps.

    • @Legotyres
      @Legotyres 3 місяці тому

      @@dodecahedra thank you so much for the replying I’m still learning and as it was for a bit of something to do, it’s ended up being a lot more complex than I thought it was going to be

    • @Legotyres
      @Legotyres 2 місяці тому

      Massive thank you! It worked perfectly, those are the numbers I was looking for. I has been calculating F1 to P1 , not x and y 😃 I’ll say, your my hero as I’ve spent a number of days playing with the ellipse (which has been really cool) and got so far, but this was the last hurdle for my needs and I hadn’t been able to find the answer 😃

  • @ritamoreira6260
    @ritamoreira6260 3 місяці тому

    Thank u for saving the ass of a computer science major

  • @saharaRabbit-t1i
    @saharaRabbit-t1i 3 місяці тому

    pweeety please add video for modal logic natural deduction

  • @suryasameerdattavaddadi9861
    @suryasameerdattavaddadi9861 3 місяці тому

    Hey man these are very helpful. thanks!

  • @zandimt
    @zandimt 3 місяці тому

    genuinely saved me for my midterm tomorrow, oh my god, thank you for this

  • @arthurramosvieira7042
    @arthurramosvieira7042 3 місяці тому

    Brazilian computer science students thank you for your videos!!

  • @rafaelcardoso6471
    @rafaelcardoso6471 3 місяці тому

    legend, saving my computer science major! hugs from brazil!

  • @emmacreelman1333
    @emmacreelman1333 3 місяці тому

    I think I found an error in the proof for you states n must be a natural number on the left of the board, but the proof has n being a rational number...

    • @dodecahedra
      @dodecahedra 2 місяці тому

      Yeah, I started out referring to n as a natural number out of simplicity, but the algebra works out better if you let n be rational. If you want, you can just set n to be "the next natural number" by rounding up. That's just adds a step or two to the argument.

  • @mihaisimtion6925
    @mihaisimtion6925 3 місяці тому

    You are a legend ; after a day of studying the rules; they finally started to click in my head after watching you explain everything once again !

  • @Ghadeer-p5d
    @Ghadeer-p5d 3 місяці тому

    Thank u so much It was very useful

  • @sekkou6898
    @sekkou6898 3 місяці тому

    life saver

  • @dodecahedra
    @dodecahedra 4 місяці тому

    This was the source of this argument: www.cs.princeton.edu/courses/archive/spring11/cos116/handouts/daviscomputation.pdf

  • @arunabhsingh7236
    @arunabhsingh7236 4 місяці тому

    goat 🙏

  • @courtneywilson5661
    @courtneywilson5661 4 місяці тому

    *intently watching as if I didn’t graduate 5 years ago*

    • @kevinzhou2151
      @kevinzhou2151 4 місяці тому

      same. I felt like I was watching an important scientific announcement

  • @premchandrasekhar7572
    @premchandrasekhar7572 4 місяці тому

    Common Rose W

  • @Elizabeth-tx3wn
    @Elizabeth-tx3wn 4 місяці тому

    important tip: instead of walking through the hallways (crowded) you can walk behind the school outside and go into the building thru the same door as the p15 kids. way less traffic so it's usually faster, and you actually get to experience sunlight and wind!

    • @jeromeglick
      @jeromeglick 2 місяці тому

      Or just use the teleporter.

  • @jeremyschwartz8874
    @jeremyschwartz8874 4 місяці тому

    Going from the portables (where learning happens) into the building, isn't the left-hand door in the vestibule (3:01) unlocked, which would put you directly into the stairwell instead of having to enter the SAC hallway and then turn back into the stairwell? That would save at least 2 seconds! Also worth noting: only 5 minutes between periods 7/8 and period 9.

  • @studentdastanay7644
    @studentdastanay7644 4 місяці тому

    hey

  • @adithisathya4165
    @adithisathya4165 4 місяці тому

    this is a profound video! however, there is one small caveat. there appears to be an alarming number of scholars in the corridors for the duration of the time during which my peers and i must traverse the campus in order to attend our learning point. it appears to me there is no solution to this plight...

    • @VeenaKailad
      @VeenaKailad 4 місяці тому

      to suggest that there is no solution to your plight indicates a lack of understanding of the geometry of hallway traffic. as we are all well-versed in the technique of weaving in and out of the traffic of individual moving students, let us focus on the greatest obstacle of the hallway hustler: the Small Set of Stationary Scholars. to simplify, visualize this SSSS as a closed circle. the first step is to enter the circle as a member, forcing it to expand slightly to accommodate the increased circumference. then, treat the SSSS like a spinning wheel. WLOG, let clockwise be your direction of travel. irritate the person to your left until they step away from you, causing a clockwise turn (birds-eye) of the SSSS. repeat this step until you are on the other side of the circle, then make a quick exit and continue down the hallway.

    • @williamroe8905
      @williamroe8905 4 місяці тому

      /gamemode spectator

    • @adithisathya4165
      @adithisathya4165 4 місяці тому

      @@VeenaKailad ah, your solution appears familiar. hath your ears set upon the "roundabout"? one of humanities most grave mishaps? well, allow me to bestow knowledge upon you. a roundabout, according to Oxford Languages, is "a road junction at which traffic moves in one direction around a central island to reach one of the roads converging on it". appears to be of a similar concept to that of which you have mentioned, hm? doesn't this sound impressive? NO. a roundabout is a barbaric free for all and a disgrace upon roads everywhere. have you considered the thought that one person does not move, and thereby causes a major crash? and how would you even infiltrate the SSSS in the first place? your "solution" would simply inflate the problem!

    • @VeenaKailad
      @VeenaKailad 4 місяці тому

      @@adithisathya4165 i see you have conceived of the enormous amount of personal effort needed to make this maneuver possible. having conceived of it, endeavor to commit yourself to its actual completion, and you will have no further problems. any student who puts in effort to make themselves sufficiently irritating to those around them need not fear the one person who "does not move"; though we cannot guarantee much about this arbitrary member of the human race, their instinct for self-preservation may be depended on. the developed capacity to irritate induces all those in the vicinity to step away, enabling the student to also force a gap in the SSSS for initial infiltration, as a pebble dropped into water creates ripples outward. of course, being this annoying is not a skill to be taken lightly - therein, the personal effort.

    • @jeromeglick
      @jeromeglick 2 місяці тому

      Based on this elaborate showcasing of your analytical faculties, us older folks can rest assured that you young people are obviously more than capable of handling the unforeseen complex problems that the rest of the 21st century will undoubtedly thrust upon us all.

  • @merug4349
    @merug4349 4 місяці тому

    Wallahi he's speed walking

    • @danielwu624
      @danielwu624 4 місяці тому

      nah for real that was a blistering place

  • @justinian1453
    @justinian1453 4 місяці тому

    Also, if it’s ninth period then you need to factor in that not only is there traffic, the traffic is going the wrong way in great numbers.

    • @gghollen6933
      @gghollen6933 4 місяці тому

      Agreed if it's 5:45 without traffic, imagine students that just stand in little groups blocking half the hallways or students with their arms linked that move slowly and you can't pass them. You can try to speed walk, but the crowd only moves a certain speed and it usually isn't fast

    • @justinian1453
      @justinian1453 4 місяці тому

      @@gghollen6933I guess if you went outside and then entered on the far side of the school you might be able to avoid the traffic. Also this doesn’t consider the affects of weather

    • @gghollen6933
      @gghollen6933 4 місяці тому

      @@justinian1453 that’s true and they said they are also assuming you can leave right when the bell rings, but that is not the case

    • @adithisathya4165
      @adithisathya4165 4 місяці тому

      @@gghollen6933 astute observation, fellow peer. i admire your ability to observe the environment around you and classify common obstacles on the great journey to room 309. your ability to relay information through these "comments" is truly remarkable. i especially relished reading the section on "little groups". i, too, find myself in this peculiar predicament in which i am unable to surmount these circles of scholars for the duration of their assembly.

    • @jeromeglick
      @jeromeglick 2 місяці тому

      @@adithisathya4165 Sounds very familiar; reminds me of my youth.

  • @justinian1453
    @justinian1453 4 місяці тому

    Mr. Lodal, there is only one wonder of the world, it’s the pyramid. The “obelisk” is the Washington monument, which along with the St. Louis arch and the Eiffel Tower, none of which are wonders of the world. 2:32

    • @eriklodal8882
      @eriklodal8882 4 місяці тому

      Maybe not to you, but they’re wonders to me. Why are they in the courtyard? Why did I not realize this sooner?

    • @courtneywilson5661
      @courtneywilson5661 4 місяці тому

      ⁠​⁠​⁠@@eriklodal8882Mr.Kaluta’s Material Science class used to make them. They’re supposed to all be to scale. In theory one of the concrete slabs in the courtyard is a model of Blair that my year made.