Podcasts about Algebraic

Janet Walkoe & Margaret Walton, Exploring the Seeds of Algebraic Reasoning ROUNDING UP: SEASON 4 | EPISODE 8 Algebraic reasoning is defined as the ability to use symbols, variables, and mathematical operations to represent and solve problems. This type of reasoning is crucial for a range of disciplines.  In this episode, we're talking with Janet Walkoe and Margaret Walton about the seeds of algebraic reasoning found in our students' lived experiences and the ways we can draw on them to support student learning.  BIOGRAPHIES Margaret Walton joined Towson University's Department of Mathematics in 2024. She teaches mathematics methods courses to undergraduate preservice teachers and courses about teacher professional development to education graduate students. Her research interests include teacher educator learning and professional development, teacher learning and professional development, and facilitator and teacher noticing. Janet Walkoe is an associate professor in the College of Education at the University of Maryland. Janet's research interests include teacher noticing and teacher responsiveness in the mathematics classroom. She is interested in how teachers attend to and make sense of student thinking and other student resources, including but not limited to student dispositions and students' ways of communicating mathematics. RESOURCES "Seeds of Algebraic Thinking: a Knowledge in Pieces Perspective on the Development of Algebraic Thinking" "Seeds of Algebraic Thinking: Towards a Research Agenda" NOTICE Lab  "Leveraging Early Algebraic Experiences"  TRANSCRIPT Mike Wallus: Hello, Janet and Margaret, thank you so much for joining us. I'm really excited to talk with you both about the seeds of algebraic thinking. Janet Walkoe: Thanks for having us. We're excited to be here.  Margaret Walton: Yeah, thanks so much. Mike: So for listeners, without prayer knowledge, I'm wondering how you would describe the seeds of algebraic thinking. Janet: OK. For a little context, more than a decade ago, my good friend and colleague, [Mariana] Levin—she's at Western Michigan University—she and I used to talk about all of the algebraic thinking we saw our children doing when they were toddlers—this is maybe 10 or more years ago—in their play, and just watching them act in the world. And we started keeping a list of these things we saw. And it grew and grew, and finally we decided to write about this in our 2020 FLM article ["Seeds of Algebraic Thinking: Towards a Research Agenda" in For the Learning of Mathematics] that introduced the seeds of algebraic thinking idea. Since they were still toddlers, they weren't actually expressing full algebraic conceptions, but they were displaying bits of algebraic thinking that we called "seeds." And so this idea, these small conceptual resources, grows out of the knowledge and pieces perspective on learning that came out of Berkeley in the nineties, led by Andy diSessa. And generally that's the perspective that knowledge is made up of small cognitive bits rather than larger concepts. So if we're thinking of addition, rather than thinking of it as leveled, maybe at the first level there's knowing how to count and add two groups of numbers. And then maybe at another level we add two negative numbers, and then at another level we could add positives and negatives. So that might be a stage-based way of thinking about it.  And instead, if we think about this in terms of little bits of resources that students bring, the idea of combining bunches of things—the idea of like entities or nonlike entities, opposites, positives and negatives, the idea of opposites canceling—all those kinds of things and other such resources to think about addition. It's that perspective that we're going with. And it's not like we master one level and move on to the next. It's more that these pieces are here, available to us. We come to a situation with these resources and call upon them and connect them as it comes up in the context. Mike: I think that feels really intuitive, particularly for anyone who's taught young children. That really brings me back to the days when I was teaching kindergartners and first graders.  I want to ask you about something else. You all mentioned several things like this notion of "do, undo" or "closing in" or the idea of "in-betweenness" while we were preparing for this interview. And I'm wondering if you could describe what these things mean in some detail for our audience, and then maybe connect them back with this notion of the seeds of algebraic thinking. Margaret: Yeah, sure. So we would say that these are different seeds of algebraic thinking that kids might activate as they learn math and then also learn more formal algebra. So the first seed, the doing and undoing that you mentioned, is really completing some sort of action or process and then reversing it.  So an example might be when a toddler stacks blocks or cups. I have lots of nieces and nephews or friends' kids who I've seen do this often—all the time, really—when they'll maybe make towers of blocks, stack them up one by one and then sort of unstack them, right? So later this experience might apply to learning about functions, for example, as students plug in values as inputs, that's kind of the doing part, but also solve functions at certain outputs to find the input. So that's kind of one example there.  And then you also talked about closing in and in-betweenness, which might both be related to intervals. So closing in is a seed where it's sort of related to getting closer and closer to a desired value. And then in formal algebra, and maybe math leading up to formal algebra, the seed might be activated when students work with inequalities maybe, or maybe ordering fractions.  And then the last seed that you mentioned there, in-betweenness, is the idea of being between two things. For example, kids might have experiences with the story of Goldilocks and the Three Bears, and the porridge being too hot, too cold, or just right. So that "just right" is in-between. So these seats might relate to inequalities and the idea that solutions of math problems might be a range of values and not just one. Mike: So part of what's so exciting about this conversation is that the seeds of algebraic thinking really can emerge from children's lived experience, meaning kids are coming with informal prior knowledge that we can access. And I'm wondering if you can describe some examples of children's play, or even everyday tasks, that cultivate these seeds of algebraic thinking. Janet: That's great. So when I think back to the early days when we were thinking about these ideas, one example stands out in my head. I was going to the grocery store with my daughter who was about three at the time, and she just did not like the grocery store at all. And when we were in the car, I told her, "Oh, don't worry, we're just going in for a short bit of time, just a second." And she sat in the back and said, "Oh, like the capital letter A." I remember being blown away thinking about all that came together for her to think about that image, just the relationship between time and distance, the amount of time highlighting the instantaneous nature of the time we'd actually be in the store, all kinds of things.  And I think in terms of play examples, there were so many. When she was little, she was gifted a play doctor kit. So it was a plastic kit that had a stethoscope and a blood pressure monitor, all these old-school tools. And she would play doctor with her stuffed animals. And she knew that any one of her stuffed animals could be the patient, but it probably wouldn't be a cup. So she had this idea that these could be candidates for patients, and it was this—but only certain things. We refer to this concept as "replacement," and it's this idea that you can replace whatever this blank box is with any number of things, but maybe those things are limited and maybe that idea comes into play when thinking about variables in formal algebra. Margaret: A couple of other examples just from the seeds that you asked about in the previous question. One might be if you're talking about closing in, games like when kids play things like "you're getting warmer" or "you're getting colder" when they're trying to find a hidden object or you're closing in when tuning an instrument, maybe like a guitar or a violin.  And then for in-betweeness, we talked about Goldilocks, but it could be something as simple as, "I'm sitting in between my two parents" or measuring different heights and there's someone who's very tall and someone who's very short, but then there are a bunch of people who also fall in between. So those are some other examples. Mike: You're making me wonder about some of these ideas, these concepts, these habits of mind that these seeds grow into during children's elementary learning experiences. Can we talk about that a bit? Janet: Sure. Thank you for that question.  So we think of seeds as a little more general. So rather than a particular seed growing into something or being destined for something, it's more that a seed becomes activated more in a particular context and connections with other seeds get strengthened. So for example, the idea of like or nonlike terms with the positive and negative numbers. Like or nonlike or opposites can come up in so many different contexts. And that's one seed that gets evoked when thinking potentially when thinking about addition. So rather than a seed being planted and growing into things, it's more like there are these seeds, these resources that children collect as they act on the world and experience things. And in particular contexts, certain seeds are evoked and then connected. And then in other contexts, as the context becomes more familiar, maybe they're evoked more often and connected more strongly. And then that becomes something that's connected with that context. And that's how we see children learning as they become more expert in a particular context or situation. Mike: So in some ways it feels almost more like a neural network of sorts. Like the more that these connections are activated, the stronger the connection becomes. Is that a better analogy than this notion of seeds growing? It's more so that there are connections that are made and deepened, for lack of a better way of saying it? Janet: Mm-hmm. And pruned in certain circumstances. We actually struggled a bit with the name because we thought seeds might evoke this, "Here's a seed, it's this particular seed, it grows into this particular concept." But then we really struggled with other neurons of algebraic thinking. So we tossed around some other potential ideas in it to kind of evoke that image a little better. But yes, that's exactly how I would think about it. Mike: I mean, just to digress a little bit, I think it's an interesting question for you all as you're trying to describe this relationship, because in some respects it does resemble seeds—meaning that the beginnings of this set of ideas are coming out of lived experiences that children have early in their lives. And then those things are connected and deepened—or, as you said, pruned. So it kind of has features of this notion of a seed, but it also has features of a network that is interconnected, which I suspect is probably why it's fairly hard to name that. Janet: Mm-hmm. And it does have—so if you look at, for example, the replacement seed, my daughter playing doctor with her stuffed animals, the replacement seed there. But you can imagine that that seed, it's domain agnostic, so it can come out in grammar. For instance, the ad-libs, a noun goes here, and so it can be any different noun. It's the same idea, different context. And you can see the thread among contexts, even though it's not meaning the same thing or not used in the same way necessarily. Mike: It strikes me that understanding the seeds of algebraic thinking is really a powerful tool for educators. They could, for example, use it as a lens when they're planning instruction or interpreting student reasoning. Can you talk about this, Margaret and Janet? Margaret: Yeah, sure, definitely. So we've seen that teachers who take a seeds lens can be really curious about where student ideas come from. So, for example, when a student talks about a math solution, maybe instead of judging whether the answer is right or wrong, a teacher might actually be more curious about how the student came to that idea. In some of our work, we've seen teachers who have a seeds perspective can look for pieces of a student answer that are productive instead of taking an entire answer as right or wrong. So we think that seeds can really help educators intentionally look for student assets and off of them. And for us, that's students' informal and lived experiences. Janet: And kind of going along with that, one of the things we really emphasize in our methods courses, and is emphasized in teacher education in general, is this idea of excavating for student ideas and looking at what's good about what the student says and reframing what a student says, not as a misconception, but reframing it as what's positive about this idea. And we think that having this mindset will help teachers do that. Just knowing that these are things students bring to the situation, these potentially productive resources they have. Is it productive in this case? Maybe. If it's not, what could make it more productive? So having teachers look for these kinds of things we found as helpful in classrooms. Mike: I'm going to ask a question right now that I think is perhaps a little bit challenging, but I suspect it might be what people who are listening are wondering, which is: Are there any generalizable instructional moves that might support formal or informal algebraic thinking that you'd like to see elementary teachers integrate into their classroom practice? Margaret: Yeah, I mean, I think, honestly, it's: Listen carefully to kids' ideas with an open mind. So as you listen to what kids are saying, really thinking about why they're saying what they're saying, maybe where that thinking comes from and how you can leverage it in productive ways. Mike: So I want to go back to the analogy of seeds. And I also want to think about this knowing what you said earlier about the fact that some of the analogy about seeds coming early in a child's life or emerging from their lived experiences, that's an important part of thinking about it. But there's also this notion that time and experiences allow some connections to be made and to grow or to be pruned.  What I'm thinking about is the gardener. The challenge in education is that the gardener who is working with students in the form of the teacher and they do some cultivation, they might not necessarily be able to kind of see the horizon, see where some of this is going, see what's happening. So if we have a gardener who's cultivating or drawing on some of the seeds of algebraic thinking in their early childhood students and their elementary students, what do you think the impact of trying to draw on the seeds or make those connections can be for children and students in the long run? Janet: I think [there are] a couple of important points there. And first, one is early on in a child's life. Because experiences breed seeds or because seeds come out of experiences, the more experiences children can have, the better. So for example, if you're in early grades, and you can read a book to a child, they can listen to it, but what else can they do? They could maybe play with toys and act it out. If there's an activity in the book, they could pretend or really do the activity. Maybe it's baking something or maybe it's playing a game. And I think this is advocated in literature on play and early childhood experiences, including Montessori experiences. But the more and varied experiences children can have, the more seeds they'll gain in different experiences.  And one thing a teacher can do early on and throughout is look at connections. Look at, "Oh, we did this thing here. Where might it come out here?" If a teacher can identify an important seed, for instance, they can work to strengthen it in different contexts as well. So giving children experiences and then looking for ways to strengthen key ideas through experiences. Mike: One of the challenges of hosting a podcast is that we've got about 20 to 25 minutes to discuss some really big ideas and some powerful practices. And this is one of those times where I really feel that. And I'm wondering, if we have listeners who wanted to continue learning about the ways that they can cultivate the seeds of algebraic thinking, are there particular resources or bodies of research that you would recommend? Janet: So from our particular lab we have a website, and it's notice-lab.com, and that's continuing to be built out. The project is funded by NSF [the National Science Foundation], and we're continuing to add resources. We have links to articles. We have links to ways teachers and parents can use seeds. We have links to professional development for teachers. And those will keep getting built out over time.  Margaret, do you want to talk about the article? Margaret: Sure, yeah. Janet and I actually just had an article recently come out in Mathematics Teacher: Learning and Teaching from NCTM [National Council of Teachers of Mathematics]. And it's [in] Issue 5, and it's called "Leveraging Early Algebraic Experiences." So that's definitely another place to check out.  And Janet, anything else you want to mention? Janet: I think the website has a lot of resources as well. Mike: So I've read the article and I would encourage anyone to take a look at it. We'll add a link to the article and also a link to the website in the show notes for people who are listening who want to check those things out.  I think this is probably a great place to stop. But I want to thank you both so much for joining us. Janet and Margaret, it's really been a pleasure talking with both of you. Janet: Thank you so much, Mike. It's been a pleasure.  Margaret: You too. Thanks so much for having us. Mike: This podcast is brought to you by The Math Learning Center and the Maier Math Foundation, dedicated to inspiring and enabling all individuals to discover and develop their mathematical confidence and ability. © 2025 The Math Learning Center | www.mathlearningcenter.org  

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Not sure what matters most when designing math improvement plans? Take this assessment and get a free customized report: https://makemathmoments.com/grow/ Math coordinators and leaders – Ready to design your math improvement plan with guidance, support and using structure? Learn how to follow our 4 stage process. https://growyourmathprogram.com Looking to supplement your curriculum with problem based lessons and units? Make Math Moments Problem Based Lessons & Units comparison is a crucial yet often overlooked concept in elementary mathematics. Many students in grades 4-6 struggle with fractions and multiplication, while those in grades 7-8 need a strong foundation to think algebraically. In this episode, we explore how understanding multiplicative comparison can unlock deeper mathematical reasoning and support students' progression. When should we introduce it? How do we leverage it effectively? Join us as we break it down with real-world examples!Key Takeaways:Understanding how it differs from additive comparison.A bridge between multiplication, fractions, and algebraic thinking.How a strong grasp of multiplicative comparison supports algebraic reasoning.Key moments to reinforce the concept in elementary math.Practical ways to help students develop this understanding through rich tasks and discussion.Show NotesLove the show? Text us your big takeaway!Get a Customized Math Improvement Plan For Your District.Are you district leader for mathematics? Take the 12 minute assessment and you'll get a free, customized improvement plan to shape and grow the 6 parts of any strong mathematics program.Take the assessmentAre you wondering how to create K-12 math lesson plans that leave students so engaged they don't want to stop exploring your math curriculum when the bell rings? In their podcast, Kyle Pearce and Jon Orr—founders of MakeMathMoments.com—share over 19 years of experience inspiring K-12 math students, teachers, and district leaders with effective math activities, engaging resources, and innovative math leadership strategies. Through a 6-step framework, they guide K-12 classroom teachers and district math coordinators on building a strong, balanced math program that grows student and teacher impact. Each week, gain fresh ideas, feedback, and practical strategies to feel more confident and motivate students to see the beauty in math. Start making math moments today by listening to Episode #139: "Making Math Moments From Day 1 to 180.

Nalini AnantharamanGéométrie spectraleCollège de FranceAnnée 2024-2025Colloque - Géométries aléatoires et applications - Bertrand Eynard : Les géometries aléatoires dans le miroir de la géometrie algébrique Random Geometry in the Mirror of Algebraic GeometryIntervenant :Bertrand EynardCEA SaclayRésuméLa géométrie aléatoire consiste à calculer des espérances et probabilités sur des objets géométriques aléatoires, typiquement des surfaces (surfaces hyperboliques, surfaces discrètes, surfaces immergées dans un espace cible, ou portant certains champs, etc.)Fait remarquable, les fonctions génératrices comptant les surfaces de topologie fixée sont souvent des fonctions algébriques. De plus, il existe une récurrence universelle appelée récurrence topologique, qui relie l'énumération des surfaces de genre g avec n bords à celle des disques (g=0,n=1) : « si vous savez énumérer les disques, la récurrence topologique vous dit comment énumérer toutes les topologies. »La fonction génératrice des disques est appelée la courbe spectrale. Cette observation permet de reformuler le problème d'énumération dans le langage de la géométrie algébrique : une fois la courbe spectrale spécifiée, toutes les autres fonctions génératrices peuvent être dérivées.Ce cadre peut également être interprété à travers le prisme de la symétrie miroir. Dans cette perspective, un problème d'énumération est le « miroir » d'une courbe algébrique, et les calculs d'énumération se traduisent en calculs d'analyse complexe sur cette courbe.

https://csjoseph.life/ Join the Skool community at https://www.skool.com/csjoseph/about Algebra finally gets its day in court for you math haters in this explanation on how simple cognitive emulation isn't enough! --- Support this podcast: https://podcasters.spotify.com/pod/show/csjoseph/support

fWotD Episode 2778: Algebra Welcome to Featured Wiki of the Day, your daily dose of knowledge from Wikipedia’s finest articles.The featured article for Thursday, 12 December 2024 is Algebra.Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of statements within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations such as addition and multiplication.Elementary algebra is the main form of algebra taught in school and examines mathematical statements using variables for unspecified values. It seeks to determine for which values the statements are true. To do so, it uses different methods of transforming equations to isolate variables. Linear algebra is a closely related field that investigates linear equations and combinations of them called systems of linear equations. It provides methods to find the values that solve all equations in the system at the same time, and to study the set of these solutions.Abstract algebra studies algebraic structures, which consist of a set of mathematical objects together with one or several operations defined on that set. It is a generalization of elementary and linear algebra, since it allows mathematical objects other than numbers and non-arithmetic operations. It distinguishes between different types of algebraic structures, such as groups, rings, and fields, based on the number of operations they use and the laws they follow. Universal algebra and category theory provide general frameworks to investigate abstract patterns that characterize different classes of algebraic structures.Algebraic methods were first studied in the ancient period to solve specific problems in fields like geometry. Subsequent mathematicians examined general techniques to solve equations independent of their specific applications. They described equations and their solutions using words and abbreviations until the 16th and 17th centuries, when a rigorous symbolic formalism was developed. In the mid-19th century, the scope of algebra broadened beyond a theory of equations to cover diverse types of algebraic operations and structures. Algebra is relevant to many branches of mathematics, such as geometry, topology, number theory, and calculus, and other fields of inquiry, like logic and the empirical sciences.This recording reflects the Wikipedia text as of 01:11 UTC on Thursday, 12 December 2024.For the full current version of the article, see Algebra on Wikipedia.This podcast uses content from Wikipedia under the Creative Commons Attribution-ShareAlike License.Visit our archives at wikioftheday.com and subscribe to stay updated on new episodes.Follow us on Mastodon at @wikioftheday@masto.ai.Also check out Curmudgeon's Corner, a current events podcast.Until next time, I'm generative Olivia.

Fredrik talks to Pedro Abreu about the magical world of type theory. What is it, and why is it useful to know about and be inspired by? Pedro gives us some background on type theory, and then we talk about how type theory can provide new ways of reasoning about programs, and tools beyond tests to verify program correctness. This doesn’t mean that all languages should strive for the nirvana of dependent types, but knowing the tools are out there can come in handy even if the code you write is loosely typed. We wrap up with some further podcast tips, of course including Pedro’s own podcast Type theory forall. Thank you Cloudnet for sponsoring our VPS! Comments, questions or tips? We a re @kodsnack, @tobiashieta, @oferlund and @bjoreman on Twitter, have a page on Facebook and can be emailed at info@kodsnack.se if you want to write longer. We read everything we receive. If you enjoy Kodsnack we would love a review in iTunes! You can also support the podcast by buying us a coffee (or two!) through Ko-fi. Links Pedro Type theory Type theory forall - Pedro’s podcast Chalmers The meetup group through which Pedro and Fredrik met Purdue university Bertrand Russell The problem of self reference Types Set theory Kurt Gödel Halting problem Alan Turing Turing machine Alonzo Church Lambda calculus Rust Dependent types Formal methods Liquid types - Haskell extension SAT solver Property-based testing Quickcheck Curry-Howard isomorphism Support Kodsnack on Ko-fi! Functional programming Imperative programming Object-oriented programming Monads Monad transformers Lenses Interactive theorem provers Isabelle HOL Dafny Saul Crucible Symbolic execution CVC3, CVC5 solvers Pure functions C# Algebraic data types Pattern matching Scala Recursion Type theory forall episode 17: the first fantastic one with Conal Elliot. The discussion continues in episode 21 Denotational types Coq IRC Software foundations - about Coq and a lot more The church of logic podcast The Iowa type theory commute podcast Titles Type theory podcasts Very odd for some people Brazilian weather Relearning to appreciate The dawn of computer science Layers of sets Where types first come in Bundle values together The research about programming languages If you squint your eyes enough Nirvana of type systems Proofs all the way down Extra guarantees If your domain is infinite Formal guarantees The properties of my system What is the meaning of my program? Building better systems

Fredrik talks to Evan Czaplicki, creator of Elm about figuring out a good path for yourself. What do you do when you have a job which seems like it would be your dream job, but it turns out to be the wrong thing for you? And how do you escape from that? You can't put the success of something you build before your own personal and mental health, no matter how right the decision may be for the thing you build. Is there ever a reproducible path? Aren't most or all successful things in large part a result of their circumstances? Platform languages and productivity languages - which do you prefer? Thoughts on the tradeoffs of when and how to roll things out and when to present ideas. Evan's development mindset and environment, and the ways it has affected Elm's design - all the way down to the error messages. Finally, of course, the benefits of country life - out of the radiation of San Francisco. Thank you Cloudnet for sponsoring our VPS! Comments, questions or tips? We a re @kodsnack, @tobiashieta, @oferlundand @bjoreman on Twitter, have a page on Facebook and can be emailed at info@kodsnack.se if you want to write longer. We read everything we receive. If you enjoy Kodsnack we would love a review in iTunes! You can also support the podcast by buying us a coffee (or two!) through Ko-fi. Links Evan Elm Prezi Guido van Rossum Brendan Eich Bjarne Stroustrup Hindley–Milner type inference Gary Bernhardt Talks by Gary SIMD Standard ML Ocaml Haskell Lambda calculus Algebraic data types Type inference Virtual DOM Webbhuset Dart Safari's no performance regressions rule Sublime text GHC Nano Emacs Titles The personal aspects A culture clash I wasn't supposed to be here This numb feeling I've never really been to the real world Is this even real? The path that Guido did This is you This isn't for me, and it's your fault Valuing my own health Reckless indifference A dispute between colleagues A nice solution will come out if you're patient enough Here's your error message: good luck Farmer's disposition These are good years Getting paid in chickens for web development Finding a place

Fredrik talks to Evan Czaplicki, creator of Elm about figuring out a good path for yourself. What do you do when you have a job which seems like it would be your dream job, but it turns out to be the wrong thing for you? And how do you escape from that? You can’t put the success of something you build before your own personal and mental health, no matter how right the decision may be for the thing you build. Is there ever a reproducible path? Aren’t most or all successful things in large part a result of their circumstances? Platform languages and productivity languages - which do you prefer? Thoughts on the tradeoffs of when and how to roll things out and when to present ideas. Evan’s development mindset and environment, and the ways it has affected Elm’s design - all the way down to the error messages. Finally, of course, the benefits of country life - out of the radiation of San Francisco. Thank you Cloudnet for sponsoring our VPS! Comments, questions or tips? We a re @kodsnack, @tobiashieta, @oferlund and @bjoreman on Twitter, have a page on Facebook and can be emailed at info@kodsnack.se if you want to write longer. We read everything we receive. If you enjoy Kodsnack we would love a review in iTunes! You can also support the podcast by buying us a coffee (or two!) through Ko-fi. Links Evan Elm Prezi Guido van Rossum Brendan Eich Bjarne Stroustrup Hindley–Milner type inference Gary Bernhardt Talks by Gary SIMD Standard ML Ocaml Haskell Lambda calculus Algebraic data types Type inference Virtual DOM Webbhuset Dart Safari’s no performance regressions rule Sublime text GHC Nano Emacs Titles The personal aspects A culture clash I wasn’t supposed to be here This numb feeling I’ve never really been to the real world Is this even real? The path that Guido did This is you This isn’t for me, and it’s your fault Valuing my own health Reckless indifference A dispute between colleagues A nice solution will come out if you’re patient enough Here’s your error message: good luck Farmer’s disposition These are good years Getting paid in chickens for web development Finding a place

Sir Roger Penrose is a renowned physicist and mathematician known for pioneering the theory of twistors and his contributions to differential geometry, which have significantly impacted our understanding of space-time. Roger's work has been instrumental in advancing theories related to general relativity and quantum mechanics, including the Penrose-Hawking singularity theorems. SPONSOR (THE ECONOMIST): As a listener of TOE, you can now enjoy full digital access to The Economist. Get a 20% off discount by visiting: https://www.economist.com/toe TOE'S TOP LINKS: - Support TOE on Patreon: https://patreon.com/curtjaimungal (early access to ad-free audio episodes!) - Listen to TOE on Spotify: https://open.spotify.com/show/4gL14b92xAErofYQA7bU4e - Become a YouTube Member Here: https://www.youtube.com/channel/UCdWIQh9DGG6uhJk8eyIFl1w/join - Join TOE's Newsletter 'TOEmail' at https://www.curtjaimungal.org SPONSORS (please check them out to support TOE): - THE ECONOMIST: As a listener of TOE, you can now enjoy full digital access to The Economist. Get a 20% off discount by visiting: https://www.economist.com/toe - INDEED: Get your jobs more visibility at https://indeed.com/theories ($75 credit to book your job visibility) - HELLOFRESH: For FREE breakfast for life go to https://www.HelloFresh.com/freetheoriesofeverything - PLANET WILD: Want to restore the planet's ecosystems and see your impact in monthly videos? The first 150 people to join Planet Wild will get the first month for free at https://planetwild.com/r/theoriesofeverything/join or use my code EVERYTHING9 later. TIMESTAMPS: 00:00 - Intro 01:22 - Cosmology and Twister Theory 15:00 - “Most Significant Thought I Had” 20:45 - “Twister Are Inherently Chiral” 25:34 - Extra Dimensions 27:02 - Algebraic and Differential Geometry 37:57 - Alexander Grothendieck 40:36 - Gravity and Quantum Mechanics 43:00 - Collapse of the Wave Function 53:04 - Gravitational Fields and the Wave Function 01:11:02 - Free Will 01:14:03 - Is the Universe Discrete or Continuous? 01:16:35 - Ai's Capabilities 01:19:09 - Many Worlds Theory 01:20:38 - Idealism 01:21:35 - CCC 01:23:31 - Roger's Legacy 01:33:25 - Outro / Support TOE Other Links: - Twitter: https://twitter.com/TOEwithCurt - Discord Invite: https://discord.com/invite/kBcnfNVwqs - iTunes: https://podcasts.apple.com/ca/podcast/better-left-unsaid-with-curt-jaimungal/id1521758802 - Subreddit r/TheoriesOfEverything: https://reddit.com/r/theoriesofeverything #science #physics #penrose #quantumphysics #theoreticalphysics Learn more about your ad choices. Visit megaphone.fm/adchoices

This week co-host's Dave and Aaron find themselves talking to a person working in the Twin Cities, who has never been to the Twin Cities. And if that isn't a riddle enough, they have to try and figure out his old poems! Adam Shaw brings poems from an old duct taped journal and when these three nerds aren't discussing LOTR's sword names, they are trying to make heads or tales of some moody rhymes that could use some work. My Bad Poetry Episode 6.10: "Windowless Room, Taos Court, & Algebraic Hymn (w/Adam Shaw)" End Poem from a Real Poet: "You're Not Even the Dirtbag" by Adam Shaw found in Rejection Letters. Adam Shaw is the MFA director of Concordia University in St. Paul, living in Louisville, KY. He is the author of the novel The Jackels and has had works appear in Taco Bell Quarterly, The Daily Drunk, and beyond. One can also submit their works to Identity Theory where Adam is an assistance editor. Follow him @adamshaw502. Podcast Email: mybadpoetry.thepodcast@gmail.com Bluesky: @mybadpoetrythepod.bsky.social Instagram & Threads: @MyBadPoetry_ThePod Website: ⁠⁠⁠⁠⁠⁠https://www.mybadpoetry.com

Whether you're in high school or just trying to get better at algebra, 9th Grade Algebra's self-study guide has all the tips and tricks to make learning easy. Sign up for a copy of the guide today at https://www.ninthgradealgebramadeeasy.com/ LP Consulting LLC City: Monroe Address: 3648 Gruber Rd Website: https://get26k.com/ Email: lpciaff@gmail.com

Arthur O'Dwyer is a C++ programmer and blogger who today joined us to talk about his musings on the algebraic structure of the popular web-game Infinite Craft. Infinite Craft is a clever little experiment in sandboxed exploration, and it turns out to give rise to a rather complex mathematical structure with some interesting background in theoretical CS. Arthur covered all this and more in his presentation, which was super interesting and a lot of fun to watch. Check out Arthur's original blog post here: https://quuxplusone.github.io/blog/2024/03/03/infinite-craft-theory/ Check out Arthur's slides here: https://bstn.cc/artifacts/arthurODwyer/infiniteCraft.pdf

E53: FTCE | General Knowledge | Mathematics | Defining algebraic functions In today's episode, we are reviewing the definition of a function. This is part of a multi-series review of what YOU need to know to pass the Mathematics subtest of the GK. About FTCE Seminar How do you PASS the Florida Teacher Certification Exams (FTCE)? On this podcast, we will be discussing concepts from the FTCE Testing Blueprint to help you prepare for the exam. ..Not only is each episode based on the FTCE General Knowledge essay subtest, English Language Skills subtest, Reading subtest, and Mathematics subtest, but I am also using my experience as a FTCE Tutor, 10 year classroom teacher who has passed the FTCE GK Exam, FTCE Professional Education Exam, FTCE Exceptional Student Education Exam, FTCE English 6-12 Exam, FTCE Journalism Exam, and the Reading Endorsement to help you pass and start teaching. ..How do educational podcasts work? Each podcast covers one concept from the FTCE Testing Blueprint. This method is called micro-learning where you listen repeatedly to concepts to reinforce your knowledge and understanding. Try it out! Check it out! And leave your questions and comments below. ----------------------------------------------- RESOURCES (Free)

E47: Teacher Certification Podcast | FTCE | General Knowledge | Mathematics | Identifying Equivalent Expressions In today's episode, we are reviewing algebraic expressions, equations, and inequalities to solve real-world problems. This is part of a multi-series review of what YOU need to know to pass the Mathematics subtest of the GK. Check out ⁠⁠the resources⁠⁠ at the FTCE Seminar ⁠⁠⁠⁠⁠⁠⁠⁠⁠website ⁠⁠⁠⁠⁠⁠⁠⁠⁠. Support FTCE Seminar! Contributions are appreciated and help support the maintenance of this resource. Donations can be made with the ⁠⁠⁠⁠⁠⁠⁠⁠⁠Listener Supporter Link ⁠⁠⁠⁠⁠⁠⁠⁠⁠on Spotify. --- Support this podcast: https://podcasters.spotify.com/pod/show/ftceseminar/support

Fredrik is joined by Emil Privér and Leandro Ostera for a discussion of the OCaml ecosystem, and making it Saas-ready by building Riot. First of all: OCaml. What is the thing with the language, and how you might get into it coming from other languages? The OCaml community is nice, interested in getting new people in, and pragmatic. And it has a nice mix of research and industry as well. Then, Leandro tells us about Riot - an experiment in bringing everything good about the Erlang and Elixir ecosystems into OCaml. The goal? Make OCaml saas-ready. Riot is not 1.0 just yet, but an impressive amount has been built in just five(!) months. Emil moves the discussion over to the mindset of shipping, and of finding and understanding good ideas in other places and picking them up rather than reinventing the wheel. Leandro highly recommends reading the code of other projects. Read and understand the code and solutions others have written, re-use good ideas and don’t reinvent the wheel more often than you really have to. Last, but by no means least, shoutouts to some of the great people building the OCaml community, and a bit about Emil’s project DBCaml. Thank you Cloudnet for sponsoring our VPS! Comments, questions or tips? We a re @kodsnack, @tobiashieta, @oferlund and @bjoreman on Twitter, have a page on Facebook and can be emailed at info@kodsnack.se if you want to write longer. We read everything we receive. If you enjoy Kodsnack we would love a review in iTunes! You can also support the podcast by buying us a coffee (or two!) through Ko-fi. Links Emil Leo Leo on Twitch Previous Kodsnack appearances by Emil Riot Sinatra Backbone.js Ember.js Angularjs React Erlang Tarides - where Leandro currently works OCaml Robin Milner - designer of ML Caml Javacaml F# Imperative programming Object-oriented programming Pure functions and side effects Monads The OCaml compiler Reason - the language built by Jordan Walke, the creator of React Standard ML React was prototyped in Standard ML Melange - OCaml compiler backend producing Javascript OCaml by example The OCaml Discord The Reason Discord Rescript Jane street High-frequency trading The Dune build system Erlang process trees Caramel - earlier experiment of Leandro’s Louis Pilfold Gleam Algebraic effects Continuations Pool - Emil’s project Gluon Bytestring Atacama - connection pool inspired by Thousand island Nomad - inspired by Bandit Trail - middleware inspired by Plug Sidewinder - Livewire-like Saas - software as a service DBCaml Johan Öbrink Ecto Mint tea - inspired by Bubble tea Autobahn|Testsuite - test suite for specification compliance Serde - Rust and OCaml serialization framework S-expressions TOML Dillon Mulroy Metame - community kindness pillar welltypedwitch Sabine maintains ocaml.org OCaml playground OCaml cookbook - in beta, sort of teej_dv ocaml.org Pool party Drizzle SQLX SQL Join types (left, inner, and so on) dbca.ml internet.bs The Caravan Essentials of compilation Reading rainbow Titles Few people can have a massive impact Impact has been an important thing for me It’s a language out there A very long lineage of thinking about programming languages Programs that never fail The functional version of Rust Melange is amazing This is not a toy project Yes, constraints! Wonders in community growth Arrow pointing toward growth Programs that don’t crash A very different schoold of reliability Invert the arrow Very easy on the whiteboard Multicore for free An entire stack from scratch Built for the builders A massive tree of things Make OCaml saas-ready Leo is a shipper Standing on the shoulders of many, many giants Learn from other people I exude OCaml these days Sitting down and building against the spec You just give it something Your own inner join We build everything in public The gospel of the dunes

Learning Mathematics can be fun if we understand and learn Algebraic Identities. These Identities have a variety of usage in the mathematical world . Here's a good beginning. Let's keep our journey full of fun and activities #mathisfun #mathematicssimplified #learningbydoing #experientiallearning

Este episódio é uma republicação de um episódio do podcast Elixir em Foco. Saiba mais sobre o episódio em https://podcasters.spotify.com/pod/show/elixiremfoco/episodes/32--A-linguagem-Lean--com-Algebraic-Sofia-e-Algebraic-Gabi-e2b8kao O Emílias Podcast é um projeto de extensão da UTFPR Curitiba. Descubra tudo sobre o programa Emílias - Armação em Bits em ⁠⁠⁠⁠⁠⁠⁠⁠https://linktr.ee/Emilias⁠⁠⁠⁠⁠. #PODCAST #EMILIAS --- Send in a voice message: https://podcasters.spotify.com/pod/show/emilias-podcast/message

Understanding algebra and its nuances is something every mathematics student wishes for . Let's work on getting there with the wonderful world of Algebra opening up. Keep learning by doing because that's the perfect way of understanding the concepts and applying them in real life situations. #mathisfun #learningbydoing #experientiallearning #mathematicssimplified

We learn about Algebraic Effects with the Scala library Kyo ( getkyo.io) from the creator, Flavio Brasil. Discuss this episode: ⁠⁠https://discord.gg/nPa76qF

You're in for a treat, listeners! Coming to our microphone is the one and only Mick Dundee, whose credentials span from being a design animator to a seasoned name in the entertainment industry. Get ready to be tickled pink as Mick retraces his humorous journey in comedy, his seafaring adventures, and unveils his peculiar lockdown hobby.Support the show

Algebraic expressions involve polynomials for which students struggle to find out the zeros. Here are some tips to find the zeros of polynomials in different types. #mathematicssimplified #mathisfun #learningbydoing #experientiallearning

Neste episódio do podcast Elixir em Foco, Adolfo Neto, Herminio Torres e Zoey Pessanha entrevistaram Sofia Rodrigues (Algebraic Sofia) e Gabrielle Guimarães de Oliveira (Algebraic Gabi) para discutir a linguagem de programação Lean. Durante a entrevista, eles exploraram vários aspectos da linguagem e a experiência das convidadas. Algumas das perguntas respondidas neste episódio: O que é Lean e quais são suas características? Por que e quando Gabi e Sofia se interessaram por Lean? Por que Gabi e Sofia decidiram participar da Rinha de Backend com uma solução em Lean e C++? O que foi a Rinha de Compiladores? Este episódio ofereceu uma visão informativa da linguagem Lean. Aprender Lean pode ser uma experiência valiosa para a comunidade de Elixir. Links: Sofia Rodrigues https://twitter.com/algebraic_sofia https://github.com/algebraic-sofia  Gabrielle Guimarães de Oliveira https://twitter.com/algebraic_gabi https://github.com/aripiprazole  https://aripiprazole.dev/ https://gabx.io/  λ Algebraic https://algebraic.dev/ https://github.com/lurasidone  Rinha de Backend https://github.com/zanfranceschi/rinha-de-backend-2023-q3  Rinha de Compiladores https://github.com/aripiprazole/rinha-de-compiler Raciocínio Automatizado com Leonardo de Moura https://www.youtube.com/watch?v=bwKFcLaeD1A  Programming Language Foundations in Agda https://plfa.github.io/   "The Economics of Programming Languages" by Evan Czaplicki (Strange Loop 2023) https://youtu.be/XZ3w_jec1v8?si=Oekqx6Zv57w6HJYa  Crafting Interpreters https://craftinginterpreters.com/  Engineering a Compiler 3rd Edition - August 20, 2022 Keith D. Cooper, Linda Torczon https://shop.elsevier.com/books/engineering-a-compiler/cooper/978-0-12-815412-0  Nosso canal é⁠⁠⁠ https://www.youtube.com/@ElixirEmFoco⁠⁠⁠ Associe-se à Erlang Ecosystem Foundation em ⁠https://bit.ly/3Sl8XTO⁠⁠⁠. O site da fundação é ⁠⁠⁠https://bit.ly/3Jma95g⁠⁠⁠. Nosso site é ⁠https://elixiremfoco.com⁠⁠⁠.  Estamos no Twitter em ⁠https://twitter.com/elixiremfoco⁠ --- Send in a voice message: https://podcasters.spotify.com/pod/show/elixiremfoco/message

Algebraic expressions involve polynomials. Degree of polynomial is an important thing to be understood so that we can build up the theory further. #mathematicssimplified #mathisfun #learningbydoing #experientiallearningofmathematics

Understanding Algebraic expressions is a great way of learning mathematics. In this episode we have discussed about the Like and Unlike terms in an Algebraic Expression. Keep learning one step at a time and you will be doing great. #mathematicssimplified #mathisfun #learningbydoing #experientiallearning

Algebra is a broad topic that sometimes baffles students. Here is an attempt to make things simple and easy to understand. Learning about Algebraic expressions is the first step towards understanding basic Algebra #mathematicssimplified #mathisfun #learningbydoing

With this 9th Grade Algebra guide, you're prepared for all those pesky creative problems you're likely to face. Grab it for free now! Find out more at: https://www.ninthgradealgebramadeeasy.com/ LP Consulting LLC City: Monroe Address: 3648 Gruber Rd Website https://get26k.com/ Phone +1-734-274-2488 Email lpciaff@gmail.com

OpenAI's large-scale language-generation tool ChatGPT may have been used to draft some content in this episode and some of the show notes of this episode. StudySquare Ltd has adapted the content, and the publication is attributed to StudySquare Ltd. This episode is a general guideline for information and not a specific tutorial for any specific syllabus; therefore, it should not be relied upon. StudySquare Ltd and any people involved in producing this podcast take no responsibility or liability for any potential errors or omissions regarding this podcast and make no guarantees of any completeness, accuracy, or usefulness of the information contained in this podcast, its structure or its show notes. The problems or questions in this episode might not appear in exam papers.The content in this episode might be more relevant to learners in the United Kingdom. Laws, educational standards, and exam requirements may vary significantly from one location to another. It's the listener's responsibility to confirm that the material complies with the requirements and regulations of their local educational system. If any content of this episode does not comply with your local regulations or laws, please discontinue listening and consult with your local educational authorities.Any references to experiments in this episode are for information purposes only and do not allow any listener to perform them without proper guidance or support. Experiments or practical work mentioned during this episode should not be attempted without appropriate supervision from a qualified teacher or professional. Additionally, the information provided in our podcast is not medical advice and should not be taken as such. If you require medical advice, please consult a healthcare professional. This episode is provided 'as is' without any representations or warranties, express or implied.This episode covers the following:• Factorising quadratics• Completing the square• Algebraic fractions• Page for this topic: https://studysquare.co.uk/test/Maths/Edexcel/GCSE/Factorisation?s=p• Trial lesson (terms and conditions apply): https://www.studysquare.co.uk/trial?s=p-/test/Maths/Edexcel/GCSE/Factorisation• Privacy policy of Spreaker (used to distribute this episode): https://www.spreaker.com/privacy

Sean Carroll is a theoretical physicist and philosopher who specializes in quantum mechanics, cosmology, and the philosophy of science. He is the Homewood Professor of Natural Philosophy at Johns Hopkins University and an external professor at the Sante Fe Institute. Sean has contributed prolifically to the public understanding of science through a variety of mediums: as an author of several physics books including Something Deeply Hidden and The Biggest Ideas in the Universe, as a public speaker and debater on a wide variety of scientific and philosophical subjects, and also as a host of his podcast Mindscape which covers topics spanning science, society, philosophy, culture, and the arts. www.patreon.com/timothynguyen In this episode, we take a deep dive into The Many Worlds (Everettian) Interpretation of quantum mechanics. While there are many philosophical discussions of the Many Worlds Interpretation available, ours marries philosophy with the technical, mathematical details. As a bonus, the whole gamut of topics from philosophy and physics arise, including the nature of reality, emergence, Bohmian mechanics, Bell's Theorem, and more. We conclude with some analysis of Sean's speculative work on the concept of emergent spacetime, a viewpoint which naturally arises from Many Worlds. This video is most suitable for those with a basic technical understanding of quantum mechanics. Part I: Introduction 00:00:00 : Introduction 00:05:42 : Philosophy and science: more interdisciplinary work? 00:09:14 : How Sean got interested in Many Worlds (MW) 00:13:04 : Technical outline Part II: Quantum Mechanics in a Nutshell 00:14:58 : Textbook QM review 00:24:25 : The measurement problem 00:25:28 : Einstein: "God does not play dice" 00:27:49 : The reality problem Part III: Many Worlds 00:31:53 : How MW comes in 00:34:28 : EPR paradox (original formulation) 00:40:58 : Simpler to work with spin 00:42:03 : Spin entanglement 00:44:46 : Decoherence 00:49:16 : System, observer, environment clarification for decoherence 00:53:54 : Density matrix perspective (sketch) 00:56:21 : Deriving the Born rule 00:59:09 : Everett: right answer, wrong reason. The easy and hard part of Born's rule. 01:03:33 : Self-locating uncertainty: which world am I in? 01:04:59 : Two arguments for Born rule credences 01:11:28 : Observer-system split: pointer-state problem 01:13:11 : Schrodinger's cat and decoherence 01:18:21 : Consciousness and perception 01:21:12 : Emergence and MW 01:28:06 : Sorites Paradox and are there infinitely many worlds 01:32:50 : Bad objection to MW: "It's not falsifiable." Part IV: Additional Topics 01:35:13 : Bohmian mechanics 01:40:29 : Bell's Theorem. What the Nobel Prize committee got wrong 01:41:56 : David Deutsch on Bohmian mechanics 01:46:39 : Quantum mereology 01:49:09 : Path integral and double slit: virtual and distinct worlds Part V. Emergent Spacetime 01:55:05 : Setup 02:02:42 : Algebraic geometry / functional analysis perspective 02:04:54 : Relation to MW Part VI. Conclusion 02:07:16 : Distribution of QM beliefs 02:08:38 : Locality   Further reading: Hugh Everett. The Theory of the Universal Wave Function, 1956. Sean Carroll. Something Deeply Hidden, 2019. More Sean Carroll & Timothy Nguyen: Fragments of the IDW: Joe Rogan, Sam Harris, Eric Weinstein: https://youtu.be/jM2FQrRYyas Twitter: @iamtimnguyen Webpage: http://www.timothynguyen.org  

Listen in as LeiLani chats with Maurice Draggon, Sr. Director of Digital Learning at Orange County Public Schools in Orlando, Florida. First they discuss the implications of AI in schools and then the emerging time and space AI known as Intelligent Calendaring for its possibilities and then the combination of both new technologies for “uberizing” learning.  Along the way, comments about what AI will not do and the human teacher intersecting live with students more efficiently makes for an interesting conversation you don't want to miss.

In episode 73 of the pharmaceutical calculations podcast, you will learn how to master two ubiquitous pharmacy calculations concepts: alligation and the algebraic method using eleven strategically selected questions. This episode was originally broadcast as a video on our YouTube channel: www.youtube.com/pharmaceuticalcalculationseasyAdditional Resources for Practice:Pharmaceutical Calculations: 1001 Questions with Answers: https://www.rxcalculations.com/shop/uncategorized/pharmaceutical-calculations-1001-questions-answers/NAPLEX Question Bank: https://www.rxcalculations.com/shop/uncategorized/gold-membership/Join Our Social Media Community:Website: http://www.rxcalculations.comForum: https://forum.rxcalculations.com/Facebook: https://www.facebook.com/pharmaceuticalcalculationsTwitter: https://twitter.com/RxCalculationsInstagram: https://www.instagram.com/rxcalculationsYouTube: www.youtube.com/pharmaceuticalcalculationseasyAbout RxCalculations: RxCalculations helps you master pharmaceutical calculations. We make it so you never have to worry about failing an exam or compromising patient safety because of a calculations error. RxCalculations is a leading global educational service platform focused on developing top quality pharmaceutical calculations products to help prospective pharmacists and health care professionals all over the world resolve one of the biggest challenges related to their profession.Our top quality products include affordable courses, personal consults, books, video tutorials, timed quizzes and apps designed to make you an expert in solving any pharmaceutical calculations question. We also have the largest pharmaceutical calculations online question bank which has over 1000 questions covering every important calculations topic as well as step-by-step video solutions. With all these resources at your disposal we have all you need to not only master pharmacy calculations but ace every test as well as passing your board exams.

In episode 70 of the pharmaceutical calculations podcast, you will learn how the algebraic method is best suited to solve this tricky dilution calculations question asked by a viewer. This episode was originally broadcast as a video on our YouTube channel: www.youtube.com/pharmaceuticalcalculationseasyAdditional Resources for Practice:Pharmaceutical Calculations: 1001 Questions with Answers: https://www.rxcalculations.com/shop/uncategorized/pharmaceutical-calculations-1001-questions-answers/NAPLEX Question Bank: https://www.rxcalculations.com/shop/uncategorized/gold-membership/Join Our Social Media Community:Website: http://www.rxcalculations.comForum: https://forum.rxcalculations.com/Facebook: https://www.facebook.com/pharmaceuticalcalculationsTwitter: https://twitter.com/RxCalculationsInstagram: https://www.instagram.com/rxcalculationsYouTube: www.youtube.com/pharmaceuticalcalculationseasyAbout RxCalculations: RxCalculations helps you master pharmaceutical calculations. We make it so you never have to worry about failing an exam or compromising patient safety because of a calculations error. RxCalculations is a leading global educational service platform focused on developing top quality pharmaceutical calculations products to help prospective pharmacists and health care professionals all over the world resolve one of the biggest challenges related to their profession.Our top quality products include affordable courses, personal consults, books, video tutorials, timed quizzes and apps designed to make you an expert in solving any pharmaceutical calculations question. We also have the largest pharmaceutical calculations online question bank which has over 1000 questions covering every important calculations topic as well as step-by-step video solutions. With all these resources at your disposal we have all you need to not only master pharmacy calculations but ace every test as well as passing your board exams.

What do I mean by algebra? And how do we get from level 0 to level 3?

Welcome back to the Heinemann Podcast. Today we are joined by Julie McNamara. She is an associate professor of mathematics education at California State University, East Bay, in Hayward California. She also provides professional development and classroom coaching to teachers in the San Francisco Bay Area.This short conversation was recorded back in September, and Julie and I talked about how students develop algebraic reasoning skills in their younger years.As always, a transcript of this conversation is available on blog.heineman.com© Heinemann Publishing 2022See Privacy Policy at https://art19.com/privacy and California Privacy Notice at https://art19.com/privacy#do-not-sell-my-info.

Pada episode ini kami membahas cara mempelajari topologi melalui sifat-sifat aljabar... kok bisa? Bahasan utama mulai dari (39:36)

In episode 59 of the pharmaceutical calculations podcast, you will learn how to use the algebraic and alligation methods to solve an interesting dilution calculations question asked by a viewer. This episode was originally broadcast as a video on our YouTube channel: www.youtube.com/pharmaceuticalcalculationseasyAdditional Resources for Practice:Pharmaceutical Calculations: 1001 Questions with Answers: https://www.rxcalculations.com/shop/uncategorized/pharmaceutical-calculations-1001-questions-answers/NAPLEX Question Bank: https://www.rxcalculations.com/shop/uncategorized/gold-membership/Join Our Social Media Community:Website: http://www.rxcalculations.comForum: https://forum.rxcalculations.com/Facebook: https://www.facebook.com/pharmaceuticalcalculationsTwitter: https://twitter.com/RxCalculationsInstagram: https://www.instagram.com/rxcalculationsYouTube: www.youtube.com/pharmaceuticalcalculationseasyAbout RxCalculations: RxCalculations helps you master pharmaceutical calculations. We make it so you never have to worry about failing an exam or compromising patient safety because of a calculations error. RxCalculations is a leading global educational service platform focused on developing top quality pharmaceutical calculations products to help prospective pharmacists and health care professionals all over the world resolve one of the biggest challenges related to their profession.Our top quality products include affordable courses, personal consults, books, video tutorials, timed quizzes and apps designed to make you an expert in solving any pharmaceutical calculations question. We also have the largest pharmaceutical calculations online question bank which has over 1000 questions covering every important calculations topic as well as step-by-step video solutions. With all these resources at your disposal we have all you need to not only master pharmacy calculations but ace every test as well as passing your board exams.

Guest: Mrs Mahloane

 Ningning Xie is interviewed by Niki Vazou and Andres Loh. Ningning first contributed to GHC at her Google summer of code project with a very ambitious goal of implementing the whole dependent Haskell. Also later she fixed several ghc bugs and worked on Koka's Algebraic effects. Her future hope and advice is to use programming language concepts on real-word problems.

In episode 55 of the pharmaceutical calculations podcast, you will learn how to use the alligation method and the algebraic method to solve an important dilution calculations exam type question which was asked by a subscriber. This episode was originally broadcast as a video on our YouTube channel: www.youtube.com/pharmaceuticalcalculationseasyAdditional Resources for Practice:Pharmaceutical Calculations: 1001 Questions with Answers: https://www.rxcalculations.com/shop/uncategorized/pharmaceutical-calculations-1001-questions-answers/NAPLEX Question Bank: https://www.rxcalculations.com/shop/uncategorized/gold-membership/Join Our Social Media Community:Website: http://www.rxcalculations.comForum: https://forum.rxcalculations.com/Facebook: https://www.facebook.com/pharmaceuticalcalculationsTwitter: https://twitter.com/RxCalculationsInstagram: https://www.instagram.com/rxcalculationsYouTube: www.youtube.com/pharmaceuticalcalculationseasyAbout RxCalculations: RxCalculations helps you master pharmaceutical calculations. We make it so you never have to worry about failing an exam or compromising patient safety because of a calculations error. RxCalculations is a leading global educational service platform focused on developing top quality pharmaceutical calculations products to help prospective pharmacists and health care professionals all over the world resolve one of the biggest challenges related to their profession.Our top quality products include affordable courses, personal consults, books, video tutorials, timed quizzes and apps designed to make you an expert in solving any pharmaceutical calculations question. We also have the largest pharmaceutical calculations online question bank which has over 1000 questions covering every important calculations topic as well as step-by-step video solutions. With all these resources at your disposal we have all you need to not only master pharmacy calculations but ace every test as well as passing your board exams.

Francesco Gardin CEO and Executive Chairman of Quantum Blockchain Technologies #QBT discusses how their new director appointment, Peter Fuhrman, will have a strong positive impact, due to his experience and vast network that he has developed in over 30 years of international business. QBT is researching multiple alternative routes to cheaper and faster Bitcoin Mining.  The R&D team is working on the following promising research areas:   * Quantum Computing   * Cryptographic Optimisation   * Deep Learning and Artificial Intelligence ("AI")   * Field-programmable gate array ("FPGA") / application-specific integrated     circuit ("ASIC") Design   * Algebraic and Boolean Equation Reduction   * Very Large Big Data   * High performance computing architectures To read the full RNS click here

Algebraic and machine learning approach to hierarchical triple-star stability by Pavan Vynatheya et al. on Tuesday 06 September We present two approaches to determine the dynamical stability of a hierarchical triple-star system. The first is an improvement on the Mardling-Aarseth stability formula from 2001, where we introduce a dependence on inner orbital eccentricity and improve the dependence on mutual orbital inclination. The second involves a machine learning approach, where we use a multilayer perceptron (MLP) to classify triple-star systems as `stable' and `unstable'. To achieve this, we generate a large training data set of 10^6 hierarchical triples using the N-body code MSTAR. Both our approaches perform better than previous stability criteria, with the MLP model performing the best. The improved stability formula and the machine learning model have overall classification accuracies of 93 % and 95 % respectively. Our MLP model, which accurately predicts the stability of any hierarchical triple-star system within the parameter ranges studied with almost no computation required, is publicly available on Github in the form of an easy-to-use Python script. arXiv: http://arxiv.org/abs/http://arxiv.org/abs/2207.03151v2

Tai-Danae Bradley is a mathematician who received her Ph.D. in mathematics from the CUNY Graduate Center. She was formerly at Alphabet and is now at Sandbox AQ, a startup focused on combining machine learning and quantum physics. Tai-Danae is a visiting research professor of mathematics at The Master's University and the executive director of the Math3ma Institute, where she hosts her popular blog on category theory. She is also a co-author of the textbook Topology: A Categorical Approach that presents basic topology from the modern perspective of category theory. In this episode, we provide a compressed crash course in category theory. We provide definitions and plenty of basic examples for all the basic notions: objects, morphisms, categories, functors, natural transformations. We also discuss the first basic result in category theory which is the Yoneda Lemma. We conclude with a discussion of how Tai-Danae has used category-theoretic methods in her work on language modeling, in particular, in how the passing from syntax to semantics can be realized through category-theoretic notions. Originally published on July 20, 2022 on YouTube: https://youtu.be/Gz8W1r90olc   Timestamps: 00:00:00 : Introduction 00:03:07 : How did you get into category theory? 00:06:29 : Outline of podcast 00:09:21 : Motivating category theory 00:11:35 : Analogy: Object Oriented Programming 00:12:32 : Definition of category 00:18:50 : Example: Category of sets 00:20:17 : Example: Matrix category 00:25:45 : Example: Preordered set (poset) is a category 00:33:43 : Example: Category of finite-dimensional vector spaces 00:37:46 : Forgetful functor 00:39:15 : Fruity example of forgetful functor: Forget race, gender, we're all part of humanity! 00:40:06 : Definition of functor 00:42:01 : Example: API change between programming languages is a functor 00:44:23 : Example: Groups, group homomorphisms are categories and functors 00:47:33 : Resume definition of functor 00:49:14 : Example: Functor between poset categories = order-preserving function 00:52:28 : Hom Functors. Things are getting meta (no not the tech company) 00:57:27 : Category theory is beautiful because of its rigidity 01:00:54 : Contravariant functor 01:03:23 : Definition: Presheaf 01:04:04 : Why are things meta? Arrows, arrows between arrows, categories of categories, ad infinitum. 01:07:38 : Probing a space with maps (prelude to Yoneda Lemma) 01:12:10 : Algebraic topology motivated category theory 01:15:44 : Definition: Natural transformation 01:19:21 : Example: Indexing category 01:21:54 : Example: Change of currency as natural transformation 01:25:35 : Isomorphism and natural isomorphism 01:27:34 : Notion of isomorphism in different categories 01:30:00 : Yoneda Lemma 01:33:46 : Example for Yoneda Lemma: Identity functor and evaluation natural transformation 01:42:33 : Analogy between Yoneda Lemma and linear algebra 01:46:06 : Corollary of Yoneda Lemma: Isomorphism of objects = Isomorphism of hom functors 01:50:40 : Yoneda embedding is fully faithful. Reasoning about this. 01:55:15 : Language Category 02:03:10 : Tai-Danae's paper: "An enriched category theory of language: from syntax to semantics" Further Reading: Tai-Danae's Blog: https://www.math3ma.com/categories Tai-Danae Bradley. "What is applied category theory?" https://arxiv.org/pdf/1809.05923.pdf Tai-Danae Bradley, John Terilla, Yiannis Vlassopoulos. "An enriched category theory of language: from syntax to semantics." https://arxiv.org/pdf/2106.07890.pdf