Teaching and Learning Mathematics Online
Teaching and Learning Mathematics Online
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Dynamical Systems with Applications using Python -- Stephen Lynch (Manchester Metropolitan)
In this talk, I will show how we incorporate programming, computational modelling and simulation throughout the Mathematics curriculum at MMU. I will provide examples of how to enhance the learning and teaching. In particular, for Dynamical Systems, I will plot implicit curves for finding fixed points and use eigenvalues to determine their stability, I will also plot some simple fractals. I will demonstrate a wide range of applications in biology, chemistry, engineering and physics using animations to provide real-world solutions. This unit has a 40% coursework component with lots of programming and a 60% examination component set in a computer laboratory, where students use Python as a powerful calculator.
I have written books in Python, MATLAB, Maple and Mathematica on this topic, however, as Python is open source and the most popular programming language in the world, I will demonstrate examples using this package only.
Stephen’s books:
- Dynamical Systems with Applications using Python, Springer (2018) [Advanced]
- Python for Scientific Computing and Artificial Intelligence, CRC Press (2023) [Intermediate]
- A Simple Introduction to Python, CRC Press (2024) [Basic]
Slides and more talks can be found at talmo.uk/2024/python.html
zhlédnutí: 419

Video

Embedding Python into Core University Mathematics Siri Chongchitnan (Warwick)
zhlédnutí 852Před 2 měsíci
I will give a survey of how Python can be meaningfully woven in core university maths modules including calculus, analysis, abstract algebra, linear algebra, differential equations, probability and statistics. Only a basic background of Python is required. I will also share my experience of embedding Python into two modules that I teach at Warwick: Vector Calculus, and Problem Solving. Siri’s b...
Understanding Bayesian Statistics Without Frequentist Language -- Richard McElreath (MPI)
zhlédnutí 13KPřed 4 měsíci
Most scholars encounter Bayesian statistics after learning classical, or Frequentist, statistics. As a result, Bayesian concepts and models are nearly always explained using Frequentist language. This can result in lasting confusion about the Bayesian approach, even among those who use it routinely. To advance this argument, I examine two cases of Frequentist language in widespread use in Bayes...
What is going on in undergraduate Bayesian education across the pond? -- Mine Dogucu (UCI)
zhlédnutí 217Před 4 měsíci
Bayesian statistics is becoming more common in scientific practice and workforce. Thus, the inclusion of Bayesian training in statistics and data science curricula at the undergraduate level is more important than it has ever been. With the advances in computing power and modern educational tools, undergraduate Bayesian education is evolving. In this talk, we will cover the current state of Bay...
Why do we need MCMC and how does it work? -- Ben Lambert (Oxford)
zhlédnutí 2,3KPřed 4 měsíci
Most applied Bayesian inference is done approximately using sampling-based methods. In my experience, most students struggle to understand why sampling is necessary and also what sampling from a posterior distribution actually means. In this talk, I will provide a few pedagogical hooks that I have found useful for explaining what computational sampling means and why it is necessary. I will also...
Why we don't teach, and why we should and could teach, Bayesian methods -- Mark Andrews (NTU)
zhlédnutí 3KPřed 4 měsíci
For the past few decades, there has been a continual rise in the use of Bayesian methods in statistical data analysis, so much so that Bayesian methods are now essentially mainstream methods in most scientific fields. Despite this, the statistics teaching curriculum in most fields remains largely, or even entirely, based on frequentist statistical inference. In this talk, I will review the rise...
Investigating the knowledge co-construction process in homogeneous ability groups Adamaria Perrotta
zhlédnutí 42Před 5 měsíci
Investigating the knowledge co-construction process in homogeneous ability groups during computational Lab activities in Financial Mathematics. Adamaria Perrotta Inclusive computational practices are increasingly being employed to enrich knowledge and facilitate sensemaking in STEM education. Embedding computational activities in Computer Supported Collaborative Learning environments can enhanc...
Discord as an online learning community Tørris Koløen Bakke, UiT The Arctic University of Norway
zhlédnutí 35Před 5 měsíci
Physical support centers for math and statistics have played an important role in supporting students and improving their success rates in maths-intensive courses. At the Arctic University of Norway (UiT), engineering students have the opportunity to study at five different campuses or to participate as an online student. The campuses are quite small, and it is difficult to maintain physical su...
Technology independent description and configuration of algorithms ... for mathematical tasks
zhlédnutí 58Před 6 měsíci
Technology independent description and configuration of algorithms for evaluation of student responses to mathematical tasks Karl Lundengård (Imperial College London) 31 January 2024 Slides and other info can be found at talmo.uk/2024/technology.html Abstract: Automated evaluation of student responses to mathematical tasks is widely considered to have significant potential for supporting indepe...
Writing about HE Teaching for Mathematics Education Research Journals, Cathy Smith and Chris Sangwin
zhlédnutí 191Před 7 měsíci
Writing about HE Teaching for Mathematics Education Research Journals, Cathy Smith (Open University) and Chris Sangwin (Edinburgh University) Abstract: Are you interested in researching HE mathematics teaching or learning? Have you considered publishing mathematics education articles? Two editors of the IMA journal Teaching Mathematics and its Applications will explain what mathematics educatio...
William Carey (Loughborough University) Wrapping up of workshop
zhlédnutí 35Před rokem
More talks on this subject plus other details and slides at talmo.uk/2023/studentstaffpartnerships.html
Francis Duah (Toronto Metropolitan University) Students as partners in course (re -) design
zhlédnutí 123Před rokem
Francis Duah (Toronto Metropolitan University) Students as partners in course (re -) design: Examples from one English and one Canadian university Abstract: In 2011, I joined The Mathematics Education Centre at Loughborough University to start my PhD in Mathematics Education. Under the auspices of the National HE STEM Programme, the Mathematics Education Centre was starting to involve students ...
Michael Obiero Oyengo, Juma Zevick Otienoi (Maseno University, Kenya)
zhlédnutí 30Před rokem
Michael Obiero Oyengo, Juma Zevick Otienoi (Maseno University, Kenya) Student-staff partnership in STACK content development at Maseno for undergraduate studies Abstract: Maseno University has for the last five years been using digital technologies, mostly STACK for the teaching and formative assessment of some of its Maths courses. Authoring a good STACK question needs quite a bit of expertise...
Gihan Marasingha (Exeter) SSPs in relation to the first-year introduction to proof module
zhlédnutí 20Před rokem
Abstract: Students as partners are engaged in (1) teach on the module, (2) development of the module, and (3) assessing the effectiveness of the module. More talks on this subject plus other details and slides at talmo.uk/2023/studentstaffpartnerships.html
Ria Dunn (University of Edinburgh) Staff-Student Partnership: A Lasting Impact
zhlédnutí 30Před rokem
More talks on this subject plus other details and slides at talmo.uk/2023/studentstaffpartnerships.html
Barrie Cooper Students as partners: reflecting on my professional journey nearly a decade later
zhlédnutí 30Před rokem
Barrie Cooper Students as partners: reflecting on my professional journey nearly a decade later
Rosalyn Hyde Educating the mathematics teachers of the future using partnership approaches.
zhlédnutí 21Před rokem
Rosalyn Hyde Educating the mathematics teachers of the future using partnership approaches.
Kevin Buzzard (Imperial College) Collaborating with undergraduates on building a library
zhlédnutí 263Před rokem
Kevin Buzzard (Imperial College) Collaborating with undergraduates on building a library
Carol Evans (Cardiff University) Students as Partners in Assessment and Feed
zhlédnutí 39Před rokem
Carol Evans (Cardiff University) Students as Partners in Assessment and Feed
Peter Klappa (Kent) From zero to gAI-hero: Generative artificial intelligence (gAI) in the classroom
zhlédnutí 84Před rokem
Peter Klappa (Kent) From zero to gAI-hero: Generative artificial intelligence (gAI) in the classroom
Cesare Giulio Ardito (Manchester) Large language models and mathematics higher education
zhlédnutí 158Před rokem
Cesare Giulio Ardito (Manchester) Large language models and mathematics higher education
Approaches Q&A and Closing Remarks. Creating accessible online mathematics and statistics notes
zhlédnutí 31Před rokem
Approaches Q&A and Closing Remarks. Creating accessible online mathematics and statistics notes
A Best (Sheffield): Using Jupyter Notebooks and Jupyter Book to create accessible mathematics notes
zhlédnutí 345Před rokem
A Best (Sheffield): Using Jupyter Notebooks and Jupyter Book to create accessible mathematics notes
C Lawson-Perfect: Building accessible, flexible learning materials with the open-source Chirun tool
zhlédnutí 58Před rokem
C Lawson-Perfect: Building accessible, flexible learning materials with the open-source Chirun tool
Peter Rowlett (Sheffield Hallam) Introduction to Approaches to creating notes
zhlédnutí 61Před rokem
Peter Rowlett (Sheffield Hallam) Introduction to Approaches to creating notes
David Hodge (Glasgow Caledonian) A primer for RMarkdown: getting started, examples and a few tips
zhlédnutí 61Před rokem
David Hodge (Glasgow Caledonian) A primer for RMarkdown: getting started, examples and a few tips
Volker Sorge (Birmingham) -- Creating Accessible STEM Diagrams
zhlédnutí 56Před rokem
Volker Sorge (Birmingham) Creating Accessible STEM Diagrams
Josh Lim (Bath) -- Colouring in: accessible use of colour in figures
zhlédnutí 37Před rokem
Josh Lim (Bath) Colouring in: accessible use of colour in figures
Huw Alexander (textBOX): How to do good ALT text
zhlédnutí 73Před rokem
Huw Alexander (textBOX): How to do good ALT text
Ben Watson (UCL) -- Where to start with digital accessibility for STEM. Outlining minimum standards
zhlédnutí 53Před rokem
Ben Watson (UCL) Where to start with digital accessibility for STEM. Outlining minimum standards

Komentáře

  • @personanongrata987
    @personanongrata987 Před 2 měsíci

    At 35:50 you said: "Accept that AI coding is going to be the norm". I've been retired now for 1.5 years after a long career of scientific software engineering, development of numerical algorithms, advanced data analysis, mathematical modeling of physical systems, reverse engineering of software and systems that nobody really understood any more, and all sorts of varied challenging endeavors. As far as this old dog can tell, using AI coding to do real work is both exciting and still very much in its infancy. I can't imagine learning it in university courses today, although of course that is happening right now. What an amazing time this is. --

  • @imsamiha
    @imsamiha Před 3 měsíci

    This is exactly what I have been looking for! I teach undergraduates and have been trying to find ways to increase in-class engagement. Definitely going to use Desmos as you have shown in my upcoming classes. Thank you for the thorough explanation!

  • @imrematajz1624
    @imrematajz1624 Před 3 měsíci

    This presentation confused the light out of me. I cannot find any correlation between the title and the talk. Was this intended to be a joke? Probably.

  • @TheLucanicLord
    @TheLucanicLord Před 3 měsíci

    7:54 you mean 1D6?

  • @Shravan_Vasishth
    @Shravan_Vasishth Před 3 měsíci

    Great talk as always. One important reason to teach frequentist thinking thoroughly is that people are inevitably going to have to read papers with (badly implemented and incorrectly interpeted) frequentist models, and as a reader of such papers I need to have fluency in the methodology to be able to determine how far the authors really are from what they want to conclude from the data. If people only know Bayes, they are not going to be able to evaluate published work or work they have to review for journals, etc.

  • @lucianozaffaina9853
    @lucianozaffaina9853 Před 3 měsíci

    Could you provide some books for studying Bayesian statistics? I have already done one course in Bayesian statistics so I don't want a 'slow' book. Thanks

  • @christopherellis2663
    @christopherellis2663 Před 4 měsíci

    Methodology, my lad, is the study of nethods in order to discover the best method for the matters at hand. Yes, I am a polyglot. It is not a top shelf synonym for methods. PS, it's not how many notes but the bird calls that indicate whether or not a cat is present.

  • @TreeLuvBurdpu
    @TreeLuvBurdpu Před 4 měsíci

    Why do teachers insist that so much of what they are talking about is "unconscious"? This is why there are so many learning disabilities. Students are attempting to learn "unconsciously". It's anti pedagogy.

  • @EdoardoMarcora
    @EdoardoMarcora Před 4 měsíci

    @rmcelreath any good reference illustrating Bayesian statistics w/o frequentist language? Particularly from the pre-data perspective of the DGP as a joint probability distribution of "equivalent" variables?

  • @sgeorg80
    @sgeorg80 Před 4 měsíci

    👍

  • @user-wr4yl7tx3w
    @user-wr4yl7tx3w Před 4 měsíci

    Awesome!

  • @dangernoodle2868
    @dangernoodle2868 Před 4 měsíci

    "Feels cringe to recommend my own book", but actually being half way through it now and having consumed a lot of other bayesian learning material I genuinely believe it's the best starting point by miles. If you're a bayesian and you haven't read statistical rethinking then it's an absolute must.

    • @djpremier333
      @djpremier333 Před 3 měsíci

      I started with kruschke and I don't think it was a waste of time but stat. Rethinking was way superior in many ways.

  • @dangernoodle2868
    @dangernoodle2868 Před 4 měsíci

    I think one critique I made of the speaker is that, like a lot of us bayesians, he's too wishywashy in his recommendations. I know that as bayesians we tend to put uncertainity and not committing to answers fully first, it's part of the strength of the framework, but when it comes to decisions for people that don't see the full picture yet that kind of recommendation just leaves people confused and not knowing what to do. The answer I think he should have given is to recognise that if bayesian stats can everything frequentism can do and do it better, and even more that frequentists are answering "the wrong questions precisely", it means that frequentism is set for extinction as bayesian methods catch on. There's no reason to keep it around other than prototyping or something like that because of computational speed. In light of that, where your decision making is free enough to make the shift, you basically should do that. The problem is that you recommend people to be trail-blazers which sets them up to do frustrating and nebulous work that isn't for everyone, so you warn them about that. However, for the people who are robust enough to follow that path you should give them the tools to get started and the reward will be that they're well positioned to handle the change when broader statistical culture shifts as it is at the moment. They'll also be able to solve problems that stump frequentists all the time, framing probability as a belief frees you to answer so many more questions that are useful in contexts where its needed most, areas with high information asymmetry and limited data. The bottom line is, given the mechanisms that are at play, is it worth investing in this approach? I cannot stress how little value I currently see in frequentist statistics other than convienience and even then I think its value is limited. So investing in Bayesian statistics seems to be a pretty good mid to long-term career investment for those who want to challenge themselves and solve problems that nobody else can.

    • @nuhuhbruhbruh
      @nuhuhbruhbruh Před 3 měsíci

      Your assessment of frequentism is extremely flawed. A lot of the properties of MCMC and related diagnostics that provide the basis for practical Bayesian inference are justified on frequentist grounds and for those contexts, the idea of an infinite sequence of samples drawn from an unchanging process is a much more tenable than for applications in science. On the other hand, "speed" is not an argument that frequentist methods have uniquely in their favor. Performing Bayesian inference with approximate methods can be just as fast. But once again, understanding how to investigate those methods in order to quantify the quality of the approximations is something that can be done very naturally from a frequentist perspective. For the particular cases where the inferences provided by both frameworks match, then one can just as easily consider frequentist approaches to be a good, fast approximation of Bayesian ones. And practically speaking, given the limited time non-statistics students get to understand these topics, having to deal with the computational difficulties involved in full posterior sampling can be a huge time sink. A simulation-based course that gives the students the tools to probe whatever method or definition they come across would be far more useful than the desperate attempts I have repeatedly seen at having them "understand" an entire inferential framework (either one) by repeating a bunch of terms and procedures handed to them from high above.

    • @cms2037
      @cms2037 Před 3 měsíci

      @@nuhuhbruhbruh I agree with your assessment. One must understand the frequentist methods of estimation to fully appreciate the utility and application of Bayesian statistics. Bayes rule and simulations like Monte Carlo methods are a good way to start. I'm fairly new to this, but one thing I'm starting to realize is that I overlooked for a long time the possible pitfalls in doing frequentist inference.

  • @forheuristiclifeksh7836
    @forheuristiclifeksh7836 Před 4 měsíci

    12:23

  • @praveenb9048
    @praveenb9048 Před 4 měsíci

    Why is it hard to do independent sampling in the posterior distribution?

  • @personanongrata987
    @personanongrata987 Před 4 měsíci

    What is a prior? --

    • @galenseilis5971
      @galenseilis5971 Před 4 měsíci

      Lookup "prior probability".

    • @Kram1032
      @Kram1032 Před 4 měsíci

      Basically, it's the thing you believe before you observe anything. Priors are gonna have some parameters and you can use certain rules to update that prior based on observations, to refine your belief to better align with reality.

  • @stevejones6330
    @stevejones6330 Před 8 měsíci

    When I was in college there was an interest in "automatic theorem proving" and it seemed impossible to convince a mathematician of the value of just formalizing a proof so the computer could check it. Times have changed, but it's clear from your video that formalized mathematics is still considered to be just a niche area by academics.

  • @sanjursan
    @sanjursan Před 11 měsíci

    When I need a break from Kolmogorov or Sternberg, I read a few pages of "How to think about Analysis." I recommend it to any student of Real Analysis as a valuable asset.

  • @edunet-lk507
    @edunet-lk507 Před rokem

    Very helpful - conceptually and hands-on. Yes, now have STACK running in our own Moodle - on a Raspberry Pi. ;-)

  • @alondrachavez1234
    @alondrachavez1234 Před rokem

    Hi, what is the difference between the book "How to Study as a Mathematics Major" and "How to Study for a Mathematics Degree". Aren't they essentially the same thing?

    • @bleeeeeeh
      @bleeeeeeh Před rokem

      If you still need to know is, How to Study a Mathematics Degree is the name of the book for UK and How to Study for a Mathematics Degree on the US

  • @pailmckinnon8580
    @pailmckinnon8580 Před rokem

    Just subscribed!!! The secret to YT success - P r o m o s m !!!

  • @leakleakyuki1107
    @leakleakyuki1107 Před 2 lety

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  • @BlueSoulTiger
    @BlueSoulTiger Před 2 lety

    "Warrant" probably has a technical definition, but it seems to mean a rationale or justification for some given statement. The key issue then, is whether a warrant is merited for a given statement, and if so, whether the warrent is explicit or is implicit - the latter case being a challenge for relative novices. Moreover, if genuine understanding is to be achieved, the reader should aim to establish what the underlying reason is that permits a statement to be sound. (Or am I just paraphrasing?!). Happy to be corrected.

  • @IceQueenaliasIQ
    @IceQueenaliasIQ Před 2 lety

    Starts @ 8:06

  • @echohasbinokiller4
    @echohasbinokiller4 Před 2 lety

    How do you get the bars and the question on itempool displayed over your web cam?

  • @alittlesliceofrye
    @alittlesliceofrye Před 3 lety

    cool video<3

  • @glasiellydemoriproenca6798

    Hello! I'd like to know, how i use the Random Group to reused variables randomics in more than one question.