In those cases at least, it is possible to add a metric to the spaces, leading to elliptic geometry.
From the 2020/2021 Oxford physics course handbooks we can determine the following structure:
- Year 1 (CP, "Coure Preliminaries", "Prelims"). Take all of:
- CP1 Classical mechanics, Special relativity
- CP2 Electromagnetism, circuit theory and optics
- CP3 Mathematical methods 1. Complex Numbers and Ordinary Differential Equations. Vectors and Matrices.
- CP4 Mathematical methods 2. Multiple Integrals and Vector Calculus. Normal Modes, Wave Motion and the Wave Equation.
- Year 2 (Part A). Take all of:
- A1 Thermal physics. Kinetic Theory, Heat Transport, Thermodynamics.
- A2 Electromagnetism and optics
- A3 Quantum physics. Quantum Mechanics and Further Quantum Mechanics.
- Short options: at least one of:
- Mathematical Methods
- Probability and Statistics
- S01 Functions of a Complex Variable
- S07 Classical Mechanics
- S10 Medical Imaging and Radiation Therapy
- S13 Teaching and Learning Physics in Schools
- S14 History of Physics
- S20 History of Science
- S21 Philosophy of Science
- S22 Language Options
- S25 Climate Physics
- S27 Philosophy of Space-Time
- S29 Exploring Solar Systems
- S33 Entrepreneurship for Physicists
- Year 3 (Part B). Take all of:
- Michaelmas term
- Hilary term
- B1 Fluids
- B3 Atomic and laser physics
- B5 General relativity
- B7 Classical Mechanics (for MPhysPhil only?)
- B8 Computational Project
- B9 Experimental Project
- Year 4 (MPhys). Select two from:
Trinity term, the third and final term of each year, contains mostly revision from the previous two terms, after which students take their final exams, which basically account for their entire grade. Trinity is therefore a very tense part of the year for the students. After that they have summer holidays, until coming back for the next year of madness.
The official external course landing page: www.ox.ac.uk/admissions/undergraduate/courses/course-listing/physics. 2021 archive: web.archive.org/web/20221208212856/https://www.ox.ac.uk/admissions/undergraduate/courses/course-listing/physics) In those pages we see the rough structure, except that it does not have the course codes "A1" etc., and some courses are missing.
At web.archive.org/web/20221229021312/https://www2.physics.ox.ac.uk/sites/default/files/2011-06-03/course_v3_pdf_80151.pdf page 11 we can see the global course structure giving the two options, 3 year BA or 4 year Oxford physics masters:
Year 1
(Prelims)
|
|
v
Year 2
(Part A)
|
+-----------+
| |
v v
Year 3 BA Year 3 (MPhys)
(Part B) (Part B)
| |
| |
v v
BA Year 4
(Part C)
|
|
v
MPhysPractical courses notes: www-teaching.physics.ox.ac.uk/
Some others with lecture notes:
A law of physics is Galilean invariant if the same formula works both when you are standing still on land, or when you are on a boat moving at constant velocity.
For example, if we were describing the movement of a point particle, the exact same formulas that predict the evolution of must also predict , even though of course both of those will have different values.
It would be extremely unsatisfactory if the formulas of the laws of physics did not obey Galilean invariance. Especially if you remember that Earth is travelling extremelly fast relative to the Sun. If there was no such invariance, that would mean for example that the laws of physics would be different in other planets that are moving at different speeds. That would be a strong sign that our laws of physics are not complete.
Lorentz invariance generalizes Galilean invariance to also account for special relativity, in which a more complicated invariant that also takes into account different times observed in different inertial frames of reference is also taken into account. But the fundamental desire for the Lorentz invariance of the laws of physics remains the same.
Like the special orthogonal group is to the orthogonal group, is the subset of with determinant equal to exactly 1.
Official support is abysmal, very focused on MicroPython and their graphical UI.
The setup impossible to achieve as it requires setting up the Yotta, just like the impossible to setup Compile MicroPython code for Micro Bit locally on Ubuntu 22.04 with your own firmware setup.
So we just use github.com/lancaster-university/microbit-samples + github.com/carlosperate/docker-microbit-toolchain:.hex file size for the hello world was 447 kB, much better than the MicroPython hello world downloaded from the website which was about 1.8 MB!
docker pull ghcr.io/carlosperate/microbit-toolchain:latest
git clone https://github.com/lancaster-university/microbit-samples
cd microbit-samples
git checkout 285f9acfb54fce2381339164b6fe5c1a7ebd39d5
# Select a sample, builds one at a time. The default one is the hello world.
cp source/examples/hello-world/* source
# Build and flash.
docker run -v $(pwd):/home --rm ghcr.io/carlosperate/microbit-toolchain:latest yotta build
cp build/bbc-microbit-classic-gcc/source/microbit-samples-combined.hex "/media/$USER/MICROBIT/"If you try it again for a second time from a clean tree, it fails with:presumably because after Yotta died it started using GitHub as a registry... sad. When will people learn. Apparently we were at 5000 API calls per hour. But if you don't clean the tree, you will be just fine.
warning: github rate limit for anonymous requests exceeded: you must log inCan be calculated efficiently with the Extended Euclidean algorithm.
The beauty of this algorithm is that because exponentiation grows really fast, there is no hope that we can ever learn all the digits of an exponential, as there is simply not enough time or memory for that. Therefore, a natural sub-question is if we can know some part of that number, and knowing the smallest digits is the most natural version of that question.
Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 3. Visual Studio Code extension installation.
Figure 4. Visual Studio Code extension tree navigation.
Figure 5. Web editor. You can also edit articles on the Web editor without installing anything locally.Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.Video 4. OurBigBook Visual Studio Code extension editing and navigation demo. Source. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact