Four-level laser by Ciro Santilli 35 Updated +Created
Josephson effect regime by Ciro Santilli 35 Updated +Created
1 by Ciro Santilli 35 Updated +Created
Mathematics course of the University of Oxford by Ciro Santilli 35 Updated +Created
The Oxford mathematics Moodle has detailed course listings, and most PDFs are not paywalled.
E.g. the 2024 course:
  • Year 1: everything seems mandatory:
    • Michaelmas Term
      • Introduction to University Mathematics
      • Introduction to Complex Numbers
      • Linear Algebra I
      • Analysis I
      • Introductory Calculus
      • Probability
      • Geometry
    • Hilary Term
      • Linear Algebra II
      • Groups and Group Actions
      • Analysis II
      • Dynamics
      • Fourier Series and Partial Differential Equations
      • Multivariable Calculus
    • Trinity Term
      • Groups and Group Actions
      • Analysis III
      • Statistics and Data Analysis
      • Constructive Mathematics
  • Year 2:
    • Mandatory big courses:
      • Linear Algebra
      • Differential Equations 1
      • Metric Spaces and Complex Analysis
    • long options:
      • Rings and Modules
      • Integration
      • Topology
      • Differential Equations 2
      • Numerical Analysis
      • Probability
      • Statistics
      • Fluids and Waves
      • Quantum Theory
    • short options
      • Number Theory
      • Group Theory
      • Projective Geometry
      • Integral Transforms
      • Calculus of Variations
      • Graph Theory
      • Mathematical Modelling in Biology
  • Year 3: pick any 8 courses. Does not say which courses exist in PDF but we can get them from courses.maths.ox.ac.uk/course/index.php?categoryid=814 of the Oxford mathematics Moodle:
    • Michaelmas
      • B1.1 Logic (2024-25)
      • B2.1 Introduction to Representation Theory (2024-25)
      • B3.2 Geometry of Surfaces (2024-25)
      • B3.5 Topology and Groups (2024-25)
      • B4.1 Functional Analysis I (2024-25)
      • B5.2 Applied Partial Differential Equations (2024-25)
      • B5.3 Viscous Flow (2024-25)
      • B5.5 Further Mathematical Biology (2024-25)
      • B6.1 Numerical Solution of Partial Differential Equations (2024-25)
      • B6.3 Integer Programming (2024-25)
      • B7.1 Classical Mechanics (2024-25)
      • B8.1 Probability, Measure and Martingales (2024-25)
      • B8.4 Information Theory (2024-25)
      • B8.5 Graph Theory (2024-25)
      • BO1.1 History of Mathematics (2024-25)
      • BOE Other Mathematical Extended Essay (2024-25)
      • BSP Structured Projects (2024-25)
    • Hilary
      • B1.2 Set Theory (2024-25)
      • B2.2 Commutative Algebra (2024-25)
      • B2.3 Lie Algebras (2024-25)
      • B3.1 Galois Theory (2024-25)
      • B3.3 Algebraic Curves (2024-25)
      • B3.4 Algebraic Number Theory (2024-25)
      • B4.3 Distribution Theory (2024-25)
      • B4.2 Functional Analysis II (2024-25)
      • B5.1 Stochastic Modelling of Biological Processes (2024-25)
      • B5.4 Waves and Compressible Flow (2024-25)
      • B5.6 Nonlinear Dynamics, Bifurcations and Chaos (2024-25)
      • B6.2 Optimisation for Data Science (2024-25)
      • B7.2 Electromagnetism (2024-25)
      • B7.3 Further Quantum Theory (2024-25)
      • B8.2 Continuous Martingales and Stochastic Calculus (2024-25)
      • B8.3 Mathematical Models of Financial Derivatives (2024-25)
      • B8.6 High Dimensional Probability (2024-25)
      • SB3.1 Applied Probability (2024-25)
      • BO1.1 History of Mathematics (2024-25)
      • BOE Other Mathematical Extended Essay (2024-25)
      • BSP Structured Projects (2024-25)
  • Year 4: pick any 8 courses (up to 10 if you're crazy). Does not say which courses exist in PDF but we can get them from courses.maths.ox.ac.uk/course/index.php?categoryid=814 of the Oxford mathematics Moodle:
    • Michaelmas
      • C1.1 Model Theory (2024-25)
      • C1.4 Axiomatic Set Theory (2024-25)
      • C2.2 Homological Algebra (2024-25)
      • C2.4 Infinite Groups (2024-25)
      • C2.7 Category Theory (2024-25)
      • C3.1 Algebraic Topology (2024-25)
      • C3.3 Differentiable Manifolds (2024-25)
      • C3.4 Algebraic Geometry (2024-25)
      • C3.7 Elliptic Curves (2024-25)
      • C3.8 Analytic Number Theory (2024-25)
      • C4.1 Further Functional Analysis (2024-25)
      • C4.3 Functional Analytic Methods for PDEs (2024-25)
      • C5.2 Elasticity and Plasticity (2024-25)
      • C5.5 Perturbation Methods (2024-25)
      • C5.7 Topics in Fluid Mechanics (2024-25)
      • C5.11 Mathematical Geoscience (2024-25)
      • C5.12 Mathematical Physiology (2024-25)
      • C6.1 Numerical Linear Algebra (2024-25)
      • C6.5 Theories of Deep Learning (2024-25)
      • C7.1 Theoretical Physics (C6) (2024-25)
      • C7.5 General Relativity I (2024-25)
      • C8.1 Stochastic Differential Equations (2024-25)
      • C8.3 Combinatorics (2024-25)
      • CCD Dissertations on a Mathematical Topic (2024-25)
      • COD Dissertations on the History of Mathematics (2024-25)
    • Hilary
      • C1.2 Gödel's Incompleteness Theorems (2024-25)
      • C1.3 Analytic Topology (2024-25)
      • C2.3 Representation Theory of Semisimple Lie Algebras (2024-25)
      • C2.5 Non-Commutative Rings (2024-25)
      • C2.6 Introduction to Schemes (2024-25)
      • C3.2 Geometric Group Theory (2024-25)
      • C3.5 Lie Groups (2024-25)
      • C3.6 Modular Forms (2024-25)
      • C3.9 Computational Algebraic Topology (2024-25)
      • C3.10 Additive Combinatorics (2024-25)
      • C3.11 Riemannian Geometry (2024-25)
      • C3.12 Low-Dimensional Topology and Knot Theory (2024-25)
      • C4.6 Fixed Point Methods for Nonlinear PDEs (2024-25)
      • C4.9 Optimal Transport & Partial Differential Equations (2024-25)
      • C5.1 Solid Mechanics (2024-25)
      • C5.4 Networks (2024-25)
      • C5.6 Applied Complex Variables (2024-25)
      • C6.2 Continuous Optimisation (2024-25)
      • C6.4 Finite Element Method for PDEs (2024-25)
      • C7.1 Theoretical Physics (C6) (2024-25)
      • C7.4 Introduction to Quantum Information (2024-25)
      • C7.6 General Relativity II (2024-25)
      • C7.7 Random Matrix Theory (2024-25)
      • C8.2 Stochastic Analysis and PDEs (2024-25)
      • C8.4 Probabilistic Combinatorics (2024-25)
      • C8.7 Optimal Control (2024-25)
      • CCD Dissertations on a Mathematical Topic (2024-25)
      • COD Dissertations on the History of Mathematics (2024-25)
Erotica by Ciro Santilli 35 Updated +Created
Glass by Ciro Santilli 35 Updated +Created
Michio Kaku by Ciro Santilli 35 Updated +Created
Well known popular science character. He just looks futuristic and wraps stuff in exciting empty words. When he shows up, you won't be learning much.
Classical mechanics by Ciro Santilli 35 Updated +Created
Pinned article: ourbigbook/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!
Video 1.
Intro to OurBigBook
. Source.
We have two killer features:
  1. 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-calculus
    Articles 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/derivative
    Video 2.
    OurBigBook Web topics demo
    . Source.
  2. 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:
    • 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
    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.
    Figure 5. . 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.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
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