study_fields.yaml

topic_fields:
  - name: quantum computing
    rules_principles_concepts:
      - id: dirac_notation
        name: Dirac Notation
        url: https://en.wikipedia.org/wiki/Bra%E2%80%93ket_notation
        description: ""
    subjects_topics:
      - id: qiskit
        name: Qiskit - IBM Quantum Algorithm Library
        url: ""
        description: ""
      - id: cirq
        name: Cirq - Microsoft Quantum Algorithm Library
        url: ""
        description: ""
      - id: quantum_computing
        name: Quantum Computing Overview
        url: ""
        description: ""
      - id: quantum_computing_cooling
        name: Cooling Quantum Devices
        url: ""
        description: ""
  - name: physics
    rules_principles_concepts:
      - id: coulomb_blockade
        name: Coloumb Blockade
        url: ""
        description:
          Stepped, staggered flow of electrons, based on the bias-voltage
          across a conductance tunnel junction
      - id: general_relativity
        name: General Relativity
        url: ""
        description: ""
      - id: special_relativity
        name: Special Relativity
        url: ""
        description: ""
      - id: quantum_numbers
        name: Quantum numbers
        url: ""
        description: Four s, l, m and q
      - id: aufbau_principle
        name: Aufbau Principle
        url: ""
        description:
          Electrons fill the lowest energy first. Order in which electrons
          fill the orbitals
      - id: hunds_rule
        name: hunds rule
        url: ""
        description: hunds rule
      - id: electron_orbitals
        name: electron_orbitals
        url: ""
        description: how electrons hang about a nucleus
      - id: pauli_exclusion
        name: Pauli Exclusion Principle
        url: ""
        description:
          number of electron field energies for a given atom; no two electrons
          can have the same set of quantum numbers
      - id: fermi_gas
        name: Fermi Gas
        url: ""
        description: related to <b>Electron Gas</b>
      - id: nmr
        name: Nuclear Magnetic Resonance
        url: ""
        description:
          Nuclear magnetic resonance (NMR) is a physical phenomenon in
          which nuclei in a strong constant magnetic field are perturbed by a weak
          oscillating magnetic field (in the near field) and respond by producing
          an electromagnetic signal with a frequency characteristic of the magnetic
          field at the nucleus.
      - id: einsteins_equation
        name: Einsteins Equation
        url: ""
        description:
          In the general theory of relativity, the Einstein field equations
          relate the geometry of spacetime to the distribution of matter within it.
      - id: hamiltonian
        name: Hamiltonian
        url: ""
        description:
          In quantum mechanics, the Hamiltonian of a system is an operator
          corresponding to the total energy of that system, including both kinetic
          energy and potential energy.
      - id: schrödingers_equation
        name: schrödingers_equation
        description: The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of the subject.
    subjects_topics:
      - id: single_electron_transistor
        name: Single Electron Transistor
        url: ""
        description: A sensitive electronic device based on the Coulomb blockade effect
      - id: quantum_mechanics
        name: Quantum Mechanics
        url: ""
        description: NEED DESC
      - id: electron
        name: The Electron
        url: ""
        description: A fundamental Quantum Particle
  - name: maths
    rules_principles_concepts: []
    subjects_topics:
      - id: linear_algebra
        name: Linear Algebra
        url: ""
        description: Vectors, Matrices, Tensors
      - id: differential_calculus
        name: Differential Calculus
        url: ""
        description:
          Differential calculus is about finding the rate of change of
          one quantity with respect to another quantity.
      - id: complex_numbers
        name: Complex Numbers
        url: ""
        description:
          Complex numbers are the field C of numbers of the form x+iy,
          where x and y are real numbers and i is the imaginary unit equal to √-1
      - id: integral_calculus
        name: Integral Calculus
        url: ""
        description:
          Integral Calculus is the branch of calculus where we study integrals
          and their properties. Integration is an essential concept which is the inverse
          process of differentiation
      - id: probabilities
        name: Probabilities and Statistics
        url: ""
        description: ""
      - id: euclidean_geometry
        name: Euclidean Geometry
        url: ""
        description:
          Euclidean geometry, the study of plane and solid figures on the
          basis of five axioms, and theorems employed by the Greek mathematician Euclid
          (c. 300 bce).
      - id: non_euclidean_geometry
        name: Non Euclidean Geometry
        url: ""
        description:
          Non-Euclidean geometry is the study of geometry on surfaces which
          are not flat; e.g. spacetime in our universe
      - id: differential_geometry
        name: Differential Geometry
        url: ""
        description:
          Differential geometry is a mathematical discipline that studies
          the geometry of smooth shapes and smooth spaces, otherwise known as smooth
          manifolds.
      - id: geometry
        name: Geometry
        url: ""
        description: Geometry is all about shapes and their properties.
      - id: algebra
        name: Algebra
        url: ""
        description:
          Algebra is the part of mathematics that helps represent problems
          or situations in the form of mathematical expressions
      - id: calculus
        name: Calculus
        url: ""
        description:
          Calculus is the mathematical study of change, in the same way
          that geometry is the study of shape and algebra is the study of operations
          and their application to solving equations
      - id: hilbert_space
        name: Hilbert Space
        url: ""
        description:
          A Hilbert space is a mathematical concept covering the extra-dimensional
          use of Euclidean space—i.e., a space with more than three dimensions. A
          Hilbert space uses the mathematics of two and three dimensions to try and
          describe what happens in greater than three dimensions.
resources:
  - id: vid_aufbau_hund_pauli
    name: Aufbau principle, Hund's rule & Pauli exclusion principle
    url: https://www.youtube.com/watch?v=9ra0BHbHdoA
  - id: vid_prof_dave_quant_no_atomic_electron
    name: Prof Dave - Quantum Numbers, Atomic Orbitals, and Electron Configurations
    url: https://www.youtube.com/watch?v=Aoi4j8es4gQ
  - id: vid_linear_algebra
    name: 3Blue1Brown - Linear Algebra - Series
    url: https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab
  - id: lessons_gilbert_strang_diff_equations_lin_alg
    name: Online Course - Differential Equations and Linear Algebra - Gilbert Strang
    url: https://ocw.mit.edu/courses/res-18-009-learn-differential-equations-up-close-with-gilbert-strang-and-cleve-moler-fall-2015/pages/differential-equations-and-linear-algebra/
  - id: lessons_khan_acadamy_diff_equations
    name: Khan Academy - Differential Equations
    url: https://www.khanacademy.org/math/differential-equations
  - id: definition_fermi_gas
    name: Wikipedia - Fermi Gas
    url: https://en.wikipedia.org/wiki/Fermi_gas
  - id: singleelectrontransistorwikipedia
    name: Single-electron transistor - Wikipedia
    url: https://en.wikipedia.org/wiki/Single-electron_transistor
  - id: coulombblockadewikipedia
    name: Coulomb blockade - Wikipedia
    url: https://en.wikipedia.org/wiki/Coulomb_blockade
  - id: quantumcomputingwithandreamorelloyoutube
    name: Quantum Computing with Andrea Morello - YouTube
    url: https://www.youtube.com/watch?v=jDW9bWSepB0
  - id: nmrspectroscopyyoutube
    name: NMR Spectroscopy - YouTube
    url: https://www.youtube.com/watch?v=SBir5wUS3Bo&t=554s
  - id: seancarrollextractingtheuniversefromthewavefunctionyoutube
    name: "Sean Carroll: Extracting the universe from the wave function - YouTube"
    url: https://www.youtube.com/watch?v=HOssfva2IBo&t=160s
  - id: physicistseancarrollonthebiggestideasintheuniverseyoutube
    name:
      Einsteins Equation - Physicist Sean Carroll - The Biggest Ideas in the Universe
      - YouTube
    url: https://www.youtube.com/watch?v=CH39SDlxon4&t=3041s
  - id: insideeinsteinsmindfullspecialnovapbsamericayoutube
    name: Einstein - General Relativity - PBS America - YouTube
    url: https://www.youtube.com/watch?v=7CZyDPELXs4
  - id: thehistoryofmathematicsdocumentaryyoutube
    name: The HISTORY of MATHEMATICS. Documentary - YouTube
    url: https://www.youtube.com/watch?v=2WcbPcGrQZU&t=4s
  - id: whatdoesanelectronlooklikeyoutube
    name: What Does an Electron Look Like? - YouTube
    url: https://www.youtube.com/watch?v=zZ5ww6aYAZ8&t=38s
  - id: quantumcoolingtonearabsolutezeroyoutube
    name: Quantum Cooling to (Near) Absolute Zero - YouTube
    url: https://www.youtube.com/watch?v=7jT5rbE69ho
  - id: richardfeynmanquantummechanicalviewofreality1youtube
    name: "Richard Feynman: Quantum Mechanical View of Reality 1 - YouTube"
    url: https://www.youtube.com/watch?v=ZcpwnozMh2U&t=3056s
  - id: nuclearmagneticresonancewikipedia
    name: Nuclear magnetic resonance - Wikipedia
    url: https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance
  - id: howgeometrycreatedmodernphysicswithyanghuiheyoutube
    name: How geometry created modern physics – with Yang-Hui He - YouTube
    url: https://www.youtube.com/watch?v=z8jdndd-x7w
  - id: ila6thed2023
    name: BOOK - Introduction to Linear Algebra, 6th Ed. (2023) - Gilbert Strang
    url: https://math.mit.edu/~gs/linearalgebra/ila6/indexila6.html
  - id: complexnumbersyoutube
    name: Complex Numbers - Eddie Woo - YouTube
    url: https://www.youtube.com/playlist?list=PL5KkMZvBpo5CE__2qeqZQa5e8gSkt1Ypy
  - id: introductiontodifferentiationyoutube
    name: Introduction to Differentiation - Eddie Woo - YouTube
    url: https://www.youtube.com/playlist?list=PL5KkMZvBpo5DwIsDKWdHYmkRZmXMi1mE8
  - id: complexnumbersalgebra2mathkhanacademy
    name: Complex numbers - Algebra 2 - Math - Khan Academy
    url: https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:complex
  - id: differential_calculus_syd_unsw_book
    name: Sydney University - Introduction to Differential Calculus
    url: https://www.sydney.edu.au/content/dam/students/documents/mathematics-learning-centre/introduction-to-differential-calculus.pdf
  - id: understanding_einsteins_equation_general_relativity
    name: How to understand Einstein’s equation for general relativity
    url: https://bigthink.com/starts-with-a-bang/einstein-general-theory-relativity-equation/
  - id: howimaginarynumberswereinventedyoutube
    name: How Imaginary Numbers Were Invented - YouTube
    url: https://www.youtube.com/watch?v=cUzklzVXJwo
  - id: imaginarynumbersarerealyoutube
    name: Imaginary Numbers are Real - YouTube
    url: https://www.youtube.com/playlist?list=PLiaHhY2iBX9g6KIvZ_703G3KJXapKkNaF
relates:
  - r_from: electron_orbitals
    r_to: pauli_exclusion
    rel_type: relates_to
  - r_from: vid_aufbau_hund_pauli
    r_to: aufbau_principle
    rel_type: explains
  - r_from: vid_aufbau_hund_pauli
    r_to: hunds_rule
    rel_type: explains
  - r_from: vid_aufbau_hund_pauli
    r_to: pauli_exclusion
    rel_type: explains
  - r_from: vid_linear_algebra
    r_to: linear_algebra
    rel_type: teaches
  - r_from: vid_prof_dave_quant_no_atomic_electron
    r_to: quantum_numbers
    rel_type: teaches
  - r_from: vid_prof_dave_quant_no_atomic_electron
    r_to: electron_orbitals
    rel_type: teaches
  - r_from: lessons_gilbert_strang_diff_equations_lin_alg
    r_to: linear_algebra
    rel_type: teaches
  - r_from: lessons_gilbert_strang_diff_equations_lin_alg
    r_to: differential_calculus
    rel_type: teaches
  - r_from: lessons_khan_acadamy_diff_equations
    r_to: differential_calculus
    rel_type: teaches
  - r_from: definition_fermi_gas
    r_to: fermi_gas
    rel_type: explains
  - r_from: singleelectrontransistorwikipedia
    r_to: single_electron_transistor
    rel_type: explains
  - r_from: coulombblockadewikipedia
    r_to: coulomb_blockade
    rel_type: explains
  - r_from: single_electron_transistor
    r_to: coulomb_blockade
    rel_type: relates_to
  - r_from: physicistseancarrollonthebiggestideasintheuniverseyoutube
    r_to: general_relativity
    rel_type: explains
  - r_from: insideeinsteinsmindfullspecialnovapbsamericayoutube
    r_to: general_relativity
    rel_type: explains
  - r_from: whatdoesanelectronlooklikeyoutube
    r_to: electron
    rel_type: explains
  - r_from: richardfeynmanquantummechanicalviewofreality1youtube
    r_to: quantum_mechanics
    rel_type: explains
  - r_from: nmrspectroscopyyoutube
    r_to: nmr
    rel_type: explains
  - r_from: quantumcomputingwithandreamorelloyoutube
    r_to: quantum_computing
    rel_type: explains
  - r_from: quantumcoolingtonearabsolutezeroyoutube
    r_to: quantum_computing_cooling
    rel_type: explains
  - r_from: nuclearmagneticresonancewikipedia
    r_to: nmr
    rel_type: explains
  - r_from: electron_orbitals
    r_to: electron
    rel_type: relates_to
  - r_from: howgeometrycreatedmodernphysicswithyanghuiheyoutube
    r_to: euclidean_geometry
    rel_type: relates_to
  - r_from: howgeometrycreatedmodernphysicswithyanghuiheyoutube
    r_to: geometry
    rel_type: relates_to
  - r_from: howgeometrycreatedmodernphysicswithyanghuiheyoutube
    r_to: algebra
    rel_type: relates_to
  - r_from: howgeometrycreatedmodernphysicswithyanghuiheyoutube
    r_to: calculus
    rel_type: relates_to
  - r_from: howgeometrycreatedmodernphysicswithyanghuiheyoutube
    r_to: special_relativity
    rel_type: relates_to
  - r_from: howgeometrycreatedmodernphysicswithyanghuiheyoutube
    r_to: general_relativity
    rel_type: relates_to
  - r_from: howgeometrycreatedmodernphysicswithyanghuiheyoutube
    r_to: differential_geometry
    rel_type: relates_to
  - r_from: differential_geometry
    r_to: differential_calculus
    rel_type: relates_to
  - r_from: differential_calculus
    r_to: calculus
    rel_type: relates_to
  - r_from: integral_calculus
    r_to: calculus
    rel_type: relates_to
  - r_from: differential_geometry
    r_to: geometry
    rel_type: relates_to
  - r_from: euclidean_geometry
    r_to: geometry
    rel_type: relates_to
  - r_from: non_euclidean_geometry
    r_to: geometry
    rel_type: relates_to
  - r_from: seancarrollextractingtheuniversefromthewavefunctionyoutube
    r_to: einsteins_equation
    rel_type: explains
  - r_from: seancarrollextractingtheuniversefromthewavefunctionyoutube
    r_to: hilbert_space
    rel_type: explains
  - r_from: seancarrollextractingtheuniversefromthewavefunctionyoutube
    r_to: hamiltonian
    rel_type: explains
  - r_from: ila6thed2023
    r_to: linear_algebra
    rel_type: teaches
  - r_from: complexnumbersyoutube
    r_to: complex_numbers
    rel_type: teaches
  - r_from: introductiontodifferentiationyoutube
    r_to: differential_calculus
    rel_type: teaches
  - r_from: complexnumbersalgebra2mathkhanacademy
    r_to: complex_numbers
    rel_type: teaches
  - r_from: differential_calculus_syd_unsw_book
    r_to: differential_calculus
    rel_type: teaches
  - r_from: understanding_einsteins_equation_general_relativity
    r_to: einsteins_equation
    rel_type: explains
  - r_from: general_relativity
    r_to: einsteins_equation
    rel_type: relates_to
  - r_from: howimaginarynumberswereinventedyoutube
    r_to: complex_numbers
    rel_type: relates_to
  - r_from: imaginarynumbersarerealyoutube
    r_to: complex_numbers
    rel_type: relates_to
  - r_from: howimaginarynumberswereinventedyoutube
    r_to: schrödingers_equation
    rel_type: relates_to