فارسی/Persian  #### Theory of Relativity for Beginners

1
Assumptions
2
Space & Time, Absolute or Relative?
3
Space-Time & Interval between two Event
4
All of them with speed of light at Space-time
5
Einstein Equation: New vision
6
Zero Mass! Light
7
Creation of Einstein
8
General Relativity (Einstein, beautiful mind, exquisite idea)
9
From Galileo to gravitational waves from neutron couple

#### Chaos Theory & Complex Systems for Beginners

1
Framework for Theoretical Physics
2
Introduction to the theory of chaos and Danaki
3
To Be & To Become
4
Dimensions of space-time
5
The chaotic reality
6
Bifurcation in the phase space
7
Creation
8
Fantasy home
9
The concept of time – "Creator"
10
Plowing space-time
11
Mandelbrot set, Riemann & Danak model

#### Quantum Mechanics for Beginners

1
Electron fall
2
Matter waves
3
Certainty and Imagery
4
To be and not to be
5
The possibility of excitement in the imaginary
6
Hidden relations and timelessness
7
Bell’s inequality
8
Quantum reality and the brain

#### Linear Algebra

1
Introduction to Affine Geometry
2
Affine Graid Transformation
3
Vector/ Matrix concept
4
Three Approaches to a single problem
5
The system of equations Aū = b
6
Transformation Matrices
7
Solving a system of linear equations
8
Column space/ Null space
9
Eigenvectors & Eigenvalues
10
Matrix Exponential e^Ax

#### Classical Mechanics (I)

1
Nature’s Equation (Euler- Lagrange)

#### Special Relativity

1
Einstein’s play ground
2
Galilean vs Lorentz Transformations
3
Hyperbolic Geometry & Lorentz transformation
4
Relativistic Effects
5
Space-Time 4-vector
6
Introduction to classical relativity fields

#### Chaos Theory I

1
Non- Linear Dynamic
2
Analysis of system behavior
3
Bifurcation
4
Mathematical Model of simple Laser
5
Oscillatory systems (1D)
6
Two dimensional flows
7
Non-Linear systems, 2D
8
Non-Linear , Applications
9
limit cycle & Bifurcation

#### Quantum Theory I

1
State space/ Complex vector space
2
Complex vector space
3
Relationship between Classic ideology and Quantum ideology
4
Postulates of quantum mechanics
5
Electron spin, Space Dimensions and Brain
6
Wave function & physical reality
7
Operators and Matrix representation
8
Similarity/ Unitary transformation
9
Uncertainty principle
10
Momentum operator
11
A window to reality (Two-slit experiment)
12
Nöether & unification in physics
13
Schrödinger equation
14
ih{...}

#### Classical Mechanics II

1
Nature’s Equation (Euler- Lagrange)
2
Principle of Least Action
3
Generalized Coordinates/ Constants
4
Constraints & Lagrange Multipliers
5
Nöether Theorem (symmetry & conservation)
6
Relativity & Quantum
7
Hamiltonian Formalism Hamiltonian Dynamical system
8
Hamiltonian Formalism Poisson Bracket
9
Hamiltonian Formalism Liouville ˊs Theorem
10
Hamiltonian Formalism Canonical Transformation
11
Hamiltonian Formalism Liouville- Arnold Integrability
12
Hamiltonian Formalism Periodicity & chaos
13
Hamiltonian Formalism Quantum chaos/ Riemann Zeta Function
14
Hamiltonian Formalism Symplectic Group/ Standard model
15
Hamiltonian Formalism Semi- classical Quantization
16
Hamiltonian Formalism Quantum vs classical

#### Chaos Theory II

1
System solubility (Liouville- Arnold Integrability)
2
Periodicity & chaos
3
Quantum chaos/ Riemann Zeta Function
4
Growth phenomena (nonlinear effects)
5
System Dynamics via vector fields
6
Dimensions of space-time
7
Fundamental elements of phase space
8
Limit cycle Bifurcations
9
Bifurcation in Nature & Technology Danaki Biology:Where have we come from?
10
Danaki Biology: Formation of organs

#### Quantum Theory II

1
From Plato to Schrödinger
2
Schrödinger equation & energy Eigenstate
3
Quantum Dynamics
4
Hamiltonian in Hilbert & phase space
5
The effect of potential function
6
Scattering states
7
Quantum tunneling (Creation, Nuclear energy)
8
Quantum harmonic oscillator (Zero- point Energy)
9
Quantum Angular Momentum
10
Quantum Angular Momentum … cont. (Spin)
11
Quantum Mechanics in 3 Dimensions (Hydrogen Atom)

#### General Relativity Theory

1
Introduction
2
Newtonian Gravitational Field
3
Principle of Equivalence
4
Geodesic of Free Fall
5
Curved surface/ Tidal force
6
Mathematical language of General relativity (1) A extrinsic and intrinsic geometric
7
Mathematical language of General relativity(2) Tensor
8
Mathematical language of General relativity (3)
9
Mathematical language of General relativity (4)
10
Mathematical language of General relativity (5)
11
Mathematical language of General relativity (6)
12
Mathematical language of General relativity (7)
13
Mathematical language of General relativity (8)
14
Mathematical language of General relativity (9)
15
Cosmological constant & Dark Energy
16
General Relativity & Lagrangian Formulation

#### Cosmology

1
Introduction
2
From Einstein to Hubble
3
Friedmann Equation (Newtonian Cosmology)
4
Dark Matter & Dark Energy
5
Black Holes
6
Geometry of Space & the FRW Metric
7
Properties of the FRW Metric
8
Friedmann Equations from GR
9
Dynamics of the Universe via General Relativity
10
Black Holes (I): Schwarzschild Metrics
11
Black Holes (II): Singularities & The Coordinates
12
Black Holes (III): Kruskal Coordinates, White Holes, Wormholes
13
Black Holes (IV): Maximally Extended Geometry & Wormholes
14
Black Holes (V): Wormholes & Penrose Diagrams

#### Group Theory in Physics

1
Introduction
2
Plato, Abstract Algebra & Reality
3
From Al-Khazini to Cayley Algebra
4
Invariance & Symmetry
5
Permutation and Quaternions!
6
Polynomial Roots: From Mesopotamiato Lagrange
7
Galois Theory I
8
تئوری گالوا -2
9
تئوری گالوا -3
10
تئوری گالوا -4

#### Mathematical Topics in MZ2

1
Emerging Universe
2
Foundations of Mathematics- revisit Axiomatic systems
3
Geometric Clifford Algebra
4
Physics unified mathematical Language
5
A new kind of physics!
6
Emergence of space
7
Clifford Algebra 1&2
8
Clifford Algebra 1&2
9
Clifford Algebra 3
10
Clifford Algebra 4
11
Clifford Algebra 5