Update app.py

app.py

@@ -1,241 +1,201 @@
 import streamlit as st
 
-# Define course outlines
-phy504 = """
-# PHY 504: Classical Mechanics (Advanced Mechanics)
-This course focuses on a detailed and sophisticated approach to classical mechanics, emphasizing mathematical methods and applications to physical systems.
-
-## Outline:
-1. **Lagrangian Mechanics**
-   - Principle of least action
-   - Euler-Lagrange equations
-   - Constraints and generalized coordinates
-2. **Variational Principles**
-   - Hamilton's principle
-   - Symmetries and Noether’s theorem
-3. **Hamiltonian Mechanics**
-   - Hamilton’s equations of motion
-   - Canonical transformations
-4. **Phase Space and Liouville's Theorem**
-   - Phase space flow and conservation
-5. **Central Force Problems**
-   - Orbital mechanics
-   - Scattering in central forces
-6. **Small Oscillations**
-   - Normal modes
-   - Perturbation methods
-7. **Rigid Body Dynamics**
-   - Euler angles and rotational motion
-   - Inertia tensors and principal axes
-   - Gyroscopic motion
-8. **Nonlinear Dynamics and Chaos**
-   - Bifurcation theory
-   - Lyapunov exponents
-   - Poincaré maps
-9. **Relativistic Mechanics**
-   - Lorentz transformations and four-vectors
-   - Action for relativistic particles
-"""
-
-phy611 = """
-# PHY 611: Quantum Mechanics I
-This course provides a rigorous foundation in quantum theory, with a focus on the mathematical formalism and physical interpretation.
-
-## Outline:
-1. **Mathematical Foundations of Quantum Mechanics**
-   - Hilbert spaces and operators
-   - Eigenvalue problems
-   - Dirac notation
-2. **Postulates of Quantum Mechanics**
-   - State vectors and observables
-   - Measurement postulates
-   - Time evolution of quantum states
-3. **Harmonic Oscillator and Operator Methods**
-   - Creation and annihilation operators
-   - Ladder operator techniques
-   - Coherent states
-4. **Angular Momentum**
-   - Commutation relations
-   - Spin and orbital angular momentum
-   - Addition of angular momenta
-5. **Symmetry in Quantum Mechanics**
-   - Group theory applications
-   - Parity, time reversal, and charge conjugation
-   - Conservation laws and symmetries
-6. **Approximation Methods**
-   - Time-independent perturbation theory
-   - Variational methods
-   - WKB approximation
-7. **Quantum Systems in External Fields**
-   - Magnetic fields and the Aharonov-Bohm effect
-   - Stark and Zeeman effects
-8. **Scattering Theory**
-   - Partial wave analysis
-   - Born approximation
-   - Cross sections and scattering amplitudes
-9. **Path Integral Formulation of Quantum Mechanics**
-   - Feynman path integrals
-   - Applications to quantum field theory
-"""
-
-phy613 = """
-# PHY 613: Statistical Physics
-This course covers the statistical description of systems with many degrees of freedom, focusing on both equilibrium and non-equilibrium phenomena.
-
-## Outline:
-1. **Review of Thermodynamics**
-   - Laws of thermodynamics
-   - Thermodynamic potentials
-   - Phase transitions and critical phenomena
-2. **Microcanonical, Canonical, and Grand Canonical Ensembles**
-   - Partition functions and thermodynamic properties
-   - Connections between ensembles
-   - Quantum statistics: Bose-Einstein and Fermi-Dirac distributions
-3. **Statistical Ensembles and Entropy**
-   - Entropy as a measure of disorder
-   - Gibbs entropy formula
-   - Boltzmann distribution
-4. **Ideal and Interacting Gases**
-   - Classical ideal gas
-   - Quantum ideal gases (Bose and Fermi gases)
-   - Virial expansion and interactions
-5. **Phase Transitions**
-   - Landau theory
-   - Critical exponents and universality
-   - Renormalization group theory
-6. **Non-equilibrium Statistical Mechanics**
-   - Boltzmann equation
-   - Langevin and Fokker-Planck equations
-   - Brownian motion
-7. **Fluctuations and Response Theory**
-   - Fluctuation-dissipation theorem
-   - Linear response theory
-   - Kubo formalism
-"""
-
-phy614 = """
-# PHY 614: Electromagnetism I (Electromagnetic Theory I)
-This course covers the fundamentals of electromagnetic theory, with a deep dive into Maxwell's equations and their applications.
-
-## Outline:
-1. **Maxwell’s Equations**
-   - Integral and differential forms
-   - Boundary conditions
-   - Continuity equation and gauge invariance
-2. **Electrostatics**
-   - Poisson’s and Laplace’s equations
-   - Green’s functions and boundary value problems
-   - Multipole expansions
-3. **Magnetostatics**
-   - Biot-Savart law
-   - Vector potentials
-   - Magnetic dipoles and multipoles
-4. **Electromagnetic Waves**
-   - Plane waves in vacuum and matter
-   - Reflection, refraction, and polarization
-   - Waveguides and cavities
-5. **Radiation from Moving Charges**
-   - Lienard-Wiechert potentials
-   - Dipole and quadrupole radiation
-   - Synchrotron and bremsstrahlung radiation
-6. **Special Relativity and Electromagnetism**
-   - Lorentz transformations
-   - Covariant formulation of electromagnetism
-   - Relativistic kinematics and dynamics
-7. **Electromagnetic Field in Matter**
-   - Polarization and magnetization
-   - Boundary conditions at interfaces
-   - Electromagnetic waves in dispersive and conducting media
-"""
-
-phy615 = """
-# PHY 615: Quantum Mechanics II
-This advanced course in quantum mechanics delves into more complex quantum systems, focusing on applications and advanced techniques.
-
-## Outline:
-1. **Review of Quantum Mechanics I**
-   - Key principles and formalism
-   - Advanced applications of harmonic oscillator
-2. **Advanced Scattering Theory**
-   - S-matrix and optical theorem
-   - Scattering in three dimensions
-   - Coulomb scattering and partial waves
-3. **Relativistic Quantum Mechanics**
-   - Klein-Gordon and Dirac equations
-   - Spin-1/2 particles and relativistic wave equations
-   - Zitterbewegung and antiparticles
-4. **Quantum Field Theory Basics**
-   - Quantization of fields
-   - Path integrals in field theory
-   - Interaction picture and perturbation theory
-5. **Quantum Electrodynamics (QED)**
-   - Feynman diagrams and rules
-   - Renormalization and gauge symmetry
-   - Applications to atomic physics
-6. **Symmetry and Group Theory in Quantum Mechanics**
-   - Lie groups and Lie algebras
-   - Representations of symmetry groups
-   - Wigner-Eckart theorem and selection rules
-7. **Many-Body Quantum Mechanics**
-   - Second quantization formalism
-   - Hartree-Fock method
-   - Bose-Einstein condensation and fermionic systems
-"""
-
-phy632 = """
-# PHY 632: Advanced Topics in Theoretical Physics
-This course explores contemporary and cutting-edge topics in theoretical physics, often including current research trends and advanced mathematical methods.
-
-## Outline:
-1. **Quantum Field Theory II**
-   - Renormalization group theory
-   - Gauge theories and spontaneous symmetry breaking
-   - Anomalies and the Standard Model
-2. **Supersymmetry**
-   - Supersymmetric quantum mechanics
-   - Superfields and superspace
-   - Applications to particle physics and string theory
-3. **String Theory Basics**
-   - Bosonic strings and superstrings
-   - D-branes and dualities
-   - Holography and AdS/CFT correspondence
-4. **Advanced General Relativity**
-   - Gravitational waves
-   - Black hole thermodynamics
-   - Cosmology and inflation
-5. **Topological Quantum Field Theory**
-   - Chern-Simons theory
-   - Topological insulators and anyons
-   - Applications to condensed matter physics
-6. **Nonperturbative Methods in Quantum Field Theory**
-   - Instantons and solitons
-   - Lattice gauge theory
-   - Large N expansion and dualities
-7. **Quantum Computing and Quantum Information**
-   - Qubits and quantum gates
-   - Quantum algorithms and complexity
-   - Quantum error correction and entanglement entropy
-"""
-
-# Streamlit app to display the outlines
-st.title("Graduate Physics Course Outlines")
-
-tab1, tab2, tab3, tab4, tab5, tab6 = st.tabs(["PHY 504", "PHY 611", "PHY 613", "PHY 614", "PHY 615", "PHY 632"])
+# Set page title and header
+st.title("Graduate Physics Course Syllabi")
+st.write("### Course Outlines for PHY 504, PHY 611, PHY 613, PHY 614, PHY 615, and PHY 632")
+
+# Tabs for each course
+tab1, tab2, tab3, tab4, tab5, tab6 = st.tabs(["PHY 504: Advanced Mechanics", 
+                                              "PHY 611: Electromagnetic Theory I", 
+                                              "PHY 613: Electromagnetic Theory II", 
+                                              "PHY 614: Quantum Mechanics I", 
+                                              "PHY 615: Quantum Mechanics II", 
+                                              "PHY 632: Statistical Mechanics"])
 
 with tab1:
-    st.markdown(phy504)
+    st.markdown("""
+    ## PHY 504: Advanced Mechanics  
+    **Credits**: 3  
+    **Prerequisites**: PHY 404G, MA 214
+
+    **Course Description**  
+    This course extends the foundational principles learned in classical mechanics, focusing on advanced topics such as the dynamics of particles, rigid bodies, Lagrangian and Hamiltonian mechanics, constrained motions, and small oscillations. Applications will include modern techniques used in the study of chaotic systems and continuous media.
+
+    **Course Objectives**  
+    - Understand and apply Lagrangian and Hamiltonian mechanics.
+    - Analyze mechanical systems with constraints.
+    - Solve problems involving small oscillations and rigid body dynamics.
+    - Apply advanced mechanics to real-world problems and chaotic systems.
+
+    **Weekly Outline**
+    - **Week 1-2**: Review of Newtonian Mechanics and Introduction to Variational Principles  
+    - **Week 3**: Lagrangian Mechanics: Generalized Coordinates, Lagrange's Equations  
+    - **Week 4**: Constraints: Types, Generalized Forces  
+    - **Week 5**: Rigid Body Motion: Euler Angles and Equations  
+    - **Week 6**: Hamiltonian Mechanics and Canonical Transformations  
+    - **Week 7**: Poisson Brackets and Hamilton-Jacobi Theory  
+    - **Week 8**: Action-Angle Variables  
+    - **Week 9-10**: Small Oscillations and Normal Modes  
+    - **Week 11-12**: Chaotic Systems: An Introduction  
+    - **Week 13-14**: Advanced Topics in Mechanics (Fluid Dynamics, Plasma Physics)  
+    - **Week 15**: Review and Final Exam Preparation  
+
+    **Textbooks**
+    - "Classical Mechanics" by Herbert Goldstein, Charles Poole, and John Safko
+    - "Mechanics: Volume 1 (Course of Theoretical Physics)" by L.D. Landau and E.M. Lifshitz
+    """)
 
 with tab2:
-    st.markdown(phy611)
+    st.markdown("""
+    ## PHY 611: Electromagnetic Theory I  
+    **Credits**: 3  
+    **Prerequisites**: PHY 416G, MA 214
+
+    **Course Description**  
+    This course covers the fundamentals of electromagnetism, including electrostatics, boundary value problems, potential theory, energy in electromagnetic fields, and Maxwell's equations.
+
+    **Course Objectives**  
+    - Apply Maxwell’s equations to a wide range of physical systems.
+    - Solve boundary value problems in electrostatics and magnetostatics.
+    - Analyze the behavior of electromagnetic waves in different media.
+
+    **Weekly Outline**
+    - **Week 1-2**: Introduction to Electrostatics: Gauss’s Law, Electric Field, and Potential  
+    - **Week 3-4**: Solutions to Laplace’s Equation: Separation of Variables, Multipole Expansion  
+    - **Week 5-6**: Conductors and Dielectrics in Electrostatic Fields  
+    - **Week 7-8**: Magnetostatics: Ampère’s Law, Vector Potential  
+    - **Week 9**: Maxwell’s Equations and Energy in Electromagnetic Fields  
+    - **Week 10-11**: Electromagnetic Waves: Wave Equations, Energy and Momentum  
+    - **Week 12**: Reflection and Transmission of Electromagnetic Waves  
+    - **Week 13**: Special Relativity and Electromagnetism  
+    - **Week 14**: Radiation: Dipole Radiation and Scattering  
+    - **Week 15**: Review and Final Exam Preparation  
+
+    **Textbooks**
+    - "Classical Electrodynamics" by John David Jackson
+    - "Introduction to Electrodynamics" by David J. Griffiths
+    """)
 
 with tab3:
-    st.markdown(phy613)
+    st.markdown("""
+    ## PHY 613: Electromagnetic Theory II  
+    **Credits**: 3  
+    **Prerequisites**: PHY 611
+
+    **Course Description**  
+    This course builds upon Electromagnetic Theory I and focuses on advanced topics in electromagnetism, including electromagnetic wave propagation, optical phenomena, radiation theory, and the covariant formulation of Maxwell’s equations.
+
+    **Course Objectives**  
+    - Understand the theory of electromagnetic waves.
+    - Analyze the interaction of electromagnetic radiation with matter.
+    - Apply the covariant formulation of Maxwell’s equations.
+
+    **Weekly Outline**
+    - **Week 1**: Review of Maxwell’s Equations  
+    - **Week 2-3**: Electromagnetic Wave Propagation: Polarization, Dispersion  
+    - **Week 4-5**: Waveguides and Resonant Cavities  
+    - **Week 6**: Optical Phenomena: Interference, Diffraction, and Polarization  
+    - **Week 7-8**: Electromagnetic Radiation: Retarded Potentials, Lienard-Wiechert Potentials  
+    - **Week 9**: Radiation from Moving Charges  
+    - **Week 10-11**: Special Relativity and the Covariant Formulation of Maxwell’s Equations  
+    - **Week 12-13**: Applications of Electromagnetic Theory to Modern Physics  
+    - **Week 14**: Advanced Topics: Plasma Physics and Magnetohydrodynamics  
+    - **Week 15**: Review and Final Exam  
+
+    **Textbooks**
+    - "Classical Electrodynamics" by John David Jackson
+    - "Introduction to Electrodynamics" by David J. Griffiths
+    """)
 
 with tab4:
-    st.markdown(phy614)
+    st.markdown("""
+    ## PHY 614: Quantum Mechanics I  
+    **Credits**: 3  
+    **Prerequisites**: PHY 520
+
+    **Course Description**  
+    An introduction to the fundamental principles and formalism of quantum mechanics, covering wave mechanics, the Schrödinger equation, angular momentum, and approximation methods. Applications to atomic and molecular systems will be discussed.
+
+    **Course Objectives**  
+    - Understand the formalism of quantum mechanics.
+    - Solve the Schrödinger equation for various potentials.
+    - Apply quantum mechanics to model atomic and molecular systems.
+
+    **Weekly Outline**
+    - **Week 1-2**: Introduction to Quantum Mechanics and the Schrödinger Equation  
+    - **Week 3-4**: Operators, Eigenvalues, and Measurement Theory  
+    - **Week 5-6**: The Harmonic Oscillator  
+    - **Week 7**: Angular Momentum and Spin  
+    - **Week 8-9**: The Hydrogen Atom  
+    - **Week 10-11**: Approximation Methods: Time-Independent Perturbation Theory  
+    - **Week 12-13**: Variational Principle and WKB Approximation  
+    - **Week 14**: Identical Particles and Symmetry  
+    - **Week 15**: Review and Final Exam Preparation  
+
+    **Textbooks**
+    - "Principles of Quantum Mechanics" by R. Shankar
+    - "Modern Quantum Mechanics" by J. J. Sakurai and Jim Napolitano
+    """)
 
 with tab5:
-    st.markdown(phy615)
+    st.markdown("""
+    ## PHY 615: Quantum Mechanics II  
+    **Credits**: 3  
+    **Prerequisites**: PHY 614
+
+    **Course Description**  
+    This course builds on Quantum Mechanics I, delving deeper into perturbation theory, scattering theory, symmetry, and invariance. Time-dependent quantum phenomena and applications to complex systems will be covered.
+
+    **Course Objectives**  
+    - Understand time-dependent perturbation theory.
+    - Apply quantum mechanics to scattering problems.
+    - Explore symmetry and invariance in quantum systems.
+
+    **Weekly Outline**
+    - **Week 1**: Review of Quantum Mechanics I  
+    - **Week 2-3**: Time-Dependent Perturbation Theory  
+    - **Week 4**: Fermi’s Golden Rule and Transition Rates  
+    - **Week 5-6**: Scattering Theory: Born Approximation, Partial Waves  
+    - **Week 7**: Symmetry and Conservation Laws  
+    - **Week 8-9**: Quantum Mechanics of Identical Particles  
+    - **Week 10-11**: Applications to Atomic and Molecular Systems  
+    - **Week 12-13**: Quantum Field Theory  
+    - **Week 14**: Open Quantum Systems and Decoherence  
+    - **Week 15**: Review and Final Exam  
+
+    **Textbooks**
+    - "Modern Quantum Mechanics" by J. J. Sakurai and Jim Napolitano
+    - "Quantum Mechanics: Concepts and Applications" by Nouredine Zettili
+    """)
 
 with tab6:
-    st.markdown(phy632)
+    st.markdown("""
+    ## PHY 632: Statistical Mechanics  
+    **Credits**: 3  
+    **Prerequisites**: PHY 504, PHY 520, PHY 522
+
+    **Course Description**  
+    This course provides an in-depth exploration of the principles of statistical mechanics and their applications to thermodynamics and various physical systems. Topics include thermodynamic description of matter, perfect gases, and quantum statistics.
+
+    **Course Objectives**  
+    - Understand the connection between statistical mechanics and thermodynamics.
+    - Solve problems involving classical and quantum statistical systems.
+    - Apply statistical mechanics to real-world physical systems.
+
+    **Weekly Outline**
+    - **Week 1**: Introduction to Statistical Mechanics and Thermodynamics  
+    - **Week 2-3**: Microcanonical Ensemble and Classical Thermodynamics  
+    - **Week 4-5**: Canonical Ensemble: Partition Functions, Thermodynamic Quantities  
+    - **Week 6-7**: Grand Canonical Ensemble: Applications to Gases  
+    - **Week 8**: Quantum Statistical Mechanics: Bose-Einstein and Fermi-Dirac Statistics  
+    - **Week 9-10**: Ideal Gases: Classical and Quantum Regimes  
+    - **Week 11**: Blackbody Radiation and Photon Gas  
+    - **Week 12**: Non-Ideal Systems: Interacting Gases and Phase Transitions  
+    - **Week 13-14**: Advanced Topics: Critical Phenomena, Renormalization  
+    - **Week 15**: Review and Final Exam Preparation  
+
+    **Textbooks**
+    - "Statistical Mechanics" by R.K. Pathria and Paul D. Beale
+    - "Statistical Physics: Volume 5 (Course of Theoretical Physics)" by L.D. Landau and E.M. Lifshitz
+    """)
+