29::009 Directions in Modern Physics: Lecture Notes

Spring Semester 1999

Instructor: Prof. Yannick Meurice

Part 1: Determinism, Chance and Chaos

1. Simple examples of Dynamical Systems
   • Introduction
   • Linear maps
   • Square root of 2 (Newton's way)
   • Translation on a circle
   • Two independent circular motions
   • The quadratic map
2. Chance
   • The quadratic map at a=2
   • Random Number Generators
   • Coin Tossing
   • Average and Fluctuations
3. Newtonian Mechanics
   • Deterministic Evolution with Continuous Time
   • Ordinary Differential Equations
   • Newton's Laws
   • Periodicity, Quasiperiodicity and Chaos
4. Strange Attractors
   • A few words about fluid mechanics
   • Limit cycles
   • The onset of turbulence

Part 2: Cosmology

1. Transition: Newtonian Gravity
2. Beyond Newton's Mechanics
   • Maxwell's Equations
   • Special Relativity and General Relativity
   • Quantum Mechanics
   • QED
   • The Standard Model
3. The Expansion of the Universe
   • The Doppler Effect
   • Hubble's Law
   • Cosmological Models
   • The cosmic microwave background
4. The history of the universe
   • The building blocks of matter
   • The first three minutes
   • The inflationary universe