Mathematics Degree Template

Undergraduate

First Year

• Proofs / Transition to Advanced Mathematics
  • Prerequisites: None / High School Mathematics.
• Calculus I (Single Variable Calculus / Series, Limits, and Continuity.)
  • Prerequisites: Precalculus.
• Calculus II (Single Variable Calculus / Differentiation and Integration.)
  • Prerequisites: Calculus I.
• Linear Algebra
• Classical Mechanics I (Mechanics of Lagrange and Hamilton.)
• Programming I (Introduction to Programming)
• Statistics I
• Geometry I (Eucledian Geometry)

Second Year

• Calculus III (Multi Variable Calculus / Partial Derivatives and Vector Calculus.)
  • Prerequisites: Calculus II.
• Complex Analysis
• Abstract Algebra / Modern Algebra I (Group Theory)
  • Prerequisites: None / High School Mathematics.
• Geometry II (Differential Geometry)
• Numerical Analysis
• Classical Mechanics II (Waves)
• Programming II (Data Structures and Algorithms)
• Statistics II

Third Year

• Real Analysis
  • Prerequisites: Calculus I and Calculus II.
• Elementary Number Theory
  • Prerequisites: None / High School Mathematics.
• Abstract Algebra / Modern Algebra II (Ring Theory, Field Theory, and Galois Theory)
  • Prerequisites: Abstract Algebra / Modern Algebra I.
• Topology (Point-Set Topology)
  • Prerequisites: Real Analysis.
• Differential Equations.
  • Prerequisites: Calculus I, II, and III.

Graduate

First Year

• Measure Theory
• Algebraic Geometry
  • Prerequisites: Abstract Algebra / Modern Algebra I and II.
• Sympleptic Geometry
• Riemannian Geometry / Riemann Surfaces
• Algebraic Topology
• Algebraic Number Theory
  • Prerequisites: Elementary Number Theory.
• Functional Analysis
• Harmonic Analysis
• Lie Theory
• Non-Linear Dynamics
• Spectral Theory
• Ergodic Theory
• Knot Theory
• Permutation Groups

Second Year

• Thesis