School:Mathematics/Undergraduate/Pure Mathematics

Riemann Zeta function, depicted, the modulus of ζ(1/2 + xi). This function — specifically, its zeros — are at the basis of Riemann's hypothesis, an unsolved problem in pure mathematics

Broadly speaking, pure mathematics is mathematics motivated entirely for reasons other than application. From the eighteenth century onwards, this was a recognised category of mathematical activity, sometimes characterised as speculative mathematics, and at variance with the trend towards meeting the needs of navigation, astronomy, physics, engineering and so on.

Courses

• Foundations of Pure Mathematics
• School of Mathematics:Introduction to Proofs
• School:Mathematics/Foundation of mathematical concepts
• School of Mathematics:Introductory Real Analysis
• School:Mathematics/Introduction to Abstract Algebra
• School of Mathematics:Introduction to Graph Theory
• School:Mathematics/Calculus
• Introduction to Set Theory

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Texts for reference

Algebra

• Proofs
• Complex numbers
• Vectors in two dimensions
• Matrices
• Vector spaces
• Linear transformations
• Eigenvalues and eigenvectors

Abstract algebra

• Groups
• Rings

• Matrices
  • Eigenvalues and eigenvectors
• Vector spaces
• Linear transformations
  • Inner product spaces
• Proofs

Analysis

• Complex Analysis
• Real Analysis
• Topology

Calculus

• Functions
• Limits
• Differentiation
• Applications of Derivatives
• Higher Order derivatives
• More differentation rules
• Summation notation
• Integration
• Vectors
• Applications

Discrete mathematics

• Set theory
• Functions and relations
• Number theory
• Logic
• Enumeration
• Graph theory
• Recursion
• Number representations
• Modular arithmetic
• Polynomials and number theory
• Finite fields

Differential geometry

• Lie Algebras
• Information geometry

Foundations

• Set Theory