School:Mathematics/Undergraduate/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
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 * 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

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