Sets
Collections of objects

Logic
The formal language of mathematics 
Sets
Collections of elements 
Functions
Mappings between sets
Real Analysis
Realvalued numbers and functions

Real Numbers
Scalar quantities 
Sequences
Ordered collections of numbers 
Limits
Behaviour as points are approached 
Series
Sums of numbers 
Continuity
Whether a function is unbroken 
Derivatives
A function's rate of change 
Integrals
The space under a function
Linear Algebra
Representations of linear systems

Vector Spaces
Spaces supporting addition and scalar multiplication of elements 
Inner Product Spaces
Vector spaces with additional structure 
Matrices
Multidimensional data structures 
Determinants
Fundamental property of square matrices 
Eigenvalues and Eigenvectors
Fundamental decomposition of square matrices 
Matrix Decompositions
Decompositions of square and nonsquare matrices 
Linear Transformations
Mappings between vector spaces
Probability
Occurrences of uncertain events

Events
Sets of experiment outcomes 
Probability Spaces
Model for assigning probabilities to events 
Conditional Probability
Using events that have occurred 
Random Variables
Mapping from outcomes to a measurable space 
Distributions
Common functions describing random processes 
Moments
Information about a distribution's shape 
Limit Theorems
Behaviour after many outcomes have been observed 
Concentration Bounds
Inequalities describing deviation of random variables 
Probabilistic Convergence
Behaviour after randomness is observed for a while 
Stochastic Processes
Models for random systems
Statistics
Drawing conclusions from data

Sampling
Selection of observations from a population 
Estimators
Calculating parameter values from data 
Point Estimation
Finding parameter values from data 
Interval Estimation
Finding plausible ranges of parameter values from data 
Hypothesis Testing
Deciding whether data supports an idea
Optimisation
Maximising and minimising functions

Convexity
Fundamental property of a function's shape 
Unconstrained Optimisation
Finding maximum and minimum values 
Constrained Optimisation
Reducing set of valid optimal values