Undergraduate-Statistical-Mathematics

The books in this repository are selected for references according to my own three-year experience as an Undergraduate of Mathematics for Statistics at Imperial College London.

Year 1

1. Calculus

• Apostol - Calculus
• Thomas - Calculus

2. Mathematical Analysis

• Apostol - Mathematical Analysis
• Rudin - Principles of Mathematical Analysis
• Polya - Problems and Theorems in Analysis
• Tao - Analysis

3. Basic Topology

• Munkres - Topology
• Armstrong - Basic Topology

4. Elementary Probability Theory

• Bertsekas - Introduction to Probability
• Stirzaker - Elementary Probability
• Anderson - Introduction to Probability

5. Linear Algebra

• Strang - Introduction to Linear Algebra
• Meckes - Linear Algebra

Year 2

1. Differential Equations

• Rogers - An Introduction to Partial Differential Equations
• Braun - Differential Equations and Their Applications

2. Real Analysis

• Kolmogorov - Elements of the Theory of Functions and Functional Analysis
• Folland - Real Analysis Modern Techniques and Their Applications
• Stein - Real analysis

3. Probability and Random Processes

• Nelson - Probability, Stochastic Processes and Queueing Theory
• Grimmett - Probability and Random Processes
• Grimmett - One Thousand Exercises in Probability

4. Probability and Statistics

• DeGroot - Probability and Statistics
• Casella - Statistical Inference

5. Basic Python

• Matthes - Python Crash Course
• Downey - Think Python

6. Mathematical Logic

• Goldrei - Propositional and predicate calculus a model of argument
• Mendelson - Introduction to Mathematical Logic

Year 3

1. Functional Analysis

• Lang - Real and Functional Analysis
• Bogachev - Real And Functional Analysis
• Kirillov - Theorems and Problems in Functional Analysis

2. Integration and Probability

• Shiryaev - Probability
• Malliavin - Integration and Probability

3. Time Series

• Fuller - Introduction to Statistical Time Series
• Hamilton - Time Series Analysis

4. Stochastic Simulation

• Martino - Independent Random Sampling Methods
• Asmussen - Stochastic Simulation-Algorithms and Analysis
• Robert, Casella - Monte Carlo Statistical Methods

5. Statistical Learning

• James - An Introduction to Statistical Learning
• Hastie - The Elements of Statistical Learning

6. Python with Data

• VanderPlas - Python Data Science Handbook
• Mckinney - Python for Data Analysis