Topics In Undergraduate Mathematics

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The PDF file is available here. The latest version can be found at this GitHub repository.

Description

I began writing this book during the mid-year break in 2023, which was when I had a bit of free time to read up on undergraduate mathematics. This book mainly serves as my notes when studying undergraduate mathematics. Feel free to refer to it too.

Content

As of now, the following chapters have been largely (>50%) completed. More will be added soon!

Preliminary Topics

• Mathematical Reasoning and Logic
• Set Theory

Abstract Algebra

• Groups

Linear Algebra

• Vector Spaces
• Linear Maps
• Polynomials
• Eigenvalues and Eigenvectors

Real Analysis

• Real and Complex Number Systems
• Basic Topology
• Numerical Sequences and Series
• Continuity
• Differentiation
• Riemann-Stieltjes Integral
• Sequences and Series of Functions
• Some Special Functions