A Mathematics Primer for Physics Students

This primer is meant to be both an introduction and summary of many mathematical methods that are needed to solve problems in advanced undergraduate or early graduate physics courses. The material is presented through example to demonstrate how it would be useful in the context of solving physics problems, with minimal use of formalism or proof. Topics include linear algebra; vector and tensor analysis; geometric tools such as metrics and curvature; mathematical groups, with emphasis on representation theory and Lie groups/algebras; complex calculus; integral transforms and differential equations; and an introduction to algebraic topology. An appendix is also included that summarizes various mathematical results which are useful to have in one place. This book would be ideal as a study guide to help students through difficult courses. Alternatively, it could be used as a supplementary text in a mathematical physics course, or even as a stand-alone book in its own right.

• Linear Algebra 1: The Basics
• Linear Algebra 2: Dual Spaces and Differential Forms
• Tensor Analysis and Euclidean Geometry
• Differential Geometry
• Group Theory 1: Discrete Groups
• Group Theory 2: Lie Groups and Algebras
• Complex Analysis
• Functional Analysis and Differential Equations
• Algebraic Topology
• Appendix: Review/Summary of Prerequisite Material