Mathematical Techniques

Notes

References

All Subjects

• Mathematical Physics by Sadri Hassani
• Mathematics for Physics and Physicists by Walter Appel

Linear Algebra

• Matrix Analysis and Applied Linear Algebra by Carl Meyer

Complex Analysis

• Complex Variables and Applications, 9th Edition by James Brown and Ruel Churchill

Partial Differential Equations and Fourier Series

• An Introduction to Partial Differential Equations by Yehuda Pinchover and Jacob Rubenstein
• An Introduction to Partial Differential Equations, 2nd Edition by Walter Strauss
• Introduction to Fourier Analysis and Wavelets by Mark Pinsky

Group Theory

• Visual Group Theory by Nathan Carter
• Group Theory and Quantum Mechanics by Michael Tinkham
• Lie Algebras in Particle Physics by Howard Georgi
• Group Theory and its Application to Physical Problems by Morton Hamermesh
• Quantum Theory, Groups, and Representations by Peter Woit
• Lie Groups, Lie Algebras, and Representations by Brian Hall
• Lie Groups, Lie Algebras, and Some of Their Applications by Robert Gilmore
• Semi-Simple Lie Algebras and Their Representations by Robert Cahn
• Affine Lie Algebras and Quantum Groups by Jürgen Fuchs
• Symmetries, Lie Algebras, and Representations by Jürgen Fuchs and Christoph Schweigert

Differential Geometry and Variational Calculus

• Differential Geometry by Erwin Kreyszig
• Tensors, Differential Forms, and Variational Principles by David Lovelock and Hanno Rund
• Theoretical Studies of Fluid Membrane Mechanics by Martin Müller

Manifolds

• Geometry, Topology, and Physics by Michio Nakahara
• Introduction to Smooth Manifolds by John Lee
• Introduction to Topological Manifolds by John Lee
• Introduction to Riemannian Manifolds by John Lee

Operator Algebras

• Functional Analysis by Balmohan Vishnu Limaye
• Introductory Functional Analysis with Applications by Erwin Kreyszig
• Notes on Operator Algebras by Jesse Peterson
• A Mathematical Introduction to Conformal Field Theory by Martin Schottenloher
• An Introduction to K-Theory for C*-Algebras by M. Rørdam, F. Larsen, and N. Laustsen