Symmetry lies at the heart of todays theoretical study of particle physics. Our manuscript is a tutorial introducing foundational mathematics for understanding physical symmetries. We start from basic group theory and representation theory. We then introduce Lie Groups and Lie Algebra and their properties. We next discuss with detail two important Lie Groups in physics Special Unitary and Lorentz Group, with an emphasis on their applications to particle physics. Finally, we introduce field theory and its version of the Noether Theorem. We believe that the materials cover here will prepare undergraduates for future studies in mathematical physics.
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