I am advising a student on her senior math thesis. She would like to involve chemistry somehow (her other major). I know no chemistry. I have read in several places that representation theory features prominently in some areas of chemistry. When I try to read anything online I am not sure how much chemistry one needs to assume. So, if my student is in her senior year of a chemistry major, are there any places where she can start to look for a project in group theory and chemistry?
Several answers and comments have suggested general texts that have good foundation information; however if a student is writing a thesis, these sources will be insufficient since they are geared towards the teaching of group theory rather than the application of group theory to generate new knowledge. Even at an undergraduate level, there should be an attempt to generate new knowledge in a thesis. To do this, the student would need to get her nose in the chemical literature, and I assume any student in an ACS accredited undergraduate program has experience with literature searches. My very brief survey of group theory reviews came up with the following potentially interesting areas:
- understanding the structure of natural and synthetic perovskites, which have a number of technological applications. Journal of Physics: Condensed Matter (2013), 25(17), 175902
- Stereochemistry of medicinal compounds: Helvetica Chimica Acta (2013), 96(1), 4-30.
- the role of group theory in furthering our understanding of superconductivity: Comptes Rendus Physique (2011), 12(5-6), 532-541.
- Group theory and biomolecular conformations: Journal of Physics: Condensed Matter (2010), 22(32), 323103/1-323103/21.
- A somewhat esoteric area of nuclear point groups: Acta Physica Polonica B (2013), 44(3), 305-318.
Almost certainly, a senior has encountered the importance of symmetry in Inorganic Chemistry and IR spectroscopy, and these areas may be more accessible to the student. In the end, however, good questions and topics for a senior thesis are going to require getting ones nose in the literature.
The first 4 chapters of Chemical Applications of Group Theory by F A Cotton* should be enough for your student. However there are numerous books available.
* The Internet Archive holds both the first edition by 1962, as well as the third by 1989. Both are available as .epub and .pdf for a 14 day loan.