Most entering students have completed an undergraduate program in physics, including such courses as analytical mechanics, electricity and magnetism, optics and wave motion, electronics, and atomic physics; some advanced undergraduate laboratory work in physics is also expected. Knowledge of linear algebra, differential equations, and vector calculus is essential. Additional study in mathematics is desirable. The quality of undergraduate work and promise for graduate work are weighted more heavily than the extent of undergraduate study in physics and related subjects. Some entering students enroll in one or more undergraduate courses to make up deficiencies. Minimum IBT TOEFL scores required for consideration are: OVERALL 78 Writing: 20 Listening: 15 Reading: 20 Speaking: 23 The Graduate School requires an overall band score of a 7.0 or higher on the IELTS.The Physics Department requires a minimum speaking subscore of 7.0. three recommendations GRE scores are optional for all applicants and will only be used when they help raise the overall ranking of the application. Although optional, submission of the general and/or subject GRE scores is recommended for applicants interested in the specific research sub-fields of Theoretical Condensed Matter Physics and Theoretical Elementary Particle Physics.