Complete, detailed course contents in a summarised version in your own words; do not write names of books, do not paste official lecture description. Please write a course description IN YOUR OWN words of the subjects YOU studied in the class. Do not attach or copy/paste official course descriptions, do not wrtiten names of books. Example of good description of the lecture Numerical Methods: FORMAT: lecture: 2h, exercices: 2h, laboratory: 3h per week, 12 weeks, programming language: C++, CONTENTS: Computing with Matrices and Vectors, Direct Methods for linear systems of equations, Least Squares, Data Interpolation and Fitting, Filtering Algorithms, Approximation of Functions in 1D, Quadrature, Iterative Methods for non-​linear systems of equations. Example of good description of the lecture Linear Algebra: FORMAT: lecture: 2h, exercices 2h per week, 12 weeks, programming language: Python CONTENTS: linear equations, linear transformations, determinants, eigenvalues and eigenvectors, bilinear forms, canonical forms for matrices, euclidean and unitary vector spaces, selected applications. Example of bad description of lecture Numerical Methods: This lecture covers the most important and useful numerical methods and algorithms for this degree programe. Example of bad description of a lecture called "Mathematcis II": Name and Name, "Elementary Linear Algebra";  Name  and Name , "Complex Variables and Applications".

Your CV must contain a full and continuous history (no biographical gaps) of your education and work experiences until present. Start with high school up to the point your application is submitted (tabular resume). Your academic history in particular should be as detailed as possible and contain all academic degrees, with most recently earned degrees or degrees still in process listed first.

For completed programmes, please upload a scan of your degree certificate in addition to the official final transcript/academic record. The degree certificate is the official final document issued after successful completion of the degree programme. It specifies the awarded degree and the date of conferral. If your degree certificate has not yet been issued at the time of application, please provide a provisional degree certificate or graduation confirmation.

Official transcripts of records.

Letters from academia or from referees with an academic background are required.

Matriculation certificate - Please provide a scan of your matriculation certificate (e.g. High School Diploma, Diploma of Secondary Education, Abitur, GCE, IB Diploma).

Provide an insightful motivation letter – about a page - on why you choose our programme and ETH Zurich.

Please upload a scan of your valid passport (only page with photo, name, date of birth, expiry date). EU/EFTA citizens can also upload a copy of the valid ID (front and back), if no passport is available.

1. IELTS/TOEFL 2. GRE