The mission of COMPOS is to help enthusiastic high school students to systematically learn mathematics and physics at a deep level.

#### How COMPOS works

- You will receive a homework assignment every 3-4 weeks. The assignment will consist of reading materials, links to online lectures and a problem set.
- We will help you learn through online teaching:
- Regular webinars will be offered by the COMPOS Academic Coordinator or one of the Oxford academics to all COMPOS students
- There will be an active online forum to discuss questions and difficulties.
- You will be assigned a tutor – normally a senior undergraduate or graduate Oxford Physics student. The tutor will provide weekly online classes in groups of 5-6 students.

- You will need to study the material in the assignment and solve the problem set before the deadline. You will then email your solutions to your tutor.
- The tutor will mark your work and email it back to you with comments and critique.

COMPOS is led by Prof. Alex Lvovsky. Academic Coordinator: Vlad Chernov

**Eligibility **

**Webinars and home work: **The homework will be publicly available and the webinars can be attended by any A-level student (Years 12 and 13)

**Tutorials**: You may participate in COMPOS tutorials if you are currently an A-Level student at a UK state school. However, in order to be eligible to participate in tutorials, you will also need to regularly submit high-quality homework. The first problem set will therefore serve as an admission test. We will assign you a tutor if you do a reasonably good job (i.e. solve most of the problems) in that set. Priority may also be given to students who are from groups under-represented within STEM.

#### Introductory video

## Syllabus and assignments

#### Year 12

**Mathematics**

- Assignment 1: The quadratic function - due November 15
- Assignment 2: Trigonometric transformations and equations - due December 05
- Assignment 3: Derivatives - due December 26
- Assignment 4: Basic integration skills - due January 23
- Assignment 5: Coordinate geometry - due February 13
- Assignment 6: Exponential and logarithmic functions - due March 6
- Assignment 7: Solving equations - due April 3
- Assignment 8: Analysis and graphic representation of functions - due April 24
- Assignment 9: Inequalities - due May 15
- Assignment 10: Sequences, progressions and series - due June 5
- Assignment 11: Combinatorics and probabilities - due July 10

*Physics*

- Assignment 1: Vectors in physics - due November 15
- Assignment 2: Equations of motion - due December 05
- Assignment 3: Newton's laws - due December 26
- Assignment 4: Centre of mass and statics - due January 23
- Assignment 5: Conservation of momentum - due February 13
- Assignment 6: Work, energy and power - due March 6
- Assignment 7: DC circuits - due April 3
- Assignment 8: Reflection and refraction - due April 24
- Assignment 9: Spherical lenses and mirrors - due May 15
- Assignment 10: Simple harmonic motion - due June 5
- Assignment 11: Electrostatics and capacitors - due July 10

#### Year 13

*Mathematics*

- Complex numbers
- Inverse and partial derivatives
- Euclidian geometry 1
- Euclidian geometry 2
- Exam practice 1
- Conic sections
- Infinite sets
- 3D geometry
- Gaussian function, Dirac delta function, fourier analysis
- Exam practice 2

**Physics**

- Circular motion and rotational mechanics
- Gravity and orbits
- Differential equations in physics
- Magnetic fields
- Exam practice 1
- Electromagnetic induction and LC circuits
- Damped and forced oscillations
- Thermodynamics
- Wave phenomena
- Exam practice 2

#### Webinars

The webinars take place every Tuesday 18:30-19:30, unless announced otherwise. The Zoom links are sent to the COMPOS discussion group. The recordings are posted below.

## FAQ

**How can I join?**

Please complete the form above to receive the first assignment and an invite to the webinar. The registration will remain open till the first homework deadline (October-November).

**How much does it cost?**

COMPOS is free of charge to state school students. The costs are borne by a philanthropic donation from Mathematics Education for Social Mobility & Excellence (MESME), to whom we are supremely grateful. Private-school and non-UK students please see below.

**Will you prepare me for Oxbridge admission tests, A-Level examinations, or Olympiads?**

Our goal is not to prepare you for a pilot license test, but to teach you how to fly! We do not target any specific tests, but we certainly hope that that the knowledge and problem-solving skills you acquire at COMPOS will help you to pass such tests, and possibly do well in competitions.

**Will you prepare me for higher education in maths and physics?**

We do aim to provide you with base knowledge, upon which it will be easier for you to build your further education. We also hope that you will acquire a somewhat accurate idea of what everyday work in science is like and learn to be not afraid of it.

**How many places do you have in the program?**

We have ~300 places in the program next year, which we hope will enable us to accommodate every deserving candidate.

**How much time do I have to commit to the program?**

In addition to the weekly tutorials, you will need to plan to work on the assignments for at least five to ten hours per week. This is a serious time commitment; you will have to sacrifice a lot of partying, sports, dating, and other fun activities! Please think carefully what you are signing up for.

**I am a private school student and/or I am not in the UK. Can I join?**

Our funder's wish is that the free COMPOS services be offered to UK state school students only. However, we are working on making the COMPOS curriculum available to private school students and students outside the UK through a non-profit organization for a moderate fee. So please do sign up via the link above and we will let you know soon if we can help.

**Can I take only math or only physics at COMPOS?**

No: the two parts of the program are deeply interconnected, so we expect our students to study both subjects.

**Do I need a tablet for the tutorials?**

This is helpful: a stylus-enabled tablet allows us to create a virtual whiteboard, on which you, the tutor and other tutorial group members can write at the same time. However, there are inexpensive alternatives such as stylus pads. In the worst-case scenario, you can contribute to discussions using your phone camera.

**I cannot attend on a specific day of the week.**

There will be multiple groups with different tutors, so we can surely find you a group that meets your restrictions.

**Will I get a certificate in the end?**

The tutors will keep track of the problems from the assignments that each student has solved. We will be happy to provide a letter in the end of the course certifying the progress you have made. However, such a certificate is not of much use for college admission: particularly at Oxford, we never ask our candidates to produce paperwork of any kind, but we do test their knowledge and problem-solving skills. These are your true certificates, and they will stay with you forever.

Registration for teachers - please fill in this form if you wish to hear about our openings

**Contact us**

If you have any questions, please get in touch with Mr Chernov by email via vladimir.chernov[at]physics.ox.ac.uk