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Attending Cambridge Immerse has taught me invaluable lessons that go beyond the framework of classroom learning. I feel that after two weeks I have developed both intellectually and as a person in general, a result of the rapid pace of teaching and the fantastically motivated group of peers I learned alongside. – Sophie, United Kingdom

Mathematics

  • Maximum tutorial size: 10 students
  • Oxbridge style tutorials
  • Personal Project and Assessment
  • Certificate of Participation
  • University preparation workshops
  • Inclusive of excursions
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Overview of course

  • Session 1: July 23rd 2017 – August 5th 2017
  • Session 2: August 6th 2017 – August 19th 2017
  • Residential in a central University of Cambridge college
  • Classes designed and taught by University tutors
  • A variety of carefully planned skills workshops
  • Dedicated university and subject specific advice
  • Inclusive of all excursions and extracurriculars
  • Diverse range of international participants
  • Participant Assessment
  • Certificate of Participation

Summary

Cambridge Immerse is a unique two week residential educational experience with a diverse and enriching curriculum, designed and taught by Cambridge University and Oxford University tutors. Tutorials and seminars are taught by experts in an optimal learning environment that stimulates academic enquiry; yet the carefully planned schedule ensures that the programme not only meets the academic needs of the participants, but also provides a unique insight into the university city through an abundance of extracurricular activities.

The Cambridge Immerse Mathematics course is both challenging and engaging, with students learning in small groups to ensure that each student’s needs are addressed. In addition to covering material that is studied at the A-level and IB-level, students are also taught advanced university-level topics in a way that is approachable and easy to understand.

In addition to consolidating students’ existing understanding of Mathematics, the course introduces students to more advanced topics and debates that will not only spur intellectual curiosity, but will also assist in preparing to study the discipline at university level.

Academic Content & Learning Objectives

The Cambridge Immerse course is designed to give students an introduction to the undergraduate level Mathematics; in addition to extending the existing mathematical knowledge of participants, the course focuses upon showing how these concepts can applied to other areas.

Core topics explored within the programme include:

  • Calculus – This is the study of ‘Differentiation’. This course moves on from the topics covered in the school environment to the advanced differentiation of functions involving many explicit and implicit variables.
  • Analysis – This is a theoretical study of Mathematics. By using fundamental axioms, students will grow to understand what a mathematical proof really involves, and the skills required to construct rigorous and knowledgeable arguments.
  • Integration – This part of the course focusses upon integration by parts and integration by substitution, and their practical applications.
  • Statistics – A course introducing statistical techniques and methods, with lots of real-life examples so students can relate the abstract methods taught to real world environments.
  • Mathematical Finance – This topic covers mathematical accounting and financial derivative, demonstrating the applicability of mathematical concepts and techniques to the ‘real’ world.
  • The Philosophy of Mathematics – Students are encouraged to explore the major developments in mathematics and the philosophical impact they have had on the topic. This course will allow students to develop an appreciation for how mathematical results often overlap with deep philosophical questions.

Subject Requirements: Students are expected to be studying Mathematics, and to be familiar with algebra, integration and differentiation. All students are sent preparatory material 6 weeks before the programme commences, to ensure that all students are familiar with the core concepts.

Induction is an extremely powerful method of proof used throughout mathematics. It deals with infinite families of statements which come in the form of lists. The idea behind induction is in showing how each statement follows from the previous one on the list – all that remains is to kick off this logical chain reaction from some starting point. In order to do this, we will first establish the mathematical language that we will use throughout the programme and we will study some basic concepts in Set Theory too.

Solving quadratic equations is something that mathematicians have been able to do since the time of the Babylonians. If we imagine the square root of −1 to exist, then there is a beautiful theory we can create. We will discuss some introductory ideas associated with complex numbers, their algebra and geometry. This includes a look at their importance in solving polynomial equations, how complex numbers add and multiply, and how they can be represented.

Topology is the mathematical study of the properties that are preserved through deformations, twistings, and stretchings of objects. Tearing, however, is not allowed. A circle is topologically equivalent to an ellipse (into which it can be deformed by stretching). A ring torus is homeomorphic to the cartesian product of two circles S1 × S1. The torus has a generalization to higher dimensions, the n-dimensional torus, often called the n-torus or hypertorus. It is an example of an n-dimensional compact manifold and of a compact abelian Lie Group. We will introduce the concept of metric and topological spaces where we will see that we can actually define square balls. What is more, we will develop the required concepts to see if we can transform a doughnut into a coffee cup.

Exceptional teaching

We offer participants a choice of a range of subjects, from the arts to the sciences. All the subjects taught at Cambridge Immerse are taught by current or past tutors of Cambridge University or Oxford University. Our rigorous vetting process ensures that all students are taught by tutors who are engaging and supportive - and most of all, enthusiastic to share their expertise.

Our philosophy is that our participants should be challenged with interesting academic concepts; whilst our tutors create a welcoming and supportive environment in which our participants feel comfortable and thrive.

You will be encouraged to delve into and explore the current debates and issues within your chosen discipline in carefully planned tutorials that emulate the unique Oxbridge system of tutor-student engagement and debate. This is an approach that goes beyond the superficial and provides unique insights that are both refreshing and intellectually stimulating.

What is certain is that you will emerge undoubtedly far more confident and knowledgeable in your chosen discipline, tackling challenging yet interesting topics that we hope will further your academic passions. Students can now opt to study up to two subjects during the programme. Subjects that we offer include:

Participant Assessments

Throughout the programme, our tutors monitor student engagement with the topics that they have been taught. After the programme, a Participant Assessment is written by the tutor, evaluating participant progress and also making recommendations on how to most effectively advance participant's understanding and interest in the topics that have been explored.

Interview Skills Workshops (Optional)

Within our carefully designed interview skills workshops, students will gain an insight into the core skills required to successfully articulate their viewpoints in a pressured environment. These workshops focus upon developing the confidence and intellectual tenacity required to tackle some of the key questions that might be asked during interview, in addition to addressing debates surrounding some of the most pertinent issues within the discipline at the moment. The Interview Skills workshops are included within the programme fee, though attendance is optional.

Personal Statement Consultations (Optional)

Over the duration of the Cambridge Immerse course, students will have the opportunity to develop drafts of their personal statements required for access to universities across the world with the expertise and assistance of highly regarded tutors. Students learn techniques to concisely express their interest in a particular discipline, crafting a compelling personal statement that showcases achievements and interest in a subject. The Personal Statement consultations are included within the programme fee, though attendance is optional.

Extracurricular diversity

Cambridge Immerse provides a truly immersive experience of university life. Not only will you discover and further your academic interests, you will also delve into the exciting and often fascinating spectrum of cultural activities available in Cambridge. The opportunity to experience daily organised excursions also allows the chance to socialise with like-minded peers from a diverse range of backgrounds and to quickly familiarise yourself with the city.

Activities organised as part of the programme include:

  • A summer’s afternoon punting down the River Cam, a quintessential Cambridge affair.
  • A day trip to Oxford, the home of Cambridge University’s arch ‘rival’.
  • Formal dining in Cambridge’s famous medieval banquet halls.

Visit our activities page to view the full range of subjects that we offer.

Timetable

The Cambridge Immerse schedule is packed with a wide range of unique academic and extracurricular activities.

Participants start off the day with breakfast in the main college dining hall, with a variety of continental and hot breakfast choices available. This is followed by the first academic session of the day, which takes place in a seminar or lecture format. Participants are then guided to lunch at some of Cambridge’s finest sandwich bars and cafés, and are welcome to explore the city in small groups. Following lunch, academic sessions continue in the format of small tutorial groups or workshops. After all the core academic sessions are finished, students are treated to one of a wide range of excursions and cultural activities, including punting, museum visits and sports activities. A three course dinner in the college dining hall is then followed by an evening social event to help participants wind down and socialise after a packed day.

The timetable shown to the side offers an insight into the typical daily schedule, although this may vary depending on the events planned on the given day.

A typical day..

Rollover each days activity to update content to the left.
 
 
08:00 - 09:30
Breakfast
10:00 - 12:00
Morning academic session
12:00 - 13:30
Lunch
13:30 - 15:30
Afternoon tutorial
16:00 - 18:00
Activity / Excursion / Workshop
18:00 - 19:15
Dinner
19:30 - 22:00
Evening social event

Unrivalled support system

We place a huge emphasis on creating a supportive and approachable environment at Cambridge Immerse. Our mentors are a team of friendly, specially trained graduates and undergraduates from Cambridge University, who help our participants quickly settle into the programme. The mentors have first hand experience with a variety of academic and non-academic issues and are therefore in the best position to offer friendly, confidential one-to-one advice. It’s an unrivalled support network that we’re incredibly proud of.

Mentors have studied a range of disciplines, allowing them to share their own insights and experiences of their academic careers. Each participant is also assigned a mentor, at a ratio of six students to one mentor, all of whom are enthusiastic to help participants to help create a ‘home away from home’.

Accommodation

Cambridge Immerse takes place in Cambridge University’s most stunning and historic centrally located colleges. To find out which college you will be accommodated in, contact us.

All participants will be accommodated in their own individual bedrooms, equipped with high speed internet access. Corridors or staircases separate male and female students, and bathrooms are en-suite or shared between just a few participants. The college site is secured and monitored at all times. Visit our ‘Campus’ page for further information.

Practical Information

Travel Information: The fee for Cambridge Immerse is not inclusive of travel to Cambridge. There are several transport options available, including arriving in Cambridge by rail, coach or flight. Please contact us if you need assistance planning your journey to Cambridge.

For international participants, we arrange a shared airport transfer service from London Heathrow Airport to Cambridge. Dedicated staff members meet the participants at the airport terminal of their arrival. Participants are able to book this service once they have secured their place on the programme.

Medical and Dietary Requirements: We are able to cater for most dietary requirements (vegetarian, vegan, nut allergies, halal, kosher); please do not hesitate to contact us if you are unsure if we can cater for your dietary requirements. Breakfast and evening meals are included in Cambridge Immerse, and participants are expected to make their own provisions for lunch at various delicious eateries around Cambridge.

Other information: Students must be aged between 16-18 at the time of attendance in 2017. Students are expected to be fluent / near-fluent in English.

Participate in 2017

Cambridge Immerse is a residential summer course consisting of outstanding academic classes, excellent skills workshops and exciting extracurricular activities in the historic university city of Cambridge. Cambridge Immerse runs in the following 2 week sessions:

  • Early July Session: 9th July - 22nd July 2017
  • Session 1: 23rd July – 5th August 2017
  • Session 2: 6th August – 19th August 2017

We would be happy to assist you if you have any questions prior to booking your place. For the fastest response to your enquiry, please email:

enquiries@cambridgeimmerse.com

Take a look at what our students have to say about the Mathematics programme

Attending Cambridge Immerse has taught me invaluable lessons that go beyond the framework of classroom learning. I feel that after two weeks I have developed both intellectually and as a person in general, a result of the rapid pace of teaching and the fantastically motivated group of peers I learned alongside. – Sophie, United Kingdom

Enrol now