MATHEMATICS

Mathematics Summer School in Cambridge

MATHEMATICS

Academic insights for 16-18 year olds

Programme Overview:

  • Programme: Mathematics university insights
  • Price: £4,495
  • Course Length: 2 weeks
  • Course Type: Residential
  • Locations: Cambridge, UK
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Summary

math summer school

Mathematics is a powerful tool and its influence can be found in almost all walks of life. From engineering, medicine and the sciences to finance, economics and business, maths is a broad subject that offers many avenues.

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Some of our most influential thinkers and most prominent theories have their grounding in mathematics. By opting to study mathematics, students are placing themselves in an excellent position to embark on a challenging yet highly rewarding career.

The gulf between mathematics at undergraduate and school level can be large. This often leaves students unprepared and overwhelmed by tertiary education maths. Immerse Education addresses this imbalance by introducing students to undergraduate level content in an comprehensible and engaging manner. Students leave with a new found confidence in approaching challenging material, something that will prove invaluable at university.

Summary

Mathematics is a powerful tool and its influence can be found in almost all walks of life. From engineering, medicine and the sciences to finance, economics and business, maths is a broad subject that offers many avenues.

Some of our most influential thinkers and most prominent theories have their grounding in mathematics. By opting to study mathematics, students are placing themselves in an excellent position to embark on a challenging yet highly rewarding career.

The gulf between mathematics at undergraduate and school level can be large. This often leaves students unprepared and overwhelmed by tertiary education maths. Immerse Education addresses this imbalance by introducing students to undergraduate level content in an comprehensible and engaging manner. Students leave with a new found confidence in approaching challenging material, something that will prove invaluable at university.

Immerse is an inspirational academic programme for the intellectually curious.

Key Facts

Dive into a number of exciting topics

Learn about the practical applications of mathematics

Study in university style tutorials made up of small groups

Benefit from the expert tutelage of some of the brightest minds in the field

Explore the historic city of Cambridge

Experience student life in the UK

Topics Covered

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Constructive Mathematics
Constructive mathematics is the mathematics of iterative methods, which arise everywhere in the subject. For example, Niels Abel famously proved that we cannot in general write down the solution to polynomial equations of degree 5 or higher; but of course there will be cases where we need to know the answer! The first place to turn to is an iterative method – a process in which we continually apply the same “action” to a given input, in the (mathematically justified) hope that this process eventually outputs something close to the true answer that we seek.

However, in the context of real world applications, imagine that the solution of this problem is an essential parameter in the design of say, a satellite or a heavy load carrying bridge. In this case, you need to be sure that the approximate solution is sufficiently close to the true solution – this requires careful, rigorous, and rewarding mathematical analysis.

Probability
The famous “Monty Hall problem” will tell you that the theory of probability is not always as simple as you may think; what does it really mean to say that two events occur independently (successively flipping a coin for example)? What is your probability of success in a game of dice? There are numerous problems in probability, however where the events are not independent, for example: two golfers (A and B) are at a driving range, their golf balls are both different, but they have ended up in the same bucket. After picking out 5 balls at random, what is the probability that all of the balls belong to “golfer A”? Of course, we need more information to determine the answer in this case, but it is immediately clear that this “conditional probability” makes things more complex.

Below you’ll find a list of topics that you’ll explore in detail with your peers/class:

  • Constructive mathematics
  • Probability
  • Integration
  • Systems of linear equations
  • Abstract vector spaces

Topics Covered

Constructive Mathematics
Constructive mathematics is the mathematics of iterative methods, which arise everywhere in the subject. For example, Niels Abel famously proved that we cannot in general write down the solution to polynomial equations of degree 5 or higher; but of course there will be cases where we need to know the answer! The first place to turn to is an iterative method – a process in which we continually apply the same “action” to a given input, in the (mathematically justified) hope that this process eventually outputs something close to the true answer that we seek.

However, in the context of real world applications, imagine that the solution of this problem is an essential parameter in the design of say, a satellite or a heavy load carrying bridge. In this case, you need to be sure that the approximate solution is sufficiently close to the true solution – this requires careful, rigorous, and rewarding mathematical analysis.

Probability
The famous “Monty Hall problem” will tell you that the theory of probability is not always as simple as you may think; what does it really mean to say that two events occur independently (successively flipping a coin for example)? What is your probability of success in a game of dice? There are numerous problems in probability, however where the events are not independent, for example: two golfers (A and B) are at a driving range, their golf balls are both different, but they have ended up in the same bucket. After picking out 5 balls at random, what is the probability that all of the balls belong to “golfer A”? Of course, we need more information to determine the answer in this case, but it is immediately clear that this “conditional probability” makes things more complex.

Below you’ll find a list of topics that you’ll explore in detail with your peers/class:

  • Constructive mathematics
  • Probability
  • Integration
  • Systems of linear equations
  • Abstract vector spaces

The Immerse programme covers a unique mix of important
theory and practical knowledge. Learn more about the topics covered in this
course by requesting a free course syllabus

Course Outcomes

The gap between high school or A-level mathematics and a university programme is vast. Students will need to not only learn practical maths skills, but also develop an understanding of the theoretical concepts surrounding the subject as well as discover how to analyse and even solve some of the most complex mathematical problems.

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On an Immerse Education residential programme, participants will have the chance to gradually explore some of these topics in a progressive pace and in a manner that is suitable to their age and level. As a result, they will be able to bridge the gap between what they now know and what they will need to know to succeed at university.

In completing the course, students will:

  • Get a headstart in studying mathematics at university
  • Experience student life in the UK
  • Learn a number of valuable study skills
  • Develop and nurture their passion for the subject
  • Meet like-minded people to discuss complex ideas
  • Be able to make an informed decision about their future studies
  • Benefit from the experience and expertise of academic leaders
  • Explore numerous fascinating and relevant topics

Students in this course will receive personalised feedback from their tutors about their performance, the material covered, and even a list of individualised suggestions for further study.

Course Outcomes

The gap between high school or A-level mathematics and a university programme is vast. Students will need to not only learn practical maths skills, but also develop an understanding of the theoretical concepts surrounding the subject as well as discover how to analyse and even solve some of the most complex mathematical problems.

On an Immerse Education residential programme, participants will have the chance to gradually explore some of these topics in a progressive pace and in a manner that is suitable to their age and level. As a result, they will be able to bridge the gap between what they now know and what they will need to know to succeed at university.

cambridge mathematics

In completing the course, students will:

  • Get a headstart in studying mathematics at university
  • Experience student life in the UK
  • Learn a number of valuable study skills
  • Develop and nurture their passion for the subject
  • Meet like-minded people to discuss complex ideas
  • Be able to make an informed decision about their future studies
  • Benefit from the experience and expertise of academic leaders
  • Explore numerous fascinating and relevant topics

Students in this course will receive personalised feedback from their tutors about their performance, the material covered, and even a list of individualised suggestions for further study..

Timetable

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

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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.

Timetable

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

A typical day

 
 
08:00 - 09:30
Breakfast
09:30 - 11:30
Morning academic session
11:30 - 13:30
Lunch
13:30 - 15:30
Afternoon academic session
16:00 - 18:00
Academic workshop / Afternoon activity
18:00 - 19:15
Dinner
19:30 - 22:00
Evening social event

Graduation & Participant Assessment

The final evening of the programme celebrates the achievements of each participant in a graduation ceremony that's followed by a Gala Dinner. Throughout the Cambridge summer programme, our Immerse tutors will monitor student engagement with the topics that they have been taught. Once the programme has finished, the tutor will write a Participant Assessment...MORE

...that will evaluate how the participant responded to the materials they were introduced to, what progress they made during the sessions, and offer recommendations on how to most effectively advance participant's understanding and interest in the topics that have been explored.

We strongly believe that our Participant Assessments are crucial element of the learning process, and reflective of our commitment to the highest standards of education. 

Graduation & Participant Assessment

The final evening of the programme celebrates the achievements of each participant in a graduation ceremony that's followed by a Gala Dinner. 

Throughout the Cambridge summer programme, our Immerse tutors will monitor student engagement with the topics that they have been taught. Once the programme has finished, the tutor will write a Participant Assessment that will evaluate how the participant responded to the materials they were introduced to, what progress they made during the sessions, and offer recommendations on how to most effectively advance participant's understanding and interest in the topics that have been explored.

We strongly believe that our Participant Assessments are crucial element of the learning process, and reflective of our commitment to the highest standards of education. 

Request Further Information


Ready to enrol?

The Mathematics Summer School is available on the following dates:

7th – 20th July 2019

21st July – 3rd August 2019

28th July – 10th August 2019

4th – 17th August 2019

The Mathematics Programme takes place in the following locations

Christ's College
University of Cambridge

Originally formed as 'God's House', Christ's College was home to leading academics such as Charles Darwin.

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Founded in 1828

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Individual bedrooms

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Shared bathroooms

Sidney Sussex College
University of Cambridge

The site of much religious conflict during the English Reformation, Sidney Sussex has produced 5 Nobel Prize winners.

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Founded in 1596

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Individual bedrooms

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Shared bathroooms

Queens' College
University of Cambridge

Queens' spans both sides of the River Cam and is connected by the famous mathematical bridge.

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Founded in 1448

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Individual bedrooms

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Shared bathroooms

St. Catharine's College
University of Cambridge

Once a small college called 'Saynt Kateryns Hall of Cambridge', St Catherine's is also known as 'Catz'.

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Founded in 1473

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Individual bedrooms

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Shared bathroooms

Murray Edwards College
University of Cambridge

Murray Edwards is one of three women only colleges in Cambridge, set in 14 acres of award winning gardens.

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Founded in 1965

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Individual bedrooms

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Shared bathroooms

Colleges are allocated according to session preference and availability. To find out more, please email enquiries@immerse.education

Read our alumni success news

Ore Ogunbiyi | United Kingdom
Ore Ogunbiyi attended Immerse in 2014. Ore returned as a mentor in 2016 and as a Programme Manager in 2017.

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clemens

Clemens Steinek | Austria
After studying Biology at Immerse, Clemens was inspired to study Biology at the University of Vienna. 

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Emilia Persson | Switzerland
Emilia is now studying Human, Social & Political Sciences and regularly contributes as a writer for Immerse.

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