Maths Summer School Programme Overview:
Programme: Mathematics university insights
Course Length: 2 weeks
Course Type: Residential
Locations: Cambridge University colleges
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2019 Maths Summer School Summary
Mathematics is a powerful tool, and its influence can be found in multiple fields. From engineering, medicine and the sciences to finance, economics and business, maths is a broad subject that offers many prosperous avenues.
Some of the worlds most influential thinkers and 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 a comprehensible and engaging manner. The maths summer programme enables participants to discover a variety of important topics in greater depth and understand the practical applications of mathematical skills. Expert tutors from some of the world’s leading university mathematics departments design and teach our programmes, guiding participants to develop their interest in the discipline. Participants leave with a newfound confidence in approaching challenging material, a skill that will prove invaluable at university.
Immerse is an inspirational academic maths summer school programme for the intellectually curious.
Maths Summer School Key Benefits
Dive into a number of fascinating 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 In Our Maths Summer School
The Immerse 2019 maths summer school programme comprises a number of key topics which are explored in-depth, with the guidance of our expert tutors. The course aims to provide participants with a thorough grounding in topics necessary for success as an undergraduate. That being said, the programme is designed to provide much more than understanding of key topics. At Immerse, our aim is to develop a student’s passion for their chosen subject, by providing them with an opportunity to put theory into practice and discover the vast range of applications this intricate subject offers. Over the course of the mathematics summer programme, participants will explore a range of complex topics.
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 to this problem is an essential parameter in the design of a satellite or a heavy load carrying bridge, for example. In this case, one needs to be sure that the approximate solution is sufficiently close to the true solution – this requires careful, rigorous, and rewarding mathematical analysis.
Furthermore, 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? However, there are numerous complications in probability 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.
These examples outline only a couple of examples of the challenges that participants will tackle during the Immerse Mathematics summer course.
Below is a list of topics that participants will additionally cover during the maths summer programme:
Systems of linear equations
Abstract vector spaces
Cambridge Maths Summer 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 how to analyse and solve some of the most complex mathematical problems.
On an Immerse Education residential Maths summer school programme, participants will have the chance to gradually explore some of these topics at a progressive pace and in a manner that is suitable to their age and level. What’s more, the small class sizes mean that each participant will receive guidance from expert mathematics tutors. As a result, they will gain confidence and bridge the gap between what they now know and what they will need to know to succeed at university.
In completing the maths summer programme, participants 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.
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
Start the day with either a continental or cooked breakfast in the college dining hall. A wide variety of breakfast items helps participants prepare for the challenging day ahead.
Ritvik Somaiya, United Kingdom
2017 Mathematics Alumnus
Ritvik participated in our Mathematics programme in 2017. Here's what he has to say about his time with Immerse Education:
I now have friends across the globe and have a strong image of what university life will be like.
Studying with Immerse I learnt that there are more opportunities than I thought, and I shouldn't limit myself to what I can do in my country but rather explore what the world has to offer. In the strongest terms, I would encourage you to go for this experience! You'll meet some amazing people and enjoy the new environment when you make this investment!
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 a crucial element of the learning process and reflective of our commitment to the highest standards of education.