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Mathematics Collection

An article inside the Mathematics Collection of UE Oxbridge Essentials



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I. Common Knowledge for Applying to Oxford and Cambridge Undergraduate Programs

Choose Either Oxford or Cambridge

You cannot simultaneously apply to both the University of Oxford and the University of Cambridge. You must select one of the universities and apply to a single program.

Apply through the UCAS System

  • All applicants are required to submit their applications through the UK University Admissions Service (UCAS), which is known as the Universities and Colleges Admissions Service.
  • Each applicant is allowed to list up to 5 program choices.

II.Timeline for Oxford and Cambridge Undergraduate Admissions for 2024 Entry


Oxford and Cambridge Mathematics Major

In 2023

Preparing for the Application

Choosing Your Major

  • Mathematics at Oxford
  • Mathematics and Computer Science at Oxford
  • Mathematics and Philosophy at Oxford
  • Mathematics and Statistics at Oxford
  • Mathematics at Cambridge

Writing Your Personal Statement
Preparing Recommendation Letters
Choosing a College

UCAS Application Opens
MAT Exam Registration Commences
UE International Education Logo
UCAS Registration Center Code: 42757
MAT Exam Registration Deadline

For students Applying to Oxford Mathematics Programs

UCAS Application Submission Deadline

For All Applicants to Oxford and Cambridge

UCAS Application Submission Deadline For All Applicants to Oxford and Cambridge
Deadline for submitting My Cambridge Application and transcripts

Students applying for Cambridge

Receive interview invitations
first three weeks
Oxbridge Interview

In 2024

Release of Oxford University admission offers
Release of Cambridge University admission offers
Cambridge STEP Mathematics exam

Students who have been admitted to Cambridge Mathematics with STEP scores

Deadline for meeting conditional offer requirements
Official commencement of the academic year

III.How to Choose a Mathematics Program

There are four mathematics-related programs available at the University of Oxford . Here are the program names and UCAS codes:

Courses Professional name UCAS code
Mathematics mathematics G100

Mathematics and Statistics

Mathematics and statistics GG13

Mathematics and Philosophy

Mathematics and Philosophy GV15

Mathematics and Computer Science

Mathematics and Computer Science


Cambridge University offers one mathematics-related program:

Courses Professional name UCAS code
Mathematics mathematics G100

In the mid-June special lecture, Professor Xie Tao provided a comprehensive analysis from various perspectives on how to choose mathematics-related programs at Oxford and Cambridge and increase the chances of admission.

Seminar-How to Choose Mathematics Major in Oxford and Cambridge

IV.What Are the Admission Requirements

1. General Admission Requirements

The general admission requirements for mathematics-related programs at Oxford and Cambridge are outlined in the table below:

Oxford mathematics
Mathematics at Cambridge
Language Proficiency: [1]
· IELTS: 7.0
(with a minimum of 6.5 in each component)
· TOEFL: 100
(Listening 22, Speaking 25, Reading 24, Writing 24)
· Cambridge English: Advanced (CAE) or Proficiency (CPE)
(with a minimum of 176 in each component)
· PTE Academic: 66
(with a minimum of 56 in each skill)
· • GCSE English: Grade 6
· O-Level with a Grade B.
· IELTS: 7.5
(with a minimum of 7.0 in each component)
· TOEFL: 110
(with a minimum of 25 in each component)
·Cambridge English C2 Proficiency 200
(with a minimum of 185 in each component)
· Cambridge English C1 Advanced 193
(with a minimum of 185 in each component)
( AAA with A* in Mathematics and Further Mathematics.) [2]
AAA with A* in Mathematics and Further Mathematics. [3]
IB Scores:
39(776, need HL mathematics)
40-42 (776, need HL mathematics)
Requirements vary and are based on conditional offers. Requirements vary and are based on conditional offers.
High School Exam (e.g., Gaokao):
Not accepted. Typically, students in the top 1% of their province’s results.
University Entrance Exam:
Yes Yes

[1] The language proficiency requirement for the Mathematics and Philosophy program at Oxford is higher than that for the other three mathematics-related programs. For detailed information, please refer to the official Oxford website.
[2] If a student has studied A Level Further Mathematics, an A* grade in Mathematics is required. If a student has only studied AS Level Further Mathematics, an A grade in Mathematics is required. The Mathematics and Computer Science program at Oxford requires A*AA.
[3] Some students who have obtained an A* in AS Level Mathematics may still be asked to achieve two A* grades in A2 Level Mathematics.
[4] Cambridge University requires all students admitted to mathematics-related programs to participate in the STEP (Sixth Term Examination Paper) exam.
[5] Some colleges may arrange specialized written tests during the interview process. Please refer to the interview invitation for specific arrangements.

2.The official statement from the University of Cambridge’s Department of Mathematics regarding admission criteria can be summarized as follows:

The official statement from the University of Cambridge's Department of Mathematics regarding admission criteria can be summarized as follows:

In selecting mathematics undergraduates, we seek three qualities:

  • Mathematical knowledge and skills
    Students should have suitable background knowledge in mathematics, on track to start our course. Students must also have good general skills in mathematics to be able to apply their knowledge in solving problems.

  • Mathematical ability and talent
    Students should have the ability to think mathematically. This includes having the creativity to make connections between different mathematical ideas, and the flexibility to understand new concepts quickly and use them to solve challenging problems.

  • Motivation for studying mathematics
    Students should have the commitment to study mathematics at university level, and be ready to work hard and persevere. Considerable interest in and enthusiasm for the subject are important, and can be expressed in many ways.

We look for evidence of these qualities using many sources of information. These include existing and predicted grades, school reference, personal statement, and what we learn at time of interview. We do not simply grade and sum these sources separately. Instead we use all available information together, taking individual context into account, to form a picture of each applicant.

STEP is an important part of our conditional offer; it enables us to compare applicants directly, and addresses all three qualities above to some extent. All Colleges use STEP for mathematics, and a typical offer is grades 1 in both papers 2 and 3. However, only about two-thirds of our places are filled by those who achieved these grades. For the remaining one-third of our places, Colleges review the full applications (now including STEP marks and scripts) of those who missed their STEP grades.

Cambridge primarily evaluates candidates based on three main aspects:

1. Mathematical Knowledge and Skills: Candidates should possess a strong foundation in mathematics and problem-solving skills necessary to excel in university-level courses.

2. Mathematical Ability and Aptitude: It’s essential to demonstrate mathematical thinking abilities, including the creative linking of different mathematical concepts and the capacity to quickly grasp new concepts and apply them to challenging problems.

3. Motivation to Study Mathematics: Candidates should have a genuine and strong interest in mathematics and the internal drive to consistently pursue mathematical knowledge throughout their university studies.

Admissions officers assess these qualities through various dimensions, including predicted grades, school recommendations, application essays, and interview performance. The evaluation process involves considering all the information holistically and building a comprehensive profile of each candidate.

STEP scores play a significant role in the admission criteria. Typically, most colleges require STEP 2 and 3 scores to be at grade 1 or higher. However, around one-third of students admitted do not initially meet the STEP requirements but are reassessed after the submission of additional materials, including STEP scores and papers.

Key data provided by the Cambridge Department of Mathematics is as follows:

Typical Mathematics entrants

(A Level and IB)

For 2017, 2018 and 2019 entry, the majority of entrants from an A Level background achieved at least A*A*A* (85% of entrants). All of these successful applicants took Mathematics and Further Mathematics, 91% took Physics and 53% took Chemistry. For the same period, the majority of IB entrants achieved at least 44 points overall and/or grades 777 at Higher Level. The majority of entrants achieved grades of at least 1, 1 in STEP II and III.

This information is intended to give you a sense of the academic standard of our typical A Level entrants. We welcome applicants from a range of qualification backgrounds.

Among students studying A Levels, 85% achieve grades A*A*A* or higher, with most students taking both Mathematics and Further Mathematics courses, 91% studying Physics, and 53% studying Chemistry. In contrast, IB students typically achieve a total score of 44 points or higher, with Higher Level Mathematics scores of 7. It’s important to note that for most admitted students, STEP II and III scores are at least at grade 1 or higher.

Therefore, while conventional admission requirements serve as a reference, for those seeking admission to mathematics programs at Cambridge, referring to the data provided by the official Cambridge sources holds more practical significance.

Both the University of Oxford and the University of Cambridge have consistently been popular choices for Chinese students applying for mathematics programs, and analyzing past admission data can help applicants determine their chances of success.

Data Analysis-Comparison of Application Difficulty of Mathematics Major in Oxford and Cambridge

V.Application Process and Required Materials

The application process for Oxford and Cambridge is relatively straightforward. Here, we’ll focus on important details and the materials you need to prepare.

1. Materials Required for UCAS Application:

When applying to Oxford or Cambridge through UCAS, you must confirm or submit the following information:

  1. • The specific program and its UCAS code at either Oxford or Cambridge.
  2. Your choice of a particular college or opting for an open application.
  3. Your personal details, including your email address.
  4. Your educational history and your academic achievements to date.
  5. Personal Statement
  6. Letters of recommendation.

2.Differences Between the Application Processes for Oxford, Cambridge, and Other UK Universities

With the exception of a few specific programs and unique circumstances (such as mature students or those already enrolled in a UK university), the application process for Oxford and Cambridge through UCAS is quite similar to applying to other universities in the UK. However, there are several key distinctions to keep in mind:

  • Early Application Deadline: The application deadline for Oxford and Cambridge is earlier than that of most other universities, specifically October 16th.
  • Selection of College or Open Application: Applicants to Oxford and Cambridge must choose a particular college or opt for an open application, unlike many other universities.
  • Single Program Application: Unless under extremely rare circumstances, both Oxford and Cambridge allow applicants to apply for only one program.
  • Transcript Requirement: Cambridge University may request transcripts from some applicants covering their secondary school academic records.

3. Official Undergraduate Application Process for the University of Cambridge

4. Official Undergraduate Application Process for the University of Oxford

Part 1: What Oxford is Like

Part 2: How to Apply

Part 3: Preparing

5. Language Proficiency and High School Stage Grades

Language proficiency does not need to meet the admission requirements by the UCAS application deadline on October 16, 2023. Instead, it should be met by August 31, 2024, in accordance with the specific admission requirements for the chosen program.

Prior to October 16, it is necessary to submit estimated high school stage grades, which are a crucial factor considered in the admissions process for Oxford and Cambridge.

6.Regarding Open Application (Choosing a College)

When faced with approximately 30 colleges at both Oxford and Cambridge universities, some students may find it challenging to decide on a college, or they may have no particular preference. In such cases, students can opt for an open application on UCAS:

  • After the application deadline, students who choose open application will be randomly assigned to a college via a computer program.
  • The random allocation aims to balance the number of applicants across various colleges and programs.
  • Once assigned to a college, the application process proceeds like that of other students.
  • For students who meet all the application requirements, there is no difference in the likelihood of being admitted whether they choose a specific college or opt for an open application.

In late June, Professor Xie Tao will host a special seminar where he will analyze how to choose a college based on the admission data of various colleges and their respective profiles. This analysis will cater to students of different levels and aims to enhance their chances of being admitted.

Seminar-How to Choose Oxford University College
Seminar-How to Choose Cambridge University College

7. Application Essay

As a part of the UCAS application process, every student is required to submit an application essay, also known as a personal statement (PS). The application essay serves as a tool for universities to better understand a student’s interests in the subject and major. Simultaneously, it allows students to gain a deeper understanding of their academic interests and motivations.

Typically, the application essay should encompass the following aspects:

  • Explain the reasons for wanting to study the relevant major at the university.
  • Demonstrate enthusiasm and dedication to the chosen major.
  • Express specific interests within the relevant field of study.
  • Articulate how one is committed to researching the subjects of interest.

8. Recommendation Letters

Recommendation letters (referred to as academic references at Oxford and school/college references at Cambridge) serve to provide universities with a better understanding of a student’s abilities and potential. Admissions officers use these letters to assess whether a student’s academic capabilities are suited for the chosen major and if they can adapt to the university’s learning environment.

As a crucial component of the UCAS application, universities typically prefer recommendation letters to be submitted by school teachers or individuals who can provide authoritative insights into a student’s academic background.

Please note that recommendation letters must also be submitted before the application deadline on October 16th.


Whether you need to submit transcripts when applying to the University of Cambridge can be found in the official Cambridge guidelines:

《Do I need to submit a transcript?》

六、What Preparation is Needed?

1. Preparing for the Oxford MAT

Preparing for the MAT exam is recommended to start 3-6 months in advance. The specific duration of preparation may vary depending on individual circumstances, academic commitments, and holiday schedules. However, starting early is always a good practice.

For more information and preparation tips regarding the MAT, please refer to the following sections:

A comprehensive interpretation-Oxford MAT mathematics exam
Oxford MAT preparation guide

2. Should You Prepare for the Cambridge STEP Exam in Advance?

All students who receive an offer for a mathematics program at Cambridge University are required to take the STEP exam. Meeting the STEP score requirements is essential for final admission. However, this doesn’t necessarily mean that you must achieve qualifying STEP scores before entering the interview or receiving an offer. In fact, the majority of admitted students attain qualifying STEP scores after receiving an offer. Additionally, applying for mathematics programs at Oxford does not require STEP scores.

Therefore, many students and parents often wonder whether they should prepare for the Cambridge STEP exam in advance. Concerns typically revolve around three points: firstly, the perception that STEP is challenging and there might be difficulty in mastering it, potentially resulting in wasted time; secondly, the belief that learning it in advance is futile because there’s no guarantee of admission, and it’s better to wait for an offer before dedicating time to it; thirdly, the fact that Oxford mathematics programs do not require STEP scores.

Here, we summarize several viewpoints that Mr. Xie Tao frequently shares with students and parents for your reference:

  1. Students who prepare for the STEP exam in advance may find it easier to study for the MAT, making it a more manageable and potentially leading to higher scores. In the last few months leading up to the application deadline, students often have limited time for preparation, so saving time on STEP preparation can be beneficial. This extra time can be allocated to improving the quality of your application materials, such as your personal statement and recommendation letters.
  2. Students who have studied STEP for over six months may have an advantage during the interview stage. The interview questions at Oxford and Cambridge are significantly more challenging than those in the MAT exam, often approaching or even surpassing the difficulty level of STEP questions.
  3. After preparing for STEP, students tend to develop a distinct thinking style that sets them apart from those who have only studied regular A Level Mathematics or AP Calculus courses. This difference in thinking style can often be discerned by interviewers during the admission interviews and may impact the interview scores.
  4. The process of preparing for STEP itself involves adapting to the learning style typical of British universities. While this aspect may not be evident in the MAT written test, it becomes quite apparent during the interview. Students with a foundation in STEP tend to excel in interviews by better following the interviewer’s guidance and engaging in interactive discussions, thus earning higher interview scores.
  5. Students who start preparing for STEP after receiving conditional offers in January have a relatively low success rate in achieving the required STEP scores. Each year, Cambridge’s mathematics programs offer around 500 places, but only about 250 students ultimately meet the requirements. The majority of those who do not meet the requirements typically fall short due to their STEP scores.
  6. Having studied STEP also pays off because once you get to university, you’ll find that higher-level mathematics courses are not as challenging. For a comprehensive understanding of the Cambridge STEP Mathematics exam, including score data, exam difficulty, and more, please refer to the provided resource.

Please refer to the comprehensive interpretation, score data and test difficulty of Cambridge STEP Math Test:

A comprehensive interpretation of Cambridge STEP exam
Cambridge STEP preparation guide

3. Interview Preparation

It is advisable not to wait until you receive the interview invitation to start mock interviews. We recommend conducting at least six mock interviews, covering various possible question types, scenarios, and topics. This will help improve your on-the-spot response speed and achieve the best interview results.

After the MAT written exam, OptiClass will provide a special seminar on interview preparation for members of the Oxford and Cambridge Elite and students enrolled in the Oxford and Cambridge Preparation Course.

Seminar-How to Prepare for Math/Computer Interview

4. Academic Research Projects

In recent years, more and more students have been participating in academic research projects at universities. Engaging in academic research experiences and achieving outstanding academic results can significantly enhance your application essays and boost your competitiveness when applying to top-tier universities.

Online research project topics are continuously updated. For more details, please refer to the following page:

Oxbridge Planning-Online Scientific Research

5. Extracurricular Reading

While preparing for exams and writing application essays can take up a significant amount of time, it is still advisable for students to engage in extracurricular reading. Typically, students are encouraged to deeply read two books and broadly read more than ten books related to their chosen field. Extracurricular reading can, to some extent, enrich the material for writing application essays, making them more appealing.

6. Oxford and Cambridge Summer Schools

There are numerous summer schools on the market with various marketing gimmicks. While there are many highlights to summer schools, the quality of the teaching staff can vary significantly. When choosing, students and parents should be discerning.

Generally, it is recommended to participate in summer schools with a relatively short duration and reasonable fees. The main purpose of attending summer schools should be to experience the learning methods of Oxford and Cambridge and broaden one’s horizons.

For more information related to applying to math-related programs at Oxford and Cambridge, please refer to the following resources.

Maths Collection - Oxbridge Essentials
Cambridge STEP preparation course+brush training
Oxford MAT Test-prep Course + Question Bank Campaign

Attachment: Recommended reading materials for mathematics majors.

According to the official recommended reading materials for mathematics majors in Cambridge, the Youyi teaching and research team has done a lot of searching and sorted out some reading materials that can be consulted or downloaded for free on the Internet, as shown in the table below.

1. History and General Studies

Makers of mathematics
Makers of Mathematics

Author:S. Hollingdale

The Man Who Knew Infinity A Life of the Genius Ram
The Man Who Knew Infinity

Author:R. Kanigel

A Mathematician's Apology
A Mathematician’s Apology

Author:G.H. Hardy

Feynman Surely You're Joking
Surely You’re Joking, Mr Feynman

Author:R.P. Feynman
Publisher:Arrow Books

How to Think Like a Mathematician
How to Think Like a Mathematician

Author:Kevin Houston

Mathematics: a very short introduction
Mathematics: a very short introduction

Author:Timothy Gowers

Solving Mathematical Problems
Solving Mathematical Problems

Author:Terence Tao

What is Mathematics
What is Mathematics?

Author:R. Courant & H. Robbins

2. Leisure and recreation category

Game Set and Math Enigmas and Conundrums
Game Set and Math Enigmas and Conundrums

Author:I. Stewart

To Infinity and Beyond A Cultural History of the Infinite
To Infinity and Beyond

Author:Eli Maor



A Mathematical Mosaic
A Mathematical Mosaic

Author:Ravi Vakil
Publisher:Mathematical Association of America

3. Textbooks and teaching materials

Advanced Problems in Mathematics
Advanced Problems in Mathematics

Author: S.T.C. Siklos

A Concise Introduction to Pure Mathematics
A Concise Introduction to Pure Mathematics

Author:Martin Liebeck
Publisher:Chapman& Hall/CRC Mathematics

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