Entrance Exams Worldwide

Conducted by the National Testing Agency, JEE Main is the gateway to NITs, IIITs, and CFTIs across India. The mathematics section (30 questions) covers the full Class 11–12 NCERT syllabus with emphasis on speed and accuracy.

The second stage of India's premier engineering entrance, JEE Advanced is among the world's most difficult undergraduate admission tests. Two papers of three hours each test deep conceptual understanding across calculus, algebra, coordinate geometry, and trigonometry.

The online entrance examination for BITS Pilani campuses (Pilani, Goa, Hyderabad), with 150 questions in 180 minutes. Mathematics carries 45 questions and tests the JEE Main syllabus; speed and accuracy are critical.

The entrance examination for VIT University (Vellore, Chennai, Bhopal, AP), one of India's largest private technical universities. Mathematics covers 40 questions from the Class 11–12 syllabus with a focus on accuracy over time pressure.

Conducted by SRM Institute of Science and Technology for admissions to their BTech programmes. The mathematics section tests Class 12 topics including calculus, algebra, and coordinate geometry in a computer-based format.

The entrance examination for Manipal Academy of Higher Education, one of India's leading deemed universities. Mathematics (50 questions) covers the standard Class 11–12 engineering mathematics syllabus.

A state-level engineering entrance for private colleges in Karnataka, with mathematics questions drawn from the Class 11–12 Physics, Chemistry, and Maths syllabus. Conducted annually in May.

The entrance examination for the Kalinga Institute of Industrial Technology (KIIT), Bhubaneswar — one of India's most prestigious deemed universities. Mathematics (120 questions) tests the full Class 11–12 syllabus.

The state-level engineering entrance for government and private colleges in West Bengal. A two-paper examination where Mathematics (Paper 2) carries 100 marks and tests the Class 11–12 West Bengal Board syllabus.

The state engineering entrance for Maharashtra, testing Mathematics, Physics, and Chemistry from Class 11 and 12 Maharashtra State Board syllabus. Widely attempted by over 4 lakh students annually.

The common entrance test for engineering and other professional courses in Karnataka government colleges. Mathematics (60 questions) is based on the PUC (Class 11–12) Karnataka Board syllabus.

The combined state entrance for engineering and medical courses in Andhra Pradesh, conducted by JNTU Kakinada. Mathematics (80 questions, 80 marks) tests the AP Board Class 11–12 syllabus.

Telangana's primary state engineering entrance conducted by JNTU Hyderabad. The mathematics section covers the Telangana State Board Class 11–12 curriculum with 80 questions.

Kerala's state entrance for engineering, pharmacy, and architecture admissions in government and aided colleges. Mathematics carries 120 marks and covers Class 11–12 Kerala State Board topics.

The state-level entrance examination for engineering courses in Gujarat, conducted by the Gujarat Secondary and Higher Secondary Education Board. Mathematics tests the Class 12 Gujarat Board syllabus.

Conducted by Dr. A.P.J. Abdul Kalam Technical University (AKTU), UPSEE is the gateway to engineering colleges in UP. The mathematics section tests Class 12 topics with emphasis on calculus, algebra, and vectors.

The state entrance for engineering and lateral entry programmes in Odisha, conducted by the Odisha Joint Entrance Examination Board. Mathematics covers the standard Class 11–12 engineering mathematics syllabus.

Bihar's state entrance for engineering, pharmacy, and agriculture courses, conducted by the BCECE Board. Mathematics questions are drawn from the Class 11–12 Bihar State Board syllabus.

The combined state entrance for professional courses in Jharkhand covering engineering and medical streams. The mathematics paper tests standard Class 11–12 topics.

The state-level engineering entrance for Himachal Pradesh, administered by Himachal Pradesh Technical University. Tests the standard PCM curriculum from Class 11–12.

The entrance test for BTech and other programmes at CUSAT, one of Kerala's premier technical universities. Mathematics (100 marks) tests calculus, algebra, and geometry at the Class 12 level.

The entrance for engineering and other programmes at Guru Gobind Singh Indraprastha University, Delhi. Mathematics covers the CBSE Class 11–12 syllabus with questions on calculus, vectors, and coordinate geometry.

Conducted by Anna University, TANCET is the entrance for ME, MTech, MBA, and MCA admissions in Tamil Nadu government and aided institutions. The mathematics section is particularly rigorous for engineering PG admissions.

The state-level entrance for professional courses in Jammu & Kashmir, testing the Class 11–12 J&K State Board mathematics curriculum.

The sole gateway to MBBS, BDS, AYUSH, and veterinary programmes in India, conducted by NTA. Physics carries 45 questions requiring strong mathematical calculation skills — making NEET Physics numericals a critical area of preparation.

Now merged with NEET UG, AIIMS was historically India's most prestigious standalone medical entrance. Physics problems in the NEET paper require the same quantitative rigour that characterised AIIMS preparation.

Also merged with NEET UG, JIPMER was known for its analytical and application-based physics questions. Strong mathematical foundations remain essential for the quantitative aspects of NEET preparation.

The entrance examination for MD, MS, and PG Diploma admissions in Indian medical colleges. While primarily clinical, biostatistics and pharmacokinetics questions reward strong quantitative reasoning.

Conducted by the IIMs, CAT is India's most competitive management entrance, with Quantitative Aptitude (QA) carrying one-third of the total score. Topics include Number Theory, Arithmetic, Algebra, Geometry, and Data Interpretation — demanding both conceptual depth and speed.

The entrance for XLRI and 150+ other management institutions, XAT's Quantitative Aptitude and Data Interpretation section tests advanced mathematical reasoning. Known for its difficulty and unpredictable question pattern.

A globally accepted management entrance used by business schools worldwide, including IIMs, ISB, and top schools in the US, UK, and Europe. The Quantitative section (31 questions, 62 minutes) tests Data Sufficiency and Problem Solving.

Conducted by AIMA, MAT is accepted by over 600 management institutions across India. The Mathematical Skills section (40 questions) tests arithmetic, algebra, geometry, and data analysis.

The entrance for Symbiosis International University programmes including MBA and MSc. Quantitative Aptitude (20 questions) covers Number Systems, Arithmetic, Algebra, and Geometry in a computer-based format.

The entrance for NMIMS and 50+ other management schools. The Quantitative Skills section (36 questions, 52 minutes) tests Data Interpretation and Arithmetic at a moderate but timed difficulty level.

Conducted by UPSC, NDA is the gateway to the Indian Army, Navy, and Air Force for Class 12 students. Mathematics (Paper 1, 120 marks) covers Algebra, Matrices, Trigonometry, Calculus, Vectors, and Statistics at Class 11–12 level.

UPSC's CDS exam is the route to the Indian Military Academy, Naval Academy, and Air Force Academy for graduates. The Elementary Mathematics paper (100 marks) tests arithmetic, algebra, trigonometry, geometry, and statistics.

India's most prestigious competitive examination for IAS, IPS, and other central services. Mathematics as an optional subject in Mains is highly regarded — covering Linear Algebra, Calculus, Real Analysis, Algebra, and Mechanics across two papers of 250 marks each.

One of India's largest government recruitment examinations, SSC CGL's Quantitative Aptitude section carries 50 questions. Topics include Number Theory, Percentage, Ratio, Algebra, Geometry, Trigonometry, and Statistics.

The SSC recruitment for Class 12 pass candidates, with a 25-question Quantitative Aptitude section. Tests arithmetic, algebra, and geometry at 10+2 level under strict time pressure.

The engineering recruitment examination for Indian Railways, with Mathematics (30 marks) covering Number Systems, BODMAS, Decimals, Fractions, Algebra, Geometry, and Trigonometry.

The nationally recognised examination for admissions to IITs, NITs, and PSU recruitment. Engineering Mathematics carries approximately 15% of the total marks and covers Linear Algebra, Calculus, Differential Equations, Probability, and Numerical Methods.

The most widely taken A-Level Mathematics specification in England and Wales, covering Pure Mathematics, Statistics, and Mechanics. A strong A-Level Mathematics grade is required for engineering, sciences, economics, and computing at UK universities.

OCR offers A-Level Mathematics with both standard and MEI (Mathematics in Education and Industry) specifications. Covers Pure, Statistics, and Mechanics with a strong emphasis on understanding and application.

AQA A-Level Mathematics covers Pure Mathematics 1 and 2, Statistics, and Mechanics in a two-year linear qualification. A key requirement for STEM and many social science degree programmes.

Taken alongside A-Level Mathematics, Further Maths covers additional Pure topics (complex numbers, matrices, proof by induction) and either further Statistics, Mechanics, or Decision Mathematics. Strongly preferred by top universities for mathematics, physics, and engineering.

Cambridge's additional mathematics examination, required or recommended for Mathematics admissions at Cambridge, Warwick, and several other UK universities. Papers I, II, and III contain 13 extremely challenging questions from which students attempt 6 — demanding creative mathematical thinking far beyond A-Level.

Oxford's pre-interview admissions test for Mathematics, Computer Science, and related courses. A 2.5-hour paper with five questions testing problem-solving, proof, and advanced A-Level mathematics.

Used by Cambridge and several other UK universities as an admissions tool, TMUA tests mathematical reasoning and application in two 75-minute papers. Covers A-Level content but requires deep understanding and logical rigour.

Required for Medicine at Oxford, Cambridge, and Imperial College London, BMAT includes a Scientific Knowledge and Applications section with significant mathematics content. Tests A-Level Physics, Chemistry, and Biology with mathematical calculations.

The aptitude test for Law admissions at top UK universities including Oxford, UCL, and Nottingham. While primarily verbal, the logical reasoning component rewards mathematical thinking and structured argument.

The internationally recognised Cambridge A Level Mathematics (9709) covering Pure Mathematics 1, 2 & 3, Mechanics, and Probability & Statistics. Accepted by universities in the UK, USA, Canada, and worldwide as a gold-standard qualification.

The College Board's primary university admissions test, with Mathematics scored out of 800 in an adaptive two-module format. Tests Heart of Algebra, Problem Solving & Data Analysis, and Passport to Advanced Math — now fully digital.

A 60-question, 60-minute mathematics test covering pre-algebra through trigonometry, accepted by all US universities. Full calculator permitted; speed and broad mathematical fluency are the key differentiators.

The College Board's AP course and examination in introductory single-variable calculus — limits, derivatives, integrals, and differential equations. A score of 3–5 earns college credit at most US universities.

The more advanced AP calculus course, covering all of AB content plus sequences, series, polar coordinates, and parametric equations. A score of 5 demonstrates university-level mathematical proficiency.

The AP course and examination covering exploratory data analysis, probability, statistical inference, and experimental design. Develops quantitative reasoning skills critical for social sciences, biology, and business.

The standard admissions test for US graduate school programmes, with Quantitative Reasoning (170-point scale) testing arithmetic, algebra, geometry, and data analysis. Required or recommended by thousands of master's and PhD programmes worldwide.

The quantitative section of the GMAT tests Data Sufficiency and Problem Solving in 45 questions over 62 minutes. Critical for MBA admissions at top business schools including Harvard, Stanford, Wharton, and IIM.

The US medical school admissions test includes Chemical and Physical Foundations of Biological Systems, which requires strong physics and mathematics including algebra, exponentials, and basic calculus concepts.

Taken in Grade 10 or 11, the PSAT is both SAT preparation and the qualifier for National Merit Scholarship consideration. The Mathematics section mirrors SAT content, making it an important milestone in US university preparation.

Though discontinued in 2021, SAT Math Level 2 covered precalculus, trigonometry, and elementary statistics at a level above SAT Math. Many competitive universities still review legacy applications citing strong Math Level 2 performance.

Conducted by the Ministry of Higher Education in Oman as a qualification test for government-funded higher education sponsorships. The mathematics component tests algebra, geometry, and analytical reasoning.

The entrance examination for Sultan Qaboos University, Oman's flagship public university. Competitive placement in engineering and science programmes requires strong performance in the mathematics component.

The licensing and specialty examination for medical professionals practising in Oman. Quantitative and biostatistics components require solid mathematical foundations.

Oman's scholarship qualification examination for students seeking government-funded study abroad placements. Mathematics is assessed as part of the overall aptitude evaluation.

The UAE's national standardised test for university admissions, with EmSAT Mathematics assessing students at the end of their secondary education. Score benchmarks are set by UAE universities for admission into science and engineering programmes.

The achievement-level version of EmSAT used for course placement and scholarship eligibility within UAE higher education institutions. Mathematics achieve scores are required by universities including UAE University, Khalifa University, and American University of Sharjah.

The aptitude assessment used by ADNOC for graduate recruitment and scholarship programmes. Numerical reasoning and quantitative aptitude are significant components of this competitive test.

The entrance qualification for UAE University — one of the UAE's oldest and most prestigious institutions. Mathematics placement testing determines eligibility for engineering and science programmes.

The Saudi National Centre for Assessment's General Aptitude Test used for university admissions across the Kingdom. Quantitative reasoning accounts for half of the test, covering Number Theory, Algebra, Geometry, and Data Interpretation.

The Saudi achievement test measuring mastery of secondary school curriculum — Mathematics is one of the two core components (alongside Sciences or Humanities). Critical for competitive programme admissions at Saudi universities.

The licensing examination for medical practitioners in Saudi Arabia. Biostatistics, epidemiology, and pharmacokinetic calculations require strong quantitative foundations.

The mathematics placement assessment for Qatar University — a key requirement for engineering and science programme admissions. Scores determine placement in developmental or credit-bearing mathematics courses.

A national academic evaluation used for higher education eligibility and scholarship in Qatar. Mathematics is assessed as part of a broader STEM-readiness framework.

The competitive entrance assessment for Kuwait University, the primary public university in Kuwait. Mathematics performance is a key differentiator for engineering and science faculty placements.

The entrance examination for Kuwait's vocational and applied education authority, covering applied mathematics relevant to technical and engineering programmes.

The admissions assessment for the University of Bahrain's various colleges, with mathematics tested for engineering and computing applicants.

The entrance assessment for Bahrain Polytechnic's technical and vocational programmes, requiring competency in applied mathematics and analytical reasoning.

Jordan's national secondary school leaving examination, with Mathematics a core component determining university placement. High Tawjihi scores are required for engineering, medicine, and science faculties at Jordanian universities.

University-level placement and admissions assessments used by Jordanian universities for competitive faculty admissions, testing Class 11–12 mathematics.

Egypt's national secondary examination, with Mathematics as a required subject. University faculty placement — especially for engineering — depends heavily on Thanaweya Amma mathematics scores.

Supplementary admissions assessments used by Egyptian universities for competitive engineering and science programme placement.

New South Wales' senior secondary qualification, with mathematics offered at Standard and Extension levels. Mathematics Extension 1 and 2 involve calculus, complex numbers, and proof — directly relevant to university engineering and science courses.

Victoria's senior secondary mathematics course covering functions, calculus, probability, and statistics. The ATAR contribution from Mathematical Methods is significant for STEM degree entry cutoffs.

Western Australia's senior secondary mathematics qualification available at Specialist, Methods, and Applications levels. Specialist Mathematics covers calculus, vectors, and complex numbers at A-Level equivalent depth.

South Australia's year 12 mathematics qualification, offered at Essential, General, and Specialist levels. Performance in SACE Mathematics directly influences ATAR scores for university admission.

Queensland's senior mathematics qualification covering Mathematical Methods and Specialist Mathematics. Both internal and external assessments contribute to the ATAR, making consistent performance essential.

The most widely participated mathematics competition in Australia, with problems ranging from accessible to highly challenging across all year levels. Strong AMC performance is recognised by universities and selective schools.

ATAR is not an exam itself but the aggregate university entry score calculated from senior secondary results. Mathematics courses contribute heavily to ATAR calculations, making them among the highest-stakes subjects in Australian secondary education.

UCAT (formerly UMAT) is used by Australian and New Zealand medical schools alongside GPA for medical admissions. Quantitative Reasoning tests numerical interpretation and mental arithmetic under severe time pressure.

Regarded as the most important pre-university mathematics competition in Canada, Euclid is a two-and-a-half-hour full-solution contest for Grade 12 students. Strong Euclid performance supports university mathematics programme applications.

CEMC competitions for Grades 11 and 10 respectively, acting as stepping stones between junior contests and the senior Euclid. Multiple-choice format with 25 questions testing progressively advanced topics.

The entry-level CEMC competition for Grades 7 and 8, with 30 multiple-choice questions in 60 minutes. An ideal first competition for developing mathematical problem-solving confidence.

Open-ended problem-solving contests for Grades 11, 10, and 9 requiring full written solutions. Develop proof-writing skills transferable to olympiad competitions.

Various Canadian provinces run their own mathematics competitions (e.g. BCSSMC, AMQ in Quebec) at the senior secondary level. These serve as preparation for national CEMC contests and university applications.

Canadian medical schools use MCAT as the primary admissions test, with Biological and Physical Foundations of Biological Systems requiring strong quantitative and physics-based mathematics.

Singapore's gold-standard pre-university qualification, with H2 Mathematics covering calculus, algebra, vectors, statistics, and mechanics. Strong H2 Mathematics performance is required for engineering and science programmes at NUS, NTU, and SMU.

The enriched O-Level mathematics course that bridges to H2 Mathematics at A-Level. Additional Mathematics covers trigonometry, differentiation, integration, and proof — critical preparation for the Singapore A-Level track.

Competitive admissions to NUS and NTU in engineering, computing, and science programmes rely heavily on A-Level and Polytechnic Diploma mathematics performance. DSA (Direct School Admission) pathways consider competition mathematics.

Singapore's high-stakes primary school exit examination, with Mathematics carrying 200 marks. PSLE Mathematics is the entry filter for secondary school placement — strong performance opens pathways to Integrated Programme schools.

An international informatics and computational thinking contest for school students, with significant mathematical logic and algorithmic reasoning components. Widely participated in across Singapore and Southeast Asia.

Vietnam's national mathematics olympiad with a strong international reputation, having produced multiple IMO gold medallists. The competition tests algebra, combinatorics, number theory, and geometry at a very high level.

The premier mathematics competition in the Philippines, with eliminations, area, and national stages. Top performers represent the Philippines at the IMO and APMO.

Indonesia's national science olympiad (Olimpiade Sains Nasional) covering mathematics, physics, chemistry, and computing. The mathematics track is Indonesia's pathway to IMO team selection.

Conducted by IPST Thailand, TMO is the national olympiad leading to IMO team selection. Problems are proof-based and cover classical olympiad mathematics topics.

The national mathematics competition in Malaysia coordinated by PERSAMA. Top performers advance to regional competitions including APMO and ultimately the IMO.

China's national university entrance examination — the most consequential examination in the world by number of participants (over 12 million annually). The Mathematics paper (150 marks, 120 minutes) is exceptionally rigorous, covering algebra, geometry, calculus, probability, and statistics.

China's national olympiad, serving as the primary filter for China's IMO team — the world's most dominant at the international level. CMO problems are among the hardest national olympiad problems globally.

South Korea's national university entrance examination, with Mathematics (Gasu) carrying 100 points and covering calculus, probability, statistics, and geometry. Among the most competitive university entrance systems in the world.

Hong Kong's secondary school exit qualification, with Mathematics (compulsory) and Extended Module (calculus and statistics or algebra and calculus). HKDSE results determine university placement at HKU, HKUST, and CUHK.

The national mathematical olympiad for Hong Kong, involving heat, individual, and group events. Covers algebra, combinatorics, number theory, and geometry with unique team-based rounds not seen in other olympiads.

Japan's university entrance system uses the Common Test for University Admissions (共通テスト, formerly センター試験) as a national filter, followed by individual university examinations. Top universities like UTokyo, Kyoto, and Osaka set notoriously demanding mathematics papers.

The University of Tokyo's own entrance examination is considered among the hardest university entrance tests globally. The Mathematics paper requires deep knowledge of calculus, linear algebra, and complex numbers with elegant proof-based solutions.

Taiwan's national university entrance system, with the GSAT as the primary filter and AST as the subject-specific deepening test. Mathematics is tested at both levels, with AST Mathematics reaching university introductory level.

CMI's entrance examination is one of India's most challenging — covering olympiad mathematics in the first part and advanced calculus, linear algebra, and combinatorics in the second. Widely considered a test of genuine mathematical talent.

The ISI BStat and BMath entrance examinations are among India's most mathematically demanding — testing real analysis, combinatorics, algebra, and proof writing at a level beyond the standard school curriculum.

France's national secondary examination, with Mathematics available at standard and Spécialité (advanced) levels. Spécialité Mathematics covers calculus, probability, linear algebra, and functions — a prerequisite for grandes écoles and engineering programmes.

The German university entrance qualification, with Mathematics as a core subject examined across all Länder. Abitur Mathematics tests calculus, stochastics, and analytical geometry — directly relevant to TU and engineering university admissions.

IB Mathematics Analysis & Approaches at Higher Level is the most rigorous IB mathematics option, covering calculus, complex numbers, vectors, statistics, and proof. HL is required or strongly preferred for mathematics and engineering at top universities worldwide.

IB Mathematics Applications & Interpretation focuses on mathematical modelling, statistics, and real-world problem-solving. Widely taken by students heading towards social sciences, economics, and business.

The Dutch pre-university track with Mathematics A (applied) and Mathematics B (theoretical). Mathematics B covers calculus, vectors, and analytical geometry — required for science and engineering at Dutch universities.

Italy's secondary school leaving examination, with Mathematics as a written component for scientific lyceum students. Performance determines university admission for STEM faculties at Italian public universities.

Spain's university admissions assessment, with Mathematics II for science and technology students covering calculus, algebra, and statistics. Scores combined with Bachillerato grades determine university placement.

Switzerland's federal university entrance certificate, with Mathematics as a compulsory subject. The rigorous curriculum prepares students for Swiss universities including ETH Zürich, ranked among the world's best for mathematics and engineering.

Poland's national secondary leaving examination, with Mathematics as the only universally compulsory written subject. The extended-level Mathematics Matura is required for university engineering and mathematics programme admissions.

Russia's national university entrance examination with Mathematics tested at both Basic and Profile levels. The Profile-level mathematics test (100-point scale) covers algebra, calculus, geometry, and probability — and is among the most demanding in Europe.

The most demanding IB mathematics option, covering pure calculus, proof, complex numbers, and vectors at near A-Level Further Mathematics depth. Required for mathematics, physics, and engineering at competitive universities worldwide.

Standard Level IB Mathematics covering calculus, algebra, trigonometry, and statistics. A prerequisite for quantitative university programmes; HL is strongly preferred for competitive admissions.

Focused on mathematical modelling, statistics, and technology use — ideal for students targeting social science, economics, and business degrees. Less pure calculus than AA but still rigorous in statistical and discrete mathematics.

An enriched IGCSE qualification covering functions, binomial theorem, trigonometry, calculus, and coordinate geometry. Strongly recommended preparation for Cambridge AS & A Level Mathematics.

The globally recognised Cambridge A Level Mathematics qualification — Pure 1, 2, 3, Mechanics, and Statistics. Accepted by universities in the UK, US, Singapore, Canada, and across the Middle East as evidence of advanced mathematical preparation.

The Pearson Edexcel International A Level Mathematics offers a modular pathway for international students — widely used in Gulf countries, South Asia, and Southeast Asia as a route to UK and international university admissions.

The US national K–12 mathematics curriculum framework emphasising conceptual understanding, procedural skills, and mathematical practice. Strong Common Core performance underpins success in AP, SAT, and US university admissions.

A specialised GRE test for students applying to PhD programmes in mathematics, testing undergraduate calculus, algebra, and real analysis. A high score is required for admission to leading US mathematics PhD programmes.

The GATE Mathematics paper tests a comprehensive postgraduate curriculum including Real Analysis, Abstract Algebra, Linear Algebra, Complex Analysis, Differential Equations, Topology, and Probability. Essential for IIT and NIT mathematics faculty admissions.

Engineering Mathematics is a high-weightage GATE section common to all engineering disciplines. Covers Linear Algebra, Calculus, ODE, Probability, Statistics, and Numerical Methods — consistently carrying 13–15% of the total marks.

The national eligibility test for lectureship and JRF in Mathematical Sciences, covering Analysis, Algebra, Geometry, Topology, and Applied Mathematics at a high research-readiness level.

The UGC NET in Mathematical Sciences qualifies candidates for assistant professor positions at Indian universities and colleges. Tests pure and applied mathematics at a level aligned with MSc syllabi.

State-level equivalents of UGC NET, conducted by individual states for lectureship eligibility in state universities. Syllabi closely mirror UGC NET but are administered at the state level.

ISI's postgraduate entrance examinations in Statistics and Mathematics are among India's most demanding. The MStat entrance tests probability, analysis, and linear algebra; MMath covers real analysis, abstract algebra, and topology.

CMI's MSc entrance in Mathematics and Computer Science tests advanced undergraduate topics including real and complex analysis, abstract algebra, and combinatorics. A strong showing opens access to one of India's premier pure mathematics research institutions.

TIFR's entrance examination for its mathematics PhD programme is designed to identify genuinely research-ready mathematical talent. Topics include analysis, algebra, topology, and combinatorics at final-year undergraduate level.