Study & Careers — Guides
Application experiences — source-linked accounts and advice for US, French / European and Japanese routes. For reading and learning mathematics, see Study advice.
US undergraduate applications · Mainland China: PhD, postdoc and preparation
US undergraduate mathematics: admission is not major declaration
The directory now lists 29 US university / college routes. These include research-focused private institutions and public universities with different curricula and costs; none is presented as a universal safe option. A mathematics major usually sits within an undergraduate college or university admission structure. Read that college’s first-year rules separately from later major declaration, honours selection and research participation.
Compare proof-based algebra, analysis and topology; the availability of advanced courses; and the conditions for an honours thesis. BA / BS names alone do not establish preparation for graduate pure mathematics. University of Minnesota’s CSE mathematics page describes later competitive major admission; do not generalize one school’s declaration rules to every university.
Use the current testing and document checklist. MIT and Stanford currently require SAT or ACT in the reviewed first-year guides; that does not establish another university’s policy. English evidence, qualification recognition, aid eligibility and financial documentation must be checked by applicant category. A mathematics placement examination after admission is not necessarily an entrance test.
Keep early and regular application rounds, optional-art deadlines, financial-aid forms and supporting-document deadlines separate. A generic annual date is not automatically a dated 2027 window. Mathematics-specific intake and admission-rate information is mostly unverified here; university-wide admit rates cannot be converted into a personal mathematics admission probability.
Mainland China: distinguish applicant category and research stage
The directory adds 10 doctoral routes, 5 postdoctoral routes and BICMR’s spring-2027 preparation semester. Domestic application-assessment, recommended direct doctorate, internal master-to-doctorate continuation and international graduate admission are not interchangeable. Hong Kong/Macao/Taiwan admissions can have a separate category-specific process. A foreign degree held by a domestic applicant is also a different question from foreign citizenship.
For a doctorate, check the mathematical discipline and exact institution / year / round. Material assessment, supervisor agreement, written mathematics subjects, language evidence and academic-document recognition depend on that route. Some currently accessible departmental pages still contain historical 2025 or 2026 notices; no new application window is extrapolated from them. The Shenzhen historical call contains conflicting email-material and ordinary submission years, explicitly flagged in the directory.
A postdoc is not a student degree. Compare host fit, contract, age and years-since-PhD restrictions, references, employment eligibility and actual salary / tax / benefit conditions. BICMR’s dated 2026 call states whole-year applications, while YMSC’s landing-page prose still refers to 2025 starts and links separate application listings. A standing institutional route does not prove a particular host has a vacancy.
BICMR’s Enhanced Program for Graduate Study is a visiting preparation course for existing upper-level undergraduates / early graduates, not admission to a new degree. Its spring-2027 notice plans about 30 participants and lists applications September 23–October 23, 2026; the closing hour is not stated. Participation does not guarantee subsequent graduate admission.
Undergraduate / preparatory routes · Research institutes · Approaching potential supervisors · Researcher search · Fee status
Undergraduate and preparatory routes
Start with your school-leaving qualification and teaching language. Degree admission, major declaration, a university-entrance foundation certificate and post-bachelor preparation are different steps. An integrated MMath entered from school is an undergraduate application route, not the same as an externally recruited master.
Oxford Mathematics now lists TMUA for 2027 entry, rather than the old MAT. Cambridge’s current timetable also names TMUA for Mathematics alongside later STEP offer conditions: check both, not an old online summary. Test registration can close before the degree application.
German Studienkolleg is needed only for particular qualification routes. TUM’s T-course includes mathematical preparation and an admission test; passing the preparatory course is not an unconditional degree-place promise. The Auckland international foundation certificate has its own provider and progression conditions.
After a bachelor, ICTP’s mathematics diploma is research preparation, not an MSc. Its developing-country scholarships and self-funded route have different conditions. Compare actual prerequisites rather than calling every preparatory programme a school-leaver foundation.
Research institutes: not always degree admission
Distinguish a research visit, stipendiary membership, employed postdoc and university-enrolled PhD. An institute’s permanent faculty appointment does not mean the institute independently grants the degree. Joint appointments require checking the actual university application.
MPIM has distinct guest and postdoctoral routes. Its current page gives October 16, 2026 for the next selection round and requires two reference letters. It explicitly prohibits AI use in the research statement: applicants must respect that requirement and write the statement themselves.
IAS describes about 35 ordinary postdoctoral memberships within approximately 85 annual Members of all categories. Those are generic approximate figures, not 85 advertised postdoc vacancies. Its December 1 page omits a deadline year; confirm the current linked call before using a dated filter.
Using the researcher directory responsibly
Current affiliation, research interests, public past student events and current student availability are separate claims. This directory does not infer vacancies from publications or former students. A public thesis completion does not establish when a student was recruited.
Check whether the programme requests prior supervisor agreement, permits informal contact or uses committee admission. Write an individual, concise message only when appropriate: explain genuine mathematical preparation, the specific topic and the question you need answered.
Use official academic contact pages. Do not send private transcripts without a legitimate requested route. When no record is shown, that means no qualifying public event verified here, not that the researcher supervises nobody.
Preparing for a research-oriented master
Compare the actual curriculum with your completed courses: proof-based linear algebra, real analysis, abstract algebra and topology form a useful core. For algebraic geometry, add commutative algebra; for number theory, add field and Galois theory; for PDE, add measure theory, functional analysis and differential equations. These are editorial preparation suggestions, not universal admissions requirements.
If your degree has limited proof-based coursework, build evidence through assessed courses, a carefully supervised reading project and substantial written mathematics. A concise expository thesis can demonstrate independence without pretending to be an original research paper. Ask each programme whether additional credits or qualifying courses are possible.
For applicants already well prepared, compare research electives, thesis arrangements, seminars and possible supervisors. Institutional prestige alone does not establish subject fit. No institution is a universally safe admission choice.
France, Germany, Switzerland and joint degrees
In France, M1 and M2 are stages of a master, not two different degrees. An M2 research specialization usually expects preparation comparable to completed M1; an international three-year bachelor does not automatically qualify for direct M2. Check the specific track, language and residence-dependent application route. Mon Master, Études en France and university M2 applications are not interchangeable.
Germany’s consecutive mathematics masters assess subject preparation and credit equivalence. “No restricted admission” does not mean every application is accepted. Do not infer teaching language from an English website: Heidelberg’s mathematics master differs from its English Scientific Computing degree, while Regensburg explicitly permits courses in English.
Swiss degrees differ in length: ETH’s mathematics MSc is 90 credits, and other universities have their own plans. Tuition categories and additional semester costs must be checked separately.
ALGANT is a two-country algebra, geometry and number-theory master. Apply once through the consortium, check mobility requirements and do not count partner universities as separate joint degrees. InterMaths is a separately labelled applied-mathematics option; old scholarship selections are not a guarantee for a future cohort.
Direct doctorates and master-to-PhD transitions
Many US mathematics departments admit students to a doctoral programme after a bachelor’s degree. This is not equivalent to saying every bachelor graduate has sufficient preparation. Advanced courses, mathematical writing, detailed recommendations and research potential matter; a publication is not a universal prerequisite.
A master earned during a US PhD is not automatically an externally recruitable terminal master. Stanford explicitly restricts non-Stanford mathematics applicants to PhD admission; its coterminal master is an internal route. Cambridge’s external Part III MASt is a genuine graduate master, distinct from the undergraduate continuation MMath.
In Canada, distinguish MSc admission, direct-entry doctoral admission and later transfer. In Australia, distinguish a coursework master with a research project from a research MPhil. Hong Kong’s MPhil and PhD paths can articulate but have different degree and progression rules. Singapore’s NUS explicitly offers an admitted research MSc, distinct from its coursework degree.
Check standardized tests every year. Berkeley’s official FAQ currently requires the Mathematics GRE Subject Test for Fall 2027; old “GRE optional everywhere” advice is not reliable.
Japan: examination and international routes
A 修士 (master’s) degree and a 博士後期 (post-master doctorate) are degree stages. A 研究生 research-student appointment is generally non-degree status; admission to it does not itself confer a master or guarantee later examination success. Do not treat it as a mandatory step for every international applicant.
Start with the current department notice, not a generic English admissions homepage. Verify written and oral mathematics subjects, Japanese and English requirements, academic equivalence, examination location, entry term and whether supervisor contact is required. International special screening can have narrower eligibility than ordinary admission. A master entrance examination for April 2027 may already have taken place in summer 2026.
Use the department’s past papers to identify gaps and practise full timed solutions. Plan language preparation alongside mathematics. Ask about the next remaining application round rather than reusing a closed summer call. Kyoto’s ordinary master route expects Japanese; Kyushu’s linked April 2026 special-screening notice is historical and must not be advertised as open.
Application materials and an evidence-based shortlist
Keep a programme-by-programme checklist: degree eligibility, proof-based course requirements, teaching language, examination or interview, supervisor requirement, funding application, official fee category and verified deadline with timezone. Record the exact source and date beside each fact. Where two pages disagree, ask the admissions office and retain the reply.
A mathematical CV should describe completed courses, genuine projects, talks and employment accurately. Separate submitted papers, accepted papers, preprints and expository notes. Describe your own contribution to joint work. In a statement, explain subject preparation and why the programme’s curriculum or supervision fits; do not claim certainty about a research problem you have not studied.
Give recommenders a transcript, course list, draft statement and enough notice. Choose people who can discuss your mathematical work in detail, not only famous names. Submit translations and certified documents in the format the institution actually requests; do not publish private transcripts on this website.
Build several options differing in curriculum, language, selection route and verified cost. Applicants from different educational systems may need different evidence, but undergraduate institution names do not justify a universal admission probability or “safe school” claim.
Fees, scholarships and less familiar destinations
Calculate total cost, not only tuition: mandatory semester charges, living costs, health insurance, visa/residence costs, travel and deposits. Fees may differ by citizenship, residence, previous studies or fee group. Quote the currency and charging period. A tuition waiver is not a living stipend; an advertised fellowship may require a separate competition and satisfactory annual progress.
French public fees have national and differentiated categories, with institution-specific exemptions. Do not apply a single rate to every applicant or private/joint programme. Germany is not uniformly tuition-free for all internationals: Bonn states no tuition but a semester social contribution, while TUM flags international tuition. ETH has distinct CHF tuition groups.
IMPA offers genuine research degrees in Brazil, distinct from professional education programmes. USP, Unicamp, UNAM and the University of Chile are further routes to investigate; language, degree recognition and funding eligibility differ. Weizmann’s Mathematics and Computer Science page has a specific 2027 MSc deadline. Hebrew University explicitly has international master and doctorate routes, but this does not make every Israeli course English. KAUST’s programme is applied mathematics and computational science. King Saud requires checking the current regular/paid programme list and international eligibility; old handbooks do not establish open admission.
Postdoctoral applications
Compare the host’s research fit, expected PhD completion date, contract length, teaching load, salary or stipend, mobility/residence conditions and any host-sponsor requirement. A fellowship and an employed postdoc may have different benefits and eligibility. A listing on a job portal is not proof the position is still accepting applications.
Prepare a research statement understandable beyond your narrow topic, a selected-publication list with accurate status, a CV and strong research references. Discuss collaborations realistically rather than promising results. Country-specific fellowship rules can restrict time since PhD or nationality; read the current call.
MathJobs, EURAXESS and JSPS postdoctoral fellowships are discovery entries, not a list of verified open positions. Always check the institution’s own notice.
Faculty and longer-term careers
Research faculty, teaching-focused faculty, fixed-term lectureships and permanent civil-service posts are different roles. Compare teaching language, workload, tenure or probation conditions, legal eligibility and the actual selection criteria. Do not treat a past advertisement as a current opportunity.
Research-oriented applications commonly require a CV, research statement, publication list and references; teaching-oriented roles also require evidence of effective teaching. Exact documents and rules depend on the call. Explain independence and a coherent research direction without overstating contributions.
Start with MathJobs, EURAXESS and the target department’s official hiring page.