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Mathematics, Ph.D.

  • Application Deadline
  • 60 months
University rank #2 (QS) Stanford, CA, United States
The doctoral program in Mathematics is designed to educate students in a broad range of mathematical disciplines, with emphasis on the student gradually acquiring expertise in a particular area of inquiry.
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  • Stanford’s undergraduate program in mathematics conveys a broad understanding of math that encompasses logical reasoning, generalization, abstraction, and formal proofs. Students learn to create, analyze, and interpret mathematical models and to communicate sound arguments based on reasoning and data analysis.
  • During their first year in the program, students typically engage in coursework and seminars which prepare them for the Qualifying Examinations. These two exams test the student’s breadth of knowledge in algebra and real analysis.
  • By the end of Spring Quarter of their second year in the program, students must have a dissertation advisor and apply for Candidacy.
  • During their third year, students will sit for their Area Examination, which must be completed by the end of Spring Quarter. This exam assesses the student’s breadth of knowledge in his or her particular area of research. The Area Examination is also used as an opportunity for the student to present his or her committee with a summary of research conducted to date as well as a detailed plan for the remaining research.
  • Typically during the latter part of the fourth or early part of the fifth year of study, students are expected to finish their dissertation research. At this time, students defend their dissertation as they sit for their University Oral Examination. Following the dissertation defense, students take a short time to make final revisions to their actual papers and submit the dissertation to their reading committee for final approval.

Detailed Programme Facts

  • Programme intensity Full-time
    • Full-time duration 60 months
  • Languages
    • English
  • Delivery mode
    On Campus

Programme Structure

Courses include:

  • Calculus
  • Linear Algebra, Multivariable Calculus, and Modern Applications
  • Integral Calculus of Several Variables
  • Ordinary Differential Equations with Linear Algebra
  • Modern Mathematics: Continuous Methods
  • Modern Mathematics: Discrete Methods
  • Modern Mathematics: Discrete Methods
  • Mathematics of Knots, Braids, Links, and Tangles

English Language Requirements

  • Minimum required score:


    The TOEFL iBT ® measures your English-language abilities in an academic setting. The test has four sections (reading, listening, speaking, and writing), each with a score range of 0-30, for a total score range of 0-120.

  • Minimum required score:


    The TOEFL®PBT is administered in a paper format and measures your ability to use and understand English in a classroom setting at the college or university level. It accurately measures how well you can listen, read and write in English while performing academic tasks.

Academic Requirements

  • This programme accepts GRE® scores. However, it does not provide a recommended score range.

    Schedule GRE®

    The GRE® General Test is a widely administered admissions test that measures the skills needed in today's graduate and business school programs worldwide. The GRE® General Test contains three sections - Verbal Reasoning, Quantitative Reasoning, and Analytical Writing. Three scores are reported: a Verbal Reasoning score on a 130 - 170 score scale in one-point increments, a Quantitative Reasoning score on a 130 - 170 score scale in one-point increments, and an Analytical Writing score on a 0 - 6 score scale in half-point increments.

General Requirements

Applications Requirements 

  • GRE Mathematics Subject Test Score (self-reported)
  • Statement of Purpose (document uploaded to online application)
  • Soft copy of transcripts/academic records (document(s) uploaded to online application)
  • Names and contact information of your recommenders; minimum of 3, maximum of 6 
  • TOEFL Scores (self-reported)
  • Application Fee - $125. Application fees are non-refundable and submitted with the online application.

Tuition Fee

Fellowship/assistantship salary and tuition guaranteed for first five years of the program  for all students, including international students

Living costs for Stanford

  • 1100 - 1600 USD/month
    Living Costs

The living costs include the total expenses per month, covering accommodation, public transportation, utilities (electricity, internet), books and groceries.


Studyportals Tip: Students can search online for independent or external scholarships that can help fund their studies. Check the scholarships to see whether you are eligible to apply. Many scholarships are either merit-based or needs-based.


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