Academic Preparation (Courses & Skills)

All 4 compulsory math courses.

Build a strong mathematical foundation. Take calculus (single‐ and multivariable), advanced calculus/
analysis, and linear algebra—these are “the most essential courses” for a math grad applicant 1 . For
applied math, also master ordinary/partial differential equations, and probability & statistics 1 . Since
you’re interested in astrophysics/space and computation, try to take courses in mathematical physics,
fluid/astro dynamics, numerical methods, and scientific computing (e.g. high-performance computing, C+
+/Python programming). If IIT Ropar doesn’t offer some courses, supplement with online/bridge programs.
In short, focus on the full calculus sequence, linear algebra, ODE/PDE, and probability/statistics, plus at
least one programming language 1 . This prepares you to tackle graduate-level work and the GRE Math
Subject Test.

• Example: NYU’s Courant Institute recommends calculus, advanced calculus, and linear algebra first,
then ODEs/PDEs and probability for applied math 1 .

Research Experience (Internships & Projects)

Gain hands-on research exposure in applied mathematics, computational science or astrophysics. Seek
summer research programs and internships both locally and abroad:

• TIFR/ICTS Summer Programs (India): For example, the TIFR Centre for Applicable Mathematics in
Bangalore offers a summer research internship for Indian undergrads in math, science or
engineering 2 . This program (May–July) pays a stipend and pairs you with faculty mentors on real
projects 2 3 . Apply by early 2025. The ICTS (TIFR Bangalore) also runs summer programs in
mathematics and physics. Similarly, NCRA-TIFR Pune runs a Visiting Students Research Program in
astrophysics/radio astronomy 4 . These are funded and prestigious opportunities to build research
skills and get a strong reference.

• International REUs/Internships: Many US/European summer programs accept strong international

applicants. For space/astrophysics interests, consider programs like the LIGO Summer
Undergraduate Research Program at Caltech (in gravitational-wave science), which is NSF-funded
and explicitly invites undergrads worldwide 5 . Likewise, apply to NASA’s internships – NASA has a
special International Internship (NASA I²) for foreign students, with sessions in spring/summer/fall 6 .
(This requires planning well in advance.) Also look for computational/space REUs: e.g., the European
“MASS” Erasmus Mundus program in Astrophysics & Space Science is a 2-year funded master’s that Backup

includes research projects 7 . Even if you aim for PhD, applying as a master’s candidate can be a
good backup (see below).

• IIT Ropar Independent Research: Leverage local faculty. For example, Dr. S.C. Martha (Math Dept)
works on water-wave mechanics, PDEs and numerical simulation 8 . Discuss with him or other
professors about a project or reading course related to your interests (computational fluid/space).

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 Even a small independent study under a professor is valuable. If possible, do a senior design/
project that involves simulation or modeling (e.g. CFD or orbital mechanics) to show initiative.

• Research Assistantships: In your final year or after graduation, try to obtain an RA position. This
could be as a project assistant at IIT Ropar (if funding exists) or at national labs (ISRO, DRDO, DAE
institutes). Although paid RA jobs are rare for undergrads, reaching out to professors early can
sometimes yield opportunities to help on grant projects.

Throughout, document any work you do (reports, code, minor publications). These experiences will
strengthen your CV and give topics to discuss in applications and interviews.

Standardized Tests (GRE, Subject GRE, TOEFL/IELTS)

Plan early to prepare for and take the required exams:

• GRE General: Many U.S. PhD programs still require the GRE General Test (verbal, quantitative,
writing). Start studying by senior year. Aim for a Quant score well above 160 (math majors often
target 165+). A high GRE Quant can help offset a moderate GPA. While some programs waive GRE
scores, don’t assume it—check each program.

• GRE Mathematics Subject Test: Most top applied math/physics programs recommend or require the
Math Subject Test 9 . A strong score (e.g. ≥80th percentile) can help compensate for weaker
grades in a few courses and demonstrate mathematical breadth 9 . The Syracuse Math Dept. notes
that many math-intensive grad programs expect it 9 . Take it in October or November of your
senior year and use it to showcase your calculus, algebra and analysis proficiency.

• TOEFL/IELTS: As an Indian student, you must prove English proficiency. Aim high (e.g. TOEFL iBT ≥
95 or IELTS ≥ 7.0). Illinois Math, for example, requires a minimum TOEFL iBT of 95 (with 22 in
speaking) or IELTS 6.5 for PhD admit 10 . Many programs have similar or higher cutoffs. Plan to take
the test by early senior year so you can retake if needed. Strong TOEFL/IELTS scores also make you
eligible for TA-ships (some schools require it for teaching).

GPA and Academic Profile

Your CGPA (7.24/10) is moderate. Improving it even slightly will help: focus on maximizing grades in your
remaining courses. If your program allows grade replacement or withdrawal, use wisely. Review every
course grade and appeal/retake if just below a threshold. Also, your math minor is an asset – highlight it.

However, be realistic: many top programs expect near 3.5/4.0 (≈8.5/10) as competitive 11 . For example,
UIUC’s Math PhD page warns they “typically do not accept students with a GPA below 3.25 on a 4.00 scale,
and GPA is a significant factor” 11 . To strengthen your profile, emphasize other factors (research, tests,
letters) and apply to programs with slightly lower GPA expectations. A stellar GRE Math score and research
can offset GPA gaps to some degree 9 11 .

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Recommendation Letters
Secure strong letters of recommendation (usually 3) from people who know your math ability or research
potential. Ideal referees are professors who taught you in upper-level math/engineering courses or
supervised any projects. UIUC notes that letters “from professors who have taught you in mathematics
classes or who have supervised you in a research project are the most useful” 12 . For example, ask your
current professors (perhaps your minor instructors or Dr. Martha) or any summer project mentors well
before deadlines. Build a relationship now: visit professors during office hours, excel in their classes, and
discuss your interests. A detailed, personalized letter (vs. generic) will carry more weight 12 .

Application Strategy & Timeline

Plan a concrete schedule for the next two years:

• Summer 2024 (Now):

• Courses: Enroll in any missing math courses (analysis, algebra, etc.). Attend workshops or online
courses to shore up weak areas.
• Identify Mentors: Talk to IIT Ropar professors in mathematics, mechanical or physics about
interests and potential projects. Express interest in astrophysics/computational work.
• Test Prep: Begin studying for GRE general and Math subject tests.

• Plan Summer 2025: Identify and prepare applications for summer programs (TIFR SSRP, LIGO REU,
NASA I², etc.). Gather transcripts and potential reference writers.

• Summer 2025:

• Research Internship: Participate in a research program. For example, apply by March 2025 to TIFR-
CAM SSRP 2 (stipend ~₹9k/month 3 ). Submit strong applications to international REUs (LIGO’s
program 5 ) and NASA (NASA I² deadlines typically in Nov/Feb).

• Undergrad Thesis: If your curriculum has a project or thesis, use this summer’s work/data in it.

• Fall 2025 (Senior Year Begin):

• Advanced Courses: Take any remaining electives in mathematical physics, numerical analysis, or
computational methods. Try to get As in these to boost GPA.
• Continue Research: If possible, extend summer work or start a small independent project (perhaps
evolving summer REU work or a new simulation). Even a part-time RA role (paid or unpaid) bolsters
experience.

• Letters: Ask for recommendation letters by November 2025. Provide professors with your CV and
summary of work.

• Late Fall 2025 (Application Season):

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 • Apply to PhD Programs: Prepare a list of target PhD programs (US and Europe) in applied math/
astrophysics that match your profile and interests. Emphasize funded PhDs only. (Most U.S. PhDs
come with funding by default; European funding varies by program.) For Europe, keep in mind many
schools expect a master’s 13 (see backup below).
• Research Statements: Many UK/Europe programs require a research proposal. Manchester’s
website, for instance, explicitly asks applicants to include “Your proposed supervisor’s name” and
“research project title” 14 . So contact potential advisors now to discuss fit. Include in your
applications the names of professors whose work aligns with yours 14 .
• Deadlines: U.S. PhDs often have December deadlines; European deadlines vary (often Jan–March).
Submit applications with transcripts, test scores, statement of purpose, and references by each
deadline.

Backup Plan (Master’s or RA)

If a direct PhD offer isn’t secured, have a strong fallback:

• Funded Master’s: In Europe especially, a Master’s is typically required for PhD entry 13 . Consider
applying to fully-funded Master’s programs in applied math/physics. For example, Erasmus Mundus
programs (co-funded by the EU) offer scholarships: e.g. the MASS joint master in Astrophysics &
Space Science (Italy/France/Germany/Serbia) is a 2-year English program open to internationals 7 .
Getting an EU scholarship would give you top-level coursework and research experience (and a
degree recognized for PhD entry). There are similar programs in computational science, engineering,
or space science. Also look for scholarships like DAAD in Germany or Marie-Curie Masters. A funded
Master’s (or even just studying with stipend support) can significantly boost your GPA, skills, and
publications before reapplying to PhD programs.

• Research Assistant (RA) Jobs: Alternatively, search for a research assistantship after graduation.
Indian institutions sometimes hire B.Tech graduates on projects (e.g. ISRO, DRDO labs, IITs). Even a
year as an RA working on simulations or data analysis will deepen your resume. If abroad, some labs
in Europe/US might hire graduate students for assistant roles, but you’d likely need a postgrad
degree. Any research work (especially leading to a publication) will help later PhD applications.

In either case, keep improving your profile: take any qualifying courses needed, publish a bit (even a
conference proceeding), and strengthen relationships with mentors for future references. As one profile
notes, without a Master’s, it’s “nearly impossible” to start a PhD in Europe 13 , so securing a Master’s or
equivalent experience is a realistic fallback path.

Summary of Key Steps Winter and Summer Break

(additional time)
Till Mid-sem (Build Cool Stuff)

• Now (3rd Year): Hone essential math skills (analysis, algebra), start programming practice. Seek
small projects or readings with professors. After Mid-Sem (ask Navneeth Sir)

• Next Summer: Apply and attend research internships (TIFR-CAM, LIGO, etc.) 2 5 . Begin draft of
senior thesis/project.
• Senior Year: Take advanced electives (PDE, numerical methods, astrophysics); aim for high grades.
Continue any research. Prepare for GRE/TOEFL early. Request recommendation letters by November.

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 • Application (Fall of Final Year): Finalize program list. Reach out to potential advisors. Submit PhD
applications (mention research area/supervisor as Manchester advises 14 ) to funded programs
only.
• If Needed: Pursue a funded Master’s (e.g. Erasmus Mundus Astrophysics 7 ) or an RA position to
strengthen your candidacy.

By following this roadmap diligently—taking the right courses 1 , securing research experiences 2 5 ,
and performing well on exams 9 10 —you’ll maximize your chances for admission to a top applied math
PhD program.

Sources: Authoritative program websites and guides have been cited above 1 5 9 11 7 2 13 ,
which reflect current expectations for math PhD applicants.

1 Prerequisites | Department of Mathematics | NYU Courant

https://math.nyu.edu/dynamic/graduate/overview/prerequisites/

2 3 Summer Student Research Programme 2025 — TIFR CAM Bangalore

https://www.math.tifrbng.res.in/academic/internships

4 TIFR | Academics
https://www.tifr.res.in/academics/summer_program.php

5 Undergraduate Research at LIGO

https://www.pathwaystoscience.org/programhub.aspx?sort=SUM-CalTech-LIGO

6 NASA Internship Programs - NASA

https://www.nasa.gov/learning-resources/internship-programs/

7 Master in Astrophysics and Space Science – Erasmus Mundus Joint Master Degree
https://www.master-mass.eu/

8 Dr. Subash Chandra Martha | Indian Institute of Technology Ropar

https://www.iitrpr.ac.in/mathematics/scmartha

9 GRE Mathematics Subject Test - College of Arts & Sciences at Syracuse University
https://artsandsciences.syracuse.edu/mathematics/undergraduate-studies/gre-mathematics-subject-test/

10 11 12 Apply to PhD Program | Department of Mathematics | Illinois

https://math.illinois.edu/admissions/graduate-admissions/apply-phd-program

13 Ph.D in Europe without a Master's degree? : r/AskAcademia

https://www.reddit.com/r/AskAcademia/comments/13ydaij/phd_in_europe_without_a_masters_degree/

14 PhD Applied Mathematics (2025 entry) | The University of Manchester

https://www.manchester.ac.uk/study/postgraduate-research/programmes/list/05305/phd-applied-mathematics/