Bairav Murugan

IMO Silver Medalist | INOI Gold Medalist

About Me

I am a 15-year-old unschooler and math enthusiast based in Bengaluru, focused on Pure Mathematics and Theoretical Computer Science. My education is self-directed and rigorous; I actively audit graduate-level courses at the Indian Institute of Science (IISc) under the mentorship of Professor Mahesh Kakde. This portfolio documents my coursework, competitive achievements, and teaching experience.

Higher Mathematics

Auditing at IISc

Under the mentorship of Prof. Mahesh Kakde.

Current & Recent Coursework:

- Introduction to Modular Forms - 2026
- Riemannian Geometry - 2026
- Ordinary Differential Equations - 2026
- Lie Groups and Lie Algebras - 2026
- Introduction to Differentiable Manifolds - 2026
- Algebraic Number Theory - 2024
- Class Field Theory -2025
- Representation Theory of Finite Groups -2025
- Commutative Algebra - 2025
- Lie Algebras and Their Representations - 2025
- Complex Analysis - 2025
- Measure and Integration - 2025
- Multivariable Calculus - 2025

Algebra II - 2025
Algebra I - 2024
Analysis I - 2024

Mathematical Olympiads

Focus: Advanced problem - solving & competitive mathematics.

Silver Medal - IMO 2026
Bronze medal - APMO 2026
INMO Awardee - 2025, 2026
IMOTC Participant - 2025, 2026
AIME Qualifier - 2025

Camps & Fellowships

Sophie Fellowship - 2025
STEMS Camp by CMI - 2024, 2025, 2026.
LIMIT & Enumeration - 2025
Epsilon India - 2022, 2023, 2024.
RAMTP - 2024.
Math.Biz - 2023.

Informatics & Computing

Focus: Algorithmic thinking & programming.

INOI Gold Medal - 2026
INOI Silver Medal - 2025
IOITC Participant - 2025, 2026
INOI Qualifer - 2024

Other Courses:

Princeton (COS226): Algorithms & Data Structures.
Princeton (COS126): Computer Science.
PACT - Program in Algorithmic and Combinatorial Thinking
RAM Crypto School

Community Contributions

Teaching Assistant for Proofs Camp by RAM in Pune - 2025
Teaching Assistant for Vijnan Manthan online program by Vichar Vatika - 2023 & 2024.
Mentored international students online during the PACT Group II Summer Course (UPenn) - 2024
Volunteer for Roots Camp - 2024 & 2025.

2026 (Age 15-Current)

Competitions:
- Represented India and won Silver Medal in International Mathematical Olympiad (IMO) 2026.
- Cleared Indian National Mathematical Olympiad (INMO) and selected for IMO Training Camp.
- Gold medalist in Indian National Olympiad for Informatics (INOI) and selected for IOI Training Camp.
Research: Continuing advanced mentorship and course audits at IISc under Prof. Mahesh Kakde.
IISc Audits: Completed graduate-level audits in
Community: Active participant in ICTS-TIFR Math Circles, Online Mathematical Club, Sophie Fellowship and OTIS.

2025 (Age 14)

Olympiads: INMO Awardee (Indian National Mathematics Olympiad), IMOTC Participant, and AIME Qualifier.
Informatics: Silver Medalist in INOI and selected for IOITC.
IISc Audits: Completed graduate-level audits in
- Multivariable Calculus
- Commutative Algebra
- Lie Algebras and Their Representations
- Algebra II
- Complex Analysis
- Measure and Integration
- Class Field Theory
- Representation Theory of Finite Groups
Fellowships: Selected for the Sophie Fellowship and OTIS (Olympiad Training in Individual Schemes).
Camps: Selected for STEMS Camp (CMI) and LIMIT Training Camp (ISI, Rank 6).
Leadership: Served as Teaching Assistant for the Proofs Camp (RAM Foundation, Pune).

2024 (Age 13)

Olympiads: Qualified IOQM (68 marks), RMO (83 marks) and will appear for INMO 2025.
Informatics: Qualified ZIO and ZCO and will appear for INOI 2025.
Started auditing Maths courses in IISc under the mentorship of Prof. Mahesh Kakde, he audited
- Algebra I
- Analysis I
- Algebraic Number Theory
Camps: Attended STEMS 2024 (CMI), Epsilon 2024 (Prayoga Foundation) and RAM TP 2024 (Coimbatore).
PACT: Completed year-long PACT course & Group II Summer Course by Prof. Rajiv Gandhi (UPenn).
Expanding into computer science, he successfully completed COS126 and COS226 online, foundational courses from Princeton University.
Community: Active member of the Online Mathematical Club and Math Circle (ICTS-TIFR/RRI). He also volunteered at the ROOTS Camp 2024.

2023 (Age 12)

Completed Cambridge IGCSE in 5 subjects (All A*).
Programs:
- REHMS: Research Experience in Mathematics for High Schoolers (Harvard-funded).
- Epsilon 2023 at CMI.
- Math.Biz at Mahindra University.
- RAM Crypto School.
- Quantum Wonder: Quantum Physics program by Dr. Hariom Jani.
Mathematics: Worked through Lang’s Algebra under Prof. Mahesh Kakde.

2020–2022 (Age 9-11)

Schooling: Part-time student at Poorna Learning Center while pursuing Grade 10 IGCSE.
Camps: Epsilon Math Camp (RAM Foundation) recommended by Mr. Vinay Nair.
University Coursework: Completed Astronomy: Exploring Time and Space (Univ. of Arizona) and Programming for Everybody (Univ. of Michigan) on Coursera.
Mentorship: Guided by Dr. Shiva and Dr. Ashwin during the lockdown.

Foundations (Age 2-8)

Age 8: Mentored by PhD associates Anil Kumar under Prof. K.R. Prabhu (IISc).
Age 7: Youngest participant in Summer School in Astronomy (MPBIFR).
Age 6: Completed Kumon Math Level F in 4 months; switched to Khan Academy for self-paced learning.
Age 5: Self-taught the Periodic Table and Organic Chemistry fundamentals.
Age 2.5: Began reading and exploring arithmetic.

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