University of Warwick · MMath Mathematics · Class of 2030

Abdul Musthakin

Mathematics undergraduate. Algebraic topology, differential geometry, algebraic geometry, mathematical physics.
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Introduction

I am a first-year student at the University of Warwick, studying mathematics on the four-year MMath course.

Most of my time is spent on independent study of mathematics. Thus far, my studies have included topics in real and complex analysis, differential geometry, and algebraic topology.

Remark 1.1. I prefer to have the intuition behind difficult ideas before I learn the underlying theory.

Remark 1.2. Beyond pure mathematics, I am interested in the mathematical foundations of physics. I am also considering quantitative finance as a possible pathway following university.

3.1 Algebraic Topology 3.2 Differential Geometry 3.3 Algebraic Geometry Fundamental Group Smooth Manifolds Varieties Homology Differential Forms Sheaves Spectral Sequences Schemes
Fig. 2 — The topology and geometry thread: what leads to what, roughly. Each box links to its subsection.
StudiedWorking onAhead

Preliminaries

Sep 2026 — Jun 2030

University of Warwick

MMath Mathematics

First year of a four-year integrated master's programme.

Options this yearST121 Statistical Laboratory, PH136 Logic 1: Introduction to Symbolic Logic, CS141 Functional Programming

Sep 2024 — Jun 2026

Cardiff Sixth Form College

A-levels

Mathematics, Further Mathematics, Physics, and Chemistry.

ResultsA* A* A* A*

Vice-president of the Maths Society. Delivered approximately 30 talks to other students on topics ranging from Faulhaber's formula and discrete calculus to group theory and exact sequences. One of four students in an advanced seminar that worked through H. N. Shapiro's proof of Dirichlet's theorem on arithmetic progressions.

Also mentored GCSE mathematics students and helped with open days. Participated in competitions, including the BPhO, the SMC, and the SPC.

Current Work

Currently on[CHAPTER AND BOOK]as of [DATE]

3.1Active

Algebraic Topology

Homotopy (specifically the fundamental group), simplicial and singular homology, from [Hat02] alongside [Lee11] for reference. After Hatcher, [tD08] and [May99] for more advanced material.

3.2Active

Differential Geometry

Smooth manifolds, differential forms, and de Rham cohomology, from [Lee12] and now [BT82]. Focused primarily on topological properties rather than geometric ones arising from extra (e.g. Riemannian) structure. Wrote one exposition of differential forms, with a longer, rigorous treatise in progress; both are listed under notes.

3.3Incubating

Algebraic Geometry

Light reading, aiming to obtain intuition for key concepts such as affine varieties, using [Rei88]. Will rigorously study the subject via [Vak25].

3.4Active

Probability and Statistics

Mathematical statistics, working through [CB02].

3.5Background

Mathematical Physics

The mathematical foundations of general relativity and quantum field theory.

See alsonotes/

References

  1. [BT82]R. Bott and L. W. Tu, Differential Forms in Algebraic Topology. Graduate Texts in Mathematics 82, Springer, 1982.
  2. [CB02]G. Casella and R. L. Berger, Statistical Inference, 2nd ed. Duxbury, 2002.
  3. [Hat02]A. Hatcher, Algebraic Topology. Cambridge University Press, 2002.
  4. [Lee11]J. M. Lee, Introduction to Topological Manifolds, 2nd ed. Graduate Texts in Mathematics 202, Springer, 2011.
  5. [Lee12]J. M. Lee, Introduction to Smooth Manifolds, 2nd ed. Graduate Texts in Mathematics 218, Springer, 2012.
  6. [May99]J. P. May, A Concise Course in Algebraic Topology. Chicago Lectures in Mathematics, University of Chicago Press, 1999.
  7. [Rei88]M. Reid, Undergraduate Algebraic Geometry. London Mathematical Society Student Texts 12, Cambridge University Press, 1988.
  8. [tD08]T. tom Dieck, Algebraic Topology. EMS Textbooks in Mathematics, European Mathematical Society, 2008.
  9. [Vak25]R. Vakil, The Rising Sea: Foundations of Algebraic Geometry. Princeton University Press, 2025.

Correspondence

Happy to talk about mathematics, reading groups, and research projects.

abdulmusthakin@gmail.com github/abdulmusthakin linkedin/abdulmusthakin