95 · The Cambridge Shelf

Recommended readings, Cambridge mathematics. Algebra and Geometry — Alan F. Beardon. Linear Algebra — Peter J. Olver and Chehrzad Shakiban. Linear Algebra Done Right — Sheldon Axler. Basic Linear Algebra — T. S. Blyth and E. F. Robertson. Calculus, Volume 1 — Tom M. Apostol. Calculus — Michael Spivak. Principles of Mathematical Analysis — Walter Rudin. Introduction to Real Analysis — Bartle and Sherbert. A Course of Pure Mathematics — G. H. Hardy. Differential Equations — Blanchard, Devaney and Hall. Elementary Differential Equations and Boundary Value Problems — Boyce and DiPrima. Introduction to Probability — Bertsekas and Tsitsiklis. Probability — Grimmett and Stirzaker. Statistical Inference — Casella and Berger. Numerical Linear Algebra — Trefethen and Bau. Complex Analysis — Lars Ahlfors. Functions of One Complex Variable — John B. Conway. Introduction to Metric and Topological Spaces — Sutherland. Topology — James R. Munkres. Groups and Symmetry — Mark A. Armstrong.

Pure mathematics, by course. Numbers and Sets: Numbers and Proofs, Allenby. Groups: Groups — A Path to Geometry, Burn. Linear Algebra: Jänich. Analysis I: Introduction to Real Analysis, Berberian. Metric and Topological Spaces: Munkres. Complex Analysis: Ahlfors. Geometry: Brannan, Esplen and Gray.

Applied mathematics and theoretical physics. Vectors and Matrices: Mathematical Methods for Physics and Engineering — Riley, Hobson and Bence. Differential Equations: Boyce and DiPrima. Dynamics and Relativity: McComb. Quantum Mechanics: Principles of Quantum Mechanics — Dirac. Methods: Advanced Mathematical Methods for Scientists and Engineers — Bender and Orszag. Fluid Dynamics: An Introduction to Fluid Dynamics — Batchelor.

Probability and statistics. Probability: An Introduction — Grimmett and Welsh. Statistics — Freedman, Pisani and Purves. Markov Chains — J. R. Norris. Computation: An Introduction to Numerical Analysis — Süli and Mayers. The complete list of the textbooks offered across the Cambridge undergraduate mathematics course.

And that is literally the BEAUTY of doing your own academic research and following the Oxbridge and Ivy course structure on your own. In course settings you don't have the agility to explore beyond the syllabus — there's an obligation to do only what's on the test. First-year vector manipulation stays capped at three-dimensional Euclidean space, and that's all. For someone with massive curiosity, I'd love to see how this operates in higher dimensions, or transcends the concept of dimension entirely. Since I'm not obligated to sit any exams — this is personal exploration — I get to do exactly that, and read the hard books about it. Another illustration: reading beyond the curriculum. I can read the works on relativity Einstein conducted at Zurich rather than just the assignments confined to special relativity.

Intellectual curiosity, and having dexterity with abstract ideas, is itself the signifier of intelligence. I used to think the skills and the knowledge were the thing — but the initial mustard seed matters far more.

The strategy is just: read like hell in the topic of quant finance, trading and investing. Read 10,000 books, take the courses, ingest sheer knowledge. If you just read four hours of hard academic material a day for the next five years — a no-brainer — your new norm will be miles ahead of the mean.

Isn't it crazy that in a couple of months I'll be done with Real Analysis, Complex Analysis 1 and 2, Calculus 1 through 3, and Topology, while finishing more than a hundred textbooks' worth of graduate formulas and concepts mentioned in quant finance? Let's make history, G. We can do this metamorphosis. God is with you. Keep pushing. Go, go, go.