Stephen Donahue
234f3697f6
2.0 KiB
Rough Notes
n = 2^x
a \implies b
x \leq 10
\infty
\nabla f
\cdot F
\alpha \beta \gamma \delta
\Alpha \Beta \Gamma \Delta
\mathbf{\nabla F}
\vec{\nabla}F
\nabla\times\mathbf{F}
Quotes
Reading List
- Terry Tao's blog and notes — search "Stirling" on terrytao.wordpress.com. He has at least two posts deriving it different ways, with characteristic clarity.
- Tim Gowers' blog (gowers.wordpress.com) — Fields medalist who writes a lot about how mathematicians actually think. His posts on "how to discover proofs" capture the guess-and-check spirit we discussed.
- Bender & Orszag, Advanced Mathematical Methods for Scientists and Engineers — the canonical reference for Laplace's method, saddle points, and the full asymptotic series for n!. Hard but rewarding. Chapter 6 is where the √(2πn) gets properly explained.
de Bruijn, Asymptotic Methods in Analysis — slim, elegant, and entirely about the "why" of asymptotic approximations. Stirling appears early and is revisited from multiple angles.
Concrete Mathematics (Graham, Knuth, Patashnik) — Chapter 9 ("Asymptotics") derives Stirling combinatorially and discusses its uses in analysis of algorithms. Very readable, lots of margin notes and dry humor.
Apostol, Calculus (Vol. 1) — older, more formal than Spivak, but unusually careful about why each technique exists. Starts with integration before differentiation, which itself is illuminating.
Tristan Needham, Visual Complex Analysis — not about Stirling specifically, but the gold standard for "geometric intuition for things usually taught algebraically." If the rectangle-sandwich picture appealed to you, this book is a feast.
Tristan Needham, Visual Differential Geometry and Forms — same author, same spirit, applied to calculus on curves and surfaces. Shows what dx, integration, and differentiation look like.
Questions
Definitions
- Benjamin Disraeli - British PM, novelist.
- "To be conscious that you are ignorant is a great step to knowledge."