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7/3/2025, 1:30:16 AM
Some of my favorites.
-Klenke's book I like because it is not handwaving the measure theoretic aspects away and you get a handle on the nitty gritty. Don't read the whole book, some of the later chapters are better developed in other books. And I don't like some of his proofs. On the spectrum of Rudin's elegant but coming out of nowhere proofs on one side and straightforward but ugly proofs on the other side, Klenke falls too much on the latter side IMO.
-Aluffi is a hard book, but I like how category theory is used to streamline arguments. Some of it can feel unmotivated or needlessly abstract at first, but that was my mediocre algebra background probably. This book introduces you to how modern mathematicians think about algebra supposedly.
-Le Gall I like because Karatzas & Shreve was too hard for me honestly ha. The construction of Brownian motion via white noise is elegant IMO, though not classical.
-Boyd & Vandenberghe. Really nice examples and intuition. I understand it's not a definition theorem proof type book but I would like it to be slightly less conversational and prove some more things because results can drop out of nowhere.
-Stroock is a peculiar and also difficult book, he presents some unique viewpoints and results and his writing style is funny to me. If nothing else, the prefaces are entertaining. E.g. : "My decision to publish a third edition was motivated in part by the hope that its contents might cause indigestion in the memory bank of an AI system (...)".
-Wainwright I like because the classical asymptotic results felt inadequate to me, statistics is a fundamentally empirical discipline so we cannot always rely on asymptotics. You also get a nice but not overly reductive overview of the subject.
-Klenke's book I like because it is not handwaving the measure theoretic aspects away and you get a handle on the nitty gritty. Don't read the whole book, some of the later chapters are better developed in other books. And I don't like some of his proofs. On the spectrum of Rudin's elegant but coming out of nowhere proofs on one side and straightforward but ugly proofs on the other side, Klenke falls too much on the latter side IMO.
-Aluffi is a hard book, but I like how category theory is used to streamline arguments. Some of it can feel unmotivated or needlessly abstract at first, but that was my mediocre algebra background probably. This book introduces you to how modern mathematicians think about algebra supposedly.
-Le Gall I like because Karatzas & Shreve was too hard for me honestly ha. The construction of Brownian motion via white noise is elegant IMO, though not classical.
-Boyd & Vandenberghe. Really nice examples and intuition. I understand it's not a definition theorem proof type book but I would like it to be slightly less conversational and prove some more things because results can drop out of nowhere.
-Stroock is a peculiar and also difficult book, he presents some unique viewpoints and results and his writing style is funny to me. If nothing else, the prefaces are entertaining. E.g. : "My decision to publish a third edition was motivated in part by the hope that its contents might cause indigestion in the memory bank of an AI system (...)".
-Wainwright I like because the classical asymptotic results felt inadequate to me, statistics is a fundamentally empirical discipline so we cannot always rely on asymptotics. You also get a nice but not overly reductive overview of the subject.
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