Mathematics

數學Sruh Heok Μᾰθημᾰτῐκᾱ́Mathēmatikā́

Mathematics is all I need.

• enthusiasm (...)

• attention (...)

Resources 🚧

如何选择一本适合你的《数学分析》教科书？北京某高校数学老师为你揭示选书的秘密_哔哩哔哩_bilibili

待考：有哪些数学书可以被称为「神作」？ - 知乎

待考：Math and Science - Subjects, Videos Lectures and Books

待考：Recomended reading for the undergrad category theorist

待考：Categories — fuller list of lecture notes and books

待考：learn-tt: A collection of resources for learning type theory and type theory adjacent fields.

精通教材学，松鼠症患者。下载过不等于看过，看过不等于核实过。

Calculus (Courant, Apostol, Spivak, Фихтенго́льцFikhtengol'ts) -> Analysis (Godement, Amann, Rudin, Loomis, Dieudonné, 张筑生, 梅加强, 于品, 邹应, 徐森林, 小平邦彦こだいら くにひこ, 高木貞治たかぎ ていじ, Хи́нчинKhinchin, ЗоричZorich)

• Vector Calculus (David Tong, Peter Baxandall) / Multivariable Calculus (Lax, Shifrin) -> Multi-variable Analysis (Duistermaat)
• 《数学分析习题课讲义》谢惠民、《数学分析中的典型问题与方法》裴礼文、《数学分析中的问题和反例》汪林
• Problems and Theorems in Analysis (Pólya), Problems in Mathematical Analysis (Biler)
• 齊震宇 臺大

Algebra (Godement, Chapter 0, Hungerford, Artin, Vinberg, Bourbaki, 李文威, 北师大, Кострикин) / Abstract Algebra (Dummit)

• Linear Algebra (Halmos, LADW, Lax) / Higher Algebra (李炯生, 丘维声) -> Advanced Linear Algebra (张贤科, 黎景辉, Roman) / Matrix Theory (张贤达 No interest, but there is a need to know.😓)
• Category Thoery (Milewski, Leinster, Riehl, Lawvere)
• Geometries (СосинскийSossinski)
• Half of Advanced Algebra (With Hints) XIONG Rui 半本高代习题集（带提示的那种) 熊锐
• Linear Algebra Problem Book (Halmos)

Set Theory (Halmos, Jech, Enderton)

Category Theory

Topology (Kelley, Simmons, Munkres, Morris, Bradley, nLab)

• Counterexamples in Topology, Steen

Analysis + Linear Algebra -> Real Analysis (Folland) / Complex Analysis / Functional Analysis (Halmos, Колмого́ровKolmogorov, Lax, )

• Introduction to Hilbert Space, and the Theory of Spectral Multiplicity Halmos
• A Hilbert Space Problem Book Halmos

Elementary Probability (鍾開萊Chung Kai-Lai, Papoulis, Ross) -> Probability Theory (鍾開萊Chung Kai-Lai, Rosenthal, வரதன்Varadhan, 伊藤清いとう きよし)

• Probability, Random Variables, and Random Processes (Schaum's Outlines) HSU (許？徐？) Hwei Piao

Probability and Statistics (Jaynes, 洪永淼Hong Yongmiao)

Mathematical Logic (Ebbinghaus, Manin, Hamilton, Shoenfield, Mendelson)

Discrete Mathematics (Knuth, Matoušek, 左孝凌)

Number Theory (Stillwell)

• A Friendly Problem Book of Elementary Number Theory (With Hints) XIONG Rui 初等数论习题

An Excursion through Elementary Mathematics, Neto

Disclaimer ⚠

❗ Warning: ❗ The list is completely

• Amazon/Douban-review-based

• Stack Exchange-recommendation-based

• search-engine-result-based

• forgotten/unknown-resource/gossip-based

• personal-opinion-based

• aleatory

My Words

I do not major in Mathematics and haven't received professional instructions on maths for a while. My enthusiasm for it has been quite worn down for a long time, partly due to my hatred for hateable boring math courses with relentless dumb damn exams, which sadly make me uninterested in doing a necessary amount of exercises. Also it's partly because of the situation that I struggle to persist in reading heavy tomes (especially those written in foreign languages), whereinto distraction, impatience and laziness easily trap me. That's why you won't find materials for advanced courses here — I haven't acquired their prerequisites yet.

• Still I'm struggling to find a way to learn maths without tears — no more cramming, no more "teaching to the test", no more motivationless knowledge born out of nowhere, no more countless tedious exercises... but following the creed „Wir müssen wissen. Wir werden wissen.“, to learn, « pour l'honneur de l'esprit humain ».

Quotations

μὴ εἶναι βασιλικὴν ἀτραπὸν ἐπί γεωμετρίαν

Non est regia [inquit Euclides] ad Geometriam via

There is no royal road to geometry.

几何无王者之道。

Superest ut ex iisdem principiis doceamus constitutionem Systematis Mundani.

Paul Halmos

如何笔记，如何“抄书”：

Don't just read it; fight it!
Ask your own questions,
look for your own examples,
discover your own proofs.
Is the hypothesis necessary?
Is the converse true?
What happens in the classical special case?
What about the degenerate cases?
Where does the proof use the hypothesis?

Roger Godement

assertion :

• (i) toute assertion qui n'est pas intégralement démontrée est potentiellement fausse et n'est, au mieux, qu'une conjecture intéressante,

• (ii) utiliser une assertion non complètement démontrée pour en prouver d'autres augmente exponentiellement les risques d'erreur,

• (iii) c'est à l'auteur d'une assertion qu'incombe la charge de la démontrer