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Jiu Ding / 丁玖 · 如何读好数学书？｜展卷
Learning & research advice · Mathematical reading & proofs · Chinese
Explains how precise definitions, simple cases and the decisive idea of a proof turn reading into understanding. A request to negate an epsilon–delta definition illustrates the difference between repeating a definition and being able to reason with it.
Use / preparation: For readers who recognize textbook arguments but cannot yet adapt them to a new example; an authorized excerpt from the chapter 读书妙法. · Authorized book excerpt / author advice · A published excerpt, not the full book; recollections of other mathematicians are presented through the author's account. · Checked 2026-10-16
Shihai Yang / 杨世海 · 【论教】数学分析教学体会浅谈
Learning & research advice · Analysis & proofs · Chinese
Discusses independent reading, purposeful exercises and reflection in a first university analysis course. Comparisons of Cauchy–Schwarz proofs and the nested-interval proof of the intermediate value theorem show why an illuminating argument need not simply be the shortest one.
Use / preparation: Read the student questions and the author's replies as well as the initial essay, especially when deciding how to practise analysis. · Author-contributed university essay & discussion · 2016-09-09 · Checked 2026-10-16
Qi'an Guan / 关启安 · 教师代表关启安教授在数学科学学院2021年开学典礼上的致辞
Learning & research advice · Mathematical learning & research · Chinese
Connects repeated textbook reading with active questions: are a theorem's hypotheses needed, can its proof be simplified, and can the conclusion be strengthened? The address also discusses explaining arguments and learning through seminars.
Use / preparation: A short starting point for moving beyond knowing a theorem's statement toward asking your own mathematical questions. · Faculty address · 2021 address · Checked 2026-10-16
USTC student contributors, including Junyan Zhang / 章俊彦 · USTC基础数学修课指南（第三版第一稿）
Learning & research advice · Undergraduate mathematics / analysis / topology / probability / combinatorics · Chinese
A 193-page student-written guide combining prerequisite planning, textbook discussion and explanations of different subjects. Selected sections discuss metric-space examples in topology and counting methods such as double counting, generating functions and the probabilistic method.
Use / preparation: Use the contents to select a subject rather than treating the entire guide as a required linear reading plan. · Unofficial collaborative student guide · 2020-09-26; third-edition draft · Selected sections were reviewed, not every recommendation in the 193-page draft. It is an unofficial student guide, not a current USTC curriculum or admissions policy. · Checked 2026-10-16
Tim L · 如何學習數學
Learning & research advice · Mathematical learning / calculus / numerical analysis · Chinese
Organizes learning around a topic's motivation, its actual content and its connections to other ideas. Deriving the quotient rule through different routes illustrates how connections reduce dependence on memorized formulas.
Use / preparation: For revising calculus or approaching a new subject; compare the explanation of why a method is needed with the method itself. · Personal teaching advice · 2023-02-27 · Checked 2026-10-16
Tim L · 不確定自己寫的證明對不對，可以如何學習
Learning & research advice · Mathematical learning & proofs · Chinese
Treats proof writing as learning precise communication through practice, feedback and revision. The author compares revising a corrected proof with rewriting a marked composition, rather than checking only the final grade.
Use / preparation: For a first proof course or reading group; a correct proof can differ from a model solution, but still needs its logical steps checked. · Personal teaching advice · 2022-11-26 · Checked 2026-10-16
Dayue Chen / 陈大岳 · 要学概率论？（作者主页链接名）
Learning & research advice · Probability / measure theory / stochastic processes · Chinese
Outlines routes from undergraduate probability and real analysis toward measure-theoretic probability, stochastic processes and stochastic analysis. Separate sequences for continuing undergraduates and incoming graduate students make the preparation differences concrete.
Use / preparation: Use the course sequence to locate gaps before advanced probability; this is a roadmap, not a sustained essay or a prerequisite for every probability course. · Faculty study roadmap · The display name follows the author's homepage link, not an independent article heading. Institutional and conference listings are historical; publication date is not stated. · Checked 2026-10-16
Siqi Liu / 刘思齐; reprint published on Sohu · 青年数学家刘思齐教授：从高中到大学的转变
Learning & research advice · Mathematical learning & note-taking · Chinese
Discusses taking responsibility for university study, comparing textbooks and writing and revising one's own mathematical notes. A useful suggestion is to prepare notes as though explaining the subject in a small textbook, then record where the lecturer's account differs.
Use / preparation: Relevant to beginning undergraduates and independent learners organizing their first university-level courses. · Reprinted incoming-student address · 2021-09-11; reprint · The reprint was reviewed. Its claimed original Bilibili publication was not independently checked; this is not an author-hosted copy. · Checked 2026-10-16
远方的学徒 (Zhihu display name) · 证明需要全部记住吗？（导读标题）
Learning & research advice · Analysis & proofs · Chinese
Reflects on an early ambition to memorize every theorem's proof, then focuses on reusable ideas instead. Sequence-limit examples show how pairing terms, adding and subtracting an expression, and the triangle inequality recur in analysis.
Use / preparation: For students who understand an argument while reading but forget its details later; extract the proof's goal and reusable moves. · Zhihu personal learning advice · Updated 2024-12-22, as shown in Zhihu's English rendering · Chinese answer link; Zhihu may require sign-in or verification. The platform's English rendering was reviewed; original Chinese wording was not checked. · The display title is an editorial summary, not a verified Chinese question title. Author credentials were not independently established. · Checked 2026-10-16
Skadiologist (Zhihu display name) · 2022申请季：纯数学与数学物理（导读标题）
Application advice & experiences · US / UK / European mathematics applications · Chinese
A first-person diary covering preparation, recommendation letters, interviews, rejections and alternatives across US and European programs. The account follows interests in mathematical physics toward a reported decision to study algebraic geometry at Warwick.
Use / preparation: Read the timeline and changes of plan rather than treating the reported grades or individual results as an admissions bar. · Zhihu applicant experience · 2022 cycle; updated 2022-08-16 in the reviewed rendering · Chinese answer link; Zhihu may require sign-in or verification. The platform's English rendering was reviewed; original Chinese wording was not checked. · Historical self-reported outcomes, not independently verified admissions records; the display title is editorial. · Checked 2026-10-16