公理是推演的起点。An axiom is where deduction begins.
Axiom 应用数学社现有 45 名成员。我们把现实问题写成可以计算的形式，用数学方法求解，再把结论放回现实里检验。Axiom Applied Mathematics Club has 45 members. We put real problems into a form that can be computed, solve them with mathematics, and take the conclusions back to reality for testing.
洛伦茨方程，取 σ = 10，ρ = 28，β = 8/3。此参数下轨道落在混沌吸引子上，最大李雅普诺夫指数约 0.9，初值的微小差别按指数放大。The Lorenz equations with σ = 10, ρ = 28, β = 8/3. At these values the trajectories settle on a chaotic attractor whose largest Lyapunov exponent is about 0.9, so small differences in the initial state grow exponentially.
定义 1（公理）在一个系统内不加证明而接受的命题，其余结论都由它推出。 Definition 1 (Axiom).A proposition accepted without proof inside a system, from which the remaining results are derived.
命题给定一组写明的前提，可以由它们推出一个模型；模型的结论，在前提成立的范围内有效。 Proposition.From a set of stated premises a model can be derived, and its conclusions hold as far as those premises do.
证明Proof.
注以上是一段类比。数学证明只对它的形式系统负责；一个模型成立与否，最后由数据判定。Remark.The argument above is an analogy. A mathematical proof answers only to its own formal system, while a model is settled by data.
校园与城市里的许多现象都可以量化：排队、作息、路线、消耗。写成变量和它们之间的关系，就能拿来分析。Much of campus and city life can be quantified: queues, schedules, routes, consumption. Written as variables and the relations between them, they can be analysed.
建模的第一步是界定问题：已知什么，求什么，假设什么。公式在这之后才出场。Modeling starts by stating the problem: what is known, what is asked, what is assumed. Formulas come after that.
入门需要的基础比多数人以为的少，欠缺的方法可以在训练里补上。对数学有兴趣的人，这里都有位置。Less background is needed than most people assume, and the missing methods can be picked up in training. Anyone interested in mathematics has a place here.
我们讲的方法，都是比赛和研究里真在用的，也尽量讲清它们为什么成立。The methods we teach are the ones actually used in contests and in research, and we try to show why they hold.
午休的时间不长，足以讲清一个想法，也足以把一道真题拆开。A lunch break is short, long enough to land one idea, or to take one contest problem apart.
周三中午Wednesday, noon
主题暂定「透过生活发现数学之美」Working title: “Finding the beauty of mathematics in daily life”
内容偏基础，讲怎样用数学的方式观察日常现象。社团以外的同学也可以参加。An introductory session on looking at everyday phenomena mathematically. Students outside the club are welcome.
中午 1:00 至 1:301:00 to 1:30 pm
以往年 IMMC、HiMCM 真题和日常问题为材料，先认出其中用到的数学，再把它系统地补齐。Past IMMC and HiMCM problems, together with questions from daily life, serve as the material: identify the mathematics they rely on, then study it systematically.
地点和具体安排，以社团通知为准。Rooms and schedules follow club announcements.
23 周的课程，从读懂第一道题开始，到正式比赛结束。每周一节 40 分钟正课，另有一节 10 分钟的线上小课。A twenty-three week course, from reading a first problem to the contests themselves. One 40-minute lesson a week, plus a 10-minute online session.
训练对所有成员开放，可以自由组队。日常训练以能力培养为目标，不以淘汰排序为目的。Training is open to every member and teams form freely. The everyday sessions aim at building skills rather than ranking people out.
四种分工，每人主攻一到两项：Four roles; each member takes one or two:
建模的完整流程，论文结构，评价类模型，以及一次按 IMMC 时长进行的五天模拟赛。The full modeling workflow, the structure of a paper, evaluation models, and a five-day mock contest run on IMMC timing.
Python 数据处理与可视化，文献检索，模型设计，LaTeX 与模型检验，再来一次 mini 模拟赛。Python for data and plots, literature search, model design, LaTeX and model validation, then a mini mock contest.
正式比赛。讲师只说明规则、时间与提交要求，不参与解题。The contest itself. Instructors cover rules, timing and submission requirements, and take no part in the solutions.
连续 96 小时内完成建模、计算与论文。Ninety-six continuous hours to model, compute and write the paper.
预测与统计，优化，仿真与随机模型，文献驱动建模与图论。Prediction and statistics, optimization, simulation and random models, literature-driven modeling and graph theory.
逐题分析往届真题，确定代表队，赛前集中训练。Past problems are analysed one by one, the teams are settled, and training concentrates before the round.
正式比赛，赛后归档论文并复盘。The contest itself, then the papers are archived and reviewed.
比赛时间以官方公布为准。Contest dates follow the official announcements.
从地铁线网到抗体序列，对象差得很远，做法却接近：先把现实写成能算的形式，再判断算出来的结果能回答什么。每一项另有专页，可点入细读。From a metro network to antibody sequences. The objects are far apart, the method is close: write the real thing in a form you can compute, then work out what the result is able to answer. Each has a page of its own.
我们按 IMMC 格式为校内模拟赛所出的题。线网更长，是否就更有利于市民？共五问，中英双语。A problem we wrote in IMMC format for our own mock contest. Is a longer network really better for the people who ride it? Five tasks, in Chinese and English.
阅读题面Read the problem 02 表示学习与贝叶斯优化Representation learning, Bayesian optimization把一条抗体序列映为一个分数，依分数排序，取最高的若干条进入实验。困难在于标签稀缺，而实验昂贵。Map an antibody sequence to a score, rank by the score, send the top few to the bench. The hard part is that labels are scarce and experiments are expensive.
阅读全文Read this one 03 逆问题与谱可辨识性Inverse problems, spectral identifiability两根弦基频相同，声音却不相同。仅凭一段频谱，能否反推张力与有效长度？Two strings share a fundamental and still sound different. Can tension and effective length be recovered from the spectrum alone?
阅读全文Read this one 04 情境模拟与多准则决策Scenario simulation, multi-criteria decisions一户人家是否该把燃煤炉换成热泵？模型把收入、住房、气候与补贴纳入同一笔账。Should a household swap a coal stove for a heat pump? The model puts income, housing, climate and subsidies into one account.
阅读全文Read this one社团现有 45 名成员，获得过 IMMC Finalist 奖。入门需要的基础不多，对数学有兴趣就可以来。The club has 45 members and holds an IMMC Finalist award. Little background is needed; an interest in mathematics is enough.
想先了解，可以来周三中午的 Incubator，社团以外的同学也可以参加。招新与报名方式，请留意校内通知。To see it first, come to the Incubator at Wednesday noon; students outside the club are welcome. Watch school announcements for recruitment and sign-up.
以公理为序，以逻辑为刃，去找事物背后藏着的秩序。With axioms for order and logic for a blade, we go looking for the order hidden behind things.