Brilliant Course Guide for Ethan给 Ethan 的 Brilliant 课程指南

A curated, broad-enrichment map of Brilliant courses for the summer before IM3 Honors — math, computer science, Python, data, science, and logic & puzzles. Each course lists clear learning goals and a full Level → lesson breakdown.为 IM3 荣誉课程前的暑假精选的、广度优先的 Brilliant 课程地图——涵盖数学、计算机科学、Python、数据、科学以及逻辑与谜题。每门课都给出清晰的学习目标和完整的“关卡 → 课时”分解。

Courses课程数 14Levels关卡数 145Lessons课时数 836Est. time预计时长 ~139h

Lesson names are kept in English so they exactly match what Ethan taps inside the Brilliant app. Everything else switches with the EN / 中文 button, top-right.课时名称保留英文，以便与 Ethan 在 Brilliant 应用中点击的内容完全一致。其余内容均可用右上角的 EN / 中文按钮切换。

Subject paths学科路径

Math: Functions & Algebra数学：函数与代数Computer Science & Python计算机科学与 PythonData Analysis数据分析Science科学Logic & Puzzles逻辑与谜题

Overview总览

Course课程	Path路径	Levels关卡	Lessons课时	~Hours约小时
Introduction to Functions函数入门	Math: Functions & Algebra数学：函数与代数	14	82	~13.7
Quadratics二次函数与方程	Math: Functions & Algebra数学：函数与代数	14	81	~13.5
Exponentials and Logarithms指数与对数	Math: Functions & Algebra数学：函数与代数	13	74	~12.3
Polynomials多项式	Math: Functions & Algebra数学：函数与代数	9	56	~9.3
Trigonometric Functions三角函数	Math: Functions & Algebra数学：函数与代数	11	67	~11.2
Thinking in Code代码思维	Computer Science & Python计算机科学与 Python	9	57	~9.5
Programming with Variables变量编程	Computer Science & Python计算机科学与 Python	4	19	~3.2
Thinking in PythonPython 思维	Computer Science & Python计算机科学与 Python	14	84	~14.0
How AI WorksAI 的工作原理	Computer Science & Python计算机科学与 Python	7	31	~5.2
Exploring Data Visually数据可视化探索	Data Analysis数据分析	6	33	~5.5
Scientific Thinking科学思维	Science科学	6	45	~7.5
Logic逻辑推理	Logic & Puzzles逻辑与谜题	7	32	~5.3
Number Theory数论	Logic & Puzzles逻辑与谜题	11	75	~12.5
100 Days of Puzzles100 天谜题	Logic & Puzzles逻辑与谜题	20	100	~16.7

Math: Functions & Algebra数学：函数与代数

Introduction to Functions函数入门

Connect inputs to outputs with functions.用函数把输入和输出联系起来。

14 Levels14 关82 Lessons82 课时~13.7 hours约 13.7 小时

What you'll learn你将学到

Read, write, and interpret functions as input-output rules, in words, tables, and graphs.用文字、表格和图像来读懂、书写并解释函数（输入—输出规则）。

Graph linear, quadratic, absolute-value, and piecewise functions; identify intercepts, intervals, and increasing/decreasing behavior.绘制线性、二次、绝对值和分段函数；识别截距、区间以及增减性。

Determine domain and range, and recognize when a relation is (or isn't) a function.确定定义域和值域，并判断一个关系是否为函数。

Combine, compose, transform (shift/stretch/reflect), and invert functions.对函数进行运算、复合、变换（平移/伸缩/反射）以及求反函数。

IM3 link:与 IM3 的关联： Core foundation for all of IM3 Honors — every later topic (polynomials, exponentials, trig) is a kind of function.IM3 荣誉课程的核心基础——之后的每个主题（多项式、指数、三角）本质上都是函数。

#	Level关卡	Lessons (English, as in app)课时（英文，与应用一致）	#数
1	Introducing Functions函数初识	Finding the Rule · Word Functions · Time Functions · Repeating Outputs · Deducing the Rule · Level Review	6
2	Function Rules函数规则	Numeric Rules · Writing Rules · Conditional Rules · Deducing Numeric Rules · Level Review	5
3	Graphing Functions绘制函数图像	Graphing Linear Functions · Graphing Squared Functions · Graphing Absolute Value · Graphing Without an Equation · Interpreting Graphed Functions · Intercepts and Intervals · Increasing and Decreasing · Level Review	8
4	Non-Function Behavior非函数行为	Function Requirements · Vertical Line Test · Valid Functions · Valid Intervals · Level Review	5
5	Real-World Functions现实世界中的函数	Discrete Functions · Depreciation Functions · Multi-Part Functions · Periodic Functions · Level Review	5
6	Piecewise Functions分段函数	Piecewise Functions · Discontinuities · Plotting Points · Plotting Piecewise Functions · Building Piecewise Functions · Level Review	6
7	Function Gallery函数画廊	The Floor Function · The Ceiling Function · Plotting Floor and Ceiling · Repeating Functions · Periodicity · Level Review	6
8	Domain and Range定义域与值域	Domain · Range · Domain and Range · Level Review	4
9	Visualizing Domain and Range可视化定义域与值域	Reciprocal Functions · Squares and Ranges · Square Roots and Domains · Piecewise Ranges · Identifying Domain and Range · Level Review	6
10	Function Operations函数运算	Adding Functions · Subtracting Functions · Multiplying Functions · Dividing Functions · Level Review	5
11	Function Composition函数复合	Chaining Functions · Applying Multiple Functions · Combining Functions · Graphing Composites · Composite Domains · Level Review	6
12	Stretching and Shifting伸缩与平移	Vertical Shifting · Horizontal Shifting · Combining Shifts · Vertical Stretching · Horizontal Stretching · Combining Stretches · Level Review	7
13	Axis Reflections关于坐标轴的反射	Reflection Across the x-Axis · Reflection Across the y-Axis · Composing Reflections · Reflecting and Stretching · Level Review	5
14	Inverse Functions反函数	Inverting a Function · Finding the Input · Finding the Inverse Function · Graphing Inverse Functions · Reflecting to Invert · Invertibility · Invertible Functions · Level Review	8

Quadratics二次函数与方程

Learn to work fluently with quadratic expressions and equations.熟练掌握二次表达式与二次方程。

14 Levels14 关81 Lessons81 课时~13.5 hours约 13.5 小时

What you'll learn你将学到

Expand, distribute, and factor quadratic expressions, including with signed coefficients.展开、分配并因式分解二次表达式（含带符号系数）。

Solve quadratic equations by factoring, undoing, completing the square, and the quadratic formula.用因式分解、逆运算、配方法和求根公式求解二次方程。

Graph quadratics in factored and vertex form; find vertex, axis of symmetry, intercepts, and max/min.用因式形式和顶点形式绘制二次函数；求顶点、对称轴、截距和最值。

Interpret the discriminant and recognize real vs. complex solutions.理解判别式，区分实数解与复数解。

IM3 link:与 IM3 的关联： Reinforces IM2 quadratics and extends to completing the square, the discriminant, and complex roots — heavily revisited in IM3.巩固 IM2 的二次内容，并拓展到配方法、判别式与复数根——这些在 IM3 中会反复用到。

#	Level关卡	Lessons (English, as in app)课时（英文，与应用一致）	#数
1	Multiplying Expressions表达式相乘	Multiplying Expressions · Multiplying Binomials · Finding the Units · Finding Linear Terms · Level Review	5
2	Distributing and Combining分配与合并	Finding Combined Linear Terms · Variables with a Multiple · Linear and Constant Terms · Finding All the Terms · Level Review	5
3	Factoring Expressions因式分解	Undistributing · Finding One Factor · Finding Both Sides · Factoring Quadratics · Level Review	5
4	Expressions with Signed Numbers含符号数的表达式	Multiplying Signed Constants · Multiplying Signed Linear · Linear with Coefficients · Finding Signs · Linear and Constant Terms · Level Review	6
5	Factoring with Signed Numbers含符号数的因式分解	Factoring with Negatives · Finding Numbers and Signs · Leading Coefficients · Finding Entire Factors · Level Review	5
6	Graphing Factored Form绘制因式形式	Solutions to Quadratic Equations · Plotting Solutions · Plotting x-Intercepts · Factors from Intercepts · Factored Form · Level Review	6
7	Solving by Factoring因式分解法解方程	Solutions on a Graph · Solutions to Quadratics · Solving by Factoring · The Importance of Zero · Hard-to-factor Expressions · Level Review	6
8	Graphing Vertex Form绘制顶点形式	Shifting Up and Down · Graphing a Vertical Shift · Shifting Right and Left · Graphing a Horizontal Shift · Finding the New Vertex · Stretching and Reflecting · Graphing a Vertical Stretch · Using All the Parameters · Graphing from Vertex Form · Level Review	10
9	Solving by Undoing逆运算法解方程	Finding Solutions · How Many Solutions · Splitting Equations · Equations with More Steps · Level Review	5
10	Complex Solutions复数解	Irrational Solutions · No Real Solutions · The Imaginary Unit · Complex Solutions · Level Review	5
11	Completing the Square配方法	Squaring Binomials · Perfect Square Trinomials · Solving by Factoring Perfect Squares · Completing the Square · Solving by Completing the Square · Level Review	6
12	Graphing by Completing the Square配方法绘图	Rewriting in Vertex Form · Using Complete the Square · Vertex Form with Leading Coefficients · Maximum or Minimum Value · Completing the Square with Leading Coefficients · Level Review	6
13	The Quadratic Formula求根公式	Completing Any Square · Building a Formula · The Quadratic Formula · Using the Formula · Rearranging First · The Discriminant	6
14	Symmetry对称性	The Axis of Symmetry · Axis of Symmetry to Vertex · Reading Different Forms · Equations from Symmetry · Choosing the Right Form	5

Exponentials and Logarithms指数与对数

Build, combine, and simplify exponential and logarithmic functions.构建、组合并化简指数函数与对数函数。

13 Levels13 关74 Lessons74 课时~12.3 hours约 12.3 小时

What you'll learn你将学到

Model exponential growth and decay, including compound interest and depreciation.为指数增长与衰减建模，包括复利与折旧。

Build exponential functions from bases and initial values; compare with linear and quadratic growth.由底数与初值构建指数函数；并与线性、二次增长作比较。

Define the logarithm as the inverse of exponentiation; evaluate and graph log functions.把对数定义为指数运算的逆运算；计算并绘制对数函数。

Apply logarithm identities (product, quotient, power), change bases, and solve exponential/log equations.运用对数恒等式（积、商、幂），换底，并求解指数/对数方程。

IM3 link:与 IM3 的关联： A central IM3 topic. Exponential & log modeling and equation-solving appear throughout IM3 Honors.IM3 的核心主题。指数与对数的建模和方程求解贯穿 IM3 荣誉课程。

#	Level关卡	Lessons (English, as in app)课时（英文，与应用一致）	#数
1	Exponential Growth指数增长	Growing · Doubling · Tripling · Powers of 10 · Level Review	5
2	Exponential Functions指数函数	Bases · Initial Values · Finding the Base and Coefficient · Deducing Exponential Functions · Level Review	5
3	Exponential Decay指数衰减	Decay · Fractional Bases · Building Decay Functions · Negative Exponents · Level Review	5
4	Exponential Comparisons指数对比	Linear Comparisons · Quadratic Comparisons · Comparing Growth · Comparing Decay · Level Review	5
5	General Bases一般底数	Building Exponentials · Finding Initial Values · Fractional Bases · Building Decay Functions · Comparing Decimal Bases · Level Review	6
6	Compound Interest复利	Percent Increase · Modeling Compound Interest · Modeling Depreciation · Interest Comparisons · Level Review	5
7	Exponentials on the Number Line数轴上的指数	Stepping Along Exponentials · Skipping Along Exponentials · Exponentials Over Negatives · Reflection Over Vertical Axis · Building Exponentials	5
8	Exponentials at Non-Integers非整数处的指数	Exponentials at Half-Steps · Exponentials Between Integers · Signed Stepping · Building Exponentials	4
9	The Logarithm对数	Counting Days · Log-Exponent Pairs · Inverse of Base 2 · Inverse of Exponentiation · Negative Exponents · Fractional Exponents · Evaluating Logarithms · Level Review	8
10	Graphing Log Functions绘制对数函数	Estimating Logs · Graphing Log Functions · Domain of the Logarithm · Fractional Bases · Graphing Fractional Bases · Level Review	6
11	Logarithm Identities对数恒等式	The Product Rule · Proving the Product Rule · The Quotient Rule · The Power Rule · Proving the Power Rule · Transforming with Identities · Level Review	7
12	Changing Bases换底	Bases 2, 4 and 8 · Bases 2 and 10 · Converting Bases · Converting Bases Graphically · Level Review	5
13	Solving Using Logarithms用对数求解	Taking Logs of Both Sides · The Unknown Inside a Log · Logs on Both Sides · Solutions and Domains · Using Log Identities · Graphing Solutions · Checking Solutions · Level Review	8

Polynomials多项式

Master the fundamentals of polynomials, one of the most important families of functions in all of algebra.掌握多项式的基础——代数中最重要的函数族之一。

9 Levels9 关56 Lessons56 课时~9.3 hours约 9.3 小时

What you'll learn你将学到

Understand power functions, their dominance, and even/odd symmetry.理解幂函数、其主导性以及奇偶对称性。

Evaluate and graph polynomial functions; relate degree, leading coefficient, and end behavior.计算并绘制多项式函数；将次数、首项系数与端部行为联系起来。

Add, subtract, and multiply polynomials, including multivariable ones.对多项式进行加、减、乘运算（含多元多项式）。

Find roots, connect factors to roots, and analyze multiplicity and sign changes.求根，建立因式与根的联系，并分析重数与符号变化。

IM3 link:与 IM3 的关联： Polynomial functions and operations are a major IM3 Honors strand and the gateway to precalculus.多项式函数与运算是 IM3 荣誉课程的重要主线，也是通往微积分预备课程的门户。

#	Level关卡	Lessons (English, as in app)课时（英文，与应用一致）	#数
1	Power Functions幂函数	A First Look At Polynomials · Power Functions · Comparing Powers · The Dominance of Powers · Between -1 and 1 · Level Review	6
2	Even and Odd Powers偶次幂与奇次幂	Even and Odd Powers · Symmetry of Even Powers · Symmetry of Odd Powers · Level Review	4
3	Transforming Power Functions变换幂函数	Vertical Shifts · Stretches · Negative Stretches · Horizontal Shifts · Identifying Transformations · Transforming Power Functions · The Shape of Power Functions · Level Review	8
4	Polynomial Functions多项式函数	Evaluating Polynomials · Coefficients · Graphing Polynomials · The Constant Term · Level Review	5
5	Graphs of Polynomials多项式图像	Even Degree Polynomials · Odd Degree Polynomials · Parity of Polynomial Graphs · Small and Large Terms · Polynomial graphs far from 0 · Polynomial Graphs near to 0 · Leading Coefficients other than 1 · Level Review	8
6	Roots根	Introduction to Roots · Degree and Roots · Roots of Even Polynomials · Roots of Odd Polynomials · Root Finding · Level Review	6
7	Sums of Polynomials多项式求和	Adding Polynomials · Subtracting Polynomials · Subtracting with Negatives · Meet Multivariable Polynomials · Add Multivariable Polynomials · Level Review	6
8	Products of Polynomials多项式乘积	Multiplying Monomials · Scaling Polynomials · Monomial Times Polynomial · Multiplying Polynomials · Powers of Polynomials · Factoring Out Monomials · Level Review	7
9	Factors and Roots因式与根	Roots from Factored Form · Factored Form from Roots · Graphical Factoring · Roots with Multiplicity · Sign Changes at Roots · Level Review	6

Trigonometric Functions三角函数

Explore how periodic patterns and circular motion give rise to trigonometric functions.探索周期性规律与圆周运动如何产生三角函数。

11 Levels11 关67 Lessons67 课时~11.2 hours约 11.2 小时

What you'll learn你将学到

Describe periodic phenomena using period, midline, amplitude, and phase shift.用周期、中线、振幅和相移来描述周期现象。

Define sine and cosine from circular motion and the unit circle; use key triangles and angles.由圆周运动和单位圆定义正弦与余弦；运用特殊三角形与角。

Work in radians, convert to/from degrees, and handle coterminal and negative angles.使用弧度，与角度互换，并处理终边相同角与负角。

Graph and transform sine, cosine, and tangent; solve trigonometric equations.绘制并变换正弦、余弦、正切；求解三角方程。

IM3 link:与 IM3 的关联： Introductory trigonometry and the unit circle are key IM3 Honors / precalculus topics — a strong preview here pays off all year.三角入门与单位圆是 IM3 荣誉课程/微积分预备的关键主题——在此提前打好基础会让整学年受益。

#	Level关卡	Lessons (English, as in app)课时（英文，与应用一致）	#数
1	Periodic Functions周期函数	Periodic Phenomena · The Period of a Function · Horizontal Shifts of Periodic Functions · Midline of a Periodic Function · Amplitude of a Periodic Function · Predator and Prey · Level Review	7
2	Periodic Functions from Circular Motion圆周运动产生的周期函数	Sine from Circular Motion · Cosine from Circular Motion · Period and Speed · Level Review	4
3	Sine and Cosine正弦与余弦	The Unit Circle · The Cosine Function · The Sine Function · Cosine & Sine Together · Complementary Angles · Level Review	6
4	Right Triangle Trigonometry直角三角形三角学	The Pythagorean Identity · Triangles and the Unit Circle · The 45-45-90 Triangle · 30-60-90 Triangles · Key Angles on the Unit Circle · Level Review	6
5	Arc Length and Radians弧长与弧度	Arc Length on the Unit Circle · Arc Length on Any Circle · Radians · Level Review	4
6	Working in Radians用弧度运算	Degrees to Radians · Radians to Degrees · Angle Identification · Coterminal Angles · Negative Angles · Level Review	6
7	Cosine and Sine with Radian Input以弧度为输入的余弦与正弦	Evaluating Cosine and Sine with Radians · Unit Circle Coordinates of 1, 0, and -1 · Repeated Values of Cosine and Sine · Negative Values of Cosine · Negative Values of Sine · Evaluating Sine and Cosine · Level Review	7
8	Graphing Sine and Cosine绘制正弦与余弦	The Sine Graph · The Cosine Graph · Cosine and Sine at Negative Angles · Sine and Cosine after 2pi · Half-period shifts of Cosine and Sine · Quarter-period Shifts · Level Review	7
9	The Tangent Function正切函数	Tangent · Tangent and Triangles · Values of Tangent · Tangent in Four Quadrants · The Graph of Tangent · Level Review	6
10	Transforming Trig Functions变换三角函数	Horizontal Stretches · Period of a Wave · Rational Periods · Amplitude · Midline Shifts · Phase Shifts · General Transformations · Level Review	8
11	Solving Trigonometric Equations求解三角方程	Equations in cos and sin · Infinitely Many Solutions · All Solutions to Trig Equations · Trig Equations with Dilations · Non-linear Trig Equations · Level Review	6

Computer Science & Python计算机科学与 Python

Thinking in Code代码思维

Build solid foundations for computational problem solving.为计算思维与问题求解打下坚实基础。

9 Levels9 关57 Lessons57 课时~9.5 hours约 9.5 小时

What you'll learn你将学到

Write sequences of commands and trace/debug program behavior.编写命令序列，并追踪与调试程序的行为。

Use loops (including nested loops) to repeat and combine patterns.使用循环（含嵌套循环）来重复并组合模式。

Control flow with if / if-else branching and Boolean logic.用 if / if-else 分支和布尔逻辑控制程序流程。

Introduce and update variables and lists to build real programs.引入并更新变量与列表，构建真正的程序。

IM3 link:与 IM3 的关联： Pure computational-thinking primer (visual, no syntax) — perfect on-ramp before Python.纯计算思维入门（图形化、无语法）——进入 Python 之前的理想起点。

#	Level关卡	Lessons (English, as in app)课时（英文，与应用一致）	#数
1	Taking the First Steps迈出第一步	Writing Programs · Sequencing Commands · Repeating Patterns · Debugging Programs · Looping With Logic · While Loop Challenge · Level Review	7
2	Loops循环	Recognizing Patterns · Controlling with Logic · Nesting Loops · Combining Loops · Loop Combo Challenge · Level Review	6
3	Branching分支	Using if Statements · Preventing Errors · Using if-else Statements · Branching with Logic · Branching Challenge · Level Review	6
4	Designing Programs设计程序	Conditioning on History · Nesting Logic · Complex Branching · Complex Logic · Designing Programs · Level Review	6
5	Applications in Automation自动化应用	Programming a Website · Automating Emails · Automating Social Media · Programming an App · Level Review	5
6	Variables变量	Structuring Code · Combining Commands · Using Inputs · Using Variables · Updating Variables · Incrementing Variables · Looping with Variables · Level Review	8
7	Working with Lists使用列表	Looping with Lists · Processing Input · Dealing with Cases · Navigating a Grid · Nesting For Loops · Level Review	6
8	Exploring with Logic用逻辑探索	Controlling Loops · Avoiding Obstacles · Finding Shortcuts · Chaining Conditionals · Using Boolean Logic · Extending Logic · Level Review	7
9	Building Programs构建程序	Building Helpers · Logical Ordering · Streamlining Logic · Solving Mazes · Building Programs · Level Review	6

Programming with Variables变量编程

Supercharge your programming skills with variables and loops.用变量与循环大幅提升编程能力。

4 Levels4 关19 Lessons19 课时~3.2 hours约 3.2 小时

What you'll learn你将学到

Declare, set, and manage multiple variables in a program.在程序中声明、设置并管理多个变量。

Update variables with expressions and inside loops.用表达式以及在循环内更新变量。

Combine variables with logic and ordering.将变量与逻辑、排序结合起来。

Use for-loops with loop variables to create patterns and visuals.用带循环变量的 for 循环创建图案与视觉效果。

IM3 link:与 IM3 的关联： Reinforces variables & loops creatively — a bridge between block logic and real syntax.以创意方式巩固变量与循环——连接图形化逻辑与真实语法的桥梁。

#	Level关卡	Lessons (English, as in app)课时（英文，与应用一致）	#数
1	Variables变量	Writing Programs · Using Variables · Multiple Variables · Setting Variables · Level Review	5
2	Updating Variables更新变量	Updating Variables · Updating with Expressions · Variables and Loops · Geometric Expressions · Level Review	5
3	Variables and Logic变量与逻辑	Using Logic · Variable Logic · Ordering Logic · Level Review	4
4	For Loopsfor 循环	The For Loop · The Loop Variable · Expressions in For Loops · Coloring with Numbers · Level Review	5

Thinking in PythonPython 思维

Build Python programs to develop strong foundations for creating with code.编写 Python 程序，为用代码创造打下坚实基础。

14 Levels14 关84 Lessons84 课时~14.0 hours约 14.0 小时

What you'll learn你将学到

Write real Python: variables, printing, conditionals, and Boolean logic.编写真正的 Python：变量、打印、条件判断与布尔逻辑。

Use for-loops, while-loops, and lists to process data.使用 for 循环、while 循环和列表来处理数据。

Work with strings, dictionaries, and nested/chained conditionals.使用字符串、字典以及嵌套/链式条件判断。

Reason about time complexity (Big-O) and implement search algorithms.分析时间复杂度（大 O 记号）并实现查找算法。

IM3 link:与 IM3 的关联： Real coding skills + a first taste of algorithmic efficiency and binary search (which uses logarithms!).真实的编程技能 + 初识算法效率与二分查找（用到了对数！）。

#	Level关卡	Lessons (English, as in app)课时（英文，与应用一致）	#数
1	Variables变量	Variables · Updating Variables · Printing · Variable Self-Update · Variable Dependency · Level Review	6
2	Conditional Logic条件逻辑	Boolean Expressions · Conditional Statements · Branching Conditionals · Setting Boolean Variables · Testing Programs · Level Review	6
3	Boolean Logic布尔逻辑	Combining Boolean Expressions · Storing Boolean Values · Negating Booleans · Organizing Logic · Complex Logic · Level Review	6
4	For Loopsfor 循环	For Loops · Structuring Loops · Loop Variable Dependency · Logic Inside Loops · Complex Dependencies · Level Review	6
5	Lists列表	Lists · List Indexing · Looping through Lists · Appending to Lists · Indexing Multiple Lists · Consecutive Indexes · Level Review	7
6	While Loopswhile 循环	While Loops · Structuring While Loops · Compound Loop Conditions · Flags as Loop Conditions · Complex While Loop Logic · Level Review	6
7	String Tricks字符串技巧	Exploring Strings · String Operations · Classifying Strings · Level Review	4
8	Nesting Conditionals嵌套条件	Nesting If Statements · Nesting Mixed Conditionals · Nesting If-Else Statements · Prioritizing Conditions · Level Review	5
9	Chaining Conditionals链式条件	Conditional Chains · Sequencing Logic · Designing Chains · Setting Priority in Chains · Level Review	5
10	Dictionaries字典	Dictionaries · Accessing Dictionaries · Updating Dictionaries · Looping through Dictionaries · Building Dictionaries · Dictionaries of Lists · Level Review	7
11	Working with Data处理数据	Organizing Data · Exploring Data · Shaping Data · Inspecting Data · Analyzing Data · Level Review	6
12	Advanced Looping进阶循环	Nesting Loops · Looping in Nested Structures · Breaking Loops · Breaking Nested Loops · Continuing Loops · Continue vs. Break · Controlling Nested Loops · Level Review	8
13	Time Complexity时间复杂度	Counting Operations · Runtime and Data · Best and Worst Cases · Time Complexity · Big-O Notation · Level Review	6
14	Search Algorithms查找算法	Searching · Searching Sorted Data · Binary Search · Logarithmic Runtime · Searching a Range · Level Review	6

How AI WorksAI 的工作原理

Take a peek under the hood of generative AI and LLMs to understand how they work.揭开生成式 AI 与大语言模型的内部机制。

7 Levels7 关31 Lessons31 课时~5.2 hours约 5.2 小时

What you'll learn你将学到

Understand language models as next-word predictors driven by probabilities.理解语言模型是由概率驱动的“下一个词”预测器。

See how models are trained: loss, gradient descent, tokenization.了解模型如何训练：损失函数、梯度下降、分词。

Explore neural networks, layers, and image models.探索神经网络、网络层与图像模型。

Build a tiny language model in Python using bigrams.用 Python 和二元组（bigram）构建一个微型语言模型。

IM3 link:与 IM3 的关联： High-interest payoff: connects probability, functions, and Python into today's most talked-about technology.高趣味回报：把概率、函数与 Python 串联进当下最热门的技术。

#	Level关卡	Lessons (English, as in app)课时（英文，与应用一致）	#数
1	Prediction and Probabilities预测与概率	Intro to Language Models · Predicting the Next Word · Larger Context Windows · Calculating Word Probabilities	4
2	Language Model Training语言模型训练	Temperature · Improving Models · Loss · Preprocessing · Capitalization · Punctuation · Tokenization · Byte-Pair Encoding	8
3	Deep Network Models深度网络模型	Deep Networks · Training · Gradient Descent	3
4	Neurons and Layers神经元与网络层	Neural Networks · Folding Data · Multiple Layers	3
5	Image Models图像模型	Reading Digits · Pattern Recognition · Compressing Images · Classifying Faces · A Space of Faces · Semantic Geometry	6
6	Language Analysis with Python用 Python 分析语言	Turning Text into Data · Using Dictionaries · Counting Unique Words	3
7	Text Generation with Python用 Python 生成文本	Bigrams and Mutability · Bigram Frequency and Tuples · Bigram Analysis · Building a Language Model	4

Data Analysis数据分析

Exploring Data Visually数据可视化探索

Build a solid foundation in data analysis with visualizations and data transformations.通过可视化与数据变换，打好数据分析的基础。

6 Levels6 关33 Lessons33 课时~5.5 hours约 5.5 小时

What you'll learn你将学到

Read and analyze bar charts, pie charts, histograms, and percentiles.读懂并分析柱状图、饼图、直方图与百分位数。

Interpret boxplots, line graphs, trends, and scatter plots (including log scales).解读箱线图、折线图、趋势与散点图（含对数刻度）。

Filter, group, and transform data tables to draw conclusions.对数据表进行筛选、分组与变换以得出结论。

Apply skills in a real Airbnb case study.在真实的 Airbnb 案例研究中运用所学。

IM3 link:与 IM3 的关联： Statistics & data literacy strand of IM3; pairs naturally with Python data work.IM3 的统计与数据素养主线；与 Python 数据处理天然契合。

#	Level关卡	Lessons (English, as in app)课时（英文，与应用一致）	#数
1	Bar Charts and Pie Charts柱状图与饼图	Reading Bar Charts · Analyzing Bar Charts · Pie Charts · Histograms · Percentiles · Level Review	6
2	Boxplots箱线图	Boxplots · Comparing Boxplots · Seasonal Variation · Level Review	4
3	Line Graphs折线图	Line Graphs · Trends · Comparing Trends · Level Review	4
4	Scatter Plots散点图	Observing Relationships · Reading Scatter Plots · Log Scales · Comparing on Log Scales · Level Review	5
5	Transforming Data变换数据	Data Tables · Filtering with Logic · Filters with Inequalities · Grouping Data · Grouping and Filtering · Drawing Conclusions · Transforming Data · Counting Cafes	8
6	Airbnb Case StudyAirbnb 案例研究	Best Property Type · Rental Rate Recommendation · Best Neighborhood · Peak Seasons · Ratings · Guest Reviews	6

Science科学

Scientific Thinking科学思维

Open your eyes to the world around you by solving puzzles with science.用科学解谜，重新发现身边的世界。

6 Levels6 关45 Lessons45 课时~7.5 hours约 7.5 小时

What you'll learn你将学到

Reason about gears, ratios, and rotational speed.推理齿轮、比率与转速。

Balance moments on mobiles and solve for unknown weights.平衡力矩，求解未知重量。

Predict collisions and momentum transfer (pool/physics).预测碰撞与动量传递（台球/物理）。

Analyze structures, degrees of freedom, and optics (reflection/refraction).分析结构、自由度以及光学（反射/折射）。

IM3 link:与 IM3 的关联： Builds physical intuition and modeling — math applied to the real world, great for motivation.培养物理直觉与建模能力——数学在现实中的应用，极利于激发动力。

#	Level关卡	Lessons (English, as in app)课时（英文，与应用一致）	#数
1	Gears齿轮	Connecting Gears · Gears Changing Speeds · Compound Gears · Compound Gear Chains · Level Review	5
2	Mobiles平衡吊饰	Balancing Weights · Moments · Adding Moments · Adding a Level · Multiple Levels · A Mystery Weight · Multiple Unknowns · Simultaneous Solving · Level Review	9
3	Pool台球	Playing Pool · Combination Shots · Predetermined Collisions · Chain Reactions · Momentum Transfer · Momentum Components · Chains of Prediction · Level Review	8
4	Structures结构	Structure Components · Rigid Shapes · Extending Structures · Building Structures · Degrees of Freedom · Equivalent Structures · Analyzing Beams · Analyzing Joints · Analyzing Screws · Level Review	10
5	Optics光学	Reflecting Light · Adjusting Mirrors · Light Bulbs · Images · Apparent Distance · Refraction · Triangular Prisms · Level Review	8
6	Compound Gears复合齿轮	Jammed Gears · Counting Rotations · Rates of Rotation · The Fastest Gear · Shifting Gears	5

Logic & Puzzles逻辑与谜题

Logic逻辑推理

Stretch your analytic muscles with codebreaking and logical robots.通过破译密码与逻辑机器人锻炼分析能力。

7 Levels7 关32 Lessons32 课时~5.3 hours约 5.3 小时

What you'll learn你将学到

Solve order, comparison, and neighbor puzzles.解决排序、比较与相邻关系类谜题。

Use negation, rearrangement, and case analysis.运用否定、重排与分情况讨论。

Assign properties under multiple constraints.在多重约束下进行属性分配。

Apply quantifiers and basic optimization reasoning.运用量词以及基本的最优化推理。

IM3 link:与 IM3 的关联： Trains the rigorous, step-by-step deduction that underlies all proof-based math.训练严谨的逐步推理——这是一切以证明为基础的数学的根基。

#	Level关卡	Lessons (English, as in app)课时（英文，与应用一致）	#数
1	Order Logic顺序逻辑	Order Logic · Neighbors · Heights · Comparisons · Level Review	5
2	Negation否定	Relative Comparisons · Value Logic · Negation · Between · Level Review	5
3	Rearrangement重排	Shuffling · Swapping · Rearrangements · Either/Or · Level Review	5
4	Handling Cases分情况讨论	At Least · At Most · Sums · Differences · Level Review	5
5	Assignment分配	Assigning Sizes · Even and Odd · Bigger and Smaller · Multiple Properties · Level Review	5
6	Quantifiers量词	More · Fewer · Mixing Quantifiers · Not and No · Level Review	5
7	Optimization最优化	Minimizing · Maximizing	2

Number Theory数论

Explore the powers of divisibility, modular arithmetic, and infinity.探索整除、模运算与无穷的力量。

11 Levels11 关75 Lessons75 课时~12.5 hours约 12.5 小时

What you'll learn你将学到

Discover numerical patterns, divisibility shortcuts, and prime factorization.发现数字规律、整除技巧与质因数分解。

Compute GCD/LCM and reason with modular arithmetic.计算最大公约数/最小公倍数，并用模运算推理。

Explore infinity (Hilbert's Hotel) and number bases (binary, hexadecimal).探索无穷（希尔伯特旅馆）与进位制（二进制、十六进制）。

Solve cryptograms and analyze decimal representations.破解密码算式并分析小数表示。

IM3 link:与 IM3 的关联： Deep problem-solving and the binary/hex bridge to computer science.深度的问题求解，以及连接计算机科学的二进制/十六进制桥梁。

#	Level关卡	Lessons (English, as in app)课时（英文，与应用一致）	#数
1	Exploring Numerical Patterns探索数字规律	Last Digits · Secret Messages · Rainbow Cycles	3
2	Prime Factorization质因数分解	Divisibility Shortcuts · More Divisibility Shortcuts · Divisibility by 9 and 3 · Last Digits · Arithmetic with Remainders · Digital Roots · Factor Trees · Prime Factorization · Factoring Factorials · Counting Divisors · 100 Doors · How Many Prime Numbers Are There?	12
3	GCD and LCM最大公约数与最小公倍数	100 Doors Revisited · The LCM · Billiard Tables · The GCD · Dots on the Diagonal · Number Jumping (I) · Number Jumping (II) · Number Jumping (III) · Relating LCM and GCD · Billiard Tables Revisited (I) · Billiard Tables Revisited (II)	11
4	Modular Arithmetic Fundamentals模运算基础	Times and Dates · Modular Congruence · Modular Arithmetic · Divisibility by 11 · Star Drawing (I) · Star Drawing (II) · Star Drawing (III) · Die-Hard Decanting (I) · Die-Hard Decanting (II)	9
5	More Advanced Modular Concepts进阶模运算概念	Additive Cycles · Modular Multiplicative Inverses · Multiplicative Cycles · Fermat's Little Theorem · Totients · Last Digits Revisited · Perfect Shuffling	7
6	Exploring Infinity探索无穷	Counting to Infinity · Multiple Infinities · Hilbert's Hotel · Infinitely Large	4
7	Number Base Fundamentals进位制基础	The Invention of Number Bases · Introducing Binary · Binary on Computers	3
8	Binary and Other Bases二进制与其他进位制	Exploding Dots · Binary · Binary Operations · Perfect Shuffles · Hexadecimal · Hexadecimal Operations · An Unusual Computer Base	7
9	Cryptograms密码算式	Divisibility · Last Digits Rules · More Divisibility Rules · Cryptograms Solved by Divisibility · Cryptogram Addition Puzzles · Cryptogram Variety Pack	6
10	Decimal Representations小数表示	Factorial Refresher · Calculation Tricks · Digital Roots · Terminating Decimals · Repeating Decimals · Repeating Patterns · Problem Solving	7
11	Beyond Base Ten超越十进制	Hexadecimal Divisibility Shortcuts (I) · Hexadecimal Divisibility Shortcuts (II) · Hexadecimal Divisibility Shortcuts (III) · Divisibility Shortcuts in Other Bases · Hexadecimal Last Digits · Last Digits in Other Bases	6

100 Days of Puzzles100 天谜题

Challenging puzzles using logic, algebra, geometry, probability, and number theory. Do one puzzle a day!涵盖逻辑、代数、几何、概率与数论的挑战性谜题。每天一题！

20 Levels20 关100 Lessons100 课时~16.7 hours约 16.7 小时

What you'll learn你将学到

Build a daily habit of flexible, creative problem solving.养成每天灵活、创造性地解决问题的习惯。

Encounter a wide variety of math fields in bite-sized challenges.在短小的挑战中接触各个数学领域。

Strengthen perseverance and multiple-strategy thinking.增强毅力与多策略思维。

Used here as the daily 15-minute warm-up.在本计划中作为每天 15 分钟的热身。

IM3 link:与 IM3 的关联： The perfect low-stakes daily warm-up to switch the brain into problem-solving mode.最理想的低压力每日热身，让大脑切换到解题状态。

#	Level关卡	Lessons (English, as in app)课时（英文，与应用一致）	#数
1	Set 1第 1 组	The Heavier Side · Count the Werewolves · Make It Equal 5 · Checkered Cubes · In Order or All at Once?	5
2	Set 2第 2 组	Find the Best Deal · Shaded Stars · Where's the Gold? · The Nine Nine Plus · Save Your Calculator	5
3	Set 3第 3 组	Venn Rectangles · Can You Make This Equal 1? · Make a Ring of Sevens · On a Roll · A Lil Goes a Long Way	5
4	Set 4第 4 组	Striking Measure · Carrrs · Compare the Weights · Draw the Line · Advances in Wolf Fence Design	5
5	Set 5第 5 组	How Did They Finish? · Make Them Inequivalent · Stack of Squares · In the Cards · Two Wrongs Make a Right	5
6	Set 6第 6 组	Werewolves Are Liars · There Are More Than Four Triangles! · How Much Faster Together? · The Star Area · Who is the Fastest Sprinter?	5
7	Set 7第 7 组	The Best Candidate · One More Flip · Inner and Outer Angles · Rearrange the Dots Again · Sock Hop	5
8	Set 8第 8 组	Go for the Gold · Fill the Diagonal · Pigeonholed Numbers · Did You Miss Any? · Two Triangles, One Trapezoid	5
9	Set 9第 9 组	Wandering Robots · Ha ha ha ha! Eh... · An Infinitely-Zig-Zagging Line · Fill the Grid · Where Is the Gold?	5
10	Set 10第 10 组	Keep Coloring Forever · Should You Stop Rolling? · The Brilliant Hotel · Fish Fictions · There's a Quick Solution	5
11	Set 11第 11 组	Gears and Ants · How Many Werewolves? · Impossible Result · Add Up to Odd · Triangles in Line	5
12	Set 12第 12 组	Dice Wars · A's Abound! · Piece of a Circle · Crack the Code! · Running Round in Circles	5
13	Set 13第 13 组	Does It Change? · Stylish Socks · Can You Find Them All? · Red or Blue? · Human or Werewolf?	5
14	Set 14第 14 组	Make It Equal 28 · How Many Ways to Fill the Grid? · Yellow Plus Blue · Coins in Boxes · Mind Your Ps and Q	5
15	Set 15第 15 组	Does It Make a Cube? · Start in the Middle · Parallelogram and Circles · Misleading Marathoners · How Many Marbles?	5
16	Set 16第 16 组	Make Six Twice · Which Has More Faces? · How Much Will You Win? · Overlapping Areas · Taking Their Time	5
17	Set 17第 17 组	Diagonal Thinking · Knight, Knave, or Joker? · Cherry Production · Angle Hunt · The Short Pour	5
18	Set 18第 18 组	Exactly 3 Divisors? · Overlapping Rectangles · Shopping for Socks · It All Comes To Nothing · Humans and Werewolves	5
19	Set 19第 19 组	Only Two Pieces? · The Eye of... · What Makes Squares a Little Odd? · Perimeter from Perimeters? · Random Numbers	5
20	Set 20第 20 组	Too Many Twos · Octagons and Squares · What Color is Shinoy's Hat? · Elephant Ears · The Maximum Maximum	5

Built from the live Brilliant catalog (logged-in view), June 2026. Course/level structure may evolve; lesson names reflect the app at capture time.依据 Brilliant 实时课程目录（已登录视图）整理，2026 年 6 月。课程/关卡结构可能调整；课时名称为采集时应用中的内容。