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yoonholee
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olympiad-books-open-source

text stringlengths 121 5.68k	book stringclasses 12 values	book_key stringclasses 12 values	subject stringclasses 9 values	level stringclasses 2 values	part stringclasses 45 values	chapter stringclasses 202 values	section stringlengths 0 104	source_file stringclasses 214 values	chunk_id int64 0 129	tokens_est int64 34 1.62k
When introduced to a new idea, always ask why you should care.\ Do not expect an answer right away, but demand one eventually.\ --- Ravi Vakil If you like this book and want to support me, please consider buying me a coffee!\ [![image](media/kofi4.png){width="32ex"}](https://ko-fi.com/evanchen)\ <https://ko-fi.com/...	An Infinitely Large Napkin	napkin	general	advanced	Front Matter	Title Embellishments		01_title-embellishments.md	0	436
The origin of the name "Napkin" comes from the following quote of mine. > I'll be eating a quick lunch with some friends of mine who are still in high school. They'll ask me what I've been up to the last few weeks, and I'll tell them that I've been learning category theory. They'll ask me what category theory is about...	An Infinitely Large Napkin	napkin	general	advanced	Front Matter	Preface		02_preface.md	0	682
The Infinitely Large Napkin is a light but mostly self-contained introduction to a large amount of higher math. I should say at once that this book is not intended as a replacement for dedicated books or courses; the amount of depth is not comparable. On the flip side, the benefit of this "light" approach is that it...	An Infinitely Large Napkin	napkin	general	advanced	Front Matter	Preface	About this book	02_preface.md	1	689
The project is hosted on GitHub at <https://github.com/vEnhance/napkin>. Pull requests are quite welcome! I am also happy to receive suggestions and corrections by email. The project is hosted on GitHub at <https://github.com/vEnhance/napkin>. Pull requests are quite welcome! I am also happy to receive suggestions and...	An Infinitely Large Napkin	napkin	general	advanced	Front Matter	Preface	Source code	02_preface.md	2	1,460
The preface would become too long if I talked about some of my pedagogical decisions chapter by chapter, so contains those comments instead. In particular, I often name specific references, and the end of that appendix has more references. So this is a good place to look if you want further reading. The preface would...	An Infinitely Large Napkin	napkin	general	advanced	Front Matter	Preface	More pedagogical comments and references	02_preface.md	3	813
I am indebted to countless people for this work. Here is a partial (surely incomplete) list. - Thanks to all my teachers and professors for teaching me much of the material covered in these notes, as well as the authors of all the references I have cited here. A special call-out to , , , , , , , , , , which were espec...	An Infinitely Large Napkin	napkin	general	advanced	Front Matter	Preface	Acknowledgements	02_preface.md	4	1,112
As explained in the preface, the main prerequisite is some amount of mathematical maturity. This means I expect the reader to know how to read and write a proof, follow logical arguments, and so on. I also assume the reader is familiar with basic terminology about sets and functions (e.g. "what is a bijection?"). If n...	An Infinitely Large Napkin	napkin	general	advanced	Front Matter	Advice for the reader	Prerequisites	03_advice.md	0	1,205
In this book, there are three hierarchies: - An inline question is intended to be offensively easy, mostly a chance to help you internalize definitions. If you find yourself unable to answer one or two of them, it probably means I explained it badly and you should complain to me. But if you can't answer many, you ...	An Infinitely Large Napkin	napkin	general	advanced	Front Matter	Advice for the reader	Questions, exercises, and problems	03_advice.md	1	764
At the risk of being blunt, Read this book with pencil and paper. Here's why: ![image](media/read-with-pencil.jpg){width="50%"}\ Image from [@img:read_with_pencil] You are not God. You cannot keep everything in your head.[^2] If you've printed out a hard copy, then write in the margins. If you're trying to save pap...	An Infinitely Large Napkin	napkin	general	advanced	Front Matter	Advice for the reader	Paper	03_advice.md	2	872
This part describes some of the less familiar notations and definitions and settles for once and for all some annoying issues ("is zero a natural number?"). Most of these are "remarks for experts": if something doesn't make sense, you probably don't have to worry about it for now. A full glossary of notation used can ...	An Infinitely Large Napkin	napkin	general	advanced	Front Matter	Advice for the reader	Conventions and notations	03_advice.md	3	306
This is brief, intended as a reminder for experts. Consult for full details. An equivalence relation on a set $X$ is a relation $\sim$ which is symmetric, reflexive, and transitive. An equivalence relation partitions $X$ into several equivalence classes. We will denote this by $X / {\sim}$. An element of such ...	An Infinitely Large Napkin	napkin	general	advanced	Front Matter	Advice for the reader	Sets and equivalence relations	03_advice.md	4	608
This is brief, intended as a reminder for experts. Consult for full details. Let $X \taking f Y$ be a function: - By $f\pre(T)$ I mean the pre-image $$f\pre(T) := \left\{ x \in X \mid f(x) \in T \right\}.$$ This is in contrast to the $f^{-1}(T)$ used in the rest of the world; I only use $f^{-1}$ for an inverse *f...	An Infinitely Large Napkin	napkin	general	advanced	Front Matter	Advice for the reader	Functions	03_advice.md	5	621
Additionally, a permutation on a finite set may be denoted in cycle notation, as described in say <https://en.wikipedia.org/wiki/Permutation#Cycle_notation>. For example the notation $(1 \; 2 \; 3 \; 4)(5 \; 6 \; 7)$ refers to the permutation with $1 \mapsto 2$, $2 \mapsto 3$, $3 \mapsto 4$, $4 \mapsto 1$, $5 \mapsto...	An Infinitely Large Napkin	napkin	general	advanced	Front Matter	Advice for the reader	Cycle notation for permutations	03_advice.md	6	655
We accept the Axiom of Choice, and use it freely. We accept the Axiom of Choice, and use it freely. The appendix contains a list of resources I like, and explanations of pedagogical choices that I made for each chapter. I encourage you to check it out. In particular, this is where you should go for further reading! ...	An Infinitely Large Napkin	napkin	general	advanced	Front Matter	Advice for the reader	Choice	03_advice.md	7	400
This chapter contains a pitch for each part, to help you decide what you want to read and to elaborate more on how they are interconnected. For convenience, here is again the dependency plot that appeared in the frontmatter. ,45:Ch ,-[Abs Alg](#part:absalg) ,45:Ch ,-[Topology](#part:basictop) ,45:Ch -,[Lin Alg](#part...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Sales pitches		04_salespitch.md	0	749
- [.]\ I made a design decision that the first part should have a little bit of both algebra and topology: so this first chapter begins by defining a group, while the second chapter begins by defining a metric space. The intention is so that newcomers get to see two different examples of "sets with addition...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Sales pitches	The basics	04_salespitch.md	1	1,149
- [.]\ In high school, linear algebra is often really unsatisfying. You are given these arrays of numbers, and they're manipulated in some ways that don't really make sense. For example, the determinant is defined as this funny-looking sum with a bunch of products that seems to come out of thin air. Where does it c...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Sales pitches	Abstract algebra	04_salespitch.md	2	892
- [.]\ In high school, linear algebra is often really unsatisfying. You are given these arrays of numbers, and they're manipulated in some ways that don't really make sense. For example, the determinant is defined as this funny-looking sum with a bunch of products that seems to come out of thin air. Where does it c...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Sales pitches	Abstract algebra	04_salespitch.md	3	892
- [.]\ In this part, we'll use our built-up knowledge of metric and topological spaces to give short, rigorous definitions and theorems typical of high school calculus. That is, we'll really define and prove most everything you've seen about limits, series, derivatives, and integrals. Although this...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Sales pitches	Real and complex analysis	04_salespitch.md	4	1,091
- [.]\ In this part, we'll use our built-up knowledge of metric and topological spaces to give short, rigorous definitions and theorems typical of high school calculus. That is, we'll really define and prove most everything you've seen about limits, series, derivatives, and integrals. Although this...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Sales pitches	Real and complex analysis	04_salespitch.md	5	1,091
- [.]\ Why is $3+\sqrt5$ the conjugate of $3-\sqrt5$? How come the norm $\norm{a+b\sqrt5} = a^2-5b^2$ used in Pell's equations just happens to be multiplicative? Why is it we can do factoring into primes in $\mathbb{Z}[i]$ but not in $\mathbb{Z}[\sqrt{-5}]$? All these questions and more will be answered in this par...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Sales pitches	Algebraic number theory	04_salespitch.md	6	677
- [.]\ What's the difference between an annulus and disk? Well, one of them has a "hole" in it, but if we are just given intrinsic topological spaces it's hard to make this notion precise. The fundamental group $\pi_1(X)$ and more general homotopy group will make this precise --- we'll find a way to define ...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Sales pitches	Algebraic topology	04_salespitch.md	7	1,432
- [.]\ We begin with a classical study of classical complex varieties: the study of intersections of polynomial equations over $\mathbb{C}$. This will naturally lead us into the geometry of rings, giving ways to draw pictures of ideals, and motivating Hilbert's nullstellensatz. The Zariski topology will...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Sales pitches	Algebraic geometry	04_salespitch.md	8	745
- [.]\ Why is Russell's paradox such a big deal and how is it resolved? What is this Zorn's lemma that everyone keeps talking about? In this part we'll learn the answers to these questions by giving a real description of the Zermelo-Frankel axioms, and the axiom of choice, delving into the details o...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Sales pitches	Set theory	04_salespitch.md	9	672
A group is one of the most basic structures in higher mathematics. In this chapter I will tell you only the bare minimum: what a group is, and when two groups are the same. A group is one of the most basic structures in higher mathematics. In this chapter I will tell you only the bare minimum: what a group is, and whe...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Groups		05_grp-intro.md	0	98
A group consists of two pieces of data: a set $G$, and an associative binary operation $\star$ with some properties. Before I write down the definition of a group, let me give two examples. The pair $(\mathbb{Z}, +)$ is a group: $\mathbb{Z} = \left\{ \dots,-2,-1,0,1,2,\dots \right\}$ is the set and the associative ope...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Groups	Definition and examples of groups	05_grp-intro.md	1	1,488
Let $S_n$ be the set of permutations of $\left\{ 1,\dots,n \right\}$. By viewing these permutations as functions from $\left\{ 1,\dots,n \right\}$ to itself, we can consider compositions of permutations. Then the pair $(S_n, \circ)$ (here $\circ$ is function composition) is also a group, because - There is an identi...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Groups	Definition and examples of groups	05_grp-intro.md	2	853
A group consists of two pieces of data: a set $G$, and an associative binary operation $\star$ with some properties. Before I write down the definition of a group, let me give two examples. The pair $(\mathbb{Z}, +)$ is a group: $\mathbb{Z} = \left\{ \dots,-2,-1,0,1,2,\dots \right\}$ is the set and the associative ope...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Groups	Definition and examples of groups	05_grp-intro.md	3	1,488
Let $S_n$ be the set of permutations of $\left\{ 1,\dots,n \right\}$. By viewing these permutations as functions from $\left\{ 1,\dots,n \right\}$ to itself, we can consider compositions of permutations. Then the pair $(S_n, \circ)$ (here $\circ$ is function composition) is also a group, because - There is an identi...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Groups	Definition and examples of groups	05_grp-intro.md	4	853
From now on, we'll often refer to a group $(G, \star)$ by just $G$. Moreover, we'll abbreviate $a \star b$ to just $ab$. Also, because the operation $\star$ is associative, we will omit unnecessary parentheses: $(ab)c = a(bc) = abc$. From now on, for any $g \in G$ and $n \in \mathbb{N}$ we abbreviate $$g^n = \underbra...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Groups	Properties of groups	05_grp-intro.md	5	956
First, let me talk about what it means for groups to be isomorphic. Consider the two groups - $\mathbb{Z} = (\left\{ \dots,-2,-1,0,1,2,\dots \right\}, +)$. - $10\mathbb{Z} = (\left\{ \dots, -20, -10, 0, 10, 20, \dots \right\}, +)$. These groups are "different", but only superficially so -- you might even say they onl...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Groups	Isomorphisms	05_grp-intro.md	6	972
First, let me talk about what it means for groups to be isomorphic. Consider the two groups - $\mathbb{Z} = (\left\{ \dots,-2,-1,0,1,2,\dots \right\}, +)$. - $10\mathbb{Z} = (\left\{ \dots, -20, -10, 0, 10, 20, \dots \right\}, +)$. These groups are "different", but only superficially so -- you might even say they onl...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Groups	Isomorphisms	05_grp-intro.md	7	972
As is typical in math, we use the word "order" for way too many things. In groups, there are two notions of order. The order of a group $G$ is the number of elements of $G$. We denote this by $\left\lvert G \right\rvert$. Note that the order may not be finite, as in $\mathbb{Z}$. We say $G$ is a finite group j...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Groups	Orders of groups, and Lagrange's theorem	05_grp-intro.md	8	1,330
Earlier we saw that $\GL_n(\mathbb{R})$, the $n \times n$ matrices with nonzero determinant, formed a group under matrix multiplication. But we also saw that a subset of $\GL_n(\mathbb{R})$, namely $\SL_n(\mathbb{R})$, also formed a group with the same operation. For that reason we say that $\SL_n(\mathbb{R})$ is a sub...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Groups	Subgroups	05_grp-intro.md	9	1,383
Just for fun, here is a list of all groups of order less than or equal to ten (up to isomorphism, of course). 1. The only group of order $1$ is the trivial group. 2. The only group of order $2$ is $\mathbb{Z}/2\mathbb{Z}$. 3. The only group of order $3$ is $\mathbb{Z}/3\mathbb{Z}$. 4. The only groups of order $4$ a...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Groups	Groups of small orders	05_grp-intro.md	10	1,070
A common question is: why these axioms? For example, why associative but not commutative? This answer will likely not make sense until later, but here are some comments that may help. One general heuristic is: Whenever you define a new type of general object, there's always a balancing act going on. On the one hand, y...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Groups	Unimportant long digression	05_grp-intro.md	11	1,508
Look at the group $G$ of $2 \times 2$ matrices mod $p$ with determinant $\pm 1$ (whose entries are the integers mod $p$). Let $g = \begin{bmatrix} 1 & 1 \\ 1 & 0 \end{bmatrix}$ and then use $g^{\left\lvert G \right\rvert} = 1_G$. [^1]: In other words, permutation groups can be arbitrarily weird. I remember being highl...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Groups	Unimportant long digression	05_grp-intro.md	12	118
A common question is: why these axioms? For example, why associative but not commutative? This answer will likely not make sense until later, but here are some comments that may help. One general heuristic is: Whenever you define a new type of general object, there's always a balancing act going on. On the one hand, y...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Groups	Unimportant long digression	05_grp-intro.md	13	1,508
Look at the group $G$ of $2 \times 2$ matrices mod $p$ with determinant $\pm 1$ (whose entries are the integers mod $p$). Let $g = \begin{bmatrix} 1 & 1 \\ 1 & 0 \end{bmatrix}$ and then use $g^{\left\lvert G \right\rvert} = 1_G$. [^1]: In other words, permutation groups can be arbitrarily weird. I remember being highl...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Groups	Unimportant long digression	05_grp-intro.md	14	118
At the time of writing, I'm convinced that metric topology is the morally correct way to motivate point-set topology as well as to generalize normal calculus.[^1] So here is my best attempt. The concept of a metric space is very "concrete", and lends itself easily to visualization. Hence throughout this chapter you sh...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Metric spaces		06_metric-top.md	0	1,341
A metric space is a pair $(M, d)$ consisting of a set of points $M$ and a metric $d \colon M \times M \to \mathbb R_{\ge 0}$. The distance function must obey: - For any $x,y \in M$, we have $d(x,y) = d(y,x)$; i.e. $d$ is symmetric. - The function $d$ must be positive definite which means that $d(x,y) \ge 0...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Metric spaces	Definition and examples of metric spaces	06_metric-top.md	1	1,088
Since we can talk about the distance between two points, we can talk about what it means for a sequence of points to converge. This is the same as the typical epsilon-delta definition, with absolute values replaced by the distance function. Let $(x_n)_{n \ge 1}$ be a sequence of points in a metric space $M$. We say th...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Metric spaces	Convergence in metric spaces	06_metric-top.md	2	1,061
In calculus you were also told (or have at least heard) of what it means for a function to be continuous. Probably something like > A function $f \colon \mathbb{R} \to \mathbb{R}$ is continuous at a point $p \in \mathbb{R}$ if for every $\varepsilon > 0$ there exists a $\delta > 0$ such that $\left\lvert x-p \right\rv...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Metric spaces	Continuous maps	06_metric-top.md	3	816
When do we consider two groups to be the same? Answer: if there's a structure-preserving map between them which is also a bijection. For metric spaces, we do exactly the same thing, but replace "structure-preserving" with "continuous". Let $M$ and $N$ be metric spaces. A function $f \colon M \to N$ is a **homeomorphis...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Metric spaces	Homeomorphisms	06_metric-top.md	4	783
When do we consider two groups to be the same? Answer: if there's a structure-preserving map between them which is also a bijection. For metric spaces, we do exactly the same thing, but replace "structure-preserving" with "continuous". Let $M$ and $N$ be metric spaces. A function $f \colon M \to N$ is a **homeomorphis...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Metric spaces	Homeomorphisms	06_metric-top.md	5	783
Here is an extended example which will occur later on. Let $M = (M, d_M)$ and $N = (N, d_N)$ be metric spaces (say, $M = N = \mathbb{R}$). Our goal is to define a metric space on $M \times N$. Let $p_i = (x_i,y_i) \in M \times N$ for $i=1,2$. Consider the following metrics on the set of points $M \times N$: $$\begin{a...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Metric spaces	Extended example/definition: product metric	06_metric-top.md	6	853
Continuity is really about what happens "locally": how a function behaves "close to a certain point $p$". One way to capture this notion of "closeness" is to use metrics as we've done above. In this way we can define an $r$-neighborhood of a point. Let $M$ be a metric space. For each real number $r > 0$ and point $p \...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Metric spaces	Open sets	06_metric-top.md	7	1,328
It would be criminal for me to talk about open sets without talking about closed sets. The name "closed" comes from the definition in a metric space. Let $M$ be a metric space. A subset $S \subseteq M$ is closed in $M$ if the following property holds: let $x_1$, $x_2$, ... be a sequence of points in $S$ and suppos...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Metric spaces	Closed sets	06_metric-top.md	8	1,457
Assume for contradiction it is completely discontinuous; by scaling set $f(0) = 0$, $f(1) = 1$ and focus just on $f \colon [0,1] \to [0,1]$. Since it's discontinuous everywhere, for every $x \in [0,1]$ there's an $\varepsilon_x > 0$ such that the continuity condition fails. Since the function is strictly increasing, th...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Metric spaces	Closed sets	06_metric-top.md	9	999
It would be criminal for me to talk about open sets without talking about closed sets. The name "closed" comes from the definition in a metric space. Let $M$ be a metric space. A subset $S \subseteq M$ is closed in $M$ if the following property holds: let $x_1$, $x_2$, ... be a sequence of points in $S$ and suppos...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Metric spaces	Closed sets	06_metric-top.md	10	1,457
Assume for contradiction it is completely discontinuous; by scaling set $f(0) = 0$, $f(1) = 1$ and focus just on $f \colon [0,1] \to [0,1]$. Since it's discontinuous everywhere, for every $x \in [0,1]$ there's an $\varepsilon_x > 0$ such that the continuity condition fails. Since the function is strictly increasing, th...	An Infinitely Large Napkin	napkin	general	advanced	Starting Out	Metric spaces	Closed sets	06_metric-top.md	11	999
Homomorphisms and quotient groups ch:homomorphisms_quotient Generators and group presentations = < r,s r^n=s^2=1>$ Let $G$ be a group. Recall that for some element $x G$, we could consider the subgroup \[ \ , x^-2, x^-1, 1, x, x^2, \ \] of $G$. Here's a more pictorial version of what we did: put $x$ in a box, seal it ...	An Infinitely Large Napkin	napkin	general	advanced	Basic Abstract Algebra	Homomorphisms and quotient groups		07_quotient.md	0	1,559
Now let me define a very important property of a homomorphism. The kernel of a homomorphism $ G H$ is defined by \[ \ g G : (g) = 1_H \. \] It is a subgroup of $G$ (in particular, $1_G $ for obvious reasons). Verify that $$ is in fact a subgroup of $G$. We also have the following important fact, which we also encour...	An Infinitely Large Napkin	napkin	general	advanced	Basic Abstract Algebra	Homomorphisms and quotient groups		07_quotient.md	1	1,568

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olympiad-books-open-source

Chunked content from 12 open-source mathematics textbooks, suitable for retrieval (RAG), embedding, and math reasoning research.

Source code: github.com/yoonholee/olympiad-books-open-source-pipeline

Books

Book	Author(s)	License	Source
An Infinitely Large Napkin	Evan Chen	CC BY-SA 4.0 / GPL v3	GitHub
Mathematical Reasoning: Writing and Proof	Ted Sundstrom	CC BY-NC-SA 3.0	GitHub
Exploring Combinatorial Mathematics	Richard Grassl, Oscar Levin	GFDL	GitHub
Discrete Mathematics: An Open Introduction	Oscar Levin	CC BY-SA 4.0	GitHub
Abstract Algebra: Theory and Applications	Tom Judson	GFDL	GitHub
Applied Combinatorics	Mitchel Keller, William Trotter	CC BY-SA 4.0	GitHub
Combinatorics Through Guided Discovery	Kenneth Bogart	GFDL	GitHub
A First Course in Linear Algebra	Robert Beezer	GFDL	GitHub
Elementary Number Theory	William Stein	Free (Springer agreement)	GitHub
Basic Analysis	Jiri Lebl	CC BY-NC-SA 4.0 + CC BY-SA 4.0	GitHub
An Introduction to Proof via Inquiry-Based Learning	Dana Ernst	CC BY-SA 4.0	GitHub
Open Logic	Open Logic Project	CC BY 4.0	GitHub

Schema

Field	Type	Description
`text`	string	Chunk content (markdown with LaTeX math)
`book`	string	Full book title
`book_key`	string	Short identifier (e.g. `napkin`, `aata`, `openlogic`)
`subject`	string	Math subject area: `general`, `abstract-algebra`, `combinatorics`, `discrete-math`, `linear-algebra`, `logic`, `number-theory`, `proofs`, `real-analysis`
`level`	string	`intro` (undergrad) or `advanced` (upper-division / graduate)
`part`	string	Part/unit grouping within a book (e.g. "Group Theory", "Single Variable")
`chapter`	string	Chapter title (e.g. "Groups", "Real Numbers")
`section`	string	Section title (empty if chunk is in chapter intro)
`source_file`	string	Original markdown filename
`chunk_id`	int	Sequential chunk index within chapter
`tokens_est`	int	Estimated token count (~3.5 chars/token)

Stats

Book	Chunks	Median tokens	Total tokens
An Infinitely Large Napkin	794	1446	945K
Open Logic	480	1464	645K
Basic Analysis	408	1056	418K
A First Course in Linear Algebra	370	1184	389K
Abstract Algebra: Theory and Applications	330	1080	335K
Mathematical Reasoning	274	1014	270K
Applied Combinatorics	229	1001	226K
Discrete Mathematics	205	1087	214K
Combinatorics Through Guided Discovery	124	930	112K
Elementary Number Theory	116	1056	118K
Exploring Combinatorial Mathematics	90	1156	94K
An Introduction to Proof via IBL	86	1491	112K
Total	3506		3.88M

Chunking method

Content-aware chunking from source files (LaTeX/PreTeXt), not PDF extraction:

Section boundaries (##/### headers) always start a new chunk
Math environments (Theorem, Definition, Example, Proof, etc.) are kept intact
Paragraph splits used only when a block exceeds the max token limit
Math blocks ($$...$$) are never split
Small adjacent chunks merged up to the max token limit (default 512-1536 tokens)

Topics covered

Napkin: Abstract algebra, topology, linear algebra, representation theory, complex analysis, measure theory, differential geometry, algebraic number theory, algebraic topology, category theory, algebraic geometry, set theory
Open Logic: Propositional logic, first-order logic, modal logic, intuitionistic logic, computability, incompleteness, set theory, model theory
Basic Analysis: Real numbers, sequences, series, continuous functions, derivatives, integrals, metric spaces, multivariable calculus
First Course in Linear Algebra: Systems of equations, vectors, matrices, determinants, eigenvalues, linear transformations, vector spaces
Abstract Algebra: Groups, cyclic groups, permutation groups, cosets, isomorphisms, normal subgroups, homomorphisms, rings, integral domains, fields, vector spaces, Galois theory
Mathematical Reasoning: Logic, proof techniques, set theory, functions, equivalence relations, number theory
Applied Combinatorics: Strings/sequences, induction, generating functions, graph theory, inclusion-exclusion, network flows, partially ordered sets
Discrete Mathematics: Logic, graph theory, counting, sequences, mathematical structures
Combinatorics Through Guided Discovery: Counting, generating functions, distribution problems, graph theory, Polya enumeration
Elementary Number Theory: Prime numbers, congruences, quadratic reciprocity, continued fractions, elliptic curves
Exploring Combinatorial Mathematics: Pascal's triangle, binomial coefficients, generating functions, Stirling numbers, partitions, inclusion-exclusion
Introduction to Proof via IBL: Logic, set theory, induction, real number axioms, topology of reals, sequences, continuity

Usage

from datasets import load_dataset

ds = load_dataset("yoonholee/olympiad-books-open-source", split="train")

# Filter by book
napkin = ds.filter(lambda x: x["book_key"] == "napkin")

# Filter by subject
algebra = ds.filter(lambda x: x["subject"] == "abstract-algebra")

# Filter by level
intro = ds.filter(lambda x: x["level"] == "intro")

# Filter by part within a book
groups = ds.filter(lambda x: x["book_key"] == "aata" and x["part"] == "Group Theory")

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