Token engineering is an interdisciplinary practice emerging from the blockchain space. Here is a (somewhat) complete list of the sub-disciplines within token engineering:

- Complex Systems Theory
- Game & Decision Theory
- Mechanism Design
- Network Science
- Markets
- Dynamical Systems
- Cryptoeconomics

Many of those topics themselves are interdisciplinary **and** have exclusive as well as overlapping pre-requisites.

Due to the many sub-disciplines as well as the immaturity of the field, it is difficult for newcomers & curious polymaths to know how to begin their study. I, myself, found this particularly challenging. The Token Engineering community has a wiki that provides many recommended resources, which is certainly a first step towards the goal of enabling friction-less inauguration into the discipline. However, an understanding of the topics' relationships to each other, the (overlapping) pre-requisites and an order in which to study the topics is just as important.

That is why I've compiled an ordered list of learning resources someone can use to go from knowing nothing beyond basic highschool algebra all the way to token engineering adepthood. I have tried to focus on resources that provide ample enough exercises so that one's work can be checked.

It's also important to note that Block Science, an R&D firm specializing in complex systems engineering, not only developed a tool called cadCAD which enables the practice of token engineering (see their case studies), but pioneered this exciting field. I highly recommend watching their many videos about token engineering as well as their tutorials on using cadCAD to analyse and design token systems.

I recommend watching some of the videos listed in the above links to get a fuller sense of Token Engineering prior to diving in. I especially recommend this one: Engineering Token Economy with System Modeling

The list below splits learning into "phases" - think of them as semesters for us autodidacts - comprised of multiple courses.

One final point I should raise is that the order prescribed here is not the order in which I went through the listed resources. Rather, it is the order I **would** go through them in hindsight now that I have a better understanding of the dependencies between concepts. Further, I have not gone through the entirety of every resource listed. Rather, the resulting list is a combination of resources I have used as well as those that seem to me to be viable alternatives. Your mileage with one resource or another may vary based on your preferences. I was hesitant to do this due to the increased risk of leading a reader astray. To mitigate that risk, I only chose resources whose material & structure seemed of relatively high quality to me as well as those that were well reviewed or those recommended by colleagues. That being said I cannot guarantee that every resource will be optimal for every person, due to natural variance in the preferences of the learner, my own biases, as well as the style, maturity & historical context of the resources themselves.

## Phase 1: Foundational Concepts & Mathematics

### Calculus

Calculus is absolutely essential, but fear not, for I've compiled what I found to be the clearest sources to learn the topic if you don't already have a background in it. For absolute newcomers, a conceptual introduction a la 3Blue1Brown's YouTube channel is a necessary first step. From there, I recommend one of the following:

- Mathematical Modeling & Applied Calculus
- Paul Lamar's Math Notes
- Khan Academy's Calculus Courses
- MIT OCW Single Variable & Multivariable Calculus

I think the first source is probably one of the best because it will provide a light introduction to linear algebra and optimization as well, both of which are also pre-requisites to later courses.

## Linear Algebra

Once again, start with 3Blue1Brown's Linear Algebra series. From there, I recommend going through Immersive Linear Algebra (free interactive online textbook) and then checking out Linear Algebra: Step by Step.

Some alternatives you can think about, or further studies in Linear Algebra after completing the above sequence, is Fast.ai's Computational Linear Algebra course and their recommended textbook, Numerical Linear Algebra.

## Proofs

Another foundational skill that will prove useful when reading more advanced texts is that of reading & understanding formal proofs. For this, I recommend none other than* How to Prove it*, which is a phenomenal book on proof methods and perfectly suited for self-study.

After the above book, I recommend checking out *Logic in Computer Science* to gain more practice. A nice online natural deduction tool to write and check proofs can be found on the Open Logic Project website.

## Elementary Math

In many more advanced texts, readers will encounter concepts from set theory, functions (through the lens of set theory), machines, recurrences, etc. Many of these topics are presented in a book called *More Precisely: The Math You Need to Do Philosophy*. Although it mentions philosophy in the title, it is not a philosophy book; it's a math book. Moreover, the topics covered in this text have a lot of overlap with topics one would find in a discrete mathematics course.

I also recommend *A Book of Set Theory* by Charles Pinter, published by Dover.

Some other *optional* resources I will recommend (especially if you want more complete mathematical coverage):

- Mathematics for Computer Science (MIT OCW course & accompanying free textbook)
- A Computational Introduction to Number Theory & Algebra 2nd ed.

## Systems Theory

A good, high level introduction to systems is the book *Thinking in Systems: A Primer*. Later, many systems theory concepts will be more formalized.

## Game Theory

For a first introduction that requires a bit of mathematical maturity but isn't too demanding, I recommend none other than the classic *Games and Decisions: Introduction & Critical Survey. *Although there have been advances in the field since publishing, this is a wonderful introduction to the foundational topics. Later, we cover a modern and algorithmic approach to game theory, anyway.

## Networks & Markets

The best textbook here that is the least mathematically demanding would be *Networks, Crowds, and Markets*.

## Phase 2: Intermediate Topics

## Optimization

Optimization & linear programming are relevant when we study complex systems and system objectives. If you used Mathematical Modeling and Applied calculus as your calculus text, then you will already have some exposure to optimization. For more exposure, I recommend the freely available (as PDF) book *Convex Optimization*.

## Stochastic Processes & Control

Probability is a prerequisite here but you should have enough exposure to probability tangentially through the sources listed in phase 1.

1. Applied Probability MIT OCW

2. Dynamic Programming & Stochastic Control.

The syllabus page lists the relevant textbooks.

## Dynamical Systems

## Algorithmic Game Theory

The best resource here is the book & course by Tim Roughgarden by the same name. Supplementary materials mentioned in the course, besides the papers, are the following two books:

## Networks & Markets

Two books can be used here in parallel. The first is *Social and Economic Networks* and the second is *A Course in Networks & Markets*.

Alternatively, you can use this MIT Networks course as a guide, which makes use of the above textbook as well as others.

## Complex Systems Theory

This is an interdisicplinary topic that covers dynamical systems, evolutionary algorithms, optimization, networks, stochastic processes & control and systems theory.

Two good sources on this topic are:

- Introduction to the Theory of Complex Systems
- Introduction to the Modeling and Analysis of Complex Systems

## Phase 3: Applications & Community Recommendations

**If you want a recommended sequence to go through the materials in phase 3, scroll down to the bottom of the page!**

By the time you've reached phase 3, you will have more than enough background material to learn the tools and practice in the field. I do recommend beginning to play around with tools such as cadCAD far earlier, though. You are also well equipped to read, understand, and evaluate emerging literature. To that end, here is a list of sources you can use to further your studies and learn the tools needed to apply everything you've learned in the first two phases. I can't vouch for all of these resources personally because I haven't dove into them yet, but they have been recommended to me from active members doing Token Engineering work today.

### Papers & Courses

- Modeling Cryptoeconomic Protocols as Complex Systems
- Economic Games as Estimators
- Le Grand Jeu
- Aligning Interests: Reward Mechanisms and the Engineering of Token Incentives
- Introduction To Systems Dynamics by MIT
- Introduction to Modeling & Simulation by MIT
- Agent Based Modeling Online Course
- Online Resources from New England Complex Systems Institute
- Modeling Agents in Dynamic Systems with cadCAD
- Paper on Engineering Token Economy with System Modeling

### Cryptoeconomics & Blockchain Journals etc

- Awesome Cryptoeconomics
- Decentralized Governance Reading List
- MIT Journal of Cryptoeconomic Systems
- Ledger Journal
- British Blockchain Journal Association
- IEEE Blockchain Initiative
- Daron Acemoglu's Economics Material from MIT

### cadCAD & Other Tools

- Get Started with cadCAD: Resources, tutorials, and case studies
- Block science recommended resources
- Mesa: Agent Based Modeling in Python 3+

Also make sure to check out the TE community on Telegram if you want to engage with other folks interested in Token Engineering.

Here is a recommended sequence to go through the above resources in order for those who like a bit more structure:

### Recommended Sequence of Learning for Phase 3

- Introduction To Systems Dynamics by MIT
- Introduction to Modeling & Simulation by MIT
- Introduction to Dynamical Systems & Chaos
- Non-linear Dynamics Course
- Introduction to Agent Based Modeling
- Watch cadCAD inspiration videos to understand cadCAD's goals and uses
- Go through cadCAD's tutorials to build a toy system model
- Read through some of the articles on cadCAD community forum and also go through case studies of the cadCAD models of non-trivial systems