Quant Roadmap
Step 1 - Master basic algebra, trigonometry, pre calculus (achieved before completion of high
school)
Step 2 - Master the basics of calculus (differential, integral, and then multivariable calculus).
These include but are not limited to differentiation, summation theorems, BASIC convergence
theorems, sequences, multivariable derivatives (i.e. partial derivatives), stokes theorem
(introductory version), divergence theorem (introductory), flux, basic path integrals, and Taylors
theorems…the list goes on but these are core topics (and all the differentiation stuff goes w/ the
integration stuff).
Step 3 - Start to familiarize yourself with the basics of programming. What is programming? How
do I write a basic program in any language – i.e. a basic hello world program? How does my
computer process data? What is a package? What is a compiler? How do I run my first
programs? Start this obviously with C++ as it is a standard language and is low level i.e. it
converts directly to assembly then to linker without any other steps making it a very optimized
language for the work we do as quants. Then start to approach basic python i.e. numpy and
matplotlib. Try to make basic plots and graphs. Add colors, headers. All of this will build muscles
for real programming.
Step 4 - Linear Algebra. This is the most important step. The book is Linear Algebra done right.
Very rarely will I recommend someone to go through an entire book but this book is an
exception. Every person must go through this book PINKER TO STINKER or don’t even bother
trying to be a quant. No theorem gets unused and everything else comes back latr. Topics
include: decomposition theorems, eigenvalues, matrix theory, eigenvectors, basis, nullity, jordan
form, jordan canonical form, the theorems go on and on.
Step 5 - Basic data structures. Now you are gonna learn the real deal of how to program. This is
in the context of C++ (although python has direct analogs). Vectors, stacks, arrays, queues,
dequeues, hashmaps, Red-black trees, linked lists, etc…
Step 6 - Now we are ready to do some real deal mathematical finance stuff. CALCULUS
BASED PROBABILITY. This is your bread and butter. The first book you need to go through is A
first course in probability by ross. Another good alternative is introduction to probability,
statistics, and random process by Nik. Both are great, do both concurrently.
Step 7 - Next, you need to understand discrete structures in order to properly do algorithms.
Mathematics a discrete introduction by scheinermann is your go-to. Its surprisingly challenging
and fun so don’t right it off. I like it after probability models so the probability stuff is ez but you
can always ignore it and just do everything else i.e. important introduction to number theory,
graph theory, set theory, etc. Once again all of this should review from Linear algebra and
probability. You can also do discrete mathematics by Knuth but thats a more computer science
side book and I value that less.
Step 8 - Now you can start doing anything that is prerequisite to high level mathematics. In no
order you can go over this material: ODEs, Numerical Analysis
Step 9 - Now you can do algorithms. The book is CLRS and needs no further introduction. Do it
and understand it will take years to complete it. But work through it as you do the next set of
steps and follow it along with the other materials. Try to relate it back constantly to mathematical
applications, which are in fact the most important and only relevant applications.
Step 10 - Now you are at a crossroads. You have all the prerequisites, math and computer
science to start to pursue high level and real mathematical finance. Now, which path do you
want to take? You can be a quant dev or a quant researcher. One is much more complex than
the other in a sense and is reflected in both the work and pay. However, there day to day
workload differs completely and the amount of education you need to pursue also varies day to
day. Decide whether or not you actually want to pursue this because chasing quant researcher
will entail graduate school.
Step 11 - Abstract Algebra, Real Analysis, PDEs, Introduction to Mathematical Finance
(recommended book is Mathematical Techniques in Finance by Amir Sadr, my old professor at
NYU), Complex Analysis
Step 12 - If you chose quant dev now you would want to pursue topics like optimal compiler
structure, advanced algorithms, distributed computing systems, computer hardware
architecture, parallel computing and parallel computing algorithms. This is mostly advanced
masters level coursework and should be pursued at that level, the rest of what I will explain will
be strictly for quant researchers and it will become more advanced and overlap with quant dev
work as most quant researchers do work that quant devs have to use and interact with.
Step 13 - Linear Programming, Stochastic Processes, Linear and Nonliner analysis (functional
analysis), fourier analysis, harmonic analysis - these last three are not required and are highly
advanced but very helpful for understanding the material if pursued at at least an introductory
level in stochastic calculus
Step 14 - Machine Learning. This includes SVMs, Kernalization, Linearization, Graduate
Descent, Conjugate Gradient Descent, Deep Learning (DKN neural networks, etc),
Reinforcement Learning, Primal-Dual Gradient Descent, LLMs
Step 15 - Stochastic Calculus.
Step 16 - Go get your job. If you make it past this stage, dm Landbus in discord and we can talk
turkey.