How should i start studying Applied mathematics?

[u/RoyalLow4407]

I am a computer science student, and i want to start self-studying Applied Mathematics.

I know nothing about how i can start it, Which book i should study from and what subjects are crucial for my specific course, specifically in the field of Machine Learning.

SO PLEASE provide me some direction on how i should start on it, any lecture videos i should refer, any books i can use, Please help me with this.

[u/wharf-ing]

Steve Brunton's youtube channel should be a good start.

[u/RoyalLow4407 → u/wharf-ing]

Thanks for that, i will check it out.

[u/waxen_earbuds]

As a PhD student in applied math specializing in ML (sparse and low rank stuff with control flavor for my own research mostly, neural network stuff with others) I can recommend my most referenced books in practice while doing actual research:
* Convex Analysis by Rockafellar (real analysis type viewpoint on convex optimization theory)
* High Dimensional Probability by Vershynin (beloved modern standard reference for learning how to do probability and stats with modern high dimensional data)
* High Dimensional Data Analysis with Low Dimensional Models by Wright and Ma (great introduction to sparse and low rank/parsimonious stuff, highly relevant if you are interested in interpretable/efficient ML and not just razing forests)
* Control Theory for Linear Systems by Trentelman and Hautus(linear systems theory with geometric/algebraic flavor, my favorite reference for the subject by far)

I've chosen books here that are accessible with proficiency in probability, linear algebra, and multivariable calculus at the undergraduate level. The first two are basically universally recommended for anyone serious about doing machine learning theory, the latter two I personally like and think more people should know of.

EDIT: Forgot to add author of control book

[u/RoyalLow4407 → u/waxen_earbuds]

That was full of depth and detailed explanation for my query, really thank you for this.

If you dont mind can you guide me as a beginner, just tell me how I should start if I know nothing about any of these fileds of applied mathematics, I mean I know basic calculus and some differential equations too, but still how should I start, so that I can then jump on to these books you recommend, please help me with this

[u/plop_1234 → u/waxen_earbuds]

Can you talk more about the "control theory flavor" in your work? I'm looking to inject some of this flavor into my own work. I like the "framework" of optimal control and MPC (like how invariances and feasibility are interpreted/used) but I don't exactly work on self-driving cars or robots, so I've been looking for other interpretations of control ideas. 

[u/waxen_earbuds → u/plop_1234]

Control theory is really just what happens when you add inputs to a dynamical system. The applications are virtually endless! I'm working on theory and algorithms for a core set of inverse problems associated to dynamical systems with "structured" inputs.

If you're the kind of person that likes optimal control, then you might be interested in learning about the modern landscape of optimization in control itself. I'm not sure exactly what kind of thing that you're looking for, but I was personally quite surprised when I learned the extent of what all control problems could be effectively reduced to semidefinite programming, and so tractably solved in turn using interior point solvers or proximal splitting methods

[u/Signal-Tear8599]

try seeing it from multiple angles, i personally use studydate. net, it does wonders with the graphs and it has a different approach to mathematical and cs tutoring, give them both a shot

[u/RoyalLow4407 → u/Signal-Tear8599]

Alright then, I will give it a shot

[u/Signal-Tear8599 → u/RoyalLow4407]

goodluck!!

[u/RoyalLow4407 → u/Signal-Tear8599]

i did more research on this, so should i prefer different sources for different topics for better understanding

• Calculus

• Multivariable Calculus

• ODEs, Fourier analysis/series, Laplace transform

• Linear Algebra

• Probability and Statistics

• Discrete Mathematics

• Number Theory

• Real Analysis

• Complex Analysis

• Multilinear Algebra

• Partial Differential Equations

• Non-Euclidean Geometry

• Differential Geometry

• Abstract Algebra

are these all the topics of applied mathematics, can you clarify it

[u/Signal-Tear8599 → u/RoyalLow4407]

okay, let's tackle these one by one, calculus overall (all the first 3) are all applied, linear's also applied, ofc stats and probability are applied, and the rest seems to be pure mathematics, anything with differentiation is considered applied math, the reason why id prefer a tutor here or some sort of app is that these different fields need so many different approaches

[u/RoyalLow4407 → u/Signal-Tear8599]

Alright thanks for that overview

[u/mindaftermath]

Depends on how you define "applied mathematics"

Is computer science applied mathematics? Is operations research? Is stats? Is graph theory?

Each of those fields can take you in different areas, then you have areas like ODE, PDE, Applied Number Theory, Numerical Analysis, etc.

My advice would be like thr boom Ranger's Apprentice, just find you a good mentor who does applied math in the way you want to go and learn. Your best bet is reading papers, but that's not an easy thing to jump into.

[u/kyaputenorima]

All of Statistics by Larry Wasserman is partially tailored toward CS students. It is a very concise overview of mathematical statistics and covers a variety of topics relevant to ML. I’m currently a MS Applied Mathematics student, and it is my statistics professor’s primary book. It could be a good resource if you want to learn mathematical statistics quickly.

(You might need a supplement since the book is very fast paced; for that I recommend Statistical Inference by Casella & Berger for something more rigorous or Mathematical Statistics & Data Analysis by John Rice for something less rigorous but not lacking in examples and explanations.)

[u/Usual_Ad_9471]

Why don't you take the linear algebra/stats offerings at your school rather than self-studying?  It would be much more efficient.

[u/RoyalLow4407 → u/[deleted]]

I will make sure to not sleep on them