Are Numerical Methods and Numerical Analysis the same courses?

[Tong Ge]

Hi, I am required to take a Numerical Analysis class. I found an online class that seems good, but it is called Numerical Methods. Are they the same?

 

[Daniel Duffy]

Numerical Analysis is the (mathematical) analysis of numerical methods to solve problems. One proves stability, convergence and other properties using (possibly advanced) mathematics.

Numerical methods is concerned with essentially 'cookbook' application of numerical schemes to specific problems. It is more applied.

Ideally, both are needed. NA is the foundation for NM.

NM is more concerned with HOW it works while NA is also concerned with WHY and WHEN it works.

It depends on what you want to do?
//
Analogy; the ability to drive a car is NM while the ability to fix the engine is NA. Designing electric cars would be NA greenfield research.

 

[Tong Ge]

Thank you for your explanation. It really helps.

 

[Daniel Duffy]

Thank you for your explanation. It really helps.

You're welcome

Here's a story about history of NA in Scotland, in this case.

http://www.maths.dundee.ac.uk/~gawatson/nahistory.pdf

 

[snowwang]

Is this for a UCB requirement? I'm looking for the same thing. Could you send me the link please? Thanks.

 

[Tong Ge]

Is this for a UCB requirement? I'm looking for the same thing. Could you send me the link please? Thanks.

Yes.
Introduction to Numerical Methods - Part 1 of 2 - Canvas Network | Free online courses | MOOCs
This is the link to the Numerical Methods class. However, as Dr. Duffy explained, it is not the same as Numerical Analysis.

I just found a Numerical Analysis Certificate, though. Hopefully that is okay.
Numerical Analysis Certification USD 99 l Course l Training

 

[Daniel Duffy]

Yes.
Introduction to Numerical Methods - Part 1 of 2 - Canvas Network | Free online courses | MOOCs
This is the link to the Numerical Methods class. However, as Dr. Duffy explained, it is not the same as Numerical Analysis.

I just found a Numerical Analysis Certificate, though. Hopefully that is okay.
Numerical Analysis Certification USD 99 l Course l Training

The second is methods course as well. It looks OK, BTW.

 

[Squasher]

Numerical Analysis is the (mathematical) analysis of numerical methods to solve problems. One proves stability, convergence and other properties using (possibly advanced) mathematics.

Numerical methods is concerned with essentially 'cookbook' application of numerical schemes to specific problems. It is more applied.

Ideally, both are needed. NA is the foundation for NM.

NM is more concerned with HOW it works while NA is also concerned with WHY and WHEN it works.

It depends on what you want to do?
//
Analogy; the ability to drive a car is NM while the ability to fix the engine is NA. Designing electric cars would be NA greenfield research.

Which one is more useful in terms of applications in real world quant roles? NM or NA?

 

[Daniel Duffy]

I have MSc and Phd in Numercal Analysis. It is highly mathematical and you do things from first principles.
Numerical Methods entails using the results of Numerical Analysis and apply them to real life (without necessarily knowing 100% how they work.) NM is a black box I/O function call thing .. I drive a car but no idea how it works; I do know it needs petrol and I can recognise a flat tire).
Actual, NA is like pure maths ... you prove things without writing a single line of code.

e.g. I have both NA and NM in my new PDE book

new book "Numerical Methods in Computational Finance, a PDE/FDM Approach" (John Wiley, 2021) by Daniel J. Duffy

https://media.wiley.

www.linkedin.com

TOC

Numerical Methods in Computational Finance: A Partial Differential Equation (PDE/FDM) Approach

<p>This book is a detailed and step-by-step introduction to the mathematical foundations of ordinary and partial differential equations, their approximation by the finite difference method and applications to computational finance. The book is structured so that it can be read by beginners...

www.wiley.com

Numerical Methods in Computational Finance: A Partial Differential Equation (PDE/FDM) Approach (Wiley Finance): Amazon.co.uk: Duffy, Daniel J.: 9781119719670: Books

Buy Numerical Methods in Computational Finance: A Partial Differential Equation (PDE/FDM) Approach (Wiley Finance) 1 by Duffy, Daniel J. (ISBN: 9781119719670) from Amazon's Book Store. Everyday low prices and free delivery on eligible orders.

www.amazon.co.uk

NM without programming

Online Courses :: Datasim

www.datasim.nl

NM with programming

Online Courses :: Datasim

www.datasim.nl

So, for real life, start NM and also try to understand a bit why the algos work.

 

[Quasar Chunawala]

Yes.
Introduction to Numerical Methods - Part 1 of 2 - Canvas Network | Free online courses | MOOCs
This is the link to the Numerical Methods class. However, as Dr. Duffy explained, it is not the same as Numerical Analysis.

I just found a Numerical Analysis Certificate, though. Hopefully that is okay.
Numerical Analysis Certification USD 99 l Course l Training

Hey there,
I would likely start a new thread for NA/NM under Forums > Computing. I have started with NA, but will be programming these along the way. Will post code snippets, so hope to see you there.

 

[Daniel Duffy]

Hey there,
I would likely start a new thread for NA/NM under Forums > Computing. I have started with NA, but will be programming these along the way. Will post code snippets, so hope to see you there.

IMHO better to discuss NA and NM without code (code here just diverts attention).
and maybe attachment >> insert code.
tip #2 use LATEX.

 

[Quasar Chunawala]

IMHO better to discuss NA and NM without code (code here just diverts attention).
and maybe attachment >> insert code.
tip #2 use LATEX.

Sure, makes sense. Do you know, if KaTeX/LaTeX is still enabled on QuantNet, because I didn't spot this "Insert mathematical functions" option on the editor, and it used to be there earlier.

Edit: Okay, I see, it used to be supported by Andy earlier, by running the Tex server, but maybe he's had some problems with it off late.

 

[Daniel Duffy]

AFAIR Andy has written quite a bit

How to display C++ code and math beautifully

Just a note for the members who currently taking our online C++ course but it would be useful for many people as well. Code highlighter Many people are used to your code but you can use your code here and paste the text code from some editor onto Quantnet. Here is how it will look using C++...

quantnet.com

Even then, it is possible to do LATEX stuff, bung it into a pdf and then attach that pdf in your post.

 

[Quasar Chunawala]

AFAIR Andy has written quite a bit

How to display C++ code and math beautifully

Just a note for the members who currently taking our online C++ course but it would be useful for many people as well. Code highlighter Many people are used to your code but you can use your code here and paste the text code from some editor onto Quantnet. Here is how it will look using C++...

quantnet.com

Even then, it is possible to do LATEX stuff, bung it into a pdf and then attach that pdf in your post.

Don't mean to digress from the OP's post here, but I did read Andy's instructions earlier. LaTeX does not render for me on QuantNet. Not on my PC, nor on my mobile. Inline TeX has been very useful for quick replies, especially when it's mathematical content.