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C++ 17 Spaceship 3-way operator <==> serves the same purpose as Python's functools.total_ordering.

I used to be OK at 2). Haven't had a watch since 1976. I just ask someone if I want to know how late it is. There are many proxies.

What research have you done into this? Or is it brainstorming at this stage? Your question is kinda general. Why not purchase a commercial package? edit: for swaptions, see "C# in Financial Markets" by Duffy and Germani (Wiley, 2013)

Just out of curiosity, is your question from a personal (student) perspective or for production software?

Well, first there are not many books in C++ for quant finance (most authors of finance books don't know/do C++). Second, PDE methods have traditionally been for equities although they can and have been applied to fixed income (CIR, Hull White), convertible bonds and such-like. Some chapters are...

What aboit GO as the C++ killer? (I apologise for posting this)

That's a great name! MARCO ANTONIO BASULTO VILLEGAS

Flow charts are very generic and have many specialisations. All kinds of enginers and busines analysts use it in one form or another. DFD are cool and useful and Missing In Action as we see a process of widespread deskilling in software expertise during recent years. Software development savvy...

EXCELIMPORTS FAQ https://quantnet.com/threads/resolved-office-2016-numerous-errors-on-excel-tlh.46879/#post-307520 @APalley @WZhang

FLOW CHARTS are useful techniques to sketch the design of a program before coding in C and C++ https://en.wikipedia.org/wiki/Flowchart

welcome!

3 weeks? That's very ambitious. It does not have to a 100 meter sprint.

You're welcome. Good luck!

My 2 cents A school that doesn't do programming (or coding as it is quaintly called) is not exactly future-proof. ML and DS are trendy, but how widespread is it really? I have no idea... I would learn C++ and Python.

New kid on the block. here's Carbon

I agree. But that is not the point. The style of the book is outdated and does not have decent examples/applications.

Fair enough. I'll post soon a nice example of an ordinary differential equation (ODE) from Rudin (1964) himself; page 102, exercis 17 page 156, exercise 22. The exercises are incomplete as he is essentially trying to jam ODE into 2 exercises, something 1st/2nd year undergrad will not grasp...

not to say there aren’t pieces that are constructive that's Double Dutch :whistle: I can't proceed with a reply. the nature of the subject is it?

Most real analysis is non-constructive in contrast to Computable Analysis https://en.wikipedia.org/wiki/Computable_analysis A great example is https://en.wikipedia.org/wiki/Banach_fixed-point_theorem

For the record, I said nothing about Ahlfors, just Rudin.

OK. Not sure if this is what I meant. Never mind.

I'll be 70 in a few weeks and even I knew in 1972 that Rudin was not useful. I wonder how many students get burned on Dedekind cuts (chapter 1)...... If Rudin is all you know then there is little hope to understand more advanced and applied topics.

A good exercise is to compute the Lebesgue integral NUMERICALLY of y = f(x) by hand from 1st principles, i.e. upper and lower sums. By doing this, you also learn what a level set is and how Lebesgue differs from Riemann. e.g. y = x on (0,1), exact = 1/2.

Unfortunately, that is not so. Been there, done that. OK, I had a look again at baby Rudin, in particular chapter 10. Long story short ... it does a great disservice/injustice to the topics of Measure Theory and Lebesgue integration. We used our lecture notes as basis for the real thing...

This book contains the standard 1st year graduate material on Real Analysis.A very solid background in undergraduate analysis is required to get started in reading and working through this book.In the United States one rarely finds a graduate level math textbook with solved problems...

It was a special honours degree in general. Actually, the dept prof gave those courses .. he was a PhD student of William Feller at Princeton so we were set high targets. 3rd and 4th years were even more intensive :) 50 students entered in year 1, 6 finished in year 4.

https://www.amazon.com/Problems-Variables-Lebesgue-Integration-Applications/dp/0070602212/ref=sr_1_19?qid=1659213620&refinements=p_27%3AMurray+R.+Spiegel&s=books&sr=1-19

We can agree to differ. I'm not joking about Schaum. Have you seen that book or is it a knee-jerk reaction? I did Rudin R & C in 2nd year undergrad :) (in Europe)

AFAIR I do Bimap in my Adv C++ course.?? @APalley // TestDNS.cpp // // Simple DNS lookup with IP addressing and domain names. // // (C) Datasim Education BV 2014 // #include <boost/config.hpp> #include <iostream> #include <string> #include <boost/bimap/bimap.hpp> #include...

I don't agree that it is a good book in the sense that you claim. We used Asplund/Bungart and Riesz-Nagy, among others, I never used Rudin after 1st year! (btw I had 4 years of Measure, Lebesgue, Functional Analysis and related Probability, challenging stuff). PhD math >> Rudin. BTW his Real and...

And for SQL-style searching you can use Bimap with Boost Multiindex https://www.boost.org/doc/libs/1_79_0/libs/multi_index/doc/index.html

I'm pretty sure that it is all doable. Also, Boost Serialization might be useful as a simple DATA STORE. https://www.boost.org/doc/libs/1_79_0/libs/serialization/doc/index.html A nice Adv C++ project if you have time to spare. @APalley

Standard C++ not, but it seems you are interested in heterogeneous data types (tuples!), Pandas is jut a whacky name for tuples aka structured or tabular data, yes? If yes, then Boost C++ might come to the rescue https://www.boost.org/doc/libs/1_79_0/libs/fusion/doc/html/ As sidekick Boost...

Rudin dates from 1958. It's stodgy. Been there, done that. Do people really use it? In my day it was for special honours maths degrees for those who do PHD later.

yeah, but it gives a warning!!! warning C4244: 'return': conversion from 'double' to 'int', possible loss of data This is taboo in production software. I suspect truncation/rounding rules...

Worlk work, work. People should relax more, like doing C++.

Did they give reasons or was it just "mentioned"? And now you're asking me?

4. does that include the person who keeps the network and printers working? :giggle:

I have written several books in C++ and C# for this stuff. See also. https://onlinelibrary.wiley.com/doi/epdf/10.1002/wilm.10647 MC is also done in the 2 Quantnet C++ courses. For MC foundations, Glasserman 2004.

UML class diagrams for Gang of Four (GOF) Design patterns. Handy card.

OK, now you want to do this code in C++? What's C++ got to do with it?? Do you have a clue what this UNDOCUMENTED code is doing?

?? what is this?? Matlab?

so. don't use auto.😵‍💫

BRESXIt is the root cause. The Tories want a Singapore in the North Sea and if they have to break International Law, so be it. The Europeans have left, and for a reason. The Blairite version of this was the belief that universities were the key to prosperity; and so they set about converting...

www.nuclearphynance.com www.wilmott.com might be useful. But their halcyon days are no more.

Ugh

Baruch is in NYC, not Euroope, right??

The list is a bit of a disjointed hotch-potch TBH. Some of the books have a cargo cult feel (e.g. Lewis). IMHO is was not quants who caused the crash. It was coming from 2006 (in fact) but no one was interested in knowing. So why have a book reference? S. Patterson:The Quants, the maths...

It's not for me to say which book. For my courses, I use several. https://www.datasim.nl/onlinecourses/103/distance-learning-pure-mathematics-foundations Nothing wrong with ambition, but legwork is needed. 2-3 years of maths. And have you a gift for maths? Imperial is top-notch.

The book by Rudin is severely outdated. I used it at maths undergrad level in 1972. For economics background, it will be a bridge too far. Imperial might be also too ambitious..

This is too soft.

I recomend literature research based on reactions from people here. The rest is up to you. In business, an employer would expect the same. e.g. for starters https://corporatefinanceinstitute.com/resources/knowledge/valuation/option-pricing-models/

C# is a great language. We have used it since 2000 on many projects.

My Datasim ODE/PDE online course is on the UCB list. https://www.datasim.nl/onlinecourses/97/distance-learning-ordinary-and-partial-differential-equations

two goals 1. learniing maths/algo 2. learning a language what is important for you. With Python a. using numpy, scipy out of the box. b. using a bit of Python (user coding) c. More extended Python. learn a bit C++ perhaps superficially) C++ is everything or nothing. It cannot be half done...

OMG, a you tube video :-)

Are you a reasonably good Python coder?. Can you design/translate algorithms into Python? Black Scholes exact Monte Carlo a bit of Machine Learning etc. numpy, scipy?

anyways, those undefined symbols mean boost lib and ql lib must be linked with your project. I'm sure it's standard. .... cmake maybe?? Maybe this is useful (caveat: I not use linux since a while)...

OK, five Euro, just kidding 🖖 Some top guys are Luigi Ballabio and Peter Caspers. They are on LinkedIn. good luck

One way is to describe a course at two levels. https://www.datasim.nl/onlinecourses/97/distance-learning-ordinary-and-partial-differential-equations @APalley @Andy Nguyen

Maybe https://sourceforge.net/p/quantlib/mailman/quantlib-users/

For me videos are not an efficient way of studying/learning (there probably a few are exceptions, i.e. How will you learn C++ otherwise? random internet copy and paste? My videos are in 1:1 correspondence with code reality. Study them and then start coding. Be patient. Get it working then Get...

yes pleeze! @APalley @Andy Nguyen

Where I find an outline of the things which are taught in the course? There is a detailed TOC for sure, I can't seem to find it. @APalley

Well no, it is not outdated, We do up to C++20. The two QN C++ courses are state-of-art. They are used by many univesities. There are zillions of C++ books out there, some better than others (most are outdated) . BTW you don't learn C++ by reading, but by doing. There are onlne C++ courses but...

Depends what you want.

Instead (or as well) of looking for famous names, why not draw up a list of the best universities and their PhD programs. I am sure there are many top professors out there at the hieight of their intellectual powers.

The 2006 C++ book is based on C++03/C++98 standard. C++ has been changed; the current version is C++20. For beginners the Quantnet C++ course is optimal. If you are (really) serious about C++ then it the best investment of a lifetime https://quantnet.com/cpp/

Jim Gatheral (Baruch)

For QN C++, having TAs is worth its weight in gold.

You don't need this stuff for PDE in finamce.. Are those notes from the pre -LATEX era?

half?? not quite 895 versus 1450 That's 39% cheaper. BTW QN has embedded C minicourse + TA support. Is there a detailed outline? i.e. the precise contents etc.

Update on ExcelDriver Microsoft can and does chang the API, so be warned. https://social.msdn.microsoft.com/Forums/office/en-US/7f26c4ea-d2db-486d-a1cd-5f3dc1a4ec35/excel-2010-c-integration-changes-in-put-methods?forum=exceldev...

Thank you. This article is part of my 2018 C++ book. A related book is my 2022 Numerical Methods PDE/FDM book.

You might like to have a look at https://www.datasim.nl/

Can you pogram stuff? e.g. C++, Python. Differntial geometry is a bit out on a limb.

# PingPong.py # import asyncio # Ping-pong/chess example, like a state machine async def pong(c): print(c, end = "") await asyncio.sleep(1) async def ping(c): print(c,end="") await asyncio.sleep(2) async def ping2(c): await SubPing(c) async def SubPing(c)...

Coroutines for Design Patterns # PAC.py # # Simple example of Presentation-Abstraction-Control pattern. More generally, coroutines are # a better mechanism for event-driven behaviour than OOP design patterns (State, Observer, Mediator, # Blackboard, Layers, MVC). # EXX. take OOP patterns and...

I am writing a new book on parallel programming/paralllel design patterns + applications in C++23, C# and Python. The software tools and cheap multi-core processors make this endeavour feasible. One new feature in C++20 is coroutines, which have many uses...

Regarding the QN C++ course(s) (I am the originator) the examples and projects are finance-focused, e.g. Monte Carlo, PDE, numerics.

double post ... see https://quantnet.com/threads/questions-for-quants.51631/

6) 2022 style state-of-art PDE/FDM (subumes all pde books in finance). https://www.wiley.com/en-gb/Numerical+Methods+in+Computational+Finance%3A+A+Partial+Differential+Equation+%28PDE+FDM%29+Approach-p-9781119719670...

OLS ODR ?

Or limbo :-)

Cute. It depeds on the context. It should be (easy to modify when requirements change) if (c == true) { /// code } else { /// code }

On a possibly analogous historical precedent: in the 80s C++ emerged and it could compile C code. Saved new investments. On migration, C developers created structs + pointers to them. Later they became OO classes etc. The chances of porting C++ libraries to Rust is well nigh impossible for...

C++ == Bjarne Stroustrup Python == Guido van Rossum C# = Anders Hejlsberg Rust == ?

Good couple of posts! Taking a contrarian viewpoint again, what's the point of Rust wrappers for Tensorflow etc. when we alreay have them in Python? On a follow-on, I would hope that function signatures/calls for Rust-TensorFlow are exactly the same as with Python. Otherwise, a new learning...

sparser math libraries (ie I don’t know if there’s a good Eigen substitute, over time this has been improving), and in general the lack of industry experience around it. On a follow on question. does Rust have support for mathsy stuff like Python numpy/scipy or Julia...

The Rust mindset of trying to outdo C++ is stoopid. The Java/C#/C++ languaage wars ended a long time ago. Now it should be Rust's turn to accept the status quo. All I hear at this stage is that Rust is for HFT, a very specific area. It's a low-level language. Rust is not for all things; be...

TIOBE June 2022 C++ to surpass in Java 23 COBOL 26 Fortran 27 Rust Don't shoot me; I'm only the piano player. https://www.tiobe.com/tiobe-index/

It does not have OOP or generics, its just different from C++ I agree. It feels like a step backwards to the 1980s.

I would also say its a gross simplification to say "stone-age applications" are the best you can get out of rust In my experience of 45 years in very many areas (e.g. 1st C++ programmer in NL in 1989, before that Fortran, Cobol, SQL) , it is NOT a gross simplication. It might be good in...

Main downsides of rust are it’s poor OOP support (ie polymorphism and inheritance is doable in rust, but harder), poorer generics/ templating support (this is actively improving), sparser math libraries (ie I don’t know if there’s a good Eigen substitute, over time this has been improving), and...

Can't go wrong wiith KKOP https://www.amazon.co.uk/Introduction-Analysis-Ostberg-Perkins-Kreider/dp/B0062EK4TK

Which country? (not joking)

I know 0.01 Rust but all languges are based on C and it compares itselt to C++ (they all do :-). Someone told me I should move to Rust but did not give any reasons... Thus, until further proof I see it as just another language. It's a cotrarian viewpoint.

e.g. https://www.datasim.nl/onlinecourses

1. What are the compelling reasons for using Rust? 2. Compare and contrast Rust's features with those of C++. 3. Is Rust trying to be a (C++)++, i.e. a better C++? 4. Which applications is Rust good at? 5. When will it take off into the mainstream? 6. Can I port C++ code to Rust?

Sure! DM or dduffy@datasim.nl are both fine.

start at the beginning.

KKOP has the major ODEs/PDEs you need.

And BEST book ever for folk like your good self is KKOP .. get it ASAP https://www.amazon.co.uk/Introduction-Analysis-Ostberg-Perkins-Kreider/dp/B0062EK4TK That's all your need. You gotta know a bit of finance as well. It is for (aspiring) quants. And program up the stuff .. staring at...

This book is too theoretical and long-winded for the current context. In a more math degree it would be OK but it too has prerequisites. No free lunch. My objective was to have my book as self-contained as possible!! Good practical books...

The discussion here might be useful. https://quantnet.com/threads/valid-sudoku-leetcode.51293/

Another focused project is Python<->C++ interop. Not many people know this IMO.

how will this strategy be value -- zero or what value, and why? Can you explain, please https://onlinelibrary.wiley.com/doi/epdf/10.1002/wilm.10647

Another 2 projects https://www.datasim.nl/blogs/26/msc-theses-on-machine-learning-and-computational-finance-2019

3rd choice; get same results as in this excellent thesis

2nd possibility: implement code based on my book https://www.wiley.com/en-gb/Numerical+Methods+in+Computational+Finance%3A+A+Partial+Differential+Equation+%28PDE+FDM%29+Approach-p-9781119719670

Here is a possible project "Reproduce and/or improve the results in this thesis by doing it in C++20 (+ Python pybind11)" V1: standard Heston V2: rough Heston https://www.datasim.nl/blogs/29/msc-theses-on-machine-learning-and-computational-finance-2020

Not much has changed in the grey matter of software since the 60s...

Doing/knowing algorithms is important. Why not start with 1) understanding and b) applying industry standard STL algorithms. Use them on a need-be basis. Writing your own b-tree ADT is nice but very 90s. Leave it to C++ and other experts, just like we don't (usually) write our own matrix...

Because Java and Python are much easire than C++. Does Leetcode Inc. have the necessary C++ skills?

In the old days there were no sites, so you had to do it yourself. We are in a new phase of software ... the copy and paste generation. I have heard this criticism from at least 6 experienced project leaders /architects in the last months. It's a big problem. I give my first face-to-face...

That's a nice one; fixed array + embedded set. Even std::set is good I reckon.

Or my book, chapters 11 + 12 https://www.amazon.com/Financial-Instrument-Pricing-Using-Finance/dp/0470971193/ref=cm_cr_arp_d_pl_foot_top?ie=UTF8 Right now it looks like my vectorized python approach is actually faster than my C++ implementation, which surprises me (maybe it shouldn't?). Can...

Even better: buy Luigi Ballabio's book https://www.implementingquantlib.com/2015/03/chapter-7-part-3-of-6-binomial-trees.html and install Quantlib C++ library. Piece of cake.

Don't read London.

Profile your applicaton. Run in Release mode. // Python faster than C++? No way.

Analogy The Ariane 5 reused the code from the inertial reference platform from the Ariane 4, but the early part of the Ariane 5's flight path differed from the Ariane 4 in having higher horizontal velocity values. This caused an internal value BH (Horizontal Bias) calculated in the alignment...

I don't see why you need those 3 vectors row, col, box. They are just views of board. And where are they initialised? maybe std::array better than std::vector here? // the original Java HashSet is so wrong. And "char"....

The specification is ambiguous 1. Is Example 1 an example of a valid board?'OK, yes it is. 2. "Each row must contain the digits 1-9 without repetition." is ambiguous "Each row must contain non-repeating subset digits 1-9 without repetition. Blanks are alowed." 3. It is a compile-time matrix...

What problems are you trying to solve? Scary code and it is JAVA!!!! The term cargo cult programmer may apply when anyone inexperienced with the problem at hand copies some program code from one place to another with little understanding of how it works or whether it is required...

Fair enough. C++ then. I was on a stream of consciousness roll ... the genius school kid. (Doing ODE is a bunch of tricks (called methods in maths), C++ is skill). \

What about Kim Ung-Yong?

Python has its place. If you are doing data science, you can't avoid it. But if your goal is to become a computer scientist or a software developer, it's to be avoided. It can only teach you bad habits and make developing sophisticated software way more difficult than it needs to be. This is...

Ouch. Any concrete examples? Clever kids start their own companies. e.g. https://www.linkedin.com/in/greg-tarr/

From C# to C++ is the wrong direction. Haskell???

I don't think any schools do up to C++20. And if they do, then well done. And few even go to C++11.

I cannot disagree with that, but it's not even wrong. Being bright and having free time is neither necessary nor sufficient to be a "good" programmer. I'm talking writing real code, not copy-and-paste from StackExchange or using Python APIs. It takes anything between 5 and 10 years to become a...

The best course (based on C++ industrial experience since 1992) are the Quantnet C++ courses. In general, HANDS-ON programming as a skill to be treasured is not on the critical path of CS educatiion. Horses for courses. Just saying. Last but not least, QN's TAs provide round-the-clock support...

why += (more appropriate for numeric types) instead of append() ++i is better than i++

I would learn C++ and after that you will be in a position to embark on useful projects. https://quantnet.com/cpp/

yes, because everything will be transacted in rubles?

There is no language that does everything. IBM tried it with PL/I 50 years ago. I learned PL/C at uni. https://en.wikipedia.org/wiki/PL/I PL/I = a*Fortran + b*COBOL, a + b = 100%. The perfect programming language goes to 11

"you cannot do that in safe rust" every freaking time from Rust expert, " Rust treats you like a child/criminal. C++ == grown-up adult.

quiz # = +++

math kids could teach themselves cs better than cs kids could teach themselves math. Because CS is a subset of Maths, although CS profs will disagree. But the best programmers I have experienced in the last 50 years (i.e. who can build complete systems) are not necessarily maths, CS...

Just thinking about succesful languages ... many of them are based on C syntax style. Even Java has it. Rust seems to have gone its own way ... so developers have to change gears in learning new syntax.

Prego, I can only say what technical projects might be interesting, e.g. PDE, Monte Carlo, ML I have have some recent theses www.datasim.nl For maths, my recent book is useful...

I would go for Sapienza for maths. Maths in Italy is strong. And learn C++ ASAP, really. Crepi il lupo. // Ho studiato analisi numerica a Pavia alcuni anni fa.

The Beatles also wrote in C, Bach in C# major Be honest: who writes music in Rust? You see, no one.

And we can add C++/CLI. BTW What about Ada (a well-kept secret?) https://www.adacore.com/company/our-customers https://en.wikipedia.org/wiki/Ada_(programming_language) Because of Ada's safety-critical support features, it is now used not only for military applications, but also in commercial...

Hugely embarassing and counter-productive for AI as a technology. I hate all those buzzwords. You would expect thsese "emiinent" computer scientists to behave better.

What would it take for artificial intelligence to make real progress? https://nautil.us/deep-learning-is-hitting-a-wall-14467/ Geoffrey Hinton, “Godfather” of deep learning, and one of the most celebrated scientists of our time, told a leading AI conference in Toronto in 2016. “If you work as...

People are very clannish. I like all languages that begin with a C.

A random guess is that C++ is a good candidate for Blockchain work.

In 100 years time we will be saying "Starship Holodeck: C++ inside". Fortran is not a good analogy (it's mostly in academia and besides it's hiding in numpy and scipy). Cobol was born 1959 and still in use. Probably 90% of all business software runs on Cobol. No kidding. For the record, 100...

These days C++ has support for parallel processing and multithreading. Also, PPL has ready-to-use parallel design patterns. https://en.wikipedia.org/wiki/Parallel_Patterns_Library...

It would be for kiddy stuff in C++. My biggest disappointment was someome telling me that I should learn Rust. I said NO and he got angry :ninja::ninja: At least he didn't mention GO. People can get up tight about languages. Funny old world.

C++11 https://en.wikipedia.org/wiki/C%2B%2B11 Not C++11 == (C++20 + C++17 + C++14) - C++11

https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2021/p2186r2.html This status-quo hasn’t changed in 12 years. The maintenance burden on the Standard is near minimal, and we hope the Committee spends almost no time agreeing to remove this unused and unimplemented feature, despite its origins...

https://www.engadget.com/google-fires-ai-researcher-over-paper-challenge-132640478.html The company hasn't detailed why it fired Chatterjee, but told the Times he'd been "terminated with cause." It also maintained that the original paper had been "thoroughly vetted" and peer-reviewed, and that...

My ODE/PDE is recommended by UCB MFE preparation. For undegrad, no feedback but it would not be a bad idea (I am a bit biased :))

An observation on PDE/SDE books and courses is that the focus is centred around the mathematical foundations (nothing wrong with that). However, these paper models are only a 1/3 of the story because we need numerical solutions which we then implement in C++. It is a kind of anti-pattern...

Just out of curiosity, could you program Black and Scholes PDE using Crank Nicolson (plain and American call/put) using C++? How long would it take you?

Fair enough. FYi I have heard many unis don't teach PDE at BS level. BTW can you "program" PDEs in FDM? I have not seen any course that does Black Scholes PDE A-Z. I do it all as well as FDM and C++ for PDE/FDM...

It all sounds a bit fuzzy Are you employed to develop software for research? Are you spending more time developing software than conducting research? Are you employed as a postdoctoral researcher, even though you predominantly work on software development? Are you the person who does computers...

These are hardly trivial. My ODE/PDE is on the UCB site. https://www.datasim.nl/application/files/9015/4809/1157/DL_Ordinary_and_Partial_Differential_Equations.pdf

Do RSE folk do C++?

I did a critique of software for COVID-19 that falls into the bespoke category. Very depressing https://onlinelibrary.wiley.com/doi/epdf/10.1002/wilm.10890

What kind of "trivial stuff"?

My 2 cents Titles and badges mean nothing. Can you program real applications?

I am the originatior of 2). For MFE students. Parts A,B,F and G and doing exercises are good for Certificate. I personally coach students and this is the only course that also does ODE/PDE for fiinance. I even wrote a book as support (which students receive :)) It is a hands-on course...

Measure Theory topics discussed here. https://www.datasim.nl/application/files/1315/5947/7165/DL_Pure_Mathematics_Foundations.pdf MT is a bridge too far without proper mathenatical backgound and training.

Nice.

And who knows, in a few years the world will have changed into one big blockchain..

You asked about what next 1. More techniques and tricks, always possible. 2. Group theory and geometry https://ekhukhro.files.wordpress.com/2017/07/group-theory-17.pdf I did 2 at 16 .. for you it would be a good "sabbatical". You learn new mathematical ideas.

Flattery will get you nowhere with me. :thumbsup: I like your sense of humour.

Robert Boyle! Take care of your punctuation.

Wow, a man for all seasons.

What about a career in Greek (Ancient, of course) and Politics?

But I met the scholars.

Yes. It's people I don't understand. You are quite precocious for a 16-year old. Are you at a public school.

You're too young. What do you do for fun?

C++, then.

Are you really only 16? BTW your questions are chaotic.

16 (school kid) and you know about PDE and Paul Wilmott? 🙂 for PDE this book is most up to date https://www.wiley.com/en-gb/Numerical+Methods+in+Computational+Finance%3A+A+Partial+Differential+Equation+%28PDE+FDM%29+Approach-p-9781119719670

If I were a student this course would be a priority. I'm a bit biased.

Absolutely! I've originated this course exactly for you :-) best on planet + great TA support. https://quantnet.com/cpp/ @APalley

Can you program in C++, Python ..

Something that is not widely known .. There is a third way between searching for an explicit solution (a big favourite!) and a numerical solution In mathematics, the qualitative theory of differential equations studies the behavior of differential equations by means other than finding their...

what was the other half? ODE?

My alma mater has PDE I and II, watered-down compared to my day https://www.maths.tcd.ie/undergraduate/modules1617/MA342T.php And much less than my online ODE/PDE https://www.datasim.nl/onlinecourses/97/distance-learning-ordinary-and-partial-differential-equations What is PDE without FDM...

Where will the rocket scientists come from??? Early 20th century things started going wrong Mathematical Physics experienced a schism into Mathematics and Physics ... beginning of the end. The mathematicians fell in love with symbols and the physicists lost touch with reality. Grosso modo.

remark: every uni should have PDE courses. It's kind of fundamental. Without PDEs where would we be? https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations

My own background has been heavily influenced by pure maths, numerical analysis and PDE research and industrial work since 1973. In those glory days of oii and gas, semiconductors and engineering using FEM and FDM had lots of jobs, but you needed Fortran on mainframes. My PhD was on PDEs which...

3. can be learned in an afternoon :) 1 and 2 useful of course! a kind of toolbox.

PDE is kind of specialised, indeed. And in C++. From your list, I think this shortlist .. getting a job is never a guarantee of course. My 2 cents o Scientific Computing with Python (and C++) o Monte Carlo Simulation o Mathematical Computation III: Numerical Methods for PDEs o Numerical...

Some unis request it https://www.datasim.nl/onlinecourses/97/distance-learning-ordinary-and-partial-differential-equations

are almost all pure math courses That's fine, but I would focus now on "applied pure maths" aka numerical maths.

I am not the best person for this but all I can say is you have a fighting chance with the above topics. My new pde is out, might be useful to look at TOC. It's PDE A-Z for finance...

C++ and Python Parabolic PDE Good numerics.

https://appinventiv.com/blog/best-blockchain-programming-languages/ "C++, introduced back in 1985 by Bjarne Stroustrup, is the best programming language for cryptocurrency development. "

Isn't it a tutor's job to help you?(?) Or maybe they want you to research into this short-list?

Overestimating your ability/underestimating complexity, for example in software.

Congrats. Benzema !!!