I'm a pure mathematician, but for calculus I would recommend Apostol's Calculus. It strikes a good balance between applications and theory. Spivak's Calculus is good as well since it has a solutions manual. However, it only covers single variable calculus and has minimal applications.
As a senior math major, I would not recommend apostol to most people. If I were to go back and use my hindsight I would've minored in physics, and put an emphasis on probability theory a bit more. Physics uses applications of pdes odes to get more thorough practice, and probability uses a fair bit of applied calculus at the undergraduate level. Apostol is something I'd recommend to someone to maybe speed through after taking calc 1-3, but as a refresher at a more advanced level. But as a stand alone apostol isn't great for many people their first or second year in undergrad. Stewart is just better at getting the basics across. It's just more accessible to a wider audience. It's like telling someone to read rudin for real analysis. It's like no. That works for some, but most people would be better off reading Bartle and Tao
Nice video. Won't comment on books but when it comes to topics, If you ask me, the most crucial one is Probability. That defines Quantitative Finance. If you can, getting some intro into random processes will be useful too. Next, I'd say the foundations of calculus, techniques to solve ODEs, and understanding of PDEs (don't really have to solve them though but you should be comfortable with differentiation and evaluation expressions / proving equations/changing their form etc.) Personally, I consider Stochastic calculus as just an extension of probability applied to random processes. Linear Algebra foundation and some basics like matrix / vector-related differentiation. This will even help in machine learning math and courses like optimization. Also, when it comes to building a good base in probability, you should also solve probability-related questions. Lots of resources online and those will be fun too. These problems will help you in improving your foundation.
at my university i take linear algebra but more in the theoretical sense, guided by hoffman's book, which is similar to sheldon axler's linear algebra book, which focuses on proving. I reviewed gilbert strang's text and it is different from the linear algebra I know, strang's book is more like "applied" linear algebra.
I would say a course in PDEs is a complete waste of time. Spend that time studying real analysis/measure theory if you want a deep dive into math. Or make sure to know statistics at advanced undergrad level (linear regression, multivariate stats).
@@julianbeatty2909 I think that too. It is extremely important and has deep connections with advanced statistics and machine learning algorithms. Furthermore, a two semesters course in Num Analysis would provide you with all you need to know about solving PDEs arising in QF (finite difference). Pure math bachelor's degree here.
Hi Dmitri, I would like to ask your take on, how important is learning/exploring numerics. I saw that there are some cool quant devs working on the buy side, that seem to focus on parallel programming, monte carlo, and it got me interested, since I have a software background, and thought its skill/direction worth developing.
hey i am doing comp science and specializing in data science ,can i break into these masters program after doing my undergrad?and i really am hoping to get in uc berkley or michigan or princeton
What do you think about “Linesr algebra done right” by Adler? I’m half way through it, and it give me an whole other view of what exactly is linear algebra.
Hi Dimitri, I have an undergrad degree in Finance and I want to get Quant Master's degree. My math skills are not on the level and I am considering taking a gap year to learn all the courses you listed here. The pinch here is that I am 25, and by the time I graduate I will be 28. Do you think it would be too late for me to start quant career at this age?
be honest with yourself, and think about whether or not you can afford the break and whether or not u will get ROI for completing the Quant master or phd. spend the next few months taking calculus until vector calculus, if it isn't too hard, consider applying to Quant masters. else, it may not be the best use of your time
Whats the best practical problem solving, critical thinking CALCULUS MATH TEXTBOOKS CALCULUS 3RD OR 5TH EDITION, STEWART CALCULUS CONCEPT 3RD EDITION, STEWART THOMAS CALCULUS 12 EDITION CALCULUS 9TH EDITION, LARSON Thank you
I do not. I set up a general set of rules for diversification and then just follow that. I have too many other priorities like my day job, family, this channel, and a long list of hobbies.
Is it a must to take a c++ course because in my university it’s restricted to IT&SE majors ? Instead of that can i take an online C++ approved course by said university?
As a soon-to-be freshman, I am trying to do two bachelor degrees simultaneously, one is a BSc in Computer Science and the other might be an integrated Masters degree in Economics. Do you think it's REASONABLY doable (should I put in the work) to get a job in quant finance right after my masters (the first program may be 3, hopefully a 4 yr honours course, while the second is a 5 year degree in total).
Meh. You need more mathematics. I don't think the masters degree in economics is going to help that much at all. Probably better with bachelors in math, minor in comp science. Then go into some quant finance program.
Can I ask please. My major is Banking and Audit. I had some courses related to Math: higher mathematics 1. higher mathematics 2, Statistics, Econometrics (two semeters). Are they enough? Also if you have certificates of the other universities courses in Math, can they help me to meet this requirement of the provided list of Math courses?
Universities will require you have taken their pre-requisites at another university and be specific courses. For example, if econometrics covers some of the topics of ODE, most schools won't accept that if you haven't taken a course called, ODE.
Hi Dmitri. I'm a high school student with limited math knowledge (I've completed up to Algebra 2). Do you have any resources or advice for me to learn math/cs that will help me get this kind of job in the future?
You are very very early in your career. Focus on optimizing your high school to college pipeline. Try to take precalculus next year, then AP calculus BC in 11th grade. 12th grade, save up some money to take linear algebra/calc 3 at community college. Look into taking AP/IB computer science as well.
you can learn everything else later, so don't skip out on calculus try to get to vector calculus as soon as you can, so that you can start college with the fun stuff 😊
So I am still an undergrad and in my finals currently doing industrial and production engineering I am interested in quant trading. I have done some of the courses listed above but I didn't have an A in most of them ( was messed up but not an excuse). So my thoughts have been on taking a master's degree in math or a statistics-related course or a CQF before applying for an MFE. I would love anyone's advice, thanks.
You don't necessarily need A's. GPA only plays part of the requirements for program admissions. I would apply to a dream school and a few middle tier programs.
Real analysis/measure theory is extremely helpful IMO. Definitely much more useful than, say PDEs. Do not spend time taking a course in PDEs, it will not help you (not even indirectly) in anything Quant finance related. You will never be asked to know how to solve a parabolic PDE (i.e. Black&Scholes).
@@DimitriBianco I'm not sure how many schools actually offer a proper undergrad level class on measure theory. I suspect its more commonly for graduate students
Gil Strang also has a follow up book and course with Linear Algebra applications to Machine Learning if that interests anyone. I don't remember what it's called but I'm sure it would be easy to Google
Hi Dimitri, what parts of programming are relevant for the master's and eventually quant job? I ask this because I understand I shouldn't get into web python with python, that's obvious. I have programmed simplex and gradient descent before and accesed databases with python. Is this the type of programming you are talking about? if so, what libraries and learning exercices do you recommend to practice?
I'm a pure mathematician, but for calculus I would recommend Apostol's Calculus. It strikes a good balance between applications and theory. Spivak's Calculus is good as well since it has a solutions manual. However, it only covers single variable calculus and has minimal applications.
Those are good books, but only as the second year in calculus.
As a senior math major, I would not recommend apostol to most people.
If I were to go back and use my hindsight I would've minored in physics, and put an emphasis on probability theory a bit more.
Physics uses applications of pdes odes to get more thorough practice, and probability uses a fair bit of applied calculus at the undergraduate level.
Apostol is something I'd recommend to someone to maybe speed through after taking calc 1-3, but as a refresher at a more advanced level. But as a stand alone apostol isn't great for many people their first or second year in undergrad. Stewart is just better at getting the basics across. It's just more accessible to a wider audience.
It's like telling someone to read rudin for real analysis. It's like no. That works for some, but most people would be better off reading Bartle and Tao
Great video. I wish I knew all this before coming to college, but this is great for future aspiring Quants.
Nice video. Won't comment on books but when it comes to topics, If you ask me, the most crucial one is Probability. That defines Quantitative Finance. If you can, getting some intro into random processes will be useful too.
Next, I'd say the foundations of calculus, techniques to solve ODEs, and understanding of PDEs (don't really have to solve them though but you should be comfortable with differentiation and evaluation expressions / proving equations/changing their form etc.)
Personally, I consider Stochastic calculus as just an extension of probability applied to random processes.
Linear Algebra foundation and some basics like matrix / vector-related differentiation. This will even help in machine learning math and courses like optimization.
Also, when it comes to building a good base in probability, you should also solve probability-related questions. Lots of resources online and those will be fun too. These problems will help you in improving your foundation.
Introduction to mathematical statistics by Hogg is a solid one.
I think that you are describing books for an applied math or math major. Real analysis is one of the hardest courses in math.
Yep...all those math courses are in the applied math pathway at my college. PDE is not required for pure math or stats where I go.
Advanced Calculus is not calc 3, its more of a taste or Real Analysis
at my university i take linear algebra but more in the theoretical sense, guided by hoffman's book, which is similar to sheldon axler's linear algebra book, which focuses on proving. I reviewed gilbert strang's text and it is different from the linear algebra I know, strang's book is more like "applied" linear algebra.
I would say a course in PDEs is a complete waste of time. Spend that time studying real analysis/measure theory if you want a deep dive into math. Or make sure to know statistics at advanced undergrad level (linear regression, multivariate stats).
I think he should have included a numerical analysis course.
@@julianbeatty2909
I think that too. It is extremely important and has deep connections with advanced statistics and machine learning algorithms. Furthermore, a two semesters course in Num Analysis would provide you with all you need to know about solving PDEs arising in QF (finite difference).
Pure math bachelor's degree here.
Thanks for the video. Is there a material you recommend to learn C++ for quantitative finance specifically?
Not specifically for C++. Learn the boost library though as it is helpful for quant finance. For online I like @thenewboston youtube channel.
I don't care how heavy it is, I will never get rid of my James Stewart calculus book.
It's a real pleasure to read. I wish I would of had this book sooner.
I’ve taken all these math classes during my bachelors
Want a cookie?
@@mr.erikchun5863 no
Statistics major?
@@maxxpro4 math with economics and quant finance
Hi Dmitri, I would like to ask your take on, how important is learning/exploring numerics. I saw that there are some cool quant devs working on the buy side, that seem to focus on parallel programming, monte carlo, and it got me interested, since I have a software background, and thought its skill/direction worth developing.
Two semesters of calculus meanwhile a masters of economics wants up to real analysis….
C++?
This is clearly targeting CS students.
hey i am doing comp science and specializing in data science ,can i break into these masters program after doing my undergrad?and i really am hoping to get in uc berkley or michigan or princeton
Thoughts on Analysis I (Calculus by Spivak)
GREAT VIDEO..I GOT ONE QUESTION HOW DO YOU TAKE NOTES DIGITALY OR traditionally..
Pencil and paper is how I do all my notes. Even for work projects I use pencil and paper.
What do you think about “Linesr algebra done right” by Adler? I’m half way through it, and it give me an whole other view of what exactly is linear algebra.
It’s one of the best
Would you recommend the math/stat that is used in high frequency trading?
Hi Dimitri, I have an undergrad degree in Finance and I want to get Quant Master's degree. My math skills are not on the level and I am considering taking a gap year to learn all the courses you listed here. The pinch here is that I am 25, and by the time I graduate I will be 28. Do you think it would be too late for me to start quant career at this age?
For quant finance a masters is required and a PHD is preferred. Most people would be entering the job market a bit older than other careers.
be honest with yourself, and think about whether or not you can afford the break and whether or not u will get ROI for completing the Quant master or phd. spend the next few months taking calculus until vector calculus, if it isn't too hard, consider applying to Quant masters. else, it may not be the best use of your time
Whats the best practical problem solving, critical thinking CALCULUS MATH TEXTBOOKS
CALCULUS 3RD OR 5TH EDITION, STEWART
CALCULUS CONCEPT 3RD EDITION, STEWART
THOMAS CALCULUS 12 EDITION
CALCULUS 9TH EDITION, LARSON
Thank you
Hi Dimitri, just curious, do you do portfolio analysis on your own personal portfolio?
I do not. I set up a general set of rules for diversification and then just follow that. I have too many other priorities like my day job, family, this channel, and a long list of hobbies.
@@DimitriBianco thanks for the reply and video!
Is it a must to take a c++ course because in my university it’s restricted to IT&SE majors ? Instead of that can i take an online C++ approved course by said university?
You have to check the masters programs to see if it is required. You can always take a python class as many programs want that.
As a soon-to-be freshman, I am trying to do two bachelor degrees simultaneously, one is a BSc in Computer Science and the other might be an integrated Masters degree in Economics. Do you think it's REASONABLY doable (should I put in the work) to get a job in quant finance right after my masters (the first program may be 3, hopefully a 4 yr honours course, while the second is a 5 year degree in total).
Nope, these degrees just don't make up for your quant journey mate ...
Meh. You need more mathematics. I don't think the masters degree in economics is going to help that much at all. Probably better with bachelors in math, minor in comp science. Then go into some quant finance program.
Can I ask please. My major is Banking and Audit. I had some courses related to Math: higher mathematics 1. higher mathematics 2, Statistics, Econometrics (two semeters). Are they enough? Also if you have certificates of the other universities courses in Math, can they help me to meet this requirement of the provided list of Math courses?
Universities will require you have taken their pre-requisites at another university and be specific courses. For example, if econometrics covers some of the topics of ODE, most schools won't accept that if you haven't taken a course called, ODE.
Hi Dmitri. I'm a high school student with limited math knowledge (I've completed up to Algebra 2). Do you have any resources or advice for me to learn math/cs that will help me get this kind of job in the future?
You are very very early in your career. Focus on optimizing your high school to college pipeline. Try to take precalculus next year, then AP calculus BC in 11th grade. 12th grade, save up some money to take linear algebra/calc 3 at community college. Look into taking AP/IB computer science as well.
you can learn everything else later, so don't skip out on calculus
try to get to vector calculus as soon as you can, so that you can start college with the fun stuff 😊
Also take physics c if possible
Thoughts on SAS? Basically all I use lol
I'm a big fan of SAS for statistical modeling. It was my primary language for 8v years.
So I am still an undergrad and in my finals currently doing industrial and production engineering I am interested in quant trading. I have done some of the courses listed above but I didn't have an A in most of them ( was messed up but not an excuse). So my thoughts have been on taking a master's degree in math or a statistics-related course or a CQF before applying for an MFE. I would love anyone's advice, thanks.
You don't necessarily need A's. GPA only plays part of the requirements for program admissions. I would apply to a dream school and a few middle tier programs.
@@DimitriBianco Oh ok sir thanks so much for the reply. I would love to see you speak on the Cqf program. Appreciate the response
surely you would need courses such as measure theory as well?
Some schools include this in the probability course but an extra class on it would be helpful.
@@DimitriBianco would discrete maths be of any use since it ties into computer science? (for quant stuff in general, not necessarily for masters)
Real analysis/measure theory is extremely helpful IMO.
Definitely much more useful than, say PDEs. Do not spend time taking a course in PDEs, it will not help you (not even indirectly) in anything Quant finance related. You will never be asked to know how to solve a parabolic PDE (i.e. Black&Scholes).
@@user-gr8fc3de9w discrete math is a must for everyone related to the computer science
@@DimitriBianco I'm not sure how many schools actually offer a proper undergrad level class on measure theory. I suspect its more commonly for graduate students
which bachelors we should do for quant finance
Math
Are you quant trader and running your own company ?
No, I'm a quant on the sell side.
@@DimitriBianco what is that ? What's the difference with quant trader ?
Gil Strang also has a follow up book and course with Linear Algebra applications to Machine Learning if that interests anyone. I don't remember what it's called but I'm sure it would be easy to Google
I took calc iii in highschool
The soda pop opening is so cringe and disgusting, silly ameriburger thinking crappy consumption is a personality trait.
Hi Dimitri, what parts of programming are relevant for the master's and eventually quant job? I ask this because I understand I shouldn't get into web python with python, that's obvious. I have programmed simplex and gradient descent before and accesed databases with python. Is this the type of programming you are talking about? if so, what libraries and learning exercices do you recommend to practice?
Pandas numpy matlib/matplot are just a few off the top of my head that are relative towards modeling
Hey Dmitri, I appreciate your Honesty.
In description you clearly mentioned that the links are affiliated and it would cost us more.
It actually does not cost you any extra. Amazon actually gives me a portion of their profit.
@@DimitriBianco Ohh, I just forgot to read the *NO* written in description 😂