Really like math. What do I learn after Differential&Integral Calculus?

I assume either Hs or college. So watch 3blue1brown and attend a uni to learn MV and LA. You probably will have to take some high level statistics classes. ie Probability stuff. That’s probably it but Econ classes will most likely be math heavy particularly regarding your next math classes.

lets get mathematical wrote:

Hi guys, I know there are quite a few posters here who have a strong math background. I hope to have one as well one day. I recently got a good grasp of basic calculus. My question is what comes after. Is there a natural progression one follows? Like for example: calc 1-->calc 2---->linear algebra--->multivariable calc---->proofs--->real analysis, or do you go into differential equations after linear algebra? I'm fond of math and have a strong interest in it, but I eventually want to go to graduate school for economics. Appreciate any help

Lots of great suggestions! Like everyone else, I think linear algebra is your best bet. I actually think your progression is really good, and yes, I would slip differential equations in there somewhere before proofs. We can break the classes into two tiers:

Definitely should take: linear algebra, multivariable calc, differential equations, statistics

Can take if you're interested: intro to proofs, real analysis, complex analysis

Get Piaggio's book on differential equations. It's ideally suited for self study.

Do all 801 problems.

(It took Freeman Dyson one month to do this. It took me one year.)

Ever afterwards you will be at home in this branch in mathematics, and some of the more common differential equations will seem like old friends.

If some of the topics seem old-fashioned, go read Isaac Asimov's short story "The Feeling of Power".

Good luck with your studies!

check out some mathematical logic - set theory, infinity, incompleteness, computability, the continuum hypothesis, philosophy of mind, philosophy of mathematics

https://www.amazon.com/Roads-Infinity-Mathematics-Truth-Proof/dp/1568814666

also relativity, cosmology, etc.

https://www.amazon.com/dp/7121189585/ref=dp-kindle-redirect?_encoding=UTF8&btkr=1

Analysis. You will hate it. You have to learn it.

Not sure if it's been mentioned yet, but I would look at learning stats. It doesn't have to be the really deeply theoretical stuff, but stuff like confidence intervals, maximum likelihood estimators, p-values, regression models and how to evaluate how well they fit, etc:

This stuff probably isn't as "thrilling" as some of the advanced pure topics in it's own right, but it is can be fascinating when applied to the real world: epidemiology, financial modelling, etc. It'll also give you a new string to your bow, and the feel for a different type of math.

heyooo wrote:

Thermodynamics of solids. I am not a physics major nor that type of in-depth simulation guy, but I am very interested in thi stopic and it will come up as proof for a lot of the stuff I'm learning. What math background is necessary for this?

Thanks.

Partial differential equations.

I would recommend basic study on number theory, abstract algebra, topology, and real analysis.

Learn to think in different ways.

It is not so much about the practicality for economics. You have a lot of time for that. Clear, logical thinking will pay dividends.

For number theory, try Davenport, The Higher Arithmetic. Can get the PDF for free. This is a classic. It is beautiful for anyone interested in math. No calculus needed -- it is a completely different direction.

Abstract algebra, I used a book by I. N. Herrstein. Topology, there are a number of books, for example one by Munkres. Real analysis, Royden -- not to be confused with Rudin or so-called Baby Rudin.

Specifically for optimization you'll want integer/linear programming

If you don't have an established career, look into becoming an actuary. The exams have some brutal algebra, but are really gratifying to pass. It's a pretty stable and well paying job as well.

What's a simple formula for matrices in linear algebra?

I foolishly sold my book back to the bookstore over thirty years ago and in the meantime forgot how to do them. Some online sites that I looked at had confusing explanations, missing logical steps--a bad habit for a lot of math and science types.

Thermo of solids: Understand thermodynamics and statistical mechanics, to start with. The partial derivative concept is key. Entropy and many other concepts are defined in terms of partial derivatives.

Process optimization: You are right: linear algebra is important. Process optimization involves system identification, which is an estimation problem: estimate of the properties of the process first, so that you can figure out how to optimize it. These properties are typically time-varying in real world. The Kalman filter is a classic response to this challenge. So you need to understand probability and statistics and signal processing.

Options: Stay away unless you have spare money. You and I will not have enough timely information to compete with the pros, nor will we have the ability to react quickly (in seconds) to that information. Google Black-Scholes for the classic mathematical analysis of how to price an option. Black & Scholes won the Nobel in economics for their model. It is insightful and not that complicated.

Sorry to piggyback, but I have a related question as an future engineering student: This question has a lot of recommendations related to Econ Math, but what about Engineering math? Just general math concepts to develop an appreciation and understanding for before starting the real technical stuff. I've taken a look at ODE's and Fourier Transforms on youtube, and plan on looking at some PDE's later on.

Do any engineers/students etc... have some recommendations? I've done basic Stats, Linear Algebra and Diff/Integral Calculus. Thanks

zxcvzcxv wrote:

What's a simple formula for matrices in linear algebra?

I foolishly sold my book back to the bookstore over thirty years ago and in the meantime forgot how to do them. Some online sites that I looked at had confusing explanations, missing logical steps--a bad habit for a lot of math and science types.

Do you mean how to multiply 2 matrices together?

future eng wrote:

Sorry to piggyback, but I have a related question as an future engineering student: This question has a lot of recommendations related to Econ Math, but what about Engineering math? Just general math concepts to develop an appreciation and understanding for before starting the real technical stuff. I've taken a look at ODE's and Fourier Transforms on youtube, and plan on looking at some PDE's later on.

Do any engineers/students etc... have some recommendations? I've done basic Stats, Linear Algebra and Diff/Integral Calculus. Thanks

What kind of engineering?

Electrical Eng

For my EE degree

Math dept

*Multivariable Calculus

*Statistics w/ calc 2

*Matrix Algebra

*Differential Equations

*Vector Calculus

*Discrete Structures

*Complex Variables

Electrical dept with heavy math

*Physics 1

*Physics 2

*Linear Systems

*Electromagnetic Theory

*Linear Systems 2

*Digital Image Processing

*Digital Signal Processing

*Optical Signal Processing

*Advanced Digital Image Processing

Would recommend getting MATLAB, learning about matrix operations. learning Fourier Transforms, and learning how to work with discrete time.

So my question to you and the majority of you Math wizards, how much of your ability is a gift and how much is hard work and persistence. I'm just "okay" at Math, but could never in my lifetime achieve what many of you have. How'd ya get to that level?

Thanks ! Going to try to get comfortable with MATLAB over the summer since I have a good amount of free time