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So you want to study mathematics

susanrigetti.com

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Re: So you want to study mathematics

#11

Post by musgravepeter »

dwohnitmok wrote: post #9
Mimmy wrote: post #6

Going from Strang to D&F seems like a steep jump. The former is an applied textbook for non-mathematicians and the latter is a proof-based text for advanced undergraduate / graduate-level math students. I would suggest working through a proof-based linear algebra book in between to ease the transition. Axler's is a good one. Alternatives include Hoffman and Kunze and the more modern Friedberg, Insel, and Spence.

Second Axler. "Linear Algebra Done Right" is probably the pure mathematics textbook I've most enjoyed reading ever (but be warned you will learn very little about applied methods from it if that's what you care about). Also enjoyed Artin's Algebra.

+1 for Artin's Algebra. I think is very under appreciated.

Re: So you want to study mathematics

#12

Post by voldacar »

musgravepeter wrote: post #2

I've been on a Math journey since I retired a couple of years ago and I agree with all the books mentioned that I know and look forward to picking up some of the one I do not know. I agree baby Rudin is essential, but I find it tough going. Some books I liked for self study because they have answers: Introduction to Analysis, Mattock. Elementary Differential Geometry, Pressley. There is also recently Needham's Visual…

Those are good, I also really like Visual Complex Analysis

Re: So you want to study mathematics

#13

Post by mbustamanter »

> My goal here is to provide a roadmap for anyone interested in understanding mathematics at an advanced level. Anyone that follows and completes this curriculum will walk away with the knowledge equivalent to an undergraduate degree in mathematics.

NO, NO, NO.

There is no real way to go up to the real deal without having understood elementary Functional Analysis, which the article doesn't even mention. FA is roughly what Linear Algebra would look like if instead of finite dimensional vector spaces we considered infinite dimensional vector spaces. It opens the rigorous path to non-linear optimization, analysis of pdes, numerical analysis, control theory, an so on. What this article mentions is a way to work around things, but nowhere near an undergraduate degree in mathematics.

I'm astonished that the PDE section has such books, they look like the calculus aspect of partial differential equations. A more appropriate book would be L. C. Evans' Partial Differential Equations. Same with ODEs, no mention of Barreira's or Coddington & Levinson's books.

Re: So you want to study mathematics

#14

Post by Py-o7 »

Mimmy wrote: post #6

Going from Strang to D&F seems like a steep jump. The former is an applied textbook for non-mathematicians and the latter is a proof-based text for advanced undergraduate / graduate-level math students. I would suggest working through a proof-based linear algebra book in between to ease the transition. Axler's is a good one. Alternatives include Hoffman and Kunze and the more modern Friedberg, Insel, and Spence.

For many years MIT students would go from Strang in year 1 to Artin in year 2. Artin != D&F of course though many would say it does less hand holding than D&F

Re: So you want to study mathematics

#15

Post by susanrigetti »

Mimmy wrote: post #6

Going from Strang to D&F seems like a steep jump. The former is an applied textbook for non-mathematicians and the latter is a proof-based text for advanced undergraduate / graduate-level math students. I would suggest working through a proof-based linear algebra book in between to ease the transition. Axler's is a good one. Alternatives include Hoffman and Kunze and the more modern Friedberg, Insel, and Spence.

Gross's review of linear algebra from his MIT algebra course bridges the gap: http://wayback.archive-it.org/3671/20150528171650/https://ww.... A combination of that and then chapter 11 in D&F should cover whatever readers didn't get from Strang.

That being said, Axler is an excellent book. I don't know if I would replace Strang with it, but I should add it as a supplement to the next edition of this guide!

Re: So you want to study mathematics

#16

Post by ghufran_syed »

I went from only having done high school math 10 years ago to completing an MS in math and statistics at my local state university while working in an unrelated field. I would recommend NOT starting with calculus if you haven’t done it, instead, just learn how to do proofs - I used Chartrand “Mathematical proofs” - You don’t need to know any math beyond algebra in order to do that most of this book. If you need to revise or learn Algebra, then I would do Stroud “engineering math” first which is designed for self-learners with lots of solutions and feedback.

At some point, it would be good to get a a copy of Lyx and start to learn to write math in LaTeX - Then you can get feedback on your proofs online at math.stackexchange.com if you don’t know any math people locally.

Feel free to get in touch with me if you want to discuss further, happy to help!

Re: So you want to study mathematics

#17

Post by Py-o7 »

This felt like it was written by a physicist or engineer.

Too much emphasis on differential equations and not enough on things like topology, functional analysis and/or non-introductory parts of algebra like say representation theory.

Re: So you want to study mathematics

#18

Post by cgriswald »

dwohnitmok wrote: post #9
Mimmy wrote: post #6

Going from Strang to D&F seems like a steep jump. The former is an applied textbook for non-mathematicians and the latter is a proof-based text for advanced undergraduate / graduate-level math students. I would suggest working through a proof-based linear algebra book in between to ease the transition. Axler's is a good one. Alternatives include Hoffman and Kunze and the more modern Friedberg, Insel, and Spence.

Second Axler. "Linear Algebra Done Right" is probably the pure mathematics textbook I've most enjoyed reading ever (but be warned you will learn very little about applied methods from it if that's what you care about). Also enjoyed Artin's Algebra.

My university course in linear algebra taught me how to manipulate matrices. It was super uninteresting, and easy. I aced every test, but got a B in the course, because the professor assigned an asinine amount of homework (that I either aced or didn't do), perhaps holding the article author's view that:

> solving problems is the only way to understand mathematics. There's no way around it.

...without also understanding that doing problems is not a substitute for understanding.

(I'm still salty about that course. I've been doing linear algebra based puzzles nearly every day of my life and this professor somehow made the topic a boring chore.)

I complained about this to a friend who had also taken the course and he turned me on to Axler. I read through the first chapter, nodding along as I went. I got to the problem questions and couldn't believe what Axler was asking was even related to the material I had read through. I really struggled at first to understand. Axler was heavily juxtaposed to my previous experience. However, when I did understand, I didn't just understand, I grokked.

It was just such an awesome experience, and I credit that book in particular with breaking me out of a mathematics plateau and with liberating my mathematics education from a strict reliance on academia. The text is almost magical.

Re: So you want to study mathematics

#19

Post by parsd »

If you're interested in both mathematics and physics, does it make sense to learn both concurrently? If yes, what areas complement each other? Or is there no overlap to warrant concurrent study of the essentials? By essentials I mean what a college student must know, or really anyone who pursues self-education without a background in these areas. Beautiful website, by the way!

Re: So you want to study mathematics

#20

Post by susanrigetti »

parsd wrote: post #19

If you're interested in both mathematics and physics, does it make sense to learn both concurrently? If yes, what areas complement each other? Or is there no overlap to warrant concurrent study of the essentials? By essentials I mean what a college student must know, or really anyone who pursues self-education without a background in these areas. Beautiful website, by the way!

Check out my physics guide: https://www.susanrigetti.com/physics. It has both the physics core curriculum AND the math essentials you need to know in order to understand the physics essentials. (And thank you!)
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