Hello, I'd like to start learning about Dynamical Systems but I'm not sure where to start. Any book recommendations would be helpful!

Have looked on amazon but it seems all options (at least the top listings) don’t have good explanations and/or have a lot of mistakes.

Any suggestions will be appreciated.

I know I am probably getting in way over my head and that this subject can be extremely challenging and boring at times, but I am seeking guidance on it. A book like this probably isn’t super common, so help is appreciated.

Hi everyone,

I’m pursuing a Master’s degree in Mathematics and coming from a physics background (undergrad in Italy). I’m now looking to dive deeper into measure theory, which I’ll need for future studies in analysis and probability. My professor has recommended a few textbooks for the course, but I won’t be able to attend the lectures regularly, so I need a resource that’s well-suited for self-study.

Here are the books my professor suggested:

•	L. Ambrosio, G. Da Prato, A. Mennucci: Introduction to Measure Theory and Integration
•	V.I. Bogachev: Measure Theory, Volume 1 (Springer-Verlag)
•	L.C. Evans, R.F. Gariepy: Measure Theory and Fine Properties of Functions (Revised Edition, Textbooks in Mathematics)
•	P.R. Halmos: Measure Theory
•	E.M. Stein, R. Shakarchi: Real Analysis: Measure Theory, Integration, and Hilbert Spaces (Princeton Lectures in Analysis 3)

Since I’ll be studying on my own, I’m wondering which of these books is the best fit for self-learners, particularly with a physics background. I’m looking for something rigorous enough to deepen my understanding but also approachable without a lecturer guiding me.

Would love to hear your thoughts, especially if you’ve worked through any of these texts! Thanks!

For instance,

Lee's topological manifolds

Carothers Real Analysis

and Jones's measure theory

all have exercises integrated into the text, such that you do a bit of reading (maybe a page) and then there are exercises interspersed in the text. What are some other books that have this?

A textbook I've not personally read but highly commended by one of the professors at my university. Suitable for the advanced undergraduate or beginning graduate student in algebraic geometry. Near-perfect condition

Nicely written book that does not require commutative algebra as a prerequisite. For the moment it is available from the personal page of Dustin Ross, but the autors are looking for a publisher. Comparing to the books by Reid or by Smith and company this one is a truly introduction.

I intend to write my graduation thesis on Predicate Logic, which is part of the requirements for obtaining a Bachelor’s degree in Mathematics, specifically in predicate logic because I am very interested in this field. However, the extent of my knowledge is currently insufficient to write a solid thesis, so I need intermediate and advanced books to study more deeply, especially concerning the meaning of predicates and the relationship between the predicate and the subject. I understand this concept intuitively, but no specific definition of this predicative relationship comes to mind except that it is a function that maps variables to a set of true and false. Nevertheless, I wonder how this function can be defined precisely. I am also particularly interested in studying the algebra of predicate logic. The courses I have taken in logic are:

1. Logic and Set Theory I in college.
2. Logic and Set Theory II in college.
3. I am well-versed in the ZFC model.
4. I have knowledge of Aristotelian logic and have read several books on this topic.

Having trouble finding a decent curriculum/text book for geometry for a very advanced 8 year old. Books are either incredibly dense or absurdly juvenile (my son complained the most recent book I got him from Amazon was just full of colors and wackiness instead of of just spelling out a rule and giving him examples).

I already have the aops geometry book, this is my baseline I will use with him if I have too, we've already worked our way through their algebra book, but their books are obviously geared towards like an advanced 12 year old and definitely on the upper bounds of what we need. We made it work over the summer when we had a lot of free time but I'd like something a little less aggressively paced/less dense for learning during the school year after he's already spent all day at school.

Ideally I'm looking for a classic 70's-1980's high school text book that simply lays out whatever the lesson/concept is for that section then works through it and has examples and questions.

Again I like AOPS, I know about AOPS, I expect the default advice is just to use those books and I don't disagree with that but I've got a unique situation where my very advanced but very young kid would benefit from a textbook that was maybe geared towards a normal 15 year old, instead of an advanced learner if that makes any sense.

I'm currently searching for a book on differential equations. I've managed to narrow down the initial selection to two books: Differential Equations with Applications and Historical Notes, 2017 by George F. Simmons and Differential Equations and Their Applications: An Introduction to Applied Mathematics, 1993 by Martin Braun.

I'm simply a person looking for a more comprehensive coverage of the subject. If you have any experience with any of the two books, please tell me what you think of it. If you have a different recommendation, please drop it and explain why you think it's a good read. If you're someone with a good background in differential equations but are not familiar with the books and have some free time, you can easily acquire free copies online and review them.

The artofproblemsolving recommendation is their five books for this!

1. Intro to Algebra
2. Intro Counting & Probability
3. Intro Geometry
4. Intermediate Algebra
5. PreCalculus

Looking at their table of contents, many topics are revisited in the book series, you can see too much overlapped. They probably go deeper on the subjects they overlapped but is it really necessary? Seems more time consuming.

I noticed some other stuff like having polynomial addition/subtraction/multiplication in the first book (intro to algebra) and doing polynomial division in the forth book (intermediate algebra).

All those books together are like ~4000 pages (including excercises).

I also posted this in r/math and r/learnmath - don't know if this forum is the right one? :) ... Here goes:

I almost finished reading (and working on exercises) in the book "Elliptic Tales" by Avner Ash and Robert Gross and it was PERFECT for the amount of time, energy and existing knowledge I have to use! :) I really liked remembering my knowledge of complex numbers, groups and modular arithmetic and REALLY liked learning a lot of new stuff!!

In the Preface they write: "A certain amount of mathematical sophistication is needed to read this book. We believe that if you've had and enjoyed a college course in calculus or beyond, and if you are patient, you probably have enough of this elusive quality to enjoy any chapter of the book"(!)

I've started reading and working on their first book "Fearless Symmetry", which is also good, but a bit too basic for me, since I've taken a few college courses in math. And since I just read the Elliptic book, which is somewhat heavier.

CAN YOU PLEASE RECOMMEND ME BOOKS SIMILAR TO "ELLIPTIC TALES" IN "DIFFICULTY"? I need to be able to appreciate it without a teacher, other students, and with around a years worth of college courses of pre-existing (old dusty) knowledge. And while doing a fulltime job and raising a kid :).

Thanks a lot in advance!

I want to get something for my siblings to help them with this course. I found these three books, but I don't know which one would be best. These options are:

-Calculus Made Easy by Silvanus Thompson

-Calculus for the Practical Man by JD Thompson

or

-Essential Calculus Skills Practice Workbook with Full Solutions by Chris McMullen

I need a book on Boolean algebra and lattices. A book with examples and question and well done theory part.

Any book suggested? Thanks.

I am self-learning mathematics nowadays and I was trying to study things from absolute basics and in-depth manner. I have 5 books from which I have option to choose one. I have that much background that I can pick and start anyone but which one would be better to start. If any of can rate the mentioned books separately on basis of in-depth theory and good questions, it would be a great help. If any of you have solved any of these books please have a look at others books too for common topics to rate correctly. These are my books :

Cengage Algebra

Chrystal's Elementary Algebra Part I

Chrystal's Elementary Algebra Part II

Higher Algebra by Hall & Knight

Higher Algebra by Bernard & Child

Very glad to have found the entire collection

For anyone who has read it, how analysis / algebra is assumed?

Is some group theory needed going in? And should point set topology have already been learned?