You appear to possess this, so you’re in good shape. The basic concepts of infinitesimal calculus could be learned by reading Keisler’s free book (see my self-study blog post on calculus). I suggest that you go through the annexes first.2) Even though it says "graduate math texts" it is one of the most simple and easy books in the field.1 Geometric algebra is treated quite well in MacDonald’s "Linear and geometric algebra" http://www.amazon.com/Linear-Geometric-Algebra-Alan-Macdonald/dp/1453854932 (Depending on your knowledge of linear algebra, you can skip a lot of this book, only part II is important here).
I believe it’s the best for your first time encounter.1 The book will also cover fascinating concepts such as quaternions and what physicists actually are talking about when they refer to the term "pseudovector" (but likely not knowing that it is a pseudovector). You might want to go through another book later though, since it doesn’t cover everything you need to know.3) It is especially made for somebody interested in differential geometry and it focuses a lot on manifolds.https://www.amazon.com/Introduction-Topological-Manifolds-Graduate-Mathematics/dp/1441979395Feel free to PM me if you want more help.1 If you like the geometrical approach (and let’s face it, who wouldn’t? ) It is possible to take this approach and follow it up by studying MacDonald’s "Vector and Geometric Calculus" that deals with multivariable analysis in an understanding of the geometrical algebra language.
Micromass, welcome to the forum and thanks for the great insights!1 I’ve had some knowledge of Real Analysis from Abbott but the questions were difficult for me at that time. This isn’t required however. http://www.amazon.com/Vector-Geometric-Calculus-Alan-Macdonald/dp/1480132454. I’m currently reading Tao’s Analysis books along with a friend of mine and he’s providing me with additional assignments since he has already has a thorough understanding of the subject.My question is: Since I’m currently learning by myself Algebra (with Artin and Pinter) and Analysis do you think that I have the right prerequisites for studying General Topology?1 I’m able to use the entire summer to focus on math as I’m about to enter the university (as an undergraduate major in math in the fall) at the end of September. C onclusion.
It’s not my first experience with topology, however I’ve never considered connectedness or compactness as an example. After you’ve read this information you’ve learned the fundamentals of the calculus.1 I’m familiar with metrics spaces.What books would you recommend given my interest in mathematical physics and differential geometry? The majority of differential topology books that I’ve read suggest a program on point-set topology.Thanks for taking the time to assist me! But don’t assume that the analysis has ended with this. [QUOTE="houlahound, post: 5470198, Member 551046”]dang it I’ve joined an analysis of my own.1 The exploration of the process is only the beginning.
I got enticed slowly but surely , after going through the analysis and looking over the suggested documents. The process of analysis goes far beyond than just an analysis of rigor in calculus. I’d like to learn more on the language and the use of sets.1 In my next post I’ll tell you how to access the most important information. There was a reason sets were a major subject in high school, however at the point I was into the first year of high school, they had been eliminated as a way to help students.
Education and experience in advanced level and math.1 Do you have any theories as to why educators believed sets were important? I think they were up until the 70’s and before they slipped off the radar of high school education until the 70’s/early 80’s.
Please share this article. and I’m not in the know about the language. as I scanned the understanding, the analysis is written in the set language? [/QUOTE] https://www.physicsforums.com/insights/wp-content/uploads/2016/03/mathanalysis1.png 135 240 Micromass https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png Micromass 2016-03-05 16:15:38 2021-04-02 10:07:12 How to Self Study Analysis: Intro to Analysis.1 I’m afraid that the concepts of set are crucial to everything mathematical. You may also like. I would recommend reading Velleman’s "how to demonstrate it" to become familiar with sets. In the wake of my previous blog post, some time ago, I spoke to Ethan Bloch about his book and Bloch responded with this (super helpful guy , by the way) The following is his response "As to Dedekind Cuts the Dedekind Cuts are definitely a very demanding subject and is far more technical and tedious than the other sections of the book.1 While any proof book should provide enough information about it.
In reality, when I teach our normal real-time analysis class I always begin by reading Chapter 2, avoiding the Dedekind Cuts altogether. It’s a shame, but I’ve taken up self-study on analysis. The sole reason for doing Dedekind Cuts would be if one has a special fascination with the subject or if someone has previously seen a actual analysis, or something similar.1
I got sucked in slowly but steadily going through the analysis and looking over the recommended documents. The reason that the Dedekind Cuts appear placed at the beginning part of the publication is due to the fact that logic would dictate that’s the right place to be even though it’s not the most intuitive spot to begin. "He also advised that those who have difficulty with proofs initially may benefit from an introduction to abstract algebra class prior to getting into the actual analysis.1 I’d like to learn more on the language and the use of sets. As luck would have it [USER=205308]@micromass[/USER] has an excellent guide for that: https://www.physicsforums.com/insights/self-study-algebra-part-ii-abstract-algebra.
There was a reason, sets were an important subject in high school, however at the point I was into the first year of high school they were eliminated as a way to help students.1