0
votes
0answers
9 views

what does well posdeness results tells us concerning non linear evolution equations?

Consider a nonlinear Shr\"odinger equation, $$iu_{t}+\bigtriangleup u + f(u)= 0, u(0)= u_{0}$$ where $u(t, x)$ is complex valued function of $(t,x) \in \mathbb R \times \mathbb R^{n}$, $i=\sqrt{-1}, ...
4
votes
9answers
287 views

Good Textbooks for Real Analysis and Topology.

I'm currently in my 3rd year of my undergrad in Mathematics and moving onto my 4th year next year. I took a course in Real Analysis I, but the professor was very confusing and we didn't use a textbook ...
1
vote
0answers
30 views

Enlightening books giving a guided tour of mathematics, in a style that Gian-Carlo Rota would not mind?

I am currently reading Gian-Carlo Rota's Indiscrete Thoughts. What more can I say apart from "the man can write"? (In other words, you should really read it if you are interested in mathematics.) I ...
2
votes
5answers
121 views

Reference Book on Special Functions

Now I'm studying the topic that uses the special functions frequently, so I find myself in need for some good reference book on the properties and equalities of the special functions. The optimal one ...
2
votes
0answers
25 views

Revise high school material

Can you suggest me a comprehensive book to revise high school mathematics (up to besic calculus)? It should be extremely clear and complete and "scientific" (not like most high school books). Thank ...
2
votes
1answer
91 views

Preferable Order of Mathematics Study

I recently bought a good amount of math books, because I want to self teach math, and they are on their way--via U.P.S.--to my house. I was just wondering if someone would be kind enough to tell me in ...
1
vote
0answers
41 views

Applications of PDEs

I teach an undergrad ODE course. As I have completed basically all the material, I thought it would be nice to give the students a brief introduction to PDEs. At the end of the lecture, I said that ...
2
votes
0answers
61 views

Calculus book advice

I'm reading Thomas Calculus now but I don't think it includes Mellin transform or Riemann-Stieltjes integration... Can you recommend an advanced calculus book which includes all of this stuff?
0
votes
2answers
21 views

what are some typical systems of equations generating from practical problems?

I want to know some typical forms of system of equations generating from practical problems in engineering/economics/physics,etc. Some examples or research articles would be good. Specifically, I am ...
1
vote
1answer
89 views

Foundations book using category theory?

I'm about to embark on a PhD in mathematical biology. My major is in computer science. I would like to acquire a more rigorous understanding of math, which I am going to need to tackle some research ...
1
vote
1answer
36 views

Suggestion for independent study of mathematical logic

Hello I'm looking for advice on mathematical logic books that are good for self-study. I would really like a text that has some if not all of the answers to exercises so I can check my progress as I ...
0
votes
0answers
26 views

Your impressions of Mattuck's *Introduction to Analysis*

Has anyone here spent much time with the Mattuck book Introduction to Analysis? What are your impressions of it? A quick browsing showed me that I liked the organization of the material, but the ...
0
votes
0answers
13 views

Is there a good introductory complex-analysis text in general setting, namely Riemann sphere?

I have studied first 1~3 chapters of some complex analysis texts (Ahlfors, Conway, Silverman) Well, i specially like Ahlfors in many ways but this text doesn't seem to develop a theory in a general ...
2
votes
2answers
47 views

Relationship between mathematics and music

I have a strong mathematical background and I am interested in the relationship between mathematics and music. I have found some introductory material on the web. Do you know any good books that will ...
1
vote
2answers
108 views

Recommendation for Number Theory Textbook

. Greetings, every mathematicians! I'm a foreigner (meaning English is not my first language) and an undergraduate student. I'm currently studying linear algebra, set theory and have already studied ...
0
votes
0answers
24 views

Measure Theory vs. Decision Theory - problem classification

I am having trouble classifying my problem, and I am seeking some guidance on book advice. I don't know if I have measure-theory problem and/or a decision-theory problem (or other field). I want to ...
3
votes
4answers
87 views

Is there a shorter path to these results?

I'm a student of Physics, however I usually study mathematics on texts aimed at mathematicians to gain a deeper understanding. Currently I'm studying differential geometry on Spivak's book and one of ...
2
votes
1answer
75 views

Book to prepare for university math?

Can you suggest some books to prepare for university math?
0
votes
1answer
29 views

Reference about the Conley index thoery

I'm reading "Isolated invariant sets and the Morse index" by Charles Conley.But I'm lost in some of the concise description or definition.Could you recommend me some references or textbooks for the ...
1
vote
4answers
95 views

Nice book on geometry to gift an undergraduate in mathematics

I would like some suggestions on a nice book on geometry to gift an undergraduate. I'm not searching for something that is common: I need something new and exciting. Suggestions?
3
votes
3answers
109 views

Most inspirational mathematical books [closed]

I would like to know which books on mathematics (from university texts to divulgative pop-math books) inspired you the most. My choice is Spivak's Calculus, which is, IMHO one of the most ...
1
vote
2answers
121 views

Why do people stick with Riemann-Integration when dealing with differential geometry?

I asked a question yesterday that is, "Is there an introductory differential geometry text using Lebesgue integration?" Then, i got an answer that "since we are dealing with differential geometry we ...
3
votes
0answers
73 views

Mathematical YouTube channels?

So I'm wondering if anybody knows any good math/science related YouTube channels? As for the math channels, I'm currently subscribed to Numberphile, and that is about it. I know few other channels, ...
0
votes
0answers
51 views

is there an introductory differential geometry text using Lebesgue integration?

Is there an introductory differential geometry text using Lebesgue integration? Every differential geometry text I saw introduces the theory using Riemann integration. (Even Spivak) Would someone ...
1
vote
3answers
94 views

University-level books focusing on intuition?

I help some students with difficulties in Mathematics and Physics (especially math, physics, and engineering majors). While in high school they usually don't study, or are not interested, etc., in ...
0
votes
0answers
31 views

Intuition analysis-deconstruction-reconstruction.

The following question is a refinement of this question, which caused a lot of people to give answers that were missing the point entirely, probably because the question was not clear. Being human, ...
6
votes
3answers
171 views

Categorical introduction to Algebra and Topology

I am self-studying Mathematics in my free time. At the moment I am reading books on Algebra and on Category theory. More exactly, I started working through the book $\textit{Algebra}$ by Serge Lang. I ...
0
votes
1answer
93 views

Books (and supporting material) that are useful in deconstructing one's intuition?

I recently came across the following problem from Paul Zeitz's book The Art and Craft of Problem Solving. Given the image below, can you find a way to connect corresponding blocks (i.e. A to A, B to ...
2
votes
2answers
92 views

Dr Seuss style prose advanced mathematics text

There are a number of Dr Seuss style mathematics books for elementary school mathematics. It occurred to me that there is no particular reason that that style of prose couldn't be adapted to a ...
0
votes
0answers
57 views

Learning about the gamma function.

I have just started learning about the gamma function but the books I have are not sufficient to give me a complete picture of it. Can you guys suggest some online resources/free books where I can ...
0
votes
1answer
54 views

Reference on Infinite Dimensional Manifold

I am studying manifold. For comprehension, I read the site http://en.wikipedia.org/wiki/Manifold, and there is some information about infinite dimensional manifold. Now I have two questions or ...
0
votes
0answers
23 views

Theory of irrationalities- Faddeev's book

Does anyone know where (if available) I can get a free access to Delone, B. N., Faddeev, D. K., ''The theory of irrationalities of the third degree'' Transl. Math. Monographs 10, Amer. Math. Soc., ...
1
vote
2answers
67 views

From Engineering-Style to Proper Mathematics

I currently have an engineering-style education in mathematics. We covered quite a lot of material (e.g. real and complex analysis, some probability theory and graph theory), but more often than not ...
0
votes
0answers
18 views

The “dynamics” of foliations

My mathematical interests revolve mainly around dynamical systems, and (unfortunately) I don't have as much general culture in geometry as I would like (and I should...) I often see foliations come ...
2
votes
1answer
61 views

Good non-textbook math books

I'm looking into learning math partially by reading, I have and am currently reading books by Dover publishing. I like these books because they don't use the formulaic textbook layout and rather ...
1
vote
1answer
50 views

Examples for Conditional Expectation (modern probability theory)

I'm in the process of learning about conditional expectation in the framework of modern probability theory. The sudden change brought about by the notion of conditional expectation being a function on ...
3
votes
1answer
131 views

Are continuous mathematical models of discrete physical phenomena messy because of a disconnect between “continuous” and “discontinuous”?

Examples from statistical mechanics and continuum mechanics abound: a discrete phenomenon (e.g. kinetic energy of molecules) is "averaged" out over the constituents of the system to which it applied ...
2
votes
0answers
45 views

A Proof-Library

Is there any source, perhaps a website or a book, which keeps track of all different proofs ever announced of a theorem? For example, I have heard that there are about $80$ different proofs of the ...
2
votes
1answer
61 views

Bridge the gap to university mathematics [closed]

Can anyone suggest some good books to help an high school student to "bridge the gap" to university math? I've heard of http://www.amazon.com/How-Study-as-Mathematics-Major/dp/0199661316 and ...
4
votes
3answers
305 views

Most useful books for a math undergrad

What are the most useful books an undergraduate in math should read? I found Alock's "How to study as a math major" and "how to study for a math degree" very useful. Are there any other good readings ...
1
vote
1answer
21 views

Reference request to study Borel summation

Could someone recommend sources to learn about Borel summation procedure? Books, articles or reviews? I have a background in basic analysis.
6
votes
2answers
150 views

Popular Topics in mathematical analysis(Functional analysis)

I am writing a text(as a duty by my mentor) dealing with the recently popular topics(including open problems) in mathematical analysis. At first part, I briefly introduced the mathematical ...
1
vote
1answer
136 views

Recommendation on a rigorous and deep introductory logic textbook

In this post, I don't mean any word by its somewhat "mathematical or logical" meaning but just "literally". It's been three years since I started "formal" mathematics, and now I'm familiar with set ...
1
vote
0answers
36 views

Resources for self-learning “relational” abstract algebra? [please see body of post for details]

I have been studying Grassman and Clifford algebras a bit, and it is fascinating to see how, for example, the rules defining the inner product operator are enough to the capture something of the ...
1
vote
1answer
79 views

Which mathematician has argued that we should move from “set” to “order”?

I recall reading (on this very site, in fact) that there is a mathematician whom argues that we ought to switch from "set" to "order" in the foundations, so as to "recover duality" or some such. Does ...
1
vote
1answer
55 views

How Should the First Sessions of an Undergrad. Course Be?

Form a teaching perspective, the first sessions of an undergraduate mathematics course are of a great importance. They can make clear the aims of the course, and point out to the main problems and ...
0
votes
2answers
86 views

What are some good introductory books on mathematical proofs?

There was a time when I avoided math proofs, but now I am starting to enjoy them. I am taking Intro to Linear Algebra and am falling in love with proofs. Are there any introduction to mathematical ...
0
votes
1answer
107 views

Most “beautiful” presentations of the basic proofs for vector spaces?

I am familiar with the standard proofs presented in textbooks for stuff like linear independence/dependence, the dimensions of common vector spaces, any basis for a vector space V must be linearly ...
4
votes
2answers
98 views

Theorems that have proofs from the outside of the original field of math

I would like to know more examples of theorems, which "belong to one field of math", but their proofs are from the "outside of the field". I am mostly interested in proofs that are not too long ...
1
vote
0answers
80 views

International undergraduate mathematics Olympiad preparation

I have decided to try out and compete at the next international undergraduate mathematics Olympiad but first I need to get selected for the team that is sent for the competition from my country. I ...