1
vote
0answers
34 views

pictures or graphs for real analysis.

Most of my previous math courses have had some graphs or pictures to help explain the ideas and concepts. I have tried looking for visual representation of the concepts of Real analysis; however, I ...
1
vote
0answers
28 views

No simple closed form for Bell numbers

The Bell number $B_n$ is the number of partitions of $[n]$. Unlike other basic combinatorial quantities, $B_n$ has no simple finite closed form. This seems surprising to me. Can anyone explain why ...
1
vote
1answer
50 views

Abstract algebra book suggestion [duplicate]

I have been suggested Artin or Herstein's books. What do you think is more rigorous but at the same time clear and good to read?
1
vote
1answer
39 views

Book to self-learn probability

I am reading some lecture notes (completed with exercises and competition-like problems) provided by my college professor, but I would like to study probability from a proper book. Can you suggest one ...
1
vote
0answers
36 views

Question regarding advanced calculus textbooks

I'd like to start off by mentioning that I'm gonna begin studying Computer Science at the local polytechnic university. As I found out, the study of mathematics stops after two years. Recently I've ...
0
votes
1answer
25 views

Applications of random walks

I am searching for a clear and interesting exposition of an application of random walks to some physics topics accessible to advanced high school students.
1
vote
1answer
57 views

Book for probability theory

I need a good rigorous book to learn probability theory. So far, I've been suggested Gnedenko’s Theory of Probability, Shiyayev’s Probability and Feller’s An Introduction to Probability Theory and ...
1
vote
2answers
63 views

Books/subjects for proof practice

So I want to practice writing proofs. I've studied general proof-writing but now I want to learn how to apply that to mathematics. From what I understand, the best and most accessible subjects for ...
1
vote
1answer
41 views

Reference request: Measure theory and/or manifolds [duplicate]

I have never encountered measure theory or manifolds yet, despite being close to my third year university level. Any texts for either or both of these subjects would be greatly appreciated.
3
votes
2answers
65 views

Books for inequality proofs

I was wondering: what books for proving inequalities are used in universities when studying mathematics (undergraduate)? I know there are lots of books, but I would like to know which ones are ...
8
votes
3answers
253 views

Resources for Integrals?

I want to learn to solve integrals of some type, probably definite integrals with results involving various constants such as Catalan's, Euler-Mascheroni,Golden-ratio etc. and involving various ...
3
votes
0answers
83 views

Why is there no collection about all mathematical theorems and open questions?

I really would like to have a giant math collection which is sorted according to the Mathematics Subject Classification, but with more then 3 levels, and it should contain all known theorems and also ...
1
vote
3answers
100 views

Recommendation on Category theory textbook [duplicate]

I had posted a question about category theory some months ago, and I got answered that there are two ways to study Category Theory. One is to treat Category Theory as a logic system independent from ...
0
votes
0answers
21 views

Problem supplement for Advanced Calculus (Loomis and Sternberg)

There are too many problems in Loomis and Sternberg's Advanced Calculus for them to be useful. Can someone recommend a collection of problems to supplement this book? A short list of its best problems ...
9
votes
6answers
417 views

Reference request for undergraduate complex analysis.

I am a second year student studying electrical engineering. I self-study pure mathematics and want to pursue a career as a mathematician. What are some prerequisites for studying complex analysis? ...
0
votes
2answers
57 views

Problem book for abstract linear algebra

Kindly suggest a good book for abstract linear algebra other than finite dimensional vector space by P R Halmos
2
votes
0answers
42 views

Entrance exam preparation suggestions.

I will be giving my Entrance Exam for (MS in Computer Science) and this is the Syllabus. Syllabus Screenshot : http://i.imgur.com/9KUDCt3.png I am worried about the maths and reasoning part. It's ...
26
votes
7answers
2k views

Mathematical literature to lose yourself in

H.M. Edwards in the preface to his book on the Riemann Zeta Function, summarises his philosophy on learning Mathematics: ...I have tried to say to students of mathematics that they should read the ...
12
votes
5answers
323 views

I need help finding a rigorous Pre-calculus textbook

I dislike modern textbooks; their cookie-cutter approach and appearance, over reliance on breaking things down into little boxes, the general spoon-feeding they engender and most of all the poor ...
2
votes
3answers
120 views

Chess and mathematics

I have to choose a research-like project to follow the next year. Because I'm a chess enthusiast, I was thinking of trying to tackle an (open) problem related to chess, and relevant to mathematics. ...
2
votes
1answer
123 views

Too Many Books - Not Enough Time

I am currently a high school student trying to get as far ahead in mathematics as I can. In doing so, I accumulated a good 10 physical math books, and a library of online resources including 2 or 3 ...
2
votes
1answer
136 views

Math enthusiast wants to learn math

I'm an english major with a vivid interest in mathematics,I've read and enjoyed What Is Mathematics? by Courant and Robbins (does this count as some background?),and I've decided to begin a serious ...
1
vote
1answer
39 views

Prerequisites for Hilbert Cohn-Vossen's Geometry and the Imagination?

I've not read this book(not really),but I would like to know how much is assumed by the reader. can I recommend this to the layperson? Also ,any more recent similar books? I already know of Courant ...
4
votes
3answers
125 views

(translated)Russian mathematics books?

Most russian mathematician(generally) are known to do and teach mathematics in a very original manner,they do in a very intuitive yet rigorous way, with/through wonderful connection to physics. ...
1
vote
1answer
186 views

Gilbert Strang's books on calculus and linear algebra?Are they for math majors?

I would to know what are the best resources to use to teach and learn elementary subjects (calculus,linear algebra),I remember when learning calculus, I used Spivak's book which had wonderful ...
1
vote
1answer
65 views

where can I get math book reviews?

The only two freely available choices are maa.org and zbmath.org ,where can get other mathematical book reviews? any one?
0
votes
0answers
34 views

Reference: Fields of characteristic p

I am interested in learning more about fields of characteristic $p\neq 0$. Does anyone know of a good reference that covers the basics of this topic and possibly galois theory over fields of prime ...
2
votes
1answer
64 views

Starting with ring theory

Can anyone suggest a book on rings explaining concepts using visual diagrams, similar to the one visual group theory book by Nathan Carter for groups.The problem with me is that after reading that ...
7
votes
1answer
102 views

Derivation of Schrödinger's equation

I recall a famous quote of the late physicist Richard Feynman: Where did we get that from? It's not possible to derive it from anything you know. It came out of the mind of Schrödinger. This ...
2
votes
0answers
25 views

Have any authors suggested mathematics-wide prefixes for “missing a quotient” and/or “missing an identity”?

The prefixes in the following terms both mean: "missing the obvious quotient by the obvious equivalence relation." seminorm pseudometric Similarly, the prefixes in the following terms both mean: ...
2
votes
0answers
56 views

Interesting examples of switching limit and integral

We learn many theorems regarding the relationship of limit and integral (Dominated/ Monotone Convergence, Fatou, Semicontinuity of norms, etc...). As I'm working on my research, I find that I often ...
0
votes
0answers
51 views

Alternatives to the notation $\|x\|$ for the norm of $x$?

For aesthetic reasons, I don't like the notation $\|x\|$ for the norm of $x$. Have any alternatives been proposed?
3
votes
0answers
135 views

Any comments on Lax's “Calculus with Applications, 2e”

There's a new calculus book titled Calculus with Applications by Peter Lax (2nd edition of an old one). I really liked his linear algebra and functional analysis books, and I was wondering if this ...
5
votes
2answers
265 views

Is there any similar math limerick?

I found this one $$\frac{(12+144+20)+\left(3 \cdot \sqrt{4}\right)}{7}+(5 \cdot 11)=9^2+0.$$ Which is : ...
7
votes
3answers
333 views

Video lectures of algebraic geometry (Hartshorne, Shafarevich, … )

I am a commutative algebra student. I wonder if there is some video lectures of algebraic geometry courses available online for free? I'd like the lectures to cover main topics of the books ...
1
vote
2answers
81 views

Books that integrate physical reasoning with mathematical reasoning? mathematicians?

As the title says, can anyone help me to find any book that shows how physical reasoning using concepts from classical/quantum mechanics and physics in general can enlighten us about mathematical ...
0
votes
0answers
34 views

Formal Trigonometric Refrence

I'm Using a textbook for mathematic which is produced to learn for normal students. Here I'm giving the link of chapter of trigonometric functions of my textbook : ...
6
votes
1answer
121 views

How do people on MSE find closed-form expressions for integrals, infinite products, etc?

I always wanted to ask this question since when I joined MSE, but because I was afraid of asking too many soft questions I never asked it. I've seen some pretty complicated integrals and infinite ...
1
vote
1answer
144 views

How do you self-study Functional Analysis?

It would be very handy to know about function spaces, distributions and Fourier analysis. It looks like Rudin's Functional Analysis covers these things, but I do not yet have the foundation for it. ...
0
votes
0answers
122 views

Self-Contained Books / Series / Lectures for Comprehensive Introduction to College-Level Math for Someone with VERY Poor Math Foundation?

I've long been interested in various math related subjects (technology, philosophy, sciences, computer science, languages, etc.) without really invested time to actually any learn any of them. I ...
4
votes
0answers
81 views

Problem solving strategy?

This question has always bothered me, and I've never had a maths coach to guide me along the way and show me what to do next. Nevertheless, I did make top 50 nationally in my national mathematics ...
12
votes
2answers
248 views

Is it normal that a pure math student doesn't know vector analysis?

Today I was watching a series of online video lectures about electromagnetism. At some point of the lecture, the professor used this vector calculus identity: $$ ...
5
votes
1answer
200 views

Russian Texts on Geometry

I recently saw a question today pertaining to Russian mathematics and I have a similar question but of a slightly different flavor. I've always heard that the Soviet Union had a history of producing ...
3
votes
3answers
72 views

Best resource to learn quadratic reciprocity?

I took a very basic intro to number theory course last semester. We learned about many of the standard topics (gcd, primes, cryptography, congrences, pythagorean triples, etc), but we never learned ...
0
votes
0answers
34 views

Koblitz - Are chapters III & IV independent of I & II

I am interested in learning about Modular forms and have heard many great things about Neal Koblitz's Introduction to Elliptic Curves and Modular Forms. However, Koblitz doesn't discuss modular forms ...
19
votes
1answer
494 views

Soviet Russian Mathematical Books

The introductory part of the book briefly describes the popularity of mathematics in Soviet Russia, touches on Russian mathematical circles and generally how Russian society took to mathematics in a ...
5
votes
0answers
93 views

Reference Request: Prereqs for Lecture Notes on “Abstract Linear Algebra”

I just found this set of lecture notes on linear algebra which seems to go over several things I've been wondering about as I study linear algebra. Unfortunately there are very few exercises in the ...
0
votes
2answers
130 views

Open Problems for High School Students

I am a homeschooled rising senior in high school, and I would like to research an open problem in mathematics. I have taken a number of undergraduate-level mathematics courses, including ...
10
votes
3answers
228 views

Areas of contemporary Mathematical Physics

I have often heard that some developments in Physics such as Gauge Theory, String Theory, Twistor Theory, Loop Quantum Gravity etc have had a significant impact on pure Mathematics especially geometry ...
2
votes
1answer
119 views

Best Less-Famous Texts for Forcing

There are many books, papers and lecture notes which give an introduction to forcing (e.g. Jech or Kunen's books) but here I am looking for some possibly less-famous useful comprehensive texts for ...